{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Diffusion maps for single-cell data analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By means of this notebook, you can solve all the programming tasks of chapter 4." ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import time\n", "import numpy as np\n", "from scipy.spatial.distance import pdist\n", "from scipy.spatial.distance import squareform\n", "from sklearn.neighbors import NearestNeighbors\n", "from scipy.sparse.linalg import eigs\n", "from scipy.io import loadmat \n", "from pandas import read_excel\n", "from math import ceil\n", "from sklearn.decomposition import PCA\n", "from sklearn.manifold import TSNE\n", "from scipy.io import loadmat\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from sklearn.cluster import KMeans" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 1: Implement the diffusion maps algorithm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is recommended to solve this task by defining a class for diffusion maps and implement a fit_transform function, which returns the embedding of a given data set. This standardizes the code when comparing diffusion maps with other dimensionality reduction methods." ] }, { "cell_type": "code", "execution_count": 247, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class DiffMap:\n", " \"\"\"\n", " Class Diffusion Maps\n", " \n", " Parameters\n", " ----------\n", " n_components: int, optional, default = 2\n", " number of dimensions in which the data will be embedded\n", " sigma: optional, default = 10\n", " bandwidth of the Gaussian kernel\n", " alpha: optional, default = 1\n", " the density rescaling parameter\n", " \"\"\"\n", " \n", " def __init__(self, n_components=2, sigma=10, alpha=1):\n", " self.ndim = n_components\n", " self.sigma = sigma\n", " self.alpha = alpha\n", " self.eig_vals = [] # For later use in Task 4.10\n", " \n", " def __calculate_P(self, X):\n", " K = np.exp((-1) * np.square(squareform(pdist(X))) / (2 * self.sigma**2))\n", " Q_raised = np.diag(np.power(np.sum(K, axis = 1), -alpha))\n", " \n", " K_raised = Q_raised @ K @ Q_raised\n", " np.fill_diagonal(K_raised, 0)\n", " \n", " D_raised_inv = np.diag(np.power(np.sum(K_raised, axis = 1), -1))\n", " P = D_raised_inv @ K_raised\n", " \n", " return P\n", " \n", " def fit_transform_stable(self, X):\n", " \"\"\"\n", " Computes the embedding using a deterministic eigensolver\n", " \n", " Parameters\n", " ----------\n", " X: array\n", " input data\n", " \n", " Returns\n", " -------\n", " evecs: array [n_cells, n_comp]\n", " array of n_comp eigenvectors or diffusion components\n", " \"\"\"\n", " P = self.__calculate_P(X)\n", " eig_vals, eig_vecs = np.linalg.eig(P)\n", " self.eig_vals = eig_vals[1:(self.ndim + 1)]\n", " return (eig_vecs*eig_vals)[:, 1:(self.ndim + 1)]\n", " \n", " def fit_transform(self, X):\n", " \"\"\"\n", " Computes the embedding using a non deterministic eigensolver\n", " \n", " Parameters\n", " ----------\n", " X: array\n", " input data\n", " \n", " Returns\n", " -------\n", " evecs: array [n_cells, n_comp]\n", " array of n_comp eigenvectors or diffusion components\n", " \"\"\"\n", " P = self.__calculate_P(X)\n", " eig_vals, eig_vecs = eigs(P, self.ndim + 1, which = \"LM\")\n", " \n", " ids = np.argsort(-abs(eig_vals))\n", " eig_vals = eig_vals[ids]\n", " eig_vecs = eig_vecs[:, ids]\n", " self.eig_vals = np.real(np.array(eig_vals[1:]))\n", " \n", " return np.real(eig_vecs[:, 1:] @ np.diag(eig_vals[1:])) # There may be artifacts like x + 0i." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 2: Perform a diffusion map analysis on the Buettner data set." ] }, { "cell_type": "code", "execution_count": 248, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class Dataset:\n", " \"\"\"\n", " Data class for simplification for later tasks\n", " \n", " Parameters\n", " ----------\n", " data: input data [n_cells, n_genes]\n", " stage_names: names of the cell embryonic stages (time points)\n", " labels: assignment of each sample to a cell stage\n", " num_stages: number of cell stages\n", " \"\"\"\n", "\n", " def __init__(self, data, stage_names, labels):\n", " self.data = data\n", " self.stage_names = stage_names\n", " self.labels = labels\n", " self.num_stages = max(labels)+1" ] }, { "cell_type": "code", "execution_count": 249, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def load_buettner_data(): \n", " # load buettner data\n", " file = loadmat('data//data1.mat')\n", " data = file.get('in_X')\n", " data = np.array(data)\n", "\n", " labels = file.get('true_labs')\n", " labels = labels[:,0] -1\n", "\n", " stage_names = ['1', '2', '3']\n", "\n", " adata = Dataset(data, stage_names, labels)\n", " return adata" ] }, { "cell_type": "code", "execution_count": 299, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_3d(X, labels, title = \"\", cols = [0, 1, 2], plot = True):\n", " if (len(cols) != 3):\n", " raise Exception(\"Invalid number of columns\")\n", " \n", " fig = plt.figure()\n", " ax = fig.add_subplot(111, projection=\"3d\")\n", " \n", " for label in set(labels):\n", " subset = X[labels == label, :]\n", " ax.scatter(subset[:, cols[0]], subset[:, cols[1]], subset[:, cols[2]], label = \"class \" + str(label))\n", " plt.title(title)\n", " if plot:\n", " plt.legend(loc = 0)\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 300, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "s = 3\n", "alpha = 1\n", "sigma = 20\n", "diff_map = DiffMap(s, sigma, alpha)\n", "\n", "buettner_dataset = load_buettner_data()\n", "buettner_transformed = diff_map.fit_transform(buettner_dataset.data)\n", "#buettner_transformed = diff_map.fit_transform_stable(buettner_dataset.data)\n", "plot_3d(buettner_transformed, buettner_dataset.labels, \"Buettner data with diffusion map\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the results may vary as the picking of the eigenvectors is not deterministic: The Arnoldi iteration *ARPACK* (the underlying C library used by *eigs*) starts by picking a random vector. Because of that, even if all eigenspaces have dimension 1, there can still occur up to 8 different results, depending on the sign of the picked eigenvector. Unfortunately, we could not identify the random number generator used to seed the seed apriori to get consistent results. Therefore, if you want to obtain consistent results, use the slower but deterministic *fit_transform_stable* instead." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 3: Perform a PCA analysis of the Buettner data." ] }, { "cell_type": "code", "execution_count": 301, "metadata": { "collapsed": true }, "outputs": [], "source": [ "pca = PCA(s)\n", "buettner_transformed_pca = pca.fit_transform(buettner_dataset.data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the lack of a better way to compare the results, we visualize the PCA data as well." ] }, { "cell_type": "code", "execution_count": 302, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_3d(buettner_transformed_pca, buettner_dataset.labels, \"Buettner data with PCA\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, the PCA is not able to detect the higher dimensional structure in the data. However, even from this image we can clearly determine differences between the classes." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Single-cell data analysis\n", "\n", "In the following, we will apply Diffusion maps to the Guo data. You can download the file from the homepage. In the files, you will find some necessary information:\n", "\n", "1. the input data, which is a matrix with a certain number of cells as row number and a certain number of genes as column number,\n", "2. the names of the measured genes and\n", "3. an assignment of each cell to an embryonic stage. These assignments have to be converted into numerical labels to use them for the scatter plots.\n", "\n", "### Pre-processing\n", "#### Task 4: Pre-process the Guo data.\n", "\n", "Take a look at the file guo.xlsx. The naming annotation in the first column refers to the embryonic stage, embryo number, and individual cell number, thus 64C 2.7 refers to the 7th cell harvested from the 2nd embryo collected from the 64-cell stage. In the first row, you will find the names of the measured genes." ] }, { "cell_type": "code", "execution_count": 154, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def load_guo_data(preprocess = True):\n", " # load guo data\n", " data_frame = read_excel('data//guo.xlsx', sheet_name='Sheet1')\n", "\n", " # data\n", " adata = data_frame.as_matrix()\n", " data = adata[:,1:]\n", " embryonic_stages = adata[:,0]\n", "\n", " # genes\n", " genes_tmp = data_frame.axes[1][1:]\n", " genes_names = [genes_tmp[k] for k in range(genes_tmp.size)]\n", " \n", " # remove undetectables\n", " detectable_ids = np.less_equal(np.max(data, axis = 1), 28)\n", " data = data[detectable_ids, :]\n", " embryonic_stages = embryonic_stages[detectable_ids]\n", " \n", " stage_names = ['1C', '2C', '4C', '8C', '16C', '32C', '64C']\n", " \n", " if preprocess: \n", " embryonic_stages = embryonic_stages[[not name.startswith('1C') for name in embryonic_stages]] \n", " data = data[[(np.max(data[i]) <= 28) and not adata[i,0].startswith('1C') for i in range(data.shape[0])],:]\n", " g_actb = list(genes_names).index('Actb') + 1\n", " g_gapdh = list(genes_names).index('Gapdh') + 1\n", " t_vals = data != 28\n", " mod = np.tile(0.5*(data[:,g_actb] + data[:,g_gapdh]), (data.shape[1],1)).T\n", " data[t_vals] = data[t_vals] - mod[t_vals]\n", " data[~t_vals] = np.tile(np.max(data[t_vals]), data[~t_vals].shape)\n", " data = np.around(data.astype(float), decimals=3)\n", "\n", " # stage_names and creating labels\n", " stage_names = ['2C', '4C', '8C', '16C', '32C', '64C']\n", "\n", " labels = np.array([next(np.where([name.startswith(sname) for name in stage_names])[0][0] \n", " for sname in stage_names if ename.startswith(sname)) for ename in embryonic_stages])\n", " adata = Dataset(data, stage_names, labels)\n", " return adata" ] }, { "cell_type": "code", "execution_count": 155, "metadata": { "collapsed": true }, "outputs": [], "source": [ "guo_data = load_guo_data()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 5: Perform a Diffusion map analysis of the pre-processed Guo data." ] }, { "cell_type": "code", "execution_count": 298, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def plot_2d(X, labels, title = \"\", cols = [0, 1], plot = True):\n", " if (len(cols) != 2):\n", " raise Exception(\"Invalid number of columns\")\n", " \n", " for label in set(labels):\n", " subset = X[labels == label, :]\n", " plt.scatter(subset[:, cols[0]], subset[:, cols[1]], label = \"class \" + str(label))\n", " plt.title(title)\n", " if plot:\n", " plt.legend(loc = 0)\n", " plt.show() " ] }, { "cell_type": "code", "execution_count": 296, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 59 ms\n" ] } ], "source": [ "s = 2\n", "alpha = 1 \n", "sigma = 10\n", "diffMap = DiffMap(s, sigma, alpha)\n", "\n", "%time guo_transformed = diffMap.fit_transform(guo_data.data)\n", "#%time guo_transformed = diffMap.fit_transform_stable(guo_data.data)" ] }, { "cell_type": "code", "execution_count": 297, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_2d(guo_transformed, guo_data.labels, title = R\"Guo data with $\\sigma$ = 10\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One can very well see, that the younger cells develop similarly until they reach the 16-cell stage. Than the separation into the TE lineage and inner cell mass takes place. However, we cannot determine a difference between PE and EPI. Theoretically, this may be the other way round, however it is far more likely that we observe the separation of TE and inner cell mass." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 6: Comparison with the un-pre-processed data." ] }, { "cell_type": "code", "execution_count": 147, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 36 ms\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "guo_unprocessed = load_guo_data(False)\n", "%time guo_unprocessed_transformed = diffMap.fit_transform(guo_unprocessed.data)\n", "#%time guo_unprocessed_transformed = diffMap.fit_transform_stable(guo_unprocessed.data)\n", "\n", "plot_2d(guo_unprocessed_transformed, guo_unprocessed.labels, \"Unprocessed guo data with $\\sigma$ = 10\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the un-pre-processed data it is almost impossible to detect the separation. We can slightly see a separation that is too distinct to be caused by outliers, however it is not clear that this is actually a lineage separation. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Comparison with other dimensionality reduction methods\n", "\n", "#### Task 7: Compare Diffusion maps with two other methods." ] }, { "cell_type": "code", "execution_count": 149, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 3 ms\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Testing PCA, assuming we should also reduce to two dimensions\n", "pca = PCA(s)\n", "%time guo_pca = pca.fit_transform(guo_data.data)\n", "\n", "plot_2d(guo_pca, guo_data.labels, \"Processed guo data with PCA\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With PCA we can actually see the separation into lineages, however the variance is far higher than in the data mapped by the diffusion maps algorithm. On the other hand, the computation time of PCA is superior to the one of diffusion maps. " ] }, { "cell_type": "code", "execution_count": 150, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 9.32 s\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Testing tSNE, assuming we should also reduce to two dimensions\n", "sne = TSNE(s)\n", "%time guo_tsne = sne.fit_transform(guo_data.data)\n", "\n", "plot_2d(guo_tsne, guo_data.labels, \"Processed guo data with tSNE\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "tSNE shows the separation very neatly and we can even guess the separation of PE and EPI at the bottom. However, the computation time is about a 1000 times slower." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Parameter selection\n", "\n", "#### Task 8: Bandwidth comparison." ] }, { "cell_type": "code", "execution_count": 153, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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rnDOFsbcm3PDcmtmw28ak1rxVW7n66feiLr//+8NbbTVSRofdFpGzgVlAAfCwqt4TsfxU4H5gKDBZVZ8NWdYABPt8/UtVJ6YiphYNvbBNJgJjTHqVzV8bc3lrTQrxSDoxiEgB8AfgTKACeEdE5qvqhyHF/gVcClznsYkaVR2ebBzGGJNuFz/0JlU19VGXF7TQASVXpOKM4URgg6puAhCROcAkoCkxqOpmd1ljCvZnjDEZN2Pe+yzf2LxTSaiLRh6SoWjSKxWNz/2BLSHTFe48v4pEZIWI/FNEzo1WSEQud8ut2LFjR6KxGmNMQv7y1paYy08+okfONzoHpSIxeJ07xdOifajbGDIFuF9EjvAqpKqzVXWEqo7o3bt3InEaY0zCGmJ01Dm4c3uevGxUBqNJr1Qkhgog9PypFNjmd2VV3eb+3wQsBY5PQUzGGJMyLV3lfNuEwRmKJDNSkRjeAY4SkcNEpAMwGZjvZ0UROVhEOrqPewEnE9I20Raka9jt/fv3M378eI455hgGDx7MDTfckPJ9GGMcNz4X/QLTk4/o0SZ6IoVKOjGoagC4ClgErAPmqupaEZkpIhMBROSbIlIBfA/4vyIS7O81CFghIquBJcA9Eb2ZTAzXXXcdH330EatWrWL58uW89NJL2Q7JmDZn3qqt1NRH7zfTlqqQglJy5bOqLlTVgap6hKre6c67VVXnu4/fUdVSVe2iqj1VdbA7/x+qepyqDnP/P5KKePxYsGkBZz17FkMfH8pZz57Fgk0Lkt5mJofd7ty5M2PGjAGgQ4cOnHDCCVRUJD7WkzHGW0tjIrVFeTns9oJNCyj7Rxm1Dc4gdpX7Kin7RxkA4w8fn9A2sznsdlVVFeXl5UyfPj2h2I0x0W2LMSbSwZ3bZzCSzMnLsZJmvTurKSkE1TbUMuvdWQlvM1vDbgcCAS666CKmTZvG4YcfnnD8xhhvJTHuq9DWGp2D8jIxbN+3Pa75fmRr2O3LL7+co446iquvvjrh2I0xzc1btZWT71nM1qqaZn3yBWcE1bbW6ByUl4mhb5e+cc33IxvDbs+YMYPq6mruv//+hOM2xjQ3b9VWbnzu/aahtZWvLtjq370T931/eJu5mM1LXiaG6SdMp6igKGxeUUER009IvI4+08NuV1RUcOedd/Lhhx9ywgknMHz4cB5++OGE4zfGfOU3iz6mpj68XU9xksLyG85os2cKQXk77PaCTQuY9e4stu/bTt8ufZl+wvSEG55bMxt225j4HXbDAs/hGwT49J7c/Z7I6LDbuWj84ePbZCIwxiSvpHsnzzu0xWqIbkvysirJGGOimbdqK/vqAs3md2pfwPXjjs5CRJmXt2cMxhgTKdjoHNm+cHDn9tw2YXCbb1sIsjMGY4xxeTU6A3TuUJg3SQEsMRhjTJNoVznHuvq5LbLEYIwxrmiNy/nS6BxkiSHN0jXsNsDZZ5/NsGHDGDx4MFdccUXM8ZSMMS27ftzRdGpfEDYvnxqdg6zxOYfNnTuXgw46CFXlggsu4JlnnmHy5MnZDsuYnDJv1VZ+s+hjtlXVUNK9E+d/oz9LPtrRNH39uKPzqn0B8viMobq8nPVnjGXdoGNZf8ZYqsvLk95mJofdBjjooIMAZyC9AwcOtDhWkzEmXOjQFwpsrarhryu3cv24o/n0nvF5cZWzl7xMDNXl5VTeciuBbdtAlcC2bVTecmtSySE47PbixYtZvXo1s2Y1H6n1vPPO45133mH16tUMGjSIRx5xbj8RHHZ79erVzJ/v3PwuOOz2e++9x4oVKygtLfXc77hx4+jTpw/FxcVccMEFCcdvTD5qmH8t77e7iE87TmFDx//gV4WPUlPfkJf3YAiVl4nh8/vuR2vDh93W2lo+vy/xweiyNez2okWLqKyspK6uLuoIrMYYDy9ey3mNL1MojYhAoTQyteA1flX4aN71QoqUl4khUFkZ13w/sjXsNkBRURETJ07khRdeSDh+Y/LOyseI/MiKwMUFi/OuF1KkvEwMhf36xTXfj0wPu713714q3UQWCARYuHBh2IitxpgWqHcvvgIa864XUqS8TAx9rrkaKQofdluKiuhzTeI3u8n0sNv79u1j4sSJTY3dffr04Yorrkg4fmPyjhR4ztZ27fKywTlU3g67XV1ezuf33U+gspLCfv3oc83VdJswIdWhZp0Nu21MFC9eCyseaT5/xI/gO7/LfDwZYMNut6DbhAltMhEYY3wKfvmvfMypVpIC+MalbTYpxCNvE4MxxvCd31ki8JCXbQzGmDy2Zi7cNwTKujv/18zNdkStjp0xGGPyx5q5UD4N6t3rFKq3ONMAQy/MXlytjJ0xGGPyx+szv0oKQfU1znzTxBKDMSZ/VFfENz9PWWJIs3QOux00ceJEhgwZktZ9GNMmdPMecyzq/DxliSHHPffcc3Tt2jXbYRiTG8beCu0jhrto38mZb5qkJDGIyNki8rGIbBCRGzyWnyoi74pIQEQuiFh2iYisd/8uSUU8fnzy1nYev2k5f7hiMY/ftJxP3tqe9DYzPez23r17+d3vfseMGTOSjt2YvDD0Qpjwe+h2CCDO/wm/t4bnCEn3ShKRAuAPwJlABfCOiMxX1Q9Div0LuBS4LmLdHsBtwAhAgZXuul8kG1csn7y1nSVPfkTgQCMAe3fXseTJjwAYOLJvQtsMDru9fPlyevXq5TlW0nnnncdll10GwIwZM3jkkUf42c9+1jTsdv/+/amqqgK+Gnb74osv5sCBA553Z7vlllv4+c9/TufOnROK2Zi8NPRCSwQtSMUZw4nABlXdpKoHgDnApNACqrpZVdcAjRHrjgNeVdXdbjJ4FTg7BTHF9OYLG5uSQlDgQCNvvrAx4W1metjt9957jw0bNvDd73434ZiNMcZLKhJDf2BLyHSFOy/d6yZs7+66uOb7kelht998801WrlzJgAEDOOWUU/jkk084/fTTE47fGGOCUpEYvL4N/Y7M53tdEblcRFaIyIodO3b4Ds5L1x4d45rvR6aH3b7yyivZtm0bmzdv5o033mDgwIEsXbo04fiNMSYoFYmhAjgkZLoU2JbqdVV1tqqOUNURvXv3TijQoFGTjqCwQ/hTL+zQjlGTjkh4m5kedtsYY9Il6WG3RaQQ+AQYC2wF3gGmqOpaj7KPAS+q6rPudA9gJXCCW+Rd4Buq2vzndohUDLv9yVvbefOFjezdXUfXHh0ZNemIhBueWzMbdtsYE5SxYbdVNSAiVwGLgALgUVVdKyIzgRWqOl9Evgk8DxwMTBCRX6nqYFXdLSK34yQTgJktJYVUGTiyb5tMBMYYk6yUDKKnqguBhRHzbg15/A5ONZHXuo8Cj6YiDmOMMcmzK5+NMcaEscRgjDEmjCUGY4wxYSwxGGOMCWN3cEuzsrIyunbtynXXXddy4TidfvrpVFZWNg2X8corr9CnT5+U78cYk18sMeS4J598khEjWuyWbIwxvuVtVdK6ZUuY/dMf8tvJE5j90x+ybtmSpLeZ6WG3jTEmHfLyjGHdsiW8MvsBAgecQfP27NzBK7MfAGDQ6DEJbTMbw24D/PCHP6SgoIDzzz+fGTNmtDiQnzHGtCQvzxiWzXmiKSkEBQ7UsWzOEwlvM9PDboNTjfT++++zbNkyli1bxp///OeE4zfGmKC8TAx7du2Ma74fmR52G6B/f2eE8uLiYqZMmcLbb7+dcPzG5Kw1c+G+IVDW3fm/Zm62I8p5eZkYinv2imu+H5kedjsQCLBzp5PI6uvrefHFFxkyZEjC8RuTk9bMhfJpUL0FUOd/+TRLDknKy8QwevJUCjuE33uhsENHRk9OfGjrTA+7XVdXx7hx4xg6dCjDhw+nf//+Te0XxuSN12dCfU34vPoaZ75JWNLDbmdDKobdXrdsCcvmPMGeXTsp7tmL0ZOnJtzw3JrZsNumTSvrjve9vQTKqjIdTauXsWG3c9Wg0WPaZCIwJq90K3WrkTzmm4TlZVWSMaaNGHsrtI/osde+kzPfJKxNnTH46RmUT3KxmtCYFq2Z67QhVFc4ZwbDpsD6V76aHnsrDL0w21HmtDaTGIqKiti1axc9e/a05ICTFHbt2kVRUVG2QzEmdYK9kIINztVbYPVTMOH3lgxSqM0khtLSUioqKtixY0e2Q2k1ioqKKC21ulbThsTqhWSJIWXaTGJo3749hx12WLbDMMakU3VFfPNNQqzx2RiTO6L1NrJeSCllicEYkzusF1JGWGIwxuSOoRc6Dc3dDgHE+W8NzynXZtoYjDF5YuiFlgjSzBKDMab1WjMXXvol1LiDUnbqAefca4khzSwxGGNapzVz4fkrQENuUlWzG+b9xHlsySFtrI3BGNM6vfTL8KQQ1Fhvo6emmSUGY0zrVNP8niZN7LqFtLLEYIxpfVq60Y5dt5BWlhiMMa3Lmrnw/H/FLmPXLaSVJQZjTKuxYOktnPXObQz9en/OKi1hQZfOzQuN+JE1PKdZShKDiJwtIh+LyAYRucFjeUcRedpd/paIDHDnDxCRGhF5z/17MBXxGGNyz4JNCyjb/DyVhYWoCJXtCynr1SM8ObTvAt/5XfaCzBNJJwYRKQD+AJwDHAtcJCLHRhT7EfCFqh4J3AfcG7Jso6oOd/+uSDYeY0xumvXuLGojhsyvbdeOWQd3/2pGYUdM+qXijOFEYIOqblLVA8AcYFJEmUnA4+7jZ4GxYjdNMMaE2L6v0nt+YcFXEzVfZCia/JaKxNAfCL3paoU7z7OMqgaAaqCnu+wwEVklIn8TkdHRdiIil4vIChFZYfdcMKaNWTOXvvUBz0V9AyHXMlhvpIxIRWLw+uUfeU/JaGUqgUNV9XjgWuApETnIayeqOltVR6jqiN69eycVsDGmlXnpl0z/ooqixsaw2UWNjUz/osqZsFFUMyYViaECOCRkuhTYFq2MiBQC3YDdqlqnqrsAVHUlsBEYmIKYjDE5ZEG7WmYd3J1aEdqpgir96gOU7dzN+H37nTGSbBTVjEnFWEnvAEeJyGHAVmAyMCWizHzgEuBN4AJgsaqqiPTGSRANInI4cBSwKQUxGWNywZq5LFg2k7JePaht5/xObeSrM4Xx+/Y75X75afZizENJJwZVDYjIVcAioAB4VFXXishMYIWqzgceAf4sIhuA3TjJA+BUYKaIBIAG4ApVjXEdvDGmrViw9BZmbXyWyi4FIOGVF8HeSOP37XfvvWAyKSWjq6rqQmBhxLxbQx7XAt/zWO+vwF9TEYMxJncs2LSAsk+fp7Yw+lfQ9sICaNfe2hWywK58NsZk3N3Lf0Vtu9g91vs2KJz7v9aukAV2PwZjTEYtWHoL1Q37IcalTEUFRUwfXQaHj89cYKaJnTEYYzLqlk+fj5kUUKWs9GzGW1LIGksMxpiMWLBpAWc9exb1PsY8GL/8oZaH3jZpY4nBGJN2CzYtoOwfZVTuq4x9tgC0V4X6GrtLWxZZYjDGpN2sd2dR21Drq2wgmDjsLm1ZY4nBGJN2lVEGyPPSNDaSjYuUNZYYjDFp1078fdU0jY1k4yJllXVXNcak3IJNC5j17iy279vOQR0OolEbW1ynnSplO79gfGFPGHerXb+QRZYYjDEpFWxoDrYpVB+obnGdooIiyv5PmXVRbSWsKskYk1LxNDQHTTpykiWFVsQSgzEmpbbv2x73On+v+HsaIjGJssRgjEmpgzp43msrpkSSiUkfSwzGmJRZsGkBe+v3xr1e3y590xCNSZQlBmNMysx6dxYN2tBywQjTT5iehmhMoqxXkjEmKaFdU7XZ7d5b9v2jv28Nz62MJQZjTMIiu6bGo1uHbtw48kZLCq2QJQZjTMIiu6aevLaBKUuVnl/C3k6AQtda2HUQPHW6sHxwQVPZNy56IwsRGz/yMjGsW7aEl/94P40N8dWFduxazNhLL2fQ6DFpisyY3HLE21uZsbSxKREU1UIHtzbpoJqvyvX+Ev5roQINLB9cQL8u/bISr/En7xLDumVLWPiH34HGXxdat3cPCx/4LQsf+K13ASmisNMYCjsOQgpAG6Brj46MmnQEA0darwvTtlSXl3PFS0qHemc6NBF4KQrAlKXKyqFF1tjcyuVdYlg254mEkoIvWktg/6KmyUDtG9R+sYfy3wmggPu/XTFjQBlYAAASdElEQVSFnU5hwHGjqNpRw97ddRR1KURR6vY1WDIxrVJ1eTmf33c/gcpKCvv1o2H/fjrUx/dZ6vUlNvRFDsi7xLBn184076GRQM0S0AAQcOdp+P/GPQT2vcrmNVDYcRCBunVUVb8BjXugXTGBulN49U91vPqnDwHo2KWAUy88moEj+7Ju2RKWzXmCPbt2UtyzF6MnT7WqLZN21eXlVN5yK1rrtCcEtm1LaDvtS0osKeSAvEsMxT17sWfnjvTuRP300AgQqHUa3wL7X6UpiTTucaedpAFQt6+BV//0IX+fU071tgVNZffs3MHCB2ZRubGa0kEn8eYLG9m7u46uPToyYEhPNn+wq2nazkCMH5W/+hVVc5+BhgYoKKD7hd+j32238fl99zclhWR0Pe3UFERp0k00XdUqaTRixAhdsWJFQusm08aQFu2KnTMFj/lF3S4Lm1Vb/VD0st0vo8Uu5G5NliUKE1kt1Oeaq9n/7rtU/WVOs7LSuTO6f7+v7dYXQE17KK513m6RCktKOGrx60lGbxIlIitVdURL5fLujCFY7ZJIryR/2gHtgTofRaMkBfCeH6usnzznltm7u44lT34EEDM5fPLW9rCzkMhk0tJy0zp5VQtV3nIrWuf9no2VFAq6d2d7YxU9vwzvkjrn7oBnYghU+r+Tm8mevEsM4CQHP/Xyc2+/mS0frPa/YbdXEkRUD3kqpLDoFKc6KcpZgOc8v2VbEDjQyJsvbIz6Rf7JW9tZ8uRHBA44N1iJTCYtLTetR3V5OZV33oVWVTkzRJqdMSdSTSRFRXzt5pu4qu5/mt26c9dBThfVSIX9rJtqLsjLxODXhbfc6atc6C/nYHUNEPKl79ErqeiUpjaE5knESRqRCotO8V3Wj727o5/VvPnCxqYv/aDQZNLScpNZXlVDQHhCCEpBNWphSQl9rrmabhMmcOo/V/P0x0+HLX/qdOG/FipFIW9VKSpqisu0bpYYUmDgyL4eX4ZnAD+Nud7fnvqIte7Fn01JJCJphGpKJD7K+tG1R8eoy6IljeD8lpabzPGqGtp2w41OA3KahLYTRLuXwoH20DHg/ByS7t3pd/NNdJswIW0xmdSxxJBFp005htOmHEO0JBJZh9+9dycqPh7kmQiknaCN/n8JFnZox6hJR0Rd3rVHR88v+WAyaWl5qnj9Es7VL5fq8nL+feddNLi/4GN9WbZUNvR1oV275kkgjUmBgoKwych7KZy8tqHZ2QIp6NFkMscSQyvmfSbi8Gr4BWLOk3agjf56JY2adERYGwKEJ5OWlqdCtEZSICvJIZkkVV1eTuVNN6P19U3ztKqKbTfe1DQd3LZ064bu2RP25a5VVWz7xS/DkkWTdCYBD90v/F7YdN8ufcPaGKYsjUgKOG0Yn993f84m9XyTku6qInI2MAsoAB5W1XsilncEngC+AewCvq+qm91lNwI/AhqAaaq6iBYk013V+JftXknrzxjreSFVNro8RiYpcOrM+90+09eXXbTnAk7Pnsba2pRcJ5AJ3S+aTL/bbmuajhxhdc7dAe8bvYgwaN2HmQnSeMpYd1URKQD+AJwJVADviMh8VQ19B/wI+EJVjxSRycC9wPdF5FhgMjAYKAFeE5GBqgnc6cOkXKwzFj/LkxWta2M2ujx6XeAVz6/gWFcKNzsDaOWq/jKHziec0PS8g1cyB+/JUNWtgB7VzT/C1iMpd6TiDm4nAhtUdZOqHgDmAJMiykwCHncfPwuMFRFx589R1TpV/RTY4G7PmKhfJNn4gkkmSVWXl6c6nKz7/L77w6bHHz6eVy54hTWXrGHIjLuRoqKw5dYjKbekIjH0B7aETFe48zzLqGoAqAZ6+lwXABG5XERWiMiKHTvSPKSFaRX6XHN1q/mCSSZJRX6JtgWxEmK3CRPod/tMCktKQITCkhLfVW6mdUhF47PXBY6RDRfRyvhZ15mpOhuYDU4bQzwBmtwU/CJJZ68kv+0kfa65ulkbw/b+o/hs6BReuWJxzHUTqvoqLIRArAsks6ulhNhtwgRLBDksFYmhAjgkZLoUiKxQDZapEJFCoBuw2+e6Jo+l8wsmnqu3I5PU5wPH8nHpuTTUSIvrFvbrF/dopCV33+XsK8FRTNPNqoXatlRUJb0DHCUih4lIB5zG5PkRZeYDl7iPLwAWq9Mdaj4wWUQ6ishhwFHA2ymIyZgWxbp620u3CRM4avHrDFr3IZsHT6ahQXyt61UlRmH032SFJSV0mzDBez0RpFOnGM8qM0KTdXV5OevPGMu6Qcey/oyxbbJNJd8knRjcNoOrgEXAOmCuqq4VkZkiMtEt9gjQU0Q2ANcCN7jrrgXmAh8CLwM/tR5JJlOSuXo7nnW96txL7r6L7hdNblY2tA3Fc71f3xuzW2uzRJKAwpISJ7aIC9lClwcFu/EGtm0D1aZrTSw55La8G3bbmKDHb1oe9ertS+46OW3rhkrkorlY13f0uebqpKqgSn7z67Crq1u6dqM1XWtiWub3OoZUVCUZk5NGTTqCwg7hHwG/V28ns26o0Oqpoxa/7qs9JVZvreD2Qn/Vh4lyFgDOhXah+/fTu6g1XWtiUseGxDB5K9hInMjV28msmyw/vbW8elEFf+0Dnsu+dvNXw3OE7itWsorWsG4Xs+U2q0oypo2KVU2VqsEJkx0qxGSW36okSwzGmKS0pRFw2zq7tacxJiPsYra2xxqfjTHGhLHEYIwxJoxVJRlj4pLu+3CY7LPEYIzxLZ7xpUzusqokY4xv8Y4vZXKTnTEYY3xLZHwpq3rKPXbGYIzxrWuPjnHND1Y9BRNHsOrpk7e2py1GkzxLDMYY3+IdI8qqnnKTJQZjjG8DR/ZlzMXHNJ0hdO3RkTEXHxO1aihW1dPjNy23M4dWytoYjDFxGTiyr+82go5dCqjb532LFevR1HpZYjDGpExkQ3NjC7etDhxoZNncTywxtDJWlWSMSQmvhub6upZvyFi7L2BVSq2MJQZjTEp4NTTHs65pPawqyRiTEn7ulR0qULeOQO0b0LiH2upi1i07wKDRY9IUnYmHnTEYY1Ii2rUMXgJ16wjsfxUa9zgzGvfwyuwHWLdsSZqiM/GwG/UYY1IichyloNAzA9oVU1h0ylfTEaRdO1SV4p69GD15qp1BpJjdqMcYk1HBnkWvPf4h6uaGpjMD3O5JjXvCpyNoo7Pinp07eGX2AwCWHLLAqpKMMSkzcGRfvnXJsU3Tgdo3aJ4EWujDGix1oI5lc55IXXDGN0sMxpiUGjiyL0NOLXEmPKqL4rFn184URGTiZYnBGJNyp005hjN/eCxScFBS2ynq2jVFEZl4WGIwxqTFwJF9OefKy0ASb8rMwb4xbYIlBmNM2gwaPYbjz74UaeeeObQrBinyvX7dvr1piszEYr2SjDFpdcal51I66KSm3krNeirFIO3st2s2WGIwxqTNumVLWDbnCfbs2kmnrgejchKFHQcBENj/MhC7rkgbWh5ryaSepWNjTFqsW7aEV2Y/wJ6dO0CVmj27qftyIbVf/A+B/YtpKSkE3XfxuXZFdIYllRhEpIeIvCoi693/B0cpd4lbZr2IXBIyf6mIfCwi77l/fZKJxxjTeiyb8wSBA17jJ9UD/sdVagwEePnBWZYcMijZM4YbgNdV9SjgdXc6jIj0AG4DRgInArdFJJCLVXW4+/d5kvEYY1qJVF6D0BgI2MVuGZRsYpgEPO4+fhw416PMOOBVVd2tql8ArwJnJ7lfY0wrV9yzV0q3Zxe7ZU6yieFrqloJ4P73qgrqD2wJma5w5wX9ya1GukVEJNqORORyEVkhIit27NiRZNjGmHQbPXkqhR38j7jaklQnGhNdi72SROQ1wOu+ezf73IfXl32w1eliVd0qIsXAX4EfAJ7ni6o6G5gNzuiqPvdtjMmS4OB3rz82m7q9yQ2N0a6wkNGTp6YiLONDi4lBVb8VbZmI/FtE+qlqpYj0A7zaCCqA00OmS4Gl7ra3uv/3iMhTOG0QVpFoTBsxaPQYBo0eE9ZttahrV+prAzTU1/jaRlFxMWdccrmNsppByV7HMB+4BLjH/f+CR5lFwF0hDc5nATeKSCHQXVV3ikh74DvAa0nGY4xphYIJItTfnvqIFS9cF3O9nz/9YjrDMlEk28ZwD3CmiKwHznSnEZERIvIwgKruBm4H3nH/ZrrzOgKLRGQN8B6wFXgoyXiMMTnitCnHtFjmtYf/NwORmEhJnTGo6i5grMf8FcCPQ6YfBR6NKLMP+EYy+zfGtG2rX11I/6MHWTVShtmVz8aYVm3x47OzHULescRgjGnVavck16PJxM8SgzEmazp2LfZVztoaMssSgzEma8ZeermvcqtfXWjJIYMsMRhjsiaeRuU1r7+cxkhMKEsMxpis+vZVP/dVThsb0xyJCbLEYIzJqkGjx/hODiYzLDEYY7Ju0OgxDDvz29kOw7gsMRhjWoVv/fgnMZNDca/eGYwmv1liMMa0Gt/68U/49lU/bzZcd2GHjja6agYlO4ieMcakVLCnUnA01uKevRg9eaoNi5FBlhiMMa2O12isJnOsKskYY0wYSwzGGGPCWGIwxhgTxhKDMcaYMJYYjDHGhLHEYIwxJowlBmOMMWEsMRhjjAkjqprtGOImIjuAz1K0uV7AzhRtKxtyOf5cjh0s/myz+OP3dVVtcdCpnEwMqSQiK1R1RLbjSFQux5/LsYPFn20Wf/pYVZIxxpgwlhiMMcaEscQAs7MdQJJyOf5cjh0s/myz+NMk79sYjDHGhLMzBmOMMWEsMRhjjAmTF4lBRHqIyKsist79f3CUcpe4ZdaLyCUh8y8SkfdFZI2IvCwivTIXfUri7yAis0XkExH5SETOz5XYQ5bPF5EP0h9xs/0mHL+IdBaRBe5rvlZE7slg3GeLyMciskFEbvBY3lFEnnaXvyUiA0KW3ejO/1hExmUq5pD9JxS7iJwpIivdz+pKETkj07G7cST82rvLDxWRvSJyXaZibkZV2/wf8GvgBvfxDcC9HmV6AJvc/we7jw/Gucvd50CvkG2V5Ur87rJfAXe4j9sFn0suxO4uPw94Cvggx947nYExbpkOwDLgnAzEXABsBA5397saODaizE+AB93Hk4Gn3cfHuuU7Aoe52ynI4OudTOzHAyXu4yHA1iy8XxKOP2T5X4FngOsyHX/wLy/OGIBJwOPu48eBcz3KjANeVdXdqvoF8CpwNiDuXxcREeAgYFv6Qw6TTPwA/wncDaCqjaqayastk4pdRLoC1wJ3ZCBWLwnHr6r7VXUJgKoeAN4FSjMQ84nABlXd5O53Ds7zCBX6vJ4Fxrrv70nAHFWtU9VPgQ3u9jIl4dhVdZWqBj+ba4EiEemYkai/ksxrj4ici/PDYm2G4vWUL4nha6paCeD+7+NRpj+wJWS6AuivqvXAlcD7OAnhWOCR9IbbTMLxi0h3d/p2EXlXRJ4Rka+lN9wwCcfuPr4d+C2wP51BxpBs/AC4x2EC8Hqa4owrntAyqhoAqoGePtdNp2RiD3U+sEpV69IUZzQJxy8iXYBf4pzhZ1VhtgNIFRF5Dejrsehmv5vwmKci0h4nMRyPk8n/B7iRFP+CTVf8OMe4FFiuqteKyLXAfwM/SChQrx2n77UfDhypqtdE1sOmUhpf++D2C4G/AL9X1U3xRxi3mPG0UMbPuumUTOzOQpHBwL3AWSmMy69k4v8VcJ+q7nVPILKmzSQGVf1WtGUi8m8R6aeqlSLSD6fNIFIFcHrIdCmwFBjubn+ju625OHXNKZXG+Hfh/Np+3p3/DPCjVMQclMbYRwHfEJHNOO/VPiKyVFVPJ4XSGH/QbGC9qt6fgnD9qAAOiYgnsvozWKbCTVzdgN0+102nZGJHREpx3utTg5/ZDEsm/pHABSLya6A70Cgitar6QPrDjpCtxo1M/gG/IbwB8dceZXoAn+I0Gh7sPu4BlACVQG+33O3Ab3MlfnfZHOAM9/GlwDO5EntImQFkp/E52df+DpzGxHYZjLkQ5+z2ML5qAB0cUeanhDeAznUfDya88XkTmW18Tib27m758zP9PklF/BFlyshi43NWdpqFg9UTp253vfs/+KEdATwcUu4/cRrbNgA/DJl/BbAOWAOUAz1zLP6vA393438dODRXYg9ZPoDsJIaE48f5tajue+c99+/HGYr728AnOD1kbnbnzQQmuo+LcM4eNwBvA4eHrHuzu97HZKAXVapiB2YA+0Je6/eAPrkSf8Q2yshiYrAhMYwxxoTJl15JxhhjfLLEYIwxJowlBmOMMWEsMRhjjAljicEYY0wYSwzGGGPCWGIwxhgT5v8D37v7WQJA+gYAAAAASUVORK5CYII=\n", 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\n", 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+a4GngA3ARuDVdMtqjDEmcwK5Ul5V5wJzo7bd43lcDnzH57j7gftj5LkM6B9E+YwxxmSeXSlvjDEmEBZQjDEmSzK5fP2dd95Jz549adeuXUbyT4QFFGOMaQZGjRrFO++806BlsIBijDGrZsLD/WFSB+f3qplpZ5nN5esBvvGNb1BUVJR2udNhy9cbY1q2VTNh9o1Q6S4GuXuz8xxg4CUpZZnt5esbC2uhGGNatjcmHwomEZUHnO0pyvby9Y2FBRRjTMu2uzS57QnI9vL1jYUFFGNMy9a+OLntCcj28vWNhQUUY0zLNvQeyIvqQspr7WxPUUMsX//Tn/6U4uJi9u/fT3FxMZMmTUq5/KlKe/n6xqSkpESXLVvW0MUwxjSwZJevZ9VMZ8xkd6nTMhl6T8oD8o1dY1++3hhjmraBlzTbAJJN1uVljDEmEBZQjDHGBMICijHGmEBYQDHGGBMICyjGGGMCYQHFGGOyJFPL1+/fv58LLriA448/nhNPPJHbbrut/oMywAKKMcY0A7fccgtr165l+fLlLFmyhFdfzf5d0y2gGGNavDmb5jD8xeEMfGYgw18czpxNc9LOM5vL17dp04azzz4bgFatWnHyySdTWpr6WmSpsgsbjTEt2pxNc5j0z0mUVzmLM5btK2PSPycBcEGfC1LKsyGXr9+1axezZ89m4sSJKZU9HdZCMca0aFPen1ITTCLKq8qZ8v6UlPNsqOXrw+Ew3/ve97jxxhvp06dPyuVPlQUUY0yLtm3ftqS2J6Khlq+fMGECffv25aabbkq57OkIJKCIyEgRWSciG0SkzvQCEckXkRnu/rdFpJe7vZOILBSRvSLyaNQxi9w8V7g/XYMoqzHGeHVr2y2p7YloiOXr77rrLnbv3s0jjzyScrnTlXZAEZFc4DHgPOAE4HsickJUsh8CX6rqMcDDwEPu9nLgbuCWGNlfpqqD3Z/P0y2rMcZEm3jyRApyC2ptK8gtYOLJqY9BZHv5+tLSUh544AE++ugjTj75ZAYPHsxTTz2VcvlTlfby9SJyGjBJVUe4z28HUNVfeNLMc9MsFZEQsA3oou7JReQKoERVb/Acswi4RVUTXo/elq83xkDyy9fP2TSHKe9PYdu+bXRr242JJ09MeUC+sWvsy9f3ADZ7npcCp8ZKo6phEdkNdAK+qCfvP4hIFfBn4H71iX4iMgGYAHDkkUemVAFjTMt2QZ8Lmm0AyaYgxlD8Rp6iP/gTSRPtMlUdAAxxf+pO5AZUdaqqlqhqSZcuXeotrDHGmMwIIqCUAj09z4uBrbHSuF1e7YG6o1QeqrrF/b0HeB44JYCyGmOMyZAgAsq7QF8R6S0irYBxwKyoNLOAy93HFwML/LqvIkQkJCKd3cd5wLeADwMoqzHGmAxJewzFHRO5AZgH5AK/V9XVIjIZWKaqs4CngWdFZANOy2Rc5HgR+QQ4DGglImOB4cCnwDw3mOQCrwNPpltWY4wxmRPI0iuqOheYG7XtHs/jcuA7MY7tFSPbrwVRNmOMMdlhV8obY0yWZGr5eoCRI0cyaNAgTjzxRK655pq4631ligUUY4xpBmbOnMnKlSv58MMP2b59Oy+88ELWy2ABxRjT4u2ePZv15wxlTb8TWH/OUHbPnp12ntlcvh7gsMMOA5wFIg8ePFjvWmKZYAHFGNOi7Z49m7K77yG8dSuoEt66lbK770krqESWr1+wYAErV65kypS6KxdfdNFFvPvuu6xcuZJ+/frx9NNPA9QsX79y5UpmzXImzEaWr1+xYgXLli2juLjY97wjRoyga9euFBYWcvHFF6dc/lRZQDHGtGifP/wIWl57+XotL+fzh1NfZLGhlq+fN28eZWVlVFRUxFyROJMsoBhjWrRwWVlS2xPRUMvXAxQUFDB69GheeeWVlMufKgsoxpgWLVRUlNT2RGR7+fq9e/dS5gbAcDjM3Llza61gnC0WUIwxLVrXm29CCmovXy8FBXS9OfWbVGV7+fp9+/YxevTomkkAXbt25Zprrkm5/KlKe/n6xsSWrzfGQPLL1++ePZvPH36EcFkZoaIiut58E+1HjcpgCRtOY1++3hhjmrT2o0Y12wCSTdblZYwxJhAWUIwxxgTCAooxxphAWEAxxhgTCAsoxhhjAmEBxRhjsiSTy9dHjB49mv79+2f0HLFYQDHGmGbipZdeol27dg12fgsoxpgW7+O3t/HMHUt47JoFPHPHEj5+e1vaeWZ7+fq9e/fym9/8hrvuuivtsqfKLmw0xrRoH7+9jYXPrSV8sBqAvTsrWPjcWgCOPbVbSnlGlq9fsmQJnTt39l3L66KLLuLqq68G4K677uLpp5/mRz/6Uc3y9T169GDXrl3AoeXrL7vsMg4ePOh7N8a7776bn/zkJ7Rp0yalMgfBWijGmBZt6Ssba4JJRPhgNUtf2Zhyntlevn7FihVs2LCBCy+8MOUyB8ECijGmRdu7syKp7YnI9vL1S5cu5b333qNXr16cccYZfPzxx5x11lkplz9VFlCMMS1au475SW1PRLaXr7/22mvZunUrn3zyCW+++SbHHnssixYtSrn8qQokoIjISBFZJyIbROQ2n/35IjLD3f+2iPRyt3cSkYUisldEHo065msi8oF7zG+lIW6QbIxp9k4bczShVrU/CkOtcjhtzNEp55nt5esbi7SXrxeRXOBj4FygFHgX+J6qfuRJcx0wUFWvEZFxwIWq+l0RaQucBPQH+qvqDZ5j3gEmAm8Bc4Hfquqr8cpiy9cbYyD55es/fnsbS1/ZyN6dFbTrmM9pY45OeUC+sWvsy9efAmxQ1U0AIjIdGAN85EkzBpjkPn4ReFRERFX3AW+KyDHeDEWkCDhMVZe6z6cBY4G4AcUYY1Jx7Kndmm0AyaYgurx6AJs9z0vdbb5pVDUM7AY61ZNnaT15AiAiE0RkmYgs2759e5JFN8YYE5QgAorf2EZ0P1oiaVJKr6pTVbVEVUu6dOkSJ0tjjDGZFERAKQV6ep4XA1tjpRGRENAeqDvtoXb64nryNMYY04gEEVDeBfqKSG8RaQWMA2ZFpZkFXO4+vhhYoHFmA6hqGbBHRL7hzu4aD7wSQFmNMcZkSNqD8qoaFpEbgHlALvB7VV0tIpOBZao6C3gaeFZENuC0TMZFjheRT4DDgFYiMhYY7s4Quxb4I9AaZzDeBuSNMaYRC2QtL1WdizO117vtHs/jcuA7MY7tFWP7MpzpxMYY0yxMmjSJdu3accsttwSe91lnnUVZWVnNsiyvvfYaXbt2Dfw88djikMYY00w899xzlJSkfTlJymzpFWNMi7dm8UKmXn8lvx43iqnXX8maxQvTzjPby9c3BtZCMca0aGsWL+S1qY8SPugsBrnni+28NtVZCarfkLNTyrMhlq8HuPLKK8nNzeXb3/42d911V70LVAbNWijGmBZt8fRpNcEkInywgsXTp6WcZ7aXrwenu+uDDz5g8eLFLF68mGeffTbl8qfKAooxpkXbs+OLpLYnItvL1wP06OEsJlJYWMill17KO++8k3L5U2UBxRjTohV26pzU9kRke/n6cDjMF184AbCyspK//vWv9O+f/UmyNoZijEnay8u38Kt569i66wDdO7Tm1hHHMfYk3+X2Gr0h48bXGkMBCLXKZ8i41JeI9y5fn5uby0knncQf//jHWmkiy9cfddRRDBgwgD179gDO8vXr169HVRk6dCiDBg3iwQcf5P/+7//Iy8ujW7du3HPPPbXyqqioYMSIEVRWVlJVVcWwYcNqxmeyKe3l6xsTW77emMx7efkWbn/pAw5UHhoYFuCybxzJ/WMHNFzBPJJdvn7N4oUsnj6NPTu+oLBTZ4aMG5/ygHxj19iXrzfGtCC/mreuVjABZ+XW5976NyVHdWySLZV+Q85utgEkm2wMxRiTlK27DgAwOudN3mx1I5vyL+XNVjcyKudNfjVvXQOXzjQkCyjGmKR079Ca0Tlv8mDeUxTnfEGOQHHOFzyY9xQlX81v6OLVaE7d+UHJ9N/EAooxJim3jjiOn4Zm0kYO1treRg5ye6sXGqhUtRUUFLBjxw4LKh6qyo4dOygoKMjYOWwMxZhmIJuzrsae1AN9ZYfvviNI/dqNIBUXF1NaWordxbW2goICiouL60+YIgsoxjQB8QJG9KyrLbsOcPtLHwBkLKhI+2LYvdl/eyOQl5dH7969G7oYLY4FFGMaufoCht+sqwOVVUyatTpzrZah98DsG6HywKFtea2d7abFsjEUYxq5WAEjMqMqMusq2q4DlWzZdQDlUBB6efmWYAo18BIY9Vto3xMQ5/eo3zrbI1bNhIf7w6QOzu9VM4M5t2m0rIViTCMXK2BEtnfv0JotMdJ4Hais4qYZK/jVvHXBtFYGXlI7gHitmlm7BbN7s/M8cpxplqyFYkwj171D3ZVlvdtvHXEcrfNyE84v8NaKnzcm1+4OA+f5G5Mzd07T4CygGNPI+QWM1nm53DriOMAZR/nFRQPo0aE1AvTo0JrD2+TFzdPbZZYRu0uT226aBevyMqaRi3RNxRtgH3tSj1rP/dbbiharKy0QMWaB0UhmgZnMsIBiTCPkN014yW3nJHy8NwjFGl+J1ZUWCJsF1iJZQDGmkUn0upKXl29h0qzV7DpQCcDhbfK4d9SJNWkirZZYrZX9B8O8vHxLZq5ViQy8vzHZ6eZqX+wEExuQb9YCCSgiMhKYAuQCT6nqg1H784FpwNeAHcB3VfUTd9/twA+BKuBGVZ3nbv8E2ONuDwextLIxTUG8acLeixlvfWElldWHlhb5cn8lt764EqBOdxhQK/hE0mf0Ash4s8BMs5T2oLyI5AKPAecBJwDfE5ETopL9EPhSVY8BHgYeco89ARgHnAiMBH7n5hdxtqoOtmBiWpL6pgmDE3S8wSSiskp9B9vHntSDtvl1vz9mfHDetChBzPI6BdigqptU9SAwHRgTlWYM8Iz7+EVgqDg3XB4DTFfVClX9F7DBzc+YFqu+acIQf0A9kYBUZ7tdhGgCEERA6QF4p3OUutt806hqGNgNdKrnWAVeE5H3RGRCrJOLyAQRWSYiy2whONMc1DdNGA4Fl+h7kozOeTOhgOR1ebt3nAH03ZsBPXQRogUVk6QgAor4bItui8dKE+/Y01X1ZJyutOtF5Ey/k6vqVFUtUdWSLl26JFpmYxqt6OtKOrTOoyAvh5tnrOD0Bxc44ycjjuPC0BLfe5KcWb6Q3rfNqUkbEStQ/TRvhl2EaAIRREApBXp6nhcDW2OlEZEQ0B7YGe9YVY38/hz4C9YVZlqQsSf1YMlt5/DwdwdTEa7my/2VtdbkAnig8CXfe5JcX/287/pdfhdA/uKiAbQ5sM2/EHYRoklSELO83gX6ikhvYAvOIPulUWlmAZcDS4GLgQWqqiIyC3heRH4DdAf6Au+ISFsgR1X3uI+HA/Z1ybQ4sWZ8rZgzlbHhMt9jusuOWmm9s8OiL4AEYJFdhGiCkXZAUdWwiNwAzMOZNvx7VV0tIpOBZao6C3gaeFZENuC0TMa5x64WkZnAR0AYuF5Vq0TkCOAvzrg9IeB5Vf1bumU1piFEXy+SI1CtTguhziKNq2bCq/8FB3YCMKu6HT/LGc+s6jNqkozOeZOfVj7l32EMbNVOtZ/Xd0W8XYRoAiLN6RaZJSUlumzZsoYuhjE1/K4X8Wqdl8svLhrgBJVVM+GV66GqdjdWheZya+V/1gSVN1vdSHFO7TsjzmnbhimHd2BbKJfCcB7/uXMf39/3GVu1M0+1+j6DL5gQ/94oq2baRYgtmIi8F8TlGRZQjMmg0x9cUO/S8j06tGbJbeew/6HjaXPAvxurtLozZxz8LaNz3mRK3u8QT+tkTts2TOrckfKcQ0OiBdXVTPpiJxfs289ByeeOqqt58eD/q9lfK5CZFi+ogGKrDRuTQfV1N43OeZMZ+69GJ3Wg9X7/YALQPWcHk0O/55FWtYMJwJTDO9QKJgDlOTlMObwDAK20gpuYXmu/XdBoMsHW8jImgyI3vwodtpz8LvOQvF0UhFtz485dfH/fZ4AzpgLEHBMByEEZH3rdd9+2kP+9ULzbvQP1ERldbdi0SNZCMSaDbh1xHPntl1NQ9BI5rXYhAhV5B/ifLnm82q7NoWAVgAk7AAAdkklEQVSShm5h/yXqu4WrmNO2DcOLuzO4dzFtj36Q0GHLa/ZndLVh0yJZQDEmg8ae1IMuRy1Eciprbfd2SUVTPfSTiIlf7qKgurrWtoLqas7cv59JnTtSlhdCRchptYuCopcIHba8zpX3xgTBAooxGfZVpf+SQGWhXOa0bVNn+xbtTO+K51FPH1ikpTGwV0+GF3evOU4VLti3nzF79pLjRqEcVcbs2cs/2rSpM7YiOZW0OeI1G5A3GWEBxZgM69a2m/8OESZ17lgrqOzXVvwyfAk9OrSmvI1zXGQWV6SlUZYX4rYunZjcsQPVCHPatuGVwnZUi4AI1SK8UtiOshhjK4R2WTAxGWEBxZgMm3jyRApyC3z3lefkcEeXTvy1TRtKqztzVdvzeb//O+wpuomx3Qtrri+JbmkgwguHFfLNI7vzi46H+87yivXPHTPAGZMmm+XlsWbxQhZPn8aeHV9Q2KkzQ8aNp9+Qsxu6WKaJmbNpDlPen8K2fdsoyC2gvKocrbNe6iHVItzWpYi8tqcghcuorKwAoKy63Lm+JHqecIQIu0O5MQdbqoECyaNcD43fFOQWMPHkiSnXzZh4rIXiWrN4Ia9NfZQ9X2wHVfZ8sZ3Xpj7KmsULG7popgmZs2kOk/45ibJ9ZSjKgaoDcYNJhORUEm63hEqtqLW9TsvE92D/gFPUqgOTzriPorZFCEJR2yIm/b9JXNDngoTqYkyy7Ep519Trr3SCSRTJyUFVyW/bDhEo37PH2VZdTWHnLgm1Yqzl07x5WyQiQrVW139QhhXkFljwMAkL6kp56/Jy7dnxhe92dadjVuzdU2fbni+287cnpgDEDBCRlk/4YEXNMa9NfTTuMabpiLRIyqvKAWgMX9CK2hYx8eSJFkxM1lkLxRWrhZIoyclh4NCRDLvquoTyjbR8rMXStA1/cThl+2IvmRI41ZhdXOAEk9cufi175THNgrVQAjZk3PhaLYlkaXU1K+fPZcOyt8jJza3p3ooVpLytHGuxNF3b9sW4OVWGtM9tw77wfsI+l9jXGnC31YNNA7BBeVe/IWczfMINFBQWppXPvi931hrYT0T4YAWLp09L67ymYaQ9BTeJHoKC3AJuP/1e7u99IUVVhy5iBGoPuK+aafeINw3Curw8osc7sk7EusCamOgxlLiiu6vq6b7y6pDfgdtOuS2xcZGH+8e4A2NPuPnDhM5nWhbr8sqAxdOnNVwwgZpWzdzHpvDa7z+iQ9FgThtzNMeeGv9b8Mdvb2PpKxvZu7OCdh3z4x7TUmac7Z49m88ffoRwWRmhoiK63nwT7UeNSjof7wyubm271RnsvqDPBbRd+B45//snOn0FOw6D588Slpzoc5V6dPBIMJgALB63OPFCx7oXvN0j3mSYBRSPWDO9sk7DhMvfZO/Ofrw+7SMWz/yY8n1h32Dx8dvbWPjcWsIHnTGZvTsrWPjcWoA6QaWlzDjbPXs2ZXffg5Y7rYbw1q2U3X3odraJBpro1kfZvjIm/XMSQE1Q2T17Nt3+5y+o20Dp8hX851wFqmoFldNXV3HpIq0/6PgoaluUTPWdMRO7R7xpABZQPOINomddtTNNWaugfF8Y8A8WS1/ZWBNMIsIHq1n6ysY6AcWvBRYZv2nqAcXbIgHqjE1oeTmfPfBzqsvLfQONN6hE8uq9dSu/jvrwL68qZ8r7U2oCyucPP1KTX0RBGG6cpVy6KMzzZzmtkP+cqxQ4L2PMoOMnpSvb7R7xpoFYQPFId6ZXoMR/7afoYLF3p39Z/bbHaoE1mpaZK153VdnPfsaumS9AVRXk5tLhku/Q5uSTa7VIYqnatavONi0v5/OHHwHclsvWrTX7BP8Pf+/MrpoAFsV77MEQNcEkoiAMly5SlpwYu7wpX08Smc1ls7xMlllA8Yh8S3/1dw/XTOttMFpOxd7XyW83jHDFGsLlbzqtlpxCwhVnAKcD0K5jvm/wyG+byzN3LKk1rhKrBVbYqXOma5Mw3+6qO+6k7IGfo9EBoaqKXX+azq4X/wyVlT65JSbSUokVkKI//L0zuyq7tCfv87qByntsfth/X6evYpdJkPSuJxl4CXPatT00/vPxU0xs19YudjQZZQElSiSoNIaWilauonz3l1BdBrifStV7CO+fz5QroUPRYHr178Tat7bV6fY6eKCain1O+ffurGD+Hz6iqPcwDnz1Uq16hVrlM2Tc+GxVqY7o1oju31/ng10rK8GndVEjjWBSc456WjeRD/+QhGp1Qf3pzBwuebluCyQROw6LvS/d6ciJjP8YE7RArkMRkZEisk5ENojIbT7780Vkhrv/bRHp5dl3u7t9nYiMSDTPTIpck1LYuUs2T+uvejM1waRGZNC+go+WlNGtd91PJq2uOx287F9F9Ox/ETkhJ31O6DAGDP1BxsdPds+ezfpzhrKm3wmsP2cou2fPdsrzs5+x9dafOt1MqoS3bvXtlmoMIh/+7Vq1q/WBPKfvHv73fGH7YcRcArI8D8qjvrqFW+Xy6vCOvumDWBF4yvtT6kxljoz/GJMpaV+HIiK5wMfAuUAp8C7wPVX9yJPmOmCgql4jIuOAC1X1uyJyAvAn4BSgO/A6cKx7WNw8/aR7HUosv738Yirr+QbbEEJtziOU3y+9PFrlcPZlx9c7NTlV0V1YgDNdtgld/1Qegv893xmYF4RVl6+q2XfGn85g98HdgDOT69rZSquoqlWHcnnz5AL6rd1H568g3LUDR916R824UH1Tk1Mx8JmBvqscR5ffGGhc16GcAmxQ1U0AIjIdGAN4P/zHAJPcxy8Cj4qIuNunq2oF8C8R2eDmRwJ5Zs25V13P356YQnU4hX6NDArvnw+QVlCJNSMsFX6D6X6zoJpCMFH3J3qKr7cras6mOewP7695vuTEXK6cH6bVgdp55YSrOKe0PX3f8f+yc0GfCwLvhurWtpvvGmN2cy2TSUF0efUAvJPeS91tvmlUNQzsBjrFOTaRPAEQkQkiskxElm3fnpkpv/2GnM3IayYSys/PSP6pc7q+0hVrplgyIi0Rb/dVzfMm6KsLTuOKu9px/fWhmmAS3RU15f0pVFbXHr9pFxVMImLNBssUv7tE2s21TKYF0ULxu9w3+itorDSxtvsFOt+vtao6FZgKTpdX7GKmp9+Qs+k35Gxef+p3rHrjb2h1NZKTg+TkpNlyCVF3jKT2fsk7Aa2M0U1Rvcd/exLadUw/UPq1RLS8nG3dTmFjr29Rkd+R/IqdHL1pFt0+D75bMmidln/KpOsnxe2KKttXRu8tbfjausNpW57LvoIq1hXtoF/Z3jr5hYqSvDgxTZFyBt2VZkw8QQSUUqCn53kxEP21NJKmVERCQHtgZz3H1pdngxh21XW1lqhfs3ghcx/9dWqZ5RQSKjjj0JTgOoRQm3MJ5fejfPe//NPkpLeYZahVDqeNOTrh9LGuEfH7Br6tawlr+46jOtcJWBUFnVh73KUAjT6ohMvK4nZFzdk0h95b2nD6B50IVTvff9qVh9jU9Qi29bgYbVtSE0CLvvqQrjff5JtPMsvmJCJ6aZ0p425v8hetmqYjiIDyLtBXRHoDW4BxwKVRaWYBlwNLgYuBBaqqIjILeF5EfoMzKN8XeAen5VJfno1CvyFns2XdGlbOnxs/oYQItT435niHMx7ibamEaoIJ4AQevzQFZ6RcdhHl+E//TNUVb7A+gfWu/K4Ref+Rv/DpgtbsO/N/6rRANvYZXRNMIqpz89nYZ3SjDyj1tSimvD+F09cdXhNMIgQ4ULWCAvm6E0CPv4zDT66m/ajz6+SRzLI5EfHWYmspS+uYxivtgKKqYRG5AZgH5AK/V9XVIjIZWKaqs4CngWfdQfedOAECN91MnMH2MHC9qlYB+OWZblkzZdhV19HjuH4sfOYPHNizE3IKyW/blxw+4cDeLyns1Jljvj6GNW/5X3gQCRreixdDBWfUCj6JpIlFcp3ZPdVVh3oEc3OV49Y+R9ctS518YyxD4hXdrbWtawlr+3yH6gM5IHVbIBX5/tNiY21P1bauJWzsMzqwbjUpKIjZoqg5575ttC3v6b/T05KszmnFyn/nM9gnWTLL5kD9ASObS+u0lEVGTXICubBRVecCc6O23eN5XA58J8axDwAPJJJnYxYZY4lnzVsLYu4L5ferCQ4FbUNUlIdxQqt/mkRJDgwbfwJAra6VXqun1wSTiMgyJLECSnS3Vn0tkPyKnVQUdKqTT37FzqTqEM+2riWsPe7S9LvV3JV/61swMtLlN31rJfP75xLO9VlRIaobMjLpIfpD+MD+Et/XM9YkifoCRraW1rGWkInFrpTPoljLpET0P7M737z0eMDpDvnHzHVU7KuKmd5LcqkbgKKuMfF+613T72rffOLNRgoVFdWatRWzBVLQiVD37hy9aVatD3uAnKoKjt40q976JCqRbjXp0KHusi0++q1xZqWvWbyQGddfWfPB3+ekr7Np+bvs+WI7rSvDHLv/K3oAOW3OgYpF1JlUUb2H8t1P1rQg23XM9/0QBv9p37EmSdQXMDKxtI5fS6Q5LzJq0mN3bMyi08YcTahV3T95QdsQ5155Qk0wAefD/6pff5NzrzzBfy4czgfP9U+cw/VPnMN1j53DuVeeUPNh1K5jftwLFmONEcQbO+h6801IwaGpqLFaGu065tP15pso+upDjl/3PPnlO0CV/PIdHL/u+eS7o0Ihcjt08N0Vr1stt0MHuv/qlxz/1lJC3bvHP4Vb78gHv/eumyvnz635oD6QF+KDnl1YfeQAcloPINTmXP+JEe4SOVq1ltPGHB3jXjt1p31LLjEnScQKDJHtQ8aNJ9SqdjBKZ2kdv79FzXMfjW2RUZN91kLJIu+S84nO6ons8w7egv/srGNP7ZbwDKGuN99U5wr2+sYOIt1AkVlefb/8B2uKx1JVdSjiRcrV/lRn8crchx+h29v3ktu+PdXgtBRyc6GqilD37rT75pnsmj4j/sWO4TDSpg3d77zj0PndllLsbrUvOeLOQ1ej+9XXr96J3GStOieHTw/fD1895bRCCs4gvP9Vv4KTo29x7KnXMfvhGB+2UTP3QqHcmK+h32rY3oARaR0ENbYRqyUiOTm+i6c2pkVGTcOwWwA3EUFPL4Vg7mqYbrnWnzM04YsfpaCAovsm037UKNb0OwFU2da1hA96l1B58K2ayQp5rb7BgH8tozi0lb4L3qhb361bawW1fZf8hJX/bs/enRWUf/mbpOp/qPkY4/9IhFE3P8lfp/wYrfJZXjinkIL2tbsfr3/inJhnS3QwPIhB81+PGxUz0Ida5dcJbMMn3GBdXk1UUEuvWEAxDSoSGBIV6t6dvgveYM3xzrjDlg7tWNXzCNTTkyjVMHDzZ/TYva9mXCSWvz+/lg//cSigle9+MpCLRWvKIjmoVgP5QCXg/WZfe2p4RLyAkojo8RpI7QN/6vVX+o/JdO5SM5Zis7yah8a0lpcxKYse6K9PZNJAqHt3wlu3sq6oY61gAqA5sK6oI0e1ibM+PE7ryhtMACS3N1od3OKJTjABqADEuXGalsec9h1qJTxzxxJ2la2g+uASqsNf1XyAJ/qBHaurasEzU5P60I/XxZbIrEbT8tigvGlQ0QP94HRtxRqEjwyeR44rz/P/TlSeF2LfJT/hmTuW8Ng1C3jmjiV8/Pa2WmmWvrKx5nG4Yg3lu34Xe4mbWDMjkqIgeRQc/mMK2l/tO2U4fFDZVbaC8P75VIedLrLIYPiaxQsTOkuswfHyPXsSzgOibuMgQmHnLtatZeKyFoppUNED/ZGxHCDupIHIca2feZwDuXU/7AsKCvnnBwVo1aGbjL0+zen+ir59crhijc8qBNEiS88J3m4rkVy3FZJgt10C3WnOzK/aZQkfrODV3z3M3Md+U28XU6zpw0DSU3utJWKSYS0U0+DajxpF3wVv0G/NR/Rd8AbtR42i/ahRFN032ZnuK0Koe/eaAXnvcceO/JZvnuUV5VTuX1Nrm1bBP2auq3le0Nb5PuX3Ae5PqR1MciDvREJtRgJ5Cdb20LTeyHTxOtedxAg6Wl1da/purNZGvGnCNrXXZJIFFNNo+QWaaJuWvxvj6DDh/fMJV9QOKt4LRWtuQJXiILxqNXrQHfTPKYif+FAJKP/yN1R89RT/b2wVx57are7Frgks+Bm5kNBPvyFnk9/OPw+b2msyyQKKadLif+MOE97/KuW7n6wTWMAJLn7bkxOOs1p0bFr1VU0rI7qF4iz4WX9vdLy6D71iQqAXORqTCAsopklL6Bt39R4nsLgtg0hXUShvQ81dL9PiXv+SrEgrI3oFhVB+v6gr8P0nBMSruw2om4Zg16GYJm3N4oW8+vgjaFVia54B5IRC5BW0pmJvgNeb5A1EKyOLZidzoPCT6bNrXSCa3zaXyvLqmtWh/SYN2IWEJkh2HYoxLhFJdI4VANXhcKDBBEAr14GEQJMLKJFWRvSyOd4A06FoMD2P7cGGd1+xCwlNo2YBxTRpi6dPS/MWzEGpSHjmcES8MQ2/ddnOuWJszLzs/iSmMbCAYpq0pjYNVnJyUNVAP/Tt/iSmsbCAYpq0eBfxNTY5oRAjr5kY+Ie83Z/ENBY2y8s0aX73AGmMCgoLMxJMoP4bbxmTLdZCMU2a3z1ADpaX+w66F3buEmxrJqcwoetPCjt3YcJjfwjuvNH5Z+BOjcakwloopsnrN+RsJjz2B34yfTYTHvtD3Iv6JCeYt3xh5y6ge+tNl42LCYO+U6MxqbKAYpqdeBf1DRw6MpBzDBk3PmYLQHJysnoxoV3EaBqLtLq8RKQjMAPoBXwCXKKqX/qkuxy4y316v6o+427/GvBHoDUwF5ioqioik4CrgUg7/g5VnZtOWU3LEmuV3GFXXQfAqjf+5nsb28gFg4unT4vbPRbJO4gbWQXBVgU2jUG6LZTbgDdUtS/whvu8Fjfo3AucCpwC3Csih7u7HwcmAH3dH+/Xx4dVdbD7Y8HEBGbYVdfx4z/Ncr7RR4nMjorXXRQ5zloGxtSW7qD8GOAs9/EzwCLgv6LSjADmq+pOABGZD4wUkUXAYaq61N0+DRgLvJpmmYxJSLzZUf2GnM2WdWtYOb/2d5nosQlrGRhzSLotlCNUtQzA/d3VJ00PYLPneam7rYf7OHp7xA0iskpEfu9p0RgTmFhjIJHtw666jvNv+Im1QIxJUL0tFBF5Hejms+vOBM/ht1SqxtkOTlfYfe7z+4BfA/8Ro3wTcLrNOPLIIxMskjHx75keYS0QYxJXb0BR1WGx9onIZyJSpKplIlIEfO6TrJRD3WIAxThdY6XuY+/2re45P/Oc40ngr3HKNxWYCs5qw/VUx5gaftew2BpYxqQu3TGUWcDlwIPu71d80swDfu7pthoO3K6qO0Vkj4h8A3gbGA/8D0AkSLnpLwQ+TLOcxviyFogxwUk3oDwIzBSRHwL/Br4DICIlwDWqepUbOO4DIvdqnRwZoAeu5dC04Vc5NCD/SxEZjNPl9Qnwn2mW0xhjTIbZDbaMMaaFC+oGW3alvDHGmEBYQDHGGBMICyjGGGMCYQHFGGNMICygGGOMCYQFFGOMMYGwgGKMMSYQFlCMMcYEwgKKMcaYQFhAMcYYEwgLKMYYYwJhAcUYY0wgLKAYY4wJhAUUY4wxgbCAYowxJhAWUIwxxgTCAooxxphAWEAxxhgTCAsoxhhjAmEBxRhjTCAsoBhjjAmEBRRjjDGBSCugiEhHEZkvIuvd34fHSHe5m2a9iFzu2f6AiGwWkb1R6fNFZIaIbBCRt0WkVzrlNMYYk3nptlBuA95Q1b7AG+7zWkSkI3AvcCpwCnCvJ/DMdrdF+yHwpaoeAzwMPJRmOY0xxmRYugFlDPCM+/gZYKxPmhHAfFXdqapfAvOBkQCq+paqltWT74vAUBGRNMtqjDEmg9INKEdEAoL7u6tPmh7AZs/zUndbPDXHqGoY2A108ksoIhNEZJmILNu+fXuSxTfGGBOUUH0JROR1oJvPrjsTPIdfy0KDOkZVpwJTAUpKSurL1xhjTIbUG1BUdVisfSLymYgUqWqZiBQBn/skKwXO8jwvBhbVc9pSoCdQKiIhoD2ws76yGmOMaTjpdnnNAiKzti4HXvFJMw8YLiKHu4Pxw91tieZ7MbBAVa31YYwxjVi6AeVB4FwRWQ+c6z5HREpE5CkAVd0J3Ae86/5MdrchIr8UkVKgjYiUisgkN9+ngU4isgH4MT6zx4wxxjQu0py++JeUlOiyZcsauhjGGNOkiMh7qlqSbj52pbwxxphAWEAxxhgTCAsoxhhjAmEBxRhjTCAsoBhjjAmEBRRjjDGBsIBijDEmEBZQjDHGBMICijHGmEA0qyvlRWQ78KnPrs7AF1kuTjY013pB861bc60XNN+6tYR6HaWqXdLNsFkFlFhEZFkQywo0Ns21XtB869Zc6wXNt25Wr8RZl5cxxphAWEAxxhgTiJYSUKY2dAEypLnWC5pv3ZprvaD51s3qlaAWMYZijDEm81pKC8UYY0yGWUAxxhgTiCYdUESko4jMF5H17u/DY6S73E2zXkQu92x/QEQ2i8jeqPT5IjJDRDaIyNsi0iuzNalT3nTr9TUR+cAt/29FRNztk0Rki4iscH/Oz1J9RorIOrc8dW7nHO/vLSK3u9vXiciIRPPMlgzV7RP39VshIg1yC9JU6yUinURkoYjsFZFHo47xfV9mU4bqtcjNM/J/1TU7talT9lTrdq6IvOe+Nu+JyDmeY5J7zVS1yf4AvwRucx/fBjzkk6YjsMn9fbj7+HB33zeAImBv1DHXAU+4j8cBM5pYvd4BTgMEeBU4z90+Cbgly3XJBTYCfYBWwErghET+3sAJbvp8oLebT24ieTbVurn7PgE6Z7s+AdWrLXAGcA3waNQxvu/LZlCvRUBJQ71eAdTtJKC7+7g/sCXV16xJt1CAMcAz7uNngLE+aUYA81V1p6p+CcwHRgKo6luqWlZPvi8CQ7P8bSrleolIEXCYqi5V5x0xLcbx2XIKsEFVN6nqQWA6Tv28Yv29xwDTVbVCVf8FbHDzSyTPbMhE3RqDlOulqvtU9U2g3Ju4kbwvA69XI5JO3Zar6lZ3+2qgwG3NJP2aNfWAckQkILi//ZqaPYDNnuel7rZ4ao5R1TCwG+iUdmkTl069eriPo7dH3CAiq0Tk97G60gKWyN8/1t87Xh2TfU0zIRN1A1DgNbf7YUIGyl2fdOoVL89478tsyES9Iv7gdnfd3RBdeQRXt28Dy1W1ghRes1DSxc4yEXkd6Oaz685Es/DZVt9c6VSOSUoG6xWv7I8D97nP7wN+DfxHgudLVSJ/y2Tr4vdFqCHmv2eibgCnq+pWty9+voisVdV/pFHOZKVTr3TyzLRM1AvgMlXdIiKFwJ+BH+B8m8+mtOsmIicCDwHDk8izlkYfUFR1WKx9IvKZiBSpapnbPPvcJ1kpcJbneTFOn2c8pUBPoFREQkB7YGcy5a5PButV6j72bt/qnvMzzzmeBP6aavmTEPlb1imPT5rov3e8Y+vLMxsyUrdI94Oqfi4if8HpzshmQEmnXvHy9H1fZlEm6oWqbnF/7xGR53Fer2wHlLTqJiLFwF+A8aq60ZM+qdesqXd5zQIis5suB17xSTMPGC4ih7tdPMPdbYnmezGwwO1DzJaU6+V2ke0RkW+4Te/xkePd4BRxIfBhpirg8S7QV0R6i0grnMHAWVFpYv29ZwHj3P7c3kBfnEHCRPLMhsDrJiJt3W+6iEhbnNc1G6+TVzr18hXvfZlFgddLREIi0tl9nAd8i+y/XpBG3USkAzAHuF1Vl0QSp/SaNeTMhHR/cPr/3gDWu787uttLgKc86f4DZ9BzA3ClZ/svcaJwtft7kru9AHjBTf8O0KeJ1asE5029EXiUQysiPAt8AKxy31xFWarP+cDHbnnudLdNBkbX9/fG6QLcCKzDM8PEL88Geg8GWjecWTor3Z/VDVW3NOv1Cc43373u/9UJ8d6XTbleOLO/3nP/p1YDU3Bn6zWVugF3AfuAFZ6frqm8Zrb0ijHGmEA09S4vY4wxjYQFFGOMMYGwgGKMMSYQFlCMMcYEwgKKMcaYQFhAMcYYEwgLKMYYYwLx/wFl4fV+4gjtBQAAAABJRU5ErkJggg==\n", 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bandwidths = [5, 10, 20, 50, 100]\n", "for bandwidth in bandwidths:\n", " diffMap = DiffMap(s, bandwidth, alpha)\n", " guo_mapped = diffMap.fit_transform(guo_data.data)\n", " plot_2d(guo_mapped, guo_data.labels, R\"Processed guo data with diffusion maps and $\\sigma$ = \" + str(bandwidth))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For small values of $\\sigma$ the mapped data points seem to be lieing on multiple lines. With increasing value of $\\sigma$ these lines get blurry until they collapse into a single blop as seen for $\\sigma = 100$. This is most likely due to the fact that for ever higher values of $\\sigma$ the implicit local graph on which the diffusion map operates gets more and more connected." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 9: Implement the rule for $\\sigma$ and plot the embedding with the $\\sigma$ chosen by this rule." ] }, { "cell_type": "code", "execution_count": 160, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def lafon_bandwidth(X):\n", " distances = squareform(pdist(X))\n", " np.fill_diagonal(distances, np.Infinity)\n", " return np.sqrt(1 / (2 * np.shape(X)[0]) * np.sum(np.square(distances.min(axis = 1))))" ] }, { "cell_type": "code", "execution_count": 161, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Wall time: 79 ms\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lafon_bw = lafon_bandwidth(guo_data.data)\n", "\n", "diffMap = DiffMap(s, lafon_bw, alpha)\n", "%time guo_lafon = diffMap.fit_transform(guo_data.data)\n", "plot_2d(guo_lafon, guo_data.labels, R\"Processed guo data with diffusion maps and lafon bandwidth\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This bandwidth gives us a decent compromise between the sharp structures of a small $\\sigma$ and the better separation of medium values for $\\sigma$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.4 Cell group detection\n", "\n", "Now, we want to apply spectral clustering to detect cell groups in the single-cell data.\n", "\n", "#### Task 10: Implement the spectral clustering algorithm using k-means with $\\Lambda$ as input." ] }, { "cell_type": "code", "execution_count": 284, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def spectral_clustering(X, M, sigma, alpha):\n", " # if lambda << M, using the DiffusionMap algorithm is inefficient as we calculate more eigenvectors\n", " # than we need. However, in this example the runtime is not a factor and it would complicate the code\n", " # unnecessarily to improve the runtime.\n", " diffMap = DiffMap(M, sigma, alpha)\n", " transformed = diffMap.fit_transform(X)\n", " l = np.argmax(np.array(diffMap.eig_vals[0:-1]) - np.array(diffMap.eig_vals[1:])) + 2 # compensating for missing\n", " # lambda_0\n", " transformed = transformed[:, 0:(l-1)]\n", " kmeans = KMeans(n_clusters=l, random_state=0).fit(transformed)\n", " return (kmeans, transformed, kmeans.predict(transformed))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Technically, this implemenatation ignores the first eigenvalue when determining the biggest difference. However, this is a wanted property as we do not want the first eigenvalue ($\\lambda_0 = 1$) to be the only taken into account later on, as it corresponds to a constant vector." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 11: Plot the first 20 eigenvalues of transition matrix $P$ for the Guo data and identify $\\Lambda$." ] }, { "cell_type": "code", "execution_count": 310, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "M = 20\n", "diffMap = DiffMap(M - 1, lafon_bw, alpha) # Diffmap calculates the eigenvalues up to ndim + 1\n", "transformed = diffMap.fit_transform(guo_data.data)\n", "plt.plot(diffMap.eig_vals)\n", "plt.title(\"Eigenvalues of P sorted by magnitude\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see, that $l = 7$. There, we even get a negative eigenvalue, so we should definately cut off here." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Task 12: Perform the spectral clustering algorithm for the Guo data." ] }, { "cell_type": "code", "execution_count": 311, "metadata": { "collapsed": true }, "outputs": [], "source": [ "kmeans, transformed, preds = spectral_clustering(guo_data.data, M, lafon_bw, alpha)\n", "clusters = kmeans.cluster_centers_[:, [0, 1]]" ] }, { "cell_type": "code", "execution_count": 312, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_2d(transformed, guo_data.labels, \"Spectral clustering for guo data\", plot = False)\n", "plt.scatter(clusters[:, 0], clusters[:, 1], c = \"black\", marker = \"d\", label = \"clusters\")\n", "plt.legend(loc = 0)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the spectral clustering, we are now able to visualize what we could not do visually in 2d with the data mapped by diffusion maps alone: Additionally two the nice separation of the TE lineage and the inner cell mass, the additional \"clustering of clusters\" in one of the brown arms suggests the separation into PE and EPI. This separation is most likely due to differences between the two lineages in the higher dimensions which are not represented in the plot but where present when k-means calculated the clusters." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }