{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "This tutorial illustrates the use of LIMIX to anlayse expression datasets. For this illustration, we consider gene expression levels from a yeast genetics study with freely available data (Smith & Kruglyak, 2008).\n", "These data span 109 individuals with 2,956 marker SNPs and expression levels for 5,493 in glucose and ethanol growth media respectively." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We start out by discussing how to do QTL mapping, implement models that consider multi loci and introduce the application of variance component models for single quantitative traits. \n", "Subsequently, these analysis are extended to the corresponding multi-trait models, combining the corresponding quantitative traits across both enviornment or multiple genes in a pathway.\n", "Finally, we show how LIMIX can be used to fit variance component models that account for gene expression heteorgeneity by fitting a suitale covariance matrix." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Setting up" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# activiate inline plotting\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from setup import *" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#import data\n", "#the data used in this study have been pre-converted into an hdf5 file. \n", "#to preprocess your own data, please use limix command line brinary\n", "file_name = tutorial_data.get_file('smith08')\n", "geno_reader = gr.genotype_reader_tables(file_name)\n", "pheno_reader = phr.pheno_reader_tables(file_name)\n", "\n", "#the data object allows to query specific genotype or phenotype data\n", "dataset = data.QTLData(geno_reader=geno_reader,pheno_reader=pheno_reader)\n", "#getting genotypes\n", "snps = dataset.getGenotypes() #SNPs\n", "position = dataset.getPos()\n", "position,chromBounds = data_util.estCumPos(position=position,offset=100000)\n", "\n", "# non-normalized and normalized sample relatedeness matrix\n", "sample_relatedness_unnormalized = dataset.getCovariance(normalize=False)\n", "sample_relatedness = sample_relatedness_unnormalized/ \\\n", " sample_relatedness_unnormalized.diagonal().mean()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#genes from lysine biosynthesis pathway\n", "lysine_group = ['YIL094C', 'YDL182W', 'YDL131W', 'YER052C', 'YBR115C', 'YDR158W',\n", " 'YNR050C', 'YJR139C', 'YIR034C', 'YGL202W', 'YDR234W']" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Olf1+oEVdQO9pP/DCmH9HvKZovGzPzikTo4jGh8Rq3INqVZyAqheWaY1UiS0W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\nMT01ldzf4VC8KHu/1jKxQbMfkx6C1ki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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot (genetic) sample relatedeness matrix\n", "plt = pl.subplot(1,1,1)\n", "pl.title('genetic kinship')\n", "pl.imshow(sample_relatedness,vmin=0,vmax=1,interpolation='none',cmap=cm.afmhot)\n", "pl.colorbar(ticks=[0,0.5,1],orientation='horizontal')\n", "plt.set_xticks([])\n", "plt.set_yticks([])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Single Trait Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Marginal single Locus Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Genetic Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indicating with $N$ the number of samples,\n", "the standard LMM considered by LIMIX is\n", "\\begin{equation}\n", "\\mathbf{y} = \\mathbf{F}\\boldsymbol{\\alpha} + \\mathbf{x}\\beta + \\mathbf{g}+\\boldsymbol{\\psi},\\;\\;\\;\n", "\\mathbf{g}\\sim\\mathcal{N}\\left(\\mathbf{0},\\sigma_g^2\\mathbf{R}\\right),\\;\n", "\\boldsymbol{\\psi}\\sim\\mathcal{N}\\left(\\mathbf{0},\\sigma_e^2\\mathbf{I}_N\\right)\n", "\\end{equation}\n", "where\n", "\\begin{eqnarray}\n", "\\mathbf{y} &=& \\text{phenotype vector} \\in \\mathcal{R}^{N,1} \\\\\n", "\\mathbf{F} &=& \\text{matrix of $K$ covariates} \\in \\mathcal{R}^{N,K} \\\\\n", "\\boldsymbol{\\alpha} &=& \\text{effect of covariates} \\in \\mathcal{R}^{K,1} \\\\\n", "\\mathbf{x} &=& \\text{genetic profile of the SNP being tested} \\in \\mathcal{R}^{N,1} \\\\\n", "\\boldsymbol{\\beta} &=& \\text{effect size of the SNP} \\in \\mathcal{R} \\\\\n", "\\mathbf{R} &=& \\text{sample relatedeness matrix} \\in \\mathcal{R}^{N,N} \\\\\n", "\\end{eqnarray}\n", "Association between phenotypic changes and the genetic markers is tested by testing $\\beta\\neq0$.\n", "\n", "The model can be rewritten using the delta-representation\n", "\\begin{equation}\n", "\\mathbf{y}\\sim\n", "\\mathcal{N}\\left(\\mathbf{W}\\boldsymbol{\\alpha}+\\mathbf{x}\\beta,\n", "\\sigma_g^2\\left(\\mathbf{R}+\\delta\\mathbf{I}\\right)\\right)\n", "\\end{equation}\n", "where $\\delta={\\sigma_e^2}/{\\sigma_g^2}$ is the signal-to-noise ratio, which can be efficiently fit for every genome wide test (parameter searchDelta). For efficient inference, LIMIX uses the identical speedups implemented in (Lippert et al., 2011) and GEMMA (Stephens et al., 2012)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Single-trait eQTL mapping for gene YBR115C in the glucose condition" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "loaded 109 samples, 1 phenotypes, 2956 snps\n" ] } ], "source": [ "#create a complex query on the gene_ID and environment:\n", "# select environment 0 (glucose) for gene YBR115C\n", "phenotype_query = \"(gene_ID=='YBR115C') & (environment==0)\"\n", "\n", "# getting the appropriate data subset\n", "data_subsample = dataset.subsample_phenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", "\n", "#get variables we need from data\n", "snps = data_subsample.getGenotypes(impute_missing=True)\n", "phenotypes,sample_idx = data_subsample.getPhenotypes(phenotype_query=phenotype_query,\n", " intersection=True); \n", "assert sample_idx.all()\n", "\n", "#set parameters for the analysis\n", "N, P = phenotypes.shape \n", "S = snps.shape[1]\n", "\n", "print \"loaded %d samples, %d phenotypes, %s snps\" % (N,P,S)\n", "\n", "covs = None #covariates\n", "searchDelta = False #specify if delta should be optimized for each SNP\n", "test=\"lrt\" #specify type of statistical test\n", "\n", "# Running the analysis\n", "# when cov are not set (None), LIMIX considers an intercept (covs=SP.ones((N,1)))\n", "lmm = qtl.test_lmm(snps=snps,pheno=phenotypes.values,\n", " K=sample_relatedness,covs=covs, test=test)\n", "\n", "pvalues = lmm.getPv() # 1xS vector of p-values (S=X.shape[1])\n", "#convert P-values to a DataFrame for nice output writing:\n", "pvalues = pd.DataFrame(data=pvalues.T,index=data_subsample.geno_ID,\n", " columns=phenotypes.columns)\n", "\n", "betas = lmm.getBetaSNP() # 1xS vector of effect sizes (S=X.shape[1])\n", "#convert betas to a DataFrame for nice output writing:\n", "betas = pd.DataFrame(data=betas.T,index=data_subsample.geno_ID,\n", " columns=phenotypes.columns)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Wk+92ywxRjEuRMzXDNOuPOzuPXmL5vPw5izWfMWal2SVTjjW5kEY1DTOSrlmf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\nWnDp2NoMtfZ6R96HZAIGLRA4pzVbwNv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pl.figure(figsize=[15,5])\n", "plot_manhattan(position['pos_cum'],pvalues['YBR115C:0'],chromBounds)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Single-trait eQTL mapping for all genes in the pathways in the glucos condition" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "loaded 109 samples, 11 phenotypes, 2956 snps\n" ] } ], "source": [ "#create a complex query on the gene_ID and environment:\n", "# select environment 0 for all genes in lysine_group\n", "phenotype_query = \"(gene_ID in %s) & (environment==0)\" % str(lysine_group)\n", "\n", "data_subsample = dataset.subsample_phenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", "\n", "#get variables we need from data\n", "snps = data_subsample.getGenotypes(impute_missing=True)\n", "phenotypes,sample_idx = data_subsample.getPhenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", "assert sample_idx.all()\n", "\n", "sample_relatedness = data_subsample.getCovariance()\n", "\n", "#set parameters for the analysis\n", "N, P = phenotypes.shape\n", "S = snps.shape[1]\n", "\n", "print \"loaded %d samples, %d phenotypes, %s snps\" % (N,P,S)\n", "\n", "covs = None #covariates\n", "searchDelta = False #specify if delta is optimized for each SNP\n", "test=\"lrt\" #specify type of statistical test\n", "\n", "# Running the analysis\n", "# when cov are not set (None), LIMIX considers an intercept \n", "# (covs=SP.ones((N,1))) note, as phenotypes is a matrix, \n", "# LIMIX automatically carries out an association scan for each phenotype\n", "lmm = qtl.test_lmm(snps=snps,pheno=phenotypes.values,\n", " K=sample_relatedness,covs=covs,test=test)\n", "\n", "# get p-values\n", "pvalues = lmm.getPv() # 1xS vector of p-values (S=X.shape[1])\n", "#convert P-values to a DataFrame for nice output writing:\n", "pvalues = pd.DataFrame(data=pvalues.T,index=data_subsample.geno_ID,\n", " columns=phenotypes.columns)\n", "betas = lmm.getBetaSNP() # 1xS vector of effect sizes (S=X.shape[1])\n", "#convert betas to a DataFrame for nice output writing:\n", "betas = pd.DataFrame(data=betas.T,index=data_subsample.geno_ID,\n", " columns=phenotypes.columns)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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E6Oqy1tgB4N+A/4tUinGkUpqBVIYZpCXfihTUwm7XTkTDushXki6kAk0jBcvt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\nQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plotting minimum pv across genes\n", "pv_min = lmm.getPv().min(0)\n", "plt = pl.subplot(2,1,1)\n", "plot_manhattan(position['pos_cum'],pv_min,chromBounds)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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tdWDW1bxYZzBQLbBlzmDWGfsY3ivwpG3KOmC3/d+8co01sTEYEC/AtPM9Jwe7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\nyaojR1I1dv7NhsCPMNdHeIe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DwXhhZ2ekyOtNF+clMfLjOzDL2AJMPJ072JY7hW0hZgfT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1PTQElbW7hn+fLCoTjisceOVhcVOaJ33FF9fGQSyPACa/TjbSdIDmWfgCoHLgcWw2s2WH1QJ8R0\nOzRevDwyBt+4sa3kv/6r/m2JBI5XXuk+dvHFs7ruuKP6+He+c2B5IJBwX3317OOvv+6f1dISKiss\ndAyUlDjDVVUFkWi0t6enJ52vExg2p5NQRYWtv6mpv3JggII339ye7Oi49o2aGm9wYCDhc7ly4qtW\nzerdsaOnOCfHkjRHW5nrfPduf8GxY5H82bNdMZhsvDGh438VKqGWBy+vAiM8dnJ0rOPSxOOLmZLE\nyAG+h+qwtwE7gD8AB7I/1NycnO/xEHn88aN2mw1HTw8FcCQfFieAR8G4dZxAAtRKukT/eQA/KqBr\nQXXa8lA7pV9//npUQPdHVOW9EtVY/D0Yb+jHceC3qEaSkQ2i4d22zVfwf/7PrhsA+6c+Vbcd6Cku\ndiY2bnxlidW6OtbWFvECFtUAbDisGyezrHcA70M1GH26fFYwsgIao42RO08p8BlUoLkJjF6V2Dlp\nkKUv9ci9A774kn5zpXrNOAbs0ssVQjVqOYBTlZ1BYJk6MBFC1aki/d+mp12CCpKqUIHNRWDsQnXq\nLgKKBgbwfu97h65yuXBaraQ2b+6Now6YAOnS0tzoK6/4Zjc2BvNfeeWVRevWrWvJTjT4/TH75s2d\nZb/4xZFVevm/ALwJxof1tmtUOxG3qjIZbwIPw8FquCaICjZ0EsIo+8Qntq6NRJLu971v0b6rrirp\n/ulPDy2OxVI5JSWuuMuVk3znO6taE4mMLRCI281OHqizCO3tIUdbW8Tj9dpTfn/U3tMTdVoslqTb\nnZNobNxdBXfW+3xRuxlofOtbK57Yu7dvTkvLYFlnZzg4d667v7U15D16NOQdGEg4otGkHbBcdFFR\ndyiUtP3oR0cuB2MFbHgv8DjDw7x/Azyj13ubrh8Ota2Mp3VQoofAfvXPIbQlK/GV0NvzYtTBr1wn\nF7rAKMsO8rdt8xVs2tRZATAwkMyNxVI55eWu4KuvvroiErkk3dIyWOB05qTKy3MHAZ544sgiMEpg\nw2fM9QvciAqEcoEKXX9AdS6zG1M76qa6nfr1v4WuG1AH6juA/bo+luj69wjwK12vC1BBr7lPrjaM\nN1eEQulcp9OaOHAgGHI6rcm2tpB3cDBpb2kJzonFyFmyJL+tstIbczqtqU2bOh27dvXM7+7eVVlR\ncVVPdbUn0tUVzY1G1dUje/f2lrW2Bud0dGQKXntt4GLgDTAW6HnORgV+RQyNGiCOOruKWi7eqcv/\nIhjm6+WopES1/v8PwANgvA60wnffizrTclwv4zK97AtRCcMoGDsYTr76dDmWo4KYBer7VAH1en0B\nxi3f+U7D0oGBmCsUyjhKSpzhSCRpdzqtcb8/5hwYSObPnu0MWK2kSktzY3fcUd28eXNnWSSSst12\nW2Xbl7606+pwOO3Ny8sJHDq0f4nDMT80ONhekJubk7zhhjld/f1xe2GhI5F9JnDXrt7SvXt7Z1ss\nZDZt6uzX5dBnAocSXctQyYe5uo62oUaRWPTy5Op1U4HqYAcZClIdN0N8i647Lai2YRB1bDED9LV6\nnf10OAgzLvrKV/Ze5nBYku9///ymtraw+6mn2qoBCgsdie7uiDcex3PwYCDW2hrymomahoaA+09/\naqvcurW9prk5VaHKhiUSUccIi+WQt6FhSdXs2blhr7ct8dJLXRWRSNq+dGlBf06ONe+113pSzz/f\nXj04GHf8xV/UNK1eXeJvbR10V1d7w3V1BWEzaTg2w4tq63LBsKOOZw2ofaMOtV836fWXj7q0L4FK\n4kSh8F3wpbAuc4OuUzV64gFUu5Kn66RNrX8jqI8xtby1wzYTTCi2eOih5iuqqjxdjY3B9oGBhGvX\nrr55O3a8vurJJ8svBeMnI4NzoxbVEXCCcTHqbJMdjCf0B+ajkpZB1PozO7/9YOyEb78P1SlYgWqf\nm8HIRe2/BagzxhFULJJg+LISwPA2Nw+4DxwIFv7wh4cutdlIf/vblz0XCMTtTU3Bgldf3VGXyVya\nnjMnd1Cd0TcD96GRS4XAzWDUAOax/ibUdo3p5w5Um+HVx43BrDbbiUqs9KLap0uAABiRcU4iVUHy\nnaiEaYKhkRkjRsOaHYVl6umG17KSi3qUJFZdvl4V17AQtb8nUJ2rfDAOwYb/1d/92wceaLiiuDi3\nr7V18Oj27b5ym82a/uhHFx34xjd2rentxbNqVeHxtWvndA4MJO2NjYHCAwd2L1i58vr2igp32Ou1\nJcCS2bq1u+L113tL02msqA5xiqEEFE79V4Tav0AlN26C1GWo/S4NNIHxOKod/+vBQSp27x4s+/zn\ndzpdLluqtzfisdmsmUTCmhcOJx2dnVF3IBC3B4OJ3J6eWFLXIx566HANwJ131raYiXgzgRoIxO37\n9u2uXrbs+u516169RdcZbrxxy/sffviqRzdv7izbvLl9fk9PbE5TU3+krS3ksdstNDcHir1eR8rn\nyzhffz20VNePIuALYPwXKr51ohIVBaj9fpZetpheJ43AQbVt9lwBzx3WyY9aVOIzoj9XoLeZRce5\nADX/+Z9vrursjBTn59tDK1fO6qiqcg+WluZG5s7NGVy1qrCzutobfu653Uvr69cW/OlPbZWhUNLx\nyCPtK9NpKlGxwc+GExnGLcBVqPrsQ+3/UbUNCKNGjlhQHfjZqj4aOu770rX684VqGxsehkY38nZd\nN3+nly2XobjY8N57776lLldO8s47a1u+9a365QMDCYfDYU3l5zvihw8HCvr6Iu6lS4v9c+fmDRYV\n2cNOZ046HE46fvazrW/bs6e28I47alqCwbi9tjYv2No66N6xo7espSWY19UVKW5pSVbp+p8Bvqjr\n90rgb1DtUD7q5MQzwFN6X3KqdTN0IvAh1EnQcob3c/R0C3WbFoJv3wXchmrjzbP4x4Bf6+9dghp9\n5FXr2YjodTlXbX9jpX7vCdig4wqufPHF9tpwmILm5lB5d3fEfe21Ze2hUNJWW5sX3rKls6K42Dn4\nyU8uOWIWKpOxWBKJeNJud8VSqYzt6qufvn1ggNlwINdurw3bbKSj0YT1mmtKO+vr+wuamgZKensT\n7vr6QElfXyI3k8GydWtHeU9Poiw3Nye2cePxhahLQH6kj0/LgHfr2SVUf2QoTjQvE1ur68hOVMw2\nS6/XDDRVw+plqPagEmjRfYoww23cLaj265ha9+pSrIceaq7r6kqXxeNY+/sDnvr6QNVPfnLkMq+X\nnJwc0keOBLypVMrV20uxzxcO5+QUtVRXewf6+3Nzjh0LlegyxIqK6LjoopLOzZs7l0ejOOPxxvye\nnitcF19c5Fu8OK+3oMCR6O2N5TY2DhQ1Nwfzd+zoDd1xx7zDhw8P5nV1RXN9vqg7FEo5gcDixXmc\n2Ij2fycqHigBI8CIWwsMJXyWoeLMuUAedKxS9dDYCPyRkcmKi3WdsoFxFBV76BH8ho7jzBFSbz3G\nzJQkxmrgEMNniX6NGvp7YNTn3KEQqfJyEtHo0BkOU2b44VDlaUIto0vP42pU5bSiVkwj8Jz+klM/\n9zPChkEwOlAN+6V6eiHUwSmEChoPAq8C2/T8vUDl3XfvuikUUkHgD37QkPzmNy/b9PDDrfNbW1Oz\nN25snx+Nptz5+Y44MJ+RN8tZC/wzageKMpwQMBuWfoZ/TeVRMBpRDe27UIFFHqoSLdQHi31AXO9E\nOpFh1Kr5EkXtnBXgLmJ4mOANqErYrqZn7Nfz9KMacK9e517UECtzFEKp/m9D7fhdeh1VoSpimuGh\nyEf0/DNAOpXCmkxiA3LSacx7DERsNnrnz3e3Hz8eLjpwIOjp7k4X6Us0itJprLFYynroULDg5ZcD\n5nC5EuAfwNjCcKY6g9ruZuCxHLgaPGmGz4Ln6Z31S01NyeWA7b//u8lz//1NFr39U04n8blznf54\nPM3atWXdR4+GvU1NwfylSwt6Cwsdibvv3v2OWAxvXZ2nq6jI1h+LpZw5OZZURYW7/+KLC32HD1PV\n0BBwr1v36jq9ffnc5/a967rrig4kEmlbMJjw/PznTUvj8Uye35/KDYXwWiyQl0d8+/aemt5eShgK\nBoxHGbkPe1ABqTnCJ6mXqxXVgIDaL2ZDcTl89QN623n1tmrT28nL0L5nlAEf+f73D1xtt5O0WIgl\nk7jcboc1FIpjsVit6XQ6vWsX1nA4NefnPz9yRSyGJx7H4nKRjETI1eWap+f/dWAjKnHYr7fJJaig\neBDV4DehApAQKjisRtXvPGAJ5JjBRY4ubwYVmFj1esnXn/cA9WCYnbHbdu3qqXY47NbBwQQWC5lA\nAFcmQ14mQ0atIyy7dgU9mQwtS5bk+/ft6ytpbY1VxmKW/McfP7Ji+fKSDr8/mt/dHc4LBNJ2iwV7\nMIhbrzOdzKQJFSyYl6ldr6fdCuxF7Stu1EH0Sl0flzLc8fHrbbxSL58F+BdgE3AYShbq6en9Fg8q\nwAjo79+t63Sz3q65qH3dpterRX+/gKFLS4zrgPc8/XTnymgUj9VKsriYvkgEdySCPZUiB7Dv3x9O\n5+YSq6yM9L36ant5ImEttNutid/+9uiKUIhStQ6SZTYbJJOQyeBobh6YlUhk7L29MbfVak1dfvms\n7lmzHNHDh0OFu3b1zGlpGahIJLA2NQWqnM6cNPAhMB7UdeR2VDsURQUM3Qx3yhfo5b8CFcQdQwV0\ndv0ZH8wqhfVlen0HUR23/qzlX6m/n9bT/q5uG59/6aU+j91OcOfO3upAAK9ej5n8fIJz5jj7Eom0\nvbc34e7ri9ij0ZStqMgRffLJlrrW1ox5pi/NcHIQiwUgk3S77YlUKmP79a+PLO7vT5ZCJh0MJlxO\npzXT0NBX4vczx2rF+stfNucfPBhosdls1oMHBwbq6/sHe3ri3o6OsEdtr7fcz2MZ6iz4Gr1v6DOi\nRFBtzWwYqucwlPTh3eq1uhJd3/y6Lnbr99tVvaNP1zkLan8qAEJgmJ2apfpzP2HmmFBs0dwcLx8Y\nSLoKChyxvXu7yltbmQc5LtR6fA6Mq3RC93ZUJ8k8vpn3ryhFnd0cRMUWbcAeVHBWh6o7DuBamL0E\ndUwq16/N0tNp039HUZ3HGtTxbCDr5EXR0aOh/B/+8NAlsRjzYjG4++5db7/xxrLDnZ2Rwvb2ZOGr\nr/ZUezy2WCAQdzB09nbIN4ElqLp5jX7Njdq3elDtsFsvXwUwG/ULBf+M2ldiqPqRh6oH5tlfbYO+\n18zQTWArIb8U1cZ3AAX6mFKJql/H9TqYp9eJBYxK1L46W6//hP5vjpqdpd+r0etwnp7GmzqodgE3\ntbdT3t4eKdu378iinBzsOTmkPvaxXQvVOsH10kv9Zbt39/fddFPZwWAw4Y3HM7ZoNGlZsiQ/6PfH\n7M8/31G5b19fRTic9CxcaO/2+RID/f28CPy7nv+tqPYGvf0dehlmgcON6gz263VlXgpr0X/W5uZE\nLSQsgBPS8crKTEdlZX7nNdeUtttslmRbW6SwrS2CzWZJPvdcx7zf/Kb9KsDyzDNHW8vL82PJZIqn\nnmqrXreu+lB1tTdssWQy/f1JJ8PHIQD7t7+9f2VbW3BWLJZxRCLYYjEKurr6PXY7dpsNayYTDyYS\n8TTDlzqmUfv6z/RygjrzHs0qv43hX6roQB3zgJ636/bzXai25BDqmNeOSkaV6c+b7tmxY2AFYMnJ\nSWYOH26bM3euy79mTemx2lpv3zveUdmzcWNbSXt7sug73zlwVSqFPTeXWDpNPup4b2fofg3GalTb\n40LtmxlUXX0ddSzcqctciDruXYTaF5xAGC5diuqo5aCSFlG9PZ2ofSMARp2ebq7arsYO4F3bt/vq\nenvj9kcfPXqRxYI3EMCty5fW308dP+6fO29ewLd4cVFnJpNm715/ud9vLd28uffSjo5I0SWXFHc9\n8cTx6paWYGl/fzp/YMA8cYnZw/yQXq5foUYE1DA8aiup13ce6r4fFagYtxQ1qqIANWK3GRVXNaNi\nYw/qOLFObdeKVWpdUIw6bnSj+kjP6HV9BHW8WKTX3WLUPpCPqnelev0t1e3Adv8gwYEAACAASURB\nVGDewABOncjPff75Xk99ff98uz2diESwBIMUxONYf/WrIyuvuqq0dfXqki6Hg3BeniPjdOYk77+/\nYXUoRJVajzk5iQQRj4fBxYsL+urqCsJ1dQXhRx9tpa0t4s3NtaUBentjrkgk6YzH046urrjDbmc2\ncLNeth+i2qOFui6/W60ro17XlxV6/a7QdWkxqi0fRJ0080FkFqrtMvs+N+np+NVnjRSqfZiNikse\nQyU6Vu/dG16ht1MgGsUZjZIPWGIx0k4nEYsllUynsWQyWHJySC1cmNd79dWl3Xa7JdbeHir1+cjN\nyyN4663zmpYvL+hrbR0sbmkZTMTj6WKXy27p60vkLl9eGNAnPWhr66zq7o6XHj06UPbCC23zKivz\nIzU1nj6wpHNzrcmiInukvz9uHz5BYp5UNxllwF+hRjSao3B+p9ddnV4Wh14fPr3Olul1U6fqmD0f\ndfxwq/phhFDHmmOqrnAJKoY+hkp8oOuSTddRM6afsUmMSkbeDOg4Krh/C68X30c/Wrfn2Wfb5h84\nMFASCKS8qMr1kD57dwtwJ2qHHkQ1nnbUDq93BEA1DvkM33XXvEZ6rOuro6hGws7wCAQzOF2mp1uC\nOkNhjnaYGwrhRO3QqUyGdGNjML+xMVgRCmW83d2RYrfbbk43Mmp+f4U+0Opy+fV8a3UZBvXrAVSj\nFtTliaMOmnFUBahEbePlwCuohsc8G79Kr5OA/kuCzcze2hjuCNtRDdpcvXzt+vNm9q2WobPpuBlO\nsnTpz1Yz3Jj7UGfCzLM7EWCjx4Pb6yW2dm1Fy2uvdVXa7Zb01VeXt7zwwvGFFostfeedC/dFo0nL\nnj295YlE2h6PZ2yvveYv8/vj+cFg3NHfH3X29cULGRqtMrR98lE7hpnIMi9/seoyl4MrijrQBlA7\nFQwf2CzhMIWoHdQFZGIxosFgIhqJpOyhUMLi90edAwNJVyqF5X/+59AlsRg1gKWhIeSpqOCY2+3K\neDz2WG6uzZ9KZWwDA7hfftk3h+GOBIClpsYbGBhIuDo6Bov6+5mjG3wb4MhkSIVC2FyuoTNA6GXM\nAe4BHtDLdEgtEzDUWODR68Kqt6MefeMtRXXe5ur6sh8VyMZR9b0/K2h/u883dG8TCxBzu+OJ3FyC\n6XTaFolgj0Zxg9UZjVKkP4NOYGSy1n8eamSTeU+GfFRQnEY19n793T5UvfagGsF5qGytvhQgbe6r\nZrCW0vMwg4sq/Z6d4YCpCpifSuHu6EhYAE9KpclcDCc1M4DVasWRTGKdMyc3eOCApSiRwAoWaySC\np6cnktvXF3V3daVnJRI4LBYyev0mGRk8oqe5HFWfclFtxDH9V6CXN6q3SYEuYwtq39nNcOfabHcW\nq3nYvfo7xfp7BQyfFXPo+VhQBwdz+Uv1Z+Ko9rVIP+7U788CynRy2JNOk/T5SNlsOFKpoQSRE7BG\nIjja26NpqxVXIpHOT6fTJBJD884FnKkU8erqnJaFC2f1L1mS39/REfZ0d0c9VqvFeujQQHTJkryU\n12tLejy2eG6uLZlOJ22pFJlkEt3xGgqizDKbAVU7qm7X6eWu0estynCwWabrTCUU56OS1+Wo+md2\nEu26zsxneGRZsW4bX9afJZGgMBBAdzRUMJpIkJw1y3U0EkkMDgwkymOxVOnzz7e5k0ksOsno1dMM\nFRTgy8uzJiGD1WpJxmIUXXPN7KZoNG23WCyWVCptdThy4pBJhcNpdyqFLZXCkpND2mq1ZGKxVE4i\nYbGFwylnKJSMqvUYK0BdMnhsjOG71Xr5bXodgEqetaDqaRdq/zKTPTfqOmqFXK/ezjqhSy/DCd4g\n8EZWfXGjAo+43uZL9V8RMyuJMdHYoiCZTPc1NPTOOnaMCka2z5pxO/BBhhILbEN14i9iOCGRYXj4\ntblP6xvq4VCf87hQx8hc1HYy2+x5qJMhT6COlSv1vJKo/bgbKGlvj3jT6aEOZ8ZiIRMMxh3xeNoR\nj6dyQqFkLmBrb49mjXbYMAjG36PaIjfDSX1TRK+bfai2IogapWVn+MzsHFSbZl5+mdR/m0aeIdtw\nGHW5aC1QDVaz/TKTqZei2vt2VFxibh+z/TBHucZR+2uLnu8yPe8eXb4iVExj3nTQ/B/Vf2nUdoyl\nUrjS6aE4y0x654VCOHbu7Oq/8sryro4Oa6KszBUxh7ZHIilbJmOxOJ22RFVVbs8nPlHe+rnP7fti\n1ojZHwLv1+u0hOHOHJDjZngf069t+HcwHBYLH3A6ydFtrR4piS0czmQ+8pGFB8zRjuGwGkYfCMTt\njz3Wbo6SoK2NhaFQsDedJsftzkk89thxx3veU7Xf5SJWWGiL3XFHxbZHHmm/CuCyy7wNBw8GauJx\nXF6vNeBwpIORCMWZDM54HEtODsm8PGe0ttbjKyyMpfftC5UAr6lRk0b2yN0Yw2f406j63ww8jbr0\nNDtmvpjhmLhff7YM1S7qkSsbtoPxD6h23AmkUimSySTe3t6Ypa0t3P+ud1W1bNvmK1CX46ZnxfT4\ngWCQmN1OPJEghKqzX9fz/THDl4q7GD4BWKw+NzS6rx8Vr87R5dKXeeZWoOpzBrXPWlD1MaWX4U1U\nfcweyQDg7O6Oe2IxPIkEKTWtoRHL5nExmU5DIJB0+3yxvNJSRzASIQcsOek09u7uiKexMVDY0jJQ\n2tNDSSYzlCjK3kfN+CKs/7bpZSxC7Uv7dPm6Ucl6s2NoQ+1vpagkRLt+vwV4D6r9capp2Tyo9us4\naj97AniW4TPsdlRiwtyXC/X6tWaVLyerzG4gUlXlCDY1xW26PI7OznRx1me8QE5fH8WbN/tK29vD\njZWV3nA0mkrYbJnkqHWdyc+nb9mygmM33jin3XzRvDTTfN7aOuguLnZEX321O+J0DuZFIpbiwcF0\nGojpOtCLqgeFqGTGQlR728TwZb4wHH9kUG1Os1p+3yLUyesgajTtQlSdyej10qbXS/7wuqUU+D3D\nSSmnXtcOVF2LFxRYei+/fPaxYDBm7euL982fn9dn/jLjmjWlgZISZ/TFF7sqly0r9JujPwcHkwf3\n7++ftXOn7aK8PPuIe32tWVMaeP31Xv/hwwOl7e3JWYkEueFwMGqxkFq7tuxoWZkzmpNjSe7d2z9b\nnRyxpFEJHUbFFublgyWoGKMSFVfMQh23rKh6Zt4vMcXwSaYkWG2oOutEnWixouLfHfq/eUJzrHuV\n2VH781su14cRN5k7q96LyvJ8TD//G1Sg8Q/DHylLQNdMSboIIYQQYoQVW2DfDWe7FFkmEFvMSUPn\nTImFhBBCCDFC9a+g9YOjX50pSYE2hoeQoB8fH/mRrlP4FRIhhBBCnBn7znYBRptAbNFpRQghhBAz\n1Fn8pdgJsKGG6dSghtbsQQ1fFEIIIYQ4FRJbCCGEEGJa3Yq6xugQ6pclhBBCCCFOh8QWQgghhBBC\nCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQggh\nhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQ\nQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEII\nIYQQQgghzl0/Bx4Y9dp1QA/w30AaWJf1nk2/Nk8//18gBgwAfuAZYMmo6X0QaAUGgd8BRVnvZX9/\nAAgClqz3VwG7gBCwE7h41LQXAw8DPqAf2Av8E2Adf5GFEEIIcQacKMb4PPBS1ustQBgVC3QAPwU8\nWe/fAGxGHeuPjDGvzUA3EAD2AO8e9f6XULFIAPgVkDfq/XcAL6LikG5gC/CuEy6dEEIIIc6KWahg\n4Sb93AU0Ah8CvoIKNPYznBQYncT4KfC1rO/+FNiaNf3lqIDgGlQw8gtU8MAY3x/NgQo4/hGwA/+A\nCnLs+v0FQB/wLaBMv7ZYz6PgxIsthBBCiGl2ohjjLkYmMY4AN+rHZahExDey3r8C+GvgY4ydxLiI\n4VhlNSr2MGODu4ADQCUqFnkcdRLFdAcqufERhpMba4H/mchCCiGEEOLMuwM4DLiBfwee1K9/BXUW\nZQ8q4IATJzEAbkONuDDdq6dhqkWNvDDPrvwU+Po45boZOD7qtVb9Onq6fxx/sYQQQghxlo0XY3yY\n8ZMYAP8JPDHG9G5i7CRGttVABLhcP38EWJ/1/lX6fRdq9OfRUe8LIWYYGWIthBjtEWA38GvUGY6P\nZ72XAf4vKqGRM873zcs/PMAHgKas95ahLvEwHQbiqBETpk+hLkXZCbwn6/XlwBuj5vWGfh3gz3TZ\nhRBCCDEznSjGGM2MJ6qAWxgZT0zEE6jkxDbU5SU79esZRvaBrIATWIS6BLYKiSeEmNEkiSGEGMun\nUNeb/ivQpl+zoA78f0Tdc+JjY3zPAnwOdVlHEHgbcGfW+17UEM1sAYaHa34HWAiUopIl/wtcPcHv\nFqOGqQohhBBi5horxhjNgrrMI4gaGdGFOoEyGe9ExQ63Ac9mvf408FGgGnW56T/r192oWAIknhBi\nRpMkhhBiLN2o+1/Uj3rdPCvyL6ibYjlHvZ8BDNTNOmtQZ0Dqst4f5K33p8hH3bgL4HVUAiQNPIW6\nn8V7sr6bP+q7BVnf9QMVJ1wqIYQQQpxt48UY2TLAX6CO+9cDS1EnOCYrhUpa3MzwjTkfQN2Pawuw\nD9ikXz+OiiUAyk9hXkKIM0SSGEKIicpkPX4OOAR8eozPmYmOY6ibcP4Xw8mOekb+okitfq9xAvOv\nB1aOem0Fw0HQc8B7JzAdIYQQQpw7XkSNzPzWaUzDjoo5QMUzXwXmo+7ptR+VwGgDDqLilztOY15C\nCCGEOEtG31Trq8BDWc+vRp1JGf0Tq6NvzLkD+Kx+vAx1CYj56yQ/B36Z9dk7UEM/raizJkHUHcFB\n/TpJi56WE/iMLqNNv1+LOoPynwzfgXyhLrP8OokQQggxc4yOMT7MiW/sWYIakWmezLCgbsR5Kyo2\ncKLiBFD3tbgVyEUlL/4GdRPxVfr9ItQvmllQcck+1OUlpveifrr1w6iRIFZU3PLDSS+lEEIIIc6o\n0QHEV4AHR33mSdRQzfF+nQTgfaizGuZPoX4A9asig8DvgMKsz76IChwCqEtL3jdqWqtQN+YK6/8X\nj3p/MfBbVHKlH/VLKp9FRp0JIYQQM8lYSYwXT/A+wP8DHtaPr0edREmj4pA0w5eF1KFu5hlEXaK6\nHXVpimkR0ACEUAmQu8co3zt0eQZQl79sQiVGhBBCCCGEEEIIcYH7LOrEhhBCnJScnRRCCCGEEEKc\nLS7USIkdZ7sgQgghhBBCCCGEEONZgbrk41He+gtkQgghhBBCCCGEEEIIce6ynPwjM8PNN9+85b77\n7tsy3vsrVqz46pkrzcTs27fvqxP53Ews+5k00fU0UVOxPqe6TFPtTNeZ010fM6WOT/d2nSnLeapm\nQr2fKetwJqyL8cyUdXQ+ONdii8nUy5lW9jNpOvZfiS2m3umsj5lSv8/ENp0py3oqZkKdnynrbyas\nixOZKetpos6Ze2I888wz153tMgghhBDi/CGxhRBCCHHuOWeSGEIIIYQQQgghhLiwSRJDCCGEEEII\nIYQQ5wRJYgghhBBCCCGEEOKcIEkMIYQQQgghhBBCnBMkiSGEEEIIIYQQQohzwplOYswFNgP1wJvA\nZ/Xrs4BngUbgGaDwDJdLCCGEEOceiSuEEEKIC8yZTmIkgH8ClgNrgE8DS4HPo4KNxcDz+rkQQggh\nxIlIXCGEEEJcYM50EqMT2KMfDwIHgErg3cDP9Os/A/7yDJdLCCGEEOceiSuEEEKIC8zZvCdGDXAJ\nsB0oA7r06136uRBCCCHERNUgcYUQQghx3rOdpfl6gUeBfwQGRr2X0X9vsX79+uvNx2vWrGlZt25d\nyzSVTwghhBDnjlOKK0BiCyGEEOJcczaSGHZUoPEQ8Lh+rQuYgxoWWg50j/XF++67b8sZKJ8QQggh\nzh2nHFeAxBZCCCHEueZMX05iAX4C7Ae+nfX6H4C79OO7GA5ChBBCCCHGI3GFEEIIcYE50yMx3gb8\nDfAG8Lp+7QvAfwC/Bf4OaAHed4bLJYQQQohzj8QVQgghxAXmTCcxtjL+6I+bzmRBhBBCCHHOk7hC\nCCGEuMCczV8nEUIIIYQQQgghhJgwSWIIIYQQQgghhBDinDCZJMZ6oHK6CiKEEEKIC4rEFUIIIYSY\ntMkkMfKAZ1DXn34GKJuWEgkhhBDiQiBxhRBCCCEmbTJJjK8Cy4FPo35z/UXg+WkokxBCCCHOf19F\n4gohhBBCTNKp3BOjG+gE/EDp1BZHCCGEEBcYiSuEEEIIMWGTSWJ8CtiCOktSAnwUWDnJ+T0AdAH7\nsl77KnAc9fvurwO3THKaQgghhDj3TEVcARJbCCGEEBcU2yQ+Oxe4G9hzGvP7KfBd4MGs1zLA/fpP\nCCGEEBeGqYgrQGILIYQQ4oIymSTGF6Zgfi8BNWO8bpmCaQshhBDi3DEVcQVIbCGEEEJcUCZzOUku\n6ufQfgc8BvwT4JqicnwG2Av8BCicomkKIYQQYuaazrgCJLYQQgghzkuTGYnxIBAEvoM6u/FB4CFg\n3WmW4QfA1/TjrwP3AX831gfXr19/vfl4zZo1LevWrWs5zXkLIYQQ4uyYrrgCJLYQQgghzluTSWIs\nB5ZlPd8E7J+CMnRnPf4x8MfxPnjfffdtmYL5CSGEEOLsm664AiS2EEIIIc5bk7mcZDdwVdbzNcCu\nKShDedbj2xl5d3EhhBBCnJ+mK64AiS2EEEKI89ZkRmJcDrwMHEPd9XsecBAVGGSY2M+i/Qq4DvVT\naseArwDXA6v0NI4An5hEmYQQQghxbpqKuAIkthBCCCEuKJNJYoz+jfV5QAR1Y67WCU7jA2O89sAk\nyiCEEEKI88NUxBUgsYUQQghxQZlMEqMl6/EnACcwiLrj9yXAf01dsYQQQghxnmvJeixxhRBCCCEm\nZDJJjGzNwHNZz2+YgrIIIYQQ4sIkcYUQQgghJuRUkxhB4FuAGwgAf5qyEgkhhBDiQiNxhRBCCCEm\n5FSTGK/pPyGEEEKI0yVxhRBCCCEm5FSTGBVZjy2oYZ8/P/3iCCGEEOICJHGFEEIIISbEeorfuwL4\nHvAx4KPAbRP83gNAFyN/r30W8CzQCDyDuqGXEEIIIS4cpxpXgMQWQgghxAXlVJMYvwc+Cfyr/vun\nCX7vp7z1J9U+jwo0FgPP6+dCCCGEuHCcalwBElsIIYQQF5TJXE6yHsighnmiHweAXcCeCU7jJaBm\n1GvvBq7Tj38GbEGCDSGEEOJ8NxVxBUhsIYQQQlxQJpPEuAy4HPgjKuD4c9TQzb8HHgG+eYplKEMN\nA0X/LzvF6QghhBDi3DFdcQVIbCGEEGIaZH6BBbgWlXjfavlrMme5SBekySQx5gKXAoP6+ZdRP4F2\nHeqsyekEG6aM/hNCCCHE+e1MxBUgsYUQQoipcy3wf/XjrwMvnsWyXLAmk8QoBeJZzxOoMxthIHoa\nZegC5gCdQDnQPd4H169ff735eM2aNS3r1q1rOY35CiGEEOLsma64AiS2EEIIMYWyRmB8BliuX74d\nSWKcFZNJYvwC2A48jhr2+S7gl4AH2H8aZfgDcBfqjMtdevpjuu+++7acxnyEEEIIMXNMV1wBElsI\nIYSYWtcC7wSKgBgQAZrPaokuYJNJYnwdeBq4Wj//BLBTP/7rCU7jV6hhoiXAMdTQ0f8Afgv8HdAC\nvG8SZRJCCCHEuWkq4gqQ2EIIIcT0My9LfB14E5XA+P7ZK86FbTJJDFBDPdNZjyfrA+O8ftMpTEsI\nIYQQ57bTjStAYgshhBDTbytq1KDc0HMGmEwS4x+BjwGPoTbgz4EfAd+ZhnIJIYQQ4vwmcYUQQohz\ngk5ayP0vZojJJDE+ClwJhPTz/wC2IcGGEEIIISZP4gohhBBCTJp1kp9Pj/NYCCGEEGKyJK4QQggh\nxKRMZiTGT1F3ETeHff4l8MB0FEoIIYQQ5z2JK4QQQpxz9M+tflo//b7cH+PMm0wS437gBeAa1A1N\n/hbYPR2FEkIIIcR5T+IKIYQQ56JPA3dmPf/e2SrIhWqyv06yS/8JIYQQQpwuiSuEEEIIMSkTSWIM\nwrhDZDJA/hSVpQUIAinUz6ytnqLpCiGEEGLmOFNxBUhsIYQQYup9f5zH4gyZSBLDO8Zr5UDHFJcl\nA1wP9E7xdIUQQggxc5ypuAIkthBCCDHF9D0w5BKSs2iyv05ienJKSzHMMk3TFUIIIcTMNV1xBUhs\nIYQQQpxXTjWJMR0BQQZ4BtgJfGwapi+EEEKImWm6Eg0SWwghhBDnmcne2NP0oykthfI21FDSUuBZ\noAF4aRrmI4QQQoiZZTriCpDYQgghxLQx9OWRGwbPbjkuPKeaxPh/U1oKxbwW1gf8DnXzrRGBxvr1\n6683H69Zs6Zl3bp1LdNQDiGEEEKcWdMRV4DEFkIIIaaF4QWK9GMkkXFmnWoSY6q5gRxgAPAANwP/\nOvpD991335YzWywhhBBCnKMkthBCCDGdSoBioBOMFklknDkzJYlRhjpDAqpMv0BdwyqEEEKcFT5f\n1A5QWupKnO2yiFMisYUQQogp8pZLRzzAFUA1EAEawHhaEhlnxkxJYhwBVp3tQkyHL395zwqAr31t\n1b4zM0fjdqAAeAo2dJ2ZeQohxPnF54vaOzujueZzSWSck87b2EIIIcSZZHiBRfpxk05UVAN1wDIg\nDbiAo8BrZ6eMF5aZksQ4L335y3tW7Nzpr9OPz0Aiw7gd+Djq+qzFYOQCYdjwpemdrxBCCCGEEEKc\nl2YDVfpxABgEchnuSydRozHCZ75oFyZJYkyjWCyVE42mHObjMzDLOmAe4AX+HDXMKaZvNiOJDCGE\nmKDskRcyCkMIIYS4oIUY7jeH9MiMINCO+onwfmAXbHjzLJXvgiNJjGl0++3zjhw7NlhoPj4Ds2wA\nuoA4wzcys+s/IcQpknsjXLj8/phse3FOOHk7JT8FKIQQU6gH2In6Fawu4PWzW5wLiyQxplFhoSNx\n1VVl7eZj83WfL2r3+2P24mJnYooD41dQw51moRIadwIO4HEVvJxfgcvUdSwlsJusC6lTL/dGOJed\n+r7t80Xtmzd3lQWDCUddXX4ACMq2FzPVydspwwv8i378DTneiZluamNlo0z9l3vFncsaGgJugLq6\ngrNxyYYH9WtX+vGGLjXSnX2AH/VrWJ7zsb81U0kSYxr198ftW7d2VKRSaevixXm9dXUFYZ8vat+x\no6e4oyPqLi93ha+4osQ/dXPc0AXG4/pJKeou7G7UNVtnyJlJCJjrESB7HU7+QHdu/Mbzxo1tJQDv\neEdlz9RN9dQO6j5f1H7wYDBfP51hHbupr3//9m9vrAyFkq7bb5/XbLdbktO/vDM/qXayJNb01NfJ\nGr1vm0avV6MW1U62ZL/31FNtcw4cCJbk5dlTeXm22JIl+cGJzvncSvKZ7QAh9W/m1jtxWtYDt+nH\nEd7yU7OGF3USxA34Tr+zN/PbsZno3Go7ps/UJpGNMmCpfsyFl8gwvKgOuAcInavL39AQcD/00OHF\nAHfeWdtovn6GExopVPuZdbwcii/yUP3qAjDaZ/J6nuKTwGa9OuNtvSQxTshYrf5vOIW7zBre73//\nwMqWltiCnBwyDz54mOpq7zaA5ubB/J6euMfvj7lycizJKShnVrBg7jRGCPUrJbmoIU4e1E1oTvL9\nCc+zTE+ze/h7Q3fuLQbjMGw4PKnFmITm5gH3sWORvEgkaWtoCOaFQklHVZU7/M53Vh2frnmOZ7qD\njnvv3be0vr6/sqzMFezqiuauXj068TXZ7TcUrF6Mamx3TuYaPr8/Zu/tjbv048jMCbZOPyE1elve\nffdrl+3e3bssHsfW19fk+chHFr0xDSOoshheYKV+/MZM7ACYZ3x37uwpzs+3R9/73uqO7Pc3bmwr\n2bWrr8J8Pr2JDKMW9RvtrScJGDxABeAG41BWO1kL3AIUAtvB2K6Dkou2bOmcFw6n3MuWFXa2tYXd\n3/1uQ93FFxf1jF7e0WZ2ki+b4UXdUb0WdazwAx1gdExn231hyW6bjVv0i1v1f49+b8oCXbvdkjxJ\n+5RBXbs96mzh0LH7ZmAB0AjGY6dWD4aCWod+zuTbsYkc04xa/Zkxymjcfv/9+xfdc8+ypsnNd7oZ\n1917776lN944p33NmtLA6OPN2Rj1N7Ez24YXuAyIjIyHx9tOZl3f8PSplmv3bn/B66/3zo7FUnar\nlVR2Etks8yR4UB1M8/E4hmKjEG9J6k5tUs7ni9p/9KOmhS5XTnKsejo1caVRi4rzclCd7xzAN34i\nZzoSj8ZF99+/f1Fubk7ykktm9a5ZUxqAUxtl86c/tVXu3u1fFI8nraFQIufGGys6zfdOVH/Vupzo\n6IjxOuWGFyjXT7oYqh9DwkCU4ZPGYdUPm7kxnPn8NJKDXqASFT/1g9E2/vKOOBZOWT2bSUmMW4Bv\no3ayHwPfHOtDZy5LbawGbgBmg7EMeIrJZZpmp1IZc9hRxu22JQHq6/sL+vrizng8ZY3HU87jxyP5\nKiEwukHJ3pFMY2388TpuGwbB2KvKz7X6/afHmU8RMA+MwFs7s2POb7b6PHNRFfc1Pd3ZwEWoUSDe\nrOzkYqD31JJBI5nbHyAQiDm6uqJuny/ijkQy+ceORYL5+fboqPKfZLTBhkEwzLNPfePN99579y09\nfjyU9xd/MfdwdqdsvA7L6Qx5y67jd9/92mV79/ZWg9Xd2xvNTybBZsuxDtcZw4u6Hg8wLj95/TTK\nUA3OYuBS1E1gAWPCZ96Ki52JWbNiUfOxWWbzgGR+7uTXZQNQg7rb83FV98Y6Kz7hjupJGN6GhoD7\ntdd6ij0eW3Lt2rKe5uYBd2GhI5E9SgqGR/cEArHcUIjceBzL4GDS094e5KEABQAAIABJREFUdTc3\nD0T8/lhiCoe4ZicDa4Al+s0gcBo3iDq1g8bJ2li/P2Z/8cXOsqamwRKrlRTA6I59e3vI3d0ddgcC\nMWt1tXdoHzi9MyajOy1GLaqNrgGOg/HsGB2auDlr4CpUmxUB4zkdYM9FBeceVCf+Td1u/WLHjoG5\nc+ZY2/bv7411dUWLe3sp2r69sxfYfqJExlNPtc3p7Ix46+oKg5NJ8k1R0DqqvRu3k2F2Wq9gKJlp\n1kN+q4OvsY4VY0xrxptQbDF1zHpKN2odV4GxGFgLJFBnhM17Ve0HwwW0w4YXRnaiJt7WZR+Hstvg\nUe4DilFJ0iXAh8B4MGt7LgRWq/JSAfSB0T257T1Ur6pQ+1MElShvGaNDwNivAW/9GcPR86kFlgNl\nYMxV627ovduB27Zv9y+5//793HPPsqbx9q3TG5o+6ZMH1wH3PPZY28o33uhrW7cuXP/8853VDoc1\n/aUvrXgdhu+/A/Dii10lXq8tYcYb0xH7Pvpoa3lz80DhvHneENAz9nowvMBfAdcz3AF+Tbc1FajO\nWlbnxbgFeId+zIkTGUZZQ0PAPXq+Dz7YPPfNN/tKe3pieZFIyl5Z6e7PLvMLL3TOLS3NjY4dOw+V\nObsj2o1q41CPh/Yz/XzoGPlpYD6q7rYAT+vjwbtQsdLTp3qCZNs2XwGAmbwyjDdX7tzZs8huz0n1\n98ddH/zg/GZzPUwsEX6y47tRC7wbWIE6DrYBnYBv7BIaXtSxoAKMAyfvC0yEcRHw7meeObbCZrOn\n6+v7O9rawkfXri3r2by5q6yrK+JesCAvcMUVxb3mN0pLXYnsut7QEHD398ftCxbkhY8eHcz3+5N5\n6TQ5x46Firu7o32zZ7tiJyqBzxe1/+xnzQuAW3Qf6ESJUbNTPgcIjmp/lqHqRgxIjJzOhkG1D9DP\n8L0IJ9ymnO4lMqf6/WPHBt2hUMJSWuoKnPiTY/WjhvYxN6oPGR/1ndH1s1J91jCPgVEwNp9uPDFT\nkhg5wPeAm1A72g7gD8CB7A/de+++pd3d0bybb65oveKK4t7SUlfi4Ycfrlmx4ubukY2ZUYYKWs2f\nugmPCnxRz4c2AqhkwTJUFm0XPH4V/OWVqAB5DaoBfwKM3Yxs9GCoMRwRQIduuKHyGLSl3W57fP36\nZW/098ftO3f6K44c2T5n4cI1x7xeRzqZzOQwIjM8VKZvos6IvAL8HjW6IYHaZoVgHAOOqbKMZ8Mg\nGNcAq/QLXcBYB5R5wGLYOA8MN9Cq18dlen6NWQmJRahgpwh1740iIAPGfv2dQVSltqCCjKWoM30B\nMK4EmoCt2UmRhoaAe6wO4Ze/vGdFLJbK+dznltebDVtnZzR348YnapYtu77b5cpJulw5CZfLlgiH\n45lkMpV54IEDK8D4N/VrLEP1IBeM46jG+yN6fbQDL8KPXajsqW54jCaAH/zg4PxIJGW77bbKtsce\nO1r9hz+0rU4mcTY29le+/LLv0Ne+tmqfzxe1797tL+jrS7jdblvK7LBs2+Yr2LHDX5abm5NqbR0M\nVFd7w2ZguWXLHyvXrVvXAmMHJQ0NAfcrr3SXtrVFvH5/1FVf31sdClFos6VjBQWO6OBg3Pab3zQt\nAf4S+CFqX5mnv74HDANoGBnUmQyv3naz4U91cJuZtImO+gxjNSwNDQH35s2dZQCzZ7uilZXucHPz\ngHv3br+9qWmgYP/+rZXLl1/TAWQuvnhWH6oTzgc/uOXtYMyHDXfp6b+g1jU/V2WhHGgDYxPqbIkX\nyAfjDVQdXAs4gU6VMLu3GL5oNtZmNvk48DY9zz+O02mr/M1vWhe2tUVmdXUN5P7iF03JSCRp93js\n0c99buWuQCBuf+klX8XAQNzW2hrKveGGOV2XX17adehQqMxiaSisqVnT3dcXsz/7bEdVT0/EM3eu\nd+CuuxYcMutmc/OA+61BlbEatZ80MmLUEjA8xPVS9Z7xrH4joZfXPXz2IDvAv/da6HtKv1aD6sg7\ngJcY3nc9qOAlAsYhVGcVMLYwnDhqHN3p9/mi9t/+tqUG4H3vq2kxg+riYmdi925/QVdXNLekxBWP\nRFK2SCTpCAbjru3bfcnlywsDZh0fHEzaDxzYNj8WW5KTSAx4fvzjppy6usKhYMM80GYfeE8coA8t\n55/r5w/rcpfo5ajTjw+pzvdQ4rcI/vd6+PBhvY6vQf2mew5Qi/oJ6ohaz7gYPvv2J3QnqrMzXRGJ\nRAkEKAE8Ph/2p55qq66sdIcLCx2J/v64PTsJtmHDziuOHBmsyGSwHDjQ3/n+988/8N//fXBpfr4j\n/ra3lXbU128qu+eeO+tBBbWbNnVWFBU5orW13oF9+/pLZs1yRmKxlBXgjjuqj/v9MXt9fX9BZaU7\nbJ7BGp9RhtoHVoKRAbYD9Wr5DDtDlwiMuGwghvpZuGI4UANLS1DJntez1nsYdZxZo+ezTdfJ0QmT\n6/TzMdqes2ZCscXGjW0lBQWOxJo1pYGNG9tKBgeT9oGBV90f/vD7m08+C3O5aUDVr8X6eQh1DKxA\nJfcrgEF4cz5clETt42nUNjik2kiKUAH0q2BYUPVz6+j2bPRZzObmAffx42FPY+NLs7u61radoL4k\nUO3tYtRxIweMn6Jin1mom9OZozZTTH4EZ/aJjHK1bM8vhj/bBMYRhuOVUSdeDC+qfuWi2vBSVAyR\nD0bDqNgOVN2dq+d1JRgVsOFXo0sYjaZsDQ0B93331V8CsH798te/8Y29lwaDUVd+viuan+9K33JL\nRWt/f9ze0PB8yVjbe+wOguEF/hkoAePXqFhMJ56M22HTlXDj/4eqD+gTOFcDC2MxZtXXh11Hjhwo\nzGQosFpJfvKTr7jXrattqqx0R0tKnJH6+v6CgwcHSs25XXppceC227bcDvCnP13/O7Nzl12uhx9+\nuMaMLR58sHkuwIc+tOAYDMcau3f7C+rrA0UlJc6ox2NL7trVW97RESnq60v01dR4xqgvQzHUar2u\ng8AO1Im9OuAQKqbrR9WT6/UXJ3AzeaMMqPn974/Pf+yxo2lzdMqDDzbP3bKlq7ara7AgnbZYvF5H\n8s03X5rr91cea24ecG/c2D7/8OGBuRZLXwK4FfjfrGnWAlcCZah93wbGUVS8F0EdH82Ywzw2v6Y6\nU6/9CFZfgqpbAVSHf45expsZGllEIxijRqSoetLfH7c3NgbzPR5b0kx0myMuOjoiBQsW5A2t4wMH\n/MV9fY2lVuviaH19f8Xu3X3B/v54P0BbW9h9+PBgUTSasn3yk7vv0Mv2g6z94CIgH7gWjCSwSb+e\n3elejNqv8xlOXnQB/nES1Mvglbvgah07GKP7TR8E4mD8TH+pTk/rzZHJV25Ubw/tj55IJOMaGIg7\nfL64KxCIu0KhpG3Pnr4yny+a39o6mBeJJK2dnRFPJJKyXXPN7I5du3pLm5oCRfn5jmhJiSv2hz+0\nLHE6rck5c1qiubnzBtJpHHPnegNz5+YGzfja54vas+MHs84/8khr1csvdy9EJaIGGbsPlM2t11kF\nqh6bCbtiVGwagu8s4i0nmDYMMtRWGl5UvBFBxbtj+sEPDs5/+eWuykQiY1uwID9QV5ffU1bmihQU\nOBKvv947q7bWO/D/s3fn4XFd9eH/37MvGmm0y7JsS5bXxHbibI6zEJsEshCgpMGh0BbS0pSlQJfU\nDdCnLZRfafkN4Qe0v9Dny5ISCAGCC6GQ4NAkxk5sJ97jTV4kS7JlLaORZjT73Fm+f5wzmpEi2ZIt\n25L9eT2PHs3cmblz7r3nnPs5y72T78RsaQm5Ozoibq/XbixYUBprbQ27Q6GUbdeugZrDh4O1cND5\nvvfd92ZxLDbW/qipcRo1NU5j8+be6q6uuKepCUtLS8gYvwNElVNgAfjsqEHTdlQd7kZ1TpSi8hZF\necELLARfCfxmDtwbotA2bED9+MQQ+HYV7b9xjH9VxHTpxFiFqija9fMfA7/HqEDjmWe63lZZSSwa\nTbs6OiKdtbXOxD//85YHoTQBvAy+/F1h/xTVOAihdtQJ1EjIMtRJJQW+AKryjepls1FBvw3ohujV\nFE74Zv2eFajKcK8q4GT199UBu/UJebhRUFZmTfzRHy08ku9weeqp1rmhUNoTCLTUrFq15mhFxfCI\niT6xD8+K+FfgLlQAsRA1ctKDCthLgQGdtk7gZ8CZMsEAhSBkYORLwwGBof5O3gAcQWW0haiMG0YF\nFof08nyAkkLNXEijRvbnok7k+/T70Mu8+vVr9PYcQM3SyFckX/zQh7a9a+5c0+CDDy48/OKLXY1O\np5q1smPH0FXZLM7nn9+08pOfnP+75mZP+PjxcPnevbuarr56bV9TU2lk4cLSUH9/0nbsWDiyaVNP\nczDIPHU8fADfRTVGFqMKzSKdJof+7rug1ECd2LooBHB3PPHEibWAZc+ewLG9e6P56VK53l7qdu/u\nz37ta4cSq1ZVD5w6FS+LxdLW/Mlp9erf/H40imfFCk9vZaUtdOBAsDqXy+bKyhyJFSvKB198ceuS\ntWvf0xUIJG3r1m37AyD38strf7h7d8Db1hYp7eqKlu7bN9AUj2ec/f05s82Gx24nXllp6V+8uKx/\n587+Rr+fWuAz4BvdgVUC/AnqZ3Uz+vi8qbfvBQpT6qvg2FLg/0dVNi5gqd5nd6hj5nu56AT2wL33\n/ubeZBJnNovVZMJUW+sKzZrlCgaDScfAQMxts9kdXV17Zp861eQ1jBy/+lUHdXUlgV27Is0M/7a2\n7/uocqmvTeVvUHnfgsr3XlSZD6GCixuAdwLXoaZBp4D5sOidOt9Z1LYyiCqnJlRDIoGahTR69saq\nAwf66wKBVOngIBXpNFaVFwzjscd2lZaVmZODg9kKr9eWDASSpdFo2lFb64xee21F15EjbZ6amjWR\nYDDlPnx4cHYolC7dtWsw88orJ+cuWlQZ2Lt3oCEQoB74A/Ct1MHsKtRISP5k9ivwHWA44KURFRg0\nouqV5agTREiVEe4C/l03SH+Nqh8HoeLD8Pl5ep+9C9VJmEA18o+hGh+lqPoBVHmcgyrnd+i8vBTo\nB9/fFh/nj35085qhoWy5y4XR2RktCQQS7lgsbU2l0ubTp406sxnKy63Rq6+u6HK5TLFTp5LlR46k\n6r75zRbbiRODVadOUWOzEbPZjpbb7UuiiUR2OJg9cSLi6eqK2tEnu6NHwxWRSNr61a8erPd4bNlF\ni0oHOzujJWq/5U9WvjWoenseqvym1ed9bgqdd3G9fInOy4OoTosEdF8DtOm8k0PV5Q6dJ5fp9+b0\nPtejdr5FFFgshR/HThsG2VOnwjXPPXcqNTiYsCeTGbfZbEosWFA2eOjQQNW+ffFlqA4R886dkcqd\nO/cvslqx2O2kXnyxJ2G1bvcEgyvM9fWuyMGDwboTJ8KzgUxpqS1stVptkUjcGgymPSYT2QMHBmua\nmkojfn+qtLIyMjwjr6srNkZnGeh8dD+qk9aKKme/RdX7lagR0/2oc1wdqm5/k+HOiRbgqkGdr67T\neWi+3n82vb8rgRrwvY4atYvr8+59qPO4nzMEbZfAhGKLb33ryOoFC8p6t271B19/3b+gqyteFgpt\nnfv44+WRUY2HOtR+bkCdM1yoUep5qM4eA1X+OimU8UWofZpWy47Vw3IDFSiDqrdqUMcrn0+X6Mdp\n9V2+n+Qb+xs3dlUfOzbk/f73O66z2ch+7Ws3vHT48FDF8ePhigMHdswPha4y2e2WbCiU6ih0ggIq\nz5v1Ok2oY3q//jNQHcFHKNykbr/e5uLOUh1P8WG9rldVJ+lwx1XxQEYKKIFTN6PqNxuqji9DnYd7\n1Hf4SlD10Y36tW69Lx36rxI1yunS+zGIqh9n6XTNVp/3VcP6f4f1PwefM5MxFm3d2tP4/PNdS5JJ\nqi0Wcn/4h9saUikqACfELA5HbMgwsubGxpLB3bu3XbV69X3dAB0dETfArl0DNdFo2pFIZKw7dvQ3\ngM8L6/8a+LTORzWojsMwMAC+FLAYwuWoOiiMagSBKmBRVNxoj8Wo0vuEI0dSS370ozbX/PmlAx//\n+OL9Ho91RGfuffdt+r1kkiaAO+/ctO6BB2btHxoy3FarKX3NNRV9993X0PPSS1sXrVhxd9/zz3c1\nPPlk5zt0Pvr1qVMxT19fvCSVyljb2kK18Thuu510Lkcincbh9dqNqipb8KmnWpd8/OO7mlT9t/4P\ndV5/Ve0r9qMa8R7gr1Hn1igqLtRT+n3L4SsPoe61Uq3/BooaNbq+YE9R3fUHzz13crnVSu7VV7sX\nLV5c3pVMZiyBQKLcMHI2i8WUSqez2fb2Aw1PPnl8MUB/f9ydTGZtwSDlwKfAt1kPSjajGvMuVD3k\n0vl6QOftN4G9On+uQNV7pajBwj+CnjtQMYVJHyNDH+MY6pwV0dtUqvaFz5XP90891Tp3y5bexlgs\nbQsGE6WxWNby7W8fjpeXO2OnTiWqUilKnE7SJ0+Gh7LZXNrhsOQqKtzJU6eOma3WxbHaWlf42LGh\n8ldf7ZkVChklAwNRRy5ncXV1ZWoozCA5oDsvSlB1/H263JhQ5/VnUYOFtaiOnHfo/NmDaiPs08dw\nFvhuQ8VODlTHVAdwlW4D9OvP3Q6+QZ1vi9pO3KL3r0m912fR+ySE6qjzMjyjcf0z4NvpdHL/wAAe\nw8Bz6FC0tLX1WJXbTc5iMfHmm5GGjRv7l1ZXY1RUOBNHjoTKOzqG6kMhvB4P0WAQSypFHWSznZ37\nzWvWXPt6Op3lvvtmt95zT0N/fnDz5MmIu7LSEc8PLnR2Rsu2bu2t7+gIe2KxXH62wKxCqfJ9UG//\nZoZni9OBqoO8qA6gG8HXoF9z6NdPwsn3Az9nfDeg4rcq8F0D/FTHhMtXrPjNxwCqqug2DNxDQ3gB\n26FD8dhrr/WGlyzxng6Fkq5AIFFeVeUcikTS+48cGSr/3e+6FiWTWN1uU7KnJ+d2ODCXlRHv7aXS\nYsEGB13Z7LJ0W1uku6sr6q6qcsTXrWs6AfDf/93Z2NeX8ASDCZvbbUvfdVf9yYEBwx2JpF19fYmM\nYWS8wWBKx2q+5jFmtC4AHtD5f6Xe9iFUXFmLKi+VqPrYpvfzXfrPAolSoBV1zszPZM8PnuZnK1qB\nY7pTbHnRd69guDOYaduJ0YAK7PNOoQrhaOUDA9i7uoaCAwOJpUePJueBxYmqeP4LVWjnoBoDc1CV\nzmlU5rsPFZCVoSr3GGqn5kf0FurP2IEEeMz69RAqQ1tQJ8v8qIqBqpCzel0lqNHW/AyPcpfLSlmZ\nbfieF4sXlw21tUUHT51iVmNjScQwcrZoNG1FZYJ8oOFGnShMqOPj1OnKd2DYURWMgcooMbXvxr12\n9RAqYM0/1nzL9TYnUBV0DxgJ1ImpHhWU1aACMqd+bGU4EKMDdZzyNw416f07gGpIwXDnCHNQFUg5\nqgDoyx94FHjQMKhta8vV+3zH5tps2LJZcpkMGb0f7EDpE0+ceMcNN5QeLSmxZaLRrD1fWeV7HJ3O\nHp57rseVfz+qMIE6Ud2mv9uk12lG5YEaKLHqbfCiZr1EgT9D5QnT3r3R/NRfCxC32chksyZ7Z2e0\nfM4cdyKdzlncbmvaYiHz8MPb7otGWQCwf3/EM3++pd1kMlmHhtKOkhJburc34Q8GcyWvvNIz60tf\narkb1bPLnXdu+vD999fue/PN/tnhcNaeSuGOxdQ+zWQweTwMPvBAU0s8nrG/8EJ/KSoPO4CPoEY+\nXtPbcAzVoM1vUw51KdEJfQx+gQqqcpDKj0qUofJzfgRjJYVZAD9BnZQ+3dWVn96LCUhmMnHHwEDc\nnUxSGothT6WSFpPJ4j5xIl2rv59TpyINOg1WCnVNvuOPonwVR1VSTlR+3qfTeRUq72YpTL9eAyXz\nKXRiJFABsUUf16Te1ip9DFvAtw11sl8dDmfLIhEsZjPmonQ4BgaYNTCQtQKmeNwI2+0W4/TphHf+\nfE/ojjvqugIB86zbb6/tamkJVx07FjKCwaw9lcIVClHV2TkwX+erfHN3L6oMuVCB7CKdtnr92huo\ncrJMp6uKwgnWq4/nPOBhvS2gytZBoBtqlzPcmBzu8dYNBhr1sU+jGiKnddpqUWV5sX5eg8rrHwf+\nTo0e8vCJE9kF+jiku7v9JXY7rnh8+Ni5AHMolE4ZxqC9vt7Zk8nkLKFQprqtbXCOft1pGGAY5lRj\no6Nl6dKK/g99aH7rwYNBb2truDyTodwwuq1LlpQORiJp669+1TH/9On4nFQK865dAcPttmSAP6Yw\n8+v9FDovsqh6shxV1+cbhgdR+cyj93cTw9NBK6w6P4X0382o8023/rOiGpwRCvVWkELgSF2de6i8\n3Ij7/YbTZKIkGs1VbNvW6wIy8ThlZjO5rq5IKB7P5fOUiUJniTudxpROkwDKwGLfvLlnRXNz2clI\nJGlNp7GaTDlTLmcyQy4TCKQ9wSDlNhumlpZgxuWydJjNavcfPTpUdvp0vLy3N1EKvF2NHo7oyIih\nylJGpyHPS2FUyY3Ke+X6tZtR5d8MmQTqHGZBBSz5kZkUKvCo0/koP3vFq/OQSx+jogBx2phQbNHa\nmrp6aGjA3dLSH+zsZB5QUhRbbAPfLfqtf4pqbCf1etOoMrUIde5Jos6nQVS+mo3Kt3FUftsBoVUU\nRqNK9Xfk7yGRQnXsWlH52arXX6vLxKJt2/rnbNjQvRyYnUiQ/dSndlnvuKO6PRxOl4RCWXdXV7zG\najVld+wYSAAVRWXJhprVmdTp9ep152ez1aLOFc9QmM1lRwWRn0CdI+Ko+iF/bfj1qCn2emR6fS/4\ntqLql5h6X/xOVD0Eqr5bjspLp/S6/KjzUFqv34/Kb06VfuZQqNcyOm1mVN1vRuXlKuC9qNl7u4CS\njo7UnERieJqz02wmkc3i0NvkAEgmcbe3B8sAWyiE90c/OrGwpsaZOHEiXNHTE3dHIkZZMGg4Bgep\nYLje9KGPb7lelu9syZc9O9jz+21IH//tunPlGquVj2QyOGw2sik1AdsLpNvaUo1mc9T2yis9fZ/4\nxJIT+YN2/fVVIUaW57JNm3quymRwuN0WY3DQKB0aStnDYdyvveaf9eSTnXfqfIXPd+xds2eb+oLB\nXFk6jTmVwk7h/ggmIJdOp8KGMVBz8mSuUadlFvieRjXEGvR33oSKF/Lxh54tSTvqXL1QbW9VfnZM\nj37PalQea0Kd72J6/S+gRuxvDoepBsyDg1mjr2+gorraFCopsSVnzSqNuN2maF9foioez7o3bvRf\n63CQqamxDAWDw/WPE/gGapT9FxQuESkdeTzIjMpvQVQHdgUqzrCDxaHzVBB1LsjH3fl9vxk1u+1O\nVJkpzc9g+PGPj10XClERj5MxDErQMU9XVyKb//54nJTZbOQOHQrV1dY6Y16vPeHxEJs/v6ynqsoe\n6eqKuk+cCM0OBKg0DCwqySPaaCWomPmpov1fRmEm4W2oslGFmjmyWOe94zrtUXWMuBs1qHgtqvzs\nQTUuO8CIUogTKnVeuRVVNnOoeN6Dqgsy+nhW6u+3Ff1lgF/pdG9dvLjidCg06I5G8aZSWAyDmlSK\nVDKZs+t9aenvJ5NOJwKZjBGPRnEmkzjsdtLZLCm9HS6wWI4fH6z6whdueLV4ptnOnf1Vvb0JT0mJ\nNelyWdOBQNK1a1ffrP5+oy6bzRo2mzmN6qDNX3r9MPAgqtzmZ2j06DwSoTB4XIqKL/ei6vX9+jKb\n93NmlaiGfz6m84OvG9WJ7gUIBPDq/Zc/xu5oFGtLS8icTGLKZChLpRKup58+nj192qiORqkGLIFA\nDsBhGGQjEWJANpPBbLViTiQyzm3behtisazX5bIagUDSlc3mzEePBuf09OQqs1ksHg+pgYGU99Zb\na9trapxRw8jk+vtznv37g3VgygLLRg7Ir+8FXymF2XU5nadadV5I6uMNKubO19mrGJ4EYHeiylsf\nsE3v4wFUPX8natDEiWo/r2DkOaZEr3PMy6CmSydGbhLvjZWVOYZ6ehJzx1iHH1WgT6BOXK2oQGMx\nhcq3+IZAJahCme959KAKVBoyVtTO1geV2RSuG84UrSPF8A3R6ChOZ2WlPVFd7Ri+JloXuo5Tp8z1\ny5aVh3bvHqzRl5N4CyMmviBq+msZqiET0esvQ1Wm+U6EpP4bNbtiTHtHPvXVUTixhFAn2pMQ7EUV\n4jpUpZZBBbX7USfsfr2do+5ePjw6VcfwVLz1bXr0pIvC6LtTr+Ow3taU3v8wKg84HMSSSSwUpvCZ\n0umsLafflZ/CnX+/xWJKL13q6Dt8OFmGCph+gKqkm3Xa7fo74qgTVRwIQnau3qe6w2t9BHz9elm+\ns8MEJJxOAosXuwcsFjO33FJzet68kojHkzTKyuxGdbUjns2OCDQytbUlA/F4ujSVytrsdnPK4TCl\nAVM4nLYxsuyZT5+OumOxbGk2S87pJG4YpIAyux2jrs4Vuvrq8uCCBaWxX/yifVFPDxU6vSdQeeEj\nqEbuKlSlPJdCwz+HyrelqApzD1ACwet15dSo15Fv4NgpdJ6NljGZSHu9RGprnYMOhynW35+0QDZj\nsWDOZnNOm41wMkmZOgljNpvJZrOE1Peu/4jOL3t1XkmhTpIx/TjfcXdCH6M+VBk+TWFqtpfCyTSn\n35cfUYij8vrrFKYmj9gOs9lsnjfPMWQYmSHIZf3+jCebxRONYtHvzdhsRJqbPb1z55aEGxrcsQUL\nSmNbtpiH7rmnob+xMRSrqLDFfv7zE+lTp9KNicRwUGjhrXahKvtGCsFuBSrIGGBkZ0MYdZLUZXG4\nwzCf/yj6jvxIUWbUPggWvdeqH+dnTOWDi5BOR4aR9Vjx+gHMmQyuROIt54gskHU4zLm6Olcsm2UA\nYtmhoWw2lyvsa7s9m/rAB5pb8lNqg8GU7dixsDEwYNgAGhs9Ma83ZZSU2JI2m5ExjHQumyWbzZry\nxyHfsHLobfGjgpBuvT35jqxjqI5oFyqAbdT7w1CvZ9Ej0QfA1473xZ3KAAAgAElEQVTqqKwu2j/5\nzuyhomuA70eN6JXeemv5rsWLywIVFfZEe3ukbP/+weZgMOlyucwxu92CYRhJkwmz1WrJLlxYMnjy\nZCgRDlMai2HOZinV+9wAYjYbLsPAbrWas+XljtTy5eU9vb3xoMdjS61aVdXb1hYpLS211Bw8GDJn\nMjibm72BW26pPQ3Q0OCOAbS1RaqSyawNlZ9G36CuHfgRKs+5UGX9IOo8UsrwFH4MCr9pnw8QsxDt\nQQV5q/S+HUTV1216PU61n+hB5aMUhWDkuF73NLuR4sRji3Q6a66uLol1dkZTjF3/3YpqtM+hUN4O\noPZBCobrgjDqnLmNQqBfjcpn34Wuz6Nmxl2LatTX6NftqP29S//dhjrOeyi6N5bTacmX3RyQs1rJ\nOp2WdC5nSrrd5pTXa4vY7WZj9mzn6JmZMdRx///088+i4hqXXv8p/b35GUlQ6MSooXAeLZ4lkB31\nHB0X5GODPug5gSp3Jag63AojOpFBxRn5Drn8JXGgRkMbUHVmVi8foHD+zJ/fKnU6KvVyh55pl+9Q\nHJo1C//tt9ef+OlPu6/X7zGZTESWLavsTaVyTrOZjN1uziYSGWsikbVmMlk7mMjlhvOQWf/ZgP8E\n1uj05fSyLMP1cc6KKj8RVGdWfrbsF9et+9HVR44MVZnNcORIuCYcVjGO3U6yosIRKSlRM1GL74Xx\n5JOrN37oQ9vfA3iqqxnU6UhZraaUy2UZfU+A4uORy2RM9mw2Z7HbMWw2jGgUZ36/2O1kS0rMsZIS\na+Itl7SPLDs5VNleiIpF46jz1guokfqFRe/Nz4wzUOe4cv2ZfCddXjWFc1l+sM9uGLjq6kq677pr\nVifAa6/5s+3tpqZMhpJYDOLxXNJsJpTNUkahfMHI81m+MyKOqhcPoOq2Lfr1dlRZuA+VvyvBGELN\n0NoJ/AT4f1DlI7++V/Qose7AYB8qT98UDuMxDGxOJwmLhWgiQQnqGJn0X8puJ1ZT4wxbLGaz12tP\nVVc7wt3dloG3va22vbLSFjt0KFQTCCQSAwPJlMWCM5MZ3jd5KVT+b0c1jjcADzF8bzqsMBwzp/V+\nCQNHimZb1uhtyXdigqqH+tT6g6dQdVeD2ifDnfEpVPkM68/YKAy85s9zWQrn1MOFy0nW9/7FX7x6\n4Ec/OhHfubO3IRTKldpsJofZnEsODmJOp7HrzxtWK9Gbb551qqUlmOzpicUaGjwDb3/7rHaf79id\nKh057HZzsrgDIxBI2iKRtC0ez1rN5kzG5bKmnU5L2mo1GzabKe1wONJz5ri6enqCzxZd+lKHypMu\nvY1WnVfyPwyQn/meK9rmEIVZBGezj0JnV5CxzycAhs1G1DBIeb2YLRbS5eWWIJjo709bnE5T1G63\npHM5w0KhPOZjvCyQ8XoJms0k7XaTd+XKypPt7WFPLpdyQY5cDnMymbWYTKacyZTLABaTiazTaU03\nNLgiy5aVh4LBlG3fvmDtmKkr2IOKC6AwszF/u4a03jf5Kxd024p+/dwC6TRqEH0LUHRfEl8dKk8n\nKMR9bka2j06i2pGdjME01sJLYDXwBdQNuAA+hzpARTfgmpWGnrEaCkIIIYS49L6IOpdPFxOJLbLQ\nM11iISGEEEKMYP9XSH3+UqdiPFbUKEUTqhdxL4Xr5oUQQgghJktiCyGEEEJcUPehpgsfR42WCCGE\nEEKcD4kthBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGE\nEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBC\nCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQggh\nhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQoiL4ofA90YtWwP0A/8J/KBoeRaIAGHgFPA4YC56\n3aHXFQK6gb8ueq0KeE2vdxDYCtw6Tppe0t9lHrX8Q8BO/f2ngeeB286yfUIIIYS4sM4US9QBi4Af\nA32oGOEo8E2gQb93LXBynHWvB/YDQ0Ab8LejXm8CXgGiwGHgrqLX7gdeRcUd3cC3AY9+7YPAoVHr\n+u04yx4bJ21CCCGEuAQqUSf2d+jnTlRw8WHgn3hrJ0azfrwA1ZHxZ0Wv/yvwO8ALLNXrvUe/5kAF\nMXm/BwR4a0fFH+p1ZEa99jdAL/A+wAVYgHcD/+9EN1QIIYQQF8SZYomFwADwVWC2fr0G+EvgA/r5\nWs7cibESFRMsBtqLPgewTa/bAfw+qsOiWr/2QeBunZ5y1ODHt/RrDai4pko/t6I6WdqKPm9FDZys\nPvPmCyGEEOJiez/qpO1GdUT8Wi//AuN3YgD8BPiPouddFAIYgH8Gnhnj+8zAe/T6qouWe4EjwM2M\nnInhRQURD05we4QQQghxcY0XS/wQeO4sn13L+J0Yo30DNYsDVKdGAigpen0z8LFxPvsA8GbR8+Oo\njg+AVcDLwJOjlkVRAydCiEtg9GinEELk/QzYjZrq+Qjw52d4r0n/Xwq8DTimn1cA9cC+ove+CSwb\n9fk3gTgqoPk2aqpp3peBJ1AzLordghpF+fnZN0UIIYQQl8B4scRdwIYp+g4TcAdwQD9fhuo4iRa9\nZx9vjT3y1hR9FlSHxx368R3AFtSlr8XLtqFmhwohLgHpxBBCnMkngbcDX0TNqBjPbtR9MQ6hrkF9\nQi/PX2MaKnpvCCgd9flr9LIPoQKFvBtRnRX/PsZ3VqE6O7Jn2wghhBBCXDJjxRLVQE/Rez6FuuQj\nDPyfSa7/C/r/k/q/h5FxB4wdewC8E3V5yz8WLfsdhQ6Lt6E6NbaMWva7SaZRCDGFpBNDCHEmfaiO\ngoNned91qKDhA6hrRPOdFxH9v6zovWWoIGW0FGqk5rPAClT99ATwV4zsqMjP+giggiCpx4QQQojp\na6xYIkDhXhigLkOtAL6OuufERH0K+CPUzToNvSzCyLgD1CWoQ6OWrQaeRl2Werxo+RbU4Eo56lLW\nbajLWuv1sttQHRtCiEtEgn8hxGTlzvDas6iTfX5EI3/n75VF77mWkdM2R7Oh7rFRBtyAusdGN/CG\nfv0UKoDYCiRR17IKIYQQYuZ4icI9JoqZKAxWnM2fAn+HujTldNHyg6g4wlO07FpGdqJch7qE9WHU\nDNJibXp9fw50AjG9fBvqvhoeYPsE0yiEEEKIS+AEcGfR8y9w5ht7LkeNgtTp5/8KbEKNXixFBQZ3\n69duBm4H7KhfF3kMNeVzln69tujvRv1d9aiODlC/TtKD+lUTt15+H/CVc9pSIYQQQlwIo2OJRaiB\njscpzMioRt0nI/+zrGtRN/Z0oO6Blf8D9atl3ai4YizbAJ9+/wP6u/K/OLIcdZ+tdWdI79Oo+OKr\nRcvyv4i25QyfE0IIIcQ0MDrw+CfgqaLnGUZ2YoD6uTKffmwHvovqnOhBXR6SdwewFzXFM4AaDbl9\nnHQ08dafWAV1H40dqI6TbuB/kJ89E0IIIaaT0bEEqF8R+QngR8UBLahfGWnQr69BDV4U/2VQP+fe\nhpqNGS76e6Jo3Y2omCIGHB713d8D0qM+u39U2v5cf9f7ipbdpNPwLxPdaCGEEEIIIYQQQgghhBBC\nCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBXhon+hNEld/fdd296/PHHN433+ooVK75w8VIz\nMfv37//CRN43HdN+MU10P03UVOzPqU7TVLvYeeZ898d0yeMX+rhOl+08V9Mh30+XfTgd9sV4pss+\nuhzMtNhiMvlyuqX9YroQ5Vdii6l3PvtjuuTvi3FMp8u2novpkOeny/6bDvviTKbLfpqo0Xf5n7Ze\nfPHFNZc6DUIIIYS4fEhsIYQQQsw8M6YTQwghhBBCCCGEEFc26cQQQgghhBBCCCHEjCCdGEIIIYQQ\nQgghhJgRpBNDCCGEEEIIIYQQM8LF7sSYC7wCHAQOAJ/RyyuB3wJHgReB8oucLiGEEELMPBJXCCGE\nEFeYi92JYQB/DSwDVgN/AVwFfBYVbCwGXtLPhRBCCCHOROIKIYQQ4gpzsTsxeoC9+nEEOAw0AO8F\nvq+Xfx9430VOlxBCCCFmHokrhBBCiCvMpbwnRhNwHfA6UAf06uW9+rkQQgghxEQ1IXGFEEIIcdmz\nXqLv9QAbgL8EwqNey+m/t3j00UfX5h+vXr26fd26de0XKH1CCCGEmDnOKa4AiS2EEEKImeZSdGLY\nUIHGD4Bf6GW9wCzUtNB6oG+sDz7++OObLkL6hBBCCDFznHNcARJbCCGEEDPNxb6cxAR8FzgEfL1o\n+S+Bj+jHH6EQhAghhBBCjEfiCiGEEOIKc7FnYtwG/BHwJrBHL/sc8G/AT4GPAu3AQxc5XUIIIYSY\neSSuEEIIIa4wF7sT41XGn/3xjouZECGEEELMeBJXCCGEEFeYS/nrJEIIIYQQQgghhBATJp0YQggh\nhBBCCCGEmBGkE0MIIYQQQgghhBAzwmQ6MR4FGi5UQoQQQghxRZG4QgghhBCTNplOjFLgRdRNtD4F\n1F2QFAkhhBDiSiBxhRBCCCEmbTKdGF8AlgF/AdQDm4GXLkCahBBCCHH5+wISVwghhBBiks7lnhh9\nQA8QAGom+dnvAb3A/qJlXwBOoX7ffQ9w7zmkSQghhBAz0/nEFSCxhRBCCHFFmUwnxieBTahRkmrg\nz4BrJvl9T/LWQCIHfA24Tv/9ZpLrFEIIIcTMMxVxBUhsIYQQQlxRrJN471zgr4C95/F9W4CmMZab\nzmOdQgghhJh5piKuAIkthBBCiCvKZGZifI7zDzTG8ylgH/BdoPwCfYcQQgghpo8LGVeAxBZCCCHE\nZWkyMzFcqKmft6OmaW4BvgUkzjMN3wL+WT/+EvA48NGx3vjoo4+uzT9evXp1+7p169rP87uFEEII\ncWlcqLgCJLYQQgghLluT6cR4ChgCvomaovkh4AfAuvNMQ1/R4+8A/zPeGx9//PFN5/ldQgghhJge\nLlRcARJbCCGEEJetyXRiLAOuLnr+MnBoCtJQD3Trxw8w8u7iQgghhLg8Xai4AiS2EEIIIS5bk+nE\n2A3cAmzTz1cDuyb5fc8Aa1B3IT8J/BOwFliJmkp6AvjYJNcphBBCiJlnKuIKkNhCCCGEuKJMphPj\nRuA1VICQA+YBR1CjGzkm9rNoHxxj2fcmkQYhhBBCXB6mIq4AiS2EEEKIK8pkOjFG/wb7PCCOujFX\nx5SlSAghhBBXAokrhBBCCDFpk+nEaC96/DHAAURQP1t2HfCNqUuWEEIIIS5z7UWPJa4QQgghxIRM\nphOjWCvwv0XP3z4FaRFCCCHElUniCiGEEEJMyLl2YgwBXwXcQAh4fspSJIQQQogrjcQVQgghhJiQ\nc+3EeEP/CSGEEEKcL4krhBBCCDEh59qJMbvosQk17fOH558cIYQQQlyBJK4QQgghxISYz/FzNwH/\nATwC/Bnwrgl+7ntAL+rn0/Iqgd8CR4EXUTf0EkIIIcSV41zjCpDYQgghhLiinGsnxnPAJ4Av6r+/\nnuDnnuStP6n2WVSgsRh4ST8XQgghxJXjXOMKkNhCCCGEuKJM5nKSR4Ecapon+nEI2AXsneA6tgBN\no5a9F1ijH38f2IQEG0IIIcTlbiriCpDYQgghhLiiTGYmxg3Ax1HXrTagftP9PuDbwGPnkYY61DRQ\n9P+681iXEEIIIWaGCxVXgMQWQgghxGVrMjMx5gLXAxH9/B9RP4G2BjVq8pUpSE9O/43p0UcfXZt/\nvHr16vZ169a1T8F3CiGEEOLiuxhxBUhsIYQQQlxWJtOJUQOkip4bqJGNGJA4jzT0ArOAHqAe6Bvv\njY8//vim8/geIYQQQkwfFyquAIkthBBCiMvWZDoxngZeB36Bun71PcCPgBLg0Hmk4ZfAR1AjLh/R\n6xdCCCHE5e1CxRUgsYWYzmL9LD3+jvVgomXhb324qy91ioQQYkaZzD0xvgT8ORAEBlHXrn4RiAJ/\nOMF1PANsBZYAJ4E/Af4NeCfqZ9Du1M+FEEIIcXmbirgCJLYQM8zS4+9YbybjMpN2qc4MIYQQkzGZ\nmRigpnpmix5P1gfHWf6Oc1iXEEIIIWa2840rQGILIYQQ4ooymZkYfwn8EHUNa61+/JkLkSghhBBC\nXPYkrhBXpN7qv/xJDjI5yPRW/+VPLnV6hBBippnMTIw/A25GTfMENTVzO/DNqU6UEEIIIS57EleI\nK5Iz01GXttb15h8DnZc4SUIIMaNM9nKS7DiPhRBCCCEmS+IKccVJuJb3uuItA/nHlzo9Qggx00ym\nE+NJ1F3E/xt1F/H3Ad+7EIkSQgghxGVP4gpxRRqsfF+nM76/DkwMVr5PZmEIIcQkTaYT42vA74Db\ngRzq7t+7L0SihBBCCHHZk7hCXJEqBn8xz2b0l+cfD1a9XzoyhBBiEiZ7Ocku/SeEEEIIcb4krhBX\nIBPE47gzO25wR7auHHTf6cNVeakTJYQQM8ZEfp0kAoTH+RuawrS0A28Ce4A3pnC9QgghhJg+LlZc\nARJbiGlosPKBTndmx0oz2M2kXUuPvf3RS50mIYSYSSYyE8MzxrJ6oHuK05ID1gIDU7xeIYQQQkwf\nFyuuAIktxHRkMsOIGDxrv1RJEUKImWgiMzHG8uspTUWB6QKtVwghhBDT14WKK0BiCzENpWwLj471\nWAghxNmdayfGhQgIcsCLwE7gkQuwfiGEEEJMTxeqo0FiCzEtvV7+5C+PBxd3HB9c3P56+ZO/vNTp\nEUKImWSyN/bM+/aUpkK5DTWVtAb4LdACbCl+w6OPPro2/3j16tXt69ata78A6ZhSjz22ayXAV75y\nw95LnRYhhBBimroQcQVcprGFmPle+G1g1quvru8AuP32wKwPf7j85KVOkxBCzBTn2onxxJSmQslf\nC+sHfg6sYlSg8fjjj2+6AN97wTz22K6VO3YElunH0pEhhBBCjO1CxBVwGcYWYubz+xO2aDRtNYzs\nucbhQghxRTvXy0mmmhso1Y9LgLuB/ZcuOVMjHDbshpG1GkbWGg4bctMmIYQQ4uK5LGMLMbP5/Qlb\nT0/C1dhYEm9ocAWamz19q1ZVBy51uoQQYiaZLj3AdagRElBpehp1DeuM9pnPXHXg3/7tTXv+cX65\n35+wAdTUOI1LlTYhhBDiMndZxhZi5jt5MuqKRDLWW2+t6S4rsxtVVQ6JB4UQYhKmSyfGCWDlpU7E\nVFu61Bv77Gev2Z1/DIUe+Px7pCNDCCGEuCAuy9hCzGyBQNIWDBpOgMpKR7i83C5xoBBCTNJ0uZzk\nspXvXc/PvhDiStPSEnKDr+5Sp0MIIYSYDjwea9rjsaYB+vuTriNHhsokThRCiImbLjMxLkt+f8K2\nY0d/VXd3wl1f74zddFN1oKbGaQQCSbmcRFwRnnqqde53vnNsFdAEvk/D+t5LnabLn8+j/q+PXNp0\nXAw+D9Ckn7RfGdssrnRySerMlp+Zm3f0aNgDEAgk43JMhRBiYq6AmRi+uks1CtzaGna3tkbKensT\nntOnE+5AIGnz+xM2w8hZDSNnlV53cTnbsKGj/pvfPLZ6cJBG4A7gy5c6TTODr1n9ndNnPcC16i/f\nmTE5fn/CNjPqpuFtfR/wXuCac93miSreNzNnP4nLSf6S1J6ehEvy38xVVeUw8n+VlfaE1UrmUqdp\nOpH69XydS9vnfGIPIS6+GTUT42tfO7SoutqR+PCHF0zwt7R9dQyP0vm4uKPAPk86nbPu2OGvzWRy\ntpUrF/RWVTmMzZt7q7u7Y+6VK6uCs2Y54xcvPdOBrw51h/i+qRgxldGoS09dKvLWkSW/P2E7cSJS\nbhjkf5UnC6QvdvpmHl8zcL1+DKxvm+QKrgbeARhACDhw5reP5PcnbEeODJXpp0PTvGyVoH4u8yog\nAswG3pzqL8nn8aoqh5HfN4FAMm4YueHz57nuJ6nDxLkKhVI2m82Ulrwz87S0hNz79g1WlJba0jfd\nVDVgtZrS27b1Nxw+POStqnK0XenHtKUl5G5rC5dFImnbvHklQ6tX14QudZqmt+LZl746YCngAgYn\n3vbxNQO36secQ+whLqDt2/1egKkqC5dL7DGjOjE2bepe5nBYUgAT78gYVjP1HRk+DyqQjo7VKP/l\nLzubenqSDSZTLrd9u7/WYiGzY8dAQzhsOE0mk2nJkrKhqUvLW9LF9Jpa7atDNTZKAS/4jp1P+tSl\nOoFKgJtuqho4v4I4vfbXha9cpmZ7W1pC7r17B6v10/7ijozW1rDbajVz7bUl3QcORA3DYDfw6Pl8\n3/nzefz+hG2y+9XvT9gCgaStqsphTN0xyY+QvKU+cgPVRY9Hf+4MdY6vGbgJ1QmSBnYzyU6MQCBp\na2kJlQNUVzum8dRmnwdYCAx3uACdU12Gi/N4W1u4ZHAw5V661DsYjbpMJSW2nNd77jfk8/sTtqee\namsG+PCHmy9Qw2Uq67Zx86y4iPKXpJ4+HfMODaWmuF6aameOkabwe/TocaHhNV4H+0SMPgf7/Qnb\nV796cBn4Hob1/3U+KfX7E7aXXuqZ3dYWqaqpcUZVXBioP3w41Gi1mtNutyX1iU8sOTGZOOBcY4ap\nbhhNBb8/YfvRj04s7OyMVVZW2uP79g1Wd3XFeh58sLH7wn/7pY8FR88+Ofsx9XmACv24FnUj46Wo\ngYz9QHvR+zjDtlUDtUWPr/BOjEufF/K+9a0j8/fuHaivry+JASfOVl43bOioBxivzOQHq06fjrmn\nRyfhue/rGdWJMTRklJjNhv348XA5MIFOjPW94CtBFcgVQBn4XkMV6vM8sfpWoQp8BjDAt39kcLc+\nkkp9FwCLxZIDiETStkQiY8vlsAwOppy7dwe8119fNcnMc7aD7fMAN+vHr09s+0b04p5HwR2eyl2i\n19E7anp3o37t1OTXPVJra9h99OhQZSKRsVosZO65p6H/3Nbk8wCL9OPz6liZrNFBVr6xbBg568mT\nEXdlpSOer1ymLtjwNQNeoF916hUfq8kJBlO2TZt65sTjaevp0zFHMJjqy6evvNxu+P0Jh9Npz7z3\nvd4jGzac/rcxGt0XsVHk8wBv/+lP25seeqipfaLBXktLyP25z72xOpXKOu67r/HojTdW9a9eXRMa\n63io4MPnOXseGp4h5gLfdcApWJ/vbPADvUWPiz+3XH/OBvSBb1/hu3x1qHK/ClXfhVHlbRJ8njfe\n6K86dChUWVZmTwWDqZkwlbcXSAHHgENqka8OqAH8ExyBGrfO6+iIuHt7E+7f/Ka9ORTC63JhHDjQ\nP+vGG+tO3nJLdd/5dPT84AdtTXv2DDZZrabcz37WkfrEJ5acOJf1jM/nARr0467zq9su5azGK83w\nOVM3KN46IhoMpmw/+9mJRQCVlY5dNTXOEEy2MXu+QfrZ6u/hy71KgRPgC3JBOjN8y1GNtmRhBNnX\n/OKLp+eWlNgMoGcyHRn5WQBlZXYD1TnK3/3djpsPH44uAsr1d/zXuaa2tTXs9vsTnqEhw223m1NF\nL5nyD842I27jxq5qgHvuaeifyC/ejZUvtm/3e/ftC9YODiadXV2x/mXLyqegIXP+Db+f/axjztGj\nQ3MCgVhJRwe5igpX0mazZBoa/LGzxz/n02k2ojOAS9F4zR/LUChl27dvoNLttqbf/e45p85SnvNt\nnBgqNqgEHEAVw+fA4XNBNfi6x5ll0Q90Awmgo7B4eJ/WoAZWOt5a5s903H11Gzd2VTc2emKTKYeT\n7Zg7n07Lt/LVAeXAXPANwfo3il674J0bxdu+cWNX9Y4d/Q09Pcn6UCgdbm4uCZypHGzY0FH/6qv+\n+alUxhyNpq1jDfgHAknb4cND5X5/omRoKG3r6oq5GxrcEyhfeVM+OFIOxM6l3E2nTox7ga8DFuA7\nwFdGv6GszBZOp3MWu92SfeyxXSsdDkumvHx/9tZb7x2nUezzoBps16CC+9nAnajRyZPAKfBtH9UQ\nQBfQteDL6ee/G7XOG4AP6HUfQxX8GPiKKk6f59Zb63qDwaSrvNyR/PSnl7YA9PTEPbt2bW4sK7sj\ntWdPsL6rK1YydsNndGU8fAO7dwJh8P24+Lt0OiPAN4A5wEb1Pt7gjIYr7mq4diWwVS+fZNA7vJ55\nqKBlEHyNqEq1X++rBsCulg2nvXn7dr93Mo3zZ599tqms7NZIKGTYs1kswaDhOPsIe/Gx9T2s0/hT\n+NVH4N21qAZjCDUtHVCVYjCYsi1YUBobb92TGaX3+xO2X//6F/MefvgPWltaQu5167b9vtqeW/67\nqsph9PQkXCdPRtzbt/fXdnVFvU1NZaHycvvxN97or3r11b451dXOJNA6/r4asY1jdSjVoY5PDWy4\nFR48jQqUWwoNE98q/f4R+aY4aMov27rVX9vZGa6LRDKukycjNVu2vJJ87LGHthTSlzOZTLlcZaU9\nzlsb5GtQ+dkA33H1feNVjG9ZvhZ8O8d+77huAG7ZuXNgntlsSk+kwej3J2z/8A87Vx8/nlkMx1w/\n+UnOG4tl9u3ZM1B5/Hi4JpXKmLq6Yp3LlpWHDh4Mel0uaxaoGFkR+zwURjf69P8S1FTPZah6aQB8\n39UdGVGGG+NEi/bBGmA1UAk75sNNm4Bu3RF1A3Ajqp6ro3DZTqU65hNuyF+7b9/grIGBVCmYoqHQ\nyE6MsUYnd+8OeAEaGz2x4jLw7LPPNq1bt669OLA4/xlGxaOt6yOqE4d8WWjX71kFLADmAwGY2wcn\nf160jYzMM7461HkhNrrO8/sTtkwmZ9206eScU6eYC1jDYXC7c9HDh0Pm0lKr0dxc+pbZdGfazmef\nfbZpxYq7+4LBlG1wMOVOJNI2t9uaOLf9MZYR57ASVHDgQo3KjXeOAYjCl98Gn99yljK1AHBS6Gib\nCc4aW4x1Dsrn4bOv/qyN+dGXUa4dv/7yfRDV+diKajQUNW2xv2MAACAASURBVMwLvvOdY1cdOZJc\nbDKRe+qp1sjq1TVvtLSE3L/61f8svOeed7fD2crZhBo1o99/g36yS29Pk35tvG2vBWbD726BNVv1\nNvXrgaXoOPHLmb5/1Ht8zaiO2xtRM7L2AAf1e5tbWoaqzWYy5eW2+OiGzYYNHfVbtvTOXrLEO5A/\nFzz77LNNa9e+p+vNNwer2toi5dXVzmh1tSN+8GDQe+xYtCYapVTvs4l0Dq8FNo2V7vJyu1FV5Yil\nUlnzokVlg9dfXxVqbPTEgJzDYTbe/vZZva2tYffAQMoJb73Z54YNHfU7dgzM6euLOXbtGgg88sii\n4wC/+93zcz7wgd8/BiMbdGfq5Ojpibv9/kRZOJyybNvmn/3yy/0LwLcA1j9YtI9BnbtKKDSY+xk+\nnxUfx/+8Dz6+HXxNQKyQryY3YGG3W1JmMw7AEo8b9oMHtzbee++DHWf+lM+Duj/SXGDHqNh+FerY\n7Rs/r3/5bfD5/GDC7eCLo/I6Iwf4xu5cPNvo91jx5Fh1zObNPXU7d/rr0mmzy2Yzpbq74878MR5j\nmx9F5cdDqLbIAeAwqu6oBebpbe8AmvV7a8F3MzAI63+j11MH2OCZEvjg6zoWfADVlnADs/RfQu0T\n3xuFGHF4ILAKfNcCgUInn68OuHPTpr750egpU1NT6eDf/M3Vx8beloKNG7uqu7piJbNmuZLNzaVD\n+fI7Xp28cWNX9cmT8bLaWmcSCh0Z43dsjL531oh6xYM6b65F5aWT4Iup+Cw/CPifC8H3wpkHfn3N\net+1F7/W0hJyHzwY9AIsW1YeKk5b8UBmflkkkrZZreac02lOeDy2WF2dMz46Hi9uW3R0RD3d3fEy\nq9Wc8/uT7rHaRlVVDsNqNWXMZlN2cDDp7O9Puvv7U56urpj77DHjcFvPrTqmz/jeTwN2+PIhGHxh\nnHUtZLijm8Hx1zW26dKJYQH+A3UtdxewA/glqjAOM5tNmcpKZ2LHjp76cDhXYxhZUyz2evm+fU2H\nVIYZrjDzgWxCr7sKFag2oRrRS1A7awfQoxsCc1ANvCT4fgNf/wiqE8AGvqU6CR4gjrru/Gogp95P\nBlVBFl+P3dTdHfesXFkduOqqMn9NjdPw+xO2a6+tHNi27fBVyeRt1s7OSFlfn8Wp01U07Xu4UigD\nhnTFsBTVSNEjjNSA7yeoho6+74DvH4HbUQXHUNvp+z3gm+r1cTNbtdpfkftRHTKDQFDvF84w62P0\nFM55wHLU/Q9cqGDXicqgLlQPMfpx/vOf+vrXD69617uGWhYvLhvSJ/jhAtfaGnZ3dcXcy5aVh6qq\nHEZra9i9cePWJQ8/vGZnRYUtAaZsLJa2/+xnHXOuu65y4Etf2nUz+ObC+o8Wfcdi1I0lG8G3BFUA\nB4AbIbIMdQwHgaNAG/g8n/zk9lVDQ4Zn1ix31GIh1dTkCQI0N3vC+YqjpSXkfvPNYGU4bNjr652x\n5ubSoT/90233pNOY/+RP5u/Ov7elJeR+443+KofDkt2+/Y2F99//vs6HHtr2HlSe5KGHtr3npz+9\n5X927Oiv2LcvUHfw4ODsdBqX35+oOHgwUB6LGSWxWM7b35+KVlf7w1u3+mvBd++oE1AjKk8CvkOo\nziOXOq6UgO9V1InMCThg8B7Uia8KlV9O6nLzXr0Oik5Sy7du7Z+bPyb50R8At9uWGhzMuJJJyhKJ\nFtfzz3fNAzr37BmoDIXSrlxOBZEj855vFfAetf/JAnvA9zbgCNAFvtOjMtpCtS2+NpXX7Hej6i4X\n+Ay97UlgJ8ON2TFPLrZAIF6yeXP33Hg8Y7311pq+o0eHynbvDtTOm+cZAnC5LOn3v79xjE7R47Zs\ndhGDgynnm2/21/T1JWuz2Zy5rS1YY7db0/39RkkwSC0qiMrP7PGgGlDvB4LAz1CjJQFUEDgLVfYX\noDpzXkbNUmpXx4z3gC+BqnNuRZUfFxxvhJvKUaOct6M6Zi2oeiiCqrdABS0Pge9Y0XrR675P7bP1\nzxQtW3jyZMQbixkOr9caaWz0xDZu7KqORNK2jo6o56WXOudXVrrj111X3QNQUWFPv/JK99x4PGNf\nvLisv7MzXGaxWNIf//iSgxs3bl2yf/+iUqvVzMqVlQMHDwa9Q0NpB+RMV13lHVi9uiZUHNQBvPBC\n16xTp2Ie8C0vzEzxNevtdKICCgN8z+k6p4SRI02rUWW9CdWJ4QdTGfi2oupNr15niEKn2mwKl99s\nYbih79t9552bam+7reKA358pQ42SWoGk203S5bLE3G5L6o03+qsOHgx684HrY4/tWhkOp5033VTV\nW1ZmS+TrrZoap7FhQ0f9U09tWfXOd67Yk8thLimxZSor7QPl5Y5EY2NJfOPGrurrr68K5c8V+ZzX\n2hp2l5fbjaVLvbH8DKCxDV+ytxR87cCrqFkqTqAefO5ReaBc55EPqv3aME9/9jWgf2SQvr4XfLfq\nfevQAX4HIxuj0/FykwnFFt/4xqHrtm6t6frjP25ur6lxGtu3+73PPffa8rKyWyMjgzrfGlTe6kGV\nqRjwbmAx+I6gyjXA66hG3u2o+knHIb4D8JV3omKJLt3Yi6u63PcwsA51bAJqOQnUuWr4WPj9CVtn\n51B1NosTyLW1BSv9/oRt61Z/zfbtOxfCdUZtrTPy1hG44Q7VKKo83ACsAULg20hhhuRtOu2/LapH\n/x5VDntQHQdvMrGAMw3HFsKaN1DxjBt1/h3UnZD5fHiGUbjh2YMx8NkYjn94F2pQZzYq3jEDv8l/\nKhRKulOpnOnEiYi3pSU03FjYsKGj/umnW6/p7EzN3rNnIA7w/vc3ntq8eVvzihV394VCaXs8nrEN\nDiadHR0R9+HDQ1UWCxYKcYKO83yfRh3f48BzwCG9v5rhXx6Av8+h4qEWimbFVlU5jLo6Z9zjsRq3\n3FLdV1PjNGpqnMbHPrb4SL4Bk07nrFYrmbIyFQ/l64PduwPezZt7Gtrbw/WGYXIEAokKgEceWXT8\nwIEdDR/4wO8f277d733kkV3rgNyzz97yzBtv9Ff19SVKqqocydmzXeHrr68KBQJJW3m53RgYiNsG\nBpLOgYGcZf/++BK9n+vA9zTwD8CLqLrvy6j6r0EffxtqgOx/UIMQvUATxO4FTuv9klJ1NVHgOmAR\n+PqBl4vK0/INGzrq77ijrr+mxmm0tITcjY2eWCCQ7K2stA2m0zl7IJD0hkKHKuDB4UZeR0fEHYmk\nbSPjfm5HdVDaUeVvh9rvzELFz1WocvrKyGPFXCAAf5+PQR7Q77egzg3Pg28