From 874d64efc37cf48f0afd16192eb6189c7f47c314 Mon Sep 17 00:00:00 2001 From: "hippolyte.pik" Date: Thu, 22 May 2025 17:35:57 +0200 Subject: [PATCH] init: exo1&2 --- BINF_TP5.ipynb | 599 ++++++++++++++++++++++++++++--------------------- 1 file changed, 337 insertions(+), 262 deletions(-) diff --git a/BINF_TP5.ipynb b/BINF_TP5.ipynb index 9a6c7bf..b7c6783 100644 --- a/BINF_TP5.ipynb +++ b/BINF_TP5.ipynb @@ -1,269 +1,344 @@ { - "nbformat": 4, - "nbformat_minor": 0, - "metadata": { - "colab": { - "provenance": [], - "authorship_tag": "ABX9TyO0SUJI6kaczFcOh8NoKcqb", - "include_colab_link": true - }, - "kernelspec": { - "name": "python3", - "display_name": "Python 3" - }, - "language_info": { - "name": "python" - } + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "colab_type": "text", + "id": "view-in-github" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "BoOWxsamkRHR" + }, + "source": [ + "# *TP5 Reconstruction de génome par alignement sur une référence - Algorithme bowtie et transformée de Burrows-Wheeler*\n", + "\n", + "On cherche à reconstruire le génome d'un organisme dont l'espèce a déjà été séquencé. On va utiliser le génome existant pour guider notre reconstruction en cherchant la position de chaque fragment séquencé dans le génome de référence.\n", + "\n", + "On appelle read un fragment séquencé. La taille d'un read dépend de la mêthode de séquençage. La méthode de Sanger produit des reads d'environ 1000 nucléotides alors que les méthodes de séquençage nouvelle génération vont avoir des reads plus courts d'environ 100 nucléotides.\n", + "\n", + "Les génomes ayant des tailles de l'ordre de 100 000 paires de bases et plus, leur séquençage requiert l'acquisition de milliers voirs millions de reads dont il faut trouver la position dans le génome de référence. Pour que cette méthode soit viable, il faut être capable d'effectuer cette recherche de manière efficace.\n", + "\n", + "La méthode bowtie propose une solution à ce problème basé sur le calcul de la tranformée de Burrows-Wheeler du génome de référence. La transformée de Burrow-Wheeler est une structure basée sur l'ordonancement des préfixes / suffixes d'une séquence permettant une recherche efficace de sous-séquence. Pour pouvoir faire le lien entre transformée et séquence d’origine, on va aussi calculer un index faisant la correspondance entre un caractère de la séquence transformée et la position d’apparition du préfixe correspondant.\n", + "\n", + "![image.png](data:image/png;base64,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)" + ] }, - "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "Wc6rm1agmoCb" + }, + "source": [ + "## Exercice 1 : Transformée de Burrows-Wheeler\n", + "\n", + "La transformée de Burrows-Wheeler (BWT) s’obtient en triant par ordre lexicographique toutes les permutations circulaires possibles d’une séquence, et en conservant le dernier caractère de chacune.\n", + "\n", + "Ecrire la fonction BWT(s) -> str qui retourne la transformée BW de la séquence s en effectuant les étapes suivantes :\n", + "\n", + "\n", + "1. Ajouter un caractère $ à la fin de s (celui-ci servira pour la transformée inverse).\n", + "2. Générer la liste perm toutes les permutations circulaires de s (on fait passer la dernière lettre au début de s).\n", + "3. Générer un tableau d’indice qui contient l’ordre de chaque permutation.\n", + "4. Trier le tableau d’indices et perm par ordre lexicographique de perm.\n", + "5. Retourner la séquence contenant le dernier caractère de chaque permutation dans l’ordre lexicographique ainsi que le tableau d’indices.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "id": "D5zJsnmQnajj" + }, + "outputs": [ { - "cell_type": "markdown", - "metadata": { - "id": "view-in-github", - "colab_type": "text" - }, - "source": [ - "\"Open" + "data": { + "text/plain": [ + "'n$iche'" ] - }, - { - "cell_type": "markdown", - "source": [ - "# *TP5 Reconstruction de génome par alignement sur une référence - Algorithme bowtie et transformée de Burrows-Wheeler*\n", - "\n", - "On cherche à reconstruire le génome d'un organisme dont l'espèce a déjà été séquencé. On va utiliser le génome existant pour guider notre reconstruction en cherchant la position de chaque fragment séquencé dans le génome de référence.\n", - "\n", - "On appelle read un fragment séquencé. La taille d'un read dépend de la mêthode de séquençage. La méthode de Sanger produit des reads d'environ 1000 nucléotides alors que les méthodes de séquençage nouvelle génération vont avoir des reads plus courts d'environ 100 nucléotides.\n", - "\n", - "Les génomes ayant des tailles de l'ordre de 100 000 paires de bases et plus, leur séquençage requiert l'acquisition de milliers voirs millions de reads dont il faut trouver la position dans le génome de référence. Pour que cette méthode soit viable, il faut être capable d'effectuer cette recherche de manière efficace.\n", - "\n", - "La méthode bowtie propose une solution à ce problème basé sur le calcul de la tranformée de Burrows-Wheeler du génome de référence. La transformée de Burrow-Wheeler est une structure basée sur l'ordonancement des préfixes / suffixes d'une séquence permettant une recherche efficace de sous-séquence. Pour pouvoir faire le lien entre transformée et séquence d’origine, on va aussi calculer un index faisant la correspondance entre un caractère de la séquence transformée et la position d’apparition du préfixe correspondant.\n", - "\n", - "![image.png](data:image/png;base64,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)" - ], - "metadata": { - "id": "BoOWxsamkRHR" - } - }, - { - "cell_type": "markdown", - "source": [ - "## Exercice 1 : Transformée de Burrows-Wheeler\n", - "\n", - "La transformée de Burrows-Wheeler (BWT) s’obtient en triant par ordre lexicographique toutes les permutations circulaires possibles d’une séquence, et en conservant le dernier caractère de chacune.