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README.html
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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="pandoc" />
<meta name="author" content="Daniel Huebschmann & Sebastian Steinhauser" />
<title>Bratwurst</title>
<style type="text/css">code{white-space: pre;}</style>
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<h1 class="title">Bratwurst</h1>
<h4 class="author"><em>Daniel Huebschmann & Sebastian Steinhauser</em></h4>
<h4 class="date"><em>20.07.2016, major update 09.10.2017</em></h4>
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<h1>Contents</h1>
<div id="TOC">
<ul>
<li><a href="#introduction"><span class="toc-section-number">1</span> Introduction</a></li>
<li><a href="#the-bratwurst-package"><span class="toc-section-number">2</span> The Bratwurst package</a></li>
<li><a href="#example-leukemia-data"><span class="toc-section-number">3</span> Example: leukemia data</a><ul>
<li><a href="#nmf-analysis"><span class="toc-section-number">3.1</span> NMF analysis</a><ul>
<li><a href="#call-wrapper-function"><span class="toc-section-number">3.1.1</span> Call wrapper function</a></li>
<li><a href="#hmatrixlist"><span class="toc-section-number">3.1.2</span> <code>HMatrixList</code></a></li>
<li><a href="#hmatrix"><span class="toc-section-number">3.1.3</span> <code>HMatrix</code></a></li>
<li><a href="#wmatrixlist"><span class="toc-section-number">3.1.4</span> <code>WMatrixList</code></a></li>
<li><a href="#wmatrix"><span class="toc-section-number">3.1.5</span> <code>WMatrix</code></a></li>
<li><a href="#froberror"><span class="toc-section-number">3.1.6</span> <code>FrobError</code></a></li>
</ul></li>
<li><a href="#determine-the-optimal-factorization-rank"><span class="toc-section-number">3.2</span> Determine the optimal factorization rank</a><ul>
<li><a href="#get-frobenius-error."><span class="toc-section-number">3.2.1</span> Get Frobenius error.</a></li>
<li><a href="#evaluate-silhouette-values"><span class="toc-section-number">3.2.2</span> Evaluate silhouette values</a></li>
<li><a href="#cophenetic-correlation-coefficient-plot"><span class="toc-section-number">3.2.3</span> Cophenetic correlation coefficient plot</a></li>
<li><a href="#compute-amari-type-distance"><span class="toc-section-number">3.2.4</span> Compute amari type distance</a></li>
<li><a href="#generate-plots-to-estimate-optimal-k"><span class="toc-section-number">3.2.5</span> Generate plots to estimate optimal k</a></li>
<li><a href="#generate-ranked-error-plot."><span class="toc-section-number">3.2.6</span> Generate ranked error plot.</a></li>
</ul></li>
<li><a href="#visualize-the-matrix-h-exposures"><span class="toc-section-number">3.3</span> Visualize the matrix H (exposures)</a></li>
<li><a href="#feature-selection"><span class="toc-section-number">3.4</span> Feature selection</a><ul>
<li><a href="#row-k-means-to-determine-signature-specific-features"><span class="toc-section-number">3.4.1</span> Row K-means to determine signature specific features</a></li>
<li><a href="#feature-visualization"><span class="toc-section-number">3.4.2</span> Feature visualization</a></li>
</ul></li>
</ul></li>
</ul>
</div>
<p><code>Bratwurst</code> is a software package providing functions for preprocessing, wrappers for non-negative matrix factorization and postprocessing in <code>R</code>. This repo hosts the code of the Bratwurst software package.<br />
A detailed description of the software and an application to cells of the human hematopoietic system are available as a preprint: <a href="https://doi.org/10.1101/199547" class="uri">https://doi.org/10.1101/199547</a>.<br />
Intermediate results for the analysis on hematopoietic cells are available on zenodo: <a href="https://doi.org/10.5281/zenodo.800049" class="uri">https://doi.org/10.5281/zenodo.800049</a>.<br />
In this README document, we present major parts of the vignette of the package. First some packages have to be loaded.</p>
<pre class="r"><code>library(knitr)
library(ComplexHeatmap)</code></pre>
<div id="introduction" class="section level1">
<h1><span class="header-section-number">1</span> Introduction</h1>
<p><strong>NMF</strong> (<strong>nonnegative matrix factorization</strong>) is a matrix decomposition method. It was originally described by Lee & Seung in 1999. In 2003, Brunet et al. applied NMF to gene expression data. In 2010, <em><a href="http://cran.fhcrc.org/web/packages/NMF/index.html">NMF</a></em>, an R package implementing several NMF solvers was published by Gaujoux et al. NMF basically solves the problem as illustrated in the following figure (Image taken from <a href="https://en.wikipedia.org/wiki/Non-negative_matrix_factorization" class="uri">https://en.wikipedia.org/wiki/Non-negative_matrix_factorization</a>):</p>
<p><img src="data:image/png;base64,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" alt="NMF" /></p>
<p>Here, <code>V</code> is an input matrix with dimensions <code>n x m</code>. It is decomposed into two matrices <code>W</code> of dimension <code>n x l</code> and <code>H</code> of dimension <code>l x m</code>, which when multiplied approximate the original matrix <code>V</code>. <code>l</code> is a free parameter in NMF, it is called the factorization rank. If we call the columns of <code>W</code> signatures, then <code>l</code> corresponds to the number of signatures. The decomposition thus leads to a reduction in complexity if <code>l < n</code>, i.e. if the number of signatures is smaller than the number of features, as indicated in the above figure.</p>
<p>In 2015, Mejia-Roa et al. introduced an implementation of an NMF-solver in CUDA, which lead to significant reduction of computation times by making use of massive parallelisation on GPUs. Other implementations of NMF-solvers on GPUs exist.</p>
<p>It is the pupose of the package <code>Bratwurst</code> described here to provide wrapper functions in R to these NMF-solvers in CUDA. Massive parallelisation not only leads to faster algorithms, but also makes the benefits of NMF accessible to much bigger matrices. Furthermore, functions for preprocessing, estimation of the optimal factorization rank and post-hoc feature selection are provided.</p>
</div>
<div id="the-bratwurst-package" class="section level1">
<h1><span class="header-section-number">2</span> The Bratwurst package</h1>
<p>The main feature of the package <code>Bratwurst</code> is an S4 object called <code>nmf.exp</code>. It is derived from <code>SummarizedExperiment</code>, has containers for a data matrix, column annotation data and row annotation data and inherits <code>SummarizedExperiment</code>’s accessor functions <code>colData</code> and <code>rowData</code>. The matrix to be stored in this data structure is the matrix V as described above, corresponding to the input matrix for the NMF-solver. <code>nmf.exp</code> furthermore has containers for the matrices W and H which are results of the decomposition. As NMF algorithms have to be run iteratively, an instance of the class <code>nmf.exp</code> can store large lists of matrices, corresponding to the results of different iteration steps. Accessor functions to all different containers are provided.</p>
<p>A crucial step in data analysis with NMF is the determination of the optimal factorization rank, i.e. the number of columns of the matrix W or equivalently the number of rows of the matrix H. No consensus method for an automatic evaluation of the optimal factorization rank has been found to date. Instead, the decomposition is usually performed iteratively over a range of possible factorization ranks and different quality measures are computed for every tested factorization ranks. Many quality measures have been proposed:</p>
<ul>
<li>The <code>Frobenius reconstruction error</code>, i.e. the Frobenius norm of the residuals of the decomposition: ||W x H - V||</li>
<li><p>Criteria to assess the stability of the decomposition:</p></li>
<li>The <code>cophenetic correlation coefficient</code></li>
<li>An <code>Amari type distance</code></li>
<li><p><code>Silhouette values</code> over clusters of patterns extracted iteratively at the same factorization rank</p></li>
</ul>
<p>The package <code>Bratwurst</code> provides functions to compute all</p>
</div>
<div id="example-leukemia-data" class="section level1">
<h1><span class="header-section-number">3</span> Example: leukemia data</h1>
<p>In this README, as in the vignette for the package, we use a dataset containing Affymetrix Hgu6800 microarray expression data of B-ALL, T-ALL and AML samples. This dataset had also been used by Brunet et al. (PNAS, 2004) and Gaujoux et al. (BMC Bioinformatics, 2010). In Brunet et al., this dataset is called the <strong>Golub</strong> dataset. Preparations: load the necessary software packages:</p>
<pre class="r"><code>library(Bratwurst)
library(NMF)</code></pre>
<p>Load the example data (the <strong>Golub</strong> dataset is stored in the R package <code>Bratwurst</code>)</p>
<pre class="r"><code>data(leukemia)
samples <- "leukemia"</code></pre>
<p>This data was initially generated by the following commands:</p>
<pre class="r"><code>data.path <- file.path(getwd(), "data")
matrix.file <- list.files(data.path, "*data.txt", full.names = T)
rowAnno.file <- list.files(data.path, "micro.*anno.*txt", full.names = T)
rowAnno.bed <- list.files(data.path, ".bed", full.names = T)
colAnno.file <- list.files(data.path, "sample.*anno.*txt", full.names = T)
# Read files to summarizedExperiment
leukemia.nmf.exp <- nmfExperimentFromFile(matrix.file = matrix.file,
rowAnno.file = rowAnno.file,
colData.file = colAnno.file)
save(leukemia.nmf.exp, file = file.path(data.path, "leukemia.rda"))</code></pre>
<p>Now we are ready to start an NMF analysis.</p>
<div id="nmf-analysis" class="section level2">
<h2><span class="header-section-number">3.1</span> NMF analysis</h2>
<div id="call-wrapper-function" class="section level3">
<h3><span class="header-section-number">3.1.1</span> Call wrapper function</h3>
<p>The wrapper function for the NMF solvers in the Bratwurst package is <code>runNmfGpu</code>. It is called as follows:</p>
<pre class="r"><code>k.max <- 4
outer.iter <- 10
inner.iter <- 10^4
leukemia.nmf.exp<- runNmfGpuPyCuda(nmf.exp = leukemia.nmf.exp,
k.max = k.max,
outer.iter = outer.iter,
inner.iter = inner.iter,
tmp.path = "/tmp/tmp_leukemia",
cpu = TRUE)</code></pre>
<pre><code>## [1] "2017-10-09 14:37:55 CEST"
## Factorization rank: 2
## [1] "2017-10-09 14:38:11 CEST"
## Factorization rank: 3
## [1] "2017-10-09 14:38:30 CEST"
## Factorization rank: 4</code></pre>
<p>Depending on the choice of parameters (dimensions of the input matrix, number of iterations), this step may take some time. Note that the algorithm updates the user about the progress in the iterations.</p>
