{ "metadata": { "name": "", "signature": "sha256:cafe975cf932e687564ba2e4a436738170daae9aeff7dc691958872e80784ccb" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "# - compatibility with Python 3\n", "from __future__ import print_function # print('me') instead of print 'me'\n", "from __future__ import division # 1/2 == 0.5, not 0" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# - show figures inside the notebook\n", "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "# - import common modules\n", "import numpy as np # the Python array package\n", "import matplotlib.pyplot as plt # the Python plotting package" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "# - set gray colormap and nearest neighbor interpolation by default\n", "plt.rcParams['image.cmap'] = 'gray'\n", "plt.rcParams['image.interpolation'] = 'nearest'" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Mutual information as an image matching metric" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When the images to match are the same modality and are well aligned, the signal should be similar in corresponding voxels. In that case, a metric like correlation is useful as a measure of how well the images are matched." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If images are of different modalities, they may well have different signal intensities for the same tissue.\n", "\n", "For example, T1-weighted MRI images have low signal in the cerebro-spinal fluid (CSF), but T2-weighted images have high signal in the CSF.\n", "\n", "When the T1 and T2 images are well aligned, the voxels containing CSF will correspond spatially, but they will have very different signal. In that case a simple measure like correlation will not capture how well the two images are matched.\n", "\n", "Mutual information is a measure of image matching, that does not require the signal to be the same in the two images. It is a measure of how well you can predict the signal in the second image, given the signal intensity in the first." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First let us look at a T1 and T2 image. In fact these images are from the Montreal Neurological Institute (MNI) standard brain atlas : http://www.bic.mni.mcgill.ca/ServicesAtlases/ICBM152NLin2009" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import nibabel as nib\n", "t1_img = nib.load('mni_icbm152_t1_tal_nlin_asym_09a.nii')\n", "t1_data = t1_img.get_data()\n", "t2_img = nib.load('mni_icbm152_t2_tal_nlin_asym_09a.nii')\n", "t2_data = t2_img.get_data()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "# Show the images by stacking them left-right with hstack\n", "t1_slice = t1_data[:, :, 94]\n", "t2_slice = t2_data[:, :, 94]\n", "plt.imshow(np.hstack((t1_slice, t2_slice)))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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0Lmw2y+qiMmW7//PKoil/Zsio7bpFn9nQlx5fIvHl5WUUi0VB0bPZDIeHh6jX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\nNa98n9xDUvFkNMumS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"text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The one-dimensional histograms of the example slices:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, axes = plt.subplots(1, 2)\n", "axes[0].hist(t1_slice.ravel(), bins=20)\n", "axes[0].set_title('T1 slice histogram')\n", "axes[1].hist(t2_slice.ravel(), bins=20)\n", "axes[1].set_title('T2 slice histogram')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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YVZK0EJgBvFrSGuBzZEOyr5F0CrAa+DBkQ7QlDQ7R3khxiPblwE7Aou4bot1t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\nTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting the signal in the T1 slice against the signal in the T2 slice:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(t1_slice.ravel(), t2_slice.ravel(), '.')\n", "plt.xlabel('T1 signal')\n", "plt.ylabel('T2 signal')\n", "plt.title('T1 vs T2 signal')\n", "np.corrcoef(t1_slice.ravel(), t2_slice.ravel())[0, 1]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 8, "text": [ "0.78707985510953171" ] }, { "metadata": {}, "output_type": "display_data", "png": 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uMIMJq2/CKty5AomvG4/TZ5mMWZ3wvl1dZjAqdLYfixW2r517ymeUT6WM+qyz\nc/EH8mo1V/DF4zTI2+7Dvb2535n7TPj7detzj4yYY6Mq8PGKohDjtr29UHffZkUEhVAX8Mz/qKNy\nf9RaB42bY2PR8QcdHfnLoLJR0/W4sQ2hGzcG1RY8GPX1RQ+KnAXVFQhTU0bXnkrRe7tmBveDBQwP\nnJs3mzKidmLCZmhuCdQwIzQQjJ3xnUdrOt61S7FQ4YzCw8NGXWULat//B/fHPmcrlmUVQSHUFfYP\ncmbGbM9k6D0Hy4V5xdiFbnwUEqRlzyptA/PMTHAgcr2mXLsFoPXSpSS42AXX9qzxDUKjo7n72Oq0\nZcuaRy0FmOfiW1XxM+AstG56cfs74lWoq+ZKpYJC23UYsLPiaq318ccHbVzu6mRiIr+7bzMigkKo\nK/hHaA/47ixzbi7oBcNtcrK0H64rPGzBwQMF98ceONgozgKM+z4wEB4HYM983QFvYiLahtLW1nyG\nbnsAt73QfIMwf0+bNwePtQWt6w6dSPjtR9xWrAg+b9fGxf0ZGzPfdyt6SomgEOqKTIZ85G07hT1Y\ndnSED5b5gt98AscXrOV62/hKfrqqidFRmh376iqwmsMe/Ox7isep75s3BweqlSuDqxdfvYZmamzU\ndwdh93tznx2rAjkWgoVF2MqL1YldXUFVnm1cDyv52kp2CRsRFELd4FPF2AbnQlqYx9SGDUF7w8yM\n3+jpHu87FiAjrNb+c9iz2nTa1Iu2B5jR0dzj7FVIb29QjTIzY55DW1tuf5qhTU0FvZw49sR1b/X9\nP/CKRGszuPue0dKl9J35Ahz7+kggt7eb75f/B2wB3ip2CRsRFEJdEKaKcYOvoprPPrFqld9V0jfg\n+Fwzw4Lg2CWXz8GrnIEBmvl3dAQDyFw3T3d1YOu+2QPL1YXzAOjq4ZtFaESpiLgNDhobjvsZ27RY\nuNv/T4lEcAKSL7jRDgr0uVC3GiIohLrA/jGmUsGgOK1zhUVPjzFijo7SDNE3KPvUD2NjpEqwZ6uu\na6ZPcNkDGs84WVXGaiefbaK9PTchYEdHcADjqHDbo6a/PzeaeG4uKBh6e+mayWTzq6bs5+JbkU1P\n+783/m59mYejGq8c+Dif+26rUK6gUHSOXJRSfxGdnVz/r4jPK4JSSof1V6gtU1NUJKi3F3jgAVMr\ngKvbdXYCV14JbNgAvPoq1T7gwjR2xTO7ToGPZJLO8frrpoZFWxvwzndSQZ2tW+l63/tesE5CPE7D\nx5Ej9H7/nUMkAAAgAElEQVTlSmD5cuqXXQ/DxVdrorub6ibcf39w++ws3du3vkXFd1591fRvzx7g\n4x+n+gpcoQ2gyn12ZbihIbr/VmR4GHjtNfo+ACpydO65VKsinTblUjMZqldhfzenngrs3m3qhwwM\nAKtWURGmY46hv9//fmE1LOz/2W3bTOndRkYpBa21KvkEYRIEwOUALvO0ywFcVo50KrVBVhR1S5jR\n0HWXLMRd0VYphakzeHVizy595/c1134Qpvrh2hi+vrDqg7PTct+3bPHXr2hvz1U5jY0Fc0bF41rv\n2lV8jYd6brzyKqXt2kX/W64xnP/XOLV8PE4ru4EBY0/yRZMPDBSmdsqXZaARQZkripIPrEUTQVG/\n5DNku0Kgv9+om9ysn+yyGpaRNZk09Sn4R+2eP8xjxnXjtAdyHrynpky8B/dlxQrjYbN0qTnOzU4b\nJahYuCWTRl3luoq2tweFRzPFXORrPpVSe3uwNsbgYNBzyVVTDQ2RsA5LJunLTOtSTvGkeqXiggJU\nYOi/APgsgKsBfBHAF8u5aMmdFUFRt/hWCq576vCwf4VgB+bZ2IN5LKb1qafmHmvbAexqer4ZJQsJ\n3o9XEmEpqsOK4nAMiLua8UUVc+vu9s92fcWQpqdNkJrtLtoMrbc33MaQz0DtJn+cm/M/v7AWj+cG\n4flWDM0YZ1ENQXEjgP8B4OcALgKwHcC/lHPRkjsrgqLucNNXjI+b2bj9eZRnT1hG0EyGZveceoMF\nBw8o9mzbVTtNT+capru7c4Pp2PffvR9XONhFcViouCozV1imUrlxFRs2mNWLz5vLlyvLdgQoZmBs\npJbPY6q3N3f1WIia0W3DwxKZXUrLvwPwYPbvQ9m/SQA/KOeiJXdWBEXdYf9YOdtr2Oe+lkoV/mNl\n/b87wLpqJ/d9b29QfWEPSv39wURx9orArlnhi6UIiwi3haXdpzB9fW+vf7XR3h70qPLZPpq1cdqO\n1atNPYqNG2mV5QZPjo8H83Dlaz5vtGanGoLi3uzfXQDWABgE8PNyLlpyZ0VQ1B359LnsBsmDe09P\nuEur1rnxClEZaNkNlwcOHkjsmfjKlcEBRCnjhmqrQNzVx8RE0F21EKOmKzhsVZhri3AFStjz4lZo\nyvNmaTMz/lK57sqxvT0YqOdbcXV1mf8B+3M2gLeCwKiGoJgD1bPeAOBJAC8A+M/lXLTkzoqgqBvs\nDK324GyrbtxUHbzicD2k7BQcrm3Btl/Yabo5k6jPgG7jW9FMT5MAYbVQf78xVJ9yirmfYoyaPgOp\nfW3Xk4lrUdvnDYv7aMWWSpnIbjvtis9QbX/nPo8xzvI7O+t/xnY9lGK+30ZCvJ6EmuAzCEYFuQG5\nuvd86TN4UGdswdPWZlRD3NwB3Wdc5rTU9rVt7yo3462bt8rH3FxQnZVO0/62LtxXOtUd5NxVw6ZN\nueqUMKN+szeeZIQ5TfBAvmEDTSj4f4VLq/JK1V1xLFkSvqIIs1c1ostsuYIikS/OQinVAeA/ATgW\nQByAyl70b/MdKzQvnZ30NxYD7riDApr27DHBZL29wCuvUPATQAFRHNQ2P0+BZ3yOVIqOGxiggKj9\n+4FDh4CxMeCaa0wA1Ouvm+vbwXQA0NEBbN8eDI665RYKzgIokO3ss+l86bS5dleX2X9iAujpASYn\nTbCVHdh3/PHAGWfQdg7s44A9mscQCwsUdLd8OQUTptN0b8kk3Vd3Nz2biQngqqvMcbFYMLjvZz/L\nfe7vehfw+OOeL6SBicUApXIDGzmgbmICOPlkYGYGePRR+mx8nJ5vKkXbH3rIfNcDA8CLL9Lr446j\n78oNdGT6+oCLLvIH1+3ZYwI/h4fpr/udtQz5JAmA2wD8XwBbAfwFgP8PwF+UI51KbZAVRd2QyQRn\n0SMjwbQM8bgxIJ96qjHE9vTkJn9jLyJfmUx3FsmeThMTwcpxbpoMd2Xi5hGyS3Da13Nnjj5316Gh\n8IA9u39hbrBTU373ywsuMPuMj/tdfKemcrc3qyfU5KTfTtHZGa6qtFdvXV2536nbbJdc1/vOrtrI\nKV4a1Z6BMlcU+XcAHinnAovZRFDUhjD9rDv4Rf0g7RaW4dWnX7aT/7nxDlzy1P3x+moa+OwZvuhu\n2w02kwlXGbl9TSZJGO7aZdRVvI99/ra2cFWW3e+BAf+1BwfD+9Rsra8vt1Kem1qcn1l/v0niuHmz\nP4o+lQqvMwKYwlZRaecbUe2kta6KoLgKwNpyLrJYTQRFbchXn/iUU+jH7Ev0xo1/uPF4sEa2O+Nz\n4y3YsOx6E/nqUvB73yrAnXWHxUNs3mwGaTa8r1yZe77hYWMjsW0LrlfO6Kg5f29v7qBj990XZTw1\nldt3LrTUzJ5QtuMCz+R9nmm+1WhYChROyeKL2Vi7Njw2w508NCLVEBSPAzgEYA+Ah7PtoXIuWnJn\nRVDUhDDvH3sAn5vLNTazEJmZCcYxuMLA/iHas2XbEBmWP8qNwrbTeviERDqd65Jq34dPKPoGjw0b\n/KnGfd5S9vltdcb69flTZw8MBFVkdir2Zq2W52uzs2Yi0t0dXq88ynEgqsXjdA7+rvnZhkXtNxrV\nEBTH+lo5Fy25syIoasKWLUbl4ZvV20KAB2YOIGMXWB4EOzuDA+/YWPCHyLmV7MHcHbzdPE2uqmlq\nymzr7Q16R3GiuTB8QjGs8JIvtUZPD/V3xQqtjzoqWMDHrrkdpqZrbzeDnh15nkzSCsNWs7VKAB57\nqvk8j+zvgKPsM5nCg+/c1tZG5/QFWDYy1RAUfZ6WLOeiJXdWBEVNKHSWbTc2DLplULk8pS0MiknS\n5tah6OqiY+1Vw/S01scfT9v6+oI2gnw+8ywU7cHdFyzHM80wQ3JY3iK3RoKdYJDbzExQzeKqthh7\nRZMvT1IjN6VoJcgrq1jMnyzRNkZnMv5nW2hzkw82OtUQFHsBHAGwP9uOAHgWwI8ArCvn4kV3VgRF\nTfDNslkNEJbdlOtfFxK0Zs8KfQkCt2wxdgN7pmgPjrx96VLaz6eWicdpcI0aAHwC0B2ER0ZyV0pR\nzU1FrrVRR7GaxK3Lbacf4T4lEjRg8srOfratYuBubw/PC9XfH1xxlSo8wwRzI1MNQfE5AL9tvT8v\na+A+G9n0HkVfFEiDkg0+DuAxAGdmVyrbs7aQ2wGkPcdV6DEKUdipMMJKgQK5gzMv3fMt4W09vS9B\noD142z9+fs1GaHt279pBOjqCs/QVK3JrO9tBcmH6/66u3AykYW142GSADXsGrosw72MLR58h1322\nmUxrpSSPahs30vNzt7e3a71smf858f9SImFUXI1svHapiXssgIezfx8s6aLAtQD+KPs6ASAF4AoA\nW7PbPgrgE57jFv8JCgXhDoy8ChgbCxpbWW9ezI+MB2fWRbvYM2fXLjA6SoOC7THU20ueVTzz5PPa\nAims1gWn9zjzTCNsli4NzmJXrAjPhutGBK9aRX3jnEI+NZvPi8vNOuuWT7WFNp+nmb2gym2xWHRM\nhbtK4drezUI1BMX27MC9ImvI3gpgByhK+0dFX5CEQk5SQQA/BnBU9vUwgB979qnIQxTyYxt0XQN0\nWJxDoeRzf7U/t3/ovb25nkpcc8LexuosWyDZqhpXNWQf6xMIYULCHqj5mvaA39kZHJCmpmifqKR3\nbjU+X+PVUa0H40ZovOp007/4WrOonbTWuhqCYhDApwE8kG2fzm5rA3B80RcExgD8AFQE6UdZ1dZS\nABlrH2W/t7ZX6jm2PPkMyrYB2k7mNzREgyF75BQyY853zajCMiyU4nHjGsteQnY2Wp9txM7dtHEj\nDdQrVuRG3fp0/7xSWLo0fyS0fU3uW2dnrrpuZIT2YXtPKkUqNF75pFImqLCQwU/a4rWw9PeNmhyw\n4oJisRuACVBcxunZ9/8EKoyUcfZ7yXOsvuyyy37T7rzzzkV9mK2MPThzgZ2wwT5shuvGNPB5bJWP\nfe6wRGv2wOku/zMZf0CVWwsjbJXi9sWe8XMfXN0/2xB8GWDte1izJphJV+tg9Li9KmMPMK3JjZa3\n2yoxdggoNOJd2uK0eJz+V3weefkcL+qFO++8MzBWVkxQAPjn7N9bPO0bJV+Q1EpPWu/PAfDNrGF7\nOLvtaFE9VRd7Fu1GSruqnCg1hx0858vD46saxzl5eIDNl6mT+2oHRbmzu6ggPYAGfdtgzWos37Hu\ndbmOBLvqdnT462e4ZDLBin18HXtF4Pr/++JGCm35qsZJi27Dw8HvY2YmqHZk1WEjUElBsS77d9LT\nNpR1UeA7AE7Ivr48a8i+AsBHs9suFWN2dfFFD3MbHTXbYjEaFH2uh8kkVSZjNQ4fMzZmCgzxjJ7t\nHPYs3Y0xCDOIu55CrAoLS2FuD7Y8yNvCiO0ajH2s7U/vrlJ8nk9Rem07j5Ablc1927zZPNv+fqMm\nCzO+S6tem54OrkDDSvjWI1VVPYFcWMvO+wTgVAA/BLAbwL9mDdx9WSO5uMfWmEzGzJw4M2smE5z5\n5jOe+lxjfQbmMFuCzyBejE3DTZXhFliy4xRc9ZadgI7Pm0zmrhjclY27MnIJc6m1K93Z+9jPW1YH\n1W+2c0IqRRMSFuLd3Y3lFVUNY/ZOAD3ZgfxJAPcC+MdyLlpyZ+lmhUXAddt08WVm5dm/Un4Dqi+w\nzKYYoeAjzI5iJ/VzDde2esme7fN1fasRNxjObvY5ONZhw4bgjD9sVeEKFrcU6qpVhbu4tlKep1q3\n3l5a6blJGxvJK6oaguLB7N8PAvib7OuHy7loyZ0VQVEy7mzcddssxJNj795gVk+3hdVZ4OuvX09u\nifmio8MIs6PY9ZXt67mxFbZQ4Ne+Mqp2zQpbRz0+HjyHz95iC6swN98wF+J8kcSckqKtLTxDqrTK\nNDefWVjMT71SDUHxcNa4fDuAM7LbJHtsg+GqZzgwLhYjuwJ/5vN4CjsPHw8YFY9d/zpMPeQOzGFE\nxVO4nlFRxmtfbIUvZXWYimx62thYbOHD6jmOH3HLpka5+frUaPnUS1NTdI1S1FCdnUYQ2So1acW1\neLwxg/GqIShmATwE4Mrs++MAfK2ci5bcWbpZoQRctY/t0x/mqeTWS7AHaB5wOMumz4XTnqHzzD2f\nesombKB1U5q7QWq28doXW2E3NrT7bA9uPWZfnQvbLTesD75VhltAacuWaAHQ1lZ+ig5eeUWtCqWF\ntzA1ZiPQcHEUZXWWblYoAdcWYM/I7ZTK7uDm2gXsH4tdXpRn16xjD5uht7XRzJb91KMI835yI5ft\nfocZr/kZ2D/8WMwIAjvvkx2A56qwgNwEfr6aCD4vKbfv1Wj8fdgJBV01irTiWmdnflfoekMEhVAS\nvsA4u16CT6DYqxBb5+/OtGOxoB3C50XkXtf90a1aRUKprY0EmY0dnc0ChwflfDEYth1g/Xp/jIXd\nP3v/nh6T5M9WM9nXtOs5+wYSfp7JpERUN3qr54A7FxEUQkmE1SCOUvHYtYcLzaBqu8naXkTj49GD\nuj2Ld2tIuNHZ9rHuysIdsHfvDqp43IA2O4jPVafZAVa+AESf6s6l1II69dIk8aBpiUTjrCxEUAhF\nwx5IrpeNmzIjTBBw0Xse+MfHaRDlQZAHeV/pVDYM+9RcNnaOJJ/hMKo8q6sic4vQ+AohcX1qe7Vg\nCyOuqexef2AgqKry9ct2RRa31uZrjbCyqKigAHASgHcB6HK2v7uci5bcWbpZoUzcYDm7EphtwOaB\nMpHwzyRdd9h87p8uUTEUvjgO37H5orJ9RWjs6+ar3jcyYgSbbdj3lTQNq7/h2jikNVdrhFQelUzh\n8SEAPwFwM4CnAMxYnz1QzkVL7izdrJCl1EyWtk1hyRIzkI2P5yY+i/K0KXYmZffXF9MQdR+lRGXb\n1eHyBQHGYqZCWpi3kj3gDwwEV1Xt7cbusGFD8J586TfCUpU3Sjv33NIqyKVSjX/vYW3duvpVQ1VS\nUDzCKwlQHYr7AHwk+14ERR3gGyTdfEK+wdcuv2nPuDl3jc8N1G1r10YP8L6BPSyOIczeEHavw8N+\nNRLP+tevN6qgfJHfbmoSdnfl1Qp7Q4WtCji2wRWoHKcCaH3MMdGfF9t8brSVsB10dZlnY6dJZzXc\n3r3F3cfq1eZ7aGZDPjtJ1BOVFBSPOu+7ANwG4B9RYmW7cpsIiiC2QZrLP/oGNHfwzWRyA86SSVM1\nLZ+gUCo3pYHrwRQ107frPLivw35gbgyET42kde51owQn2w544HXtIb58VolE0M6wYkXuM+/sDA6E\npQiFsbHKDmaFNn428Tj9X0xNBb8jX8lRu6VSWm/alOuqzN9Ts5ZvrTdDdyUFxR0AxpxtSQBfAnCk\nnIuW3Fm6WSGLO+DbAxL/wH01HbTOn7o6n3rAXgUkErkBfGH5l9w6D5kMDTaDg7k/LNcm4EuTwfvx\nzJ/VPAMDVOfBN9Pm1OnuAO+64YYJTH7mY2O5nlG2BxnvE5ZpN+zZdnYGa1T4Bu5atba28FWi3U46\nib6TzZv9q07+/vn4k0+m/UtRZ9Vzq5fAvEoKip8hWx/C2a4AnFPORUvuLN2sYGHP0u1ByqdPd3+o\n7KXkm9UNDpIqyvfP392dO0C4gmV6urRkf/YPy93uM2D7VlG8erC3uaqO0dHcfEkrVxqBs3GjuX48\nHhQ4y5bRsRs3GoHIEeB2OnPbScD+LlasqO5gVakB0I64D1N92QO/b9B0V4R795IDwdSU+Q57ehrX\nWyyRyJ2A1IJKCoqa2CEiO0s3K1jYPzRfTWhbCPhUUHbeJ7dFqQWmp3NVM3yeQtJz2IS5uobFRNgC\nxB3sOXGfvRpIp+nHysJMKTrH7t3BPrvCpbc3dwbvriLchITsnrt+vX/239XV+LEIiURuHE2++JBi\n/yfc/+1SizfVQ0smi7vvSlBJQfEMgP8K4C887b+Wc9GSO0s323IUWnPaVe3Yaqm2tlwdva/CGjff\nbNge7DZuzFUHFeoW6+LOKu3srTMzuS6oPltHOm305657qz1btYUf1/kudDDic+UL6gtTx9RabVRs\n6+gI/2xmJvg97N3rV9W5qdRLJZOh77ccJ4Bat1NOqV2t7UoKil8BuCyslXPRkjtLN9tyFKqacbHd\nRG0bAu8bVXzI59K5dm1u3YUoryJXkBXqzmv3q78/OoeST8jwyoGLy9jXdW0Ibo2KsMGxu5v07cPD\nfocB25g/MuI/h52ltx6bK8iiVpTxOAVeTk0ZVaD9+dveZsrFluLCHQYHbW7aRIJ+aIj6UetnV0yr\nhd1CVE8tQD7VTFhltUyGPuvpMbriRIJe5zMa2oNGV5eZrecrU2rjCrJ8go3Jl6WVyeeCy9exBY+t\nqhobyx3I3BKp9uAeNptVKnicb+Dy2XXqqcXjWp96amH72v8bSgUnIfaz8v0PVAI3pUs9N7s2ezUR\nQdEChM3aM5ng4GVnc+XBbzH81QcG/J5LPuxru55PUULG9lyKSklun9+X2NAeMDiA0BY8U1OmxoQb\nXGivXlzj9MREeCzFrl3B/XhF0Wiun/nK24Y1nwDt7y9+YlEOfJ1kkmxP7sqxXlqt6lhUUlD0l3Pi\nSrRWFRRR2IMgB8yVO3P1DXCFFpJ3i/6EGXrz6fU5fUdUmu6wZHxLltBAxassO8AwlTLb5+b8grS9\n3bh1btxohIqvjsO6dcGUHlu2NKaHDnvnTE8XV68iFiNBOTubu7LgoMdS7FbF4vOeqrcI8Ftvrewz\niEKSArYoPLPm2Zxd7N2exS3WrLbQfDb5Vg32rNyX9dW9FzftBwvG/v7wZHy+/EtugOGSJdEDuj1L\nTiRopWGnSU8mg7EOy5dTP4sZnOrNuM33UGy/eCXrrtCAwicYlSCTCa4eay3Aa5k8UARFE+PTwUdV\nW3OjlfNVTSumdXQEVwJhEc/2zC6qPKmrq81kgrp9X4I+e7C3VwKuUd0nrIpxr0yl/Gom+1muXx9U\nb5QikBvZgyfsf2Pv3qD9q54yq9pp7mvRaik0RVA0GWE6eN/AyYOaOyiyvr9S+XQGBqIFlU+YJZPG\nY8ouT2oTNcDbrrB26+/PVWX57ChbttC+dk0NwKSmAPIP9l1dQWER5T5ayVbP0ct23RG2EdULvpVl\ntdrYWG2fhQiKJsMWBDwQcRoOOxK2s5NcA+0ypm7uokJbWGnMdNrMeu2SmvY+PkEVZRS14xpcfK6u\nboI/99xu7Wl35cUrHnu/0VGyQdj3Uqw+e2LC7+3ja0uWFHfuQlqYt1Ghx5YzYEb9f61fXz27RCmw\nOsoX9Dg6uniTq1iMfjtsv6n1sxBB0WTYM2g39sFnpOYiQplMYXUP3B9CLJYbLMUlP1130fb24DVG\nRvyDgn0ud1AZGvJ7MPl+SD7XykwmOKN2I4LzxYj4aoFzrexCB4H2djoHlzWtVSvVS+mCC+h7ZeFY\njPG6EIFaL/mNouBVj+1Z50bmh7Vi4mHq5VmIoGgyonTtdu0E3z9kKTrvnp6gK2tbm7/eNTcemFmt\n4Bvs+Vxh0d2st47ysfcFzjE8qHd304qKB8yBAZMB13efHBzmquXCZpFh/VeqPgzRpfbBTasepru3\n63kANEnItxJZurS+sqaGwb8zX2R+KqX1WWfR7+wzn6G/iQQF+bEdzhaYYSrIVKp+noMIiibGVcXw\ne/7xunEGpaoiePAOq9jGqpOeHhqYbRdXnx2F+xkmMNioF+Uh5QucY6Hk1vjm6+WbEba31zbPUj0I\nF7vZke6+XE27d5NgbW83BZnCMuEmErkOBo1GvhghGzt5Ydhq9NxzK9/nQhFB0eT40mCw3p7tExxd\nHLaiiMrbBAQNbb7B2xUGtsqDBxi7cJCdGtyNmLWvFfXDtFcyfIwrPOJx6gsLLXtmzK6sLExt11Zp\nwUp8Yem9CxVs7n6VDq6rN8ImKCMjte6ZoVxBkYBQ1+zZA9x1F72enweefx645x56f/rp9PlFF5l9\nfPz617nb4nHg8GF6nckAJ50EHDwItLcD/f1AOm327emhv11dtO/+/eazU0+lfZcsAWZmgO99D3jz\nTfrswx+mPn7rW8D4OLB8OXDNNebcW7fS/Vx4IbBtW/CafI9KAf/7f9NnnZ20belSuqfDh4F9+6gB\nwPQ09UFr4J//GbjkEuBTn6K/mQywY0fko2567O/8rbfof0Ypel4+wraH7ZdKAeeeC1x9dfC7bHb4\n92GjFPC2twELC03yLMqRMuU0AHEADwC4Jfu+D8B2AHsA3A4g7TlmkeVsfRBVhY1n1u3tpPpxZ2+d\nncX78A8Pm+VyKhWuskomaZbuegjZr/v7c1VQ3NggvnKlsR3Y+uuw8qZaB1VEHR20jc/lS8+QzxWT\nk8nlS4fNz3rXruKeqf08ar1aqEVLp2uXnqLWsCfV1BTZMWz7Rb2o4FDmiqLkA8ttoBTmXwHwjez7\nKwBszb7+KIBPeI5Z3KdXJ/i8mVx9vy+qNB5fnGRo+bxn7GvYBk5bpcXnYFWPPXD77A1a5xrKbWHB\nqhClTOEXN7LbboUGM2UywcE8kQgaaNPpyriz1rqFuUAvRnOFfKtTrfxWxVCuoIhVa+Vio5QaBTAF\n4POginkA8DsArs2+vhbATA26VnHm54HJSWBqipalAPDEE/Q3Hqe/ExPAVVfRvjMzwKuvAskkfRaz\nvrElS4AXX/Rfh89VCF/8IjA0FP75W2/R395e4IEHgJtvBlauNH1auhRYtYpUPw8/DMzOAmvWUN+n\npsx+AKmgrrqKXm/bBgwPm8/27aN7BoD77gM6OoD/+B+BD32IzvPYY8CBA/R5wlKa9vUB3/8+/d20\nyTxXH+k08PrrwXuzVWlHjgQ/bxaWLKG/3d2Lf+4zz2wS9coisW0b/Qa2b2+i51KOlCm1AbgBwDiA\nDTCqp4z1ubLfW9sXV8zWAJ9LqK0OsQPS7Jn+pk2kmrrggsqkVN61y1zPZ/weHTVG89FRv/HTntXb\n97l8Oc3iuVCQjR1E50uXbp+Hl/S9vbTKWLGC4kiiakzYzM3V32pBqcLUYeU0TpfODhDT04sXVX7K\nKfUzaxbCQZkriqobs5VS7wXwvNb6AaXUpG8frbVWSmnfZ5dffvlvXk9OTmJy0nuKuoUNsrxqAIBD\nh8zniQTNxDs7gTfeMNuXLgWefppWI2GriHJ4xzto9jM0RIZt2zieTlMfv/xlGh7CUMq85lVSTw9w\n9NHAD35A7889l4zanZ3A4CDw1FO0SorHaeW0Ywdd//HHgwZsgIzko6O0akmngWOPzTXid3eTAZuZ\nnyeD/xNPAC+/XH+rBa2DK5pKcOgQcP/99HpmhlZu9v9WKaTTQFsb8G//1kSz5iZi586d2Llz56Kd\nT+moX34FUEr9PYA/BPAWgA4APQD+FcDpACa11vuUUkcDuFNrfaJzrK52fxebhQUavK66yvzANm2i\nAXJsjAQCe/x0dNAPursbGBgAXnqJBrtKP4J4nPoWj5NAO3DA9CmMtWtp0OZ7Ouccc8zwMA1OExPk\nVcXbBwbChd7sLHD99fS8TjrJHH/yySRcOjtpAOTn9tRT5NnEx6bTJCAeeshsb3WUoomIPTEphWTS\nnKO/HzjjjFyvNaG+UEpBa63y7xlCOcuRchuCqqcrAHw0+/pStJAx2xeNPTAQNEBWKsFfVOMgN1+k\ncyKh9THH0GcdHcFobq2DUeS9vSYqms+1dKkxKrtqLNcIaD8fWxU1NGTKbfJ529rI8F+L55WvcZxL\nvdVJWKz/FaF+yY6dKLWVfOBitKygYK+nPgA70ELusVHBdLYnTi2yhabTuQMzD3DsCpnPW8tNFeHz\nrhodDbrn+kqe2rieUmE5sLjVS5W51atNuohK2iRqEf1dT949gp+GFhRFd5Zutmlw4wjsWAT7B1/t\nso49Pf4iSHZenFWrjCDgv/E43RMPGmx07+zMTTxoDzDFuBP6jN+1rjNgt+Fhv6G4rY3uv5gEfIW0\nQhJBVrJFZQMW6gcRFA2MOzvm2W88Xv2cRIkEDXJTU+FqH3sFZMd1uCserl+9YYPJMKu1GdBPOcUE\n4wYunN0AABxGSURBVLnXcPElHdyyJVy1VMsqZrFYbt1uYPGFg52OpJb5o3p6REg0CuUKiqobs8uh\nGYzZNgsL5BFUrgfKYrBrFxmgo5icNF5GbW3khdTZSWk6ePv4OG1jg/XgIBmht22j96edRuk3Dh0C\n1q0Dbrgh2ghqX3PlSvJaeuEFk4rChftVSxIJE3tSCTjtRixGcR8++Dn09hpHg8Vm0ybg9tsX/7zC\n4lOuMVsERY2xvYNsEgkaDKt1u21twAUXAL/6VdB19YkngBUryM2VvYwmJoAvfAE4+2wKrOvupuPb\n2ijPz5o1wDPPBHMLsReTPfDb2xnbnXXFCgq8O3iQ8gglk5VxDW4kOM+VS1cXTThYQE1N0b5XXUU5\nt775TfKaK/T/qauL3JWj6OujYDvxeKp/RFA0KDwg7tplZoU9PeT+Go/Ttmrfqp0gznaBZGZmgN27\ngZER01cWcrZL6u7dwejoiQkTpTo1RUkCAXJrvfPO4CBz9NEmyV+94ns2laCzE3jtNXo9OAisX29i\nTQBaKTz9tHH/5X7Z8Sw9PXSOqP66QiEqUaCvb66wF+qPhnaPLbZRd5uDKE+demzxONkYbIM7Rzlz\nqVb3nsbHyX3VtXnMzJjtbkJE1/ZQb/WhE4lc43m1XHHZjjM9bWw85VbZ6+zMfcZRkf+xGGUJ4Gcg\nHk+NQXbsRKmtJrmeWp35eUrHXW+Mj1OQH0CzUztf1OHDNJP96U/pfXs7qYQACsg76yyT02lsjNRG\nnZ259oJ0GrjpJsoXxSuQu+4iVdU99+Tq9is9c1dFzrFOPRX47neD2xbTHsE5rOz8WICJ5Ofo+UyG\n0rMfc4zZp9D8XpzvaWyMvnP3GUep91Ip6uPnP9+E+YyEcMqRMtVu1N3Gp15XE+vX+1OO2zPmZcto\nxunzyhocNCuFsDKn7gqiEnmrFqMpVX3PM9s7yr62G1viulUDuWVLfa2ri76/M8+k4/buzfW8K7TZ\ntc+F+ic7dqLUJjaKGrBsGc2g65GhISomZOu7lQr3rvGxYQMdz4bv7dupSFGjpNQYHSU7SSU9l2y4\nqNOvf03PzLYZ9PYCP/95cNbOdp6JCeDGG6kwE+cN43QnYdhpUxIJWiF0dJAnWbHeYmKbaBzKtVGI\n6qkGrFhR6x6Ek8nQQMkqKK2jhYRP3XHXXcC3v02DHA9w/+f/0HYWErE6/c+Lx4ETTwx3v10M2tro\n7+rVlJr9jjtIQD/0EAlYVj9xWndXtbNtG7kKt7cDf/InRiWVTlMyxZUrSUXG98OsWUPqJoZTrP/y\nl8ULibExI5yEFqCc5Ui1G3W3sZmbq59cP9UK1vKl9q6XZ1Dt1tlJqeIHB8Or/QFG3eQLOHT3dwsH\nhamgWC24cmV4/1Kp/EWOpFBR45EdO1Fqq9N5XfOyZ0/tA8LWraOZq9aln6MYI7AvtXctn0GxBuxS\nedvbcq/7ve/RLP6FF0jNdNppFFvy6KNmv74+WnWuWUNxKXfdRaqmD3zA7GOnX7cLPtmf2QbxU04h\nNdNJJ5FLrY/+fnJtbm8PvydetYgBu7UQQVFh3Ip29g+8FnR1UW2Ccr2JtPYPuFxJrZ7x9b0cVVg8\nnnv88DBw771kr7Gv+3d/F6xJMjJCguDFF+n19DQN5vfcQ3Ys205iC3a7OqBd2wQgzzQ3nfgjjwBf\n+lK07WX/frJ3bNwYfq+rV4d/JjQx5SxHqt2ou41FvXo4SVvcNjxs0ojbsQVbtpg4hbEx2m7ntuI4\nCDsRI2+zPZ/WrDHnnJuj66XT/hTvpSYKHBuj/uY7XlKKNx7ZsROltqpXuGs1uNJbPaEU+dK//HJp\nx3Muo4kJ8ta56SYaQmpJpfMrRdHeTjW7UylSJbW3k9poxQqq880z+2OPNSob9hZasYJWDi+/TLEo\njz9uth0+TKuMM84gFRQfu2dP0LOJqwfOz9M+xXyva9aQF94jjwDPPkuqp6jvUozYrYkIigpTj7mJ\ntM4/mNh5mpilS0mV8tnPkopiyRLg619vTSFh51waGAAuuohUSiMjJq2J7QI9MWHKwh48aBIiPvWU\n2YdtDT095hg3oG1+nryjmO5u4JVXjPppZqa47+Pll+k+XnnF77asFHlfrVtH93fNNWKfaEnKWY5U\nu1F3G4taq0SKaUppvW5dsDaGW/hnYIBUI0ND4QFp69ZVt8/Vfk7r1wdrhHClPsAEwLH6JhYj1dPu\n3blqyNnZYEqU3l5SH23ZQs+ZvaJszyd7f07hbqdoLyaleU9PsEBWVBN1U2OTHTtRaiv5wFq0RhAU\nduTxUUdVfxBbrLZ8eeGDSCs2rlI3NmbyHnV10Xc/M0MDuFvhz46CHh8PFm3q7TU2Cjeq3ReJ7cux\nNDdXWEW/vj7zuhBBa9tPhMZEBEUdMTdX+4pji9H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IgiA0Ew2teloMF9j164EnnwS++10J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\nCkEQBCGS/wcIEgon+dLBlwAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that we can predict the T2 signal given the T1 signal, but it is not a linear relationship. For example, for T1 signal between 20 and 30, most corresponding T2 signal is low, but there is some T2 signal that is high. This pairing of high T2 signal with low T1 signal is from the CSF, which is dark (low signal) in the T1, and bright in the T2." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Arry that is True if T1 signal >= 20, <= 30, False otherwise\n", "t1_20_30 = (t1_slice >= 20) & (t1_slice <= 30)\n", "# Get T1 signal for voxels in given T1 signal range, 0 otherwise\n", "t1_in_20_30 = np.where(t1_20_30, t1_slice, 0)\n", "# Get T2 signal for voxels in given T1 signal range, 0 otherwise\n", "t2_in_20_30 = np.where(t1_20_30, t2_slice, 0)\n", "plt.imshow(np.hstack((t1_in_20_30, t2_in_20_30)))\n", "plt.title('T1, T2 signal for T1 >=20 <= 30')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 9, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can capture this more complicated relationship by doing a 2D histogram. This is a histogram that divides the scatterplot into squares, and counts the number of observations inside each square. Numpy has a function for doing that:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "hist_2d, x_edges, y_edges = np.histogram2d(\n", " t1_slice.ravel(), \n", " t2_slice.ravel(), \n", " bins=20)\n", "# Plot as image, arranging axes as for scatterplot\n", "# We transpose to put the T1 bins on the horizontal axis\n", "# and use 'lower' to put 0, 0 at the bottom of the plot\n", "plt.imshow(hist_2d.T, origin='lower')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 10, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The histogram is easier to see if we show the log values to reduce the effect of the bins with a very large number of values:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Show log histogram, avoiding divide by 0\n", "hist_2d_log = np.zeros(hist_2d.shape)\n", "non_zeros = hist_2d != 0\n", "hist_2d_log[non_zeros] = np.log(hist_2d[non_zeros])\n", "plt.imshow(hist_2d_log.T, origin='lower')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 11, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mutual information is a metric from the joint (2D) histogram. The metric is high when the signal is highly concentrated in few bins (squares), and low when the signal is spread across many bins (squares).\n", "\n", "Mutual information is defined like this:\n", "\n", "$$\n", "I(X;Y) = \\sum_{y \\in Y} \\sum_{x \\in X} \n", " p(x,y) \\log{ \\left(\\frac{p(x,y)}{p(x)\\,p(y)}\n", " \\right) }\n", "$$\n", "\n", "See " ] }, { "cell_type": "code", "collapsed": false, "input": [ "def mutual_information(hgram):\n", " \"\"\" Mutual information for joint histogram\n", " \"\"\"\n", " pxy = hgram / float(np.sum(hgram)) # Convert bins to probability\n", " px = np.sum(pxy, 1) # marginal for x over y\n", " py = np.sum(pxy, 0) # marginal for y over x\n", " px_py = px[:, None] * py[None, :] # Broadcast to multiply marginals\n", " nzs = pxy > 0 # Only non-zero pxy values contribute to the sum\n", " return np.sum(pxy[nzs] * np.log(pxy[nzs] / px_py[nzs]))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "mutual_information(hist_2d)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "1.3399511058289812" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we move the T2 image 15 pixels down, we make the images less well registered." ] }, { "cell_type": "code", "collapsed": false, "input": [ "t2_slice_moved = np.zeros(t2_slice.shape)\n", "t2_slice_moved[15:, :] = t2_slice[:-15, :]\n", "plt.imshow(np.hstack((t1_slice, t2_slice_moved)))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 14, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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sTnPPWQ0o+NnsN8/TfiXaxZnlSVrmWtDMWUeD0R5PTZEMm9qsNtNQO6FzNxKJ\nAIBU+aSviD4eAiKaj8wIHJtwNi0HplCe97tuZnSNSSt6TBfdS7fn7uy0fTbVChOV2+6hiT6ZTIpJ\nhbZxRnOcnJzg6OgIe3t7OD4+FqcJhcZ4PMba2hpef/11bG5uCmomkRBhUJWt1+vodruCuHVKveu6\ngmRZHZFMjZNjpuVzARE1k0h0urPODNX1XzhO3GKOwoGqOImeY8yEpul0imq1irOzM3S7XaytrQHA\nTOIPAFnEukwunWnHx8eYTqfY2tpCo9GYyR4lEwIg0Qe9Xm8mAUszfUbktFqtmZrtNoa7CD0vYtB6\n8S06z2zznm0776poj78xOogF0JgdTPpm1FUmkwEAEZbVahX379+XzONWqzWDkjXj0RohTTEMVaXg\nBy7DC+m3YV6D7j+ZL0NiSccUMIx+qdfraLVaYtLT9nfNtE3hpoWPDrHU/aEjV9viuYkLkT5r8HMN\nemUbX1UDZB/1f/3ZC+2bdGCiedsxr/bcbeS2Ng+xey0eTYyMmlheXkY2m0UikYDf7xfV8unTp9jf\n3xdzCJH4cDjE1tYW3nrrLbzwwguCmrlRsuM4kqBABk2POR00zLjUDJMER0FAJ6W5ByIXEgBZABoF\n817UDJigQzMOG+3sOt6W53Oh9Ho9KT07mUxwcnKCRqMh11PI6NKlOs2aY87zGW6ZSqVQKBSwvr6O\n999/H/V6Hb1eTzQBorNWq4WPP/4YzWYTOzs7MzHNnCsuVq0eA/N3jbrqwtP0ZDvfCzTYFrcNaMxD\ndDYGbi5m0jPDB9PpNJLJJFZXV8VcWCwWhZYYivr48WNB4Row8J6afmmKYEVPRnHRKcq1RDogigYu\nmCnpkwyTkUd8FtEk+0iNoF6vS7b0wcGBFJZjxIlOZmLfuYa0kxW4zCaltkMtmGGxBEc6ES8cDouG\nqYMHtPnHi1a0Q9IU0Ka2aDOZmejdRhMmfVwFkHxqRu44zi6AJoAJgJHrul93HCcH4N8DuAFgF8C/\ncl237nUP/QL6pc3YWk6euSi07ZBRKEzOWVpawtraGtLpNPx+P548eYKHDx/i7//+70W9isfjcF0X\njUYDsVgML730Er7//e/LcRIzo0i0M4i1wAOBAI6OjtButxEIBMSUwbDC8XgsduxEIgHXdWfC7bTt\njpmSRNp0gpKpkslruyCdqzzOhcUMTMawU5jRoXl0dIRGo4FGo4FyuYxKpQLHcQT5ua4rxA8AjUZD\nkAyfpzc0x/uNAAAgAElEQVTIIGp85ZVXJPb9rbfewtnZGf7mb/5GnGtkFD6fD+fn56hWq2g2m1he\nXsbS0hIymYxsVt1ut3F+fo5AIIBmsymLncLnEzoUmjD/L0LLNtozf/dC0aQ985g2B/LetoJOXgtd\nmwwYbbK1tYVcLifhs3RgdjodVCoVibTiWAKXpj3XdcUB6PP5JAmOZsdUKoWVlRVh1hT+1FR5vs/n\nw+npKer1+oy/BoBogLyGNvvhcIi9vT2JLGFy2/r6ujBN0s/JyQlOT0/RaDRm9pxtNBrir6IphoCE\nTScONRoNATvUXAl4GNWTTqdnNlChg51/pC8bczXphfOteRabvtY0C2paML+btOFlitHtsyByF8B3\nXNetqmO/B+AvXNf9t47j/O4n339v0Y1M9K1RyTyppmNU4/G4JPcwQoLmBjo2d3d3xUNPM8hgMJCq\nh1tbW0IklOg6G9MMidMxsboGN7Mw2T++A5MgKHyINulZT6VSM/cFLj3euniXtumZTESjIEbEUPDw\nHO3gpIrLhUxtgpE3jO3WOwPpOWE0BE1aOp05Go2iVCrhm9/8JnZ3d/Hw4UPs7+/L4tKhjUzPpuAk\nOgwEAqjXL7AAVXcyG9PUMs8EZzt+FWbvhcBt19u+m3Rt+8+m/RjRaBTFYhGpVArr6+vizIxGoxJL\nvbu7i7OzMzx58kTC7/QckhnSMZ3NZrGzs4N8Po+bN28ik8kIenVdVyI/dLp8v98XYc74ctd1Zwqx\n6XN1mWTOGf071EK1EGZC0p07d3B+fi5/7IcuIcF3JHJnv0xGR1MNz6XmzYJwOmqGQQY0Ken3MePQ\nTfOJCS5tzXaOF32adPTLgJLPalox7/4vAXz7k8//DsBfw8LIbfYk87htkZqfdShWLBYT5xyjU6hC\nVSoVPHnyBMfHxzKpoVAIvV4PrutiZ2dHMhN1oSA6Cfk8XZhKhxRxIRCRUNUjAjZtkjRDUFJToJDZ\nUlXVqck66cNUAW3qOoUF78PzqCLrAlo66oUagdYqGCVDxs9UbKq4tJ1zATO6p16vw3EcccoVCgUJ\nM2TMOuPegQuEn81mRdXn+NGEwBodfC61m6uooRoxXWVxLVp0XrRrIinzmI2mtcmM5gw6hOnMpODj\npiW1Wg0ff/yxIHHHuazoSTuwzkAuFAoolUq4ceMGUqkUcrncTOgr6VdnIutQV0YgUZDTt6Ibf2N0\nEs2NZIr0JWkHK8HSrVu3sLa2hnK5jJOTE6GrdruNbreL4+Njyfcwq42yH9qc47quOPH5PJbPphZL\nenVdF71eT9b2YDAQUxHnx2vObUDT1uaBDNt5ui0yqwCfHZH/peM4EwD/s+u6/wuAZdd1Tz/5/RTA\n8lVvZkMyPG4uKk6YtomXSiWsrKygVCpJRcDT01McHx/jyZMn+OCDD9Dr9cQ80e12sbW1hddeew03\nbtwQe2Kv1xNGQQZNhENhQfTCuFkuBu2VJ8rV/eW9AMizGArGMEZ64LkYT05OxLyiy+QS3ZPIGElC\nhqVVeRI3/7M+eLfbnbFHMtU+EAhIrDkRHb38RMe03+r5YjQBUQ8X8WAwkNj0XC6Hx48fY3d3F4eH\nhyLcmOX5j//4jygUCnjzzTcRj8eRyWTw0ksvSXw/7avn5+ciXHTJYL6Lqe7aVF7d5iEq/XmeOcZU\nw7WpxXZPbRJjDZvNzU2JtNre3pb6P4PBALVaDf/0T/+Es7Mz1Go1MeeRIZHxjcdjsaeXSiVsb28L\nSCFtlMtl0YzI4DTT1mF+ZIwU3uw/aZ60zfNoBw+FQlheXhbGTNSutUya/drtNqrVqtTSp+a6uroK\nn8+HF154QaKtuK6Pj48lDp7JTHx/jruuvEjaodbDWPtisSj0HY/HpZY+C9PRN6DpyLQMLIp60fSj\nk3+u2had+1kY+X/huu6x4zhFAH/hOM5HxoNdx3HmPp2DYDYv9dNk6mQcrOHN4ldMFa9UKuLc1Aya\nDPitt97CrVu3EAqFpEAUUUMoFBJVUKM+qradTkeIF5hl1mRgNvMH+84JZX+0g5GCgck1Gn1qsw8R\nBBkatQfNODRjN0PndP0Yqp1cvPF4XPqtF6jjXO5rqhmDvjdVVwpAlhwYjUZYWlqSQlzNZhO1Wk2u\n8/l8Ep9fKpWwuroq+6Y6jiN2fPcTuy8Rp00NtS0i/m7Sma2Z6rr5m1ezoXE2G71zfAgSSqUSlpaW\nUCgUUCgUMJ1OcXJyglqthvPzc+zt7UkWLeeBiJJaXTqdxmuvvYb19XXJayCdkfHq+UokEuLs07TG\na3TqfDwelzIVNPGR1jU9aOejdtyzHhErZjJp7/T0VJA2beGO44jmSk0jHo/jG9/4BiqVCo6Pj8Wm\n/vTpU1SrVezu7kqNf14LXK4DlhygJsqN1CkQNXDTgkCvV3O+TeY+r5l8zczo1Mdtz/Bqn5qRu657\n/Mn/M8dx/gOArwM4dRyn5LruieM4KwDKtmupspBxERWaL8tzzOM0caTTaSGG27dvI5vNIp1OC8r9\n8Y9/LNX9yCjb7TYKhQK+9a1v4cUXXxTiGA6HCAaDODg4kNA4HRPLvhItV6tVmdRgMCjmFBJIu92+\nGOBPkI1mxEQ53PtyMplItAZrZBBd6DjqfD4vTjAyt3q9LtEnS0tLSCaTc9V4AEin03LPeDwu6c6M\nxV1eXkYqlRLGQ2HR6XSkIJbjOGI3d11XIiAoXInwyWgYO+zz+bCysoLBYIDXXnsN/X4f//zP/4x2\nuy1CrNfr4d1330Uul8ONGzfw0ksvIZfL4ZVXXkG5XJayA41GQzaCpnnAfN95DN5rfPT5+r+ZoWee\na6J3m91TN9qTY7EYtra2UCqVcPfuXXFU1+t1HBwc4P3330e5XJaoIu5mRYcncLF5yfr6Ol5//XXc\nuHEDL7/8MhqNBg4ODoR50bHI+dLVCMPhMBqNxkxmJ1EqmX2hUBCzCt+PgoFmHQpx08cDQPoQj8ex\nvLyM7e1tZLNZtFotfPTRRxJRo4UNzU5cK+FwGF/96lexsrIidYym0ylef/11jEYjnJ6e4vz8HGdn\nZ/jggw9wdnaGRqMhtv5sNivrmmapRqMx45tJJpOSB8E4dl2wy0woAp7dZEK3RSY2TY+aqVPgXKV9\nKkbuOE4MgN913ZbjOHEA/wLA/wDg/wXwXwH4Hz/5///Yrrc5KRYxb2C2yhudeVS/WeHN5/OhXq+L\nF5yqFp0aiUQCd+/exebmptwjEAiIHVqnoxOp6JAtIhNtW9S2cJ3ww4ViJgFoJygAiX2lucLn84mZ\nhvehwAuHwxKBMp1OpcohAEEPVEFNTYCfOW50Lmo1Wmel6nngO9A5RkLje2kUTmRGZEPERm2FjISx\nwtvb2zg4OJhB54wmAIBSqSQ2zUKhgMlkgnQ6LYKUzEmHRhr0OoNybOaReYjHhsA1c/cysdjmgMfo\nfGN1SFanLBQKwqB2d3clVLbdbsN1XWSzWcleJGPf3t7GysoKlpaWsLGxgWKxKGY3jSKpkeosSm2O\nYd91jDjt5eyrrk9OuuD7kT4pzAHM5AHoXAACo/F4LHV3gMsQV96fz+Kap9+LyWz0zzBje2trCysr\nK2i1Wshmszg8PMTBwQE++ugjeTaBRiQSkSJhBEzaVMV1RgZO8EOfFsfrKojZhrZta1OPDzOx2bjO\nbe3TIvJlAP/hk04EAPyfruv+R8dx3gXwfzuO89/gk/DDeTe5CvM2mzY/aEbOqJXxeIxqtSohgVSv\naCe7e/cubt26NVOfRKf1shAPJTAZEdN9uelwPB6fSWRg7XBOMrPKdElN/Q5klDqBgcyUC0gvQh2W\nxkVC84suvq8ZOQBr6FskEkEymRR0QQbMMdULVaNYCjHWidFzRASmo2O4uKkuc7zof0gkEphOp7h9\n+zai0agsOt5jOByiVquJLZ1b5TELlSayer1uZeRednGtCus5MT/bGPCiZmoAtntSKDNctlAoYGVl\nBcvLywiHw+j3+zg9PcWjR49wfHwsC5imL5r2/P6Lrf5eeeUVZDIZySpmDRXSF+eZpjfSl6Z5ncim\nmTQ1LpbAJdjh+2nHO+mH0U6j0QjNZlMcqJpZsTQyz+HYmCVpdRw7EfVoNMLx8bFUJwUgETPFYlFK\n9MZiMdy4cUOS1c7OzsQkyo3JWROJ9vvz83Mkk0nRUgjYCFT02GnTqklTphlN04WNv+kxtzH3RbT3\nqRi567pPAHzVcrwK4J2r3mcR8+ZgkClQKtMmvry8jPX1dZRKJSHws7Mz/PSnP8Xe3p6o8n6/H/1+\nH1tbW3jnnXdkgsj8aaekUyMej0uInpaiJPhAIIDl5WX4fD40Gg1RMRlfS/scGaR+H96Ppgtu2BAM\nBpHJZODz+SQbj0iWETi051FY0KNPRt7tdhGLxSRqhGNMVZLN7/cjn88jEolgf38f0+kU6XRadk4i\nU+bY6c0GiKRpcuJ40FnHmHkK3MlkImai0WiEarWKer0uZh3aKfP5PLa2tvDBBx+IHZh1an7xi1/g\n5OQEX//615HP55HJZPDyyy8jl8vh6OgI0+kUlUplxjdxFeLn+HBezOPzkDjP15FB84QBadnnu6jH\nk0gkcPPmTZRKJaytreHWrVsIBoN4+PAhnj59iidPnuDRo0cAIAzH5/Ph4OAArusin8/jO9/5DorF\notT01g49AFhaWsLKyor4HhiVou3ljP7Q8dmkWdd1xSzpui42Njbguq7QuEbZPp9PNGMm+zBTmA5J\njgtR+JMnT5DNZsWBrmuNAxDHOcvyLi8vo1QqoVqtCnPWxdoAiGZNLbxYLOLOnTt4++23cXBwgD//\n8z/H6ekpms0mTk9PEY1Gkc/nAVyYdOr1Oo6OjmZizguFgpSgOD09FeSuHala49Tg5yomPjZerwXA\nVWgY+AJldnotGt24EMiImTzCFHh6r8/OztButwWZ0gb9yiuvzBTcIdOi95wEz2exqD0lr54EbtpM\nBKHt6GTMlOq2RkTGbeEYVaCZHh1DOqGISUdUCTWDNjMvbeOoI1i4Y9B4PJ5h4iYhkZnr/Tr5G4Ug\nx9RUvQEIgun3+xK/rgWEFga3bt1CIBDAu+++K2owVdqjoyP4fL6ZYlHD4RDVanVmMwQbY7aNyVXO\nA7zV53mM3rxWa2F09JEx5fN5BAIBdLtdibUvl8syL9T+GM65urqK7e1trK+vw+fzidOXZhDgwqnX\nbrdlI2/NsHXfGeKqhbaJHnVEFgUC0bqmEa5LXVqBQEPbeqkJdLvdGROldrQSgRPAsFpmNBqVDUl0\nzgbHl4KGtMa1eefOHRSLRXS7XTFXffzxx5KbQB6SyWRmNmSZTCbI5XKisfb7fekzwzFt4cA6DFJr\nt15o3KYl/jLtuTFyW4c10ZuNjJYEQy+/jq89OzuT7DMSLQnxzp072N7eFvWP6FIX4CFzo5Q3FzqR\nJomGpgESLeulOI4jadWMLLG9Dx2LJFyW4aTNcjAYiL2OJg0SGBm9RnoAnnkWTTvms4mos9msRAlQ\nCOnoG+AyrNB13RlGT1s5nVsUOLov7CcZreu6Ev5FHwS1mnA4LGWGmb5PDWw8HuPk5ETmIZvNArhA\nnQcHBxiPx5IFas6dTfOzMXAbkuI1ps/A1uahMdIuBThLSNAUwFjpx48fy76wLDk8mUwks/XFF1/E\niy++iFKpNJP6rhkgne+NRkNCDKndMF6ddmg6NYFLJyNpxsyeZeYj7cQ8j+9GTY3RVrQra3+Ppgut\nLRLd8xw6T2k+ZZ6H4zgzfaAwMQMm+D4M8XVdF6lUCnfv3hVTViAQQLlcxuHhIUajkfAUDagYrkiN\nk2G5FEw0IdkiWkyaWER/HGsbKl8EOJ4bI19kp9THiPyo/nG3n+XlZfHwP3r0CA8ePMCTJ0/Ek0+U\nEggE8O1vf1uuYygTmReJgAiAsc9MXNHZdhQOXNiZTAbJZFIkM+/D9Gi+g7mw+aeL6JfLZWHi9JbT\nlqxrdtPJqKNgqFkwfRuYTQoyG+2cutiWOQ9cmERE4/FYiigxTp4Fkpi8omPLtfpNlZeRN1wUVPU5\nzsFgEMvLy+h0OvjZz34mppNAICCbW9Trdbz99ttS2OnmzZs4OTlBr9dDtVqdqQmi6c1mczSdTOY1\n88JjNfIyhZ++t+M4M+Bje3sbq6urEvo6GAzwk5/8BA8fPsTu7i4ACLOfTCY4OjpCMpnE22+/jW9/\n+yLfjlEcenwdx5HicMwTOD8/x9raGnK53IyfQl9DZkhB6ziOhORSuwqHw1KPR5sSCVxc150J8SUi\nJijS6JnBAAwsADDD7AOBgJg1isWiRKM5zmVWMs0qvD/NTzQLUVgR6PE61vQvFAr41V/9VUwmE7z/\n/vvY3d3FwcEBjo6OZL1xF6tKpYJOpyO135eWlhCJRNDtdsXhPB6PJQLN1OBN5q1pR/MCG3iYB251\ne+7VD82Xtakd/KO6xYp/ZMjD4RAnJyc4OTkRexvts9PpFIVCQSIxGPpH9V47boBLpyITjej80UjU\nZMjUEjQDNZm4qWKZDkh9b16r+0KUoEOzKIhoztBVEPWzeH8uII269HkmQ+N/v9+PdDotjjGiODJy\nv98vKfW8j0Zz9C2QyMnUiOg1OuQzNzY2ZOcaZgrS11Gv13F+fi5milwuh263i3g8LoKBiMm0XdvM\nI/PQkf7P6/mOvLeJ/s25pjmQJhXGiVPDqlQq2Nvbw9nZmUTn0BndbreRy+Xw8ssv44033kAkEpEy\nE0SknFdtLuEcM9uSgp70wmYyHEa18I9rJBaLiVmM53FNApDdebSWpteJzsXgMY2odfkL0kcgEJA6\n43xH+gIACHjSQQB0+JLeCMCouZyensr1NMvevXtXzFx//dd/jVqthvF4jEKhMJOrMRqNxLzIoAfH\ncSSngWYa8h2Tp9lAhEmTNkB1FfPfc7eRm4zbROokCKrYRIfLy8uCZsvlMu7fv4+joyOxuwEXE72y\nsoJ79+4J46OdUQ+wDg+keQDAjKnB1kez/zpskPcgeuFiMq/T1+dyOfj9ftTr9RlHIJ2XjHmnmkc1\nWodlatOPjpoxFxI1C6JuL1ME78UMQ52tqmPNtbDV6nEgEMDq6uqMcOLcMLaXKNJxHFHLS6WS+Cve\ne+89DIdDWazc6abb7WJ1dRXr6+uIRCKCjoDLsgL6vc0FZc4lv9tochGSt5lkdCINNzZZW1vDzs4O\nEokEzs7OsLe3h4cPH+LBgwdwXRelUknKR9TrdaytreE3fuM3sLOzg2w2K2Nh9oVz3ev1ZDMGx3Fm\n4q9TqZRomQQ6utFcwYQfCsp0Oo10Oo3Dw0NhaMyXoCmCYbqcU9KJHmOuMw0AdBE2vhMdnAwppGCm\npsrMZGoQFE4si6wjyEiHjGaj45Vj02w2EY1Gsby8jK2tLdy4cQPvv/8+7t+/L3X2M5mMmGkYz88S\nwul0GpFIREJldfEtM6JF055G415WCU2jX0hEblsQJjLUCJGqHh1uROMARF1iRUPgEn0yZIoTSXVR\nMx4AYsejGYEJR16OSo2o+Q6acZu2UjN5wEtSB4NBKQFA5M29Fl3XlaQhahf6ucClucR8psnEtSnA\n1AxspgYbEWli1ONJxk8mQQHKzwAEadIEppOIiLy1/TWdTqNWq83ML2uOxONxZLNZQVfdbhf9fh+1\nWk1QH99JI2hzPm2oxzSt6Dk1mY/5O79T2Ooa+RRcBwcHePz4MQ4PD8XMRUFVrVaxubmJu3fvShx9\np9NBLBabCR3kWPGPZZSJjJm6z/EkwqbDzpxfzjvXC/ehBS4T+TQwobZIbZc0Rd8I54sgxzQ/2cLt\nqPWRiTP8V88rnbf6nXSdH5O+fT6fOGnNFH5to2eSUiqVwt/+7d+iVqtJ5cRYLCaaR7VaFe0pm83C\ncRzx6QCXhbvMtc/3tI27rc3TGHV7rohcMwFb04xB24C5EcF0OpU0b53UwIkpFAooFotwHAdnZ2cS\ncsdoCU4ky6PyfjSVsKysWTZT952fNbPkd74Xn2WaZGzvyfhWMkIdW87FqQlU29j0s81x1aicgk0/\nXzMkraFo8wqP873N5+gx0gJFm3VarRYajYbEv/Odiap0kSMuBpp1GJJJ53YoFBIbMEP6GCVBJqDH\nXM+Xfnfbf/OznifTjGJrmokzwqlYLMqOS51OB7u7uzg+Pkar1RJmz5oq0+kUX/3qV3Hjxg3ZI5Yo\nleUkOH5aeDKHwYaIOUeO40gEhhbAROo8nz6aeDwu86dBhjZp0NGvQ3B12Qgidm1C0XRi4wE6Covh\ntsw+ZcSW1kS12c/UAmgO0k5JftbvxcipWCyGk5MTSf0nfTGHotlsypgz6qharaLT6cBxnJlNNjRY\n8kLZJrg1zbOL2nPbs9PrJWzn0qzC4vcMqapUKtjd3cXu7q4MHOsij8djfOtb38La2hqi0ajU3eZi\nYNq84ziSPt5sNoVhhkIh1Ot1hMNhrK+vz5TmZL80sZAgtf3aZP46y5NEwMXD+wAXqmCpVAJwyYD1\nuWRQjnNZi4LvoRkt0RiZpclo9TP5LPYTuDSDmEKD76sZumYAHE86munlbzabqFQqktDCSAFuost3\n9Pl8+PDDD3FwcIDpdCoqNp17pInz83NMpxe7EtGEw76fn5/L4uUY2cwpXtqGiRL1+5vMXAtCjgs1\nJ9YAun37tmRusv7PL37xCzFRLC0twe/3Y29vD6urq/iVX/kV3L59G67rYn9/X0wHLKRVr9cF9eoI\nLQoCjhnnh3RApky/BRmYZoicAzodI5EIyuUyXNeVLQtZd4WZqY5zUQun2+2iVquJkGCtF10ql6BA\nM1QdstrpdMQXwGio8fhiM3E6u2keoVYaDAaRSqXQbDbR7XZFCPHezO2gSU/PHc/z+/04PDwEAOzs\n7OC3f/u3cXx8jD/8wz/EwcEBDg8Phff0ej2pgQNclEjY2dlBrVYTGztt57rukl7T/GzSjqZRrUnO\na8/NtALMV9k1QiJzpBOE3ulGozFTTJ/Mk0k9GxsbyOfzIgh4/ng8FpsviZP2WDotWXsFmK0XQXXR\nJjXJYDTCJsFyQrRZxWSsphcbgNULrq810Tj/mwjTRI62OTCRtulA0+OgtQ7zfYmkKVAZI80oBm6P\nR+ZDpMMxYigpFyfjl5PJJGq12ozphZEDdBCm02mx0zKrUQs/cwy8xsWr2cxiumnzEH06jEDh/qyn\np6c4PDxEr9cTRuXzXeQwZDIZvPnmm7hz547YhZmty/EkqKETUDNGMmZe4zjODICg2VDH8XPuNSPX\n9mw6CrW2RHMGtVfa1rnT1nQ6FfMk/T3hcFgylvVY65IAAKTeuuM4EoHEcEaWzzDnkxoBww35nfck\nQ2X/ifbJ6PW88rd0Oo1QKIRvfvOb+Oijj/Dw4cOZ6p/T6UVtJZYRLhQKYholn9HzYgJWUxM2j2t6\nW9Seu7OTzUu11YicMaVktiwYpSsWkpGvrKwgn8/LfpyM8GAIX7PZlExKRmNwcdDjzet06Vmb9502\nQhOl808zY76XaWM3mykgTJuf6cQzmao5+USyNK3wGWSIREQmWrUhdzZtWtFESWavHVpMciJaYtEn\nqqFEZ81mU5g4NwoBgFqthnK5LMyCDjWNQJeXlyWxiVvdmaaDqywk21yYGqRNu9HzxVBZOqcZf9xu\nt6UEK3AZqkr773e+8x28+uqrCIVCUuWQNmcKLr2vpk7yASDJU3rLQU03FHDa9KL7zmYKBfqRaOrg\nmiAD1ptREOxw3dLXxIQhvQWdpmfgcjs6MmMWRNOJRbpOuF4fjuNIko5eq9RWNfPmmE4mE3EOs48s\nr8FsUTqnU6kUfvSjH6HT6SCdTst7sVwCQ6EBiJZJUGiaQ00fi6n5mbS3CGA8N9OK2cwX0guCjoZc\nLieOzl6vh4ODA5yenoqqRxV+e3sb3/72t8VEwvoVrutKOjMArKysCBrSoY1ElUym0KGFWj1ifzU6\n1WjGnCDTIUqiIhoy7Xpe40QGzGbawzW612YSCifTdkxhoxmf2S8zMkabk7QDCbjUapjhp8PlaEIA\nIBssP336VHaQoTlifX19xom2tLQkJReOj49nTAp0eq6srKBYLGIwGEjWra7ZbrNV2r4vol1tRuN9\ndbar3uFnY2MDa2triEQiqNVqePjwIT7++GM0Gg3JQfD7/djd3cXW1ha+9a1viT2YmZG67MPZ2Rl6\nvZ4wFgCSPBYIBMT8VKlURPOkpqQ3D9E+Ih0LTtrjs4+OjsQkwvBDZizTbEbbME1qOmxWx3ZTYHEt\nkm6obeg1Rb8VwQAFOBG/pn2aLgjQCE44tvxtPB4LMgcg5h9qC+FweCbmnvQbiURw69Yt2evgvffe\nw89//nOpb8MaLUywi8fjuH37NjKZDMrlMp48eSL1ZrSPQNOPFmqfBmx8IaJWKJ1M5sdBJrohYwYg\nhEWnirbv0qSi08q1ys/jekNWfYzNppqynza7lWYWmmkDs04XzSh1I7LSKN4UFpqBcuw0mjH7w2YK\nB2oS5nvYzDK8r0bf2rZnPstxnJlMVP5G9MlEEN6HMd+xWAwbGxuSeEX1n+9dLBbFlFatVuU3CoTh\ncCghmnQSs+iZ+Y76XU0zk36nRQJVn8/PLFdAJJ5KpdDr9XB2diaM2O+/rLzZ6/WQyWTw6quvSm0S\nhvnxj2PQ7XZFQNNkoTVCbR6g9kNhxn5qh6RJ11qQU6AQdEwmEwFGfEdmb7K/ruvOjD3DY0mr1BB0\n41rQdO7zXZQeYGIcSzyQnjTtc11rezQ1c8dxZhA9fyc9a02egQ3mGuQ4+Xw+3L59G47j4P79+2i1\nWiIEgIuyyrxnKpWSoIXT01MxNWraspn1NA+0rUmv9txNK5q5meYELvRAICCxrNlsFoPBAOfn52g2\nm+IsYpU9AFLdkEyDWWa65KsOd1taWrIm/Jiok8kbZo1gplJTRdMmC95PM0Pes9ls4s/+7M/EZED1\nbGVlBW+99ZZkswGzjJIEpseQDiwSLglKP5f3MUMWea4WGiaq1/4HPlujUNPU4/P5JPNWO5NisRgm\nk+qCexcAACAASURBVMstvBKJBF544YWZOQ8GgxJTz0iM0WiEQqGAarUq5hRGsDQaDYTDYVSrVUl7\nz+fz6Pf7qFarmE4v64loE5FNEPO/jYGbDM8EIWSm8Xgc6XQaGxsbUrHxgw8+wIMHD7C/vw8A4nDv\ndrs4PDzED37wA2xsbEhUBs0I1DyovR0dHYn6n8lkhNHouvXsD80Q1Fw4Xxptuq47g8j1e47HY/E/\nTadTqZ3u9/slk5LaEZ8Ti8VEwHCcKAS0k1yHl5KmtNOf71GpVMR8Y5ojOU/U+rTpjs5wAr9GozFT\nLpcmxkAgINUOdY3/RqOBWq0Gn88nDJmmmHv37uEHP/gBfvjDH+L+/fvY2NhAKpWSbeja7Ta2trYk\nSY4bQlPY0Txljrfp99Ja+hfatGKzPZqLR4cd6sI1RAJ0lNDmxSJD2nzBEEOGdZHhMcnEZppgo1pG\nDzQTKsgUqHb2ej1ks1nkcrkZZgg8O0HARanRg4MD/OIXv0Cz2Zyx53300UeoVCq4ffs2XnrpJbme\nYZBkcJqR8D+JXqNm01xFTYemK17vZY/T76Pjw/Vc2pAGGffq6upMuKN2VGpUSLME67Boeybvz8Wn\nQyjJSHg/qslU/8kwrkqXVzlmc3RzPAOBy20BGUVVLpdlI2HS82QykUW+vr4u78r31oKV70k6pyOU\njFBneWrHoeu6MwXkgNl0eS2wtHAimiUDJaOl4KfjVpvlzLhy4DLDklqASbdaANoEqw2ZmsyNa5BO\nUWohRMxk9hRcfC7fh98nk4lUbuSaZrw9nbkUWPfu3UO320Wz2US73RYfG/0azWZTIofy+bxUVvTS\ntjWtmdr7VdoXqmiWSVTApTeai5IMWNu6AoGADBBTZ4lUXNeVtO5Wq4VisSiOCh3jqgeRi7TT6UiG\nHRcO7YRUp7Rq57quhGIBs+iXqJXHqbbStkznHRfOz372M+zv7yMajaJQKAgxUh0nQ9WZmWa0j6ny\nk3D5mULBZjYigmLTmYAakfK5piDQAoShnhwv2muJlOnI08lOrI1BdR2AOMko3LWaTNWZdal1nXcy\n83mLwtRwbLRqLizzPGqPdERym7NGoyEa5Hg8lsxcMovl5WVEIhHZdUozUT5HAxPgMpRVC2uNcudp\ncBpg6GgVbdYwTX82jUvXzKfTUJsHeQ3XBzUMcwz1GtTM2aQj3X9Na4wrpzBzHGcmw5prRzv8tc+H\ndYMI2rQ923EcMR0RdPC+b7zxBsrlMv7yL/9StEjyG5aiTiQSUqeIVRv12rIBp0/TvjBFs/RkmWYV\n2lYZesg0WdrsotEo2u32THUzMlqm1k4mFwV+WG2O9ciJzoFLpEKba6PREDWejIJF6zWiIENpNpto\nNpsSMscFZWY2AhfbrW1tbWF5eRmHh4dCIJoB12o1/MEf/AEKhQK2t7fx2muviUDheSzO5fP5BMXy\nuUzPJkLRtlYydfodeB/aIrVTTDNCHQVBQaUXlWnr5NxqlM7n6oJh/GPUSq1WmwnbZK1tJmqlUqmZ\n/RR1tmgqlZKd6LnHKhfiIgZh0iKbSaemz8Hnu0ye4Ubg8Xgc1WoVT548wd7enpgeMpkMJpMJzs7O\nsLq6it/8zd+c8d9QUJMmdP84phSCuq/anOaVEKTjtTkf2mbMc7kVnKZbOiTD4TBarZag4Ha7LffU\nm0hQgFD4MG1dm/G00CAq1oJGAwCtfZrfGZqo6d/sFzUNjgPXO+lNjxX9co7joFwuCw3w2U+ePMHX\nvvY1/NZv/RY+/PBDnJycIJlMin+G2+wVi0Wsrq4iEong5OQEgUBAHLImDel1qdfOVdpzdXba0I2J\nRMjM+UcnDNUkTbTJZBLZbHYGwXNQuJcnB4jlbOkw48ImA+92u2LvYvp/OBwW9KT7S+ZGpL2IEbju\nhUOoVCrh5ZdfRrfbxdnZ2YxdkZNMZwkzydbX15HNZmWhkFhpaiBzpVOM9zFrPxCJUdVn1EMwGBRb\noelYNbUK/R+YLczF7/q/nn+OiX5n4AJZ05dh1r3WJXc5v2TkOo55MBiIHVkjcr2Q9Zzws40eNVMx\n+6+vIx2y0FMqlZL6Hufn52LG44bJpKdXXnkFd+7ckV19yIiYtUn618/WJg2tNVFbMbVMMjYyCts8\n6Hc3GaamSTJlRoHoYAOdzWj2lfdj3/T4aWDCOeK7cDz0PbyYuimktRbB8bGhftIZ+0NHLte5Tlwi\ncKE5L51O46WXXhLQRHOaz+eb2ZOX64qRN9p8xb5c1Yxia8/d2Wm+gCY2Tch6MdKJo1Uk172oN0xH\nCxc7J6hQKEhsMYlLX0vG2Gw2JXOMjjISKieXziHehwiK6EMzu3m2rlAohDfeeAPT6RTvvvsuKpWK\n2DL1InLdi6Sln/70p3j8+DFef/11KbNJIUL1Vju0TJubOe46HFEvUj32ZLQMA+O1PEer5Gy2Z/G/\nyRBNcw1VTzqnaadMp9OSns65oL+E92LiCutus26O1ihsJguzn/OaCTi0UCTdMQmI9WBYqI1RUa57\nYdNdW1vDq6++KhFW1Ehoc2bUjk7gIY1pLUMzSxMEAbN+E00fmkFqIc37mMKa80UTBICZKpO6lopN\nMJgmOc2QtTDRY0rBZGoR7D/f07yf7rMeG518pPvK4zrpUFc/NRE0NX6fz4d79+7J+qS2yWQ0xt+z\nmiqd/FrQmtYJPQ8m3Xm1L0StFTYOkmlaYQghiU2nf/P6cDiMUqkkzJu2SA46mTijHTQhcEKZ4TmZ\nTKQ2Bj333PKKjIGNklVrGfq92BcTIREtLC8v49d+7dfwne98B7//+7+P/f19KQdKYubEDgYDnJyc\n4E/+5E/gOBe1pzc3N2X7M5qUdIQAr9XqLE0mruuiVquhUqng4cOHaLfbCAQCeOuttySl3JwvExmZ\n781iRqbwM22gnG/93+/3o1AoiJkhmUzOMGWdTZjL5cSHwagMJgYlEgkUi0WJY2boqulD4H9zIWnh\na1tsJo2SxrhY6Yd57733cHBwgHK5LNpiKpWS/Icf/OAHWFlZwePHj5FIJJDP55HL5dBoNCQhxnEc\nMUOl02kxM/V6PTmPTjSOoUbxJk3qOGbGY+sQTQpTPeea1oHLWufaDEFNkMBGNxN1mqY30zmr94TV\n2q5eVzZnvw24UHiZtnmfzyeJP6SpaDSK1dVVpNNpSVjrdrsSKUVBEQ6HsbOzIzkpr776KpaXl/Hk\nyRMBf8ViEQBEs+eerFybjAbSdWG0FmwKvUXtudcj101Lcv4nsyYqp3TUti4yDNZDYUjieDyW7DYt\nUW2okAOotysDIKiPZho92JxYzcjJMEhkWsWzMTMumkQige9973v4+c9/jvv37+P09FQWh+lAAiBm\nFW4NFo/Hsb6+jlQqJTY5Ch5N8Bw/It7Hjx9LfW/XdQVNMhNRVxxk0+o5x4MxvnQSUYD5/X5JdeYY\naqSoncEAEI/Hsby8LBEHTGTSSMtxHNk0OxQKzdhg6TzltZpu+BwTffK4ZiY2BKQZvEmrNEsx7NV1\nL5JaGMWQSqWEPhuNBlKpFNLpNE5PT9Hv9yXevFAoSIVE7ZegMCISpvqvY5P5vqRTTeO6/+y79t2Q\n4XGNmCjWpAE9Z9qWrcGHjd51f8zP+n6252jtQd/b1DT4O5m0zbSjQYFG4gxxJvDz+XwSqTadTqWm\nvE4cBC40/tu3b6PZbIpPjrTHnBf6dlqt1jORV7ZxMt9/XnvuiNxrwbBphxyZs96dhMRI1G2mJPMz\nbadMAkomkzP2LwCy9RpwMeksfENprO3pvD9NPFSbaV82pal2DmqHFd91NBrh5s2b2N7exmg0wk9+\n8hM8ePAADx48kEVBpML3J6piXWVuhUbGzcQEnejEGGWdROG6LrLZLFZXV/HCCy/ga1/7GoBLB5EW\nVkRPXLy9Xg+VSkUyAOlEZrIIz9F1PbRw9vl8M4WVyPhfeuklMXGxQJIOu2TcPh3dACTxo16vY2Nj\nY8YUprMZ9bh7mb/m/W4ieDIC1sOOx+Oo1+sol8tSdjWTySAejwtz+N73vic+GABSGpXbmrGuNlPU\nq9Wq7Iij54S78lDr0U5Dc01Np1OpaaM1NPP9fL7LbEldupZmFAIEPRbaRs3vpsar/8w1oAWMCbZ0\nhJYGUlq4c15NlM7G0hsaODBZiVocbeKNRkMqUkYiEaytrcl13L6x3W7LnDCa7Nd//dcRi8Xw4x//\nGO12WzRCghLO63A4xP7+/oxvgO9lA7eaZ3i1524j92okNjMOmBNFSaYRgN4NRduyAQgj0XZH3k8T\nABMI6AikGjsYDBCPx2dCw4hWdCYfn6dtv/yvCZJNMwUKqWAwiNdffx0rKyuyGzlVQ1ON1X/6eUQL\n3HWGC9hkRjS1bG5u4sUXX8T29rYICy4ovfA0oZGRMHpBq4UaIelx4rhpgcsqd7FYTOzFen9ECi72\nV2tamjZoH6eQorAgENBaiW56LPj7IoRknuvz+cSM4/f7Z8w+OsO4Vqthc3MTm5ub4nzn3FP7YDz0\n+fk5Wq0WXNeVFHjW9eC86NBNvoNG0JpBUwhr+tMOPL4PgYPPd7mjFiNCeG8dyqfn2zQ96fEyBaWp\nKeqm17uNkfF6HtfRKlqD0/3Q40R6ZfkPZquyAipNLaFQSAIoSLP9fh+NRkPyWVjka2dnBy+99BIe\nP36MWq02U3aaoZf6eaRfLQBNbeWq5pUvHCM3F4l2UmnCMNUkbWvS8dI8Xxf54WSScfK46RCjU7XR\naMhiA2brGAOQGum0qxEZOo4jiSmO40hEiz4GzGZy8fpoNIpbt27hzTffxIcffjiz+5Gu6sbFpd8f\nuFQj2U86BU21l+Fw9+7dw+3bt5HNZgWl63RqjrW22XPRaKFFRssaHnw2P5smHlar4xyxJnQymRSH\nEjdToBlBmwU4l1pDYvIJ31efZzM52JrNHGCaAfSYEP0zUYYbXOj5nk6nqNVqePPNN5FIJGRzAs3Q\nSMtM6WfdbWpRTNnXqFzbw3Xf9J/JFChgKXw1GiYjC4VCWFpakj7yncjItO/HNi+cb426TU1Hz50+\n7nW+7qsJljQN2rR98gQdmEBNhtotY8aJ1sns+V4s1MdaMNQ6CSRv3bqFW7du4Sc/+Yn4bqjhcENt\n7voViUQk6sykL22uWsTEgS8AI7cNuMm0iaY5KFoFIaLo9/s4OTnB8vIylpeXZaIYAcBBJbMYj8co\nl8tSTpW73rNuMh062svM4lzAZfJHIHBROzyVSsHn8+H8/BzValU2qY1EIrLVXK1WEyfHCy+8II5J\nvqceCzKib3zjG3jttdewt7eHP/qjP0K1WpXnEwXqzD4SqSnlNaKlVpJOp/H222/j9u3buHv3rjBd\njYK0wCRa47gDlxXtzPnsdrvI5/NC4DQhJJNJETqTyUVmIxmTrnXN4lo0W+i4X920/8Dn88mc6a3I\nGEuvzTOm6cHGuE0G4YXEmeadTqeRyWSkUiMrFXKDkqdPn6LVauGrX/2q1IUhE89kMsjn80gkEiJ0\nzG3D9JrQ76/nSIfdcr70Jtg8ptG16btwHAfpdBqbm5t44403pLAchUin08Hjx49xfn6Ox48fixlG\nC2tGgWgnqo5qMemIAgW4RPt6nrTtXgsOba7TKJ98Qq8FjglpgBElWlNmrDwjwliOFrjc2YphhewL\nzXblchl37tzBO++8gx/96EcSQko/G02E6XQahUJBouT01n02fsi+zWvPnZHbmn4ZEiibztZiI1pm\n0XmW8OQC0M4HSjqm0TYaDSQSCanMppmSLg2g6zBrs4+2P4/HY9RqNclK5OLgri18D27ltbS09Axz\n4PuTkY5GI4RCIdy4cQM7Ozt49OgRyuXyTMQBG+9PjYGftVPG7/dLLZDV1VXs7OxgZWVFFrxGzRqJ\nVatVRKNR2daKi4rInYvXnD8dSspytTxXm4TYiD7p1NOmE55Ppk8Bps/RQk3b4bWqzrHWi+eqzVxs\nGpHzjw4vAGImct2L2jpMJiOw4PgVCgXZ0k3vckRNSs+v/kwGRmcrNRlt+mDdFo6/+b48V897IpGQ\n+tp8V2q1jJXmRhKsP6SBg+mHILAi8DIjY7SNm7/pGjP6fjRZUMCYfed33Q8tPDStTKfTmQ3b+ft0\nehlWTNTNzwz/5NjzXD6D5kEdiuw4jlSw9Pl8EhprMwF9Gtp87ozcJn1MJq0nQCNN095NRt5oNGac\nOYxkoK2SNkgiDEp+zVxc15VY5Wg0KgKEC5cZXGTQZISM2mBJVuDCUUSpTQFQrVZlyzpg1iMPXPoC\neN9gMIivfOUr4jwhIzMRvRcS53ODwaAwjZs3b2JlZQXJZHKm5olWl6ni7+7uIh6Piy2bzIgCTjNb\njZTYyJTIwMg82Hf93sDl5smcB96bi4YhYSay1vZcak/6ndhsC8Wm9nvRpr6Omh6FPhkn0Rhjitvt\nNm7evDlzHd8vl8shk8lI3Lnesd4cI5Nx0ebKjZJpo+d76CisVqs1o01w/DRAIpPk+OlQP5oyc7kc\n4vE4Wq0Wnjx5gvPz85kkNN7bpEdtbuFcalCg51HPOR2VWkPTGq1Xs825OZ7cWUsLZ/ICziOvoUZI\nv5g2a1Gbj0ajyOfzKJfL0m9zPHQJCe0D0DQ5jw7N9twZOfBsPLHuvH5BTiiRMFVmv/+iRken05Ht\nmOr1utQ9Yeo0cBm3GQgEkMvlxFZNVE8H1HQ6lThTbkDBTFBGp5BRnpyczJh6XNcVWxjjm7nDOxfM\n/v4+ptMp7t27N6PuealYw+EQq6urWFpaQqFQwOHhoew0w6gajbpJfBRyTFfPZrN49dVXJa6Vpg5N\ncFxg3W4XJycnsgnCZHKRZcp76kL/HFdGBlE15nvxnq1WS6I3aEsng+AcABBES9OYDtfa29vD4eHh\nM8ldHH+GQuoCTmaonaY90xZps8vq79rMQibOTTAikYjU9QmFQkin08jn8/j5z3+OcDiMr3zlK1JD\nhvPOBJTpdIq9vT0RUpxXLRTZ/0AggKWlJYk/Z3giy0voxnHw+/2SkUmmwzVBQMNwznK5jFAohJs3\nbwoyNYEDwcXOzg6q1So+/PBDqStjamcUalq4AhBtRdMu1xDXPpkn5zGRSMz0ibZtc/54jfbpmILF\n5DXUGFkLSZfhdRxHfGGlUmkmP8JxLqpeskTH1772NfzVX/0Vut0uUqmUCFdq/gw/ZVE109xngozP\nFLXiOM7/BuC/BFB2XfeVT47lAPx7ADcA7AL4V67r1j/57b8H8F8DmAD471zX/Y8L7i+fTWO/Ps5z\nSQw2xk+Jx5K1k8lFvWaWqNRRG5qIqIpr6UyViMSiERCZFYlVO9Y00+L9JpOJZPaRIBhWxuOaaPV7\n62PaPri5uYl0Oo2VlRUkEgmp2MZFSqaqTUDZbBbpdBrFYhFra2vI5/OyKzjNE3wu+05nDrckm0wm\nqFQq0hf2j2YrhmsSqTA0TjskqS2RcdGByXlmKjvL3XJhTadTnJycoFwu4/T0VMwZunAa542MSZsM\ntHmF42lDuzb6M3/TGogWFFrAMZadSL3b7WJpaQm5XG7GxOHzXaRyM0yRjIHzTzOb7gsr7ZVKJcTj\ncbHBj8cXG0poQUGVnuNAu7XphCQT47kMZ61UKigWizNAQ9MntVOupVqthmAwKJUoaZag8NGaBNcz\nI5o4njxfm4fMqDMAopV6MTmbxkVw4cXMNY0AmBkrMnWWEKZm6roXjtJOpyPXra6uysYSfDaL/XGH\nKw00TNrUtHaVtgiR/+8A/icA/4c69nsA/sJ13X/rOM7vfvL99xzHeRnAvwbwMoA1AH/pOM6O67qe\nokQjHk3A/I2EZ6JU7bjiQDLGGoAg5/v37yOTyWB1dRXFYlHUbt6XC56bpZKIGV9NhnV2diaChh5s\nSlEyI/aTHm16xBl2pt9hOBzi5OQEh4eHWF1dRalUQjQalUk0Fy+v5cJmaGUmk0GxWBSPuDYPsXEB\nJBIJUZdZxkBHuphxwX7/xTZqp6enePToEZLJJDKZjDh+dQF+2hmpttfrdfHKU8AydK7dbuPp06fS\nLxYp4ztScFJga6YMYCZxYzq9SBVnNi6Zja6yRzoxo5g0E7uKCqtRurbDUlDqxDPmLOgqjMPhEPfu\n3UOhUJDFzcgmCvVoNCpakvbJAJfhrEwq0dExND2Nx2OcnJzMRPdouy8ZJyMz2LQ2pMNFu90u/viP\n/xg3b97Eiy++iNXVVRkD01np9/tx48YNbGxsYHt7WwDV8fGxVBRkCKWuz0IQwP5qB7vff1H3nONC\nB2Sn00GlUsH9+/elWJaeJ22m0eYMzpcWJhRgPJ/HNJLXgEWfyx3F6GBnUl2j0cArr7yCx48fo91u\ni1bFGlGtVgulUkn8GQQ15DmmkNEap1eby8hd1/2R4zhbxuF/CeDbn3z+dwD+GhfM/PsA/i/XdUcA\ndh3HeQjg6wB+4nFvqwmBv3EAtVrEhU4C17HLPJ8Ey5TuZrOJDz/8UNQaXbmQG6dWKhVUq1VJGqCt\nmypfu90WAqhWq8/Y+uiQ4mdOOBkImR6rIurEhGaziUKhMCN5TS3EhjhI6IyP1nHl+lr2W9vj+AzN\nlEwCMlVbMgguGpampZ2aDjJmNZK5k6lxnjTCofClKsv5NAW1yczIaEw1WX/XdGFqe16mFJMOtQan\nzzHP4zxTYHOOKcyIRpmHoLUH9pXvl0gkZPy8hAtpkhmCOpSQ99X95prQY2Imx+hG5jadTsWxPhqN\nkMlkBEXqMSaz4b1YwpebarNmDiPAGIOtzYFs1LQoHKl10gwaDAZRLpdRrVZnKi3a+IgprKiVazOb\n67oS4mmuCc17+L4sUcsSCq7rSjw5NYjRaIRIJIJCoSBaI/tGcyD7QWBorkHbvMxrn8ZGvuy67ukn\nn08BLH/yeRWzTPsAF8jc2mwLQjN3c7GZDk/+ZqJV4HJhMcuuUqngvffeEwmqkxxo3+Xg6t1SiOwZ\nKkSv9XQ6RalUElWL6InX0cY4Hl+WLeW9gQvzwcHBwTPxqlrl0++nidTrdzIQbWvTyJEaAm2SGgGZ\nC1ELKl7PrEXNEMiAWQWOjl+eQxS+v78vKJFqKfebnEwuywUQ0SeTSSwtLUlUAsf94OBAtvfTG99q\nzcLUZjgONtu4bTyv2kxhSxu+pl065KhFhcNhKaCkfQCavhntpOld95shawBkTlnjhYLcJqw5jtqv\nwHNsqjx9UcPhEOfn5xiNRlhfX5daJGb8vk1rDofDyOfz4odhdcp6vS6hf2SAOsGPptBYLIZisSib\nWHP9MJSPa1E/VyNx7Vuhv4pgZjKZzDhLdUisHgsKG4I/bvRer9cl25W0zjGjYOXuUNzPE8BMiDA1\nJA2mTDrkWC5qn8nZ6bqu6zjOPOq3/qZVIY0SAXvWnUksZs1mDrYZF8s2mUxQKBRQKBSwuroqC0/v\ntcfCQ1xwdEJpO9hoNML9+/dnogPIyDVqdl1XNv9NJpMzsb5EmuzjvXv35Bo2Eho1EN1IrGSSR0dH\naLfbUse73++L6qxDLhOJhJhHXn75ZSwvLyOdTiMWi81kQmpGzg2NaT4yd39hWCWZp9Y+iNJ1jRCf\nz4disSjMjWOXSqVkt5V0Oo1cLjdTH4XPu337tgjJ9957T8wy3JSZGgrNNmRe2gymacwmIE1mbtpP\nTdTESBW+p1a9dSIQ7cjmOGqmz9Rv7eMwkTntsPpdGLHCBCMyCPp5aL4xd7jSwkgLfP6us01rtRr+\n9E//FNlsFqVSCa+99pqUHTABhR4fRpU5jiMBAltbWzLWjJbSjl1TIyMwoFD5u7/7O1QqlZkx0CCK\nDJljl0wmsba2JrkIjJ6i2ZPOd60Z6Yg2rg+GHXY6HTx69AjxeByxWAzZbFaeRU281WphdXUVW1tb\nOD09lfFgHD7Xpt6LmECOPE1vnrOofRpGfuo4Tsl13RPHcVYAlD85fghgQ523/smxZxptesCzzgVg\ndqHpF+NvWsU2VTPNwDudjtSCvnv3riT88DwOHJE50RLtqVTx4vG4pOKyD2RSDMnjpNMOptUzOjaC\nwf+vvTeNrTQ78/v+7yVZ3Pe1qshau6pbcreWESRjAilWgiSjJMLMBDZg+0NiJBMggIE4QALHsD8k\nQQJMnACZBAjgfHEcTIx4jAGCMWQPBnIGEjAj2ZIs96Luruqqrqpmcd8vt0uySN775gPr9/B/T733\nkq0Zd7UkHoDgXd77Luc85zn/5/8spy34W7heJlQ6Adw85lm573K5rLW1Na2trenhw4dhspIqT5/5\nREXZb29vq7OzMwT+8uXLdSiCBoocGBjQ7u6uVldXQyFBWznXiiIi6sEpF8xafzYWyuPj49i0Nq2U\n6IkqWBqtra3Bl3qGI3KUWm7Oh/qzFb1OW9F3bs0gB+l/ruvUEHQFvgnfSR45gSbgM37rityVMGjO\nKQ9AAmClVCpFFA8RWd5fKD2nHFypuQwdHBxoZWVFlUpFbW1tunr1qu7cuROAqFF/8T+1kJAbZC29\nJteVFGGwjx49CllEefvY+yJIH3V2dsaiimKE2mltbY25yW89goYFhXlLQIHvjuQhyICwarWqjo4O\n9fX1xbOjbzw5y8crBQlYW7Q0GsnbT6PIvyXpr0j6n57//0f2+T/Isuy3dEKp3JH0o6ITNDJr3cSn\nOXeFAgdxpQqLzjw+Ptbm5qZKpZJeeeWVMNO5NkoDjpY4bSgSDzFkhxkUNHw5zqCDg4MoI9ve3q7t\n7W2tr6/HHp84QgcHB9XV1RXRLt3d3bp+/foLg8fzMKkQKvpsfn5e3/72t2P/R1/U6AMmImiiVquF\nQ62lpUXr6+uamJjQtWvX9LWvfU1DQ0N1Ga9cG6VJqCd9gMl848aNOnOd3ZScFycRhQnnixalaDc3\nN0OZsBDjnGVxKJVKsSuNdLLB9pMnT6J/SZzCpMcyoP8aIe5U/lI5daXgTicHAkzGdBy4l/b2du3v\n72ttbU1jY2ORzeqhfCxKrjg9Vholw7jSVz09Pbpy5UosjCBk7uXw8DAyjUkyAkXmeR41XfI8Zt14\nuAAAIABJREFUD4utWq1qcXExlA3gCaVSqVT04x//WD/5yU80OzurW7duhYXnFnTa396P6Tz3sfdx\nODo60u7urr7//e9renpa6+vrcQzn8cgmXjMuLj+S6vQAm7XA5UP/YIm4JSWdblq9t7cXUUZQXeQL\nIC/Hx8eRG+A0ys7OTmSGUsslpXxcBorksqidFX74OzpxbI5kWTYr6b+R9Lcl/W6WZb+h5+GHzwfs\nXpZlvyvpnqRjSX81bzBrznNzbh5J9Y4VJhFKm1WWY3A43rlzR2NjY7GyOVrD5EvTljm3o+jd3d06\nPt2TZzA78zyPkD4yE91sBpEiyMQXF5nyjl5ADS0tLXr69Knef/99LSwsRMgj/eGmpX+OQLvJieI8\nOjrStWvXJClqj3Ne6ZQe6e7u1tjYWGR3suekm8EekcA9EKng48a4Y/EQR44iZJEm4sOF3M1dJhiT\n1sc2RfJcr0h5uDw2UuZ+TApC+MwnIsd4/+d5HrkE3LMjMiY/5yZeuq+vL/b6TOvo86x+Lh87Fmas\nyVqtFnVs8PtQxY/zkh26vr5eh26RRRRilp3UDnr06FFw35/97GfrZDHtp7Q1s4Y4x/b2dkROEV0G\nAPP7IdGPkFeUpztU3X/g3zHHsJgZrzzPgzrz+/XiZtKpVeH3jWOV3zFWyCEJik4hunyl/XOWvjwr\nauUvN/jq32pw/G9K+s2mV2zQ/GG8ORpJiX8fDBecWq0W2VVwUD5hfLJzTb7HMeKx547ImVA4pVhQ\ntra21NbWpomJCUmKtF+QDtmhCAjJHAV9WEcpcU/Pnj3TO++8oydPnkQmmpvPpVKpTgmnisdfHx8f\nB1d67949HR4eRtlU6TR2FqErlUoRew6v5/H8OD3dkSMpYojpR6cb+B3nopE0QjlgpxdYfA8PD0PJ\np+GWPpbukHOusZECcdlrpNDTc6R8blHjXojxJpOW8cLy8LDJlpaWqI0tneY3uIxgTbrzF6sSvwBW\nIYsN2cS+56krIsZgYGAgzkXzfuZ5y+VyzI+rV6+qv7+/rh8cmBQthN6fTlnxzPPz84HEUYhunWD1\njI+P69mzZ7EAuX/IF5bUApYUyhzKkIXUQyO5lifYuf8CEMh99fb2xjg4LUxf8wyp3Dio+DjtU7Wx\nhPQi3eLCSrosChQU4c4Iyp+SCMSqB+KT6ivieYbn/v6++vv7w9QCcXuSDYsCg8795XmutbU1dXd3\nq7u7W3/mz/yZ+A1Kr1ar1e3mI71YF4U+gSrY2dnRhx9+qPv37+vBgwfh1XfTkvtDMTiKYrFzgXYP\n/FtvvaVHjx5pe3tbd+/e1eTkZNBMXn+djWUZN59wmL8eAVStVoPzRsAdeRNFQJVHLCNCtqBlSKzx\nRdypNn9OQv5IwmEyco/0sS/6PIdbQf5dqmB4Dl/oUoDh8sYzDw0NaW5uTm+99ZZ+9Vd/NbaCQw6p\n3YEzk+dh0QYxusVFvaClpSW1tbVF2WXQP6ADMJNlWdTdbmlpCWDS09MTizf0wec//3k9fvxYjx8/\njjmX+lF47r29PT18+FCHh4e6ceOGvvCFLwR16XKSOpu9X10XsE/u4uKi/tk/+2daX1+PfmQ+Mvbd\n3d26ceOGrl69qkqlEglyBC6waTsK2JOSuru7Y9GkeF53d3eMC8+Q5mdkWVYXzou1w7mGhobU29ur\nx48fxx4BgLKOjo66SCsACiGpKZhI5bJR+9RsLJFOIkcdzn05SmNlc1TuEQvOxaXoHcFoa2tTX19f\ncIc9PT1xHX5HBmSWZREZwGKCsgP1QVsMDQ3VJdkwyITdSfUDhXBxf8S0v/nmm3r48KGWlpZemFCe\noOBxyd6nmJOOfN1UJJnowYMHwW2/8cYbdaZ+aip73/C/SMmi0FKERtlf+nlkZCQmMyga5y3PkBYh\n8jC6dDy5rlNm9GuqiIomSRHF4go9RXnpOf0Y6bRQ2draWuzY7hs0s2ClfC/OLVd8vkCgXCiyhQPP\nZZ5FzamIVLGSRYtjvlqtqr+/X2NjY3ry5EmddZjKLYtstVrVwsKCjo+PNTY2poGBAfX09ATooE8Y\nqyILGyW9vr6ulZUVzc3NxdaM+Dx8gaVW+MjISCjV3t7eOCe8NXJB/xG9Qr9wf9VqNUIlyTB2fcKz\nM1YtLS1R4qNarYYlPzExoa2tLc3Ozr5QrdSpwCLaibH/uO2lKfIibtj/0xBuR2B0sHNkqWA4WkX5\nSaf8JOdkRUTBIJicG4eHJ70QXYAA+ETBmcEuOSmacwWTokMGkBT+p0+f6s0339TW1lZEPHDv/DYN\nfXR0Q60POG6Pe4fzp1rk1taWZmZmlOe5bt68qZ6enoaUVjpOxOdLCmckJq8XvAIRdnV1RVabh6f5\ns3kFwZ6enlhYWFzSkEImCYoL+UitBFfm56FYXLZS5Ojf05wL9fA50OH29rYeP36sq1ev6sqVK3Uc\nNv3EebBCSWJDeUkKus0VhCtYaqmgbNzy8005kF9f9JHTgYGBUHreL0X9gw9jbW1N09PTGhsbi5IQ\nLK5FlItbTMRlLy8va2lpScvLyzF/mTN+zfb29tgHFYuC7E9/NvoLa5rnlU43pEB2iDJh31ysUBYg\ndAoOVOrssPhh8bz77rt69OhRJBD6OKVz3+XXfYHNZDJtL0WROwL1FdaVMJ9Bqzh94nUX3Pnoio0o\nDFAsk8u5TSYH98Cq7oMmKfhy6lyvrKzUrdJs9AA6IgxwYmIiOE5HQtKLKJfJt7u7q/v37+tb3/pW\nhOXxDEzGVIFhAk5OTmpgYEBTU1NB/aTRL9wvSon47UePHqlSqWhmZkbvvvuubty4oZGRkcJFIkUN\npVJJY2NjQRuhhLFymEA40kDdaZRCqVSKEEkmAL8jtJPrLi8vB5XAPWEag/bxa+CMS5V4I2uwSGH7\n+zRcz8+RLnw4HBmjg4MD/dEf/ZF6e3v1pS99SePj47Hg+WSmdXR0RG327u7uOsoA2oXtw4g6cW47\ny7I6i5L+odQzSTXQFeRRLCwsSJKGhoYCVUJPeVieAyQWz0ePHml5eTkiagj/g/by/vWoKuLcp6en\nI8qGcFQHT5JijmNllkonYZjSiZMduUFXgM53dnZibngSEotbX1+fBgcHg6KSFFYFCxy0X0qFVCqV\nKGT37W9/WxsbG7HNm1Rfchrrw63aolYko0XtpShy5x7Tz33VRzl6tIJ0WifcBxVEQESDF+lHkaSo\nz2M5ne+UFIkkUr2ixUzzicJAQSewuPjO296KFArOsHfeeUdvvfVWUDhcw1dxztnS0hI7rw8NDWlq\naiomIsd6JI73Kef2/QoxzdnpyOO0U7omNQtZ2DyTz52bvE7pppSSYSF2CoEFzMMcWVTdiYmyZPKi\nEFM0XmQNNpsoLqd+jqJx5T/Uh4eA8p6Y/lKppKmpKd26dUtDQ0NhxbgjjNwHEsxIKGJRQJnu7u6q\nWq3WIUrknL5HzjyGmoqJnDsFNlATHlvNcxbJNveDxYelwb34RubSKUXGgkuxrSIrIB27NNnLqU5o\nVkJR000tXNF7BJbTdOgHzsV9+J/PBebM4eFhHXAsovRcd/nvXY4+TnvpZWzTScJndDiInAw+FBVx\nxmwQzGCxMw18t6/GIFAEjJrh1DpxIdzf349sT1Zh7o9JlEa++KKAUnJHJt9BE7DC7+/v6/Hjx/rt\n3/7t2FYupWBYZDo7O/X666/r6tWrEZvO+R0x+z0VodDUOrh8+XIgQ/otFShXXiky98XNOfhGyNYV\nrUeXMK5elwYrh2221tbWouKjFyxDLig6Rdx/Wu8lVbjpJEsXKZ+QTpk4cnau3i0oxpp9Hck9OD4+\n1o9+9CN99NFH2tnZ0Te+8Y3gbwEQHsqJzwW/AY7Mzc3NKELW0dGhN954Q3me6/3334/FC4dxnueR\nYn7r1i21trZqaWkpZJTrUuOktbVV8/PzL4x72icu34wnyXLU32FsmI8pFQTHT92itbW1iPLBskw3\n2Uhr/zDeLA7oAxyMUDdw2viNLl++HPvtImNE+xCGzA5QVBldW1urYwlInhseHo5y0/fv39e9e/ci\nRJMYf58TrrxJLExb0TxK20ujVhzhpfxjuoo5f4bCBXmhZFF6oAo3A1PlCvogA1Oqj+3lWAYT9A/V\nU6lUIqqACevIBMFPnSS+QHHNnZ0dPXnyRP/yX/7LSCxI+4H34+Pjunnzpr70pS+FBx/u3CNj4EdR\nLoQ8Fa34KB6PyaZsrddq94UqRRA8n38GIk0dx36s9wmvsXpYvDC3GXcmoXRaR5tFj92aQPNMZl9M\nUw4yVdpntVRWaX4Nd2iljmm3qtjSbnx8PJQ4Sh60ube3F4qQRQFww2JGmCeRFKT5c03n0jlub28v\nMms5L6GIZDizcHj/pHOE34KEpRMrDytxZGQkcgKgSTzenUZVTuY58lMul0OhOpUDNQIgA8gRiQMI\nIDrHc0AcfLGPJv1Loh1BAMwzdE65XNbGxkbE9rPQQg3hJL527Zr29/dVLpc1PT0dx/qCR/8VAayU\nITirvXREnrbUDOHhQdFHR0cRl+3ZeygNEgIczXKMp+LDmfrEdJMShfXs2TNtbm6GcmAQ2UQgDW3k\nmk7poNhTZVer1fT48WO9+eabevDgQaGS4J66u7v11a9+VVevntQhQ7iYvJ6lyv6hOF+5Fxcm5/xA\nS3wGbUE4J0LOczKZaI4+pfpCP+5A4575rIgXZNFBCUGjMSkxe0GlvtgR7ogycpkpkq20j4tautCk\n50Exe5+47yV10CEHpVJJ165d0xtvvKFXXnklECaJVVB/eZ6rXC6HIgRxknSGP8apALc+UOQ8CzIJ\nGGFxgdqgdo6kqPSH8i2ipFJ6rL29XVNTUxG5Mjg4WAc00sXcrRz6iy3vSqWSFhYWIlzP5QWn/fb2\ntjY3N8PZjnLHL4LjE7+GJ+JwPaw+whBR+gAaSlqQkYkS9w1VHCRWq1W9+uqrGh8fj3Ba5g3P4RSj\ny0ijdhbd8tIVeaq0fBJIqjORe3p6tLOzo6GhIQ0ODsZ2a54CXqlUVC6XNTg4GJOeVXlnZ0flcjkG\n68qVKxHmh5JgMvT29mpiYiIcb75jS6lUigpstVotkgOkU/MUU8wFFiUK6i2Xy/re976nmZmZEDqO\nZ4Jdv35db7zxhm7fvh11xAmxAvH5REFQ3WsP+qO/sVJ4ZpQVE4X7ZvHjO5Q1iJnJkCo2zoPi9+No\nKFq+B22jkKAh3FF5eHgYiwx1yJnwJIBBN7HlH2gMS82pk0YyiMJJKRd/Ph9P/jzCgrhuFkQW0yw7\nidy5fPmyvvGNb6ivry82DseC4Hyk1O/s7Ki3tzeShugX6ALphFqgpERvb2+EEYIooaF8UwYWPa9I\niNKuVCp69OjRC1y1W6CAJcbzzp07unPnjl5//fW6zEZf1IuUlgOA1taTnY8GBwej/vmjR4/09OnT\neE7mRrV6smMVcwdlTlmC3d3dkC1oQygUrgWHjgXOfUpSuVyu26cWXVSrnYZ8MkdKpZMM6M3NTe3v\n72tsbEyjo6OampqKvAx/fo/tp7m1mIKls9pLV+S01MxwagAz080jMjBR5EwWSVpZWdHU1FQoZTdJ\nt7a26tAIu3bAoTvyIMKCCUbyBPw5nKOn2lar1SjU47yx9GLkA5EEHpLE65aWFo2Ojuob3/iGrl+/\nHqt6ys1yLuduXWmi6Dy6wBcL7ttNOeeQnQ/28XEqKn02fusIiu+dDoAS8P1PCfX03VQw79mgAMrB\nHaq1Wi1Md+k0E9KtkEaI3FszU7aIkmHcsCDcSQs6S7NKp6am9Oqrr6q/vz/6gUQg5D6N4OLeQOMU\nJcvz071licbwfvQ/0Cr9zwLL+bh+a2trxHK7rPjcSO+vp6dHd+/e1c2bN19IT3f/kvexz3W3egAm\n/f39unXrlqSTKCUWLg89xtG7vLwc1jZyAnWKjHgIJNaDU1buZ5IUtJ2Xq8URi5VA3wKaWCjZaJtF\nwmlNrsOi7/L008il9ClKCGrEPYJ03EFJp5GBCV9Gx8zOzurmzZsRX0r4Givpzs5OICbp1NlGDCrX\nbWlpiUL/oCvQFpMKJY8wIjQ4dhhklCHCx4QbGRmJXUQODg6iyM+XvvQlvfrqq/rCF74Q94P5xrl8\n8F1QXGGltA6C5IrNkZNTIUXcv18jbb4QSfVhmfTh7OxsLLwcx3NTjB+aAeVDSYTt7e2oYw3CZlKA\nyhkb6rywALsypxXxkP6Mflyj7+hLuHjuBQXl12XhuXv3rm7duhVRGr4pgY+1pLo+QAZBgzRkBost\ny7JIwfcwOjhnomZQVH59KEoojbQV0Wa9vb2ampqKOcd3jZSUvy/6zinOiYkJtbSc1BlaXFwMqwEF\ni7ytrq7W7bjkG7xwv26BSqqj4VwWfBwAE1h/LLy7u7t1c57FHP2xt7f3wnxwCs4pwqI+8QXuPO2l\nhR/6f+lFx56jclZZ+FJMzqtXr4aHmYzK1tZW/eQnP1Fra6uGh4cDhXjml6SIme7u7tbNmzdDQBmI\nNJKC34EGfc9OFHqen2Rk+n6YrLw8o6Qww7q6uvTrv/7rYWnwfL44MfD0j0d7pP3kXCbXSmmNIvTP\ncxYhJRRRWmub33APzpd6BmCtVotIgJ2dHW1sbGhvb0+VSiUiMPr7+yOZwhM0fLHZ2dnR6uqqqtVq\nmK/O21PHvK2tLeSBOiAo8iKF3MiiSOW0aEGkD7AeOB8p8Cwmbl3cvHlTn/vc59TV1aWZmZlYbHx8\nfRLz7MfHx7FrvVN83BfIEiXv2aIscCjtg4MDLSwsxAJAOGKWZVFRk+0NnYbwMc6yE7/NL/3SL+n6\n9esaGRlRV1fXC+i6aE6n3xVZ4vRxZ2enpqam9Cu/8itaWFjQo0eP9PDhQ0mnGzdnWRaWXgpUarVa\nPLtndxKi6rkIHgWDw3hvb08zMzMx7+jfarUaYYvw5Mwv+gjOnXkIEO3p6YlFFwAA0nd6pUgvNmqf\nCmolReNFAwu68NKtFP9hFyAUAMV2iHbIsixKtfb29kZHuzMENOIxoNJp9AUdijnGwOBYYWKNjo6G\nQvJnSldWR7+dnZ11Cj8d0JRK8QgEEFeqAKTTxA1MR6dF3MTk+FSpFVlI6TOl4+bHk2wE+mNRYCHr\n7u6O6Au+Hx4efiGkE8VfrVbDAQdHz6QkFl56sfaLo/9UvlI6qail36XWjdMXjCl9zuRFWeMk96Ss\ntI89OodruAO0yOnnu+ZIioUD/wg8MZbi9vb2C7V5sPhQZi4rLi+SYi/cz3zmM8HJpwiykWwVPXca\n0eMyXCqV6jZymZ+fV6VSqTtPmvCHHHjzOdnS0hILLHPDo4VYPKvVaiTmYR3leV6Xy5JabyxAeX7K\nu4P88/x031+XHV+8pHpgVSSDaXtpijy9yaIVyB9qe3s7Om9tbU0dHR0aHR2NCQNHxsT+6KOPtLi4\nqFu3bgUq6+zsDBSIIkc5EDEAv+07BXl1PsKNenp6wimISS29uKErA8V3KeJwDg8FVpS8kkZFOEdd\nRJ2kkSKOEhy18zrtf3do+XN7tqwjekeHeX7Cuz5+/Dj2a/SJ7CVoJYUTc21tTSsrK7HfI87r2dnZ\noMQ2NjZULpcjWUWSxsbGNDk5Kem0RgvRRZ5MVjQ5ihaqVP78udLPUQAeHotFVavVwgxn8vb29gaY\noNa4+2H8fhgzT2hzJyx9z96z+/v7mp6e1uTkZJ2l6A7xsbGxCKnd3t6O7zxKCz+PWyFYZey285Wv\nfEVDQ0N1e7QWzW2/XxShl9UlkADLhN+y8HCN7u5u9fb26rXXXlOlUtH09LTm5+djHFyR+/zj++3t\n7cg5AWix8EGBVqsnBcOwWtzZ73O1q6srsm2r1Wpd5BBzbmRkRDs7O1pcXKzLD8DBChpnwXUKzFsK\nlhq1l1prJRXaohWIgTk+Po6HxjkEhTE4OBi1rRG4UqmkR48eaWxsTJcuXQo6BkXPyrq/v6+tra2Y\nKAwy3Bqe/qLQN5ADComJJtUj+SIPtFMfIIQiZOhC5MrdBTXtO598fm/OERYhfY5rJDxF10kVuHTq\n1+BYd0yymwoKj/ug/On8/LzW19e1uroaaBorDDRO3DD3Pzg4qP7+/jieSetcfNEkaYbEGyHJdAFE\nOaXOaxCXp+j7og9a9sXeF15kJrWguDe32qRT5/nm5qaGhoZiTJxGQ5ZB5p4TASDyZ03n4+joqK5f\nv67bt28Hd13kd/C+4rdYSWzKAHWxubkZlrb3a6lUippDfX19MdepHzQyMhKLgFuvDm48XBafy87O\nTixUHrPOWBFDzpi6hZBlWfSfW1RY9SyWhAOvra1FDXrmt4fdMk8cuBW1s5S49ClydtJhjSgW5yIJ\nPaP87MDAgLq6uur2uLt06ZI++OADXblypS7gn/NKp5ENKGqUvHS6FRTKgkJPjl6YmAyEm20Ikjth\neU5/boSOhcM56yJl4srceW5QSXqNRr+leYIFv/FYb+7LLQ7+fOFyRy6LJJm3HR0dgVq4FyYAqJT8\ngPHxce3v70ctFZxboCqiLfyahN2BjohacO4ylTv/n772/vL+L2r0PTQOSgKqIY1mAXkRHsezg/xc\nkfm9+TxwU9zvE7DDDu8eicJ9IudeasJBAuPv/QA6fu2113Tr1i2NjY3VJW1xDw4aeHY45UqlotXV\n1QgPho4EfHkIMOdkPhM7T5QaST0s5kWVMF1mkfM8z6OoHc9M/4OQvTxAKgvul8BR7POOWH+yrdmZ\nyeeJK3KnVXxu+vVcbzRrL70eeZF5S/Obx8nY2tqqcrmsS5cuaWJiQh0dHZqamtL169eDggF5LC8v\n6/d+7/c0OzurP//n/3xw5js7O1pfXw8nG2U82Y6LcC6/L4oXTUxM1HFymEwMPqu5Ux7+2k0/6RS5\n+6LgJvTm5mZk3HnqfBGqdh7TJzrXkF7cC9QpF1rq6ec4qX43FB8jf06UxfDwcNQKwWTH+cREJAWa\nyBSeaXx8XGtra3ry5ElEJKyvr4dS4d7Gx8d1+fJldXZ2anl5Waurq1pZWdHW1lYoAl9om8liM/lM\nn9MXXOK0SRRjm8A8P+FIt7a2NDExodbWVi0vL0e5ASIb3BkLusN6ASGmFk+e5xET7eOKIuzt7Q1K\ny7l15MutTD+HXyfLsojnvnv3rl5//fU4R0oDcc+Hh4daX1/X5uamNjc3Y0HGV5Bap45U/bV0ujCR\nlIdc8R30WpZldUW1fEH0+cD84lhk3EOXeRanP90CQo4Zk9bW1qB/+vv7Y/el3d3doHc92IHSIVia\n+FGKQmRTK7BZe+mKPH1dNKEQMLzInrlFlAfJO/BNDM7BwYE++OADra6uqr+/P5IF9vb2NDk5GQoZ\nU25zczMiEDCh2CQ5jT5xM86RKUIAIvTv0xWWY90xyff7+/taWVkJhxXJPUwikJWjZX7r9+rnTekW\nfpcqOkfktDROPV0UOCfPi5k5MDAQzmoKPZGIweT0czN5KQ5FmV2eF0uHmiydnZ3BsxO9UOTk9H5P\nxyF930jxN5JPlA5IDR8An+Pf2dnZifErQl6MB6FxjsJdOTEevlm4JA0PD2t4eFhHR0eR7JaCCcbV\nxy9VIIzLtWvXdOfOndhf1q0cl61SqRS+iY8++ijoE3aiSi07p4Tow7TPHVBA+6RoO51b3peppeAg\nCUWcNl/IUusZBU8f+Ph4xmZra2s4+Z89exbztlQqRaAE8ullllM5O49FSPtUUCsp8klpiJRTgic/\nODiIaIWJiYkIc0udDxsbG7p3756uXbsWkw1e3R0d0um2ZfCapOiC3L2D3Qzkfao0/bUrV1/100mc\n53lMCsKXQAGSwiRvaTkpbYoi9ImZIulUyJuNR/pbvnOaqJEC8kWR8SPzNXUIepw5Tj32VsXcbW09\n2TUHugBzuq2tTYODg1E1EGXP+DsST9FMM3RT1D9FSt3H2WO9KcSG7IBGQdgUW0I+XblIquOwUV5S\ncVE0Fuy+vr5Y4KgDvru7G0lB8OD+B53jFhtWIQtRd3d3KPHu7u66yCca8nB4eBix3nNzcxEK6Ofl\n+DT5CEXPouMgh+d2WfN680VzKJXbdCEDlPG5OymLFhv3eXBfRU5cLHMoJaxp352IBRoF7old55XH\novZSi2b5f0eFvhK5wmBSUuJ1aWlJR0dHunz5cqTzlkolbW1thVMDrvIP//APdevWLf3yL/+yXn31\n1cgMpTAQKI74biYecaygQ78XXqehf0w053JTh4mjDZQ6E6paPdnFHAUmnSQruSMLhy9KESUIAk5R\ni09Yp3m4P19Y+I1/T9w3iTulUikWxTzPo68wdekXrIla7XSrKxyRa2tr8XuUh/OUS0tLWlhY0PLy\nsrIsi6qGeZ7r2rVreuWVVzQ1NaWVlRXt7u5qYWFB6+vr2traqgv589aMQilq6fGphcOCQ51raBTi\n4olMoCpnuVzW6upqWH+gMfpmfHw8QMbDhw/rOHh4beQGnhmwgYIm5I3IH3d4EmVCNBF1+1G4KMnx\n8XFNTU3p7t27Ia8pqs+yLCoBPn36VG+//XYdIEJJgv6RPUIknV9mkUCh8t8Tw+h3QABBDYwJz8hr\nruELFcd6foUvmNw7II97S5Vtf39/WJWMCfdVrVY1PT2tmZmZOP7g4CCqQba2tmpra0vb29t1Bc6K\nZPAsSoX2UhOCvKUrfSPTFqVCKCGFhC5fvqzh4WGNjIxEBINHSzDRcURkWRZmKYPu9AlIB87TKQXu\ng+Ocfkjv2c/Nc7kS5zc+4TzEDzPMi0C1t7eHw4dnJKYdEx7OMVXQLuTe15585OGWNCYT91IqlcIf\nUaudJJ309fXFJs48S4qaWIAo+JSm2SPQ5XI5donJ8zycXCzOV65c0dDQkCRF7RXP/HRncSpPqeI+\na7KgQIosR1c4/EmKjRToo+3t7dhHdmlpSTdv3gy5oN9ZhIeHh0NGXE48lBTZIlIF+ganMRw9ERSM\nAbVVPDOU53dHqKevu5Xm/XdwcKAnT55odnZWKysrkXjn48nxnjjjNcP9+qmFyz1hgflnMn6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kQPHz7U7du3Y6d6kC4UA5QDA3p8fBxhYm6O4tjyojjQH17LpAiJ8DmOQSaDK3wXKKdA0uamcxqX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\nZdmHWZb9jU/y2p+WlmXZ38uyb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"text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the scatterplot is a lot more diffuse:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.plot(t1_slice.ravel(), t2_slice_moved.ravel(), '.')\n", "plt.xlabel('T1 signal')\n", "plt.ylabel('T2 (moved) signal')\n", "plt.title('T1 vs T2 signal after moving T2 image')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 15, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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97C0n16BU/chn1qnssXHFZqvqNjyj6BHE7SCY+I2NkappZYUkACmaA+FgJ8kE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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The joint (2D) histogram shows the same thing:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "hist_2d_moved, x_edges, y_edges = np.histogram2d(\n", " t1_slice.ravel(), \n", " t2_slice_moved.ravel(), \n", " bins=20)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "# Show log histogram, avoiding divide by 0\n", "hist_2d_moved_log = np.zeros(hist_2d_moved.shape)\n", "non_zeros = hist_2d_moved != 0\n", "hist_2d_moved_log[non_zeros] = np.log(hist_2d_moved[non_zeros])\n", "plt.imshow(hist_2d_moved_log.T, origin='lower')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 17, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because the signal is less concentrated into a small number of bins, the mutual information has dropped:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "mutual_information(hist_2d_moved)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 18, "text": [ "0.45778273778245288" ] } ], "prompt_number": 18 } ], "metadata": {} } ] }