\n", - "\n", - "Ecrire la fonction BWT(s) -> str qui retourne la transformée BW de la séquence s en effectuant les étapes suivantes :\n", - "\n", - "\n", - "1. Ajouter un caractère $ à la fin de s (celui-ci servira pour la transformée inverse).\n", - "2. Générer la liste perm toutes les permutations circulaires de s (on fait passer la dernière lettre au début de s).\n", - "3. Générer un tableau d’indice qui contient l’ordre de chaque permutation.\n", - "4. Trier le tableau d’indices et perm par ordre lexicographique de perm.\n", - "5. Retourner la séquence contenant le dernier caractère de chaque permutation dans l’ordre lexicographique ainsi que le tableau d’indices.\n" - ], - "metadata": { - "id": "Wc6rm1agmoCb" - } - }, - { - "cell_type": "code", - "source": [ - "print(\"votre fonction ici !!\")" - ], - "metadata": { - "id": "D5zJsnmQnajj" - }, - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "markdown", - "source": [ - "### Exemple\n", - "\n", - "Transformée de chien :\n", - "\n", - "* Ajouter un caractère \\\\$ à la fin : chien$\n", - "\n", - "* Générer le tableau perm des permutations cirulaires :\n", - "\n", - "$$\n", - "\\begin{array}{l}\n", - "chien$\\\\\n", - "$chien\\\\\n", - "n$chie\\\\\n", - "en$chi\\\\\n", - "ien$ch\\\\\n", - "hien$c\n", - "\\end{array}\n", - "$$\n", - "* Trier ce tableau par ordre lexicographique :\n", - "$$\n", - "\\begin{array}{l}\n", - "$chien\\\\\n", - "chien$\\\\\n", - "en$chi\\\\\n", - "hien$c\\\\\n", - "ien$ch\\\\\n", - "n$chie\n", - "\\end{array}\n", - "$$\n", - "* La transformée est la dernière colonne de ce tableau (le dernier caractère pour chaque ligne) : n$iche\n" - ], - "metadata": { - "id": "bG6dMzI1ndK-" - } - }, - { - "cell_type": "markdown", - "source": [ - "## Exercice 2 : Transformée inverse\n", - "\n", - "Pour vérifier que la transformée est correcte, on va implémenter la transformée inverse. Pour ce faire, on va recréer l’ensemble des permutations de manière itérative en faisant un nombre d’itérations égal à la taille de la transformée. On va commencer avec un ensemble de séquences vides qu’on appelle table de même taille que la transformée qu’on va modifier à chaque itération :\n", - "\n", - "* Pour chaque caractère en position i de la transformee, l’ajouter au début de la ième séquence de table.\n", - "* Trier table par ordre lexicographique.\n", - "\n", - "Le résultat est la séquence de table qui se termine par le caractère $. Notez que c’est pour ça qu’on a besoin d’ajouter ce caractère au moment de la transformée.\n", - "\n", - "Ecrivez la fonction iBWT(t) -> str qui retourne la transformée inverse de la transformée BW t.\n" - ], - "metadata": { - "id": "JgSWho3GorwJ" - } - }, - { - "cell_type": "code", - "source": [ - "print(\"Votre code ici !\")" - ], - "metadata": { - "id": "oH-bAVbgpOUe" - }, - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "markdown", - "source": [ - "### Exemple :\n", - "Transformée inverse de n$iche :\n", - "\n", - "$$\n", - "\\begin{array}{lllllllllll}\n", - "ADD1 & SORT1 & ADD2 & SORT2 & ADD3 & SORT3 & ADD4 & SORT4 & ADD5 & SORT5 & ADD6\\\\\n", - "n & $ & n$ & $c & n$c & $ch & n$ch & $chi & n$chi & $chie & n$chie\\\\\n", - "$ & c & $c & ch & $ch & chi & $chi & chie & $chie & chien & $chien\\\\\n", - "i & e & ie & en & ien & en$ & ien$ & en$c & ien$c & en$ch & ien$ch\\\\\n", - "c & h & ch & hi & chi & hie & chie & hien & chien & hien$ & chien$\\\\\n", - "h & i & hi & ie & hie & ien & hien & ien$ & hien & ien$c & ien$c\\\\\n", - "e & n & en & n$ & en$ & n$c & en$c & n$ch & en$ch & n$chi & en$chi\\\\\n", - "\\end{array}\n", - "$$\n" - ], - "metadata": { - "id": "MMRvEACHpVDs" - } - }, - { - "cell_type": "markdown", - "source": [ - "### Exercice 3 : Recherche d’un mot dans la transformée\n", - "\n", - "Maintenant que l’on dispose de la transformée, on va développer un algorithme permettant de trouver efficacement si un mot se trouve dedans. Pour cela on va implémenter l’algorithme suivant qui provient de l’outil Bowtie base sur un principe similaire a la construction de table de l’exercice précédent. L’algorithme va reconstruire itérativement l’ensemble des lignes de la table contenant des fragments de plus en plus longs du mot recherche, jusqu’à obtenir l’ensemble des lignes contenant le mot entier. Vu que la table est toujours triée lexicographiquement, on sait que ces séquences vont se trouver cote a cote. L’algorithme est un peu plus complexe que la transformée inverse de l’exercice précédent car il ne reconstruit pas la table entière mais se base sur les propriétés de celle-ci pour trouver les indices :\n", - "\n", - "![image.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWIAAACeCAYAAAAIewCsAAAgAElEQVR4Xu3dB7ReRfU28OPf3rtYQcRGUwFFSlR6L6GTQOi9907oSWihhN5LKBEIRVpoSgdpggiKoAI2FDv29vmbb81dh5Pztnvf2/esdVdy73vOlOe855ln9uy95zX//V8pogQCgUAgEAgMGgKvCSIeNOyj4UAgEAgEEgJBxPFFCAQCgUBgkBEIIh7kBxDNBwKBQCDQQ8R33HFHccMNNxT/93//V7zmNa8JZAKBQCAQCAT6AQHbcq997WuLjTfeuFhggQVebZr4/ve/X3z3u99NRBxldCKQJ+BW+7eu8+O6Vtc2QtL3LN+f6xqdqMeoRyMCvvNf/vKXi4985CNhIx6NX4AYcyAQCAw9BBraiP/5z38Wr3vd615lpvjrX/9a/O1vfyve9ra3Fa9//ev7PJr//Oc/xT/+8Y/iDW94w2xK/N///nfxpz/9KbXz1re+tc9tlSugxML8Mjukv/71r4u3vOUtCW/P/+9//3vxr3/9q/CcfBfe8Y53pJuee+654he/+EXxhS98IX0XOi2e7Xe+851U54ILLlj87ne/K970pjd1/Tl32q+4PhAYLARqidiLd/LJJxef+tSnilVXXbWnb48++mj6+wYbbFCsvPLKfe7zgw8+WFx66aXFVlttlV7IX/3qV8Ub3/jG4p3vfGd6OU888cT0su666649JNCXRv/whz8UzzzzTPH73/8+EQ4i6TbJ96V/g3nv888/X3zve98rvvrVryZy/eUvf1nMmDEjEfG8885bvPLKK+m5+Py2224rkKnvgMny2WefLd773vem70s7xffroYceSu1tttlmxdNPP1385je/KRZbbLE0KUcJBEYbArVE7MVac801i0984hPFlVdemchR8dKNHTu2WGuttYqddtqpz1g98sgjqf5NN920+OxnP1tMnTq1WGaZZRJBKocddljx5JNPFmeddVbx7ne/u0/tIY5p06YVTzzxRLHKKquk/yOBzTffvKdeShkB/eUvf0kKjVp/85vfXLznPe8pXnjhhYTDxz72seJnP/tZYXUw55xzJuJALLDxuftyQV4vvfRSukY9PjMJlG2jbKXqp0Zd98EPfjDdjgB//vOfpzrnmGOO9Df1KYhS39xjXNlmqx8f/vCH0+SlP8aiXXWYeF5++eW08vjABz6QiI/idb1y8803p+dtQsxll112SXasjTbaKD2HSZMmFdtss03aaEDKn/vc5xKhImzPzOZDu8Wke+eddxbrrLNOWmVp/5Of/GSqM0ogMNoQqCXiSy65pLjqqqvS8vHiiy8ullxyyYSLF92Ls/zyyxc77LBDWp4+9thjiUCQgRd7zJgx6cXyd9cjq/nnnz9tBD711FNJXSGYT3/608Wf//znwiahe7S13377Feuvv36aBOwmUt/3339/sd1226WlMhL8zGc+U/zgBz8oqPP55psvkdpPf/rTYuGFF07kok+umWuuuV71LBEb9a0eykudlP2OO+7YY6bQ38svv7z48Y9/nPpAlVuG6xM8qOnddtut+Na3vpXIaKWVVkrkiuAuvPDCYtFFFy2+8pWvpHaN8fbbb08TjCX9Pffck8jL9e696667iqWWWiqRq3HAxo/+IGaT4XnnnZdUZ67ziiuuKP74xz8WW265ZeqXicwEde+99xZf/OIX09jgAJO777471fv2t7+9mDVrVsIYabrG/bAwvm233TZNPMh0iy226Fkh+GyfffZJE+7nP//5wurl1FNPLfbYY4/UB2NCvp6hidJkMX78+Nr3x3MxaeiLepG/CQQRw5n56ZZbbkmTi/HCJ0ogMJoQmI2IvTBXX311eon33HPPYvHFF08mgqzS1l133WSu8AIdeeSRiWS9QLfeemux9NJLF1/72teKCy64IJE35XbTTTclFW3pigBWW221RNhebi/vQQcdVEycODG9mDvvvHMiotVXXz2R6SmnnJKIcd99903qDnkhZ8TrOqTDrDFlypRESIhAe1526s2LXy3U7NFHH53Ic/LkybMRtknohz/8YTFhwoR0q3aNBbEiHHUiRhPJu971rnSN/hxzzDFJ0SEuRAgzZg9EZ5Ki+Ix7kUUWScSnDwcccEBSvnCiuJHhuHHjEqEj+xtvvDGNaaGFFkqT29e//vWCm6GVA0XO1OLe4447Lil7O7CUJuKlhE2Wiuepvw888EAaN4K1ItD27rvvnkwE2nN99poxAZ5++umF502lw8QzNPkgTaoaEeuX6xoRse+GSRjpqscEaZIxGZp4fB8Qsb6Z6HxXsi16NL2IMdbRjcBsRDxz5syknJAcBYTUvvGNbyRliywpYkTJhLD99tsXe++9d7rmsssuK44//vikAr2Y7IiICkF40RCVl2y99dZLpg3kRA2y/yJVLzXlecIJJyQiUpDFddddl4jdEh/pImZ9sVymNo866qjCEhrBIrKLLrooqXj/UtC5IEdEiDgoSXVbdlN42fSSScv4LdM//vGPp8klK7SHH344tYe82EoV9bGv/uQnP0mql5nlox/9aCJgP0sssUS6jhL1w0SQJwMTDPLUNysI9VD0yA9JMaOY2ExaVgH6f8011ySs1lhjjZ6J4qSTTkpmFpMXpQxDOLtX8dy0DR/1UL4wev/7358mDv1GjptsskkPEZ922mmpP+rNZpVsNkH0iDcT8RlnnJF+N4lUC7K3wtBvkxA7sv551iYNCtj3w4oI7iZ4JB8lEBhNCLyKiCksy2EvAtOA5eihhx6ayNaS3AvtRaFiECGiViy5KWMvvpfy3HPPTQTqRd96663Tclw9TAFULzJXKDGk5m/a8/mBBx6YyMlSm/KjpM4+++xEMAibYkV0FCuSo+4oOS+8tl2LcM4///xXqV3K1rX6SJkjAMtqapHSy8W91N/aa6+dCIi5ggr2g2wt+RGpCYa6Q5z33XdfwswkgbjdS+VTssZq0qGakXC2NyN0YzWpKMwLJi6TnrFT+MauPkSM/EwI+vajH/0orQIQmHqpb/3xDEyKiI4JKBMjta3/yJAihhd88irExGQi8Kz01d89F8RpYqmWMhFT90gbEedVBLWub2zVCvvytddem+zLlC9zlInEJp3VlWv1gXL2dxhFCQRGEwI9ROyFooa9kJSnF9n/KSZLbMtfLzMVjACRGaJETkiIgqSUkS6zgOU7gr7++usTwX7oQx9K9VJ7CJUK/eY3v5kIy9/dqy2EPM888yTCV48lMjVt2XrssccmAkKAyBvRIQzKklpEbmyflvTI6Utf+lLPs2RyOeSQQxJhMLcgK8tsbWbFS5maRKhD46PYTUb6higRhknIpIIsEB2VzEbO3mtVgFz0CeEx1yB85gOmDRi9733vS/foHzVu5aFMnz49TTAUNnKn1k06+ghHCnnFFVdMdnC4wMxz8IxMQEwYWQHDTL+RHPJH1nPPPXfChqkAXsw+2UzhXzZwKwumCXUyO1GtG264YVMi9lyYbEy6vhvGarWBxNmlFWYZP1YIJhf9NlZmlmwj9nfPCL7lDc/R9DLGWEcvAj1ETEl5AakZS06q1EuGaJGcF8dL5ve84eRlZuujKNlmvcQIjhJSF5WKABCrJTFVi4DdgyAoIwovb+hRbpbDTA5I33LV7j/bK7WOMBA65Yjw9MfvL774YlKuCJry5ZlgmV51p3I/FW6zKS+ty+5S6vA5LHyOiJGz/jMTWJqrV9tMJfqF5PydGQM2xmjnHzEhX9fByzVUrjYoWn02bvho4/HHH0+E7nd4u047zCueSX4uiPrb3/526p++aFNd6tefPKn4W/YLtjkGd2PwjEyyJhsrAmqbAjYJL7fccglPz8W4PHO25axs82vCRqxOk6bxass1rjUp+y6YcEyExsEM4vllknXvb3/720TE2UxFMbsnb0yO3lcyRj4aEeh10h8vtReMWkTElucIjJIsL/VHI6jDbczIkheKiYrtv5UvLxOHSdAqoErSxm4C9znCNbmec845ye6PiHMxyTBTsEGbmEyAViomsCiBwGhDoNdEDCgvmZeOomNPZSqIAInh+RWiwpEj80krrwWTLqXPjbEusi57c1DnVijUPqVPMSuIn63dyoT5BBEz+1RdDocnktHrQKBzBHqImBnBznonob9enrLPp/stc6MMPwRy4h3fgzqVWx4ROzOzDfNRXah7OaGP74drcjh7JmIknANdcjaq3iYQGn5oR48DgSK9F5k/e4iYDXc4Zl8rTxzVF7ndbGLxpfj/CLSLF6L1Y9LtDXlqxxfQvQg6l97UFc8uEBiOCOTsazmytYeIbYpZUnaiiAcKAH2qpuf0AufkPT4vv9DlfpXV2UD1N9oJBAKBQKAVAjyvmHSTCBouZ9ZlomX+oKby8pnbHb9eXh48McrF8pnnAo+GVhtQrUCLzwOBQCAQ6C8EhgURU+tCcPnXIlVkzDOD6xVzis0gO/Jcr8oFQfOd5dnBJS5KIBAIBAJDEYGWRGzzBhFSoHW5G3o7qLyx167zvjBe7lUSA1G5gjsEO/ClpXz5rNadLiJSzTV5x763/Y37AoFAIBDoLwRaEjHf4BwGLAqqneIeQRWc++vc2eyYC0oQfdVOektmCVFoiNePYIC99torBSAIPkHEXOf83YRhV5/9mCHcOXxIuN1cue2ML64JBAKBQKCbCLQkYpFcwn7tkAuBFeElYosZoM51ifeFyCw2WeG4wpvL17HpSucooi4n1Mn5eSla0VoirMpFchhh0fLdIlTmCBuLwqVFllHtot+EyfJtFpQgv4HcC/xY+cYGEXfzaxN1BQKBQDcRaEnEGkOcSFUOX478ciXIa1B15qd05XuQeF2CcYQsZ0L2lUOgsrIJsaVWs/tS9mH1L8d/uRXKRXawM888MyWrYRtGvGzFNucoa4qZDdh18lfIxSDfgWu1I/QXUUcJBAKBQGAoItAWEcsqxtwgqYtlP5uxfA/VBN5yQ8h+dvDBB6fcB9kvNLvEyUmALBEpswXVnK9BphQxAq+GuSJVeRFkgKvalBGxwkQhwZAJQ5i1BD+ymDGNIG1kHCUQCAQCgaGIQEsiRppyBbD5SofJHkvpSmyTfeDywJgbJC+XtYtadg+TQDlSS33IGGkvu+yyyWxRNk3k5EK5Tht0chYzN8ijW/VzRsQIXDtUM+WL5OUu0A+f+1uYJobi1y/6FAgEAhBoScSIEHHyckCGSBXJ2RyrEnFOcC5vAQ8Lvr11m3E5rwE7cz6Pre5xUMmSC8ltgEwlY6+2iWiROTOE/MjSTrqGXZiyjs26+KIHAoHAUEegJRH3ZgDtHlefzRG9aSPfI/cucwn7tPy/8ujmpDXqdzgp9R5+xH1BOe4NBAKB/kSgX4i4PztcrZti9kOpsznzxMgqXACIk0K4ucVm3UA+lWgrEAgEOkFg2BNxDnGWQrEaxszFjZeH5OpVk0YnIMW1gUAgEAj0JwLDnojrwLEh6IQJG4ZVn2Q+0Lw+kHOdH3R/gh11BwKBQCBQh8CwJmIbiA6ddEowc4TNP77FiJivM/c1Psvl4mgfR/TY+BP63Glhd+YiR2HXJUXvtL64PhAIBAKBtojYRhgXsYEgHhF8Vf/kusfEr9lGnD45jNKZbAJPuNeNHTs2nfrgKJ9qiDWSZjfmW5wP7izXL3KQz7KgkqpiRvxc9PhKSzLE/S5KIBAIBAJ9RaApESMtPsPChIUZzzfffClwolXhnobQkCQCR2w5B4TfGyUPkkXNZ1zPmhVeEo5w1z+hz9n+e9ddd6XEQLwkHELqIEp2Y9fl43sQthOFBZzUjYVJw/FP8mBUI/x4gxiXgBWKut3cG63wis8DgUBgdCPQlIgFZDiafoUVVkgn88rrILgCETIF1ClXiXeEMueoOYEUTAGuFW4suo5SrfoPyw0hgg958j/ORy4xBQjQYHbI2dWkxHSE+wEHHJByU+SST11Gpn60kwNITA7+n4+gz6c4Vx+/1JkmH4ddNpowctSe9JpRAoFAIBDoKwJNidhSnBK24XXJJZekthz2yC5LEdaZKriSnXHGGcmNzH1ClkXbIcIJEyakZb3TepGkQqnefvvtyQ+YSmVKKJ+24f+i7bifZSKmhqnnU0455VXmA/1lTnjqqadSqkxtaFvd1KtovpzDuEzE+kYFux8RSxxE/fNHFijCI6Mc0Tdx4sSUdjOIuK9fv7g/EAgEINCWjTifZ0dNUqdUL4KqKmKkyTYrbSb1jLQlAEKY1DAy3HnnndMR6hSnoi422xymTEnnY5B8zhyAoHk5ZCIWyow4jz/++J6naAON3zCFjIiZU5goDjzwwGLrrbdOG3e5iLajurNpgrmBiqf01UG1CwBBxAhbnooyER966KGp/8YWJRAIBAKBviLQkoip31mzZiVVKK8vQqSS/b+agAf5ya5GDQuLRl42tWRkQ1wIlVlBFreq/ZWXAzMI26yznMrJgJCmzbVMho8++mgxY8aMlGKTwuWSZhNN31yXidhnkydPLjbccMNEpsha2LOQ6UY24lamCep6zz33TKp+3Lhx4Z/c129g3B8IBALNFTGbKmK1pLchRlVy+ZJrwtK8ekYc/1yf+Tu1bNONuxjzwJJLLplMGUwMSLCuIH0E3SpTGvvxY489ltzWkDRzBBsyE4aSTRNSdeoP8wczCbOH65lCGhExs4QVgImjOllQ6pT4LbfckgidPTu3Gd+lQCAQCAR6i0BTRZy9BBAy8kOkvB+yLbbRic+W+q5DkM6Ms9SXS5iCbhZEoT11t3vQJ4LVN5NEeVJAvnlTUJu8Npg1soJ3fBL1LHFRtbjWJiXi5mFRLRLlZ9OJsbTb194+oLgvEAgERj4CLU0TfYEAqc2cOTORa06N2Zf62r2XCufKxqZdDdqgoplabDbakIsSCAQCgcBgI9CvRGxw2dbr/40UdLdBQPwUMVNE1U2OHdsGIbNJuweXdrt/UV8gEAgEAmUE+p2IBwtuG4pMB+0cTtppHyl9kX3sxHXmi07ri+sDgUBgdCMw7IlYIIjgDa5mXOvYitlxeWFwZeuW+UGd7ORUNpJ3Np48Fvyke6P01SVznPqyW97o/irG6AOB0YtAW0RsQwxZDCXCsCHIH1g0neg9hMYtjS8w9zmmCV4TjaLjyo/cPVRunXq2MacudmVtbLTRRomQ2aApbt4gVSJ2j41EbZePicptcqPj3vfss88mV75qPozR+3WMkQcCoxOBpkSMUKhNxGEpPuecc7Z0Lct24bJnBeJC4gidW1sjQkdMyI3Pcqty4YUXpnwS2267bY8dmB+y/MM24gSU5FwT6hI9x8OhTr2yG/NNrgvQYOPmRaE9OBxxxBGpaxS38TilulonYuf2Z7PQIavVgvTvvvvu5NZ3wgknzOYm12rs8XkgEAiMLASaErHluAAMUXSIyubWJpts0tR9zUaYMGfk5D5+ttQf8qU4fU5FVglKIMX06dOLMWPGJCLOuSYQIX9e12fCe+ihh4qTTz652GmnnRIR5oIw3SfAI7uvUaQPPvhgUqiIWDRdVfm6lpoWINKoIE0+xAcddFC6xFl5Jqo6Ikb6ogtXXHHFhjZqvs5CwctHO42sr1aMJhAIBNpFoKVpgrqjLh1Vj0C5g1mWW/5Xl/1U8NSpU5NqFuFGQSI+JOaz9dZbL+WsUA/CVZC94Iynn346EW3VywGx8nAQcpxDqoU4I0KHhZY9H3IKzXKuCcEXgjTknTCZaJey1x/hzFStfwWtOHgUuYrs81Mul112WQpOaUTEJgy2Y0Et6hY0QhGbRNit2a/LIeEmK3k3RB3mM/bafWhxXSAQCIwsBFqaJhAlswSFR91SeVQtYqkGZwgztnQfP358CoGmPP0gTB4G66yzTrHbbrulkGNkrCAvQR8+F2BBOWc17HPEKLgCQWeThvqQItLPReixRD8IGxEjV/mGESe7LlJEln7Uw7bMvOBfE4aMa0waiJnN2YRTNjmYTLS5//771ypi/UTm1LX/U+HGg4SNzYRUnjT0UQY5RBw24pH1UsVoAoFOEWiZBpOiXH755dPGGPKQtMdGmVDhquuW0OCLLrqo2HLLLZOitEQXjXfssccmUqJsEZo6EHkuFCSVzQwiUQ8Vmf2PkfLcc8+diDETMfuqiWGbbbZJpMkkwb6M9E0AOdcErwkTw+abb56uQ9ZMHFXiQ54PPPBAUux1xWREhUtoNGnSpHR/nWkin17t+nxoac6bUSZ1ZG8M6pwyZUqK8msnGX6nDzeuDwQCgeGBQFMi5l7FHmvpTO1SpVy2KMm6NJgIiFsXkkXSCJXiZPtdbLHFkiLMyYPq4EHGsrS1yjXBXIK0KXMKGJHrI7JF1tk0YbMu26cz8SP1ao4MRHzvvfcmpV5X2K+FRSN8ZG1CgYFJopGNWESh1UPVxKF+9mr9h60MddRyHG46PF6Y6GUg0B8ItLQRa9TSXbH5RvUhXKRa54GAnChPG2OUo+OMLOmpZOq4WTQbQs0qup3B8nagzinh8uafXBO8J9iFETPTCsWZTwyp1o0YeYfMP//8tc2akJC/8eZ62Jv9TXKgqhdIPtkEYVdJXwPuU6f6/MApFHE7TzyuCQRGJgJtEXFvh44knbqBXDfddNMBU31MJBQnP2KKudvFxHTttdcmM0idH3G324v6AoFAYGQj0K9EnNUxCBsFN/QHvNQmVzMKnv2124WJgr2Y94WNxCiBQCAQCPQFgX4l4r50LO4NBAKBQGC0INAvREyRlvP/DgUw2WX1qS7keCj0L/oQCAQCoxeBrhOxzTw+tLwYupVwpy+PJ5+jx92MV4WTRaIEAoFAIDCUEGiLiG228URwvBD3smYFEfNA4C3ARltXJGcX5FB3CnSjuhFqb5IO8WBwMCj/ZWfYNXJRG0oPJfoSCAQCowuBtoiYX64QXz6v/IEbFe5nNsm4gznfru4YIW5ffHsl2KmGSHNBy0EiNvq4vQmvtiHG3GES4BLWaUHGgif4EjcK2ui0zrg+EAgEAoFuIdCSiAVkCDxwsKcgDhFugh/qAjr49Qr8uOmmm4rdd989qd5ckLN8Eo8//ngiaJF5VK6Sw46FJOd7+CILOxYYkdti8thll10SWSNXdVLrWSmrT90IvWwL5kYnr4MDRoOIu/XViXoCgUCgWwg0JWIEhgwRnRBgNl+KmJ8ue2s1xBkp3nnnnYlst99++1eZHtho5fQVAOFedVePUeIOllUyoqXEhVYzJyB5wSGylYlCk1yHus7BGgChotmmqfFyIh39ykQs30WUQCAQCASGEgJNiZjilMgGacqdIJxXQh8kKHy5LhpMLgYRasJ2y3mF1SERj0ALKjuHMWcyFmGGQMs5KIQVI32pNwWGSDq01lprpWg06pe5IqvqDKpJg326bE/m9yvlJEUsAVB4Tgylr2D0JRAIBJoSMZKkMqninC8CGd9///3FsssuO1tCc6Qooxg7ruQ9NveqRYY0CW9EvTEhZCJFrswKZXKXZU0+ieWWWy5tAMrd0GnKSPVLs2mzTt4HRIzQowQCgUAgMFQQaGkj1lE+uFQsU4QfuSaqqjMPiPJlVuAR0egsN0pbCs26PAy5HsndTzvttJTKEhG7vjdK1mTiRAzmCf1h1ogEO0Pl6xf9CAQCAQi0RcSDARU7M9PESiutlEwWUQKBQCAQGKkIDFkitgnHLMEXue7ct5H6QGJcgUAgMPoQGLJEPPoeRYw4EAgERisCA0rE7LVSSLIhU7rVo5bYoV0jPy9F7DobbNXrRurD4gXCf9qY64Jhykc9ZQzyqSCdYtLqPnZ1tnzuhNXAm07biusDgUCgOQIdEXGrl7cdsB0eyoPBWW2OMsqFdwMfYf8eeOCBxXnnnZcO4DzssMPSqSADWXobTt3XPj7//PPpdGq5m3mdVIvjoPhTL7744j3eJVzzJMFH3ia3ZmHgNl15kDgnkAdKHdnnNgXfwJ53y7bbbtur8PK+4hH3BwKjBYGWROzFF7bM08AxQ83y73J1QwS8E8r/L/v6CsJwZt2JJ56YPCKy2qV+HSKq8Bvmt3z88ccXxxxzTPJfVng+II9G3hiuySc5lx9gO8TqGmOlxLm38ZOulrq6XdNsgirfU/5/3T1WBMa72mqrpcCXakG4VLMTsjMGyJU7IbdAATGeEbfBOkJ++eWXU6Si54lkGx1aqp8UsTMBRVJOnDgxEb8+ewbNTlkZLS9OjDMQ6CYCLU9xFil3xRVXJM8FwRSOJWpUEBkVyy3NyRhIl0+xkyycRzfPPPMk4t1uu+0SGSN1RIJoEeyNN96YPl9jjTWKW2+9tTjuuOPSYZ0UsbBquSwQgr5UEwohUmYPG3wIxsQhgMT1OQBEP6oucMjlhRdeKKhRZ9MJ+qA4y1GD+RqBLDYOqU/Eh6y0xWVPAvrypqJlvfq4+sEMQT755JNJjQp0QbrGgPSpWn7SyPPCCy8s1l133VdlidO+sSBS9dSZCoz9iSeeSBgIH1ev3BzVoBs+3LxRkGs16RICltzJGX7acOirZ2OFYiySJ2U3wkUWWSRMFt18E6OuUY1AUyKmUr3cSANBIRvEiVCcylz1x6Um99lnn0Qqhx9+eLHvvvsmZbfbbrsVp59+ekoahMSELG+22WYpAu+EE05ICnjs2LHFXnvtlXJVCGu+7bbbEhEzYQiPRhATJkxIRK9fyKFMMohqxowZPerZZyYCROgQUUTOHzmn5kQ6+omAERwFLDtbneJ3UKh8G8wFCJby5OeM0PTdMl59G2+8cc+XyT0IXr2iE7fYYouUxOiUU05JStOE4ZQPfzfRybHBVHP00UenU6fLihjhU7HXXHNNIUS7zmyRG6aanaRtIoFxNQAGEV9//fWJiKuKGEZMIyZcSnjPPfdMmBkXpS40nalCAiUTrQm1GuY+qt+mGHwg0EsEWkbWITgEy6/XkhSpIR6qtC4gwzJ5v/32S4rXkfeUlaW2e5dZZpl07D3ymjx5ciIbIdOS+njp5YO45ZZbEjEhYiSNnJEAZY1YkBp1hrfxr1oAACAASURBVIjLm3j6yMaMpEX9qfOCCy5Iy3iHiFJ3fJL1XzG5aI+SHjduXMP0nq5zL0IzWViaC8OWFY755OCDD06Z6fyO3HJBsuyxlL5sc/ruPn00VuQPn9VXXz2Nd4cddkhK+ZBDDkkTVpmIKW6TxjnnnNNzXfV5I2u5OTwvWFPFwsirRNmMiE16d9xxR5oI1QGXBRdcMP0Y57nnnltQwiYLp3XrT0Qp9vLNi9sCgRICTYnYDr6MZwhURjUkuOuuuyZybWQXRVRIh2Kk/JgYqD8ExMQgd4QTndmIKSwbU4iSaqa0EDBionynTp2aCHfatGmJ9JGy+tlJ2ZezrdLf7rvvvmQCyOYN2d+ockRHbbI3H3DAAUnZK8wc+kJBMg0gLkqzOrkwt7hXPSYf49YuEqW2V1555UToFCKiVqhj6pwqZ6+FwQorrJDI/uKLL04JkdSLyNdcc81E5FtvvXUy3VhFVE0T6tQes8bSSy+dCDbbgI2D8jcRUN9WLdRsoyhEqle7hx566GwrGs/EoajsyLA0HhMC84R+WaF4Vp4J0pe/Y4455ogXKhAIBPqIQFMiRnhsxF5KSpZNk0nCy7z88ss3zPvAK8LLTkF5WSWCp2qpQ8l7KCrLWoRx0EEHJYLbaaed0rXskAiBcmPOoK4RKYKlzCg8ZDpmzJge0wQ1iKiQM6VJKSMkxGEpjRiZHJBItSBTNlF9NHmYHKi+bPbwubaRL/ss04xrqGQkRMUyV7BrZxKnso2FbdqJICYV7cMPyW211VapTQS9//77J1Jzj/qZBpwMbYIqezUwN+iTZErMK3mzTttMHhS7vjRz9YMNrxWTlslAJr3yxhsVr98mDH2xIjGRHHHEEWmlwi5usmCu4nVhcqlL/NTH72TcHgiMOgRaek0gY6rRi081UoQICwk1Ul3Ii8r0EvsXESIh9zIr+BviQAJUnn+RLaJAdO7Trt8t5xGv+5COa/2tvNGkXhtp2tUnm2bsoOzNVB0FX87qVveUqWrLeuqdOYMtOxd9sQmGGNWF+KltJhbkpy9VJW01wVziM+PPnhv+BgvtqcfSHpkZq399bozs0GWSg5nxVX2M1aMtClkb+UdfKeRqXmbP0j0wMjlUiVT7nokJT//UZ5PT82dPZ/qBQZgkRh1XxID7EYGWRNyPbfdb1ciCqkYmlHcnASHZ1a6ZPy47qo065g+EOZgFcVqhmCgy6TJXmNgo6wgPH8ynE20HAu0hMCKJmHK0uUXFIcpOiLgd2NRNgVOFgx11ZjVg8ign2TcGY88+3e2MKa4JBAKBwUNgRBLx4MEZLQcCgUAg0DkCo5KILd3ZSSlJ6jmfcwc+atdmlA277BFAbToqSuFFEBtUnX/R4o5AIBBojMCoJGIbgldddVUiXa5ZfIVtBDpZmose7wFuZTkYw4abDUqbVa5pFl0YX7ZAIBAIBDpFoC0ithFk1573QrNTNTptvJvX82xgC27XHswlizK24YaEubrZ3OK2RfFyO6OERfTxcrDxx1+Xr3ErD4xujivqCgQCgZGPQEsidl4dhYjgbEzxPR3ogigFQHDryu5e5T5wt+Lnyrc5q9UccMKToOoBwZ1s7733TlF2wnn5x3JHE9HG28DnSyyxRHLjQvDImWub6EImC9dECQQCgUCgWwi0PMVZmDDyE3yB5PwIRkBOzdIodquDzAFOfhZEIRJOmHKOjmNi4L6FhBG1YIecJUz7PAcEP1QPMc0h0oiX8pXLQl1yYHAFMy55MKhhwRhCkvnqClkOIu7Wk416AoFAICPQlIgpRekS5YrI7lAi6yzRRaxVs3d1G1bKVE4KARbrrbdeiu4zAWTzCKIUuCG8GFEzNZRTbuqPgItycIa/zZo1K0X+Id5sbvGvMSJ9ZggJeNiLXUstsxEHEXf7CUd9gUAgkETj/5bw/20EBZV50kknpZBcS3OJXiQJZyPtRpL4Vo+A2kWCzAeS+FCtSlbiosSERPtXJriyWUL/mCQo4mo+BLkj1CV8uprbGBGrn2lCuK/oM+G8oswQcyjiVk8tPg8EAoFOEWhKxFy7br755mSbzUfSI0R2Y7bi