tKlY5pF9D1afrD4DP\n81d/9cYN3d2J2upqx9CRI0PlN9xQ6b/++qrQCy90zdq9O1BbW+uKZTI5WzqN+eabU93NzZ5wR0fE\n/d3vbr7l2LGlrkceWXS8tTXs/vnPO+cfPDgwr78/U2oYWF0ujFAo5Zw1yxVjxGCnrw74DOo8Xoa6\njPQHqIbgPlQ5r0TV/S59DAxUm2WtOsYsB9+/Ap/Tx9YD7boTwvdxve3z9H4w9HrCOg9UqGO5vg0V\ny61CDcrMQc0SRXdk1AA1+/f769Nps6O7O179yU8OVdx1V/3JO+6o6wf43Od232C3m7Nf/OLKPaDO\nd08/3XZ1b2+0Yu5c7+DKlRVdn/vcjkYAr/c15/79i0qdTkv6859fcRhUHH70aLiyvz9VAoQWLy4F\nVDnv6op7mpo8sVde6alTcefwYFl+wDUHxFVMMJyPSnSeWKb3oe6sG45FFoP5ZuCFkevyGQyfE6kF\nfk9v/1bwbdL5bc26ddv+BLBWVnL6ppuq2665pqJv8eKyoR//+MRCMFluvbX2tMdjSe/ePVDjdlsT\nS5eWhb1eW9Lvj0STSbPphz9svSoUSnlratxDkUj6WF9fwhmLZez797++qLT0llhpqT3rdptjdrs1\nM3duSTQQSNp27w54I5G0LV/OABYtKg2XlFgyiUSGeDzrHBxMOkOhlBW46gwd03luoF799xUNhBCl\nMDDykP4rgUUWWBdgeIBuuJ4vzqc65ike+Dt7J+h06cRYhToRtOvnP0ZlgBGBRnt7qnr5cttJl8ua\nHRxMWoNB3GDx7N4dXQJ8FPh73UD6Y1Sg0Yu6JqwTtfM8qMJbitphzagCaEI1AOehAoc7oHYp6mQ5\nD3Wiz6FOkmlUgJHQfzn9ngTDnRE+D2DL5XKm0lJbUveyA+D12g2Px5T0eKxxs9nkzeVMNpUmX/uo\nGRdfYrhyJavTnQ9gHcDb9esvoBrf+e9I68eVqIDegjqB/BJ8Py86eeQbvv16XzjBbEbliaD+TAPQ\noRqPwxm0FtXpUan/J1WnAQG9vgrUFMw46oRfo/fzbfq1vfq9oE4Wdxw8GGs4dOjYrPvvrz108GCg\n2um0G/fe29D6ve8dvy4Uos5kIrF2bdXh2lpnLBZLO0KhnGdoyLBef31Vf1tb2N3SMlRz8mS08okn\nTtym09cEvu8C/wL8BSqArdbHz6P/l6ntdnhQFfOg2gc+D/DIli3B6wDbsWPRcCyGCfwOu51kbS3+\nZ5/tCPzt3y57s60tXNbWFq6Ix7PWaDRt/cd/PHB7Msl8wPTEEydq1qyp3Pfccyeb4/GMw263WCoq\nHNFgMOtsbQ27czkc+TyRy2H/3//trt+8uadpYCBRlkziTiaxDwwYzlzOqDOZoLSUZGlpJvbyy50L\nOzqYp46tD9To0zbUCeZFVEBnQZ3IS3Xe6dbb/d8MN3CNhD6eFn385+rPzlb7gaspzOK5Z/Pm7oU2\nm8nYubO75plnTkRqa/9ve3ceX8dV3///dfcr3at9t7w7sWM7zuJsTgiJsxASAoTNhbAXStNSKIXg\nUuiXNm36a0svSdukX75AypIAZS0JJCxZyGJnsU0cb7ElW/EmS7J2XV1d3X35/XHOta4d2bFs2ZLD\n+/l43IfmjubOnDlzZuacz5yZKU00NPhHr7iiftdLL/U3jIxka7u6ciVbtw40btnSP2N4OFNaUeHJ\nNjQEwoGAu+iBnqEg8B1bfnJ2W9gGJ712fXbZ7wnM/Z2LOXQSDoXhxzdiggNOzP6HXYcw8CRwH4Qu\nsuvfBqFOzBWVCxOJtCsWyzT9+MftM3/2s/bE6CjlDgc+v39wdHQUD5B74omujssvr++aNy8YvvPO\ni9d96UsbnN3d6XnvfOfszeFw0ut0ulyxWM4ViVCWz1Nlzu8EGDuetmEO8EuAjzAW8FwAPIGpZGzC\nHJMuwlSyCvtbG/BrTMDyTXa8B7PfdJn1GK232/OjmJNqJSaA0Y85ie7FHC/m2O15sZ1+CBMsvcLm\n6bA9Wf0Qs59e2NmZqEun8Y6MDPr/9V+3uQcGEjWDgxl/JEIFEGhvj6U2b24/5+yzfT3RaJJ4nIp8\nHnbvTjSk0wQB7yc+sfEcvz/lbWvrrq2rKx2ORFLe8nJvurs7XuZ0OpwjIxn38HDKMzCQDoyMpL3f\n+MbO+mg07XO7XZ5wOBkEPgyhBzDHsY9hKhMe+xkw6xGahTmeFHqjBGye+zENd1vO/WWYytgMm6cz\n7TbahmnkVzEWBBqAUC+wBltRfe65oUvr6+lyu4m63cRnzPAMNjcHeq67runAli1Dtc8+2zc/l8uy\nYUN/Q09PvHTPnui8oSGCa9cO5SorGQSyXi/Z8nL36OBgpjoWy9WvXdtz1pw5gd7Zs4Mjl1xS1+N2\nO7K7do1UHTgwWvb73w/EWlvDlfF41nfzzbNecTgcjp6eeFltrX90+/ZwvL8/FTx4MBYwjeniHoIU\n8uA6m1+F4N5DmArHOZhjXhumMV9j8+qDmOCPD2p9dh4rgccgtNvOd5f9Wyh3NXa4GRNkX2/L8WWY\nc+2PmD6Oq26xfXt80eBgZ5XX68itW9fXtHNnrDmRyM3csmXbHOARCG3C5OFHMcfKOKYMxTDlZzbm\nmJTA5O+lmH3tfA5dpSQAdMO8Gsw+X4fZBhEIfQ5z7q5k7LYCL+ZcP2sskBIKvvTSQEV9fUn44MF4\nHMjNn18Vvu++trO6uuJVQ0PZ4Pr1/XPr6vy2h1Ch4XPowsgXMPWLMOZ41WCXc6XNk0pMORnE9NL4\nJSYwezmmPM2x63ItphfUQ5hjW3GQutAwjAC9MDqEOSa5MfvhLDuPszHnrkr7w/l2X261eQOm7Dbb\n3xbOGQcw+/HZmPNeGWafd5s0r94DoUt6euLl8Xje/eijB/y/+92BeRUV/tE77rjwxf/8z5ZLh4Zo\nBEpSKXzPPHNwVi6Xd3V2ZqvD4ZSnudk/mkhkXPl83vGb33TM7+5OlHm95MrLGY5E2IA5p3wa+KTN\nv6uBdwPtENpltvmSJsx+6LblxPaKDX3xppuevmXmTG/0Yx9buI0ihcZFd3fCXVHhTY+Oph1utyNj\nx5W8//3rbgYC554b6Mhmc+lkMuf2eHzu/ftjdWvW9ITB4fz97/trvvCFl99q84pVq174wLnnluwZ\nGIgHq6tLk6lUOh2Pp32Vlf5kOJzwptOO0rIybyqZTHp5tV/Z7QUmiLHX5C8BW2bOsv+/H9PrdjaU\nFI63ZzFW13oRc4xZhgkS+yD0G7uNP3f33S2X3ndfS7S2tjQKEAz6HStX1u9/z3vm9G/Y0F+zdetg\nKhym+p//edMlDgeOpqaykf37h2s7OmjCXKj7mG3s/AuHbgfhSsw57l2Y+k/cboNyDgW9Qlea31MB\nuGDZQky5LsXs14Ugxq2Yc2uEsQsmbqAHQn3AVVu3Ds4ZHaWitzcW3LVrqO6xxzoXpVI4UimCyaS5\nqFhRQaKpqWQ4Hk85N270JDdt6m86eNDR9OCDne62tkhNMOhOv/LKUFNPDzXptKlLpFL4h4cTVbt2\nvXIWpg70KVt3vxZzPCqz6Q1w6NbB1VEbuJ9p1+9imyfdmH3NZccVtu3XgYeBTmhaaLftCswx3oc5\nLmXseufsss4FPm3Pl5dj9umATU8AU3f5LqYe15dO5xzDw7mSzs5MRUdHovrAgZGG++9vjYfD+aDd\nF/PXXff0gmuvrdoNjuzevaMzIxHKotHhsm3bhhtjMeoBB+S8ra3ddW43+eHhlO+P//isXdu3hyu8\nXle+pMSZqaryxMEEMLZtCze0tg43rF17MJNOUwp8yB5fdthy/C6b1p2Yun+h7rkEcz6rNsskb/O4\nUBddAGXNdpoBzHnvXJv/Q5iLIW6bL5WY/aAXQjHM+ScAMDjIvEcf7S9/4on+0WwWZ0kJPrebXEfH\naKXH40j29SXqAwF3sq0t0hsOJwMDA9m6V16JlWP2Kc/evZFUS0ukJhh0OuPxnCuXS5e/9NJgo8/n\nzJx3XnWfx+NMB4Pu9COPdMzZsWO4Nh7PeL///bZ8U1Mwessts/bMmBFIVVR4hxsb/XF7e355PJ4r\nXHQuBCKsUAPmPLAAc8zeYvNlns1LLyYIHrXrnrBlrMHknd+NCYQ/j6lbzMWcY1ox+5Ubc3xosL+d\nZ8pbaCFm322yCXlV3WK6BDGaOfwZFx0ceq7DmGyWhqGh0YNf/vJF67/1rV2pdetGloHTgzkIfRxC\nP8QUvGrMhghjDj7r7acf0/gvx+yQo4wd1AqNOHv1OuDBFNx6zE7vxLZWMDv0PszVkcK9YkfeP96/\ncGHZUHW171BXxsJJyuMhfc01jT3pdN4Ti2W9mI0JY108/wmzg1RgKkfDmA07itngSbuOF2EOzLYb\nzuq/ttFAMAXrLZhtPB9TqeoBHrQF8g2YysywXZcYZFKYCtg8m09zMQ3LwhVuD+Yg3oypfOXM76iw\n6cnbPO/GNNLAFL63Yg4MOcauEoOpeJQB5fk8JY880nuBx4Mnl4vnW1pemY/Z+b35PBVPPTXgX7q0\nZK/f7yEez3tdLrKLFpVH3G5HZsOG/uaOjmg1Yw1Jr03fm+x6NBRtHwdmp3ABPlt++m0ettp5vMWu\nE7EYaTu/klSKfEcHZYnESOXXv74re8MNTQdqavyxRCLjbmgoidl5FyqgnpaWwUanEzIZfGVl3qTH\n44hns3nnnj2jleefX7Jvy5Z4GcBFFwV3v/TSQNPgYKo2myVXVuYZcTjSrnicesCfz5P2ehkMBFyD\nW7aw1KatBPgzzEG10S7zRrs9/JiyW7h6VPwq5Xbzv579mFuOlthtcJEtC8OYBnHClpMrgOv6+6mF\nfB5wt7dH06Wl0fSsWaW9113XsP3f//3S9V/84saLDh5kxoED6cZUyhwAM5l0dNYsR09zc2lxV74n\nbfkCsz8V0ttktgcpW058dh0vwpyMfRzq2VM2y6bRadJJ1m7fJrsuDkw5LLdlyHZ5Cz3f2Bi4paVl\ndFYiQdD+3w84Rs2NGyWAa9eupD8W66lYvDjRGQy6d3/jG2985stf/rXjrW9tbn/hhb6GbBbf8HDc\nk05n3bEYhW6Jh+5nPkLhnudCJeMSm7ZNmIpD4YTpwuyzA4zd03oBY43uFcCPgd9CvNAro5BnDpsH\ne4D/xZyUr8cEQAKYyn49Zv+81OZJFaYhsRL4oR0uj0YpzeXwJBKUDA5Gq226sHnttp90V1ey2u8n\nms+TA/KZDE7sfgKUJBJucjnweOKJ6uqqWF1dSSocTpWAg9JS96FXCT7zTFdzV1d8ZiqF0+EgU1rq\nyhelrdCDrrpoO+ftetcwdv7ahzk2tmNOohsxZawK0oUof6FRMc/+bjamzLjssBtT1n/P2AkTwJ9I\n4LrqqupdPp8rfc45FYNve9vMrpdeGqjYt2+kqr091pTP4xwY6CvLZHAMDVG4RcMdDhO024be3ozt\nFejy9fXFy5Ytq+pYtKhscM6cYCwcTnkeeaSjqqcnUb1uXf/cSIQqjwfHD37wSsWFF9bsdzrdbnDk\nvV5H+uDBWKC3N1lhtmnowBFdmgtXuWcWthPmmBa327/ernMNY/tOnkNl1+Gxv3dhGgFLMOX3HMw5\nOYU5H+y3v13I2Dn0YsyxaC7TK4hxXHWLfJ6K0dFs7JFH9i/q7CxUyF1+TF58DVMhrcbsO2WYsl7J\n2K1bATtt4Rw0gMn/mYyVVw/gA3/AzifA4fWGOKYsb8NU9hZjtkfMTGsCES0tkbqzz64aSSRyu4NB\nb2bp0oqBlpbhmnA4XZ5M5lz5vMMViaTL2ttj5Ry6vQ0wAf2r7XJzmOMQJk2UY/bdFKY8JDHnmRl2\nfWJ2+iG7LvMZu4DzGw713AsVLlg0Y86rG2Gol7EgEpjj2hw7335MYG2eHV8oSymbx4U6Bpjy7cA0\nkJ2YuorP5nMG00NiP6Yb/Hk9PfkawB2JkAVKOjsTiVWrXpjD2C1WuXweZyqV869b1z9/eJiK557r\na7z55uYDLpcjs3Zt76yOjnh9NJrylpZ60rNnl/Rt2BD5rV2XRjsfn93u5Zh64AVmm/q9Np9HOBTg\nCX0R+HgyyYzdu1OJ++9vS3/965evKcqXQ3XE3btHSpPJvK+3N+kD+OQnN74ZU0fl5ZdHvddeW/Oi\nw5HPxuP5wJw5gTBAJpN3hsMZH4ef7519fcnakRFKBwZi+VQKH+Dp6EjkAFyufDaXSw4sWlTZMWNG\nbnT9+kgzsB1WfwDTo7PAy9htNA67ziV2+8/E1GHL7P87MMeGmqJykMAcm4tvnXsbcFkkwoxIBDo7\nY0mXi3x1dTxSXu6KXndd48GFC8sjmzcPNfb05KrS6VwlwJ49w4XzRwUmyPCfdl7Jonk77P8rMMf/\nrZiG12bMeeRaxsppmVmf8hmMnWMKt37W2u91mHP2AUwd3PakAqDe6XR6IJcdGcGZSlGfz+O1eZS3\neZcdHqbU6YxngkF3RSyWjXd2pqtzOYc7kaBs796Rutmzg2G/35cLBpND2SylmQzZWIxyxhqUH7MN\n4QdsemzjmyDm3Bcx63vYMywWYsrkhcAjmIDO05ieyYVjv49D9aRMClNfLhybsnbbHsTU62OMtZnm\nYPbPSvs3itkXS206bjUXSEKJ8nJ/uqsr4QH80SjuaDRb3EgOAK58nrLnnx8KzJzp2ef1kigpwVtS\nQnxgADdj9XX36CjVLhfJzZv7Zz37bEWktNSd9Xqd6fPOqxyprvbFd+0aqXrllWjlnj2RiqGhRFk4\nnHO5XJTavLjQHqeuxAQeSjHHsqhdnza73gHM8XjArvMKW5aCNk/A1CeSNi8LvTYytkztYKw+VG2X\nMd5tRr5s1tRZ43EyHg+p/v5EeTqNM5mkMpVKx6urs4MlJe5ExpxpHHaeHsA7MoJjZMTuyi6nd9eu\naOOyZRUds2aVhpcurRzes2ekfN++aEVHR6Sut5fqXA5XT084FYvlArfeOmdboednXZ1/eMGCsph9\nWUIHY+Uf2w74OGYfq8Xsc9/C1C3mYY5Lfg4F9nBh6gFBWy6SNr0LbH7PxRyjChezBzB1jDmMXQQo\n1NEK5aOKV92SzqEMmQ7ejWmAfcJ+/yCmovHpsUkac9A9XdIrIiIihzl/LWy5aqpTUUR1CxERkTPa\n4t9Cy01Hjp0uPTE6sVFmaxaveoNFtxMRERGZprZMdQKOpLqFiIjIGa3ltSeZQm7Mk6vnYrrgbMZ0\npRQRERE5EapbiIiIyCl1E+Yer1cwT8sVERERORmqW4iIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiI\niIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiI\niIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiI\niIiIiIiIyJnl+8C3jxh3NdAPfB1IAxH72QncCzQWTbsSyAEjdppW4KNF/68Dfgh0AmHgWeDSov9f\nA2wFhuwyfw7MGCed1UAfsLZo3KPAXxd9b7ZpGW9c/TjzFBEREREREZEzSDVwELjefvcDu4APA38P\nPGDHu4AlwE8xAYlCIGMlcKBofjdhAh8L7fd5wF8BDYAD+AQmGBGw/68vmpcH+Arwi3HSeR/wDLCm\naNyXgEeKvt8K7BhnXOs48xMRERERERGRM9B7gD1AlmOXpwAAIABJREFUKfAvwK/s+DuA7x0xrRPY\nDITs95UcHsQA6AHefYzlDQMXjjPeZ5f/8hHjrwCex/TwKO6J8UZMD46C/wv8KdBdNO5rwDePkRYR\nEREREREROcP8DPgl5paOZjvuDl4dxAD4B2CdHV7JWBDDCbwdyALnH2U5FwBxoKxo3GxMMCILpDC9\nQApcwEZM0OOjHB7E8AGxomVtw/T8eNYuB0xA5INHSYuIiIiIiJxB3FOdABGZNj4J7MbcotH5GtMe\nxNyGUjADE4QowRxXPgtsGed35ZigyB2YZ2gUtANV9vMJzLM3Cv4SEzDZxKsDI0lgPeYZHgeACmAv\nJtBxlZ3vYsxtKCIiIiIicoZzTnUCRGTa6MX0wth+HNM2AwNF37swAYhy4B7gunF+UwI8jLkt5CtH\nme8QcD/mmRhOTHDk08D/OUZa1mACFlcCz9lxzxaNO8Crb3cREREREZEzkHpiiMix5McZ5wTeBjw2\nzv9SwBcwPSluYewBnT7gIUzPiNteY5kezMM+yzFvMWnCPKwTTCCkBBM0abbpWwP8GbCPsYd+Pg/8\ntx2nXhgiIiIiIiIir0N7gWuLvt/B2DMx3JhbM36MCSIc7e0kAH+BeY4FmKDEw8CDmOdbHOmdmDeZ\nODGvY/0J8KL9nxcT0Ch8CreWFL8utRQTPOkGzi0av82O+/jRVlZERERERM4sup1ERI4lD7wX8/yK\nMKZnRR9wEYe/AeTIHhvfxjys82bMm0VuBt5k5zFiP2+w0zYDvwUiwFYggwlsgAlO9BZ9hovGFcQw\nQQ8Ph7/VZA0mKFL8SlYREREREREREREREREREREREREREREREREREREREREREREREREREZFJ45jq\nBByvG2644em77rrr6aP9f9myZXecvtQcn23btt1xPNNNx7SfTsebT8drMvJzstM02U53mTnZ/Jgu\nZfxUb9fpsp4najqU++mSh9MhL45muuSRiIiIyFQ4Y95O8thjj1091WkQERERERERkalzxgQxRERE\nREREROQPm4IYIiIiIiIiInJGUBBDRERERERERM4ICmKIiIiIiIiIyBlBQQwREREREREROSOc7iDG\nLOApYDvwMvCXdnw18DiwC3gMqDzN6RIRERERERGRae50BzHSwGeBpcAK4C+AxcDfYIIYC4Hf2e8i\nIiIiIiIiIoec7iBGN7DZDkeBFqAZeDtwvx1/P/CO05wuEREREREREZnmpvKZGHOBC4H1QAPQY8f3\n2O8iIiIiIiIiIoe4p2i5QeB/gc8AI0f8L28/r3L77bevLAyvWLFi36pVq/adovSJiIiIiIiIyDQz\nFUEMDyaA8T3gITuuB2jE3G7SBPSO98O77rrr6dOQPhERERERERGZhk737SQO4FvADuA/isb/EviI\nHf4IY8ENERERERERERHg9PfEeAPwQWArsMmO+yLwr8BPgI8D+4A/Os3pEhEREREREZFp7nQHMZ7l\n6L0/rj+dCRERERERERGRM8tUvp1EREREREREROS4KYghIiIiIiIiImeEiQQxbgeaT1VCRERERERE\nRESOZSJBjDLgMcxzLT4FNJySFImIiIiIiIiIjGMiQYw7gKXAXwBNwBrgd6cgTSIiIiIiIiIir3Ii\nz8ToBbqBAaBucpMjIiIiIiIiIjK+iQQxPgk8jel9UQv8CXDeBJf3baAH2FY07g6gA9hkPzdOcJ4i\nIiIiIiIi8gfAPYFpZwF/BWw+ieV9B7gXeKBoXB64235ERERERERERMY1kSDGFydheWuBueOMd0zC\nvEVERERERETkdWwit5OUYF6z+iDwc+CzgH+S0vEpYAvwLaBykuYpIiIiIiIiIq8jE+mJ8QAQAe7B\n9Jx4P/A9YNVJpuH/Af9oh+8E7gI+Pt6Et99++8rC8IoVK/atWrVq30kuW0RERERERETOEBMJYiwF\nlhR9fxLYMQlp6C0a/m/g4aNNeNdddz09CcsTERERERERkTPQRG4neQm4vOj7CmDjJKShqWj4nRz+\n5hIREREREREREWBiPTEuBp4DDmDeKDIb2IkJOuQ5vtet/hC4GvOK1gPA3wMrgQvsPPYCt00gTSIi\nIiIiIiLyB2IiQYwbj/g+G4hjHvi5/zjnces44749gTSIiIiIiIiIyB+oiQQx9hUN3wb4gCjmbSIX\nAv85eckSERERERERETncRIIYxXYDTxR9v2YS0iIiIiIiIiIiclQnGsSIAF8FSoFh4NeTliIRERER\nERERkXGcaBBjg/2IiIiIiIiIiJwWJxrEmFE07MDcTvL9k0+OiIiIiIiIiMj4TjSIcQnwEWCL/b4I\nBTFERERERERE5BQ60SDGL4B1QI/93nCcv/s2cDPQCyyz46qBHwNzMG9A+SMgfILpEhEREREREZHX\nqYkEMW4H8pjbR7DDw8BGYPNxzuM7wL3AA0Xj/gZ4HPg34Av2+99MIF0iIiIiIiIi8gfAOYFpLwL+\nDPM8jGbgNuAm4D5M8OF4rAWGjhj3duB+O3w/8I4JpElERERERERE/kBMpCfGLGA5ELXf/w7zatWr\nMb0xvnKCaWhg7LaUHo7/1hQRERERERER+QMykSBGHZAq+p7GBBxiQGKS0pO3n3HdfvvtKwvDK1as\n2Ldq1ap9k7RcEREREREREZnmJhLE+AGwHngI81yMtwH/AwSAHSeRhh6gEegGmjAP/RzXXXfd9fRJ\nLEdEREREREREzmATeSbGncCfYt4cMoR5JsY/AKPAB04iDb/EvK4V+/ehk5iXiIiIiIiIiLxOTSSI\nAeYWkpz9pE9geT8EngcWAQeAPwb+FXgTsAu41n4XERERERERETnMRG4n+QzwCeDnmNtJvo95M8k9\nE5jHrUcZf/0E5iEiIiIiIiIif4AmEsT4E+AyzO0jYHpMrGNiQQwRERERERERkRMy0dtJckcZFhER\nERERERE5pSbSE+M7mLeTFG4neQfw7VORKBERERERERGRI00kiHE38AxwJZDHPJTzpVORKBERERER\nERGRI00kiAGw0X5ERERERERERE6r4wliRDE9L8aTB8onLzkiIiIiIiIiIuM7niBGcJxxTcDBSU7L\nPiACZIE0cOkkz19EREREREREzmATvZ2k4FfA8slMCKZXx0pgcJLnKyIiIiIiIiKvAxN9xWqBY1JT\ncernKyIiIiIiIiJnuBMNYtw3qakw8sBjwIvAJ07B/EVERERERETkDHait5N8bVJTYbwB85yNOuBx\noBVYWzzB7bffvrIwvGLFin2rVq3adwrSISIiIiIiIiLT0IkGMU6FwoNC+4AHMQ/2PCyIcddddz19\nmtMkIiIiIiIiItPEid5OMtlKgTI7HABuALZNXXImT19fwtPXl/BMdTpEREREREREznTTpSdGA6b3\nBZg0/QDzfIwzWmvrcOk99+w4z+t15v72b8/fVFfnT091mkRERERERETOVNMliLEXuGCqEzG5QsF7\n7tlx3rZtw4ucTnJf/er21Fe+ctHmqU6ViIiIiIiIyJlqugQxXpdGRlLeVAqPy0VuZCTtner0iIiI\niIiIiJzJFMQ4hVasaDjY27uvyuNxpG65ZdaeqU6PiIiIiIiIyJlMQYxTaN684Egg4Bl1OslVVHj1\nPAyRUy4UNH9XR6c2HafDH9K6To3CQ5nP3OcZqYyIiIjI64+CGKfM6ugjj9w3e3AwXe/xuPI/+tG+\nRQsWlJ2Gh3uG3gnMB9bC6g2ndllnkiMr86rcv/6EgkCVHWYyt+30a8yeunVtbR0uBTjnnIrYic5j\n+uXXxPX1JTz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plotting all manhattan plots\n", "pl.figure(1,figsize=(15,16))\n", "lim = -1.2*sp.log10(lmm.getPv().min())\n", "for g in range(P):\n", " plt = pl.subplot(P,2,g+1)\n", " pl.title(lysine_group[g])\n", " if g!=P-1: xticklabels = False\n", " else: xticklabels = True\n", " plot_manhattan(position['pos_cum'],pvalues[lysine_group[g]+\":0\"],\n", " chromBounds,lim=lim,xticklabels=xticklabels)\n", "pl.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multi locus Single Trait Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Genetic Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In addition to a single-locus marginal analysis, LIMIX can be used to performa multi-locus scan by step-wise regression. \n", "In the univariate (single-trait) case, this approach is analogus to the proecudere described in (Segura et al., 2012).\n", "Briefly, the standard univariate scan is extended by iterative inclusion of the most associated SNP as a covariate. The proceudere is terminated after a predefined p-value or q-value treshold or the maximum number of iterations is reached.\n", "\n", "Note, care needs to be taken when interpreting these signifance levels as they are compromised by an intrinsic multiple testing bias. It is adviced to interpret the model output carefully, consdering both signifiance levels and other metrics, such as BIC (see discussion in Segura et al., 2012).\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: Single-trait eQTL mapping for gene YBR115C the glucose condition" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "loaded 109 samples, 1 phenotypes, 2956 snps\n" ] } ], "source": [ "#getting data\n", "#create a complex query on the gene_ID and environment:\n", "#select environment 0 for gene YBR115C\n", "phenotype_query = \"(gene_ID=='YBR115C') & (environment==0)\"\n", "\n", "data_subsample = dataset.subsample_phenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", "\n", "#get variables we need from data\n", "snps = data_subsample.getGenotypes(impute_missing=True)\n", "phenotypes,sample_idx = data_subsample.getPhenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", "assert sample_idx.all()\n", "\n", "sample_relatedness = data_subsample.getCovariance()\n", "\n", "#set parameters for the analysis\n", "N, P = phenotypes.shape \n", "S = snps.shape[1]\n", "\n", "print \"loaded %d samples, %d phenotypes, %s snps\" % (N,P,S)\n", "\n", "covs = None #covariates\n", "searchDelta = False #specify if delta should be optimized for each SNP\n", "test=\"lrt\" #specify type of statistical test\n", "\n", "# Running the analysis\n", "threshold = 0.01/snps.shape[1] \n", "# inclusion threshold on pvalues \n", "#(Bonferroni corrected significance level of 1%)\n", "maxiter = 10 # maximum number of iterations\n", "lmm, RV = qtl.forward_lmm(snps,phenotypes.values,K=sample_relatedness,\n", " qvalues=False,threshold=threshold,maxiter=maxiter)\n", "# RV contains:\n", "# - iadded: array of indices of SNPs included in order of inclusion\n", "# - pvadded: array of Pvalues obtained by the included SNPs before inclusion\n", "# - pvall: [maxiter x S] SP.array of Pvalues for all iterations" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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POAjh84ArT54cbkwm8Zh0Wb3JimiU0EMP9bjq6hzRrq5iU6Hgrr7//sjOYhFP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\nmQzOEyfi1Xfd1dnQ3Z2qbGjwZbLZ4jBAZaUrF42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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot primay p-values and conditional association results\n", "pvall = RV['pvall']\n", "plt = pl.subplot(2,1,1)\n", "pl.title('Primary association analysis')\n", "plot_manhattan(position['pos_cum'],pvall[0],chromBounds,xticklabels = False)\n", "plt = pl.subplot(2,1,2)\n", "pl.title('Secondary association analysis')\n", "plot_manhattan(position['pos_cum'],pvall[1],chromBounds,xticklabels = True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Variance Component Models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In addition to association testing using fixed effects, LIMIX enables flexible fitting of variance component models. Here, we illustrate the usage of variance component models fit to single genes." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Genetic Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model considered by the LIMIX variance decomposition module is an extension of the genetic model\n", "employed in standard GWAS, however considers multiple random effects terms:\n", "\\begin{equation}\n", "\\mathbf{y} = \\mathbf{F}\\boldsymbol{\\alpha} + \\sum_{x}\\mathbf{u}^{(x)} + \\boldsymbol{\\psi},\\;\\;\\;\\;\n", "\\mathbf{u}^{(x)}\\sim\\mathcal{N}\\left(\\mathbf{0},{\\sigma^{(x)}}^2\\mathbf{R}^{(x)}\\right),\\;\n", "\\boldsymbol{\\Psi}\\sim\\mathcal{N}\\left(\\mathbf{0},\\sigma_e^2\\mathbf{I}_N\\right)\n", "\\end{equation}\n", "where\n", "\\begin{eqnarray}\n", "\\mathbf{y} &=& \\text{phenotype vector} \\in \\mathcal{R}^{N,1} \\\\\n", "\\mathbf{F} &=& \\text{matrix of $K$ covariates} \\in \\mathcal{R}^{N,K} \\\\\n", "\\boldsymbol{\\alpha} &=& \\text{effect of covariates} \\in \\mathcal{R}^{K,1} \\\\\n", "\\mathbf{R}^{(x)} &=& \\text{is the sample covariance matrix for contribution $x$} \\in \\mathcal{R}^{N,N} \\\\\n", "\\end{eqnarray}\n", "\n", "If $\\mathbf{R}$ is a genetic contribution from set of SNPs $\\mathcal{S}$,\n", "with a bit of abuse of notation we can write\n", "$\\mathbf{R}= \\frac{1}{C}\\mathbf{X}_{:,\\,\\mathcal{S}}{\\mathbf{X}_{:,\\,\\mathcal{S}}}^T$\n", "where $C=\\frac{1}{N}\\text{trace}\\left(\\mathbf{X}_{:,\\,\\mathcal{S}_i}{\\mathbf{X}_{:,\\,\\mathcal{S}_i}}^T\\right)$.\n", "\n", "LIMIX supports an arbitrary number of fixed or random effects to be included in the model.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: cis/trans Variance Decomposition in the glucose condition" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we use the LIMIX variance decomposition module to quantify the variability\n", "in gene expression explained by proximal (cis) and distal (trans) genetic variation.