<p>Several getter functions are available to access the data in the generated <code>nmf.exp</code> object:</p>
</div>
<div id="hmatrixlist" class="section level3">
<h3><span class="header-section-number">3.1.2</span> <code>HMatrixList</code></h3>
<p>Returns a list of matrices <code>H</code> for a specific factorization rank <code>k</code>. There are as many entries in this list as there were iterations in the outer iteration. Of course the number of rows of the matrix <code>H</code> corresponds to the chosen factorization rank.</p>
<pre class="r"><code>tmp.object <- HMatrixList(leukemia.nmf.exp, k = 2)
class(tmp.object)</code></pre>
<pre><code>## [1] "list"</code></pre>
<pre class="r"><code>length(tmp.object)</code></pre>
<pre><code>## [1] 10</code></pre>
<pre class="r"><code>class(tmp.object[[1]])</code></pre>
<pre><code>## [1] "matrix"</code></pre>
<pre class="r"><code>dim(tmp.object[[1]])</code></pre>
<pre><code>## [1] 2 38</code></pre>
<p>If no value for <code>k</code> is supplied, the function returns a list of lists, one for every iterated factorization rank.</p>
<pre class="r"><code>tmp.object <- HMatrixList(leukemia.nmf.exp)
class(tmp.object)</code></pre>
<pre><code>## [1] "list"</code></pre>
<pre class="r"><code>length(tmp.object)</code></pre>
<pre><code>## [1] 3</code></pre>
<pre class="r"><code>class(tmp.object[[1]])</code></pre>
<pre><code>## [1] "list"</code></pre>
<pre class="r"><code>length(tmp.object[[1]])</code></pre>
<pre><code>## [1] 10</code></pre>
</div>
<div id="hmatrix" class="section level3">
<h3><span class="header-section-number">3.1.3</span> <code>HMatrix</code></h3>
<p>Returns the matrix <code>H</code> for the optimal decomposition (i.e. the one with the minimal residual) for a specific factorization rank <code>k</code>. As in the previous paragraph, the number of rows of the matrix <code>H</code> corresponds to the chosen factorization rank.</p>
<pre class="r"><code>tmp.object <- HMatrix(leukemia.nmf.exp, k = 2)
class(tmp.object)</code></pre>
<pre><code>## [1] "matrix"</code></pre>
<pre class="r"><code>dim(tmp.object)</code></pre>
<pre><code>## [1] 2 38</code></pre>
<p>If no value for <code>k</code> is supplied, the function returns a list of optimal matrices, one for every iterated factorization rank.</p>
<pre class="r"><code>H.list <- HMatrix(leukemia.nmf.exp)
class(H.list)</code></pre>
<pre><code>## [1] "list"</code></pre>
<pre class="r"><code>length(H.list)</code></pre>
<pre><code>## [1] 3</code></pre>
</div>
<div id="wmatrixlist" class="section level3">
<h3><span class="header-section-number">3.1.4</span> <code>WMatrixList</code></h3>
<p>Returns a list of matrices <code>W</code> for a specific factorization rank <code>k</code>. There are as many entries in this list as there were iterations in the outer iteration. Of course the number of columns of the matrix <code>W</code> corresponds to the chosen factorization rank.</p>
<pre class="r"><code>tmp.object <- WMatrixList(leukemia.nmf.exp, k = 2)
class(tmp.object)</code></pre>
<pre><code>## [1] "list"</code></pre>
<pre class="r"><code>length(tmp.object)</code></pre>
<pre><code>## [1] 10</code></pre>
<pre class="r"><code>class(tmp.object[[1]])</code></pre>
<pre><code>## [1] "matrix"</code></pre>
<pre class="r"><code>dim(tmp.object[[1]])</code></pre>
<pre><code>## [1] 4951 2</code></pre>
<p>If no value for <code>k</code> is supplied, the function returns a list of lists, one for every iterated factorization rank.</p>
</div>
<div id="wmatrix" class="section level3">
<h3><span class="header-section-number">3.1.5</span> <code>WMatrix</code></h3>
<p>Returns the matrix <code>W</code> for the optimal decomposition (i.e. the one with the minimal residual) for a specific factorization rank <code>k</code>. As in the previous paragraph, the number of columns of the matrix <code>W</code> corresponds to the chosen factorization rank.</p>
<pre class="r"><code>tmp.object <- WMatrix(leukemia.nmf.exp, k = 2)
class(tmp.object)</code></pre>
<pre><code>## [1] "matrix"</code></pre>
<pre class="r"><code>dim(tmp.object)</code></pre>
<pre><code>## [1] 4951 2</code></pre>
<p>If no value for <code>k</code> is supplied, the function returns a list of optimal matrices, one for every iterated factorization rank.</p>
<pre class="r"><code>W.list <- WMatrix(leukemia.nmf.exp)
class(W.list)</code></pre>
<pre><code>## [1] "list"</code></pre>
<pre class="r"><code>length(W.list)</code></pre>
<pre><code>## [1] 3</code></pre>
</div>
<div id="froberror" class="section level3">
<h3><span class="header-section-number">3.1.6</span> <code>FrobError</code></h3>
<p>Returns a data frame with as many columns as there are iterated factorization ranks and as many rows as there are iterations per factorization rank.</p>
<pre class="r"><code>FrobError(leukemia.nmf.exp)</code></pre>
<pre><code>## DataFrame with 10 rows and 3 columns
## 2 3 4
## <numeric> <numeric> <numeric>
## 1 0.5583464 0.5139642 0.4641748
## 2 0.5583473 0.5139693 0.4644978
## 3 0.5583461 0.5139688 0.4646465
## 4 0.5583477 0.5139639 0.4644630
## 5 0.5583457 0.5139707 0.4645478
## 6 0.5583460 0.5139682 0.4644090
## 7 0.5583472 0.5139721 0.4644547
## 8 0.5583457 0.5139675 0.4646729
## 9 0.5583472 0.5139689 0.4645166
## 10 0.5583456 0.5139694 0.4646634</code></pre>
</div>
</div>
<div id="determine-the-optimal-factorization-rank" class="section level2">
<h2><span class="header-section-number">3.2</span> Determine the optimal factorization rank</h2>
<p>In NMF, Several methods have been described to assess the optimal factorization rank. The Bratwurst packages implements some of them. They are computed by applying custom functions which subsequently update the data structure of type <code>nmf.exp</code>.</p>
<div id="get-frobenius-error." class="section level3">
<h3><span class="header-section-number">3.2.1</span> Get Frobenius error.</h3>
<p>The most important information about the many iterated decompositions is the norm of the residual. In NMF this is often called the Frobenius error, as the Frobenius norm may be used.</p>
<pre class="r"><code>leukemia.nmf.exp <- computeFrobErrorStats(leukemia.nmf.exp)</code></pre>
</div>
<div id="evaluate-silhouette-values" class="section level3">
<h3><span class="header-section-number">3.2.2</span> Evaluate silhouette values</h3>
<p>In 2013, Alexandrov et al. published an NMF analysis on mutational signatures. They used an approach which a modified silhouette criterion is used to estimate the stability across iteration steps for one fixed factorization rank <code>k</code>.</p>
<pre class="r"><code>leukemia.nmf.exp <- computeSilhoutteWidth(leukemia.nmf.exp)</code></pre>
</div>
<div id="cophenetic-correlation-coefficient-plot" class="section level3">
<h3><span class="header-section-number">3.2.3</span> Cophenetic correlation coefficient plot</h3>
<pre class="r"><code>leukemia.nmf.exp <- computeCopheneticCoeff(leukemia.nmf.exp)</code></pre>
</div>
<div id="compute-amari-type-distance" class="section level3">
<h3><span class="header-section-number">3.2.4</span> Compute amari type distance</h3>
<pre class="r"><code>leukemia.nmf.exp <- computeAmariDistances(leukemia.nmf.exp)</code></pre>
<p>After having executed all these functions, the values of the computed measures can be accessed with <code>OptKStats</code>:</p>
<pre class="r"><code>OptKStats(leukemia.nmf.exp)</code></pre>
<pre><code>## DataFrame with 3 rows and 9 columns
## k min mean sd cv sumSilWidth
## <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
## 2 2 0.5583456 0.5583465 7.751192e-07 1.388241e-06 20.00000
## 3 3 0.5139639 0.5139683 2.577000e-06 5.013928e-06 29.99996
## 4 4 0.4641748 0.4645046 1.482698e-04 3.191999e-04 39.99228
## meanSilWidth copheneticCoeff meanAmariDist
## <numeric> <numeric> <numeric>
## 2 0.9999999 0.9999999 2.709082e-08
## 3 0.9999988 0.9616090 3.969754e-07
## 4 0.9998071 0.9866591 8.592894e-05</code></pre>
<p>These quality measures can be displayed together:</p>
</div>
<div id="generate-plots-to-estimate-optimal-k" class="section level3">
<h3><span class="header-section-number">3.2.5</span> Generate plots to estimate optimal k</h3>
<pre class="r"><code>gg.optK <- plotKStats(leukemia.nmf.exp)
gg.optK</code></pre>
<p><img 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" alt /></p>
</div>
<div id="generate-ranked-error-plot." class="section level3">
<h3><span class="header-section-number">3.2.6</span> Generate ranked error plot.</h3>
<p>It may also be useful to inspect the Frobenius error after ranking. This may give an estimation of the convergence in the parameter space of initial conditions.</p>
<pre class="r"><code>gg.rankedFrobError <- plotRankedFrobErrors(leukemia.nmf.exp)</code></pre>
<pre><code>## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing</code></pre>
<pre class="r"><code>gg.rankedFrobError</code></pre>
<p><img src="data:image/png;base64,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" alt /></p>
</div>
</div>
<div id="visualize-the-matrix-h-exposures" class="section level2">
<h2><span class="header-section-number">3.3</span> Visualize the matrix H (exposures)</h2>
<p>The matrices <code>H</code> may be visualized as heatmaps. We can define a meta information object and annotate meta data:</p>
<pre class="r"><code>entity.colVector <- c("red", "blue")
names(entity.colVector) <- c("ALL", "AML")
subtype.colVector <- c("orange", "darkgreen", "blue")
names(subtype.colVector) <- c("B-cell", "T-cell", "-")
anno_col <- list(V2 = entity.colVector,
V3 = subtype.colVector)
heat.anno <- HeatmapAnnotation(df = colData(leukemia.nmf.exp)[, c(2:3)],
col = anno_col)</code></pre>
<p>And now display the matrices <code>H</code> with meta data annotation. Bratwurst provides a plotting function to display the matrices <code>H</code> with meta data annotation:</p>
<pre class="r"><code># Plot Heatmaps for H over all k
lapply(seq(2, k.max), function(k) {
plotHMatrix(leukemia.nmf.exp, k)
})</code></pre>
<pre><code>## [[1]]</code></pre>
<p><img 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ktLSzMxMWnvgK+urv7kk0+6d+/ekuKMjAxFRcWW3I1HKBSWlJRERka2tn9i7t69q6qq2syvjVRPnz49ffq0urp6K5eemJiYmZnZ+is5S0tLZ82ahVsHAshHmwX8rVu3Gm90VlRUCAQCqYfnORxOC/+x0lRUVLp06bJp06amCh48eJCSktLMHOrq6kxMTIyMjBpPys7OnjNnjra29pMnTxQVFcX7/8EHHyxcuFB8KYsXL25mKdHR0W5ublpaWvTLTp06GRkZiSfZH3/84enp+fHHHzc1hx49eqxatWrkyJFNFVhZWdXX1zfelHzx4sW9e/f8/PyKioqqq6s5nJcjCQmFwmfPnn3++eeiyqKiIi8vLzc3t2Y+SCvp6+vb2to28/OytbVdvHixvr6+1Kl37twJCQmJjY2VOvX+/fuFhYXiP6k3U1lZeePGjWXLljVTU1VVRR+JMDU1VVNTe/To0fXr10U/X0KIUCiUuMqOz+dnZWUxxuG9e/e8vb1HjRrVkq6+2X0XAgMDExMTBw4c+AbvFVdWVnbz5k2JT5ScnCzr5YXV1dUrV64UX3uMKisrR4wY0dRvAgA0o20CfuPGjRs3btTT05NoFwqF1dXVo0aNqq6uLikpEW3XEkJqa2s/+OAD0Yl7tbW16urqhw8fbpP+SFVXV/fixYvt27c3nnT37l0DAwNFRcUhQ4aMGDFC9E3l3r17RUVF4v/Xfv/99+nTp3fp0qWppWhoaCxbtqxXr15NFfz5559St85bzszMbNasWc3cvefTTz/V0dEZNmwY/VIgEBw8eFA8IeLj4zMzM9s14BlRFGVubr5582apU4uLi//555+goCCpu8SfPHliYWHB5/NLSkrEY76qqsre3n7w4MH0y4aGhmfPnu3cubOZPvB4vMmTJzdVIBAIlJSUxLeA6e+s4sFWW1u7fv16iW8bxcXFom39r7/+WiAQNP76W1tbm5iYqKKiQp9UISrg8/lKSkrjxo0TVd67d2/nzp39+vVrqp8jRoyg9+FLtJeUlNTV1QkEgtLS0oaGBvHvfA0NDbNmzRJVFhYWzp0719XVtalFTJs2LS4uTqJR4sybcePG/fjjj03N4fLly7Gxsb169RJ1IyQkROq5OxLi4uIaL7oxJyenhoaGwsJC8fVQUlIyZcoU0a4gPp9PUdS8efMY5wbAAi0KeEtLy+b38o0ePVpXV7eZ+8lkZmbu2LFDPFEuXLhgZWUl2ln35MmTCxcuNLOILl26NPPfhxCipaXl4eHRTIGysvLs2bOlbgmJGn19fX/55ZdmTnZbtGhR80dhJ02apKur20zBhAkTmjoyTRszZkzzF0SNHDmyd+/ezRRMnDixT58+Q4cOFbVI/EfT1NRs/G1MnI2NTfNn/PXv37/5T8F4RMDc3NzNza2ZDdPevXsXFxdL/aV6/vy5pqbm3bt316xZ89FHH4naL1261KdPH1GyVldX5+XlNdMHNTW16dOnN1NAUdScOXOav4XwggULli9frqDwnz8l8XF6Hjx4EBgY2Mx+6fnz53/44Yei60FKSkoKCwvFP1dSUpLE/CWMGjVqxYoVjX8rKioqampqOnfuvHnzZg6HY2hoSLc3NDScOXNGfOU3NDRIPe4j4uHh4eXl5ezs3FRBampqZWVlz549myo4e/ZsfX29+Lf8fv36OTg4KCkp0S+Lioq0tbWbP7Fj+/btkyZNajzp5MmTDg4O+fn5YWFh4n2orKzMz8+vra2lX9bU1Dx8+BABD+8JqiUneAMAAMC7hdPRHQAAAIC2h4AHAABgoSYP7FFUsDz7IZWQNHd6s3xQRPpZYCzzNqxqgI6Bw5TAUtiCBwAAYCEEPAAAAAsh4AEAAFgIAQ8AAMBCCHgAAAAWQsADAACwEAIeAACAhRDwAAAALISABwAAYCEEPAAAAAsh4AEAAFgIAQ8AAMBCCHgAAAAWQsADAACwEAIeAACAhRDwAAAALISABwAAYCEEPAAAAAspNDVh2eIP5NkPqYz6BzZfcOLU5uYLRn6yrJV9WJbV8etBDhhXdUvI4cchh0W0HmMnGb0NK+otWdVy6Mb9Vr4f4G2FLXgAAAAWQsADAACwEAIeAACAhRDwAAAALISABwAAYCEEPAAAAAsh4AEAAFgIAQ8AAMBCCHgAAAAWQsADAACwEAIeAACAhRDwAAAALISABwAAYCEEPAAAAAsh4AEAAFgIAQ8AAMBCCHgAAAAWQsADAACwECUUCju6DwAAANDGsAUPAADAQgh4AAAAFkLAAwAAsJBCk1MoSo7daMLxGIYCFXWGAjUthoKGOoaC2mqGgoIchoKaKoaC+nqGgtJihgIlJYaCihcMBSsiGAoIIQ9vMRQYmTMUcLgMBYIGpjk0/RvbQsWFDAWqGkyzYPrT4CkzFCgoMhQ0MK2HyjKGAi7TIjhMn4J5Vbfg9B1lNeaa5gn4DAV8pj8fxm4qdWp5dwDeIdiCBwAAYCEEPAAAAAsh4AEAAFgIAQ8AAMBCCHgAAAAWQsADAACwEAIeAACAhRDwAAAALISABwAAYCEEPAAAAAsh4AEAAFgIAQ8AAMBCCHgAAAAWQsADAACwEAIeAACAhRDwAAAALISABwAAYCEEPAAAAAsh4AEAAFgIAQ8AAMBCCHgAAAAWQsADAACwEAIeAACAhRDwAAAALISABwAAYCEEPAAAAAsh4AEAAFgIAQ8AAMBCCHgAAAAWQsADAACwEAIeAACAhRDwAAAALISABwAAYCEEPAAAAAsh4AEAAFgIAQ8AAMBCCHgAAAAWQsADAACwEAIeAACAhRDwAAAALISABwAAYCEEPAAAAAsh4AEAAFgIAQ8AAMBCCHgAAAAWQsADAACwEAIeAACAhRDwAAAALISABwAAYCEEPAAAAAsh4AEAAFgIAQ8AAMBCCHgAAAAWQsADAACwEAIeAACAhRDwAADSZWRkjBs3ztDQUEVFpV+/fitXriwrKxNN1dLSioiIaKdFJyYmxsXFtdPM4T2h0NEdAAB4G6Wnpzs5OdnZ2a1atUpTUzM7OzsiIiItLe306dM8Ho8QYm9vb2Bg0E5LT0xMrKiomDp1ajvNH94HCHgAACm2bNnSt2/fU6dOKSoq0i2urq5Dhw49fPjwxIkTCSGHDh3q0A4CMMAuegAAKW7fvm1mZiZKd0KInZ3d4sWLO3XqRL/s3LmzaBd9XV3d0qVLu3fvbmpqunr16m3btllaWtKTunfvvmfPnuDg4L59+2pqanp4eJSWltKTysvLv/zySzMzM2Vl5R49eqxdu1YgEBBChg4dunfv3pSUFIqiysrK1NTUoqOjRd34/PPPnZ2d6edGRkaxsbFBQUE6Ojr5+fmEkOjoaFtbW1VVVSsrq71794relZGRQVFUeHh4+6wteBsh4AEApLC3t09JSQkICLh9+7aoMSQkRBSu4nx8fH799dcFCxZs2LAhNTX1hx9+EJ8aERFx+vTp4ODgb7/9NiUlZc2aNXT7nDlz9uzZM2PGjKioqLFjx27YsCEmJoYQsn///k8//dTR0fHmzZvq6urN9zMqKiomJsbHx0dHRycsLMzHx2fYsGFRUVE2NjYzZ84UfTPQ1NR0dHQ0MjJqxSp5KxgZGSkrKzduv3//PkVR9vb2bzbbX375haKompqaZmrWrl1LUdSGDRtELQEBARRFhYSEEEIOHTo0aNAgFRUV+rtafX39m/WkDWEXPQCAFMHBwXw+f9u2bVu3bv3ggw8cHR2dnZ2dnZ0VFCT/bebm5u7du3f//v3u7u6EEFdXVxMTEzU1NVHB06dPT506xeVyCSGXLl26dOkS3S4QCLZu3erl5UUImT59ekZGRlZWFiHE2NhYXV2doqjevXsz9jMnJycrK0tXV7eioiIoKGjZsmXff/89IWTKlCkCgWD16tVeXl4URVlZWR0/frxtVs1bSVVV1c/Pr1evXjK9SygUlpWVHTlyJDAwkLF45syZGzZsSEpKor+iCYXC5ORkLpc7ffr0vLw8Nzc3NTU1X1/fv/76a8OGDVwud926dW/4YdoItuABAKRQV1ePjIwsKSk5duzYZ599lp6ePmHChH79+t26dUui8ty5czwejz4wTwjR0NAYM2aMeIGLiwud7oQQfX19Pp9PP09ISPDy8hIIBDdv3oyMjLxx4wa9i14mn376qa6uLiEkJyenrKxs1qxZokkeHh4PHjx4+PChrPNsb5cuXaIoytnZefLkyRoaGoMHDz537pybm5uGhoa5ufmxY8fosoiICHNzcyUlJX19/Xnz5tXW1lpbWz948KC2tpaiqOzsbIqixo8fv2nTJjMzs8rKyu3bt6ekpBBCfv31V4qiPvzwQ6FQGBoaSlGUo6Oj1HX7+PFjHR2dGTNmvHjxgrHb5ubmQ4cOzczMvHPnDiEkOzu7oKBg7NixXbt2TUtLq6+vDwwMDAsLS0hIIIQcPHiwDdfYm0HAAwBI4vP5FRUVfD5fRUVl1KhRmzZtys7OTk1NLSkp+fLLLyWK7927p6enJ4pwQki3bt3EC/T09KQu5dy5c/b29pqams7Ozunp6U2VSRAKheIvTU1N6SeFhYWEEBsbG+VX3NzcCCHPnj1ryWzlLzU1tb6+ftCgQZcuXRo2bNiTJ09Gjx598+ZNf39/QsjZs2f9/f0pilq5cqWFhcX27du3b9++b98+PT09RUXFzMxMeoWfP39+8+bNxsbG4nP29fUdPXr0+fPnd+zY8fXXX6urq0dFRXE4UvJOV1c3MzMzMzOzZ8+eLekz/f0pKSmJEJKcnEwI8fT0JISMHTv2zz//9Pb2JoTQX+A0NDRat3raAHbRAwBIunHjhqWlZVpa2siRI+kWiqJGjx7t6uqampoqUdytW7fi4mI+ny/K+MePH4sXUBTVeBHPnj1zcHDw9PSMiooyNzcnhNjZ2bWkbxIzFx0yoL9VpKen6+joiBd07969JbOVPxsbm+Tk5OLi4i5dumhpaZ04cUJBQaFLly53794lhGhra+/atcva2rqhoYHea1JQUGBhYcHj8TgcjrW19Y0bNwghSkpKubm5Ghoa9+/fF82ZoqjIyEhLS0s/Pz9CyI4dO0RfgyQoKipaW1sTQkTnTjZvypQpixcvTkpKWrJkSVJSkpaW1oQJEwghPXr06NGjByEkNzfX3d1dU1Pz22+/beX6aT1swQMASOrVq5eurm5oaGhdXZ2osbKy8vTp0wMGDJAoHjx4cF1dHb09RwgpLy8/evQo4yIuXrxYV1e3du1aOt2rqqroYGuMy+UWFxfTz8vKyjIyMqSW9e3bV0VFJS8v74NXEhMTv/rqKyUlJcbOdAj6mwedrIaGhnRyi06g69y5c0JCwpAhQyZMmJCTk9PUTPr37y91W9nY2Jjenu7WrRv9pE3o6uqOGzcuIyPj4sWLmZmZU6dOFT/jb+/evYMHD66urj579uyHH37YVgt9Ywh4AABJysrKwcHBBw8etLW1Xbt2bURExIYNG4YMGXLv3r2vv/5aonjQoEGurq7e3t4//PDDrl27HB0d9fT0pG61i7OwsFBQUFixYkV6enpCQsInn3xSU1OTmZlJ72nncDg5OTn0kV1ra+stW7bExMQkJyePHTu2qTPhtbS0AgMD586d+9VXX+3Zs2f+/PmrVq366KOP6J5cv37dyclJ9C3k7RcSEnLo0KEffvjh4cOHs2fPFp8kfpBC/MiIuFu3bu3YsYPL5T569KhtLw6cNWuWUCicO3cuebV/nu5SQEDAzJkznZ2dr1y50rdv3zZc4hvDLnoAAClmz55tZGT066+/xsfH371718DAwM7Obs+ePQMHDmxcvHfv3sDAwJCQEA0NjYCAgOzs7MzMzObnb2pqGhMTs3r16uTkZCsrq++++66kpGTBggWRkZHr16/38PA4c+aMq6vr/fv3d+zY4efn5+vr26tXr0WLFhUVFTW1Eb9mzRptbe0dO3aEh4ebmJiEhoYuWrSInvT8+fO0tDRXV9dWrha5aWhoIIQkJCTcv39/9+7d5FWuKykp1dXVhYWFjRo1qqn38vn82bNnV1MrG2sAACAASURBVFVVxcbGLl68eMWKFWPHjqX3lLTeuHHjtLW1r169amZmNnToULoxPT1969atXC5XS0tr+fLlhBADA4O1a9e2yRLfGCVxvobYFIavn/JwPIahQIXhClGipsVQ0FDHUFBbzVBQ0OS+o5dqqhgKGC+XLC1mKGDcBVfBdILoihbcUvuh5MnDkoyY/n440r9rvyZoYJpDq7+SFhcyFKgynhrD9KfBk3KR7n8oKDIUNDCth8oyhgIu0yI4TJ+CeVU38a9DnLIac03zBHyGAj7Tnw9jN5VadPC1GZWVlbdv37awsBDdFWf69Ok1NTWJiYmtnDNbXbp0afDgwZMmTTpw4EBFRYW6unq/fv2ys7MJIUZGRkVFRQ0NDY8ePfLy8jpz5oyZmZmnp2dAQICZmdm///4bFha2Zs0aBQWFv/76y8rKaty4cfQtBe/fv29sbPzRRx9lZGRs3bo1ICDA0dHxzz//3Llzp6+v79ChQzMyMpra3CeEWFpa/vPPP9XV1VIvspfg7+8fERHxzTffrFq1im5ZuXLlxo0bxWtEn6gDIeAR8IQQBLwYBPzLAgR8S927d8/U1PT48eOOjo6EkIaGBlNTU19f36CgoFbOGaA1sIseAKBVjI2NnZyc5s6dGxwcrKGh8eOPPz579ow+fxveEmlpaXPmzGncPnLkyKioKPn3Rz4Q8AAArUJRVExMzLJly+bNm9fQ0GBjY3P+/HmJS+GhYzk6OtJ3p3mvIOABAFpLT09PfDwYgLcBLpMDAABgIWzBAwCAHP3xBwkJkaHe25tMny56VVhYOG/evIyMDGNj402bNo0fP16iXGpBTk7OF198cfnyZVVVVU9Pzw0bNjQeNIjZ7dukqdPSJRgZER5P5vm3NQQ8AADI0bZtRKZx7crLxQN+xowZZmZmeXl56enpkydPzsvLMzExES9vXKCjo/Pxxx/7+vrGx8ffu3fP3d1dXV195cqVMvfcyopUVraoMieH9Okj8/zbGnbRAwCAHNXXEQ6R4cF/fdXo9evXz507FxwcrK+vP23aNAcHh507d4rPW2rB33//XVlZuX79el1d3YEDB/r5+bXkXsIsgIAHAAA5UuIQVa4MD6XX92zIz8/v1auXtrY2/XLQoEEFBQXi85ZaYGdnd/PmTR6PRwgRCASnTp0yMzOT16d9be3atRRFffPNN+KNWlpaje8fLLXxDWAXPQAAyNHAAcTD4+XzhBjy91kpNX2tiNerGwnkvL4fXHFxsaampuilpqbmkydPxN8ntUBVVVVVVZUQcvv27UWLFpWVlcn/2nc+nx8dHe3k5BQdHb1q1SrGoQraBLbgAQCa4+joSFEUfYNxcba2thRF/fjjjxLtJSUlCgoKFEXRdyp1dna2t7eXU1/fCdUVJC/r5aOqnKjwpDzqq17XVLy+b6Ourm55ebno5fPnzyXGxm2qoLa2dt26dXZ2djY2Nunp6V27dm3/z/kfaWlpNTU1MTExDx8+PH36tHwWii14AIAmPXr06OTJk2pqavHx8Rs3bmy84bV//37RgC60lJQUPp/pDrvvs9LH5Nyp1y950m6rXFxEEve+fN7HStRsbm5eUFBQXl5ODxF77do1Gxsb8fdJLRAKhR4eHtXV1VlZWfr6+m3+gVoiKipqzpw5enp6kyZN2rVr18cffyyHhWILHgCgSfHx8RwOZ/Pmzbdv37548aLE1P79+585c+bhw4fijQkJCf3795djH981igpESZaH2DcAKysra2vrdevWVVdXHzly5MSJE/RIsocPH6aH75NacOLEifT09NDQ0Jqamjt37ty5c6eoqEien7ikpOT333+nR5j19vbev39/RUWFHJaLgAcAaFJsbKyLi4unp6eKikpcXJzEVFtbW2NjY/FR454/f/7nn3+6u7vLt5vvFA4higoyPP47XlBiYmJubq6BgcGyZcsOHDjQo0cPQkhAQMDevXubKjh//vyLFy/69evX45WpU6fK8xPHxMTU1NR8+OGH+vr6U6dOrays3L9/vxyWi130AADSFRQUXLhwIT4+XkVFZcKECfHx8cHBwRzO6+0iiqLc3d0PHDiwcOFCuuXQoUOamprDhw/voC6/CxQVCU+W6Pnv+K2GhoaNL3K7ceNGMwWrVq0SjevaIaKior799ltvb2/65TfffLNr1y7Ry/aDLXgAAOni4uI0NDToW6F5eHg8ePDg7FnJU74nT578119/iXb5JiQkTJw48U3ukvb+UOQSBQUZHorvdk5lZmZmZWV5e3vrv+Ll5XX69On8/Hy6oLKyskyMQCBoqlFW7/aKAwBoP7GxsePHj+fz+RUVFcOHD5e6l37IkCGGhoZJSUmEkMrKyqNHj06aNEnWBQkEgoZX2H+CHpciChwZHnK5oqz9REVFOTk5iZ/cZ2tr27NnT9HoRDNnztQWQ5/SIbVRVgh4AAApsrOzs7OzY2Ji1NXV1dXVu3TpUlVVdeDAAYkA5nA4kyZNog+pHjlyRElJacSIEbIu68SJE4qvBAYGttlneDtRXKKoKMOD827n1E8//ZSamireQlHUrVu36DvelJWVCf/LyMhIauMbLBr7kQAApIiNjVVWVj5y5Ihof/uZM2eWL19+6tSpkSNHile6u7v/9NNPT548SUhI+Oyzz3iyjzJiZ2dHnwROCNHT02t9599qigqEy5WhXqYD9iAGKw4AQJJQKIyLi3NxcXFwcBA1DhgwYO3atXFxcRIBP2zYsK5du8bGxh46dCg2NvYNFqeurm5tbd3KPr8zKA5RkCXgObIUgxgEPACApL///rugoEDituHq6uqjR49OTEz8+eefFRVfX5xN76UPCgqiKGrUqFGN5/b48WPRAVealZWVxB1a3iMcSsaAb7eeyEouF6+3IQQ8AICk2NhYHo83btw4iXY3N7dDhw6lpaU5OzuLt7u7u4eHh0+bNk1JSanx3PLz8yWuiQoMDHx/A16BQ2S6yoD7tuSUmlpYZWV9Sypzcrz79NFt7/4wenu+GgEAvC1CQ0Nra2vp252K8/b2FgqFdLpfunQpMjKSbv/kk0+EQmFMTAz90t7eXigUWlpaEkKOHj0qbGTTpk1y/DRvGa4iUeDK8PjvOQ2FhYXjxo3T1NS0tLQ8dOhQ49k3U7Bv3z76znc0X19fSkzjSyTedW/LNyMAAHgvcIlsu+j/e5XcjBkzzMzM8vLy0tPTJ0+enJeXZ2Jiwlhw5cqV5OTk7du3jx07VlT577///vjjjxMmTKBfsu/0RmzBAwCAHFEU4SjI8nidU9evXz937lxwcLC+vv60adMcHBx27twpPu+mCq5fv15aWtqtWzfx4ps3b9rZ2XV/hR5Stv1IHQ+eoihDQ0OJay+HDx9OURR9J5zWjA2PgAcAADniKRFFriyP1+cz5ufn9+rVS1tbm345aNCggoIC8Xk3VeDl5RUeHu7k5CSqrKioePToUVhYWO/eve3s7LZt2yYU/uem921LfDx4iQWVl5enp6eLXt6+fTsrK6tNFopd9AAAIEd9bcnnK18+T9hOzh+XUmM5hHgte/n8wuuC4uJiTU1N0UtNTc0nT56Iv4+xQOTBgwdmZmbDhw9fv359VlYWfTze39//jT4SM9F48KampqdPnxYfLnby5Mm7d+8WffmIiYlxc3OTuOzizSDgAQBAjvKyyPF4QggRCEhNlfSb3ty4Qr7+nBBChELSWZ+McKWbdXV1y8vLRVXPnz/X0dERfx9jgYiFhcW///5LP+/du3dOTk5sbGz7BXwz48FPmzbN3d29oqJCTU1NKBT+9ttv27Zta5OAxy56AACQI46Q1NaQ2hpSX0e4CtIfHO7Lmrpa8XvRm5ubFxQUiCL82rVr5ubm4vNmLBC5du0aPYIATUVF5Q1uQdhCzY8H361bt2HDhtGDDl++fLm+vv7DDz9sk+Ui4AEAQI44HMKV5cF5vafZysrK2tp63bp11dXVR44cOXHiBH3Z2+HDh+l7/TZV0JiysrK7u/uuXbtKSkrOnj0bGho6c+bMdvrEjOPBe3p67t69mxCyZ8+emTNnUm00vg4CHgAA5IjLbXLDXepD4T85lZiYmJuba2BgsGzZsgMHDvTo0YMQEhAQsHfv3mYKGrOwsDh48GB4eLiJiYm3t/fy5cu9vLza6RPT48FfvXr16tWrWVlZCxYs2LVrl3jBZ599dunSpTt37sTFxbXh9wwcgwcAAPmS6Tr4/zI0NDx69KhE440bN5ovoAUHB4u/dHFxcXFxeeOetBA9HvyRI0dEI8Z6eXkNGTIkPz+/d+/edIuKisqkSZN8fHx69OhhZmZWU1MjPgd6bHjRSw0NDU7LRtjDFjwAAMiRApdwZXkoSLn77zuEcTx4mqenZ3p6+qxZsxrP4Y3HhscWPAAAyBFHQbYB4rhtc0C6o/z0008SLfR48PRz0TXx9N2O6efKysqi5+Lb7rJCwAMAgBxRRLbBZrCn+U0h4AEAQI4UFKRf+94UxbdlPPjr12e38GZ3xsbq7dyXFkHAAwCAHFFc2XbRU29LwPfooclc9DZBwAMAgBxxObJtwctUDGIQ8AAAIEccDlFQZC4Tr4c3ghUHAAByxOUSiiPD479b8IWFhePGjdPU1LS0tDx06FDj2TdTsG/fvqZubMdK2IIHAAA54nBkO4ue+5/iGTNmmJmZ5eXlpaenT548OS8vz8TEhLHgypUrycnJ27dvHzt2bJt8iHcCtuABAECOKEq2G92IuX79+rlz54KDg/X19adNm+bg4LBz586WFFy/fr20tLRbt25y/aQdDVvwAAAgR51UidmAl88f3SbVlVJqeMrEsNfLceTqXt+3NT8/v1evXtra2vTLQYMGFRQUiL+vqQIvLy8vL6+lS5c+ffq0rT/P2wtb8AAAIEdaXUlPy5cPPWPC4Up56HYjvaxe1RiJ3lpcXKyp+fpaNU1NzSdPnojPm7GgNdauXUtR1IYNG0QtAQEBFEWFhIQIBIKtW7daWFgoKysbGhp+8cUXEveT7xAIeAAAkKOSR+RU4svHowLpu+WfPnhd8+D1Nrqurq5orHdCyPPnz3V0dMTnzVjQGvQ4b6JR5IVCYXJyMpfLnT59elJSUkBAgLa29urVq7t16xYeHh4WFtZWy31j2EUPAAByRFEynmT3ekPU3Ny8oKCgvLxcQ0ODEHLt2jUbGxvxWsaC1jA3Nx86dOj58+fv3LnTvXv37OzsgoKC8ePHd+3a1cTE5Keffho/fryamtrjx48vX77cq1evtlruG8MWPAAAyJGCAqFkeYidRW9lZWVtbb1u3brq6uojR46cOHGCvuzt8OHDmZmZzRS0FXq0N3ojPjk5mRDi6elJCBk8ePDChQsVFBT09PTCw8OnTJkyadKkNlzum0HAAwCAHHEowuXI9hCTmJiYm5trYGCwbNmyAwcO9OjRgxASEBCwd+/eZgraypQpUxQVFemAT0pK0tLSmjBhgmhqly5d0tPTJ0yYsG/fvs2bN7fhct8MJWzq3vnUWzBC3/EYhgIVphv6q2kxFDTUMRTUVjMUFOQwFNRUMRTU1zMUlBYzFCgxjZdc8YKhYEUEQwEh5OEthgIjc4YCxhtQCxqY5tDqg0rFhQwFqhpMs2D60+ApMxQw3sargWk9VDKNIMllWgSH6VMwr+oWDLuhrMZc0zwBn6GAz/Tnw9hNpU4t7w60gVOJ5DHTn6E4bV0yama79UZmEydOTElJuXDhwpAhQ+bNm/fLL78QQgoLC0tKSnr37q2mpvbo0SMDA4MhQ4ZcuHChY7uKLXgAAJAjLpdwFWR5yHJf2/Y3a9YsoVA4d+5c8mr/PCFk165dAwcO/N///kcIuX//PiGkU6eO/+KIgAcAADniyHKXGy73bbsX/bhx47S1ta9evWpmZjZ06FC6cdKkSQoKCkFBQQsWLJg+fTohZMaMGR3aTUIQ8AAAIFf07eXf2YBXUlKaMmUKIcTLy4t6dSy7X79+KSkpRkZGu3btoigqNDT0888/79BuEoLL5AAAQK64Ml4m99aMBy/yyy+/0Ifexbm4uLi4uHRIf5qCgAcAADmiuMzn24rjIqfeEFYcAADIEUfGgH/LdtG/Q7DiAABAjjgynkX/34B/s/HgpTb6+vpSYuLi4tr7o8sZtuABAECOKI6MW/D/KX6z8eClNv77778//vij6E41enp6rf5sbxfc6AY3uiGE4EY3YnCjm5cFuNENtI/sM+QZ0/80caqaZNAI+un169cHDRr05MkTekDYsWPHDhkyZP369aJaqQXu7u5S32VgYJCcnDxkyJA2/HBvFWzBAwCAPHEI9w2Pwb/ZePBSGysqKh49ehQWFnbhwgVdXV0vLy9/f3+q2S3bRX/tq+MzffkmhBASZDdBX4VxU6HdIeABAECONLSJwav7wz+5R56XSKlR1SQGPV8+rygVNb/ZePBSGx88eGBmZjZ8+PD169dnZWXRx+P9/f2b6fjRu/9UMe70JYQQEjBwFAIeAADeMw0N5Nnjl8/rayTGknmJX/e6hghEzW82HrzURgsLi3///Zdu6d27d05OTmxsbPMB/87BWfQAACBH/HpSXvzy0VAn/e51gobXNWJnKYmGe6dfXrt2zdz8P6f+SC2Q2njt2jV6UDiaiooKj8drp0+spqYmOldfR0dnypQpxcWynIXwX0VFRRRF1dTUiJ40VYmABwAAOeJwCKUow0PsGPybjQcvtVFZWdnd3X3Xrl0lJSVnz54NDQ2dObMdx6zbs2dPcXHx48ePT5w4cevWrSVLlrTfskQQ8AAAIEcciihwZXj89+qbNxsPvnGjhYXFwYMHw8PDTUxMvL29ly9f7uXl1X4fWlNTs3Pnzl26dLG2tvbx8fnnn38a15w9e9bOzk5dXd3GxiYtLY1uzMvLGzNmjIaGhqmp6datW5u88E0aHIMHAAA54ii25k52hoaGR48elSi5ceNG8wVSG+V/93ihUHj37t2UlJRPP/1UYlJRUZGzs/NPP/00YcKE3377zdXV9cmTJ0KhcPTo0bNnz963b98///zj7u6upaXV8j4j4AEAQI44rbrRzTtqypQpioqKfD6/oqLCwsJi3759EgVxcXE2Njb0XoRFixapq6uXl5efO3eOx+MFBQVRFPXRRx8FBAQcO3YMAQ8AAG8lDiXbHatYcS/6H3/80dHRkRBSU1Pz66+/9uvXLzs7++DBg4sWLSKE2NraWllZ9erViy6mKMrHx4cQcvfu3fv379NHGQghdXV1ffv2bflCEfAAACBHFFfG4WLZkFNdu3bt3r07/fybb74JCwu7evWqp6enp6cn3bh58+Zjx47Rz4VC4YYNGyZPnmxkZGRsbCy6nO/Bgwe1tbUtXygbvhkBAMA7g6vwckC5Fj5kuu3d26qioqKsrKysrKyoqOjnn39WVlbu16+feMHkyZPPnDnz22+/PXv2LDw8/Pvvv9fR0Rk1alR5efmWLVtKS0svXLhgZ2cnOvmuJdjwzQgAAN4ZFId5rARxrNhFP23aNPqJgoJCnz59EhISunTpIl7QvXv3gwcPLlu2zM/Pr1evXgkJCV27diWEpKamfvnll+vWrdPW1p43b97nn3/++PFjKQuQBgEPAAByJOt48O/+FnxFRUVLyhwdHa9cuSLROGDAgJMnT4q36Ovr0xfLiZ40BQEPAAByxOEQBZky+50P+I6CgAcAADlS4BCBTFvw/8mpwsLCefPmZWRkGBsbb9q0afz48W3cvabFj53bwvvMGKtrt3dnWgIBDwAA8sSR7TI57n+GcJ0xY4aZmVleXl56evrkyZPz8vJMTEzauINNMP5rh5DfotHkFMcsIRpdmOvaGQIeAADkiFIgHAFz2ev615v7169fP3fuXEpKira29rRp03bv3r1z587169e3fSeleZYaIqitbEmlxkeeXAQ8AAC8X7gc2aJHbDzZ/Pz8Xr16aWu/3AE+aNCggoKCtu0dm7Dh8gMAAHhnKCoRdZ2XD6VOhKsg5cFTfl2j2En01uLiYk1NTdFLTU3NJ0+edMRnkIGzszPViL6+/pvNreVjxRJswQMAgFwJhKSm6vVLqcfjheR1Def1MXhdXV3RsO6EkOfPn+vo6LRPL9vMvn376uvrCSHffffd1atX4+PjCSEURTG9rw1gCx4AAOSIyyFcrgwP6nVOmZubFxQUiDL+2rVr5ubmHfQxWooeKLZz584qKio8Ho9+rqurK1HW5mPFkua24GWckRT1TGcb8hsYCq6mMxQ8YDr60n8YQ8ELpvv6qmsxFAwdzVBQynTXod7WDAUlDxkKVJk6qchjKFDpxFBACPEfx1DA+J20e0+GgiqmE1gEfIYCPlOB9VCGgk6qDAW11QwFAqYTiBh/HIxrspDpN5/x5l+Ma1Jbj6Ggrrl9gy81MP2NM3ZDppuWS8X4r8xrdWsXATKR9c50Yj9AKysra2vrdevWfffddydPnjxx4sRPP/3Utr3rEO0xVizBLnoAAJArisv8FVbcf7+iJSYmzpkzx8DAwNDQ8MCBA6KR1t5p7TFWLEHAAwCAXMl6+Pm/9YaGhkePHm3L/nSQ3bt3t+tYsQQBDwAAIH/tPVYswUl2AAAAHas9xoolCHgAAICORY8VGxISYmho+Ouvv9JjxWpoaKSmph48eNDExMTd3Z0eK1am2WIXPQAAQLv75ptvmpna5mPFEmzBAwAAsBK24AEAAJh19dkhZLx9CyGEEAUtg/buTEsg4AEAAJjdIMMEVItuAdefasm9w9odAh4AAIBZSmJ2XR3TvRcJIYT06KnTqZNie/eHEY7BAwAAsBACHgAAgIUQ8AAAACyEgAcAAGAhBDwAAAALIeABAABYCAEPAADQXnbv3q2lpaWlpeXk5CTnReM6eAAAgPYiPiysnGELHgAAgIUQ8AAAACyEgAcAAGAhBDwAAAAL4SQ7AAAAZr3MOjfUt2iwGR6P296daQkEPAAAADPvzwd3dBdkg130AAAALISABwAAYCEEPAAAAAsh4AEAAFgIAQ8AAMBCCHgAAAAWQsADAACwEAIeAACAhRDwAAAALISABwAAYCEEPAAAAAsh4AEAAFgIAQ8AAMBCCHgAAAAWQsADAACwEAIeAACAhRDwAAAALISABwAAYCEEPAAAAAsh4AEAAFgIAQ8AIF1GRsa4ceMMDQ1VVFT69eu3cuXKsrIy0VQtLa2IiIh2WnRiYmJcXFw7zRzeEwod3QEAgLdRenq6k5OTnZ3dqlWrNDU1s7OzIyIi0tLSTp8+zePxCCH29vYGBgbttPTExMSKioqpU6e20/zhfYCABwCQYsuWLX379j116pSioiLd4urqOnTo0MOHD0+cOJEQcujQoQ7tIAAD7KIHAJDi9u3bZmZmonQnhNjZ2S1evLhTp070y86dO4t20dfV1S1durR79+6mpqarV6/etm2bpaUlPal79+579uwJDg7u27evpqamh4dHaWkpPam8vPzLL780MzNTVlbu0aPH2rVrBQIBIWTo0KF79+5NSUmhKKqsrExNTS06OlrUjc8//9zZ2Zl+bmRkFBsbGxQUpKOjk5+fTwiJjo62tbVVVVW1srLau3ev6F0ZGRkURYWHh7fP2oK3EbbgAQCksLe3j4yMDAgIWLhwYY8ePejGkJAQqcU+Pj6///77mjVrunbt+tNPPxUXF6upqYmmRkRE6OrqBgcHFxQUBAQE6Onp/fzzz4SQOXPmnDhx4osvvjA3N8/IyNiwYYO5ufnMmTP379+/cOHCysrKiIgIdXX15vsZFRV19+5dHx8fHR2dsLCwJUuWLFy4cNmyZUeOHJk5c2Z9ff3s2bMJIZqamo6OjkZGRm2ycuCdgIAHAJAiODiYz+dv27Zt69atH3zwgaOjo7Ozs7Ozs4KC5L/N3NzcvXv37t+/393dnRDi6upqYmIiHvBPnz49deoUl8slhFy6dOnSpUt0u0Ag2Lp1q5eXFyFk+vTpGRkZWVlZhBBjY2N1dXWKonr37s3Yz5ycnKysLF1d3YqKiqCgoGXLln3//feEkClTpggEgtWrV3t5eVEUZWVldfz48bZZNfCOwC56AAAp1NXVIyMjS0pKjh079tlnn6Wnp0+YMKFfv363bt2SqDx37hyPx6MPzBNCNDQ0xowZI17g4uJCpzshRF9fn8/n088TEhK8vLwEAsHNmzcjIyNv3LhB76KXyaeffqqrq0sIycnJKSsrmzVrlmiSh4fHgwcPHj58KOs8gR0Q8AAAkvh8fkVFBZ/PV1FRGTVq1KZNm7Kzs1NTU0tKSr788kuJ4nv37unp6YkinBDSrVs38QI9PT2pSzl37py9vb2mpqazs3N6enpTZRKEQqH4S1NTU/pJYWEhIcTGxkb5FTc3N0LIs2fPWjJbYB/sogcAkHTjxg1LS8u0tLSRI0fSLRRFjR492tXVNTU1VaK4W7duxcXFfD5flPGPHz8WL6AoqvEinj175uDg4OnpGRUVZW5uTgixs7NrSd8kZi46ZEB/q0hPT9fR0REv6N69e0tmC+yDLXgAAEm9evXS1dUNDQ2tq6sTNVZWVp4+fXrAgAESxYMHD66rq0tOTqZflpeXHz16lHERFy9erKurW7t2LZ3uVVVVd+/elVrJ5XKLi4vp52VlZRkZGVLL+vbtq6KikpeX98EriYmJX331lZKSEmNngJWwBQ8AIElZWTk4ONjb29vW1tbV1dXAwKC4uDguLu7evXuxsbESxYMGDXJ1dfX29r5165aent62bdv09PSkbrWLs7CwUFBQWLFixZw5c0pLSzdt2lRTU5OZmVlYWGhsbMzhcHJyctLS0j7++GNra+stW7bQN9T7/vvvmzoTXktLKzAwcO7cubm5uf379z979uwvv/yyadMmuifXr1+nT7B3dXVtk1UEbz8EPACAFLNnzzYyMvr111/j4+Pv3r1rYGBgZ2e3Z8+egQMHNi7eu3dvYGBgSEiIhoZGQEBAdnZ2HxX8/wAAIABJREFUZmZm8/M3NTWNiYlZvXp1cnKylZXVd999V1JSsmDBgsjIyPXr13t4eJw5c8bV1fX+/fs7duzw8/Pz9fXt1avXokWLioqKmtqIX7Nmjba29o4dO8LDw01MTEJDQxctWkRPev78eVpaGtL9vUJJnK/RlurrGAr4DQwFV9MZCh4UMBT0H8ZQ8KKMoUBJmaGgkxpDQeljhoLe1gwFJUwnwapqMRQo8hgK9Ftwdaz/OIYCpk0W0r0nQ0FVJUOBgM9QwGcqsB7KUNBJlaGgtpqhgPFEaMYfB+OaLGT6zecwHX1jXJPaTCd81dUwFBBCGpj+xhm70eiaNJkx/ovzWt3KJVRWVt6+fdvCwkJ0V5zp06fX1NQkJia2cs4ArYFj8AAArVJSUmJlZfXXX3/RLxsaGk6dOtW/f/+O7RUAAh4AoFWMjY2dnJzmzp2blJSUlpY2adKkZ8+e+fn5dXS/4H2HgAcAaBWKomJiYoYPHz5v3jwPD4/q6urz589LXAoPIH84yQ4AoLX09PTEx4MBeBtgCx4AAICFEPAAAAAshIAHAABgIQQ8AAAACyHgAQAAWAgBDwAAwEIIeACA5jg6OlIUtXz5col2Z2dne3t7qW9pZpI4JycnSoy2traTk9OVK1faoNOv6Ovrh4aGNn4uISkpafDgwZqamg4ODs10IDc3d+LEibq6uqamphs2bBAIBISQ48ePU9KIhteDjoLr4AEAmvTo0aOTJ0+qqanFx8dv3LiRcYw4WVlYWNBfHQQCQVFR0fbt20eNGvXPP//o6+u37YKakZqa6ubmNnXqVD8/v//973/Dhw/PyckxNTWVKMvNzf3444+HDBnyww8/XL58ee3atTweLzAw0MzMbPPmzeKV2dnZMTExffr0kdtHAKkQ8AAATYqPj+dwOJs3b/b397948eKQIUPadv76+vqzZ88WvRw9evTgwYOPHTvm6enZtgtqRnBwsIODw969ezkczpQpU8zNzelxZiXKNm/e3Ldv399//53L5c6ZM0dFReXixYuEEFNT06VLl4rK+Hz+sGHDVq5caWFhIbePAFJhFz0AQJNiY2NdXFw8PT1VVFTi4uLae3Fdu3YlhHTu3FnqVD6fHxQUZGFhoa2tPXr06OzsbNGk6OhoW1tbVVVVKyurvXv3tnyJZWVlx48fnzZtGofDIYSoq6tPmDDhwIEDEmXV1dX79u3z8/Pjcrl8Pp8QEhwc3LiMELJ9+/YXL16sWLGi5X2AdoKABwCQrqCg4MKFCzNnzlRRUZkwYUJ8fLyAcSxgGdXX1z99+vTp06dPnjzJysqaP3/+gAEDHBwcpBbPnz8/ODjYx8cnIiKivr5+6NChhYWFhJCwsDAfH59hw4ZFRUXZ2NjMnDmz5ffNffjwISHE0tJS1NKvX7+HDx9KjCR+//79qqoqQsjHH3+soqJibGz8zTff8BuNzlxaWrpy5cpNmzYpKSm1sAPQfrCLHgBAuri4OA0NjfHjxxNCPDw89u3bd/bs2ZacPddyZ8+e1dPTE73kcrmHDh1SUVFpXHnr1q3IyMjdu3fPmDGDEOLi4tKtW7ekpCQfH5+goKBly5Z9//33hJApU6YIBILVq1d7eXm15IwBOuC1tbVFLTo6OtXV1S9evNDQ0BA1FhUVEUJ8fX39/f2XL19+7ty5oKAgPp+/bt068blt3bq1Z8+eEyZMkHU9QHtAwAMASBcbGzt+/Hg+n19RUTF8+HB6L33bBnz//v23bNlCP6+pqTl06JCLi0tcXJyHh4dAIBDtMKAo6sKFC0Kh0N3dnW5RV1cvLCzk8Xj//PNPWVnZrFmzRPP08PD47bffHj58aGhoyNgBektd/KsA3dLQ0CBe9uLFC0LI3Llzg4ODCSEuLi7l5eWbN29etWqVgsLLHCktLQ0LC4uOjm7zUxHhzWAXPQCAFNnZ2fTZ4Orq6urq6l26dKmqqjpw4EDj/dKtQV8aRxs/fnxERMQnn3zyzTffEEJOnDih+EpgYOC9e/d0dHTEd31ra2urqqrSe+ltbGyUX3FzcyOEPHv2rCUdoI/6ixc/e/aMx+OJb9OTV6cFjBs3TtTi5ORUWVl5+/ZtUcuePXt4PB42398e2IIHAJAiNjZWWVn5yJEjoi3UM2fOLF++/NSpUyNHjmy/5Q4YMGD37t2EEDs7u8zMTLpRT0/v+PHjZWVl9fX1ioqKdOOlS5dUVVXpgefT09N1dHTE59O9e/eWLI7eyr9x48aHH35It+Tl5ZmYmEhshdNLqa6uFrXU19cTQtTV1UUt0dHRHh4ePB5Plo8L7Qhb8AAAkoRCYVxcnIuLi4ODg/0r8+fP5/F47XouvVAoPHfunLm5OSFEXV3d+hVDQ0NbW1s+n5+YmEhXVlRUjBo16siRI3379lVRUcnLy/vglcTExK+++qqFp7np6uqOHDnywIED9J75mpqaw4cPiw4EiBgZGQ0aNGjPnj2ilgMHDpiYmNA7AAgh//77b2Zmpqura+tXArQVbMEDAEj6+++/CwoK6F3lIurq6qNHj05MTPz555/pzejHjx9LnK9uZWVlY2PT/CRxRUVForKampojR478/fffUr9D9OvXb9q0aXPmzCkoKDA1Nf31118JIVOmTNHS0goMDJw7d25ubm7//v3Pnj1LX8Xe8gPhS5cuHT9+/P/93/85Ojru2LGjvLzc19eXnrRly5YjR44kJyerqamtWLFi8uTJXC53zJgxaWlpsbGxsbGxoqWkpaVRFDV06NAWLhTkAAEPACApNjaWx+OJH3Kmubm5HTp0KC0tzdnZmRCSn5/v7e0tXhAYGEineDOTxOXl5YnKuFyuhYXFrl27PDw8pPYqOjp69erVkZGRT548sbGx+fPPP+kd7GvWrNHW1t6xY0d4eLiJiUloaOiiRYta/mHHjh27b9++H374ISoqytbW9sSJEz179qQn5ebmpqWl0Sfcubu779u3b+vWrQsXLrSwsEhISKAP9tNOnDjRt29fTU3Nli8X2hslcbFjW6qvYyjgNzAUXE1nKHhQwFDQfxhDwYsyhgIlZYaCTmoMBaWPGQp6WzMUlDxkKFDVYihQZDoqpm/EUEAI8Zf8ZyeJcYuhe0+GgqpKhgIB0/lNjCdAWTNtYXRSZSiorWYoYLxUmvHHwbgmC5l+8zlMR98Y16S2HkNBXQ1DASGkgelvnLEbCq3eCGH8F+e1urWLAHgr4Rg8AAAACyHgAQAAWAgBDwAAwEIIeAAAABZCwAMAALAQAh4AAICFEPAAAAAshIAHAABgIQQ8AAAACyHgAQAAWAgBDwDQHEdHR4qili9fLtHu7Oxsb28v9S3NTBKZOnUq1QSJQW7emL6+fmhoaOPnEpKSkgYPHqypqeng4HDlyhWpNeXl5YsWLerevbuqqurAgQNjYmJaMgk6FgabAQBo0qNHj06ePKmmphYfH79x48aWD9HGyN/fnx6xhhCyatUqIyMjf39/+uXAgQPbaimMUlNT3dzcpk6d6ufn97///W/48OE5OTmmpqYSZX5+fikpKYGBgebm5klJSTNmzNDU1KQH42lmEnQsBDwAQJPi/7+9Ow9r6sr7AH6SsBNAohTc0Aroi+CKymjFXWtVpo4LyIgLKk7BpVqxLmhrabVjQetaN3CjFhVF62itj4q1tra29vEdW3dFK4pOLYJQJZKE+/5x3ubNG8M5Vw7r9fv5iyQ/7j3LvZwsN19271ar1cnJyXFxcT/++GOXLl0qa8s9e/bs2bMn/TklJeXll18eP358ZW1cvpSUlF69eu3YsUOtVkdGRrZs2ZL+t1nLmoKCgp07d65evXrq1KmEkMjIyH//+9+fffbZ4MGDGQ9Vf1/ACt6iBwAoV0ZGxqBBg8aOHevi4mLz37RXG5PJtGjRolatWnl6eg4YMOCXX34xP7R169ZOnTq5urq2adNmx44d8rdZWFh47NixqKgotVpNCHFzcwsPD9+zZ49VWX5+/uDBg/v27UtvqtVqLy+v0tJS9kNQ47DAAwDYlpOTc+bMmejoaBcXl/Dw8N27d5dx/xdwlYmPj09JSZkwYcL69esNBsNf/vKX3NxcQsjKlSsnTJjQrVu3zZs3h4SEREdHb926VeY28/LyCCHBwcHme4KCgvLy8qz+jbi/v//BgwcDAwP1ev21a9fS0tLOnj07atQo9kNQ47DAAwDYtnPnTnd39yFDhhBCIiIi7t69e/r06RppyY0bN1JTUzds2DBnzpzIyMgDBw4QQvbt2/fHH38sWrRo9uzZq1atioyM3Lp165gxYxYsWGC1QpeHLvCenp7me3Q6XUlJSXFxsc36FStWtGzZctKkSZMmTRo2bJjMh6Cm4DN4AADbMjIyhgwZYjKZ/vjjj7CwMPouPffy+EpRVlZmfrdApVKdOXNGkqQRI0bQe9zc3HJzcx0cHC5cuFBYWDhmzBjzL0ZERKSnp+fl5TVu3Ji7F/o8wPLKQXqP0Wi0WT9mzJjQ0NDTp0+///77zs7OycnJch6CmoIFHgDAhl/+ZPm9rz179qxcuVKj0VT13rOzs/v3709/njVrVoMGDXQ6naOjo7mAvuym79KHhISYF2n6tKCgoEDOAu/t7U2LzfcUFBQ4ODhYvqa31Lhx48aNG/fu3buoqGjFihVLliyxt7fnPgQ1BQs8AIANGRkZTk5Ohw8ftrP737+T33777dy5c0+ePNmnT5+q3ntoaOi5c+foz15eXseOHSssLDQYDOZV8+zZs66urg0bNiSEnDhxQqfTWf568+bN5eyFPgm4fPly165d6T1Xrlzx9fW1+jbgvn37Fi9efObMGfMzm4CAgNLSUr1ef/DgwfIewgJf4/AZPACANUmSdu7cOWjQoF69enX/U3x8vIODQ/VcS+/m5tb+T40bN+7UqZPJZMrKyqKP/vHHH/379z98+HDr1q1dXFyuXLnyX3/Kysp6++23LV/rM9SvX79Pnz579uyh78zr9fpDhw6ZPwgw8/f3/+mnn06dOmW+5+uvv27WrJmbmxvjIdEhAGF4BQ8AYO2HH37IycmxSpRzc3MbMGBAVlbW2rVr6cvT//znP1aXrLdp0yYkJIT9UAUEBQVFRUVNnDgxJyenWbNmGzduJIRERkbWq1dvzpw5kydPvnTpUtu2bU+fPk2/xS4/kCchIWHIkCFvvfVW3759N23aVFRUFBsbSx9atmzZ4cOH9+/fHxQU1L59+1GjRiUkJPj4+GRnZ6enp6elpdGGlfcQ1Dgs8AAA1jIyMhwcHJ5Naxk2bNjBgwePHz9OQ+iuX78eExNjWTBnzhy6ijMeqpitW7cuWLAgNTX1t99+CwkJOXr0KH2DfeHChZ6enps2bVqzZo2vr++KFSumT58uf7Ovvfbarl27Pvroo82bN3fq1Ck7O7tFixb0oUuXLh0/ftxoNKrV6sOHDyckJPzzn//U6/WBgYG7du0aOXIkIYTxENQ4lcxvU1SEgZd1YLJ9oeb/+e8TnIK7OZyCtt04BcWFnAJHJ06Bs5ZT8PA/nAL/9pyC/DxOgWs9ToG9A6fApwmngBASx4um4r5oaN6CU/DkMaegzMQpMPEK2v+FU+Dsyil4WsIp4H5Vmjsd3JHM5R35at6nb9yR9PTiFJTqOQWEkHIuxn6OZtgJvwjh/okbt0B0FwC1Ej6DBwAAUCAs8AAAAAqEBR4AAECBsMADAAAoEBZ4AAAABcICDwAAoEBY4AEAABQICzwAAIACYYEHAABQICzwAAAACoQFHgAAQIGwwAMAACgQFngAAAAFwgIPAACgQFjgAQAAFAgLPAAAgAJhgQcAAFAgLPAAAAAKhAUeAABAgbDAAwAAKBAWeAAAAAXCAg8AAKBAWOABAAAUCAs8AACAAmGBBwAAUCAs8AAAAAqEBR4AAECBsMADAAAoEBZ4AAAABcICDwAAoEBY4AEAABQICzwAAIACYYEHAABQICzwAAAACoQFHgAAQIGwwAMAACgQFngAAAAFwgIPAACgQFjgAQAAFAgLPAAAgAJhgQcAAFAgLPAAAAAKhAUeAABAgbDAAwAAKJBKkqSabgMAAABUMryCBwAAUCAs8AAAAAqEBR4AAECBsMADAAAoEBZ4AAAABcICDwAAoEDPscAbDIb9+/f//vvvNh81Go3Xrl27f/8+/d7d/v37r1y58rytMRgMxcXFVpu9efPmkydPrCofP358//59qztNJtP169d/++23Z7dcUlJy+/btwsJCxtcC5dSU106ZzaCsxsp8p/yelrdZOVuQJKmoqOjhw4fsbtrsxfM2UnBCK0WF21CJx4zNGX+2nYzzy2ZHnrfg0aNHly5dKi0ttbqf2wuZ3eQe+XIa+ew4iB91AC8oSbaCggJCyIkTJyRJMhqNH3744fDhw+nPixYtcnFxoRv09fXNyMgghNjb2y9atEiv15e3wQMHDkRFRY0YMWLPnj0mkykhIcHBwYEQ0qxZsy1bthgMhqSkJGdnZ0KIo6PjzJkzS0tLzb+bnJxMCPnyyy/pTZPJtHjxYldXV9qGl19+ed++fZIknTt3bvz48fXq1TP318HBITg4eNmyZfn5+fR3uTXsdk6cOJHdDO5YGY1Gbk/ZUyNnC7du3ZozZ46fnx8to9309/efO3duTk6OnF5wdyE+oexuyiHeBvFjhjvjNltueX5xO1JWVsYt+Pzzz19//fWBAwd++umnkiQtXbrU0dGRNvW9994zmUzcnrILuMeMnF6wx0H8qLO5C4AXhO0/qaNtGTlyJCGkX79+o0ePbtu2LSEkISFBkqSkpCSNRjN9+vQDBw7s3bt31KhR9CQfN25cly5dAgMDDxw48Oxplp6eTghp2bLlK6+84ujoOGXKFEdHx7fffnvTpk1jxoyhv65SqaZPn56ZmTljxgyNRjNmzBjzr9NzOzk5md5ctmwZISQmJiYrK2vfvn1jx44lhKxevdrZ2blPnz4pKSlvvPGGnZ3dvHnzUlJSRo4c6eLi0qRJk1u3bn3//ffsmo8//pjdTm4zxo0bxx6rmJgYbk/Zs7h8+XLuFpydnX18fGJjY1esWLF9+/Zt27atWLEiLi7O19fX09OT24s33niDuwvxCWV3k6tSDirxY2bmzJnsGe/Rowf7/OrWrRu7I9OmTWMX0DZ07tx5yJAh9vb28fHxjo6OSUlJX3zxxezZs9Vq9fz589m92L9/P7uAe8zMnTuX3ciwsDD2OISEhAgedZmZmYIHFUDdZftPap8+fQghWq32FQuhoaGEkODgYHouxcfH0+JGjRotXLjQ8tdHjx5NT36j0bhmzRoPD4+OHTvu3bv36dOn5pq2bdtGRESYTCZJkjZt2kQIWbJkifnRcePGOTk5TZkyxXzPli1bCCH0ZYH0zALfvHnzuLg4yzZERUV5eHgMHTrU/Nxi7dq1/v7+9Oavv/7asmXLsWPH9unTh13j6enJbie3GdyxktPTWUyenp7cLYSFhRUVFUnPKCkpCQ8P5/bC2dmZuwvxCWV3s1OnTuwCLy8v8TaIHzOurq7sGXdzc2OfX66uruyOuLi4cAuio6Npq+g7aosXLzYXTJ48WavVsnvh4+PDLuAeM9xeuLu7s8dB/Kjz8fFhHzOzZs2SABTK9gJvMpk++eQTrVY7duxY89uSlm+d6XS6tLQ0SZKMRqODg8MXX3xh+ev0PDSf/Pn5+YmJiVqtVqfTxcXFffnll4WFhc7Ozp999hktuHr1KiEkOzvbvIXt27erVCr61qLZ8OHDW7RoUVJSIv3/Bd5gMBBCDh48aFm8bds2qy3cuXOHEHL16lV6c/Xq1Y0bN3Z3d2fXqFQqdjvlNIM9VnJ6Sl9k63Q6P1vUajV3C6mpqVI5Dhw48LyDaXMX4hPK7ma9evXYBdzJktMG8WNGrVazZ9zNzY19fnHPDu5oW3aEbvmrr74yF6Snp3PPDm4B95jhNlKr1bLHwdXVVfCos7e3Zx8zfn5+EoBC2b7ITq1Wx8XFnT9/Pjc3NygoiC4Alnr06JGVlWUymTQaTWhoaHZ2tvkhSZKOHDliWazT6T744INbt269884733333cCBAz09PY1GIz0hCSFNmzb98MMP6WsC6v79+xqN5quvvrLczooVKx4+fEif0Vveb2dnFxAQcPv2bcs78/Ly7O3tc3JyzPfcvXuXEGJvb09v5ufnE0K8vb3ZNWq1mt1ObjO0Wi17rFxdXbk9PXPmjEajmTdv3nVbOnfuzN3C8ePHJVtXSEmSdPz4cW4vnJycuLsQn1B2NwsKCtgFTZs2FW+D+DHj4ODAnvHg4GD2+eXl5cXuCPew1Gg0P//8M715/vx5y9mhP3PPDo1Gwx0KinECshvp5OTEHofg4GDBo87Dw4N9zFy/fp0AKBV7/TeZTGvXrnV1dY2OjqZnAn1mfeHChfr16/fo0WPHjh07duxwcXGZMWPG0aNHDxw4EBERQbdsfgVv5fLly5988om/v7+zs/Pq1asvXrxo+ajRaMzOzn7ppZc6dOhACJkwYcKuXbuePHlCH921axchZOLEiXFxcYSQ+vXr9+rVa+LEiT169PDy8rp16xZt88GDB3U6HX2rMz09/d69e999912HDh1at25dVlb24MGD2NhYe3v7efPmvfPOO+yakJAQdju5zZg0aRJ7rOgnGuyeSpLUrVu38oZ06dKl3C0QQnr37r1hw4Zvv/324sWLly5dOn36dFpa2qBBg9RqNbcXvXr14u5CfELZ3aQYBVOnThVvg/gxExsby57x3bt3012Xd35xO9KqVStuTzUazT/+8Y+FCxe+9NJLXbp08fHxOXLkyIMHD3bv3q3VasPCwti96N69O7uAe8xwz53o6Gj2OMg5sOXsgntQASiSrMuacnJyevfuTd/pMl/le/HixZiYGPPlwWYhISGZmZmMBZ569OgRveBo8ODBlveHhIQQQtq3b3/nzp2FCxd6eHgQQi5dumQu2L17N11WCSHLly+fMmXKwIEDAwIC7O3t6YdzJ06coItZUVERXTup5s2bnzt3jhZ4eHgkJiY+ffpUr9ezax48eMBu59atW9nNePr0KXusjEYjt6eSJJ08efLnn3+2OZhytvDll1/269fPqgEqlapv376HDx/+/PPP2b148uQJdxfiE8ruJsUoqJSDSvyY4c64VbOfPb+4Hbl69Sq7IDc395133mnUqFGDBg1mzpxpMBiGDx9ubkZ4ePjDhw/ZveCePnv37mUfM9xz5969e+xxkHNgy9kF96ACUCS5/y62rKxs69atFy9ejIuL8/PzM99fUlJy586d+/fvFxcXN2jQoFGjRvTy2mPHjgUEBDRr1oy92YKCgvz8fH9/f/M9+/bt8/f3DwoKoi8rS0tL79y506hRIycnJ3NNaWnpqVOncnJyYmNjzXeaTCaTyeTg4JCXl3ft2rWwsDC6hcuXL58/f97Lyys0NJT+wdXr9XZ2dnZ2dubf5dZw28ltBmOszJ2S2dPyyNlCYWFhXl5eXl6eJEne3t5NmjTR6XTPbqq8XnB3UYkTWmHibaiUY4bwZtySzfOL2xE5h6UkSSqViv7wzTff3Lx5MygoqGPHjvRObi/kdJMq75iRf+6UNw7iRx3Ai6lu/D/4kpKSBw8euLu7e3h40D9MFWYwGA4dOtS9e/cGDRqI1NRFRqMxNzfX29vb6pXl48ePi4uLfXx8rOofPXqUl5fn5+dHv1hsJklScXGx0Wj09PS0mo7K2kU1FMg/qAwGg16vp5e+V0pP9+/fHxgY2KpVK8ZO2bvIzMzs2rUrdwtyOmK5u5s3b7q5uXl7e9scEG4BYxeMY0YmmVswmUw3b950d3c3v8QHeHHV3JsHfHIiR56XVZxIhWvqFjmBIdxcFHZUTqXsohoKBHONysrKxHtKeDFQcnYhHiTFzV/ixvVwx4p9zMg5dAUDmuTsAkCpau8Cz40ToVf0MHDjespjVVM9/a1ScpJwCDMXZcGCBeyonFmzZgnuYvLkyVVdwE134eYaZWZmig8m4cVAydmFYJBUZGQkYabxREVFsQtmzJjB3sXSpUvZxwz9UJ/h7NmzggFNR48elX+aACiM9QdpVEJCgs37zU6ePNmzZ092TUpKCruAbf78+a+++mpWVhZ9O65NmzYff/zx1atXVSrV7du3+/fvP2jQoNdee42xhVOnTt2+fVur1bZr1858p9FoJITcv3+/pKSEEOLo6Jidnc2ouXXrFnc0BHsqjtvCzZs3x8fHr1y5khAyYsSIdu3axcTEDBs2bOjQoeaa6Oho+k3xnTt3RkVFLV68eP78+YSQ11577dGjRx9//HGnTp0OHTr07Luver0+IiJi3bp1grtIT0+v6oJVq1axD6qkpKSIiIiMjAy1Wp2amhobG7tkyZJ58+YRQiZNmqRWq5OTkwsLCwV7unHjxuDg4LS0tPXr148ZM8bPzy8xMXHIkCHmDxHWr1/P3QV7C8nJyeyOZGRkxMfH0+cK69evnz9/flJSEv3dYcOGaTSazMxMdsGGDRvYu/jggw/Yx8zrr79On0yXZ9euXewt/Otf/zLfs3r16ri4uE8++YTeHDp0qMFgGD9+vDlbszw1fv4CVBWby35CQoJg5Ih4fAQ3TkSr1XLbwI7RkGRE+nCHojYEZXAbKScJh5uLwo7Kea4MGZu7qIYCOeku3GwWOekr3HayY6Dk7EI8SIqbv8QNs+Lugn3MODo6co9bwYAmBweH2n/+AlQR25eYJicnC0aOiMdHcONE5ERYsGM0iIxIH+5Q1IagDG4j5SThsHNRHB0d2VE5cuJ62LtwcHCo6gJuugs3QMbJyUlO+gq7GZa/azMGqqysTGbKU3lb4AZJ2dvbs9N4PD092QWOjo7csB32MdOhQwf2cduhQwfBgKaAgIDaf/4CVBXG4i8SOSKOGycyb948mW0oL0ZDfk2dCMoQTMJh56LQt1IZUTn0Y1eRXfTt27eqC7jpLnKyWcQHk/BioNpzMXbyAAALmUlEQVS0acPdhWCQVHh4ODuNZ/ny5eyCgQMHsndBP8VjHDN79+5lH7dZWVnsLRBe2M7cuXPZuwBQMNYCLxI5Ik5OnMhztcFmXI/MmjoRlCGYhMPORXn8+DE7Kkd8F48eParqAm66i5xsFvGeMpZn+fMlGCR17949bhoPu0DOLtjHDK1nn1yCAU3P+1cCQElq+/fg5edsyFFeXM/z1tRRckJmJGYuCuFF5VTKLqq6oFJyjUR6evz4cTkxUIxdHDp06M033xQPkiIy0njYBXJ2ITNeiUEwoAngxVTbF3hKkp2SYZlRIzNOxAqCMuSzTDV5rtFmhMxUelQOm83wFvltqOYIJu4W5OfYiIft2JwOdhtk9oI9DuUVVOJcAChEdb9l8DwqkJJheQE8kREGgqAM+dipJnJGmx0yUylROewucMNb5LSB25GKDa/V9zvy8vIyMjJ27txZXFxM7ykqKrpx48aPP/74+eef9+zZUzDHhjtfcoaCG3QjPg7cAu5ccEeyAo0EqBNq7wLPzbgYNGgQO6OG8MJAJEkiCMqQhxucwh1tbnLRwoULBQNkNm3axO4FTZFjhLfExMRw21ANEUyvvvoq/QCeEBIQEHD37t3w8HDLV6X0Z5EcG+58yczzYYcCCY5D8+bNuQPFnov9+/ezR1KtVrMbCVB3VeST7Ooxc+ZMdsbFN998U1BQwM6xYYeBWLEZlLFo0aJnr/FRHm5Uzvbt29mpJtu2bWOPNje5aOXKlYIBMomJiZcvX2b0YuPGjezwFhr/wm5DNUQwXbhwwcnJKT093cfHZ86cOZ07d9br9R999FFgYKCdnV3Dhg2jo6MDAwNFcmx27NghHrbDPiSmTZv2/fffi4xDQUHBjh07GAW//PILey7i4uLYI2n51T4ApanpZxjlcnNzY2dceHh4sDNqCC8MxLKmvKAMNze3qulf7cKNyuEmwHBHm5tcJB6VY29vzw1O4aa7cNtQDRFMOp0uKSmJ3v/DDz8QQtatW2fZKvEcG+58yQnbYbeBOx3cceDmUHHnQq1Ws0cSQMFq7yWmLVu2ZGdcBAYGcnNszGyGgQQHB5sLygvK8PX1rawe1WbcqJymTZuyU00st2ZztPV6PTtkxt7eXjBApkWLFuxe/PWvf2WHt8iJ66mGCKaHDx82btyY/kyPQKsvdHh5eQnm2FhurcJhO+w2iI8DN4eKOxdlZWXskQRQshp8csHGzbigKRlS+Rk1hBcGMmLECCIvKOMFwcgDmTp1KjvVhDvarVu3ZofM9O7dm4gFyCxYsIDdiwsXLrDDW+ilG+w2VEMEEyFky5YttObBgwfkmWtBuNPBzbHhzpecsB1uKJDgOHALuHPBHUkABau9C7zEy7iwKn42o4bxJ8xMZlDGC4KRB8JNNeGONje56MmTJ+JpPOxeSLzwFjkJM9UQwcRdlsRzbLjzJWcouG0QHAduAXcusMDDi6wOfA9efkqGVUbNsWPH5MSJWEJQBhsj1SQ7O1vOaHNDZiolKoeLHd4ipw1VGsGkUqm2bNkyfvx4Qsjvv//u5eV19OjRZ5/siuTYyDw7uEMhpw0VHgeZBYy5kDmSAIpUexf4CsTU2AwtsSIeJ6J4kuxYofLIjByxyhSqrKicyiows8rSqYZIH61Wa2dnp9FoCCGSJJWWlppvmun1ekY7xRtZudPBJf+ok5OEYw7bUalUFRhJAIWosfcOeIiMIA52lIfN3+LGaLywKhArZIUdOcLNFOLOOHcXlVLAzdIRb6ecDJlEHnY7xRtZKdPBJRhmJfHyl7jDmJiYKKedAHVR7X0Fr1Kpxo0bd+nSpeLi4qVLlw4ZMsTqeX1SUtK7776bkJCQnJz8/vvvv/fee1OmTOnXr5/BYMjMzNy5c2ePHj2aNm1qtdnS0tLMzMx+/fp5e3sTQj799NPq61It9tNPP4WFhXl4eISHhwcFBel0OkmSCgoKrly5cujQoeLi4uzsbPpBe3nOnDnTu3fvrl27Dho06Pr166mpqbNnz65fv/6ZM2cOHTqk0+nu3LmTnJxMv3C/fPnyWbNmxcTE0NSRffv20S/asWecu4s1a9ZERUWJFMydO3fq1KmdO3f29vY+cuRIbGxsWlpaYmJip06dTpw4sWzZsg0bNsTGxgq2MyYm5oMPPpg2bVpYWNi33367evXqv//973QECCEpKSmzZ89mn5i7du0aNWoUo51lZWWCjbxz547gFr755hv2RwDco65r1670E3dLlqfwzZs3T58+3bJlSy8vr7Nnz06aNCk1NfXNN98MCAj4+uuv09PTMzMz6bW0AC+imn1+wUAISU5ONhqNa9as8fDw6Nix4969ey0veWvatGl8fDz9uVGjRgsXLrT89dGjR9P36LRa7SsWQkNDCSHBwcH0ZrV2qRYLCwsLCwsrKip69qGSkpLw8HBfX99ZTL6+vkOHDjUHoq1du9bf35/e/PXXX+kXqMxXdTVv3jwuLs5yL1FRUdwZ79OnD3sXPj4+ggWenp7R0dH0HprnunjxYnMDJk+ebL6cUKSd7u7u9MtmFP1WujkX2RyIy9CuXTt2O8UbKb6F1q1bs4+ZJk2asI86urozTmFXV9eIiAgaUbxp0yZCyJIlS8wboVF97JEEULDavsDTn20Gceh0OnaUh5ubGzslA8y4sUKOjo7cDBl25AjhZQpxZ/x5o3IEC2xm6dCPgaoh0qe8uaCcnZ3Z7RRvpPgWuIE/NAKvvD7KCbPiBv5otVr2SAIoWN24RNxmEIfBYGBHeQQHB8tPwnnBcWOFOnTowA4t8fPzY0eOmB8qL1PI8mbFonI0Go14ATtLx+pDn6qL9GFr0qQJu53ijRTfAjfopkOHDoJhVtzAH8uL/wFeODX57IKJ8II4BgwYwI7y2L17N63nxmiAzFghRmiJnMgRdqYQd8a5UTndu3cXLOjduzc3S0e8nXIifdjztXTpUnY7xRspvgVu4I94mBU38IeG7QC8mOrkAm/GjvKwKubGaLzg5MQKMUJLuJEje/fuZWcKcWecu4uioiLBgsePH3OzdMTbKSfShz1ZBoOB3U7xRopvQU7gj2CYlZzAH/ZIAihY7b2KXn5MDTu0xBI3RgPkxwrZJD/+5dlMocqKyhEvIMwsHZlHZqVE+nCV187jx48LNrKyuilHhcOs6J2VG7YDoBi1d4GH6seIXikuLvbx8eEWVG976zbxwVTGdGAcAKoInt4CIYSYTKb333/f3d29RYsWOp3urbfeote6U+vWrWvYsCG3oCYaXifJGe2q3kJtgHEAqFIVyc0G5Vm1atW7775rjl5ZtWrV77//bo5eobgFIJOc0a7qLdQGGAeAKlWHF3iaicZw8uTJnj17smtSUlIqr0V12Pr16+Pj41euXEkIGTFiRLt27WJiYoYNGzZ06FBzDbdAkPiEis84tw0ysfciZ7TZ5GyB3ZfaMJibN28W7IWcLQC8sOrwAq9SqdLS0goKCnQ63bN5loSQ/Pz8GzduMAoIFvg/3b17t2vXruab48ePP3jw4KxZswYOHGi+BIxbIEh8QsVnnNsGQsjf/vY3bg17L3JGm03OFjZv3lzLB/PRo0eCvZCzBYAXV81dwF8Jrl69qtFoGF/m4RYAFRoaOmnSJMt7cnNz69WrN2HChLKyMpqtxi0Qb4b4hIrPuJwtCO5FzmiLb6H2D6Z4L8RHEkDB6vAreEJIQEAADaaucAFQw4YNmzNnTllZ2auvvhoeHu7s7NykSZMNGzZERkaqVCr677lSU1PZBeLEJ1R8xuVsQXAvckZbfAu1fzDFeyE+kgBKVtPPMESxYzTkFIAkSUajkRu9IpjNIpP4hIrPuJwtiOxFzmhXyhZq+WCK90J8JAEUDN+Dh//DjV6plGwWoMQHUxnTgXEAqCJY4AEAABQIQTcAAAAKhAUeAABAgbDAAwAAKBAWeAAAAAXCAg8AAKBAWOABAAAUCAs8AACAAv0PH+ay+ubnyDcAAAAASUVORK5CYII=" alt /></p>
<pre><code>##
## [[2]]</code></pre>
<p><img 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" alt /></p>
<pre><code>##
## [[3]]</code></pre>
<p><img 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" alt /></p>
</div>
<div id="feature-selection" class="section level2">
<h2><span class="header-section-number">3.4</span> Feature selection</h2>
<div id="row-k-means-to-determine-signature-specific-features" class="section level3">
<h3><span class="header-section-number">3.4.1</span> Row K-means to determine signature specific features</h3>
<pre class="r"><code>### Find representative regions.
# Get W for best K
leukemia.nmf.exp <- setOptK(leukemia.nmf.exp, 4)
OptK(leukemia.nmf.exp)</code></pre>
<pre><code>## [1] 4</code></pre>
<pre class="r"><code>signature.names <- getSignatureNames(leukemia.nmf.exp, OptK(leukemia.nmf.exp))
signature.names</code></pre>
<pre><code>## [1] "ALL B-cell 0.64\nAML - 0.36" "AML -"
## [3] "ALL T-cell" "ALL B-cell"</code></pre>
<pre class="r"><code>FeatureStats(leukemia.nmf.exp)</code></pre>
<pre><code>## DataFrame with 0 rows and 0 columns</code></pre>
<pre class="r"><code>leukemia.nmf.exp <- computeFeatureStats(leukemia.nmf.exp)
FeatureStats(leukemia.nmf.exp)</code></pre>
<pre><code>## DataFrame with 4951 rows and 7 columns
## cluster deltaCenters deltaMean explainedVar oddsVar coefVar
## <character> <numeric> <numeric> <numeric> <numeric> <numeric>
## 1 1000 0.5598768 40404.983 0.9290739 0.07634068 0.9366928
## 2 1011 0.3803309 2573.797 0.9388679 0.06511258 0.3902262
## 3 0101 -0.4294660 -24040.664 0.9588564 0.04290901 0.5927406
## 4 1000 0.5226433 5657.101 0.9607982 0.04080124 0.8355173
## 5 1100 0.2919822 3304.288 0.7907449 0.26463040 0.4499437
## ... ... ... ... ... ... ...
## 4947 1000 0.3247738 1558.5093 0.9386278 0.06538501 0.4453941
## 4948 1011 0.3931513 22919.0305 0.8101850 0.23428596 0.4533714
## 4949 1000 0.4427220 11509.2834 0.8894812 0.12425081 0.6686290
## 4950 1001 0.2278627 929.7619 0.7930793 0.26090794 0.3449582
## 4951 1011 0.4895291 13897.9083 0.7588860 0.31772096 0.6473873
## meanSil
## <numeric>
## 1 0.5842238
## 2 0.6015913
## 3 0.7912017
## 4 0.6246600
## 5 0.4495862
## ... ...
## 4947 0.5933313
## 4948 0.4366444
## 4949 0.5301540
## 4950 0.4561943
## 4951 0.3617552</code></pre>
<pre class="r"><code># You might want to add additional selection features
# such as entropy or absolute delta
# Entropy
leukemia.nmf.exp <- computeEntropy4OptK(leukemia.nmf.exp)
FeatureStats(leukemia.nmf.exp)</code></pre>
<pre><code>## DataFrame with 4951 rows and 8 columns
## cluster deltaCenters deltaMean explainedVar oddsVar coefVar
## <character> <numeric> <numeric> <numeric> <numeric> <numeric>
## 1 1000 0.5598768 40404.983 0.9290739 0.07634068 0.9366928
## 2 1011 0.3803309 2573.797 0.9388679 0.06511258 0.3902262
## 3 0101 -0.4294660 -24040.664 0.9588564 0.04290901 0.5927406
## 4 1000 0.5226433 5657.101 0.9607982 0.04080124 0.8355173
## 5 1100 0.2919822 3304.288 0.7907449 0.26463040 0.4499437
## ... ... ... ... ... ... ...
## 4947 1000 0.3247738 1558.5093 0.9386278 0.06538501 0.4453941
## 4948 1011 0.3931513 22919.0305 0.8101850 0.23428596 0.4533714
## 4949 1000 0.4427220 11509.2834 0.8894812 0.12425081 0.6686290
## 4950 1001 0.2278627 929.7619 0.7930793 0.26090794 0.3449582
## 4951 1011 0.4895291 13897.9083 0.7588860 0.31772096 0.6473873
## meanSil entropy
## <numeric> <numeric>
## 1 0.5842238 0.41736287
## 2 0.6015913 0.09377805
## 3 0.7912017 0.19862689
## 4 0.6246600 0.32592530
## 5 0.4495862 0.10924133
## ... ... ...
## 4947 0.5933313 0.09745639
## 4948 0.4366444 0.12369820
## 4949 0.5301540 0.21847701
## 4950 0.4561943 0.06351516
## 4951 0.3617552 0.26069339</code></pre>
<pre class="r"><code>leukemia.nmf.exp <- computeAbsDelta4OptK(leukemia.nmf.exp)
FeatureStats(leukemia.nmf.exp)</code></pre>
<pre><code>## DataFrame with 4951 rows and 12 columns
## cluster deltaCenters deltaMean explainedVar oddsVar coefVar
## <character> <numeric> <numeric> <numeric> <numeric> <numeric>
## 1 1000 0.5598768 40404.983 0.9290739 0.07634068 0.9366928
## 2 1011 0.3803309 2573.797 0.9388679 0.06511258 0.3902262
## 3 0101 -0.4294660 -24040.664 0.9588564 0.04290901 0.5927406
## 4 1000 0.5226433 5657.101 0.9607982 0.04080124 0.8355173
## 5 1100 0.2919822 3304.288 0.7907449 0.26463040 0.4499437
## ... ... ... ... ... ... ...
## 4947 1000 0.3247738 1558.5093 0.9386278 0.06538501 0.4453941
## 4948 1011 0.3931513 22919.0305 0.8101850 0.23428596 0.4533714
## 4949 1000 0.4427220 11509.2834 0.8894812 0.12425081 0.6686290
## 4950 1001 0.2278627 929.7619 0.7930793 0.26090794 0.3449582
## 4951 1011 0.4895291 13897.9083 0.7588860 0.31772096 0.6473873
## meanSil entropy absDelta.V1 absDelta.V2 absDelta.V3 absDelta.V4
## <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
## 1 0.5842238 0.41736287 16700.196 -55929.744 -74379.973 -62019.591
## 2 0.6015913 0.09377805 -4424.995 -10895.600 -6643.628 -6175.400
## 3 0.7912017 0.19862689 -68083.015 -30868.132 -76178.055 -17230.281
## 4 0.6246600 0.32592530 1648.302 -8626.609 -10557.755 -9813.338
## 5 0.4495862 0.10924133 -4115.362 -8767.533 -14313.137 -11786.910
## ... ... ... ... ... ... ...
## 4947 0.5933313 0.09745639 -1224.0405 -4621.225 -4470.665 -3931.287
## 4948 0.4366444 0.12369820 -67440.3287 -93600.108 -39650.117 -36195.695
## 4949 0.5301540 0.21847701 -472.5316 -23193.018 -27132.367 -20147.910
## 4950 0.4561943 0.06351516 -3307.7331 -4171.742 -4835.147 -1980.109
## 4951 0.3617552 0.26069339 -7152.3087 -47534.210 -32293.208 -19769.663</code></pre>
</div>
<div id="feature-visualization" class="section level3">
<h3><span class="header-section-number">3.4.2</span> Feature visualization</h3>
<pre class="r"><code># Plot all possible signature combinations
plotSignatureFeatures(leukemia.nmf.exp)</code></pre>
<pre><code>## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing
## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing</code></pre>
<pre><code>## Warning: `panel.margin` is deprecated. Please use `panel.spacing` property
## instead</code></pre>
<p><img src="data:image/png;base64,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" alt /></p>
<pre class="r"><code># Plot only signature combinations
plotSignatureFeatures(leukemia.nmf.exp, sig.combs = F)</code></pre>
<pre><code>## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing</code></pre>
<pre><code>## Warning: `legend.margin` must be specified using `margin()`. For the old
## behavior use legend.spacing</code></pre>
<pre><code>## Warning: `panel.margin` is deprecated. Please use `panel.spacing` property
## instead</code></pre>
<p><img 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jKZrJ6uZqscAPDY0T7gKysrFyxYMGDAgD619O7de+bMmSwRP9STTz757LPPbtu2TdOSnJzctWtXa2vrjh07ent7Jycnq5ffKyoq9uzZExQUJISopwsAgD+j/c/klixZsnz5cicnp9LS0mvXrnl7eyuVytOnT3fu3PnTTz/VYYmSIZPJFixYMG7cOAMDg5EjRx46dCg+Pj4+Pl49F587d25AQMC7777r4+MTFxdXUlIyffp09Rvr6QIA4KG0n8EnJiYOHDgwJyfnxx9/NDQ03LBhQ2Zm5nfffVdSUmJlZaXDEqUkKCgoMTGxoKDgzTff/PHHH1NSUiZMmKDu8vPzS0xMzMrKmjhxYllZWUZGhr29/V92AQDwUNrP4K9duzZu3Di5XG5qauru7n7y5EkHB4cePXqEhob+4x//4EY3fyY4ODg4OPihXUFBQX+29l5PFwAAD9J+Bm9mZmZsbKze7tOnz5EjR9Tbbm5u3377rQ5KAwAA2tI+4Hv16rVz587ff/9dCOHm5vbll1+qH4z2ww8/VFZW6qxAAADQeNov0UdERPj5+XXp0uXq1auDBg26ffv2K6+84uLisn79ek9PTx2WCAAAGkv7GfyoUaO2bds2aNAgIYSzs/OHH36YlJQUGRlpaWmpeYYKAADQC+0DXggxceLE//73vwqFQggxf/7869evnzt37sKFC9xVDQAA/Wrqk3pPnTqVkZFx586dsLAwuVxuZWXVpg1P/wUAQM+0n8HX1NTMmDHD3d09PDw8Ojr69u3bBw4csLW1Xbp0qfqeawAAQF+0D/j169fHxcVNnz79u+++U7eMHDnyhRdeiIyM3L59u47KAwAA2tA+4Ddu3Dh48OANGzY4OTmpW7p06ZKcnOzp6blmzRodlQcAALShfcBfuHBh1KhRdZ5pJpfL/fz88vLymlwYAADQnvYB37lz5+Li4gfbCwoKuBc9AAD6pX3ADxo06LPPPrt161btxrNnzyYlJXl4eDS5MAAAoD3tA3758uUqlapv374LFy4UQqSkpLzzzjtDhgxRd+msQAAA0HjaB7ytrW12dvbAgQNXrlwphIiJiVmzZs1zzz2XlZXVvXt3nRUIAAAar0k3pbG3t09JSamoqLh06ZJSqXRwcDAxMdFVZQAAQGuNm8H36dNn9erVdRqNjIxcXFx69+5NugMA0EI0LuDPnj178+bN2i2LFy/u1KmTTksCAABN1aSHzQgh7t27d/fuXZ2UAgAAdKWpAQ8AAFogAh4AAAki4AEAkCACHgAACWr07+C/++67jz76qPZLIUTtFrU333yziZUBAACtNTrgDx48ePDgwTqNb731Vp0WAh4AAD1qXMCnpqY+ojoAAIAONS7gX3rpJc32Tz/9ZG1t3b59e12XBAAAmqpxF9kplUrN9lNPPZWVlaXerqqqWrhw4bVr13RZGgAA0FbjZvBLliz57LPP+vbt27dvXyFEcXGxSqWSyWRKpfKf//xnQEBAly5dHk2dANA4J06c2LJlS+1pCXTCyMgoMjKSm5S3fI0LeD8/v6Kiou+//z42NlYIMW7cOIVC8cwzzzg4OAghTpw40a1bN1tb20dSKQA0RkJCwrp1m4Vw0XchElMpRM7w4cMDAgL0XQn+QuMCfsCAAQMGDBBCqFQquVz+3nvvGRsbnz9/Pi8vTwjxzjvvvPPOO7a2tn379t2zZ88jqRcAGuFJIU7puwaJuSpEd5VKpe8y8NcaF/A//fRT27ZtO3fuLJPJhBBeXl6+vr5CiIqKivbt22/fvt3AwODMmTPff//9IykWAAA0TOMCfsuWLR988IGVlZX6HPzXX39tbm7+zDPPtG3bVghhb2//3HPPjR8//pFUCgAAGqxxAf/GG288++yzZ86cOXPmjBBi2bJly5YtE0J07txZCBEXF3ft2rU+ffo8/fTTcjk3wQUAQG8aF/BWVlYvvPDCCy+8IISQyWRJSUl2dnbnz58/d+7cypUrk5KSNm/eLIQwNTUtLS19JPUCAIAGaPStamuzsLAYOHDgwIEDKyoqVq5c+dVXX3Xr1u3s2bOcgwcAQL+0D/jS0lIjIyP1tlwu9/HxMTc379y5c+fOnf38/HRUHgAA0Ib2AW9qaqrZNjQ0fPAJNAAAQF+4FK5ZlZSUvP322927dzcxMenbt++OHTtq96amprq7u5ubm3t5eZ0+fbqBXQAAPIiAb1YzZ87ctGnT1KlTN23a1KNHj4kTJ2ruCLR///7AwEAHB4fY2FilUunp6Xn16tW/7AIA4KEI+OZTVFSUkJCwYsWKRYsWhYSEJCQk9OzZUzOJj4mJ8fLy2r59++uvv753714zM7N169b9ZRcAAA9FwDefu3fvjh492sfHR/1SLpdbWVlVVlYKIYqLiw8ePBgSEqK+f4BCoRgzZkxycnL9XQAA/BkCvvk4ODikpaX16tWroqLi4sWLn3zyyalTpyZMmCCEKCwsFEK4uPz/p2I4OzsXFhaqVKp6upr9EwAAHhtN+h08tLNq1aoFCxYIId54443AwEBxP+AtLCw0YywtLcvLy0tLS+vpMjMz0zTu3r371q1b6m1TU9NXXnmlWT4KAKCFIuD1YPLkyQMGDDh+/PiSJUvat28fHR2tno6rH+Gjpm6prq6up6v2PqOjo48dO6be7tKlCwEPAK0cAa8HdnZ2dnZ2w4YNKykpWbVq1bJly6ytrYUQRUVFmjFFRUWGhoYWFhb1dNXe5969ezWRz4MAAAAkQfNJTU3t37+/UqnUtPTo0aOysrKiosLOzk4Icf78eU1Xfn5+165dZTJZPV21d65QKCzuMzc3f+QfBgDQshHwzcfBweG77747evSopuXIkSPdunVTKBQdO3b09vZOTk5WL79XVFTs2bMnKChICFFPFwAAf4Yl+ubj7Ozcp0+fCRMmzJ0718bGJiMjY+vWrZ988om6d+7cuQEBAe+++66Pj09cXFxJScn06dP/sgsAgIdiBt985HJ5enq6r6/v8uXLZ82alZOTk5iYOHXqVHWvn59fYmJiVlbWxIkTy8rKMjIy7O3t/7ILAICHYgbfrGxsbLZt2/ZnvUFBQX+29l5PFwAAD2IGDwCABBHwAABIEAEPAIAEEfAAAEgQAQ8AgAQR8AAASBABDwCABBHwAABIEAEPAIAEEfAAAEgQAQ8AgAQR8AAASBABDwCABBHwAABIEAEPAIAEEfAAAEgQAQ8AgAQR8AAASBABDwCABBHwAABIEAEPAIAEEfAAAEgQAQ8AgAQR8AAASBABDwCABBHwAABIEAEPAIAEEfAAAEgQAQ8AgAQR8AAASBABDwCABLXRdwGAlB06dCgpKUnfVUiQjY3N+++/b2BgoO9CgJaLgAceoZUrV+7dmymEjb4LkZhyIW5OnjzZwcFB35UALRcBDzxCKpVKiGFCpOm7EInZL8QolUql7zKAFo1z8AAASBABDwCABBHwAABIEAEPAIAEEfCPh9TUVHd3d3Nzcy8vr9OnT+u7HABAS0fAPwb2798fGBjo4OAQGxurVCo9PT2vXr2q76IAAC0aAf8YiImJ8fLy2r59++uvv753714zM7N169bpuygAQItGwLd0xcXFBw8eDAkJkcvlQgiFQjFmzJjk5GR91wUAaNEI+JausLBQCOHi4qJpcXZ2Liws5C4fAIB6cCe7lk4d8BYWFpoWS0vL8vLy0tJSMzMzTeP69et/+ukn9ba5ufmCBQv+726OChHx6IttVb5r8Mjz/PF17UqDR97lj69rJY0Z/A+mkbpW3fChBHxLp56py2SyOi3V1f/nX/PXX3996tQp9batrW3tgO/fv78Qp4TY2Rzltia2ts//5ZjevXvn5+fzx9c5IyOnTp061T/GycnJ3t6SP77OyWRPP/XUU/WP6dGjh729vRApzVNSa9LV0dGxgUNlrPS2cD/88EPv3r2PHz/+/PP/GyerV6+eP39+RUVF7dQHAKA2Fk9aOjs7OyHE+fPnNS35+fldu3Yl3QEA9SDgW7qOHTt6e3snJyer11oqKir27NkTFBSk77oAAC0aS/SPgfT09ICAgLffftvHxycuLu7IkSPfffedvb29vusCALRczOAfA35+fomJiVlZWRMnTiwrK8vIyCDdAQD1YwYPAIAEMYMHAECCCHgAACSIgAcAQIIIeAAAJIiABwBAggh4AAAkiIAHAECCCHgAACSIgAcAQIIIeAAAJIiABwBAggh4AAAkiIAHAECCCHgAACSIgAcAQIIIeAAAJIiABwBAggh4AAAkiIAHAECCCHgAACSIgAcAQIIIeAAAJIiABwBAggh4AAAkiIAHAECCCHgAACSojb4LQHP45z//uXLlSn1X0YpUV1f36tXLxMRELuc7dDP54YcfHB0d27Vrp+9CWosbN26Ym5ubmprqu5DWJTY21s3NrYGDCfhWITc393/+53/0XUXrkp2dffnyZXt7e30X0loYGBiEhYVFRUXpu5DWwsPD49atW1euXNF3Ia1FTk6Om5tbUVFRw9/C9AIAAAki4AEAkCACHgAACSLgAQCQIAIeAAAJIuABAJAgAh4AAAki4AEAkCACHgAACSLgAQCQIAIeAAAJIuABAJAgAh4AAAki4AEAkCACHgAACSLgAQCQIAIeAAAJIuABAJAgAh4AAAki4AEAkKBWFPA+Pj4ymSwiIqJO+6hRowYPHvzQt9TTVZuvr6+sFgsLC19f39OnT+ug6PtsbGxWrVr14DYAAA/VRt8FNJObN29mZmaampomJSV9+OGHMplMt/t3dHRUf3Woqam5devWhg0bhg8ffu7cORsbG90eCACAhmgtAZ+UlCSXy6Ojo8PCwk6ePOnh4aHb/dvY2Lz22mualyNGjHB3d//qq6+mTJmi2wMBANAQrWWJPj4+3t/ff8qUKcbGxgkJCY/6cNbW1kKITp06PbRXqVRGRUU5OjpaWFiMGDEiNzdX07Vly5b+/fubmJi4urpu3779UdcJAJCqVhHwBQUF2dnZkyZNMjY2HjNmTFJSUk1NjW4PUVVVdefOnTt37vzyyy8//PDD7Nmze/fu7eXl9dDBs2fPjomJmTZt2vr166uqqp577rlr164JIVavXj1t2rSBAwdu3ry5X79+kyZN2rJli27rBAC0Eq1iiT4hIcHMzCwgIEAIERwcnJiYePz48YZcPddwx48ft7Ky0rw0MDBIS0szNjZ+cOTly5c3bdr0+eefT5w4UQjh7+9va2ubmpo6bdq0qKioefPm/etf/xJCjB8/vqamZuHCha+++qrOrxgAAEheqwj4+Pj4gIAApVJZVlbm6empXqXXbcC7ubnFxsaqtysqKtLS0vz9/RMSEoKDg2tqajQLBjKZLDs7W6VSBQUFqVsUCsW1a9cMDQ3PnTtXXFw8efJkzT6Dg4O3bt1aWFhoZ2enw1IBAK2B9AM+974dO3ZoGpOTk1evXm1gYKCro6h/Gqd5GRAQkJ+fv3Tp0uDg4IyMjOHDh6vb58yZ06lTJ0tLy3bt2tV+rxBCvUrfr18/zXxd/bWgqKiIgAcANJb0Az4+Pt7IyCg9Pb1Nm//9sFlZWREREYcPH/b29n50x+3du/fnn38uhBgwYMCZM2fUjVZWVgcPHiwuLq6qqmrbtq268dSpUyYmJra2tkKIr7/+2tLSsvZ+unfv/uiKBABIlcQvslOpVAkJCf7+/l5eXoPvmz17tqGh4SO9ll6lUn3zzTc9e/YUQigUij732dnZ9e/fX6lU7tq1Sz2yrKxs+PDh6enpTk5OxsbG+fn5z9y3a9eu+fPn157rAwDQQBKfwZ84caKgoGDp0qW1GxUKxYgRI3bt2vXxxx+rp9G3b9+uc726q6trv3796u+q7datW5phFRUV6enpJ06ceOh3CGdn55CQkNDQ0IKCgm7dum3cuFEIMX78+A4dOoSHh8+YMSMvL8/Nze348ePr1q1bvnw5V9gBALQg8YCPj483NDQcPXp0nfbAwMC0tLRDhw6NGjVKCHHp0qWpU6fWHhAeHq5O8Xq6asvPz9cMMzAwcHR0/PTTT4ODgx9a1UGprqcAACAASURBVJYtWxYuXLhp06ZffvmlX79+Bw4cUJ9lj4yMtLCwiIuL++ijj7p27bpq1aq3335b+w8PAGjFZCqVSt814JELCQlphtv7oI7Lly/b29vru4rWwsDAIDIyMioqSt+FtBYeHh6//vrrlStX9F1Ia5GTk+Pm5paZmTl06NAGvkXi5+ABAGidCHgAACSIgAcAQIIIeAAAJIiABwBAggh4AAAkiIAHAECCCHgAACSIgAcAQIIIeAAAJIiABwBAggh4AAAkiIAHAECCCHgAACSIgAcAQIIIeAAAJIiABwBAggh4AAAkiIAHAECC2ui7AECyfvvtt6KiIn1X0YqUl5fzB2821dXVNTU1/MGbTUlJSWPfIlOpVI+iFLQovXr1On/+vL6rAAA0ydatWydNmtTAwczgW4UePXqUlpYGBwfru5DW4ptvvvn222/1XUWr89xzzz3//PP6rqK12LZt2x9//BEaGqrvQlqLO3fubN26tXPnzg1/CwHfKpiYmDz11FMrV67UdyGtxeLFiwn45jdy5MioqCh9V9FaHDt27Ndff+X/Ks0mJydn69atBgYGDX8LF9kBACBBBDwAABJEwAMAIEEEPAAAEkTAAwAgQQQ8AAASRMADACBBBDwAABJEwAMAIEEEPAAAEtTUW9XeuXOnU6dOQoi7d+9u3LhRCBEcHPz000/roDQAAKAt7QP+5s2bL7/8ckFBwa1bt6qqqoYNG5aTkyOEWLFixdGjR11cXHRXJAAAaBztl+gXLFhw4sSJKVOmCCH27duXk5Ozdu3a06dPt2nTZtmyZbqrEAAANJr2M/gDBw4EBgauWLFCCLF3794uXbrMnj1bLpePHj06MzNTZwUCAIDG034Gf/fuXVdXV/X2sWPHfHx85HK5EMLR0fHWrVu6qQ4AAGhF+4B/8sknT548KYQ4d+5cbm6ur6+vuv3s2bM2Nja6qQ4AAGhF+4APDg5OS0sLDQ0dO3asiYmJn59fUVHRnDlzkpKShg0bpsMSAQBAY2l/Dn7BggW5ubmbN29u27bthg0bLC0tT506tXLlSicnpw8++ECHJQIAgMbSPuAVCsXu3btLSkoMDQ2NjIyEEPb29llZWf369WvXrp3uKgQAAI3W1DvZXbhwYc2aNfPnz79y5UppaWmPHj1acrr7+PjIZLKIiIg67aNGjRo8ePBD31JPl8aECRNkf2Lp0qU6qdzGxmbVqlUPbgMA8FDaz+BrampmzZoVFxenfhkYGJibmztr1qyoqKj33ntPJpPpqEKduXnzZmZmpqmpaVJS0ocffqjDCsPCwkaNGqXefu+995588smwsDD1y759++rqKAAANJz2Ab9+/fq4uLjp06fPmjWrX79+QoiRI0e+8MILkZGR3bt3nzRpku6K1I2kpCS5XB4dHR0WFnby5EkPDw9d7Xno0KFDhw5Vb8fExDz11FOvvfaarnYOAIAWtF+i37hx4+DBgzds2ODk5KRu6dKlS3Jysqen55o1a3RUni7Fx8f7+/tPmTLF2Ng4ISFBj5UolcqoqChHR0cLC4sRI0bk5uZqurZs2dK/f38TExNXV9ft27frsUgAwGNN+4C/cOHCqFGj6ix0y+VyPz+/vLy8JhemYwUFBdnZ2ZMmTTI2Nh4zZkxSUlJNTY2+ipk9e3ZMTMy0adPWr19fVVX13HPPXbt2TQixevXqadOmDRw4cPPmzf369Zs0adKWLVv0VSQA4LGmfcB37ty5uLj4wfaCggIrK6smlPRIJCQkmJmZBQQECCGCg4Nv3Lhx/PhxvVRy+fLlTZs2bdiwITw8fPz48bt37xZCpKamlpWVRUVFzZs3b82aNePHj9+yZcvkyZMXLlyoUqn0UicA4LGmfcAPGjTos88+q3NX2rNnzyYlJenw9LauxMfHBwQEKJXKsrIyT0/P5lylr6mpqb5PqVRmZ2erVKqgoCB1r0KhuHbtWmho6I8//lhcXDx58mTNG9VfRAoLC5unTgCAlGgf8MuXL1epVH379l24cKEQIiUl5Z133hkyZIi6S2cF6kJubm5ubu6OHTsUCoVCoXjiiSfu3buXnJysVCqb4egZGRlt7wsPD//5558tLS1r/5jQwsLCxMREvUrfr18/o/sCAwOFEEVFRc1QJABAYrS/it7W1jY7O3vevHkrV64UQsTExAghRowYERsb2717d13VpxPx8fFGRkbp6elt2vzv583KyoqIiDh8+LC3t/ejPvqAAQPOnDmj3raysjp48GBxcXFVVVXbtm3VjadOnTIxMbG1tRVCfP3115aWlrXf3tL+mACAx4L2AS+EsLe3T0lJqaiouHTpklKpdHBwMDEx0VVluqJSqRISEvz9/b28vDSNvXv3fv/99xMSEpoh4BUKRZ8+fTQv+/fvr1Qqd+3aNX78eCFEWVnZ8OHDIyMjp02bZmxsnJ+fP3XqVPXIZcuWffvtt19++eWjrhAAID3aB7xcLg8ICNi9e7eRkZGLi4sOa9KtEydOFBQU1LmjnEKhGDFixK5duz7++GP1TPr27dt1Lll3dXVV/76/ni4tODs7h4SEhIaGFhQUdOvWbePGjUKI8ePHd+jQITw8fMaMGXl5eW5ubsePH1+3bt3y5ctb4C2DAAAtn/YB//zzz+fm5iqVSgMDAx0WpHPx8fGGhoajR4+u0x4YGJiWlnbo0CH1TeguXbqkmTqrhYeHq1O8ni7tbNmyZeHChZs2bfrll1/69et34MABOzs7IURkZKSFhUVcXNxHH33UtWvXVatWvf3221ofBQDQmsm0/hXWjRs3XnzxRXt7+9WrV9vY2DDRbMlCQkKuX79+9OhRfRfSWixevHjRokX6rqLVWbRoUVRUlL6raC08PDx+/fXXK1eu6LuQ1iInJ8fNzS0zM1Nz49S/pP0MPjQ01NjYeOfOnTt37rSwsKhzadilS5e03jMAAGiiJl1kZ2xsPHLkSF2VAgAAdEX7gN+3b58O6wAAADrU1OfBAwCAFkj7GXz9V9VxB3UAAPRI+4CfM2dO7Zd//PHHxYsXDxw44OnpOWHChCYXBgAAtKd9wKvvTVtHTk7O0KFD33jjjSaUBAAAmkrH5+BdXV3feuutOreNAwAAzUz3F9l17tw5Pz9f57sFAAANp+OALy8v37Fjh7W1tW53CwAAGkX7c/CDBw+u01JTU3Pp0qVff/01IiKiaVUBAIAm0T7gq6urH2x0dnb29fWdP39+E0oCAABNpX3Af/vttzqsAwAA6JD25+C9vLy+//77B9v37t07duzYJpQEAACaqtEzeM1j4g4fPnzu3DlTU9PavTU1NWlpaV999ZVuqgMAAFppdMD36NFDsz1p0qSHjhk+fLj2FQEAgCZrdMCvW7dOvREWFvb3v/+9Z8+edQYYGhr6+fnpoDQAAKCtRgf8rFmz1BvJycmvvvpq7969dV0SAABoKu0vsjt48OBD0/3zzz+3s7NrQkkAAKCptP+ZXGVl5aJFizIyMv744w9No0qlunDhgo2NjS5qAwAAWtI+4JcsWbJ8+XInJ6fS0tJr1655e3srlcrTp0937tz5008/1WGJaLqrV6/m5eVx8WOzuXjxor5LaI22bt2alZWl7ypai3PnztXU1PB/lWZTVlYmhCguLm74W7QP+MTExIEDBx49evTevXsdO3bcsGGDg4PDxYsXBw4caGVlpfVu8YiUl5efP39e31W0Fur/CG1tbQ0MDPRdS2tx/fr1goKCgoICfRfSirRp04b/qzSbqqoqIYRKpWr4W7QP+GvXro0bN04ul5uamrq7u588edLBwaFHjx6hoaH/+Mc/UlNTtd4zdK5bt24GBgZHjx7VdyGtxeLFixctWnTs2DF7e3t919JaGBgY1NTU6LuK1uXJJ5+8cuWKvqtoLXJyctzc3CwsLBr+Fu0vsjMzMzM2NlZv9+nT58iRI+ptNzc37mILAIB+aR/wvXr12rlz5++//y6EcHNz+/LLL9Vfn3/44YfKykqdFQgAABpP+yX6iIgIPz+/Ll26XL16ddCgQbdv337llVdcXFzWr1/v6empwxIBAEBjaT+DHzVq1LZt2wYNGiSEcHZ2/vDDD5OSkiIjIy0tLWNiYnRXIQAAaDTtA14IMXHixP/+978KhUIIMX/+/OvXr587d+7ChQuOjo46Kg8AAGhD+yV6tZKSknv37qm35XK5paXlnTt3hBDc6wYAAD3SPuB//vnn8ePH/9kF8436rR4AANAt7QP+b3/727fffhsSEtKnTx+5vElL/QAAQLe0D/jMzMzp06dv3LhRh9UAAACd0H7mXVVV9eyzz+qwFAAAoCvaB/ywYcOOHz+uw1IAAICuaB/wa9euPXbs2OLFi0tKSnRYEAAAaDrtz8G/+uqrZmZmixYtWrRokbW1tZGRUe3en376qamlAQAAbWkf8B06dOjQoUP37t11VwwAANAN7QP+iy++0GEdAABAh7QP+D9bhG/btq2VlZWhoaHWewYAAE2kfcA/9dRT9fR26NDB29s7PDzcw8ND60MAAADtaB/wqamp0dHR2dnZAQEBTk5OBgYG586d271796BBg4YOHXrjxo3du3enpaWdOnXK1dVVhxUDAIC/pH3Aq58dd+bMmdr5nZubO2zYsLlz56p/PjdgwIDIyEjO1gMA0My0/x38J598MnXq1DqzcxcXl4kTJ/7rX/8SQpiZmc2YMePs2bNNrREAADSS9gF/5coV9ZPg61AoFDk5OertJ5544tdff9X6EI8XHx8fmUwWERFRp71///4ymWzNmjV12u/evdumTRuZTJabmyuEGDVq1ODBg5upVgCA1Gkf8M8++2xiYmKd29iVlpYmJSW5ubmpX+7du/fpp59uUoGPiZs3b2ZmZpqamiYlJT30Ubk7d+6s0/Lll18qlcpmqQ4A0OpoH/CRkZGXL1/28PBYv379sWPHjh07tmHDhgEDBly4cCEyMvLmzZtBQUE7duyYNWuWDsttsZKSkuRyeXR09JUrV06ePFmn183NLSsrq7CwsHZjSkqK5psQAAC61aSHzSQnJ1dWVoaFhXl6enp6es6aNau4uHjHjh0jRoy4cePGgQMHFi1aNHPmTB2W22LFx8f7+/tPmTLF2Ng4ISGhTm///v27dOmya9cuTctvv/124MCBoKCg5i0TANBaaH8VvRDipZde8vf3P3Xq1MWLFysrK3v27Nm/f38TExMhhJubm/ocs47qbNEKCgqys7OTkpKMjY3HjBmTlJQUExMjl///L08ymSwoKCg5OfnNN99Ut6SlpZmbm3t6euqpZACAxDU1gA0NDQcOHDhw4MAH25u458dIQkKCmZlZQECAECI4ODgxMfH48eN1rpgbN27cv//971u3btnY2AghUlJSxo4d20q+AAEAml/jAqZ///7t27c/evSoeruekadOnWpSXY+V+Pj4gIAApVJZVlbm6empXqWvE/AeHh52dnapqalhYWG///77vn37UlNTG3ugmpqampoa9bZMJjMwMNDNBwAASE7jzsEbGRlpHgtrWq9HUGoLlZubm5ubu2PHDoVCoVAonnjiiXv37iUnJ9e5Ql4ul7/88svqa+nT09PbtWs3bNiwxh4rIyOj7X3h4eE6+wwAAMlp3Az+2LFjmu3MzEwd1/J4io+PNzIySk9P16y3Z2VlRUREHD582Nvbu/bIoKCgtWvX/vLLLykpKS+++KIWZzEGDBhw5swZ9baVlVXTiwcASJWW54ArKyvlcnntSNu7d6+FhcXw4cN79+6tu/JaOpVKlZCQ4O/v7+XlpWns3bv3+++/n5CQUCfgBw4caG1tHR8fn5aWFh8fr8XhFApFnz59mlgzAKA1aHTA5+XlzZgxIzs7+8cff3RwcBBCREdHz58/X90rk8mWLFnyj3/8QyaT6bjSFunEiRMFBQVLly6t3ahQKEaMGLFr166PP/64bdu2mnb1Kn1UVJRMJhs+fPiDe7t9+/aWLVtqt7i6uvbr1+/R1A4AkLLGBfyNGzfc3d1rampefvnlDh06CCF+/vnniIgIa2vrTZs2GRsbL1u2bOHChc8//3ydyatUxcfHGxoajh49uk57YGBgWlraoUOHRo0aVbs9KCjoo48+CgkJadeu3YN7u3Tp0tSpU2u3hIeHE/AAAC00LuCXLVv2xx9/ZGdnP/vss+qW7du319TULFy4UP0jscGDB3ft2nXt2rWtJOBXrVq1atWqB9unTp2qieraPygYOnRo7RvZDh48WPNy3759j7JSAEDr0rir6I8cOfLSSy9p0l0IceDAATMzM02YGRoajhgx4ty5c7qsEQAANFLjAv7KlStOTk6al/fu3cvKyvL29lbfvU7tiSeeuHbtms4KBAAAjde4gG/fvn1VVZXm5ZEjRyorK318fGqPKSws1PxWHgAA6EXjAv7pp5/++uuvNaeN4+LihBC1T7dXV1efOnXK0dFRhyUCAIDGalzAv/rqq99+++3ChQuvXbv23//+94svvnB0dOzVq5e6V6VSLVmy5OLFiy+//PIjKBUAADRU466iDw0NTUlJWbZs2bJly9QtS5cuVf/kfd26dVu2bDlx4oSrq6vmmWkAAEAvGhfwhoaG+/bt27p16/Hjx4UQISEhmvX5/fv3//jjjzNnzly6dGn79u11XykAAGiwRt/Jrk2bNrV/5K2xbds2ExOTVnIDOwAAWjidPY+8VT1BDgCAFq5xF9kBAIDHAgEPAIAEEfAAAEgQAQ8AgAQR8AAASBABDwCABBHwAABIEAEPAIAEEfAAAEgQAQ8AgATp7Fa1aMl+//33W7dubdy4Ud+FtBYnTpwQQiQkJHTq1EnftbQWKpVK3yW0OqWlpfxfpdncuHFDCKFUKhv+Fhn/VbQGvXr1On/+vL6rAAA0ydatWydNmtTAwczgW4U+ffp06tTp6NGj+i6ktVi8ePGiRYsuX75sb2+v71paCwMDg8jIyKioKH0X0lp4eHicPHlS31W0Ol26dGn4YM7BAwAgQQQ8AAASRMADACBBBDwAABJEwAMAIEEEPAAAEkTAAwAgQQQ8AAASRMADACBBBDwAABJEwAMAIEH6D3gfHx+ZTBYREVGnfdSoUYMHD37oW+rpqs3X11dWi4WFha+v7+nTp3VQ9H02NjarVq16cLuO1NRUd3d3c3NzLy+vegrIy8sbO3Zsx44du3XrtmTJkpqamjoDampqfHx8Gv6kAQBAq6XngL9582ZmZqapqWlSUtKjeK6do6Pjp59++umnn37yySfz5s27ePHi8OHDb926pfMD1WP//v2BgYEODg6xsbFKpdLT0/Pq1asPDsvLyxsyZEhlZeWKFStGjx79/vvvR0dH1xmzYcOGjIyMZqkaAPB40/PT5JKSkuRyeXR0dFhY2MmTJz08PHS7fxsbm9dee03zcsSIEe7u7l999dWUKVN0e6B6xMTEeHl5bd++XS6Xjx8/vmfPnuvWrVu+fHmdYdHR0U5OTrt37zYwMAgNDTU2Nq7zpKYrV67Mnz/f1NS02SoHADy+9DyDj4+P9/f3nzJlirGxcUJCwqM+nLW1tRCiU6dOD+1VKpVRUVGOjo4WFhYjRozIzc3VdG3ZsqV///4mJiaurq7bt29v+BGLi4sPHjwYEhIil8uFEAqFYsyYMcnJyXWGlZeXJyYmzpw508DAQKlUCiFiYmJqD6upqQkNDR07dmzv3r0bfnQAQKulz4AvKCjIzs6eNGmSsbHxmDFjkpKSHjzr3ERVVVV37ty5c+fOL7/88sMPP8yePbt3795eXl4PHTx79uyYmJhp06atX7++qqrqueeeu3btmhBi9erV06ZNGzhw4ObNm/v16zdp0qQtW7Y0sIDCwkIhhIuLi6bF2dm5sLCwzvmI69ev37t3TwgxZMgQY2PjLl26LF26VJ30auvXr8/Ly/uzc/wAANShzyX6hIQEMzOzgIAAIURwcHBiYuLx48cbcvVcwx0/ftzKykrz0sDAIC0tzdjY+MGRly9f3rRp0+effz5x4kQhhL+/v62tbWpq6rRp06KioubNm/evf/1LCDF+/PiampqFCxe++uqrMpnsLwtQB7yFhYWmxdLSsry8vLS01MzMTNOovixg+vTpYWFhERER33zzTVRUlFKpXLRokbi/OL99+3ZLS0ut/xQAgFZFnwEfHx8fEBCgVCrLyso8PT3Vq/S6DXg3N7fY2Fj1dkVFRVpamr+/f0JCQnBwcE1NjWbBQCaTZWdnq1SqoKAgdYtCobh27ZqhoeG5c+eKi4snT56s2WdwcPDWrVsLCwvt7Oz+sgD1TL32VwF1S3V1de1hpaWlQogZM2bExMQIIfz9/UtKSqKjo9977z25XB4aGvrSSy+9+OKLTfhLAABaF70FfO59O3bs0DQmJyevXr3awMBAV0dR/zRO8zIgICA/P3/p0qXBwcEZGRnDhw9Xt8+ZM6dTp06Wlpbt2rWr/V4hhHqVvl+/fpqQVn8tKCoqakjAq8/6FxUVaVqKiooMDQ1rz+nF/csCRo8erWnx9fVds2bNlStXjh49+v3338fFxRUXFwshqqurKysri4uLTUxM2rZt28i/BwCgtdBbwMfHxxsZGaWnp7dp8781ZGVlRUREHD582Nvb+9Edt3fv3p9//rkQYsCAAWfOnFE3WllZHTx4sLi4uKqqSpOap06dMjExsbW1FUJ8/fXXdZbHu3fv3pDDqb8EnD9//vnnn1e35Ofnd+3atc7yvvoo5eXlmpaqqiohhEKh+PHHH4uKihwcHDRd2dnZO3fuTE1Nfemllxrz0QEArYh+LrJTqVQJCQn+/v5eXl6D75s9e7ahoeEjvZZepVJ98803PXv2FEIoFIo+99nZ2fXv31+pVO7atUs9sqysbPjw4enp6U5OTsbGxvn5+c/ct2vXrvnz59ee69ejY8eO3t7eycnJ6pX5ioqKPXv2aE4EaDz55JPPPvvstm3bNC3Jycldu3a1trYOCwv7uhYXFxdfX9+vv/5at+cyAAASo58Z/IkTJwoKCpYuXVq7UaFQjBgxYteuXR9//LF6Gn379u0616u7urr269ev/q7abt26pRlWUVGRnp5+4sSJh36HcHZ2DgkJCQ0NLSgo6Nat28aNG4UQ48eP79ChQ3h4+IwZM/Ly8tzc3I4fP67+FXtDrrBTmzt3bkBAwLvvvuvj4xMXF1dSUjJ9+nR1V2xsbHp6+hdffGFqarpgwYJx48YZGBiMHDny0KFD8fHx8fHxMpns6aeffvrppzV7Mzc3t7a2/rMfAgAA8L9U+vDOO+8YGhr+9ttvddo3b94shEhPT1epVCNHjnyw2vDw8Pq7avPx8ak9wMDAwMnJ6dNPP62pqXloVX/88ce8efPs7e1NTU2HDh168uRJdXtNTc2aNWtcXV3bt2/v6Oi4atUqzR6sra3//e9/P7hdx86dO93d3c3MzLy9vU+fPq1pDw0NFUIUFRWpXyYmJg4YMMDU1LRfv34pKSkP3dWgQYMmTpz48D/rn5swYcLgwYMb+y5o7YMPPhBCXL58Wd+FtCJyuXzRokX6rqIVcXd3fySZhHplZmY2/N+RTPUIbhCLliYkJOT69etHjx7VdyGtxeLFixctWnT58mV7e3t919JaGBgYREZGRkVF6buQ1sLDw6PO3TbRDDIzM4cOHdrAwfp/2AwAANA5Ah4AAAki4AEAkCACHgAACSLgAQCQIOkHvI+Pj0wmi4iIqNPev39/mUy2Zs2aOu13795t06aNTCZTPy521KhRTb+lTGpqqru7u7m5uZeX1+nTpx86pqSk5O233+7evbuJiUnfvn1r38FXCJGXlzd27NiOHTt269ZtyZIlOn/sHgBAYiQe8Ddv3szMzDQ1NU1KSnroDwJ37txZp+XLL7+s/ZzWptu/f39gYKCDg0NsbKxSqfT09Lx69eqDw2bOnLlp06apU6du2rSpR48eEydO3LNnj7orLy9vyJAhlZWVK1asGD169Pvvvx8dHa3DCgEA0iPxgE9KSpLL5dHR0VeuXHnwJ5tubm5ZWVnqJ7pqpKSkuLm56bCGmJgYLy+v7du3v/7663v37jUzM1u3bl2dMUVFRQkJCStWrFi0aFFISEhCQkLPnj01k/jo6GgnJ6fdu3eHhob+5z//mTNnDj8/BQDUT+IBHx8f7+/vP2XKFPWzaOv09u/fv0uXLpr7zwshfvvttwMHDjx4r3itFRcXHzx4MCQkRC6XCyEUCsWYMWOSk5PrDLt79+7o0aM1t96Ty+VWVlaVlZVCiPLy8sTExJkzZxoYGKiXFmJiYh7cAwAAtUk54AsKCrKzsydNmmRsbDxmzJikpKQ6p65lMllQUFDtsExLSzM3N/f09NRVDerlARcXF02Ls7NzYWFhnfMFDg4OaWlpvXr1qqiouHjx4ieffHLq1KkJEyYIIa5fv37v3j0hxJAhQ4yNjbt06bJ06VLdnkQAAEiPlAM+ISHBzMwsICBACBEcHHzjxo3jx4/XGTNu3LgjR47cunVL/TIlJWXs2LGaJ9g2nTrgaz/93dLSsry8vLS09KHjV61a1bNnz9dff/31118PDAwUQqhrmz59uoeHR2pq6muvvRYVFVXnOT0AANQh5YCPj48PCAhQKpVlZWWenp4PXaX38PCws7NLTU0VQvz+++/79u17+eWXG3ugmpqa6vvqzK3VM/Xaj55Tt1RXVz90V5MnT87IyFi6dOmmTZvmz58vhFB/FZgxY0ZMTIy/v/+SJUveeOON6OjoP9sDAABCwgGfm5ubm5u7Y8cOhUKhUCieeOKJe/fuJScn1wlguVz+8ssvq6+lT09Pb9eu3bBhwxp7rIyMjLb3hYeH1+6ytrYWQhQVFWlaioqKDA0Na8/pa7Ozsxs2bNh77733zjvvrFmzpqqqqlOnTkKI0aNHa8b4+vr+/vvvV65caWydAIDWQz/Pg28G8fHxRkZG6enpmvX2rKysiIiIw4cPe3t71x4Zw9/MYQAAAzdJREFUFBS0du3aX375JSUl5cUXXzQ0NGzssQYMGHDmzBn1tpWVVe0uOzs7IcT58+eff/55dUt+fn7Xrl3rPE4+NTX1n//8Z3Z2toGBgbqlR48elZWVFRUVtra2Qojy8nLN4KqqKiGEQqFobJ0AgNZDmjN4lUqVkJDg7+/v5eU1+L7Zs2cbGho+uEo/cOBAa2vr+Pj4tLQ07a6fVygUfe5TJ7pGx44dvb29k5OT1SvzFRUVe/bsefAoDg4O3333Xe3HuR45cqRbt24KheLJJ5989tlnt23bpulKTk7u2rWrem0AAICHkuYM/sSJEwUFBXWuRFMoFCNGjNi1a9fHH3/ctm1bTbt6lT4qKkomkw0fPvzBvd2+fXvLli21W1xdXfv169fAYubOnRsQEPDuu+/6+PjExcWVlJRMnz5d3RUbG5uenv7FF184Ozv36dNnwoQJc+fOtbGxycjI2Lp16yeffCKEkMlkCxYsGDdunIGBwciRIw8dOhQfHx8fH19nDQAAgNqkOYOPj483NDSsfd5aLTAw8O7du4cOHarTHhQUVFxcHBAQ0K5duwf3dunSpan/14P3v6uHn59fYmJiVlbWxIkTy8rKMjIy7O3t1V15eXmHDh2qrq6Wy+Xp6em+vr7Lly+fNWtWTk5OYmLi1KlTNeUlJiYWFBS8+eabP/74Y0pKivoXdAAA/BnZQ2/gCokJCQm5fv167VMAeKQWL168aNGiy5cva77M4VEzMDCIjIyMiorSdyGthYeHB7fUbH6ZmZlDhw5t4GBpzuABAGjlCHgAACSIgAcAQIIIeAAAJIiABwBAggh4AAAkiIAHAECCCHgAACSIgAcAQIIIeAAAJEiaD5vBg6qrq2s/lh6PVEVFhRDit99+42/enMrLy/mDN5vq6mp9l4C/wL3oW4VJkyZt375d31UAAJrk2LFjgwYNauBgAr5VyM/PP3z4sL6raEWqq6tzcnL69OnDU32bTX5+vq2trZmZmb4LaS2Kioru3LnTo0cPfRfSihgZGb3yyitt2jR06Z2ABwBAgrjIDgAACSLgAQCQIAIeAAAJIuABAJAgAh4AAAki4AEAkCACHgAACfp/XPA14fF1h04AAAAASUVORK5CYII=" alt /></p>
<pre class="r"><code># Try to display selected features on W matrix
sig.id <- "1000"
m <- WMatrix(leukemia.nmf.exp, k = OptK(leukemia.nmf.exp))[
FeatureStats(leukemia.nmf.exp)[, 1] == sig.id, ]
m <- m[order(m[, 1]), ]
c <- getColorMap(m)
#m <- t(apply(m, 1, function(r) (r - mean(r))/sd(r)))
Heatmap(m, col = c, cluster_rows = F, cluster_columns = F)</code></pre>
<p><img 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" 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