/lbEso4xjVCrFKrfKeJqu4888khSsrKu5YREeaJAwjnoglqmqiW8EbYrz0M1O1lWxMY3ZcqUlKhILgy2ZjZi+SzCRtzp1yyuDwQCgWYItNysYxtlm0VETATUoty4CGogTmqgxG2aMUfIT0GN153QoU+i6Jr1CRHbeJTGkydEOYNbBqmsiNWpSMEpF0Qo4niZAoFAoD8QaEnE/dFof9XZDXMJ8wuTBht4udigZAaxuReKuL+eYNQbCIxOBEYUEXfjEdqI5DkhoCMn9GFPZqJhGvH3gVgJdGMsUUcgEAgMDwSCiCvPiacGwmUKKfsf8yf2e5Dw8PhiRy8DgeGEQBBxzdPKG5M2+QSySKvJlY97HDt5OdcEzxKRhxKmd4OktYX0tdHolOVmXzB2cAEw+t4oX3SnX1ArAmHgVTfATuuJ6wOBQKAegSDiEi68RHhgSA6PyGxMIiEmCuYKRORUinIYtQRBTjERHGJTry8FqdsY1XZORsRvu5MkQ7xC5NConkTdl36ZmJhsBPbwWulNMYk5TNWKQx3thqL3pq24JxAYbgi0PDxUIAM1xM2L4que+jDUB5wJrVmid2MwRscYud5GHZc5RwpJDuSsPIrYKc9VVeh65/o5XkhQSV2hUpEQr49GqpKK5bfMG8WRTnyoHTklotExTO0UHi4CUHiDUOjdLI5zEkDjxJM6EmXO8V3hd12Xj0SuEuf1wVmy/kic1M2nE3UNdwSaErFUkQ7ypLIoGVFqG2ywwYAnQ6dKBW3wH3biBFMAFzY/OUF7nWp88skn0zK/fAZdI6JEeg899FA6GDOTJde5u+66KxEz5YuIc3AILwqEhHTcBxuHetYVatChqJSgKMC6Mn369MIJ2AJYuNYp11xzTTrMc9KkSWlicECo55CjASlV6hfB65fn5Ky/zTffvMe+jSCNQ50m0boCw3yEk8CYfHyVexXtmShsWDo3UJBMtbhH5CEFX5cUyTMUzcglUFBQHuNwf4Gi/4FANxBoScRUEDXpBeK2JW0kdeP/A7G8pDi5lGmP4pL9DME6MBMx5vPz9KusevkLCwZxzh7y49rmB5FRY8gE6SjUqhOe119//VepT9fmU6MffvjhpDSRjLDqHORictAu80UjFZqJmH2Z4q0rTrFmkpg4cWIPrvyWnX7toE9mknzWn4NOBa/cc889yWad/brzOX9OgVZMFvJowA5e1GxVifKPpujl4/B/+CJzbZnA+FwzczC7mBQQKpyqxUSpv42I2PVygjBxOLE6iLgbr2/UMVIQaGmaoDoty73I0kSyn7KXLrPMMgOijKk1EXAUJ7L1orPJsuUKvUYa1NwWW2yRzCdIz6nLEvsgamoxH6jpofk/wlNfjqpDaMKenaDs9OdcTAIIlwJHxNrXriTxTlmmSBGTyQARlxWxdth7qVEbcAiI+UK7JgAJispJkyQW8rvcHvnv2hTdN378+KS6V1999RRh6FBUZOxz14t0tLGHCE0MEiPlc/soZSHiFL02q2YDfXSqtkx0Eh2ZoJy0DXfK2knacJSH2Tl9CBfuCqzV61oYmfxgkA8mNemUNwxvuummFJ0YRDxS6CPG0S0E2tqsYyelJiktLx87H4LrZBOpNx3Wpg0sgRRUsfYoxBtuuCEpNbZbeYWpNWRl0qBiLZGpZqTDZkmx5pQaPmd6QBJZEbve0fHqzr7DyMVqAAkhZERIIU6bNi0p3wkTJqQ6LdmRc9U04TMTmEkCZlQndc6OnKMUyyR12WWXFQ4lRawIW7n00kvTuHfcccdkP95mm22SKlc3tQ+DY445Jl1LucPFxIE0mSlOO+20YuONN073mDDgZ4LIKxlkbTVgktA2otYG8oXROuusU1DqTqt2MgkiNumY9BRYMpdo29+ROlypXROCzb3yKoVpw2TBNBE24t68EXHPSEWgJRHbADrrrLNSbgabRpaslsJshZnI+gscBGaDR9tULEKWhQ0JIUpKz3LZkrvqsaDfyI0609dMxP5FEsguK09juvDCC9MSnlcEgqE4kRHiRKaIWFTd1VdfnQheIiAkjMyYAKqKuIwJErz11ltTHxuZJqjrqVOnps255ZZbLq082K2ZCnhkUOwmAIRoYmBGYHc2dv0xFqsWK4Fx48alSeCSSy5JOUEoXUSJFJkqPEd4+ps9AJuDlDtClUsEucPM5GLciBhmbLyKoJZqoZQROtKvJllyLXvzjBkz0jPccsstk7mo1QZqf32vot5AYKgh0JKI2R29jNkrwBKU2kRK/X1aB9KkuChwhGfZi5zPO++8ZEIo/9QBS03bREJ+rezZSImXBKVPVWYzgnqNORMx1Y1M8sYhZWe5rS+NNuv03aZfM7LWDmJn9sjua/oi4ZCCmCnvrDS15zkgXMSn7UzOiNN4KXp/MxkZDzJk35bWVF9MECacnNWOWYKqvfLKK3uSOsHOGNVjMpGVDkFXi8/1h+nEKqRaED0TkElNOyaUgchnPdReuOhPIFCHQEsiHmqwWUJTivvss09bfrud5p+oc3fLG1rUXk5Kn3ExSSBwHhGN3Nf0QR1WEO1krKNMEWmnihHR2hBDlMwM1WJs7LhIGTlXi5XA+eefn2zQhxxySM9E6+/ULtJnp67rFzK3CjF5BMEOtbcm+jPUERh2RMyey/5pc6l68kZ/gc1swL6JRG1SltU1FUgtO6aJTXSwCxMBEwUlXSVEREx1N8pgh0ypVqsg5oo8afjdKoBpJRIeDfYTjvZHIgLDjogH6yEwcyAyJoHyJiWly17t790KKe7rGClqfexWfyhiJN3fewJ9HXfcHwgMVwSCiGueHOJhTigTGbJl6xUUUV6aM00gPnbUTk0Jjb402s9HU/Xmi8WOri/d8mrpdn29GVPcEwiMZASCiEtPl2sX+yi/XOYH9mAbd3x0Rb2xfzJBlAmaHy0b8corr1y7idXJl4cJhEsawtcXm3CdhirzmmAHthlWPX2kk76Ur2Xu4Cljg7a3iY1MLswi2X2wW5NEb8cU9wUCQwmBtojYC+TFaWejaSgNTl+Qmr7XnepR7qvrBILwq+XCxasAwXLZ4kvLe4NLF1/gcrFB5TqE2SzXBM+LZpt1VPW5556b7N6i5pAfv2C2Xvbwdgoi59KmH7wdWo25nTozhiYiJMp2XFf0P2/W1U0AvCX4RTPvCAhpFG7dbp/iukBgJCHQlIiRE7cjLxj3KQqxkYtWf4KiH4iMMjUZMAcozAdebO5SdaTz/PPPp74j0GZFPaK+kNjuu+/eE13nfl4IAiQkvRHckfMosA1TzdSxYI1mrmmW9rw9eFbwia4rCJ97mCjCHNDB75bbm0ATpg+uePoqYEK7OaqPuxu1Tgk76kmwSd5Q1LZnx0uikULmbQEn15i0ELprmWPUTQVbKZhw5BqpU8X6lvNx1G3oIXGBQeqR9CdCnPvzjYm6hxsCTYnYC4ogqMCcd2HppZdOS0zEMBDLS20J5fXyW67zQeU5YfPMpOBfu/n8V8s2WsQgEIXCzK5cSEwdSMs9mZhMNgcffHBSooIhckFi2lfKuSaoQ8QFH8RMDTbzI9ZuDuhoNJFxx0Oe3MaytwO/YSHOO++8c/JWQGL6bCLyHPgc+x0GAj/0VRKgDTfcMPXZ5MXtTDFxCAwx9nJxPXOISc5kZhwmJIrVc/e54BUTnu8CP2JBJ9WC7D0XLn6NouZyZF2EOA83moj+9jcCLU0TFJaQVy/oZpttlly0uDjJSJZPR+7PTiJTL7n8CQiHnRIRihCT78HL73NBDMgaeVKR1CwSpvIQDAJWctIfy/es7NQnmkz0WjlCz7UmmxzQIUqN6xz1LKRaRB6CQsR8d8v2XO0JlhAook+InNLNE4DIsrJ7GfMHMiwTcU76oy3/Z592n7qsEhCxZEV+z4pYkA17tfbPPvvs1H/Rd8bIxFH2H9b3yZMnJ6WOyE1e8D3zzDPTdZ73fvvtl5IO6Tf/bc/fJKDoA3t6TjYEG7iKSETG8ChP1pFroj/flKh7OCPQlIgpLy8wpSV6jJoTVmzJSgm2ilbrKzAU57777pvspFSZl5oZgrLi17r33nsnAqUWEbHPkYP8DCLEmAEQFELNxf+RjM8yESN1CX+OO+64Ht9ky36RaWytiAbZISmTEoLP+RYs4xFiNddEPjEauekTdcu0g5wQMEItmwpMONTrUUcd1bNsF07tZ4cddkih3pRkVvfsyTbQJOzJE4xrc9IfE9FJJ52UTAmSFdUVE4VcHbCjcpG4Seucc85JmDPFwJi5hDpGxP4tEzE1XUfEMEbKZSLOilg+izjto69vR9w/khBoSsRIRKIX+R3kU6DKZGCjAKVf7NaufCNAETGClGyHArdMRrpySJgMmBGQhsmBaaJcmBvYWHkeIN2cBhNBWnZTgbn/lu0S5FCFIse0i2AQpnpNRDnE+aKLLkrKVr4FahcJ6VcjG7F2kfrtt9+e2kTsddF+6kKqNsOof30yNvUiUwRNkTMN6A/1abWCnPXTBGPyUY/rETHyNoEZgz4y3QhAoayRro1JeTuktaR0KXyrCyHOMLVBqS2Jg+DNNOFZlLHOY7FayWkwYV4do989DxM6Iu7tSR8j6eWLsQQCGYGWm3WWnl5Om0PUkBfYpgxS6M2Zap1A7+WlSu24M4PY4NE+8rD0RbCUVaMEMiLMco7d8qSRk8qX+4J0qH8k4lqEbzlu3DkNJkWMePVJu/nEDeTWKtcEIjZ51dlXcz9MdpS31YbViBWHiU9/ECvctWsi8ENBI0/XW60gYWlBKVxFXQgUbsbFFGFilVUN8SJvqwF48OjISX6YdnIqTQrcxAVLfzcp13nPaDsTcV2uCUTNTm5yp7blOI5Q6E7ehrh2JCPQ0kZs8Mgnv6x+Z/NEUN1yj2oFMEWJlL24yMUSWSpFarHVy6yv7ZpQKH1qOJ+8kceHzJkfbEQhQHVS1jCAjfzMrdzX5GnIiYKajddYESb1mjfQ8vXaRZ7GnDcmXWv5r8/Imwse8szeGcakIHN9NbGaNMqeDa7JqULZlfVB6k3j83emFR4T2pKdrq7kjHBIvy4CT7/Vo8BVfwfq+9Pq+xWfBwKDjUBbRDzYnSy3z/5LCa699toDtrzlIcGTgPJkGih7ZzARUNJ8j+uykg00dpS9nzFjxswW4pzPlUPEdSRIrXIxo56ZXrJ9l9plk7ciGIgN2oHGLNoLBAYbgWFHxIMBGDXORxeRMYOUI+vYXpkumBx6G3XWzTHpqw1EqrnVaqHddilppb/Tnrbbn7guEBhpCAQRj7QnGuMJBAKBYYfAsCBiNkv20exe1ReU2SrZM9lMe5OdLN9P/Q5EQEtfxhr3BgKBwPBAoC0itsnCpjhYxMNLwa47u2cjl7l2E8DbNONCxQ2r7tj3Zo+N9wjvB+YILl2Rm3d4fMmjl4HAUEeg5SnOsnnZaWdvZAetO4+sPwfJO4GLln+5btWlmuRaZRc+H/zZqD/ImjsXW6+62vWmyPVR5YISbBiWc1L05/ij7kAgEBj5CDQlYptQDtUUAEAFIkQ+qAiJi1K38u82gpkZwCYZP13RYTkZTvl6nwsUEL7LGyCHMmfiznkPkLDd/5ygR9RYbwq/WweWCvsdCidy9GYMcU8gEAgMLQSaErHotFNOOSVFb1HFfEkllPF3xNjfaTGpV22ZDES8CSLJxWfyTFDDzBU5ZDaf1ozEKficmtLkoS6pJV2fQ5TVJ2CE61a1qLOa2Q2RizALIh5aX+ToTSAwnBFoSsTIS2gvswS7qhDaXXbZJY2XiaLTpX2nQFG1Qo1nzpyZwpnLmcvYeilhdlr2Xtfmky204/9yO5RNKezMwqMdL18OTJBzQZrLsm8tQhdZx12t/Hd4iE6TyrFOoXc6xrg+EAgEAoGWRCz1IpITWcYcwdEfobUT1dYNeIUz83JgekCK5Q