\n", "To do so, we build a linear mixed model with a fixed effect intercept,\n", "two random effects for cis and trans genetic effects and a noise random effect:\n", "\n", "\\begin{equation}\n", "\\mathbf{y} = \\mathbf{1}_N\\mu + \\mathbf{u}^{(cis)} + \\mathbf{u}^{(trans)} + \\boldsymbol{\\psi},\\;\\;\\;\\;\n", "\\mathbf{u}^{(cis)}\\sim\\mathcal{N}\\left(\\mathbf{0},{\\sigma^{(x)}}^2\\mathbf{R}^{(cis)}\\right), \\\\\n", "\\mathbf{u}^{(trans)}\\sim\\mathcal{N}\\left(\\mathbf{0},{\\sigma^{(x)}}^2\\mathbf{R}^{(trans)}\\right),\n", "\\boldsymbol{\\Psi}\\sim\\mathcal{N}\\left(\\mathbf{0},\\sigma_e^2\\mathbf{I}_N\\right)\n", "\\end{equation}\n", "\n", "where $\\mathbf{R}^\\text{(cis)}$ and $\\mathbf{R}^\\text{(trans)}$ are the local and distal relatedeness matrices,\n", "built considering all SNPs in cis and trans (i.e., not in cis) respectively.\n", "As cis region is defined by the 50kb region around each gene.\n", "\n", "The gene-model is fitted to gene expression in environment 0 for\n", "all genes in the Lysine Biosynthesis pathway and variance components are averaged thereafter to obtain pathway\n", "based variance components." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "running variance decomposition on (gene_ID=='YIL094C') & (environment==0)\n", "running variance decomposition on (gene_ID=='YDL182W') & (environment==0)\n", "running variance decomposition on (gene_ID=='YDL131W') & (environment==0)\n", "running variance decomposition on (gene_ID=='YER052C') & (environment==0)\n", "running variance decomposition on (gene_ID=='YBR115C') & (environment==0)\n", "running variance decomposition on (gene_ID=='YDR158W') & (environment==0)\n", "running variance decomposition on (gene_ID=='YNR050C') & (environment==0)\n", "running variance decomposition on (gene_ID=='YJR139C') & (environment==0)\n", "running variance decomposition on (gene_ID=='YIR034C') & (environment==0)\n", "running variance decomposition on (gene_ID=='YGL202W') & (environment==0)\n", "running variance decomposition on (gene_ID=='YDR234W') & (environment==0)\n" ] } ], "source": [ "# loop over genes and fit variance component model\n", "gene_var = []\n", "genes_analyzed = []\n", "K_all = dataset.getCovariance(normalize=False)\n", " \n", "for gene_idx,gene in enumerate(lysine_group):\n", " #create a complex query on the gene_ID and environment:\n", " # select environment 0 for all genes in lysine_group\n", " phenotype_query = \"(gene_ID=='%s') & (environment==0)\" % gene\n", " print \"running variance decomposition on %s\" % phenotype_query\n", " data_subsample = dataset.subsample_phenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", " \n", " #get variables we need from data\n", " phenotypes,sample_idx = data_subsample.getPhenotypes(phenotype_query=phenotype_query,\n", " intersection=True) \n", " assert sample_idx.all()\n", " if phenotypes.shape[1]==0:\n", " continue\n", " #snps = data_subsample.getGenotypes(impute_missing=True)\n", " pos_gene = data_subsample.pheno_reader.get_pos(phenotype_query=phenotype_query)\n", " K_cis = data_subsample.getCovariance(normalize=False,pos_start=pos_gene[\"start\"][0],\n", " pos_end=pos_gene[\"end\"][0],windowsize=5e5)\n", " K_trans = K_all-K_cis\n", " K_cis /= K_cis.diagonal().mean()\n", " K_trans /= K_trans.diagonal().mean()\n", " \n", " # variance component model\n", " vc = var.VarianceDecomposition(phenotypes.values)\n", " vc.addFixedEffect()\n", " vc.addRandomEffect(K=K_cis)\n", " vc.addRandomEffect(K=K_trans)\n", " vc.addRandomEffect(is_noise=True)\n", " vc.optimize()\n", " \n", " # get variances\n", " # vc.getVariances() returs a vector of variances explained\n", " # by the three random effects in order of addition (cis,trans,noise)\n", " _var = vc.getVarianceComps()\n", " \n", " gene_var.append(_var)\n", " genes_analyzed.append(gene)\n", "# concatenate in a unique matrix\n", "gene_var = sp.concatenate(gene_var)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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hWA/cCed2wMclcD9QAriRCAGeBeJelzPQSui/v9YH/DnsXQSjquA+WY8qCsAy4H64JqMm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\nrus+RBFPEXu3oht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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#normalize variance component and average\n", "gene_var/=gene_var.sum(1)[:,sp.newaxis]\n", "var_mean = gene_var.mean(0)\n", "column_labels = [\"cis\",\"trans\",\"noise\"]\n", "colors = ['Green','MediumBlue','Gray']\n", "p=pl.pie(var_mean,labels=column_labels,autopct='%1.1f%%',colors=colors,\n", " shadow=True, startangle=0)\n", "#convert var to a DataFrame for nice output writing:\n", "gene_var = pd.DataFrame(data=gene_var,index=genes_analyzed,columns=column_labels)\n", "\n", "#convert betas to a DataFrame for nice output writing:\n", "var_mean = pd.DataFrame(data=var_mean[sp.newaxis,:],index=[\"lysine_biosynthesis\"],\n", " columns=column_labels)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Multi Trait Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Denoting with $N$ and $P$ the number of samples and phenotypes in the analysis,\n", "LIMIX models the $N \\times P$ matrix-variate phenotype $\\mathbf{Y}$\n", "as a sum of fixed and random effects in a multivariate mixed model framework.\n", "\n", "Single-trait models only consider the across-sample axis of variation and thus\n", "- fixed effects need only specification of a sample design (denoted by $\\mathbf{F}$ so far)\n", "- random effects need only specification of a sample covariance matrix (denoted by $\\mathbf{R}$ so far),\n", "which describes the correlation across samples induced by the random effect\n", "\n", "Conversely, multi-trait models also consider the across-trait axis of variation and thus\n", "- fixed effects also require a trait design (denoted with $\\mathbf{A}$ in the following)\n", "- random effects also require a trait covariance matrix (denoted with $\\mathbf{C}$ in the following),\n", "which describes the correlation across traits induced by the random effect\n", "\n", "Different forms of trait designs for fixed effects and trait covariances for random effects\n", "reflect different hypothesis on how these contributions affect phenotypes\n", "(e.g., shared and trait-specific effects).\n", "In the following, we will show how LIMIX can be used for different analysis of multiple traits\n", "wisely choosing trait designs and covariances.\n", "\n", "We decided to start with multi-trait variance components models before going to\n", "multi-trait GWAS analysis, including single-locus and multi-locus analysis.\n", "In the next section we will be discussing more subtle problems as regularization and model selection. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Variance decomposition" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Genetic Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The general multi-trait linear mixed models considered in the LIMIX variance decomposition module can be written as\n", "\\begin{equation}\n", "\\mathbf{Y} = \\sum_i\\mathbf{F}_i\\mathbf{W}_i\\mathbf{A}^\\text{(cov)}_i + \\sum_{x}\\mathbf{U}^{(x)} + \\boldsymbol{\\Psi},\\;\\;\\;\\;\n", "\\mathbf{U}^{(x)}\\sim\\text{MVN}\\left(\\mathbf{0},\\mathbf{R}^{(x)},\\mathbf{C}^{(x)}\\right),\\;\n", "\\boldsymbol{\\Psi}\\sim\\text{MVN}\\left(\\mathbf{0},\\mathbf{I}_N,\\mathbf{C}^\\text{(noise)}\\right)\n", "\\end{equation}\n", "where\n", "\\begin{eqnarray}\n", "\\mathbf{Y} &=& \\text{phenotype vector} \\in \\mathcal{R}^{N,P} \\\\\n", "\\mathbf{F}_i &=& \\text{sample designs for fixed effects} \\in \\mathcal{R}^{N,K} \\\\\n", "\\mathbf{W}_i &=& \\text{effect size matrix of covariates} \\in \\mathcal{R}^{K,L} \\\\\n", "\\mathbf{A}^\\text{(cov)} &=& \\text{trait design for the fixed effect} \\in \\mathcal{R}^{L,P} \\\\\n", "\\mathbf{R}^{(x)} &=& \\text{sample covariance matrix for contribution $x$} \\in \\mathcal{R}^{N,N} \\\\\n", "\\mathbf{C}^{(x)} &=& \\text{trait covariance matrix for contribution $x$} \\in \\mathcal{R}^{P,P} \\\\\n", "\\mathbf{C}^\\text{(noise)} &=& \\text{residual trait covariance matrix} \\in \\mathcal{R}^{P,P} \\\\\n", "\\end{eqnarray}\n", "\n", "\n", "The variance decomposition module in LIMIX allows the user to build the model by adding any number of fixed and random effects, specify different designs for fixed effects and choose covariance models for random effects. In case of only two random effects LIMIX uses speedups beaking the $O(N^3P^3)$ complexity in $O(N^3+P^3)$.\n", "\n", "In the following we show two different example.\n", "In the first example we construct interpretable trait covariances for random effects and build\n", "a model that dissects gene expression variability across environmental and cis and trans genetic effects,\n", "and their interactions (cis GxE, trans GxE).\n", "In the second example we show how to use the fast implementation for a two-random-effect model,\n", "one for genetic effects and the other for residuals.\n", "Such a model is the natural extention to multi-trait analysis of the null model in single-trait GWAS\n", "and it is the first step of any multi-trait GWAS analysis performed in LIMIX.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 1: GxE variance decomposition for Lysine Biosynthesis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indicating with $N$ and $E=2$ respectively the number of samples and the number of environments,\n", "we considered for each gene a model consisting of\n", "an envoronment-specific intercept term,\n", "a random effect for cis genetic effects,\n", "a random effect for trans genetic effects,\n", "and a noise random effect term.\n", "\n", "The model can be written\n", "\\begin{equation}\n", "\\mathbf{Y}=\\mathbf{FWA}+\\mathbf{U}^\\text{(cis)}+\\mathbf{U}^\\text{(trans)}\\boldsymbol{\\Psi}\n", "\\end{equation}\n", "\\begin{equation}\n", "\\mathbf{U}^\\text{(cis)}\\sim\\text{MVN}(\\mathbf{0},\\mathbf{R}^\\text{(cis)},\\mathbf{C}^\\text{(cis)}),\n", "\\mathbf{U}^\\text{(trans)}\\sim\\text{MVN}(\\mathbf{0},\\mathbf{R}^\\text{(trans)},\\mathbf{C}^\\text{(trans)}),\\;\n", "\\boldsymbol{\\Psi}\\sim\\text{MVN}(\\mathbf{0},\\mathbf{I}_N,\\mathbf{C}_n)\n", "\\nonumber\n", "\\end{equation}\n", "where $\\mathbf{R}^\\text{(cis)}$ and $\\mathbf{R}^\\text{(trans)}$ are the local and distal kinships,\n", "built considering all SNPs in cis and trans (i.e., not in cis) respectively.\n", "As in the single-trait analysis, we considered as cis region\n", "the region of 500kb downstream and upstream the gene.\n", "\n", "To dissect persistent and specific variance compoents we considered a 'block+diagonal' form for $C^{(x)}$:\n", "\\begin{equation}\n", "C^{(x)} =\n", "{a^{(x)}}^2\n", "\\left[\n", "\\begin{array}{cc}\n", "1 & 1\\\\\n", "1 & 1\n", "\\end{array}\n", "\\right]\n", "+\n", "\\left[\n", "\\begin{array}{cc}\n", "{c^{(x)}_1}^2 & 0\\\\\n", "0 & {c^{(x)}_2}^2\n", "\\end{array}\n", "\\right]\n", "=\n", "\\left[\n", "\\begin{array}{cc}\n", "{a^{(x)}}^2+{c^{(x)}_1}^2 & {a^{(x)}}^2\\\\\n", "{a^{(x)}}^2 & {a^{(x)}}^2+{c^{(x)}_2}^2\n", "\\end{array}\n", "\\right]\n", "\\end{equation}\n", "Variance of persistent and specific (GxE) effects from term $x$ are ${a^{(x)}}^2$ and $\\frac{1}{2}\\left({c_1^{(x)}}^2+{c_2^{(x)}}^2\\right)$ while the variance explained by pure environmental shift can be calculated as $\\text{var}\\left(\\text{vec}(\\mathbf{FWA})\\right)$." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "running variance decomposition on (gene_ID=='YIL094C')\n", "running variance decomposition on (gene_ID=='YDL182W')\n", "running variance decomposition on (gene_ID=='YDL131W')\n", "running variance decomposition on (gene_ID=='YER052C')\n", "running variance decomposition on (gene_ID=='YBR115C')\n", "running variance decomposition on (gene_ID=='YDR158W')\n", "running variance decomposition on (gene_ID=='YNR050C')\n", "running variance decomposition on (gene_ID=='YJR139C')\n", "running variance decomposition on (gene_ID=='YIR034C')\n", "running variance decomposition on (gene_ID=='YGL202W')\n", "running variance decomposition on (gene_ID=='YDR234W')\n" ] } ], "source": [ "# loop over genes and fit variance component model\n", "var_gene = []\n", "genes_analyzed = []\n", "K_all = dataset.getCovariance(normalize=False)\n", " \n", "for gene_idx,gene in enumerate(lysine_group):\n", " #create a complex query on the gene_ID and environment:\n", " # select (all environments for) the current gene in lysine_group\n", " phenotype_query = \"(gene_ID=='%s')\" % gene\n", " print \"running variance decomposition on %s\" % phenotype_query\n", " data_subsample = dataset.subsample_phenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", " \n", " #get variables we need from data\n", " phenotypes,sample_idx = data_subsample.getPhenotypes(phenotype_query=phenotype_query,\n", " intersection=True,center=False) \n", " assert sample_idx.all()\n", " phenotypes-=phenotypes.values.mean()\n", " phenotypes/=phenotypes.values.std()\n", " if phenotypes.shape[1]==0:#gene not found\n", " continue\n", " #snps = data_subsample.getGenotypes(impute_missing=True)\n", " pos_gene = data_subsample.pheno_reader.get_pos(phenotype_query=phenotype_query)\n", " K_cis = data_subsample.getCovariance(normalize=False,pos_start=pos_gene[\"start\"][0],\n", " pos_end=pos_gene[\"end\"][0],windowsize=5e5)\n", " K_trans = K_all-K_cis\n", " K_cis /= K_cis.diagonal().mean()\n", " K_trans /= K_trans.diagonal().mean()\n", "\n", " # variance component model\n", " vc = var.VarianceDecomposition(phenotypes.values)\n", " vc.addFixedEffect()\n", " vc.addRandomEffect(K=K_cis,trait_covar_type='block_diag')\n", " vc.addRandomEffect(K=K_trans,trait_covar_type='block_diag')\n", " vc.addRandomEffect(is_noise=True,trait_covar_type='block_diag')\n", " vc.optimize()\n", " \n", " # environmental variance component\n", " vEnv = vc.getWeights().var()\n", " # cis and cisGxE variance components\n", " Ccis = vc.getTraitCovar(0)\n", " a2cis = Ccis[0,1]\n", " c2cis = Ccis.diagonal().mean()-a2cis\n", " # trans and cisGxE variance components\n", " Ctrans = vc.getTraitCovar(1)\n", " a2trans = Ctrans[0,1]\n", " c2trans = Ctrans.diagonal().mean()-a2trans\n", " # noise variance components\n", " Cnois = vc.getTraitCovar(2)\n", " vNois = Cnois.diagonal().mean()\n", " \n", " # Append\n", " var_gene.append(sp.array([[vEnv,a2cis,c2cis,a2trans,c2trans,vNois]]))\n", " genes_analyzed.append(gene)\n", "# concatenate in a unique matrix\n", "var_gene = sp.concatenate(var_gene)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KPhSGHo3s51JbRAHZxpFdRxgwwfH9BxWfbGHp+zl4IvXr6y5cWxjAOrAcgt2f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\nE2oqOUV949ixY8yePdvp9XqHAHW+z4f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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#normalize variance component and average\n", "var_gene/=var_gene.sum(1)[:,sp.newaxis]\n", "var_mean = var_gene.mean(0)\n", "labels = ['env','cis','cisGxE','trans','transGxE','noise']\n", "colors = ['Gold','DarkGreen','YellowGreen','DarkBlue','RoyalBlue','Gray']\n", "p=pl.pie(var_mean,labels=labels,autopct='%1.1f%%',colors=colors,shadow=True, startangle=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 2: fast variance decomposition" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example we consider a model with only two random effects: one genetic and a noise term\n", "and show how to perform fast inference to learn the trait covariance matrices. The mathematical tricks used in LIMIX have also been proposed in Rakitsch et al., 2013 and Zhou et al., 2013.\n", "We apply the model to the expression in the glucose condition and for 11 genes of the lysine biosynthesis pathway.\n", "\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#create a complex query on the gene_ID and environment:\n", "# select environment 0 for all genes in lysine_group\n", "phenotype_query = \"(gene_ID in %s) & (environment==0)\" % str(lysine_group)\n", "\n", "data_subsample = dataset.subsample_phenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", "\n", "#get variables we need from data\n", "phenotypes,sample_idx = data_subsample.getPhenotypes(phenotype_query=phenotype_query,\n", " intersection=True) \n", "assert sample_idx.all()\n", "\n", "sample_relatedness = data_subsample.getCovariance()\n", "\n", "#set parameters for the analysis\n", "N, G = phenotypes.shape \n", "\n", "# variance component model\n", "vc = var.VarianceDecomposition(phenotypes.values)\n", "vc.addFixedEffect()\n", "vc.addRandomEffect(K=sample_relatedness,trait_covar_type='lowrank_diag',rank=4)\n", "vc.addRandomEffect(is_noise=True,trait_covar_type='lowrank_diag',rank=4)\n", "vc.optimize()\n", "# retrieve geno and noise covariance matrix\n", "Cg = vc.getTraitCovar(0)\n", "Cn = vc.getTraitCovar(1)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot trait covariance matrices\n", "plt = pl.subplot(1,2,1)\n", "pl.title('Geno trait covariance')\n", "pl.imshow(Cg,vmin=-0.2,vmax=0.8,interpolation='none',cmap=cm.afmhot)\n", "pl.colorbar(ticks=[-0.2,0.,0.4,0.8],orientation='horizontal')\n", "plt.set_xticks([])\n", "plt.set_yticks([])\n", "plt = pl.subplot(1,2,2)\n", "pl.title('Noise trait covariance')\n", "pl.imshow(Cn,vmin=-0.2,vmax=0.8,interpolation='none',cmap=cm.afmhot)\n", "pl.colorbar(ticks=[-0.2,0.,0.4,0.8],orientation='horizontal')\n", "plt.set_xticks([])\n", "plt.set_yticks([])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multi Trait GWAS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The genetic model considered by LIMIX for multivariate GWAS consists of\n", "fixed effects for covariates,\n", "a fixed effect for the SNP being tested,\n", "a random effect for the polygenic effect\n", "and a noisy random effect term.