1DfxfSS6mLJhNskE0TNhip4XJGNGqWImZeEW6ck5PnPBTV/lZDoV0nP/E111yTJiR5I6IEAoFAINBXBJoSMbcx+QMECCClHLSA0Hgw9LdpwuAkttE+FVs9uDMPXtJ1eTBycp/89yqRmlQoWrkO2Hc7DVBgI5cvgUoXSSfKrltBE319kHF/IBAIDF8EWrqv5eToSMsPpcnrQB6E/t6sA2tuD+k3yk2gj/IltJoY+hp1pg22aYUyl/RnsFz6hu9XLnoeCAQCs62+/0dO/w1YAoFAIBAIBAYPgZaKePC6Fi0HAoFAIDA6EAgiHh3POUYZCAQCQxiBIUPE7M45gs8BoZ3kqmUj5n6m2NQr55BQr7SQvDxcZ6ONWxuviSiBQCAQCAwFBIYMEfOMcJAln17nsXWSUtImmiOVnCBx/vnnpyCMXBC0c++cvcarYtddd03/OqstSiAQCAQCQwGB2YhYbgnkRVkKWOCylY9bd85Yu4nBGyXhaZach8/wFVdckU7g6PQYJv7BiNx5aw73zEXEnNwQjuahihEx4j7jjDN6rmk3YdBQeGDRh0AgEBh5CMxGxCLWhDWvscYa6RRfR+/w0XVKBb9iZ5k1Sx8pL4QTKxQhwg6vlCjHEUdO/3UYJRcwh1P6HOm7HvHK48DXFxGXj9txAjKCFVnHpIBY1St7muCKVVddNeWROPjgg4sDDzwwhTKrT1i0kyUc464946GOqW9jZLKQTU2hwNVTPm5+5D3uGFEgEAgMRQRqTROUJdIUQHHqqaemZb0jgSz9hQYjPbkmqqqVmqY4XSPs2CnCDr9kKthpp52KvfbaKwVT7LHHHil7mVOT99lnn6RWEb9Ti+WPoIrLRCz5kJBixL355psXu+22W7HVVlul3BOCOZxaLFWmv0+dOjXZgqdNm5aOgc+nIPtMngztUcTG6Fw20XqrrLJKcemllybbcQ7hHooPK/oUCAQCIxOBWiI+7rjj0vH18jggNPZUeSaoYyHOSFJkWjU3MKKWTGeHHXYoFlpooRR6zMSB7Bz26Uj4RRddNBHflltumU4XRpDMBCLVHFx5/fXXpxwSVRuxjGcnnXRSus/n1LEz1IQwq9OZchMnTkyZ0eQN1gd1mxSoYQTuBOL99tsv5aFA7MhfuPOyyy6bFLuAEP2MEggEAoHAQCIwGxFTk4cffnhSxLwXbH5Jgi7dpMQ/66+/fvJoQKJVE8UzzzyTMrWNHz8+kRz7rOgzSnnnnXcuEDzzABMAwqaOkSVSRPDUrBBi5gb1lwtydWAodS3zmWuZKQ455JBkonDo5WGHHZYmC+1R4HvuuWcah/soaOPQD2OcNGlSsdlmm6UcFptuummyhSPoBRdcsCOPjYF8WNFWIBAIjEwEajfrKFOEtNxyyyUbrsMjuYEhR0qU0l1mmWVm27iz6YUQuaFRwsKTqeEXXnihOOussxIRIs9jjjkmmSOQMQXMLk3VsuUygRx00EFJUZeLum3mSVmJvE888cSUtIdC1o5Umerymb5S2WPHjk2Jf9iDETIlfvzxxycipp7Zj6l4k4O/ybZGZUcJBAKBQGAgEZiNiG2k2ZijdhGvfBKSwvudDVV2M583y7Pw0ksvJYVJvarD7zKlSZAjN4P/qzen0rS55m9yWSB9JoK6Y4gQrh9mC2SrDuYRf9OGvumnNnzuMwRO6fqb+vXd3ySM5wHC/vzyyy+nTbqBPn1kIB90tBUIBAJDF4Eh40c8dCGKngUCgUAg0L8IBBH3L75ReyAQCAQCLREIIm4JUVwQCAQCgUD/IjBoRMxOa4OM7TZy+vbvQ47aA4FAYGgjMBsR2/hCkHljzQaYiDobY908jYJrW/a+sPEXJRAIBAKB0YrAbET84osvprBf7mWORuL94Jw2UW3c2ZqVV155JbmicStD3rwW+Pgid8l8eEZIuKM4xJPPLx9i/sQI31l4vCV4RXB549nAg4JXBQ8H9ajT5zw51K0dIctzzTVXW4eZiqoTZq1uh5/yTxYhqO88LvI5dnXjFFHoGvfyvnC/9vWr6vc8Wr9QMe5AIBDoHIHZiJgrFz9fQRei67iTnXnmmYmABEMgHiSEjKomBfcKBvF3kXcID9HyD0bCSA7hyRNx9NFHp/PohDsL/vB3eSKWWmqpYt11102+xMhfYAY/YGQrig4pi5I74YQTUoSffspRoT/8kqvRfmVI9E8ui9xvpC8Iheub4BWBIAsssMCrDhx1P1e4Rx99NLm9uVdb6uIv7dBSE4gESQsvvHDnTyDuCAQCgVGPQK2NWNCDAAtRZ4rcDznfA9JyACeSrsvEJpeDA0dFvCFXhCUKTrIdJId4fSZQ5PLLL08JfhAbpSoEGSFOmTKlOOCAA1LWN5/rj8RBQq2ZNFZeeeX0uUg/4c4+EzAyc+bMpJIbFf2Wz0LYM1JH5M8991w6CVro8/Tp05OvMaIvFxPG1VdfnSLxrBCMGykLIhEY4nP1yG0RJRAIBAKBThGoJWKK2AnFTmpWECYCom4pW6Qs+KEuCxuSZd5AjD4/7bTTUq5gSpmpA2GJXmOWQG6i+JgGmBsoWqYL1wpXlshH2/Jd3HvvvSncOicaQviU6HnnnZfqkYfCv3WBIMbA9KFfQqjZpmVmE1atfnWaWNRhspB/IhcrgNNPPz1F9AmtRsDMEA888EBKUCQ3BXJ3nURGUQKBQCAQ6BSB2YiYMpWHgY2YCUFBdohI7gYqF6FRlFUzALKTqY1qZToQWSeZjvSU8j0wIzzxxBMppJgd+pJLLknqU5Y3S3z1q5NqVg/yd41wZakwEbKUnGyyzCRstkiQEkaW1LOcyXWF7RoJU9OzZs1KxL/aaqsl0tcvBUGbDBCsKEKkrC2q2wSkr2zXFLFsbUwnxiIXMvPKvPPO2yn+cX0gEAgEAsVsRGxTDbEgR1nJEDP16l+5G3hPsJci6moaTGYLxMk2jMSpauSM2BApklUvpY1kr7vuicnPNwAAAWxJREFUuuShIQeEdJVyP1C+EruzBSNPWdkkHGK/lQtZWk3/v+iiixI5IkA5kJkxEGtW8dVny8bsupzVDWFTsYhYX20KmlzYtuXLsBGHtP2rH+pHvEwX7MFHHnlkyodhYqCQmVSiBAKBQCDQGwRq3deQp4KELMWpQoWpQeY1v+f/lxuV08FPPvGi7O6GyHOeiLxZph1EXFbWfleHtst15XbUmdvxN/0pn7DhvmYF+WbfZZuI7MNMCuzU2dQi8ZB+SBiU/5bzXGiffZvJhYLnrdEsUX5vHkrcEwgEAqMLgUEL6BhsmBGrUz+o93HjxqUkRgpSz+5yjY6FkvuYemdLpuSjBAKBQCDQFwRGLRH3BbS4NxAIBAKBbiIQRNxNNKOuQCAQCAR6gUAQcS9Ai1sCgUAgEOgmAj1ELOLMJlQk4OkmvFFXIBAIBAKvRiA7FzhgmZus0kPE3MkEavBCiBIIBAKBQCDQvwgIissuwP8P3cRsju2gZTEAAAAASUVORK5CYII=)\n", - "\n", - "Ou P est la séquence recherchée de taille p, C est un tableau qui donne pour chaque caractère le nombre d’occurrences dans la transformée de caractères qui lui sont lexicographiquement inferieurs et Occ(c,k) est une fonction qui retourne le nombre d’occurrences du caractère c dans la transformée jusqu’à la position k (non-inclue). Les indices sp et ep indiquent le début et la fin respectivement des lignes contenant un fragment de P dans la table. Si P est présente dans la transformée, alors elle sera présente dans toutes les séquences entre les indices sp et ep. Le tableau C peut être précalculé. Attention dans l’algorithme ci-dessus les indices commencent à 1.\n", - "\n", - "Ecrivez la fonction exactmatch(p, bwt) -> (int, int) qui retourne la paire d'indices (sp, ep) (avec sp < ep) de toutes les séquences dans la transformée bwt qui contiennent la sous-séquence s." - ], - "metadata": { - "id": "ZveHazSWsOJ_" - } - }, - { - "cell_type": "code", - "source": [ - "print(\"Votre code ici !\")" - ], - "metadata": { - "id": "C63yJjfjtUSQ" - }, - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "markdown", - "source": [ - "## Exercice 4: retrouver les indices dans la séquence d'origine\n", - "\n", - "A ce stade, il reste une feinte !! En effet, les indices que l’on a récupérés sont des indices dans la transformée et non dans la séquence d’origine. Or ce qui nous intéresse c’est d’obtenir toutes les positions ou apparaissent la séquence recherchée dans la séquence d’origine. Pour ce faire, on va se baser sur le tableau d’indices que l’on a calculé dans la transformée. Ce tableau fait un lien régulier entre une position dans la transformée et position dans la séquence de base. Pour chaque position sp≤k≤se on va chercher si k est dans le tableau d’indice, si oui alors on le retourne, sinon on va dérouler la transformée inverse jusqu’à tombe sur un indice présent dans le tableau d’indice et on retourne la position correspondante plus le nombre d’étapes de transformées inverses effectués. L’algorithme est le suivant :\n", - "\n", - "![image.png](data:image/png;base64,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)\n", - "\n", - "ou k est l’indice recherché, idxs le tableau d’indices et stepleft est la fonction suivante :\n", - "\n", - "![image.png](data:image/png;base64,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)\n", - "\n", - "Notez que le modulo apparait car on peut se retrouver à dépasser la taille de la transformée initiale dans la recherche de l’indice le plus proche.\n", - "\n", - "Ecrivez la fonction index_from_match(k, idxs) -> int qui retourne l'indice dans la séquence d'origine à partir de k l'indice dans la transformée et idxs le tableau des correspondances des positions." - ], - "metadata": { - "id": "uRHVKu1s9n1l" - } - }, - { - "cell_type": "code", - "source": [ - "print(\"Votre code ici !\")" - ], - "metadata": { - "id": "3RzUM2FJ91u_" - }, - "execution_count": null, - "outputs": [] - }, - { - "cell_type": "markdown", - "source": [ - "## Exercice 5 : Transformée progressive\n", - "\n", - "Le calcul de la transformée BW a un énorme coût en mémoire (il faut déterminer l’ordre des préfixes pour chaque position) ce qui la rend inutilisable pour des génomes. Une version légèrement modifiée permet d’échanger de la consommation mémoire contre du temps de calcul en séparant l’ensemble des suffixes à trier en k sous-ensembles, générer la transformée pour chaque sous-ensemble et les concaténer. Pour générer les sous-ensembles, on va simplement tirer k positions aléatoires le long de la séquence.\n", - "\n", - "Ecrivez la fonction BWT_prog(s, k) -> str qui retourne la transformée de la séquence s en utilisant k graînes.\n" - ], - "metadata": { - "id": "PtBlbmeNtaA2" - } - }, + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def BWT(s) -> str:\n", + " s += \"$\"\n", + " tab = [s]\n", + " for a in range(len(s) - 1):\n", + " tab.append(tab[-1][-1] + tab[-1][:-1])\n", + " tab.sort()\n", + " return \"\".join([a[-1] for a in tab])\n", + " \n", + "BWT(\"chien\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "bG6dMzI1ndK-" + }, + "source": [ + "### Exemple\n", + "\n", + "Transformée de chien :\n", + "\n", + "* Ajouter un caractère \\\\$ à la fin : chien$\n", + "\n", + "* Générer le tableau perm des permutations cirulaires :\n", + "\n", + "$$\n", + "\\begin{array}{l}\n", + "chien$\\\\\n", + "$chien\\\\\n", + "n$chie\\\\\n", + "en$chi\\\\\n", + "ien$ch\\\\\n", + "hien$c\n", + "\\end{array}\n", + "$$\n", + "* Trier ce tableau par ordre lexicographique :\n", + "$$\n", + "\\begin{array}{l}\n", + "$chien\\\\\n", + "chien$\\\\\n", + "en$chi\\\\\n", + "hien$c\\\\\n", + "ien$ch\\\\\n", + "n$chie\n", + "\\end{array}\n", + "$$\n", + "* La transformée est la dernière colonne de ce tableau (le dernier caractère pour chaque ligne) : n$iche\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "JgSWho3GorwJ" + }, + "source": [ + "## Exercice 2 : Transformée inverse\n", + "\n", + "Pour vérifier que la transformée est correcte, on va implémenter la transformée inverse. Pour ce faire, on va recréer l’ensemble des permutations de manière itérative en faisant un nombre d’itérations égal à la taille de la transformée. On va commencer avec un ensemble de séquences vides qu’on appelle table de même taille que la transformée qu’on va modifier à chaque itération :\n", + "\n", + "* Pour chaque caractère en position i de la transformee, l’ajouter au début de la ième séquence de table.\n", + "* Trier table par ordre lexicographique.\n", + "\n", + "Le résultat est la séquence de table qui se termine par le caractère $. Notez que c’est pour ça qu’on a besoin d’ajouter ce caractère au moment de la transformée.\n", + "\n", + "Ecrivez la fonction iBWT(t) -> str qui retourne la transformée inverse de la transformée BW t.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "id": "oH-bAVbgpOUe" + }, + "outputs": [ { - "cell_type": "code", - "source": [ - "print(\"Votre code ici !\")" - ], - "metadata": { - "id": "aoWF2thh8zEn" - }, - "execution_count": null, - "outputs": [] - }, + "data": { + "text/plain": [ + "'chien$'" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def iBWT(t: str) -> str:\n", + " tab = [\"\" for _ in range(len(t))]\n", + " for _ in range(len(t)):\n", + " tab = [t[i] + tab[i] for i in range(len(t))]\n", + " tab.sort()\n", + " for a in tab:\n", + " if a[-1] == \"$\":\n", + " return a\n", + " return \"Not Found !\"\n", + "\n", + "iBWT(BWT(\"chien\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "MMRvEACHpVDs" + }, + "source": [ + "### Exemple :\n", + "Transformée inverse de n$iche :\n", + "\n", + "$$\n", + "\\begin{array}{lllllllllll}\n", + "ADD1 & SORT1 & ADD2 & SORT2 & ADD3 & SORT3 & ADD4 & SORT4 & ADD5 & SORT5 & ADD6\\\\\n", + "n & $ & n$ & $c & n$c & $ch & n$ch & $chi & n$chi & $chie & n$chie\\\\\n", + "$ & c & $c & ch & $ch & chi & $chi & chie & $chie & chien & $chien\\\\\n", + "i & e & ie & en & ien & en$ & ien$ & en$c & ien$c & en$ch & ien$ch\\\\\n", + "c & h & ch & hi & chi & hie & chie & hien & chien & hien$ & chien$\\\\\n", + "h & i & hi & ie & hie & ien & hien & ien$ & hien & ien$c & ien$c\\\\\n", + "e & n & en & n$ & en$ & n$c & en$c & n$ch & en$ch & n$chi & en$chi\\\\\n", + "\\end{array}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ZveHazSWsOJ_" + }, + "source": [ + "### Exercice 3 : Recherche d’un mot dans la transformée\n", + "\n", + "Maintenant que l’on dispose de la transformée, on va développer un algorithme permettant de trouver efficacement si un mot se trouve dedans. Pour cela on va implémenter l’algorithme suivant qui provient de l’outil Bowtie base sur un principe similaire a la construction de table de l’exercice précédent. L’algorithme va reconstruire itérativement l’ensemble des lignes de la table contenant des fragments de plus en plus longs du mot recherche, jusqu’à obtenir l’ensemble des lignes contenant le mot entier. Vu que la table est toujours triée lexicographiquement, on sait que ces séquences vont se trouver cote a cote. L’algorithme est un peu plus complexe que la transformée inverse de l’exercice précédent car il ne reconstruit pas la table entière mais se base sur les propriétés de celle-ci pour trouver les indices :\n", + "\n", + "![image.png](data:image/png;base64,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)\n", + "\n", + "Ou P est la séquence recherchée de taille p, C est un tableau qui donne pour chaque caractère le nombre d’occurrences dans la transformée de caractères qui lui sont lexicographiquement inferieurs et Occ(c,k) est une fonction qui retourne le nombre d’occurrences du caractère c dans la transformée jusqu’à la position k (non-inclue). Les indices sp et ep indiquent le début et la fin respectivement des lignes contenant un fragment de P dans la table. Si P est présente dans la transformée, alors elle sera présente dans toutes les séquences entre les indices sp et ep. Le tableau C peut être précalculé. Attention dans l’algorithme ci-dessus les indices commencent à 1.\n", + "\n", + "Ecrivez la fonction exactmatch(p, bwt) -> (int, int) qui retourne la paire d'indices (sp, ep) (avec sp < ep) de toutes les séquences dans la transformée bwt qui contiennent la sous-séquence s." + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": { + "id": "C63yJjfjtUSQ" + }, + "outputs": [ { - "cell_type": "markdown", - "source": [ - "## Exercice 6: reconstruction de génome\n", - "\n", - "Téléchargez le génome de la mitochondrie humaine: https://www.dropbox.com/scl/fi/ux5m9r80ejm4lz7w3qv0c/sequence_mito.fasta?rlkey=qoaz38vwmg3fgkymx09c7m59j&dl=0\n", - "Téléchargez l'ensemble des reads ici: https://www.dropbox.com/scl/fi/uajxylv3yfo1is876x1e9/reads_sequence_mito_l69_seed43_N2000_mu0_norc.fasta?rlkey=h16uoh8xjostqbbmy1tc1k86d&dl=0\n", - "\n", - "1. Calculez la transformée BW du génome\n", - "2. Alignez chaque read sur le génome\n", - "3. Calculez la séquence concessus" - ], - "metadata": { - "id": "RsY4KN-x83cM" - } + "data": { + "text/plain": [ + "(3, 3)" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" } - ] -} \ No newline at end of file + ], + "source": [ + "def exactmatch(s: str, bwt: str) -> (int, int):\n", + " d = list(set(bwt))\n", + " d.sort()\n", + " C = {d[0]: 0}\n", + " for i in range(1, len(d)):\n", + " C[d[i]] = C[d[i - 1]] + bwt.count(d[i - 1])\n", + " occ = lambda c,n: bwt[0:n+1].count(c)\n", + " top = 0\n", + " bot = len(bwt) - 1\n", + " for c in reversed(s):\n", + " top = C[c] + occ(c, top - 1)\n", + " bot = C[c] + occ(c, bot) - 1\n", + " return (bot, top)\n", + " \n", + "exactmatch(\"ACA\", BWT(\"GATTACA$\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "uRHVKu1s9n1l" + }, + "source": [ + "## Exercice 4: retrouver les indices dans la séquence d'origine\n", + "\n", + "A ce stade, il reste une feinte !! En effet, les indices que l’on a récupérés sont des indices dans la transformée et non dans la séquence d’origine. Or ce qui nous intéresse c’est d’obtenir toutes les positions ou apparaissent la séquence recherchée dans la séquence d’origine. Pour ce faire, on va se baser sur le tableau d’indices que l’on a calculé dans la transformée. Ce tableau fait un lien régulier entre une position dans la transformée et position dans la séquence de base. Pour chaque position sp≤k≤se on va chercher si k est dans le tableau d’indice, si oui alors on le retourne, sinon on va dérouler la transformée inverse jusqu’à tombe sur un indice présent dans le tableau d’indice et on retourne la position correspondante plus le nombre d’étapes de transformées inverses effectués. L’algorithme est le suivant :\n", + "\n", + "![image.png](data:image/png;base64,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)\n", + "\n", + "ou k est l’indice recherché, idxs le tableau d’indices et stepleft est la fonction suivante :\n", + "\n", + "![image.png](data:image/png;base64,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)\n", + "\n", + "Notez que le modulo apparait car on peut se retrouver à dépasser la taille de la transformée initiale dans la recherche de l’indice le plus proche.\n", + "\n", + "Ecrivez la fonction index_from_match(k, idxs) -> int qui retourne l'indice dans la séquence d'origine à partir de k l'indice dans la transformée et idxs le tableau des correspondances des positions." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "3RzUM2FJ91u_" + }, + "outputs": [], + "source": [ + "print(\"Votre code ici !\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "PtBlbmeNtaA2" + }, + "source": [ + "## Exercice 5 : Transformée progressive\n", + "\n", + "Le calcul de la transformée BW a un énorme coût en mémoire (il faut déterminer l’ordre des préfixes pour chaque position) ce qui la rend inutilisable pour des génomes. Une version légèrement modifiée permet d’échanger de la consommation mémoire contre du temps de calcul en séparant l’ensemble des suffixes à trier en k sous-ensembles, générer la transformée pour chaque sous-ensemble et les concaténer. Pour générer les sous-ensembles, on va simplement tirer k positions aléatoires le long de la séquence.\n", + "\n", + "Ecrivez la fonction BWT_prog(s, k) -> str qui retourne la transformée de la séquence s en utilisant k graînes.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "id": "aoWF2thh8zEn" + }, + "outputs": [], + "source": [ + "print(\"Votre code ici !\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RsY4KN-x83cM" + }, + "source": [ + "## Exercice 6: reconstruction de génome\n", + "\n", + "Téléchargez le génome de la mitochondrie humaine: https://www.dropbox.com/scl/fi/ux5m9r80ejm4lz7w3qv0c/sequence_mito.fasta?rlkey=qoaz38vwmg3fgkymx09c7m59j&dl=0\n", + "Téléchargez l'ensemble des reads ici: https://www.dropbox.com/scl/fi/uajxylv3yfo1is876x1e9/reads_sequence_mito_l69_seed43_N2000_mu0_norc.fasta?rlkey=h16uoh8xjostqbbmy1tc1k86d&dl=0\n", + "\n", + "1. Calculez la transformée BW du génome\n", + "2. Alignez chaque read sur le génome\n", + "3. Calculez la séquence concessus" + ] + } + ], + "metadata": { + "colab": { + "authorship_tag": "ABX9TyO0SUJI6kaczFcOh8NoKcqb", + "include_colab_link": true, + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.2" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}