\n", "\n", "The model can be written\n", "\\begin{equation}\n", "\\mathbf{Y}=\n", "\\sum_i\\mathbf{F}_i\\mathbf{W}_i\\mathbf{A}^\\text{(cov)}_i\n", "+\\mathbf{XBA}_1^\\text{(snp)}+\\mathbf{G}+\\boldsymbol{\\Psi},\\;\\;\\;\\;\\;\n", "\\mathbf{G}\\sim\\text{MVN}(\\mathbf{0},\\mathbf{K},\\mathbf{C}_g),\\;\n", "\\boldsymbol{\\Psi}\\sim\\text{MVN}(\\mathbf{0},\\mathbf{I}_N,\\mathbf{C}_n),\n", "\\end{equation}\n", "where\n", "\\begin{eqnarray}\n", "\\mathbf{Y} &=& \\text{matrix-variate phenotype} \\in \\mathcal{R}^{N,P} \\\\\n", "\\mathbf{F_i} &=& \\text{sample design for covariates} \\in \\mathcal{R}^{N,K} \\\\\n", "\\mathbf{W_i} &=& \\text{effect size matrix of covariates} \\in \\mathcal{R}^{K,L} \\\\\n", "\\mathbf{A_i}^\\text{(cov)} &=& \\text{trait design for the fixed effect} \\in \\mathcal{R}^{L,P} \\\\\n", "\\mathbf{X} &=& \\text{genetic profile of the SNP} \\in \\mathcal{R}^{N,1} \\\\\n", "\\mathbf{B} &=& \\text{effect sizes of the SNP} \\in \\mathcal{R}^{1,M} \\\\\n", "\\mathbf{A}_1^\\text{(snp)} &=& \\text{trait design for the fixed effect} \\in \\mathcal{R}^{M,P} \\\\\n", "\\mathbf{K} &=& \\text{sample relatedeness matrix} \\in \\mathcal{R}^{N,N} \\\\\n", "\\mathbf{C}_g &=& \\text{genetic trait covariance matrix} \\in \\mathcal{R}^{P,P} \\\\\n", "\\mathbf{I}_N &=& \\text{sample noise matrix} \\in \\mathcal{R}^{N,N} \\\\\n", "\\mathbf{C}_n &=& \\text{noise trait covariance matrix} \\in \\mathcal{R}^{P,P}\n", "\\end{eqnarray}\n", "\n", "Prior to any multi-trait GWAS analysis,\n", "LIMIX learns the trait covariates matrices on the mixed model without the fixed effect from the SNP.\n", "However, LIMIX allows the user to set refitting of the signal-to-noise ratio $\\delta$ SNP-by-SNP during the GWAS\n", "as in single-trait analysis.\n", "\n", "In general, LIMIX tests for particular trait designs of the fixed effect\n", "$\\mathbf{A}_1^\\text{(snp)}\\neq\\mathbf{A}_0^\\text{(snp)}$.\n", "As shown extensively below, specifying opportunately $\\mathbf{A}_1^\\text{(snp)}$ and $\\mathbf{A}_0^\\text{(snp)}$\n", "different biological hypothesis can be tested.\n", "\n", "An alternative efficient implement of multi trait GWAS is available in GEMMA (Zhou et al., 2013), however LIMIX permits more flexible models to be constructed and enables automated regularization of trait covariances (see below).\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Any effect test" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Association between any of the phenotypes and the genetic marker can be tested by setting\n", "\\begin{equation}\n", "\\mathbf{A}_1^\\text{(snp)} = \\mathbf{I}_P,\\;\\;\\;\n", "\\mathbf{A}_0^\\text{(snp)} = \\mathbf{0}\n", "\\end{equation}\n", "This is a $P$ degrees of freedom test.\n", "\n", "In this context, multi-trait modelling is considered just to empower detection\n", "of genetic loci while there is no interest in the specific design of the association." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example: any effect test for gene YJR139C across environments" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we test for genetic effects on expression of one gene\n", "either in environment 0 or in environment 1.\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ".. Training the backgrond covariance with a GP model\n", "Background model trained in 0.04 s\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/limix-0.7.9-py2.7-macosx-10.8-x86_64.egg/limix/modules/qtl.py:262: FutureWarning: comparison to `None` will result in an elementwise object comparison in the future.\n", " if K1r==None:\n" ] } ], "source": [ "# Get data\n", "# select all environmens for gene YJR139C in lysine_group\n", "phenotype_query = \"(gene_ID == 'YJR139C')\"\n", "\n", "data_subsample = dataset.subsample_phenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", "\n", "#get variables we need from data\n", "snps = data_subsample.getGenotypes(impute_missing=True)\n", "phenotypes,sample_idx = data_subsample.getPhenotypes(phenotype_query=phenotype_query,\n", " intersection=True) \n", "assert sample_idx.all()\n", "\n", "sample_relatedness = data_subsample.getCovariance()\n", "\n", "#set parameters for the analysis\n", "N, P = phenotypes.shape \n", "\n", "covs = None #covariates\n", "Acovs = None #the design matrix for the covariates \n", "Asnps = sp.eye(P) #the design matrix for the SNPs\n", "K1r = sample_relatedness #the first sample-sample covariance matrix (non-noise)\n", "K2r = sp.eye(N) #the second sample-sample covariance matrix (noise)\n", "K1c = None #the first phenotype-phenotype covariance matrix (non-noise)\n", "K2c = None #the second phenotype-phenotype covariance matrix (noise)\n", "covar_type = 'freeform' #the type of the trait/trait covariance to be estimated \n", "searchDelta = False #specify if delta should be optimized for each SNP\n", "test=\"lrt\" #specify type of statistical test\n", "\n", "# Running the analysis\n", "# when cov are not set (None), LIMIX considers an intercept (covs=SP.ones((N,1)))\n", "lmm, pvalues = qtl.test_lmm_kronecker(snps,phenotypes.values,covs=covs,Acovs=Acovs,\n", " Asnps=Asnps,K1r=K1r,trait_covar_type=covar_type)\n", "\n", "#convert P-values to a DataFrame for nice output writing:\n", "pvalues = pd.DataFrame(data=pvalues.T,index=data_subsample.geno_ID,columns=['YJR139C'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "REMARKS:\n", "- kronecker_lmm always considers Asnp0=0\n", "thus only Asnp1 needs to be specified\n", "- if trait covariance matrices (arguments K1c and K2c are not specified)\n", "kronecker_lmm implements the variance decomposition module to estimate them.\n", "In this case, the user can specify the trait covariance model to considered (covar_type and rank)." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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U/cGhzTh/PuK9cSO9Jx4vuJzOIfX++/esdL8U1eebTqW+diel9uLF6DAATExM\nNNVAoN9vZYs1UKl492if7mEPRbuF3JOTrnwspqa8XiXzwAO+WCSSU/x+W0FVS3XrV/19PmnFTq+x\n5YXfd/D//alWo4Jxr+GNhMYB3AWRBeSECHpcG+vRiGq3rkyEZYjAp8/UadHcTuWkHw7q6qCiqTI5\nIPatOABdDnMnWkw3HDxaKmL5b+Pomxnlyt28IwCijfOZQ4cAHH/jjegYANQLfgzEBWAskSjYo1HV\nxgX9GpFpQRtax10A7OjqbJKh8enpmLNRD47Xa1UnJhwpuz1fOHx4ONr93p6aPcA7OP/Uq+R1pydo\nZibhvHkz49HuJwMB+wC08OsnuwlpFZuyayhfLzvZ29P5oPSuu0ZiimIq6INMiIY/RCI5JRLJKe3c\n/0+dCsSuXIlHrNah3NGjnujISC8zARqm/jf4u3HJwDYWyyuRSC6j/+534bXNBdEQbobIVghDnAfk\nuJ40ulxPM0Tg0/0out4FsPz79wHIAHil82Vp3hYtEDXGLm2YoQ0A0ltf2IPLQOgKgHXxmliqvHY3\ncuPL73MnxPiifppR7jaIE0B0qycCOHzlSmzPffeN3OpwmfrBLQDZYnEdw8NKzbz4XuuPljoREGv3\noc0iKReHjGs/uzA4VDTiXLmS2AMA9Sp0+oC92TSc6emYs9FrtmgMgBdizY8dGsxKXPW+Wq+XocP7\ntBOiwUfSfbedTm/rdFAaTE5MnCv3vi0tZct1qkDArk5Px5xXriT2JJMFSzSaj8rjYKfb/uzZsDeT\nWbcPDZksCwsZt6KYN4zX7n1KaWgc4jvfos7Q7PMGz1/91fUDmUxR+bEfm5oLh7MdH4PT5nNnE5rO\nYLoFcR6+ASAGcY1KodJgne/2926IwAfoRWWk1hcVckMEPe/THgMIasFPcFkXLHU9FaVR17q4384d\nL/gWEApr93WftROpZ+XX1OeJuiAOtGH0dEa5DcYgxj3ZsfVkD34A/kSiYF9YSDshThZG5gLgu3o1\nNmIymda3O9NRp/VZS52zqiFBXuyaTFkNjUNs91udvOjUC3hqNcLISqJ8vLMLeDmn3AEgpkt10/7e\nztmjupNSe/jwcHpuLhWX96v/Xm+8jnxca6xP5/fpYFLr6QHKLbsyON/JtuqfQFRO3FGvVT+ZLFgS\nCdW6upq3h8PZtPzbTrd9Nls053LrQ06tWXJuLunM5Uo2+ffeBT8hNyoTFgB1xzuHxiHSn6yNn9c/\nmh0T981GLks4AAAgAElEQVRvLkxcvhyfUNWS5eWXV1JHj3o6Wg9p77mzGS1nMC1iQ69O+dolzwld\nZZjAp/tq5o7vQXkWM9Q4MFoNeHp9ci9f0Nc2/q6p/63zWTv2WaziFgLEgXQTImBY7IeLoyaL5id7\nWB0ZseU6XJ5+cQDAe1ZW1PFSKW574YXlyCc/eeAm0C8TCvSL4Ky2f8tgeA8q6Z15bFgUrpFyzvUw\nAC8QutriGhrLQAhHjgyvbecCu9X4Bq11vF0zHmXQlQtrd84xd989kqj1+0apNVLvei2Dy6isb9fO\n9GY/EIo17jXqdFAaGn/99TW/9qA8eYc+yLTZTPmREWfW41EK7Vp/7fDh4fT166nU3r321P79rrhM\ndbtyJWHb6n+7RO5/0QaNxCOoLMRc53nds1WPSSvjslKpgiWbXbcXi+um+fmk+/z5iPeBB3ybevu6\nYfuTVzVV/3Sg4eQE1VlDcs2e8hTWutfvTmMcwMBnm2q2AMp8xdchtmum0tuzrfdoaxdwIGBXZctU\nawfehp3yGBCKoP8WTdTnimLnAyY7oVxpxdbpHcFXgBA+8IHRozIA6H87CtJXACy5XOas16uk3G5L\nuYXaGAOA26mc3ran6g+ttqTbIXpFI5v/1Mx3GVw+duxCW1sVjx3zpqPRvGKxmOwul1La2XSvtXrY\na523m7nYBpPaDGQAgvPbL9PObBW4xGL58oKx9VJr9L/rbqNCUzOituIogAkA8yKoatSo2NFrgCsW\nU22AWJgUqJy35ueTzni8YF1fhwko5D0eBfrFTnf6xnfdNRIDxHii6tfrbaqbvsF0y22fh2ic7OmE\nLO3oMdGfr8bG7FmPxxKLRrP2eLww/NxzN+9YWEjfPHEisAa0/5jTl1d/f/uTV23Zyy0DFy8AdYvA\nSqa6+iHqxlkgFIDoIEhrjSIu7KgxrjUDt47PTtYx2JnQeCWncdPf3BBdtn6IHWERwFr952/5Xvqu\n4rbMgBMOZxVVLVnkibfF8owD+CiAR8UtdE87yqS99g7XxShvKz82pJDJdTf6SXC2+Zz24CsDFvTU\nmJ+/WcFZAM/cdZf32smTvvnHH58qj8n40peuHvvSl64ea1tRDUG/phiA8joa5b9tJQVxATJD9Ijo\ndGftq1RKNSmKqVBrccftTGleW3C5cYWq3PN1HMCd9T9v6BDEtMu3o8drztRbr0OumfTii8tj3/rW\n4lSt/52ejjnPng175TW0N2v6tGX/cqGyZIJji+d22q19+xyJffscier0w+XlrOP69ZQrkVCtxSLM\nW73Qc88t+J97bsG/1fMA8X0riqlQfQwdO+ZN9358T0t6kuq0HfW2OVAJMC5fjnsuX457isWS5cgR\n76rP50jm8yVrIlFwrK2p9k6Wr953H4vlFXRmJsVb2HL8ZDCJyoxtsmwOiEaL27SfXZ/OeqACnx6e\nrGU+40Fxf9NipmMQX+IkAB9Ea+pOd/I0KjuMa/tBVFsFAOxHywdRveCmbRfBvRAXQW93JlDojt4F\n+VvZ9H26ICqPx1E+iYU+LG7Nvh4UVS3Z5uZSe2TKwRe+MH3s0qXYwUuXYge/8IXpngc//fV91Azs\nXU3u/2MQF58h1K44OtGhKYfD4axy+XLcc+tWzr2ykqt5Hq8XFG2Pfl9tZhHquu7Qbn3rmWcWpmZn\nk7ddvBg78PTTswf1f5uejjnPn18LvPFGdOzcucjogC8o64KYHSoNkVmxRW+B3AdabWRr5vnB5IkT\n/siJE/5IIGBXz54Ne2dmEs5USjU5HJaizWZeTybVIbfbovr9troLYD733IL/1VfXJl99dW2ymeAn\nHM4qs7PJ4dnZ5HA7z0mVtKidaPq6nkbX1vhr7Ngxb3pszJYcG7MlawUP4XBWmZ6OOZttPL7rrpHY\n/fePLD3++OS7ExPWiNdrjv/QDwWWBmeh7WbOlc2eT4PLEAtvXwUwDaCk3RIQY7Blj+0lAG+L53W2\n0XqgAp962lshafbkuGFsTwpiTE8JQEG7aV9oK6+54bXXIHYWYEPQtT07W3m4vOOmALgBHGn+83S8\nBTkFMd4hjq6cRNvRQ9XM/4fc/bHKerWavTuBjbfQh1HpHWwy+MEdN29mRufnM6OvvLLik780m4dK\nZvNQST7uVfARDmeVj370zKc++tEzn9rp+09Px5wyuNu58rkiD9HzeV8TvRIpiClFl8St5iLMXV9r\nJRzOKufOrfiuXUt56wVFFc0cR7XOPfqAsemLrb/qVv0+J8Wt87ba/6uPF71MpmDOZotmAPD5bNu4\nHmz33Ne24FO6BbFMwg2IWTsblKl8vrpT+9nkdaj565bshXvuuQX/yy9H9r7xRnRsYSHtdDotRafT\nUlCUoVI0Klr721XpnZlJOK9cSYxeuZIYnZlJtC0rRJcW1cL1fVu9/O3YD9pCBjUul1KqlWIrt8vK\nSs7xgx+s+C5dinqrX0PWr44e9cSPHvXEJybsmccfn1qZmnKm/X5H3u935OXzuvW5JG1B3e3Uje7W\nbg00yqypPu7LQ0I8EA3VaWw47waXtayYju8PAxX41OpqrNcLtL2Wi3onu+AyxJoD12rki++BqEjc\ngEhxW9HdoAUrsqKoC1xC46KC0mjxTQAtdANudVGslybRpAxEK5sZotfn4DZfRyeYhKiw7WA6w2AS\nlZaEDk9bvdMgrjtpRB3mQiUNU+6bMl1hm1NRB5MA5kZHrbHRUWtyfFwssvi5z91/4f3vH51+//tH\npz/3ufsv6I/16emYs9a+Xu8Y2GnA9NhjZ36iVMK+Ugn7HnvszE9s93Wmp2PO119f87/++pq/zcGP\nC8ADAO6BaJho0EhSrvCfr5F66UJ5opD2pyAEAnb16FFP/MiR4bWjRz1x/fkoEskp0WjBtrSUdS0s\npBv0mJePo6nNn3NTSvIWQVzTF9sIao+HOgngQ+LW2eBH7v/nzq34zp4Nb6p8/dIv3X316NHhuaNH\nh+d+6Zfuvqr/m89nU/futactFhTNZhTltaC1oGc7565GweeOKs3vAHgXW1foXBBpiscgsjE6IhzO\nKrGY6kilCtZstmiemnKmjxwZXhsdVdJjY/as221peG58/PGplfe9b8/i0aPDYTkIvtZ7bDyHyYbz\nXqlbX2q2J6Dn6ejT0zHnN74xP/nSS+GAlhK24W/6c/TiYtq5vJxz3byZddUKNvXHUySSU86eDXsX\nFtLOPXtsWbvdXKh+/W6QdWa0VMcKubUGyx2c1xqdowE0P8lTq+87rqtb120AHKjJDX75l1+9/yd/\n8vAsIE4C9U7a2x/QBaBykdQvhKn16tR9HRdEr4OK8uqzZSMQqVh7ANzSDeR6L0TvyUztgVzlHUdB\nuYW2fpd+ZweCh9wQs6TNQqzP08JAxEaz6pTHRkFslx0FP9v435YH2VZNotCW16yjsj5EL1qJGgQJ\nKVTWIZL7+S2I/V+uKfNq5enB7zb3jsFXFOV/5EqldRw44E7LxTE/97n7L1Q/c34+6QRMJVUtbdg+\n9Y6BRr/Xv243tvMrr6z4ZmdTI3v3OjLtm7ksNA5xjnEBaHJWp+pzSbniov9+tRTb9g48rjfJis9n\nUy0WrA8NldaHhy3FLV5GtzaMPHfICVgAVGZ3rKOV41RMNqK5iM0DeTtSodbPMhUOZ5VIJKfMzyed\n8/OZ4Xi8YB0Zsar6tJzp6Zjz/e/3rwJinZfDh4fT+m2cTBaUQgHmtTXVudXisw04IRqrdjhZwU7X\n12l6prgARMOjApHW2WQFsPXZ4CYnnelUqmCZnHQkTp0KxMLhrHLkiDc1P590ms2mgs9na3h+eeAB\nX0w27EQiOcXns6n1zmGHDw+nV1fzq/J+M+XbygsvLPtTqYIFbemF6bfxtZuFw1nl+98Pj09PJ8cc\nDnPe61XysjFGP9nBkSNYm5iwZ157regFALvdXPfcJFN5L12Kj6TTBWV83J52OIayIyOO9clJV74T\ni3M3mqREju2GmPF2i5ndyhO9KBANaOOoW9fbcg0fF0TvuAdi6QVZv7uFSh1bm5m0bYvZyyEpU6jM\nfFpzTPVA9ficORN+oHqgc70UrvYN6GqmVaN8gdWtQLvhixyG2BFGIfLr5Uq2w6iZYx9yo1LJHkEL\nCxM+/fQ7d3ZwPMQsRCvbKsozeTSjbsuOHBt1m3YfWmvDoZ2k9W0/DWbL51shvpM66/Bs9Zqtde/v\nsIeurJneDv1z9D0rmz9HMAmR9qjvXXNBrF11PyrH3KsQMy41+T2GfnR5OTc2N5ea/MM/nLn7ypXE\nnuoeEV3rFQqFkqXZFrSnn549+Od/fu2g/vn61vNz5yKjW6UUPv/8I39hMuG6yYTrzz//yF8095k2\nOns27F1dzbuz2YJVVYvrIyNWtbLd6w6s32JfLk/uoUD0SLwL4EprwcqG3mtAfL8qRKXx4M6OxY1k\nhaLW9wsAbrdFHRtzZDyeRivR1xwwC1TSKDzY2BtZVTGsPk4bTlxzj9biOafdqo/vFWzq5d85/XY6\nezbslak2mUzR5PUqOaezdmC4vJy1v/baqu/ixehIrX06my1akkm15n7eOAUzmITYx5woV6KArVt2\n253S1EovkRg7CBGoeVHJzmhSaz0Si4tpZzpdsGipRQDK9RC4XErp8uW4p5le3lgsr6ys5BqmOQcC\ndvXECd/qiRO+1XZcI77+9bm9L7+8uv+tt+KT2DK9SeqfdLXtcrkshZWVtG1pKeWYmnJWNxRYksmC\nBRCNNfn8ujWRyCkOx1C22QWZAeDIEU9cPw19o+Psy1+e2fflL8/sa/a1ZaB1+XLcs7MU7HLQcBTA\nhyEaMRMA3sWm2Ymrx7xvei19XcmBcvZA+VwRg0i17pmB6vEpFDBksw3la+Ulb2+q5pq20XoSTGLT\nnORlfoiKiRmVACYF0VXvQznHfsPJXFZAVIiT9pYCAbv6hS9MH7t8ObHfZDLhP/7HC4Vf/dV7L7X+\nWWoJJoHQGERwYkPNi0c5WGul5yYF0VJtBfC29hr3ab8Lo7mFsWqVo3rK2jb1wsiLPmrMi1/+/PXK\n1OL7h9z61qHtTj3bTE9g9XO24ccAnIQ4n9yASD28DyLFZAUIvdauXgOfz6aqaikdi+UVv9+24TxQ\n6/7v//7l219+eeWOXK6oAIB+IblLl2KepaWMc2zMno3F8oWJCXvd2cQCAbv67W8/8vXq92mVw2Ep\nTEw4Unv3OtKqWrKcO7fiSSaLFoiK40KNfaqZVnEnKov13oBoVWtCvX22fD4LNPc67TU0hFL1d1vD\nn0E03H1Md4zLlGOgPD31lq32Yyh/zurzTegeAD8LsW2fB3BZ+0MaQF7XC/ROs5+tFcvLWTsAjI3Z\nkrFYXrlxI+3yeJTc1JQ1Vt3bI62t5WyxWN5hs5nX5+dTWf0+PTnpTCcSBWV4WMnL3gd9Bez8+TW5\nHWr08pWDCCtEqvPHgNAtAC9BXOO0NaRq9dzX2vb670a+ft3GJEmmYULbP+X9Ou8BoBKMOrRyHgTw\nVp3nbtvMTML52murY4lEwVUsAiMjVlXfwxOP55VCQczs1miqcdnrcujQcDoWyyuplGqKRHJqrcVR\neztIvtnrfduuvW2nLfFhSSaLzqGh4vp3vrM0ubCQdh4/LqYJN5tRGB5WCgDw9ttR7/x82qOqJmuh\nsD40PR1z6nvk9K8JIO732zLRaF6Rx6k8ziKRnFJv2uwvf3lm34svhssTqPzUTx3ecur8SCRXnsI+\nEsltOmfqHrcSnJq0n9cAvNHk/9SyAnHcWbC5ztimhYw3SQH4e2yRpj1Qgc+BA9brJ0/6l/VBztmz\nYe+3v710m6KY1h98cOxWJJLLANsd0FUdwJSj2bXK76QNlRIXaqdsjQE4BNH1VoJokT0A0fOzCmAe\noudkHJUIWUVl8VMZGDhRmeigoWJx3WQymbZ+4vZYUFmcVbfg2IYVmKObK3B1HQBwGOLguKb9zgNR\n0WjTwVCv8thqKkMwicoK5EBlZqGq96gOVDftJ01crMX/nDu34hsdtWUOHx5OX74c92h/jHfigheL\n5ZV4PK8oikjJkD8bpGDqP4MNohJagthHxiC6ybVevGbGigSf/cAHvvaPAeAjH5lYBmqvpSA/e63G\nj1rBYSZTtFy8mJ4AYD5yZF1WihGJ5JRYTLWtr8M8NGRab6KijW9+c2ECaO6CVIu+lVB+pwsLWdeX\nvvTO/QB+C6KS3ep+74KYEnQcNceg1FMe9D2CSu+J7txVax2cnau33gQgvpN4vNDEIqyhMwDerz34\nGyD0cVSOP22FcKB+ZXpDpbtRgPdDENNd2yFSPi5DNFbJ1DYrNgSZcrxU65U9mcqmr0zdvJl2AsBD\nDwXUt9+OOm/dytqcTkuxXtAzN5d0AoDfb884neb86Kg1q68ki2ujOI1EIjlFXwlT1eJ6IqHKbV/v\neE1DBA8/DNGwkYfYh17DtmboKgesdYL78j4qW45NEJWpRqnGWl6/HLcVOghxXopj04CYrdJ1tkzn\nKYvF8kout27O50tD2WyhXK/yeq2q12tVUynVVCiUNvQGVXvuuQX/5cuJQC5XNMfj+fjYmCO/vg6T\n05krRqN5pTp1sZFWG8rk0gmpVMHyzW8uX2z87PL3cjsACxC6WGOsIBp/t72j7xmJRHLu9fWSNZ1W\nh15/fW1/OJwfmZlJRg8edCccDksJKJnefHPNl0oVLC6XJed0QnW7rcWVlZxDSyHblDot10yUx6ku\n3QyplGq6dCk2ks0WzWNjtg3bI5UqWPL5dUXeb+az+Hw2dXQ0l5X3az1HlG+rbV8+36cgjpVRiN6e\nGt/rVteG8vlVgagPaBlPG/6vTb2/5feTvVCAGBbScNmQgQp8Dh70RN99N+lVFPOQxZIoms2mwtmz\nkcm33oruM5tNhaEhU+nUqUDY67XKlJgWu2DLXXTQTqByrYB51F60Uw6cHYdI14pCdOPJ95QDvoe0\nnwcgLhp+iMH430blJC7T2vLaa9yC+CL3AshBVCLrfpZwOKv8yI9MLl6/nvQpypD6cz93Z7tbIW9B\nVCq07k995QIjEKkErY60dEB0qcrPnoJIp4sDuLm9Cld1QNMoLWJbeeVAecXpujmz2uD/UFPBah1+\nmcsvLqolG7C5VSccziozMwlnvcpQs6u1x+N5ZXEx40omi5bJSUdGu0DXe75f+5nXgrlXIFqBVQDP\nQHyP70LsD8tosgfiX/7Lo+/K+2fPhr1nz4a9tVIKGvVaVa9c/73vLe6DqO2Z3nzz1l7g7vKYofFx\nezaZLBT273cmthrv8OUvz+x7/vmbd8nH9YKfrSoc+s8zM5Mo/PEfv/OeVAr7Ic41/wXAT1f9Sx7N\n9aLK1KcmLnKb7INI39RP3IJ2j+2RZGWgVr57vRSuGqpbd6rHZm5R4Sr/LtngIj4HcU63ALgAsX87\nIAKhEYhxj2sbL7KtV/bkbHYzM0nv2Jg9+eijE7fefjvqTSaLzny+OPTMMwtTExPO/Pp6yZLNFk21\nKjjT0zFnLley7dljy9lspsTJk/5I9T6ttTxDVtpSKbW8DaemnOmlpYwMeGocr+UgQrbeynWgvBDX\nthjan/IkJ1KZggg21za+T3WAGToEMaW+HQg5IdJp/Nr/5ADMiet4yA1xbfVBLKaIGj1cuvECoRub\n0302OnDAnb79dnc0Gs1n77tvT1hue9lIe+pUIN1MMJLLFS25XNHsdFoKbrdFjccL1mSyYBGL+mY3\nXF+bGOOMZp4vPfzw+Ir4v6vNjLvwAziCcov+VovIVutNT5B+2yiKqfDAA6PhpaWMK5k029xupdxo\n6XZbVI9HKSwvZ6w3b2ZdAHD4sHttasqZHhmxqqoqUq3lRFvhcFb54hcvHwGAxx6bvPH22zHZOLKk\nP14XFtLO5eWMO59ft168GB3RB7Of+tSBG8mkaPj51KcOlBvpGpE9TLr7O5GCON5k5sa12k/bMB60\n0d8BEfwA5caUTQ0b2N4+UH2ebc1ABT7PP79yzy/+4h1nwuGsDRApEclk3loqlcwmE4pDQ6bi4mLa\nubiYxkc+MlFrmla00ooDEfRMAChpG7d6ggEnxGDacYiotrrin4IIcAoQF4nbIYIfL8SsFh5ULtQu\niEqOR/e/CsQFvqkxPouLaeeBA56Yw2FWZ2YSzkDA3nQe6taCSSD0hlZOeZPbN43K5A6tzKwWgahY\nrKMyKURq42ts5+DQP7ccCG1jhqqa751COTjGmKj461syyhdrQPSKVbVyNEqJ21BmNZcrIpUyWfbs\nUTA6at3UqiMrTM8+u3jIarXkf/ZnD1+UlUqg9RNhKlVU0umMWVxwRZpFjafJHgb9hdUDkQq0gvJ3\nF5L7b7rVdMOzZ8PeN96IjmUyBUssllf0C5o2UmvlerN5aN1kggpgyGqtzKx07Jg3HY3mFZvNpDQz\nOPjGjbQ7kSi45P1az5HfBwAcOjQcf+WVFZ/LZSnUWog2HM4qq6s5Rz4PCypjLXUzP23oRdzq2I9A\nHH8RNJ3mFkxqgbkXYn91AKG09v9NV9xlCofcL5vZ5/Qr24+O2jIyGJSVRdlz0cC/BfAnuvvAtsdz\nNpy45jWIijQAfEf76YNorBmH2E43UbtByg+x/zfcfrLh4ty51bG5uaR/fNwRPXDAlZyacqadzmiu\nUCja5+YS3mSykLvjDk98/35nQv5frW09Pm7PHjkyvFYvkNdSRS2ASMeKxfI52QvxxS9ee1x7Wo1G\ntvIirgBwDmKfdUI0VJlRTi1sVcOedznRxrD2XiaUzyc1nw+IoNSNynVUrhfytghQQ26Iqa0PauXW\nxhrIRbk3NHDeBeAjAG4CoZVGrcg+n009fNgdTyYLmQMH3Glgw8DyhpMxSQ884IstLGQiAPDgg4Gw\nz2dTZ2YSzlgsr7z4Ynjy+98P49Ofvv0d+ZrA1sdbJJJTWnl+c4JJIHQTosLtQd01C+t9t/3RE6Sd\ns+JPPHHbO16vVY3F8koyWVCOHx+J+Xw2NRLJKamUaspmixZANA7Ic5V23lPkmj5PPz178M03o4cA\nIBLJ2R0OZQgAbrvNET92zFu+fi0upqzDw0o+k1nfVJ5IJKc89NDYUis9e0BHUh4bpAxVZwo0Ss+u\nTj3e9Do73Qd0jV2tZSgMVOADQJmejnpPnQosqWpJcTotxXvv3bNstVqKIyNK/sABV/LVV1cnAWD/\nfld887/ru8NkK8+mrvGxyuOQE+LEKQOgd6tah2SPjxniS57D5opHGqKnRLYUXoP4wq9AtIbL9Cd9\nC7ucSlYeMLFmvkyz2VS4cCE8arEMlR55ZKzcIr3divBmG3L/A7pt+CGIi80FbAyItpKGmFbXBZH6\nhxoH0X3a/Td2eILUpuht9iALjUMc3Ok6KXJybIB+O8gKcdWsZ5veb4uyiHz6XK6omEwYcrmUkt9v\ny1TnFEciOeXMmaWp69fT44oyVHjmmYUYgIWVlZxDn1Kx1RifQMCujo7aMrlcbNRkwtDKStYajar2\nZ599634g9F+A4L/VPd0F8Z3cCeA8RI6/HFh/rSrNU2tkKHd7AzVnMKwQ08LmlUymYFlayrhUdX1d\nXpS8XqsqZ0uq/iyBgF2dmUkULBZTQf/Zv/a1R8/8xE/83VCxuD70pS996Lv6tIRCoWTJ5Uo2fUph\nvWPk0UcnFufmUj55v9ZzZmYSzvn5zHAmU7C89FJ4bHEx61cUUxEQqSTV5V5ezjpOntyz+L3vrdkg\nKpC/Wm+7aNuuuoV7HMDHIHqFzwN4s/UGgtAKyt9Ta557bsE/P5/xlEow5XIFHDrkTsmFHLf630az\nk+VyJduf/dnc5NiYLVHn3x0A/hzi3HsY4jwpGyMOQgQnGQAXG2+PciUYdfZLF8R5WrsfnNXOf6MQ\n2xwQOfC6CnH5GnIAojehbku4DACvX095wuGMM5EoOCyWXG5hIe18+OHxlXvvHVn+/vfDk9msyf3q\nq8u+paW047HH7l+s1bPp89lUmy2Z83pr9/xK+ul2V1ZyjlyuZFtdzVl++Zff+geoNMj8ve7z1RLR\nnnMMlYCkAf01tpaGjVwqxPaNaO+lawSofn75mn0QlQbDOESjQEo7XrQJO1CACIjmtd/9kPaa0AU/\nd0P0aowDeBh1ZojSW1+HSVuDalvX2hMn/GtApSHB5VJKf/u3N277wQ9WDg8NmUoOh1l94ol9DTMJ\nqo+/paXspnpevXPoCy8s+wHsBYJbpfPegqjUuiB60+qQjV4bsiOamB21M6q3jaqWLC6XUhoZEdcM\nefzIoLVYLFmcTrPqcJgL8jmA+H5mZxOexcW0U1H2FAAglyuWJwsrlTYeE/J9ZSNeMllQHn54fEWm\nnAKVMXYjI9a2TGrUunI6f7tmqUxBjPdFh4JbWf+OAki20uM4UIHP3r1Dq++8E9+7Z48t+/DD47cA\n4IMf9MdPnsxFADFV7De+sfx+ANi3z7la52XughiTENZ1jUOX36ilt4WcWre4EyKNxw1xstSfENIQ\nFXbZUvpWjS/4Tu1/ZZffC9r7z2HzLEBh3fNuQZwgFrf6QuUF9Nlnb9weiaiTJhNK/+t/vRs7dSrw\nqmiFjowCwOioNVsvJWr7QichZvPyQGzLWSD0reZ2wuCstt39EGkI1dvuIMSFBxAXr1rphh1QTt+T\nPTf5GsFP1diADS0dVeMlNpEpAudQO0h0AZhIpYpWm81cs7U/HM4qKys5BwCsrxcLijKUdzjMBXEy\nzrgmJ53JiQl7RoxlEUFDrdcAxElZBBtFZX0d5mw2ZXruucUjsRhuA+DRKm+/riv7KYhWH9lzuYDG\nLe4+VFoGVdT5HuV+7HIppXS6gGRSNQPwfOMbNxwWi9k0OmrNXLkS9yQSqs3vt2cefXTilj6QcbmU\nUqFQ2rDO1/R0zPnUU+95w+u1qvIio+81SyYLlkymYFtczLhWV/PJerMkHT48nP7oR/dek/drlX9k\nxKouL6ftuVzRnEyqlrW1nMdmM+dv3cra9SkWsgx33eVdvXgx6vvwh0evffe7q/9146ttStmU4+jS\nupFQQC0AACAASURBVFa2BwH8KMTxMw5REanatlv1tJWPQVQqpiFAzNKXgUhjrCH0E888s3BoZMSm\nJhKqxWo1o1iEMjpqy2zV0ywD7Xi8YK2V2vbaa6u+d99NToTDWa84v2xKM3oVIj1vCpWedBPEMeXT\nHsugqVGKkpxVssZ+WW7EiEBsh1va71SI6+ZeiPTC0Ropr05UzgU3sMX0/9pMdul4vOBZXy+ZlpYy\nrsuX4/njx0diS0sZ97PPzk8mk+veoaGs9emnZw+ePOlfXV3N2+NxMWOYz2dTL1+Oe3K5kq1QKJXq\nDbyW5O9XVnKOZLJgGRoSg+4b0+8nuAXR+OGHyFLYasyN7hpbL/gpnz8fAUJJiB5k/Ri0mPY+1krW\nRnlcrT5oTUNcp8cgvlfZ4nwQImDV0joxB2BW+1wnUTnX+7SyHNA+m0l7nZazJ5pNM65+zvnzEW8q\npZq0HjklEsnak8mivVTC0I0bqWE5YUWj16zXwAXUn/BGjjECcFz0/tZM79eLALgOLdWqtnLjgg8I\nzULsOyMoV1jbWSHecszWpgmD5ueTzni8YL16Ne6Jxws2OVW1PMd7PFb18OHhqMejbJiOPBLJKTdv\nZp3JZMHqdifzx49716anY7eWl5Num81cvPPO4TVApEBWl0IGP/ops/Vj7Botc9C+RuyGiqg0vld9\nP+VMgTp1nGbHTrc6xnoTF0T9YxjAJDZNqtJ4XxiowKdUWi/lcnBdv57xpVJqeaEveZJ/8snvfxJi\nY+D3fu/dj9S4IB0AcAfEiUwetNXrXsjeHbv2xagQ6WhFiLQGfY/OStX96krqQVSmazZpr7MCsVI4\ntLKGURkQ/16Ii8k5bJzBpt5YkrJYLK8Ui4DJhNLQ0FAJMJllGsX8fNqztpazO52W7MGD4kDcfvCz\nIa0rBbG95OQOVq38GSD0bJM79C2I7XCvljamvzCmsTGdbpu2dZDJ91MhPteIaA2RB1J11+qGvNZG\nQc/7ADwEkd6X2XzAltmBEoaHFdViMRVUtWSRLXdy8OT162n36Kg973AkM4piymYyRcvf/M2N281m\nc8njseYikZwyO5vwJJMFxe+3RfQn/JmZhLNQECkQMzOJQrFYsths5nWgtF4olEzr63Wnus+gPKsV\nhiC+bzsqMxXKSnoKlf08BbFvjwGYAELX6m2fWCyvXL+edivKkMlqNZvy+fUhh8OMfL5oWVpKu+bn\n112xWGF4eFjJjIwoueo0OK+3MpuSDA71lcRCAebR0VxWrrBtsZgK16+nPIuLGffNmxlXJJJL1Luo\n3HWXt+YF/uzZsFemSUSjeYco81DObh9KeL1K7r3vHV2VAaj2L+X0k6NHR1ZXV3N2YPXG5pP0hpbw\nSYjzSBwixQAQ52851kKmHunUy4PedLGqrozeDbGfav+3aTrTDwN4cGEhMxGJZKOHDnmiPp8973JZ\n8vpW0UZOnQrE5HPluUimzY2N2RLf+97ioZUVjAL4B9gUvASTQOgliMr3Pu0z5iF65+UFewjA8Bbn\nTjlWxYYNMzWW0zk+qP39O7rfOyHOV/JzHgOQqOqRDgNYggjEtux9mZiwZzKZoikazdvz+aLlxo3M\n8JUr744eODC89uCDgVsvvbS8N5nMuE0mmBwOc8Hvt2Xi8bwSjxess7PJYVSCPMj9vHrgda33jkRy\nmVRKNblcSunf//tjz/zGb0z/uPbnx2qXeMPkDQ5tu5lRSSvbqUcgelay2mP9IHuZYixbebWeCeRQ\nHlcbugfi+7BDNEoVIc5XS9rv9ms3OfZQraS4YVn7PHGI/eouVGZKTGiv09C+fe50LJZX9ROltFpB\nnZlJOC9dSgSy2aLl9ttdq1NTzuwdd3gjV6/GJ9LpkuPKlejYf/gPb77n858/+erWryZ0ppIcTIqA\nU/am1W3ofB+AD0BsWz9Er5kDle+4TUIfhtgfqrNy5N/dAL776KNnRv7gD97319Wz7unJ87RcJkX+\nvno7OhyWYqFQKp45szSVTKqWYnHdVCqZnXNz6YnxcUfqYx+bWmi2njU15Uw7HJZ1YGPDmn7SE2Dr\n7A09uchxK1Nva2RjRp0U62ASLU3CU6/xrdm6WN0hBzGIY7l6uQLdem61G536KfD5UQCfhziR/iGA\n36x+wt69rlvFIhwHD7qisgW7ahCfvvXQhNoTAiQhLoqy9U6XlhRcBkLzECfJAkQAJFPVLmFDKk+5\nMq1b6HTTF5mGCLC82udKQpxEnRAtkyrEycCCyhzqFoiTwvc2baE65EXsn/2zOy9/9asz68AQ/vk/\nv3MaEK3QFoupaDabii0MHN5COUXwIYjtmIQIYIa38WJjEItlTQHwb0wNCc4CoSOV+zsqc6spQEDl\nu5Utj9gYqFQPBq81+9+Gv7sgLqh7Ib7jgxCTANQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pl.figure(figsize=[14,5])\n", "plot_manhattan(position['pos_cum'],pvalues['YJR139C'],chromBounds)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Common effect test" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A common effect test is a 1 degree of freedom test and can be done by setting\n", "\\begin{equation}\n", "\\mathbf{A}_1^\\text{(snp)} = \\mathbf{1}_{1,P},\\;\\;\\;\n", "\\mathbf{A}_0^\\text{(snp)} = \\mathbf{0}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example: common effect test for gene YJR139C across environments" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ".. Training the backgrond covariance with a GP model\n", "Background model trained in 0.03 s\n" ] } ], "source": [ "# Get data\n", "# select all environmens for gene YJR139C in lysine_group\n", "phenotype_query = \"(gene_ID == 'YJR139C')\"\n", "\n", "data_subsample = dataset.subsample_phenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", "\n", "#get variables we need from data\n", "snps = data_subsample.getGenotypes(impute_missing=True)\n", "phenotypes,sample_idx = data_subsample.getPhenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", "assert sample_idx.all()\n", "\n", "sample_relatedness = data_subsample.getCovariance()\n", "\n", "#set parameters for the analysis\n", "N, P = phenotypes.shape \n", "\n", "covs = None #covariates\n", "Acovs = None #the design matrix for the covariates \n", "Asnps = sp.ones((1,P)) #the design matrix for the SNPs\n", "K1r = sample_relatedness #the first sample-sample covariance matrix (non-noise)\n", "K2r = sp.eye(N) #the second sample-sample covariance matrix (noise)\n", "K1c = None #the first phenotype-phenotype covariance matrix (non-noise)\n", "K2c = None #the second phenotype-phenotype covariance matrix (noise)\n", "covar_type = 'freeform' #the type of the trait/trait covariance to be estimated \n", "searchDelta = False #specify if delta should be optimized for each SNP\n", "test=\"lrt\" #specify type of statistical test\n", "\n", "# Running the analysis\n", "# when cov are not set (None), LIMIX considers an intercept (covs=SP.ones((N,1)))\n", "lmm, pvalues = qtl.test_lmm_kronecker(snps,phenotypes.values,covs=covs,Acovs=Acovs,\n", " Asnps=Asnps,K1r=K1r,trait_covar_type=covar_type)\n", "\n", "#convert P-values to a DataFrame for nice output writing:\n", "pvalues = pd.DataFrame(data=pvalues.T,index=data_subsample.geno_ID,columns=['YJR139C'])" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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nua+dPIXAZ2fSMrnnE5IW7ecZmWDJrnRsO1SuiTSqe8Pdw0Nvz37qlpv1XnAP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\nwb7VYrFslUplz5EjofT73z+5FI8XrGy2pMOHA7l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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pl.figure(figsize=[14,5])\n", "plot_manhattan(position['pos_cum'],pvalues['YJR139C'],chromBounds)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Specific effect test" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a specifc effect test for trait $p$\n", "the alternative model is set to have both a common and a specific effect\n", "for transcript $p$ from the SNP while the null model has only a common effect.\n", "\n", "It is a 1 degree of freedom test and,\n", "in the particular case of $P=3$ traits and for $p=0$, it can be done by setting\n", "\\begin{equation}\n", "\\mathbf{A}_1^\\text{(snp)} =\n", "\\begin{pmatrix}\n", " 1 & 0 & 0 \\\\\n", " 1 & 1 & 1\n", " \\end{pmatrix}\n", "\\;\\;\\;,\n", "\\mathbf{A}_0^\\text{(snp)} = \\mathbf{1}_{1,3}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Example: specific effect test for gene YJR139C across environmentsExample" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ ".. Training the backgrond covariance with a GP model\n", "Background model trained in 0.04 s\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/limix-0.7.9-py2.7-macosx-10.8-x86_64.egg/limix/modules/qtl.py:373: FutureWarning: comparison to `None` will result in an elementwise object comparison in the future.\n", " if K1r==None:\n", "/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/limix-0.7.9-py2.7-macosx-10.8-x86_64.egg/limix/modules/qtl.py:379: FutureWarning: comparison to `None` will result in an elementwise object comparison in the future.\n", " if K2r==None:\n" ] } ], "source": [ "# select all environmens for gene YJR139C in lysine_group\n", "phenotype_query = \"(gene_ID == 'YJR139C')\"\n", "\n", "data_subsample = dataset.subsample_phenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", "\n", "#get variables we need from data\n", "snps = data_subsample.getGenotypes(impute_missing=True)\n", "phenotypes,sample_idx = data_subsample.getPhenotypes(phenotype_query=phenotype_query,\n", " intersection=True) \n", "assert sample_idx.all()\n", "\n", "sample_relatedness = data_subsample.getCovariance()\n", "\n", "#set parameters for the analysis\n", "N, P = phenotypes.shape \n", "\n", "covs = None #covariates\n", "Acovs = None #the design matrix for the covariates \n", "Asnps0 = sp.ones((1,P)) #the null model design matrix for the SNPs\n", "Asnps1 = sp.zeros((2,P)) #the alternative model design matrix for the SNPs\n", "Asnps1[0,:] = 1.0 \n", "Asnps1[1,0] = 1.0 \n", "K1r = sample_relatedness #the first sample-sample covariance matrix (non-noise)\n", "K2r = sp.eye(N) #the second sample-sample covariance matrix (noise)\n", "K1c = None #the first phenotype-phenotype covariance matrix (non-noise)\n", "K2c = None #the second phenotype-phenotype covariance matrix (noise)\n", "covar_type = 'freeform' #the type of the trait/trait covariance to be estimated \n", "searchDelta = False #specify if delta should be optimized for each SNP\n", "test=\"lrt\" #specify type of statistical test\n", "\n", "# Running the analysis\n", "# when cov are not set (None), LIMIX considers an intercept (covs=SP.ones((N,1)))\n", "pvalues = qtl.test_interaction_lmm_kronecker(snps=snps,phenos=phenotypes.values,\n", " covs=covs,Acovs=Acovs,Asnps1=Asnps1,Asnps0=Asnps0,K1r=K1r,K2r=K2r,K1c=K1c,K2c=K2c,\n", " trait_covar_type=covar_type,searchDelta=searchDelta)\n", "\n", "\n", "#convert P-values to a DataFrame for nice output writing:\n", "pvalues = pd.DataFrame(data=sp.concatenate(pvalues).T,index=data_subsample.geno_ID,\n", " columns=[\"specific\",\"null_common\",\"alternative_any\"])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simple_interaction_kronecker not only compares the alternative model (where the trait design of the SNP is Asnp=Asnp1)\n", "versus the null model (where the trait design of the SNP is Asnp=Asnp0) but also compares\n", "the alternative model and the null models versus the no association model (Asnp=0).\n", "Three pvalues are then retured:\n", "- pv for alternative vs null (specific effect test)\n", "- pv for null vs noAssociation (common effect test)\n", "- pv for alternative vs noAssociation (any effect test)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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g3gpDAL+RjmavdbNtnPBbkgPUuBhs10iPZTnEhcF2Nu2trfK4p+zm2VcgLWWd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\not0zef6Az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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tests = ['Any effect test','Interaction effect test']\n", "lim = -1.2*sp.log10(sp.array([pvalues['alternative_any'].min(),\n", " pvalues['null_common'].min(),pvalues['specific'].min()]).min())\n", "pl.figure(figsize=[15,10])\n", "plt = pl.subplot(2,1,1)\n", "plot_manhattan(position['pos_cum'],pvalues['alternative_any'],\n", " chromBounds,colorS='k',colorNS='k',lim=lim,alphaNS=0.05)\n", "plot_manhattan(position['pos_cum'],pvalues['null_common'],\n", " chromBounds,colorS='y',colorNS='y',lim=lim,alphaNS=0.05)\n", "plot_manhattan(position['pos_cum'],pvalues['specific'],\n", " chromBounds,colorS='r',colorNS='r',lim=lim,alphaNS=0.05)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: any, common and specific effect tests across environments for all genes in the pathway " ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "running GxE GWAS tests on (gene_ID == 'YIL094C')\n", ".. Training the backgrond covariance with a GP model\n", "Background model trained in 0.03 s\n", "running GxE GWAS tests on (gene_ID == 'YDL182W')\n", ".. Training the backgrond covariance with a GP model\n", "Background model trained in 0.03 s\n", "running GxE GWAS tests on (gene_ID == 'YDL131W')\n", ".. Training the backgrond covariance with a GP model\n", "Background model trained in 0.04 s\n", "running GxE GWAS tests on (gene_ID == 'YER052C')\n", ".. Training the backgrond covariance with a GP model\n", "Background model trained in 0.03 s\n", "running GxE GWAS tests on (gene_ID == 'YBR115C')\n", ".. Training the backgrond covariance with a GP model\n", "Background model trained in 0.04 s\n", "running GxE GWAS tests on (gene_ID == 'YDR158W')\n", ".. Training the backgrond covariance with a GP model\n", "Background model trained in 0.03 s\n", "running GxE GWAS tests on (gene_ID == 'YNR050C')\n", ".. Training the backgrond covariance with a GP model\n", "Background model trained in 0.03 s\n", "running GxE GWAS tests on (gene_ID == 'YJR139C')\n", ".. Training the backgrond covariance with a GP model\n", "Background model trained in 0.03 s\n", "running GxE GWAS tests on (gene_ID == 'YIR034C')\n", ".. Training the backgrond covariance with a GP model\n", "Background model trained in 0.03 s\n", "running GxE GWAS tests on (gene_ID == 'YGL202W')\n", ".. Training the backgrond covariance with a GP model\n", "Background model trained in 0.03 s\n", "running GxE GWAS tests on (gene_ID == 'YDR234W')\n", ".. Training the backgrond covariance with a GP model\n", "Background model trained in 0.03 s\n" ] } ], "source": [ "pvalues_dict={}\n", "\n", "for gene_idx,gene in enumerate(lysine_group):\n", " # select all environmens for gene YJR139C in lysine_group\n", " phenotype_query = \"(gene_ID == '%s')\" % gene\n", " print \"running GxE GWAS tests on %s\" % phenotype_query\n", " data_subsample = dataset.subsample_phenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", "\n", " #get variables we need from data\n", " phenotypes,sample_idx = data_subsample.getPhenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", " assert sample_idx.all()\n", " if phenotypes.shape[1]==0:\n", " continue\n", " \n", " snps = data_subsample.getGenotypes(impute_missing=True)\n", " \n", " sample_relatedness = data_subsample.getCovariance()\n", "\n", " #set parameters for the analysis\n", " N, P = phenotypes.shape \n", "\n", " covs = None #covariates\n", " Acovs = None #the design matrix for the covariates \n", " Asnps0 = sp.ones((1,P)) #the null model design matrix for the SNPs\n", " Asnps1 = sp.zeros((2,P)) #the alternative model design matrix for the SNPs\n", " Asnps1[0,:] = 1.0 \n", " Asnps1[1,0] = 1.0 \n", " K1r = sample_relatedness #the first sample-sample covariance matrix (non-noise)\n", " K2r = sp.eye(N) #the second sample-sample covariance matrix (noise)\n", " K1c = None #the first phenotype-phenotype covariance matrix (non-noise)\n", " K2c = None #the second phenotype-phenotype covariance matrix (noise)\n", " covar_type = 'freeform' #the type of the trait/trait covariance to be estimated \n", " searchDelta = False #specify if delta should be optimized for each SNP\n", " test=\"lrt\" #specify type of statistical test\n", "\n", " # Running the analysis\n", " # when cov are not set (None), LIMIX considers an intercept (covs=SP.ones((N,1)))\n", " pvalues = qtl.test_interaction_lmm_kronecker(snps=snps,phenos=phenotypes.values,\n", " covs=covs,Acovs=Acovs,Asnps1=Asnps1,Asnps0=Asnps0,K1r=K1r,K2r=K2r,K1c=K1c,\n", " K2c=K2c,trait_covar_type=covar_type,searchDelta=searchDelta)\n", "\n", " #convert P-values to a DataFrame for nice output writing:\n", " pvalues = pd.DataFrame(data=sp.concatenate(pvalues).T,index=data_subsample.geno_ID,\n", " columns=[\"specific\",\"null_common\",\"alternative_any\"])\n", " key = \"pvalues_%s\" % gene\n", " pvalues_dict[key] = pvalues\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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WtlwJTLsiNAzKE6PYbjdTSYk6WG0yql4N5/MJSulB3BVd8Xib0b/0JTv4zDM+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ZXpvvM5Uf7P99LQ2UfbaARzaAg7c5g3RWD2bavZFWrHB/Tdcw/Zzk7Me+45M8nQ5z8P11yDGQqh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\ntw6Ffny+wKu172BztEDn9u3sWxqh0tLVX63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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plotting all manhattan plots\n", "pl.figure(1,figsize=(10,16))\n", "lim = 20\n", "for g in range(G):\n", " plt = pl.subplot(G,2,g+1)\n", " pl.title(lysine_group[g])\n", " if g!=G-1: xticklabels = False\n", " else: xticklabels = True\n", " pv = pvalues_dict['pvalues_%s'%lysine_group[g]]\n", " plot_manhattan(position['pos_cum'],pv['alternative_any'],\n", " chromBounds,colorS='k',colorNS='k',lim=lim,alphaNS=0.05,xticklabels=xticklabels)\n", " plot_manhattan(position['pos_cum'],pv['null_common'],\n", " chromBounds,colorS='y',colorNS='y',lim=lim,alphaNS=0.05,xticklabels=xticklabels)\n", " plot_manhattan(position['pos_cum'],pv['specific'],\n", " chromBounds,colorS='r',colorNS='r',lim=lim,alphaNS=0.05,xticklabels=xticklabels)\n", "pl.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All any-effect eQTL are explained by environmental persistent signal\n", "with the exception of the peak on chromosome 2 for gene YNR050C that has\n", "an almost significant specific component.\n", "These results together with those obtained from the GxE variance decomposition analysis\n", "suggest that the strong transGxE signal of the genes in the pathway is due to interaction\n", "of the poligenic effect with the environment.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multi trait Multi locus models" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Predictions and Model Selection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this section we discuss how to use the phenotype prediction tool in the LIMIX variance decomposition module to monitor overfitting and perform model selection.\n", "We start by discussing how to impose regularization on the trait covariance matrices and how to make phenotype predicitons. Finally we show how to use cross validation to select the extent of the penalization." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regularized maximum likelihood" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When considering high number of traits,\n", "flexible models for trait covariance matrices\n", "are characterized by a large number of parameters\n", "and may lead to overfitting.\n", "For example, general semi-definite positive matrices (\\textit{freeform} matrices) are\n", "parameterized by $\\frac{1}{2}P(P+1)$ real values,\n", "with the number of parameters increasing quadratically in the number of traits\n", "while the data only linearly.\n", "\n", "In order to prevent this, LIMIX makes available to the user\n", "less complex covariance models (e.g. block and low rank models) as well as\n", "the possibility to add a regularization term over the trait covariance matrices\n", "\n", "\\begin{equation}\n", "\\min_{\\boldsymbol{\\theta}}\n", "\\underbrace{ -\n", "\\log\\mathcal{N}\\left(\\text{vec}\\mathbf{Y}\\;|\\;\\sum_i\\mathbf{F}_i\\mathbf{W}_i\\mathbf{A}_i,\\;\n", "\\mathbf{C}_g(\\boldsymbol{\\theta})\\otimes\\mathbf{R}+\\mathbf{C}_n(\\boldsymbol{\\theta})\\otimes\\mathbf{I}\\right)\n", "}_{\\text{data fit}}+\n", "\\underbrace{\n", "\\lambda \\sum_{i \\neq j}\\left({\\mathbf{C}_g(\\boldsymbol{\\theta})_{ij}}^2+{\\mathbf{C}_n(\\boldsymbol{\\theta})_{ij}}^2\\right)\n", "}_{\\text{regularizer}}\n", "\\end{equation}\n", "where $\\otimes$ denotes the Kronecker product and $\\lambda$ is the extent of the penalization.\n", "Notice that the penalization is only applied to off-diagonal elements\n", "to preserve unbiased marginal heritability estimates." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: setting regularization" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "optimizing model with lambda=1.0e+04\n", "optimizing model with lambda=1.0e+03\n", "optimizing model with lambda=1.0e+02\n", "optimizing model with lambda=1.0e+01\n", "optimizing model with lambda=1.0e+00\n" ] } ], "source": [ "#create a complex query on the gene_ID and environment:\n", "# select environment 0 for all genes in lysine_group\n", "phenotype_query = \"(gene_ID in %s) & (environment==0)\" % str(lysine_group)\n", "\n", "data_subsample = dataset.subsample_phenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", "\n", "#get variables we need from data\n", "phenotypes,sample_idx = data_subsample.getPhenotypes(phenotype_query=phenotype_query,\n", " intersection=True) \n", "assert sample_idx.all()\n", "\n", "sample_relatedness = data_subsample.getCovariance()\n", "\n", "# variance component model\n", "vc = var.VarianceDecomposition(phenotypes.values)\n", "vc.addFixedEffect()\n", "vc.addRandomEffect(K=sample_relatedness,trait_covar_type='lowrank_diag')\n", "vc.addRandomEffect(is_noise=True,trait_covar_type='lowrank_diag')\n", "\n", "# setting different extent of panalization\n", "lambds = [1e4, # very highly penalized model\n", " 1e3,1e2,1e1,\n", " 1e0 # lowly penalized model\n", " ]\n", "Cg = []\n", "Cn = []\n", "for lambd in lambds:\n", " print \"optimizing model with lambda=%.1e\" % lambd\n", " # fit the model with extent of penalization lambd\n", " vc.optimize(lambd=lambd)\n", " # store trait covariance matrices\n", " Cg.append(vc.getTraitCovar(0))\n", " Cn.append(vc.getTraitCovar(1))" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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fdEDdf1hzcL+mKGwsMIHBIjUsFhnaXDR4OZGAs4XgRYuEOPGZrprmda3IckOW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p3XLG8eTEUq5Ofm1JtcciARk/MT4JoC6SFACfhSYHzBYCKYqktKr5Ha4feC8a5iv1nRbVaMfYXA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OOnVUtqWuO7QW1vUl2/KSTT2wqSK6VKTCMbjqsGkfE+rziPRU+b7mfUqgPJZMzfyzR4T6stLp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\nLvijA5OQJOQB4knhtcZEg+osdFKYes43AL1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pl.figure(1,figsize=(6,8))\n", "for i in range(len(lambds)):\n", " plt = pl.subplot(len(lambds),2,2*i+1)\n", " pl.title('Cg - lambd=%.1e'%lambds[i])\n", " pl.imshow(Cg[i])\n", " plt.set_xticks([])\n", " plt.set_yticks([])\n", " plt = pl.subplot(len(lambds),2,2*i+2)\n", " pl.title('Cn - lambd=%.1e'%lambds[i])\n", " pl.imshow(Cn[i])\n", " plt.set_xticks([])\n", " plt.set_yticks([])\n", "pl.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Phenotype predictions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let $N$ denote the number of individuals for which we have\n", "both phenotypes $\\mathbf{Y}\\in\\mathcal{R}^{N,P}$ and genotypes $\\mathbf{X}\\in\\mathcal{R}^{N,S}$\n", "and $N^\\star$ denote the number of individuals for which we have genotypes\n", "$\\mathbf{X}^\\star\\in\\mathcal{R}^{N^\\star,S}$ and we want to predict phenotypic values.\n", "Moreover, let us introduce\n", "\\begin{eqnarray}\n", "\\mathbf{F_i} &=& \\text{fixed effect sample design for the $N$ samples} \\in \\mathcal{R}^{N,K} \\\\\n", "\\mathbf{F_i^\\star} &=& \\text{fixed effect sample design for the $N^\\star$ samples} \\in \\mathcal{R}^{N^{\\star},K} \\\\\n", "\\mathbf{R} &=& \\text{sample relatedeness matrix} = \\mathbf{X}\\mathbf{X}^T \\in \\mathcal{R}^{N,N} \\\\\n", "\\mathbf{R^\\star} &=& \\text{cross relatedeness matrix} = \\mathbf{X}{\\mathbf{X}^\\star}^T \\in \\mathcal{R}^{N,N^\\star}\n", "\\end{eqnarray}\n", "\n", "The LIMIX variance decomposition model implements\n", "best linear unbiased prediction (BLUP) where $\\mathbf{F}_i$, $\\mathbf{R}$ and $\\mathbf{Y}$ are used to estimate\n", "the model parameters while $\\mathbf{F}_i^\\star$, $\\mathbf{R}^\\star$ and $\\mathbf{Y}^\\star$ are used\n", "for predicticting:\n", "\\begin{equation}\n", "\\mathbf{Y}^\\star=\n", "\\sum_{i} \\mathbf{F}^\\star_i\\mathbf{W}_i\\mathbf{A}_i +\n", "{\\mathbf{R}^\\star}^T\n", "\\mathbf{Z}\n", "\\mathbf{C}\n", "\\end{equation}\n", "where\n", "\\begin{eqnarray}\n", "\\text{vec}\\mathbf{Z}\n", "& = &\n", "\\mathbf{K}^{-1}\n", "{\\text{vec}{\\left(\n", "{{\\mathbf{Y}}} -\n", "\\sum_{i} \\mathbf{F}_i\\mathbf{W}_i\\mathbf{A}_i\n", "\\right)}}\\\\\n", "\\mathbf{K}\n", "& = &\n", "\\mathbf{C}_g \\otimes \\mathbf{R}+\n", "\\mathbf{C}_n \\otimes \\mathbf{I}\n", "\\end{eqnarray}\n", "\n", "While here we show only the case with two random effect, a polygenic random effect and a noise random effect,\n", "the implementation in LIMIX can be used for any number of random effects." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: predictions for gene YJR139C" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example we predict gene expression from genotype for gene YJR139C. \n", "We split the samples in two parts:\n", "- training samples (~90% of the samples), whose phenotype and genotype values are used to train the model\n", "- test samples (~10% of the samples), whose genotypes are used for predictions.\n", "\n", "Predicted phenotypes for test samples are then compared with the corresponding measured phenotypes.\n", "The code for the multi-trait case is identical.\n", "\n", "To use the prediction method in the variance decomposition module, it is sufficient to specify for each fixed and random effect to use for predictions the test sample design $\\mathbf{F}^\\star$ and the cross covariance $\\mathbf{R}^\\star$ respectively (in addition to $\\mathbf{F}$ and $\\mathbf{R}$). Predicting using only part of the fixed and random effect terms is also possible.\n" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [], "source": [ "#create a complex query on the gene_ID and environment:\n", "# select environment 0 for gene YJR139C\n", "phenotype_query = \"(gene_ID=='YJR139C') & (environment==0)\"\n", "\n", "data_subsample = dataset.subsample_phenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", "\n", "#get variables we need from data\n", "phenotypes,sample_idx = data_subsample.getPhenotypes(phenotype_query=phenotype_query,\n", " intersection=True) \n", "assert sample_idx.all()\n", "\n", "sample_relatedness = data_subsample.getCovariance()\n", "\n", "# split samples into training and test\n", "sp.random.seed(0)\n", "r = sp.random.permutation(phenotypes.shape[0])\n", "nfolds = 10\n", "Icv = sp.floor(((sp.ones((phenotypes.shape[0]))*nfolds)*r)/phenotypes.shape[0])\n", "Itrain = Icv!=0\n", "Itest = Icv==0\n", "pheno_train = phenotypes.values[Itrain,:]\n", "pheno_test = phenotypes.values[Itest,:]\n", "\n", "# variance component model\n", "vc = var.VarianceDecomposition(pheno_train)\n", "vc.setTestSampleSize(Itest.sum())\n", "#1. add intercept\n", "F = sp.ones([pheno_train.shape[0],1])\n", "Ftest = sp.ones([pheno_test.shape[0],1])\n", "vc.addFixedEffect(F=F,Ftest=Ftest)\n", "#2. add polygenic random effect\n", "Rtrain = sample_relatedness[Itrain,:][:,Itrain]\n", "Rcross = sample_relatedness[Itrain,:][:,Itest]\n", "vc.addRandomEffect(K=Rtrain,Kcross=Rcross)\n", "#3. noise\n", "vc.addRandomEffect(is_noise=True)\n", "# train the model on the test\n", "vc.optimize()\n", "# predict on the training\n", "predicted_phenos = vc.predictPhenos()" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot predicted versus real phenotypes\n", "rho = sp.corrcoef(predicted_phenos.T,pheno_test.T)[0,1]\n", "pl.plot(pheno_test.ravel(),predicted_phenos.ravel(),'o')\n", "pl.xlabel('Real Phenotype')\n", "pl.ylabel('Predicted Phenotype')\n", "pl.plot([-2,1],[-2,1],'r')\n", "pl.xlim(-2,1)\n", "pl.ylim(-2,1)\n", "pl.text(0.3,-1.5,'r = %.2f'%(rho))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cross-Validation Model and Selection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "LIMIX variance decomposition has a method for cross-validation that builds on the prediction methods we have just showcased.\n", "The entire dataset is split into $n$ folds, each fold is predicted independentely after training the model on the remaining $n-1$ so that the whole matrix of predicted phenotypes can be obtained.\n", "This can be used to perform model selection across different genetic models.\n", "\n", "In the following we show how the cross-validation method can be used to select the extent of the penalization on the trait covariance matrices." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: selecting the extend of the penalization" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimizing model with lambda: 10000.0\n", "Optimizing model with lambda: 3593.8136638\n", "Optimizing model with lambda: 1291.54966501\n", "Optimizing model with lambda: 464.158883361\n", "Optimizing model with lambda: 166.81005372\n", "Optimizing model with lambda: 59.9484250319\n", "Optimizing model with lambda: 21.5443469003\n", "Optimizing model with lambda: 7.74263682681\n", "Optimizing model with lambda: 2.78255940221\n", "Optimizing model with lambda: 1.0\n" ] } ], "source": [ "#create a complex query on the gene_ID and environment:\n", "# select environment 0 for all genes in lysine_group\n", "phenotype_query = \"(gene_ID in %s) & (environment==0)\" % str(lysine_group)\n", "\n", "data_subsample = dataset.subsample_phenotypes(phenotype_query=phenotype_query,\n", " intersection=True)\n", "\n", "#get variables we need from data\n", "phenotypes,sample_idx = data_subsample.getPhenotypes(phenotype_query=phenotype_query,\n", " intersection=True) \n", "assert sample_idx.all()\n", "N,P=phenotypes.shape\n", "\n", "sample_relatedness = data_subsample.getCovariance()\n", "\n", "# variance component model\n", "vc = var.VarianceDecomposition(phenotypes.values)\n", "vc.addFixedEffect()\n", "vc.addRandomEffect(K=sample_relatedness,trait_covar_type='lowrank_diag',rank=2)\n", "vc.addRandomEffect(is_noise=True,trait_covar_type='lowrank_diag',rank=2)\n", "\n", "# values of lambda to be considered\n", "lambds = 10**sp.linspace(4,0,10)\n", "\n", "# options for cross validation\n", "seed = 0\n", "n_folds = 10\n", "\n", "# cross validation for different values of lambda\n", "MSE = []\n", "for lambd in lambds:\n", " print \"Optimizing model with lambda:\", lambd\n", " predicted_phenos = vc.crossValidation(seed=seed,n_folds=n_folds,\n", " lambd=lambd,verbose=False)[0]\n", " mse = ((predicted_phenos-phenotypes.values)**2).mean()\n", " MSE.append(mse)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt = pl.subplot(1,1,1)\n", "pl.plot(sp.log10(lambds),MSE,'--',color='k')\n", "pl.plot(sp.log10(lambds),MSE,'o',color='white')\n", "plt.invert_xaxis()\n", "pl.xlabel('$log_{10}\\lambda$')\n", "pl.ylabel('Mean Squared Error')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Accounting for gene expression heterogeneity" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "LIMIX provides implementation for preivously proposed mixed models to estimate gene expression heterogeneity due to unobserved confounders (e.g. Kang et al., 2008 & Fusi et al., 2012). \n", "\n", "LIMIX estimates a sample-by-sample covariance matrix that accounts for both genetic and non-genetic confounders. This approach is applicable in studies with high-dimensional molecular phenotypes such as gene expression levels. \n", "In the following we briefly introduce a generic model for expresison heterogeneity that is closely related to the PANAMA approach (Fusi et al., 2012) and show how this can be used for eQTL analyses." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Genetic Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sarting form a generative model that includes both hidden and known covaraites, we start with the a generative model of the form\n", "\\begin{equation}\n", "\\mathbf{y}_p =\n", "\\mathbf{u} + \\boldsymbol{\\eta} + \\boldsymbol{\\psi},\\;\\;\\;\\;\\forall p\n", "\\end{equation}\n", "\\begin{equation}\n", "\\mathbf{u}\\sim\\mathcal{N}\\left(\\mathbf{0},\\;\\sigma_g^2\\mathbf{R}_g\\right),\\;\n", "\\boldsymbol{\\eta}\\sim\\mathcal{N}\\left(\\mathbf{0},\\;\\mathbf{R}_c \\left(\\boldsymbol{\\alpha}\\right)\\right),\\;\n", "\\boldsymbol{\\psi}\\sim\\mathcal{N}\\left(\\mathbf{0},\\;\\sigma_e^2\\mathbf{I}\\right)\n", "\\nonumber\n", "\\end{equation}\n", "where we assume independence of the traits conditioned on the latent factors and we have introduced\n", "\\begin{eqnarray}\n", "\\mathbf{R}_g &=& \\text{sample genetic relatedeness matrix} = \\mathbf{XX}^T \\in \\mathcal{R}^{N,N} \\\\\n", "\\mathbf{R}_c &=& \\text{inferred sample relatedeness matrix due to unobserved covariates} \\in \\mathcal{R}^{N,N}\n", "\\end{eqnarray}\n", "The parameters of the model are $\\left\\{\\boldsymbol{\\alpha},\\sigma_g^2,\\sigma_e^2\\right\\}$.\n", "As full rank matrices might overfit the data explaining away genetic signal,\n", "LIMIX models $\\mathbf{R}_c\\left(\\boldsymbol{\\alpha}\\right)$ as rank $r$ matrix and allows the user to choose $r$.\n", "A sensible value for $r$ can be chosen by looking at\n", "the number of PCAs of the sample-by-sample empirical covariance matrix explaining 70\\%-90\\% of the variance; see also discussion in Fusi et al. 2012\n", "\n", "Once $\\mathbf{R}_c$ is learned, the new sample relatedeness matrix $\\sigma_g^2\\mathbf{R}_g+\\mathbf{R}_c$\n", "can be plugged in the GWAS and variance decomposition tools in LIMIX both for single and multivariate analysis.\n", "In the following we will refer to $\\mathbf{R}_c$ (after normalizing) as *hterogeneity matrix* while\n", "we will refer to the new sample relatedeness matrix $\\sigma_g^2\\mathbf{R}_g+\\mathbf{R}_c$ (after normalizing) as *total sample covariance matrix*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: Accounting for gene expression heterogeneity in the yeast dataset" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# import panama\n", "import limix.modules.panama as panama\n", "\n", "# import data\n", "phenotypes,sample_idx = data_subsample.getPhenotypes(intersection=True)\n", "assert sample_idx.all()\n", "sample_relatedness = data_subsample.getCovariance()" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ,\n", " ,\n", " ]" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# determine the number of ranks to consider in the PANAMA matrix\n", "# by looking at the variance explained by PCs\n", "cum_var = panama.PC_varExplained(phenotypes.values)\n", "plt = pl.subplot(1,1,1)\n", "pl.bar(sp.arange(30)+0.5,cum_var[:30],width=1)\n", "pl.xlim(0,31)\n", "ticks = sp.linspace(0,30,4); ticks[0] = 1\n", "plt.set_xticks(ticks)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# train panama with rank=15 (~60% of the variance)\n", "p = panama.PANAMA(Y=phenotypes.values,Kpop=sample_relatedness)\n", "p.train(rank=15)\n", "# retrieve stuff\n", "Kpanama = p.get_Kpanama()\n", "Ktot = p.get_Ktot()\n", "vComp = p.get_varianceComps()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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sNdXqTSbD9aqf7QMsl41qXch3DXx9T//MQOX3N9JnZnNE7PfW8bGGk9jSuMYY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\nu5OcNGbOUYusQI2/G++75nOTQrFjf+zL59sd4eRMV16YMza5c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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# compare Kpanama matrix, Kpop, and the total matrix\n", "pl.figure(1,figsize=(10,8))\n", "plt = pl.subplot(2,2,1)\n", "pl.title('Kpanama')\n", "pl.imshow(Kpanama,vmin=0,vmax=1,interpolation='none',cmap=cm.afmhot)\n", "pl.colorbar(ticks=[0,0.5,1],orientation='horizontal')\n", "plt.set_xticks([])\n", "plt.set_yticks([])\n", "plt = pl.subplot(2,2,2)\n", "pl.title('Kpop')\n", "pl.imshow(sample_relatedness,vmin=0,vmax=1,interpolation='none',\n", " cmap=cm.afmhot)\n", "pl.colorbar(ticks=[0,0.5,1],orientation='horizontal')\n", "plt.set_xticks([])\n", "plt.set_yticks([])\n", "plt = pl.subplot(2,2,3)\n", "vComp_a = sp.array([vComp[k] for k in ['Kpanama','Kpop','noise']])\n", "pl.bar(sp.arange(3)+0.2,vComp_a,width=0.6)\n", "plt.set_xticks([0.5,1.5,2.5])\n", "plt.set_xticklabels(['Kpanama','Kpop','noise'])\n", "pl.ylabel('Variance Explained')\n", "plt = pl.subplot(2,2,4)\n", "pl.title('Ktot')\n", "pl.imshow(Ktot,vmin=0,vmax=1,interpolation='none',cmap=cm.afmhot)\n", "pl.colorbar(ticks=[0,0.5,1],orientation='horizontal')\n", "plt.set_xticks([])\n", "plt.set_yticks([])" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }