{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# SYDE 556/750: Simulating Neurobiological Systems\n", "\n", "Accompanying Readings: Chapter 6\n", "\n", "Terry Stewart\n", "\n", "## Transformation\n", "\n", "- The story so far:\n", " - The activity of groups of neurons can represnt variables $x$\n", " - $x$ can be an aribitrary-dimension vector\n", " - each neuron has a preferred vector $e$\n", " - current going into each neuron is $J = \\alpha e \\cdot x + J^{bias}$\n", " - we can interpret neural activity via $\\hat{x}=\\sum a_i d_i$\n", " - for spiking neurons, we filter the spikes first: $\\hat{x}=\\sum (a_i(t)*h(t))d_i$\n", " - to compute $d$, generate some $x$ values and find the optimal $d$ (assuming some amount of noise)\n", " \n", "- So far we've just talked about neural activity\n", "- What about connections between neurons?\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Connecting neurons\n", "\n", "- Up till now, we've always had the current going into a neuron be something we computed from $x$\n", " - $J = \\alpha e \\cdot x + J^{bias}$\n", "- This will continue to be how we handle inputs\n", " - sensory neurons, for example\n", " - or whatever's coming from the rest of the brain that we're not modelling (yet)\n", "- But what about other groups of neurons?\n", " - How do they end up getting exactly the amount of input current that we're assuming with $J = \\alpha e \\cdot x + J^{bias}$ ?\n", " - Where does that current come from?\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A communication channel\n", "\n", "- Let's say we have two groups of neurons\n", " - one group represents $x$\n", " - one group represents $y$\n", " - can we pass the value from one group of neurons to the other? \n", "- Each neuron $i$ representing $x$ connects to each neuron $j$ representing $y$\n", " - each connection has a weight $\\omega_{ij}$\n", " - total input to each neuron $j$ is the sum of the weighted outputs from the $i$ neurons\n", " - $J_j = \\sum_i a_i \\omega_{ij} $\n", "- We want the current $J_j$ to be the same current as we would have got from $J=\\alpha e \\cdot x + J^{bias}$\n", " - can we find $\\omega_{ij}$ values that would achieve this?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy\n", "import syde556\n", "reload(syde556)\n", "\n", "\n", "x, X = syde556.generate_signal(T=1, dt=0.001, rms=0.3, limit=10, seed=3)\n", "\n", "N_i = 20\n", "encoders_i = numpy.random.choice([1, -1], N_i)\n", "intercepts_i = numpy.random.uniform(-0.95, 0.95, N_i)\n", "max_rates_i = numpy.random.uniform(250, 300, N_i)\n", "alpha_i, bias_i = syde556.find_alpha_and_bias(intercepts_i, max_rates_i)\n", "\n", "N_j = 19\n", "encoders_j = numpy.random.choice([1, -1], N_j)\n", "intercepts_j = numpy.random.uniform(-0.95, 0.95, N_j)\n", "max_rates_j = numpy.random.uniform(250, 300, N_j)\n", "alpha_j, bias_j = syde556.find_alpha_and_bias(intercepts_j, max_rates_j)\n", "\n", "\n", "A_i = syde556.activity(x, encoders_i, alpha_i, bias_i)\n", "d_i = syde556.decoders(A_i, x, noise=0.1, dx=1.0/len(x))\n", "\n", "A_j = syde556.activity(x, encoders_j, alpha_j, bias_j)\n", "d_j = syde556.decoders(A_j, x, noise=0.1, dx=1.0/len(x))\n", "\n", "xhat_i = numpy.dot(syde556.add_noise(A_i, 0.1), d_i)\n", "xhat_j = numpy.dot(syde556.add_noise(A_j, 0.1), d_j)\n", "\n", "t = numpy.arange(len(x))*0.001\n", "figure(figsize=(8,4))\n", "subplot(1,2,1)\n", "plot(t, x, label='$x$')\n", "plot(t, xhat_i, label='$\\hat{x}$')\n", "legend()\n", "xlabel('time (seconds)')\n", "ylabel('value')\n", "ylim(-1.5, 1.0)\n", "title('first population')\n", "\n", "subplot(1,2,2)\n", "plot(t, x, label='$y$')\n", "plot(t, xhat_j, label='$\\hat{y}$')\n", "legend()\n", "xlabel('time (seconds)')\n", "ylabel('value')\n", "ylim(-1.5, 1.0)\n", "title('second population')\n", "\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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wF93irkNV5GGfU1zr9NSDYFinwazK35xyM87PPO9TXQQKIvoEQTFaTIhWuxd9\npVQJkayRl6Vf32hEpNL3eca2y9v6XjmBwIOy+rJgN0FQotVUP/wr/y+frjeaqdU06kj2UtRB28Gn\nuggURPQJgmKymBAT5V6QFRIFRFJ+ln69np/oEwjBotbQvGJL1Grq/zoDu+Q6zgz4sj8AQCblJkVn\nnmK3rp/gChH9MCLhnQRsObsl2M3wiNlqRIwX975Vwm9Ov0FvRKSKiD4h/Kgz+iaOoYpUSSXK4ruZ\nFdf0uiI0n5TZgYaIfhhRVl/msxstEGSXZsMUdxLaaM+Wvk5yAT9XLvK5ngaDAZoIuc/XEwjBotHU\nlE0y1JeftRcNQl/j8x7LdEpKBsB/22quot/SdtgTEiL6Ycbx4uPBboJbfjqzGQCgifQ8pw8Ah01r\nfK6nwdSI6Egl5+tSNCm217nluRDNJ9YCIbDYZ4TMrcgNYku8IzZFopvyDo9lurRKg+j0RNTrAyv6\nJov77bsJniGiHyYoFlLp67bmbg1yS9xTW091RJnEs3sfAFRG9zt3eaPBokNCVBTn6/Y9ss/2+mz5\nWZ/rJxB8xd5C7bKySxBb4h2DyQJ1pMRjGZGIWjqrqwus6CtYbsVLcIWIfhhgsVpgMLvfFjZUMBko\nsZeJ3bv3VVIqpadUn+hTHWaLGVXJG5EYreF8rVTcNBhpLuukCeGF84Yx9Dr1UMRosrCKqpdLZKgJ\nsOh3iQ/tAVMoQ0Q/DAiXiF+TnhJ7e3F1RiaR4YW0dTAYfZuTO1F8AgAgVtZzvlYibrJaJm+a7FP9\nBAIfnDd8OlZ0zC/1zPp1Fo4WHuV1D6PJzEr0FVI5dPXcjRL7ARBX0Sf4Dvmkw4C8yrxgN4EVxmui\n7y1TXlSkzGfPRZ2BSg16f8/RnK+ViDy7KgkEf+McgOavVLfv7n8Xnx/9nNc9TGYLotTe+4xCKkNt\nPXdLn8zLBwci+iHOb+d/Q+9VvR2O/XouNNNOfnD+aVblotRyGHzN4FVnhDh/INQq7nN69pY+gRAM\nnC39BqN/89vzub/B2sDK0lfKZaipb/Razhm+Ef8E3yCiH+IU1hS6HDtw9YBf6qpqrMKlKv57Y9MR\n+u6IVstgtPhm6RdX1kIm8e1nSyx9QrBxDiDdd2Wfm5L8uVR9CRFvRXgvyEBRbREa4vYjSuO9rxkj\n8/BV4cuc67C39H1dvqg1d4EGST5d21Ihoh/iMCW9oIPhhGbKpilIez+N933UcrXH89EaOUw+JvP4\n9x+joU/1niS8AAAgAElEQVTO8ulaT7EGBEIgWLpvqcP7b09+67e6qvW+Z8Cic+Jr1N4lwiyv9KkO\nB9EHd9HvHNcZQ+MehclElt5ygYh+iMPkBvdX7umi2iK/3NeZGLUMJqsBgc5NwuTeP1l8MrCNIBCc\nCMW5bcu1GDsNizl9uYclup7g+3f/M+MfPHrTVBjMel73aWkQ0Q9xKqsdO4bk7DgYzRY3pX3HYrXg\ncMFhwe/LRIRCDrT9CxM3PBiQ+miY3PvrTq0LaBsIBGfss/SFCrXXFgyxmUqTSX2bNhPCvX99dwXM\nIj2MJDyANUT0Q5zLV6lf84b7N2Dn1J1QymQoLBI+BWXiO76tm3dGDO8PADq6//szawWpky1My4LI\nUiFCsPF3MJ8v6GooEWbTPxQy/pa+L+59ANBqFIC8DgM+GYL1p9b7dI+WBnnihThXCijRV0lVyEjL\nQEPbzXh+7yRB6zCajShvKLe955MISCLy/gCQS4KTN18kcp37I8F9hEBhsQDi/EEAHDPKCW3p08GC\nfHL763TsvYnyIFr6dCKwA6U7/Bof0Zwgoh/iFBRTok+nr7VIuCel8Ybz2uEle5b4fC82ou8pY5+/\n+fuxv4NWN6Flc/EiIJVRQmefUU7otfpzs+byvkdVDdVO5wyCTMhlvom+wcQ/loFpIE/wDBH9EOeY\ndg4A/wql89rh17Ne9/lebNbC87H0Iy2t0Ufqu6fjusTrHN776lYkELhy+jSgiqSEbnjH4cholwFx\n0U24UFQmaD30+vfdl3f7fI+qGuoebERfKffNvU8PLAAgJSrFQ0l2tKSpup9yfvL52pbzKYUh9mKc\nrEn2Xz0CblMpZSH63jL2eSK28Ub0j57o8/VyiRzP3vKs7X2ob29KaD5cuAAYI6g8GLek3IKd03Yi\n2tgJ+3OF3W2P7972ALAh/10A/hX9ymoTZBU9YZ1rFeT51pKsfj4brxHRD2HKq6jO2z2hO9Jj0/1W\nj7OlD/ie+pfNWng+lr7BZGa1jMgT47qNs73OKc8JyUAqQvPj2KULqJdQy2Jpq1QrS8Kl0lJB6xEi\n093eWmp+nI3oK+Ri1mXtqaw2QspiOpAtRkPLEX0+hhoR/RDmYM5VAMD47uP9Oopl+gH9dv43n+4l\nlbCw9HlMVQgh+vYDk43ZG/HZ0c943Y9A8MamM5twtrgp2yU9DRYfGY+rlcK69xsMwq1fYzP9FaeO\nBsBsPHiiusYEqY9r/Jmoqmo5os91gGUPEf0Q5und9wIAYlWxLudE84X7gTNtM/v4lsc53aOxkXo4\nTOs9zWtZ2r0fj66c6gAAo9mMaDW/B4Vt0NFAfa7fnfqO1/1ClZyyHOhNelQ2VHJ+IBOE5Z7v78GJ\nqKYAWXrVSEKUBuW1NYLWVVbpmKyGzxQWG3FZOpz6u0wcf2NVOpMgsUp7Ht5D3a8ytES/sKYQxbXF\nfrk3sfSbKRcbjwMApved7td6Bnw+gPc9iisaAZMSi/+1yGtZuqOrTNzn8UxmE6I0/Cx92nqJ1N0A\nAPgr/y8U1BTwumco0u3Dbljy1xLEvh2Ld/e9G+zmtHga9E2Ba7SlH6sVo7ZW2GRb5TWOW3GLF3B/\nzMeYqAE5G9HXRqoBQwRqarkJka7WBJkAln63hG4AgNPWH9B3dV/e9xOK7h91x42rbxT0nqo3VUh9\nL5XXIJ6IfghiMBtQZ6izvff3uvayev7uxeKKeojN7PYEUEgVGK2eB52Vu9AaJZWI5in6tQbqoaiO\nbrKIUt7lHz3MxGdHPkN5fbnb86L5IpwuOS1IXb3/2xuHrh5C5j+ZtmM1esqKrGioEKSOQCDEpk+h\niEjS5HanLX1tjAS1dcKKvk7P33MQWzMQbeQ9cFub21iVF0GCimpuS/Cqa02QS/mLvv1eJH8Xhs6S\n3KrGKhTUFGDL2S28ou1n75iN3ZeolRiNpkZc0V0hlj7AL6FMqDFx40S3IvTcrc8JXp/Jyn+9bGll\nAyQW9jt69Yq5HdWyHE5zUwaTCeaEE9Co+bnxEiOp7INKtf/Tn/737//iRPEJj2W25m6FxWrhNU8H\nAMeLj+PN3W/iru/uwuQfJwMAlu1bBgCIUkTxuncgmb1zNuOUU7ijiGgS/VbqVgCAOK0YtfXCin4j\nXD87ri5+vdGAe5NnQSVjN5AXWSWoquYmRDUCib7zrp6eBtlCs+viLrfnRBDBCivuXn837l5/t891\nvLn7Tbx/4H2HY3z2LWg2oh+K+at95UTxCbc7ZL07PDTdtGXV9ZBa2e/+J1JSu3hx+fG+sO0VAIDe\nwi9B0XWJ18E614rE6Ghe92GD0Wy07Vjmjpf+eAn/PfxfSBZIsCNvBzaf3YzXd/qWK6HGQFl5dHYy\n21SGPNKn+wWDb058A+0SbbCbITh1sftwc8rNaHitAT1b9QQAxMaKUVdvEWzzKasVMEtcLX2uRpHe\nZEBUJHsPoxhSVOs4uvfrTD6n8LXHOch5S+4W3vd0x6Yzm6B+i9pFtM5Qh4w1GS5lPjvyGTL/ybTF\nLgmxoZLz38hH75qN6DcnhFw37w17C+DUE6fQUdvRp/tcrLgKlZV9/n6rnLvobzxDBdzR7nm+rLlv\nlSD38YTBbEBpfSkMZoPNja836V1c2E9tfQoAsPbkWry5+0288ecbPtVX2cC8zekz257B50c/9+me\nwSL1vVRcqLwQ7GYIysnikw6WaaRKDIgsqKvzcBEH8q7WQdwY73Kcq0jozXpEqzmIvkjikGyHDTV1\nRp+z+XlCaANw+4XttumxQwWHUGd0/LKc59f/7+f/w7PbnhU0oZoIRPRd+PXcr8FugmCwDdIQIrHM\nxaqLttc9Env4nCTjRMU+tDbdyrr88A6jAHATfdO1/T6ZVjP4QrekDpAYhLmXO4wWIx79+VEkvpOI\n6z6msgHOy5qHtPfTGMt/dvQz7L+y3+f6PFl0m89u9vm+weCK7gqOFx0PdjMExTnlrlgkhkJpgVBL\n9Tt+poZFfdUW0U7DRSTqDHWojz6CGI3Ce+FriCHhZOlfrr6MrFb34JzB96yB7pi+eTqvVOLO/Ovr\nf2HBrgUAHJcb09NxTMmQohRRvJKQOVNcV4x6Y5OH848Lf/h8r6CK/rZt29C1a1d06tQJS5Ywf0kz\nZ85Ep06d0KtXLxw9etTtvab9NM1PrQw89kLYKbYTq3K+MvDLgYzHO4r+xek+hfWXkShln0CoXUI8\nRI1aTn+DxUINcu5ofwentnlCIvPvnpx0ohT76ZqSuhK/1af3sLe4t2kGvgjZn2mae5pksUgMpdKC\nMmGX6iNWFYsJPSbY3tca2LsS3tn7DsxRedBq2Fv6ErEU1TXsRb/TB9RzrdbM7Jniy485Pwp6v1pD\nLQpqChzSjNOizzTQrmqscrHO+fDnpT9x/YqbBblX0ETfbDZjxowZ2LZtG7Kzs7Fu3TqcOXPGoczW\nrVtx7tw55ObmYvXq1XjiiSfc3q/eWI//5fzP380OCPZCyBS530qZ6lLOV5yjursndAcAnLf+Ydut\niw11hnpEqdjPG0dFAbBIOf0NZouwAU8AYBU3ddh3972LY0XHBL2/sxVgtVpxuPAwgKbIendUNzYN\nFPKr81ktKzxXcc7tubOXmONEhEDo/kzT3NIkL8hY4PDeYrWgIvUbLDs6W9B6FFKFg0AdPMc+1a9M\nRFn4XOb0JSIJdBzc+7RQJkeksb7GExlpGQ7vhc7D/9nRz5DyborDZkaeRP9S9SVUNjoOaETzRbx+\nzxdqhVnlEzTRP3jwINLT05GWlgaZTIaJEyfip58clzVkZmZi6tSpAIBbbrkFVVVVKC52n+xgxtYZ\nfm1zoLCf02dyEX03YgcAYXJs602OluHKkSuxsCuV15lLfud6Yz2iI9hH72s0gNUs5bTTllIkfOCd\nGU2f4azfZmHxnsU+3+tcxTk8t+05/HX5L9sx5wfCX/l/2aL5oxZ7jqgfuXakbU67/fvt0f/z/gCA\nqf+bit/P/865faV1/lu254/+DPDLPBaKzB7oKO703/dXWSZTcZ9RSBS2zJNSfQJyLrN3JShBBVEq\nZVwsfQknSz9SRhkI60fsZH2NJ5xTaZfXlwsW+8PE3vy9aLe8HQBuQZJ7Lu/BoauHYLaYUWeoww/Z\nP/iriW4JmuhfvXoVqamptvdt2rTB1atXvZa5cuWK+3vWXBU0U12wsJ/TZ3IR3dSRcqOnvpfqco5z\nXU5Bg1KxFO3baAAACREJrO/TaGpAjJp99L5EAoisUlSztA7MFjOKjGfRtXEq6zrY4CwqfIIo155c\ni+UHluP2L25Hq6WtYLVaXfKgc1mDvjd/Lzqu6AidXgez1Wzzinx1/CtsyN4AACiuLcby/cuxN3+v\n1/uZIi9z+Gu44Y/+DDQ/975zFDb999WZhM3KJ5fIbbkAFCI1rpawX/FiNlCWvkLCfk6/UnQO35jH\nsi6vllMR8KkJwqzScI5ZyK3IxeObuWUV5UL/z/vbVsrQon/f9/ex0p+bP70Z285tw9cnvsZ9G+5D\nWX2Zgwdg27ltGLd+nIc78CNoos82l7yzO0ToHPRmiznkNlyxd3kzPfQir3nR/TVHm5RAWQgaOfu1\n3Y2WesSq2Vv6ALXMp0rHTvTpAKgEeRqnOrzhvFqBz5SJ/QCipK4EDaYGF2/M5E2TOd1TLVcjejHl\n4YhWNHk6tErqYbn25Fo89+tzNi+AJ2gR8Af+6s9s3KHVjdU4dPUQq/qDAR2Z/1K//7ico/++Rotw\nVmkndW8kRCbYvm+lJBI5lae85ougMTRQ3kU222TbUyn5h3VZWvST49Sc6nAHU6Ain758tNB7vAkN\nLfo/nPFutdMxVGKR2GYQJLyT4LD/x3envrNNVXsZE/tE0EQ/JSUF+fn5tvf5+flo06aNxzJXrlxB\nSoqbzGk7m/5lZWWxbser219FxFsR+Pr41yGTn5y2NvuoxuLrcV/7ta6+kfdAbeiIz8Y2/eiUKkq8\nGhvYd3qDpRGxUUrvBe2QiNiLPt2xpAphl+Mcne7Yufn8Bpy9Bh8e/NDnHc/+pXkGgOPyRLlEbquD\nfmjSLly3gp4HW7+4r+Q+n9rCBkH7s11f/nDDh17rfn3n67j5U2GCnPzB//2PsjjfGLzA5Rw9qG8Q\n8Y/k+/mfnwEAG0dREfG0aKtlavxlWoFe/+3F6j619VQf8Ovz0EpJj0wqzEDUeVUEAKw/vd7n+92w\n+ga89PtLrMquPbmW81y9SqZyMAge/flRbDqzCTvydtj6ssVqwbx5dhfZ9WXwmBUJmuj37dsXubm5\nuHjxIgwGA9avX4+xYx3dQ2PHjsVXX30FANi/fz9iYmLQqlUr5hve0fQvIyPDa/16kx4miwk55TkA\ngIf+9xCkbwi34xMf6M42MvVBXJd4nV/rsuo16G+ejX/3+bftGD3Pv2zfUtbrpE1mE6I13JaoiEXs\n3fu06IsU/BLzOKNRaBze87EOnB+SL/3xks9xF3fe6jp1IxKJbIGXr2dRyXvomA+maYnXB74OtIet\nX3yz4huf2sIGQfuzXV/eLfa+pEuI2BZ/8t05Kh8EU1AuLRZKA/800Kv/Xg0AaJ9CuQKHdhhK3VvB\n7blWW0f1ASEChd1htQgrPT+O/xHbHtwm6D3/e/i/rMrN3zUfWWe5pf/Nr87HrN9mORy75/t7cP+G\n+21BiJIFEnx3/uOmAnZ9GTwWMAVN9KVSKVauXInhw4eje/fumDBhArp164ZVq1Zh1Sqqk4wcORId\nOnRAeno6pk+fjo8++kiw+lPfS8VDmx4SPMpTCOjO1iHJNcmG0FQ3VKOVU2Y6WmAPlu7E+/vfZ7rM\ngQ8Pfoh67WHOOfGt8ioUV7NLt0oPRMQy4TMv/jOjyS0plHufL86DEQA4UngEV3RN/r6JGyc6bBMc\nTPzZn9u/3x4v//Ey5zbduPpGvLHLtyRHgcI2fWfgnybZYKJ+fxoNNWVyb3dql85oFTcXem0D1Qc6\nx3Xm3SZ3XBfdD9rL3Ka6PHFj8o0Ynj4cr97+Kq/7fPL3J7aBtRVW1u71wV8M41TPplO/MB6vaKhw\n0KS6jCc53ZcNQX1ijBgxAiNGjHA4Nn26445yK1eu9EvdpfWlOFp01LZELZSgHwS909r5vS6dsQIp\ncY7BNPbRqM7LTpigU75GR3ETfb28EB+efxbP4aDXsrY2SYWPv0iLSbO9PllyElarlVPsiNVqxa5L\nuzgHAcolcreRv7T73hl7z8v60+sxvONwTnX6E3/154tVF5F1McvteXfroY8UHoFSqsScQXM41ykU\nf1760+N5eqBoEsBbQW9vbY9pjgmPb3wFByvYW8F19WZc1/AE4iLieLfJHQYDkFAnXL4NGvsENgAw\n7X/T8NnYz1jHJzy2+TFbfIDFasGoUQDuoc5JRBL3fVzFLd/Arj1GIIn5HBtDtEtcF/wD9jEUDvf3\n6aowh06OklOWwyv7mT+wF4E+ab6lxOVCnbUCbRMdRf/2trfbXrNxndIPXW00tzFkjKEHrpffxaos\nnXTGIhHWvQ84Ztkqqi3CgasHOF2fV5WHO9bcAV0ttwe3p6U+7uboz+c5eiKa00ZTnnC3FwXQFAxo\ntpix+u/VEM0XYdr/pgEI/jr/QV8OAgCMki1lPE+3zwz+32Oj3tXTJBFLOG9QVddggorjlABXGg1m\nqCP8n4J3zfE1OFZ0jJMHj76H3mBGR7tHsJCePKXKfXvELAYoOTNyfK672Yh+m6imoKGdeTs9dnb7\nlL2hto+6/bp5gRcqMGK06JGc4LjUTqvSIkZEzSmzcR/TOXOUcm6dON06CoZGdtfQn4tZLLyl72zV\ne4pyd7YkduTtQMcV1JNh1YnlnOpVSBTYOXUn/n7MdT7Q/gFj356FXzoOUh/f0rQsKVLsuvypXTTl\nLXp3WGhu1MSWnDL3Dzl60PnhoQ8xfTPlWVhzfE1A2sWWpBjmHBO0V88qMsDAU/eZRB8A5HJuD5L6\nRhOUcv+Kvl5vQWSE8PIz42bXXC19P+mLjw59hHvW34Op//O+5PelP6gAPrNIj9lLmvTBfiXVfd3Z\nBcVueYB5859efdyLfs4/rudKXyxFr1bsAjG90WxE/52h79heD/5qMLJLs92WFTInstAEMijp13O/\nwqDJRWK8awe3iimRZSP6ZjP1UOG6xCdCrkBdo/u0sfbk66io7ygVt2WBvrDyELMLes/lPYh8yzHr\noP3e9e5w534enj4cGWkZtkQlj9/YJOD2v9HWmta217oe77mt58Mxy7FzqmNY7/HHj6P65Wo8d5vw\nWzKHGqE2gLcnXuv5mSOSGVDJMyOt3sAs+lzTwfKx9NkmzWw0mBHpB0u/R2IPxuOVDZXYlLMJ609x\ni+i/a/MtjMfZxoJ1juuMmldcczD8csH9PhhZ+a6JtzRyDbZN3oYjjx1B0awiVnW7o9mIPr1HOo3R\nYsTak2sZl0wxRdGGClzdtXzcl3d+eycAIC7WtfMpZVRiDjZru2nR5xpUFqlUoN7ATvTPV1wAckfi\ni7s/816YJ18d/4rxOFNaYned/8fxTbm/s59iHoB+dy+1ayC97e37I97H87c+jw7aDri76934cxo1\nH0yvyfeGWCRySEc6pdcURCujEaXgHyQWCvxTxjyH6S3+wmwx40jhEX80iTXxscx9w9Z/JfxF32Bk\nVtyESPZJtgCgQW9ChNI3QWa7W6DBaEFkZODk58/LVF/imuzJPnDWHm/PRXolgUwsg1quhn42u+cc\nAFiiXVdMySQyJKmT0Kd1H7RSu1nBxpJmI/q0G5PmZPFJPPjjg/i70NV1KuSWh0LDVfSFmGeKYBjV\nW0WUi4mNlWA2XbP0OSZ/iVTKUa9n9/fW1hshq+yBOLXwqXiZEM8XI6csB18c/QKP/fwYAGoTDXus\nVit25O1wubZ/an/c1bUpVqFrfFfGOujBJ535TCaWYdnwZTg/8zykYikGtBuACFmEy86H34z7FjNT\nvnW5n/1vYcsDW5Aey34DpHDAUzAfwBw0t+/KPkjfkOLG1Tf6qVXsSIhjfubQ35lVVovzRZ5TEnvD\nnejPvGUmp/s06M2IUPpm6VdWsXse6Q0Wv8zp2xNt6GZ7TfdToeblnb2aD/d+2OE9HYhLe+z4GppC\nrjJrNqLfMbajQyT+Q/97CACzEHn6Apwf7IGGq+jzSRtLw2Shm6zUyDRaGeO9DT6699VKBRqN7EbA\nNfVGKOWBG6xZYcXpktNYeWglPjnyCQBqy1GaemM9NmZvxPFi161fRSIRxCIxPhnzie3Y0zc/DQCY\nnzEf799JLYOkP6+4iDgsvGMho8Va92qdSyR//7b98H9jrnff9rlWjOw0ku2fGjbYW2m/5P5i66sf\nHPwAACXwoYom0o2lb/c3/V3AzxthMDE/C7h64Br0JkSquF1T+iK1N/DbBxayKm8wmaH2k6V/U/JN\nAIBq+RkvJZv47fxveG6b5ymwXq16oX1MewCOOTkWZCzAe8Mdp91So6mYKKWUW8IyZ+JUwq+gaDai\nDwCnn3TdhYhphORp1KRdosW+/OA9POjpiBhJay8lKYQYuTKJNR0tX9fgPeqVtvS5PlyiIhVoNLEX\nfZUfRZ9pcDh983QHt7D9Z/3q9lcxfuN4xnvR3hF7S3vFiBXYNGET5gycY0uaQiMWifHawNfcts35\n9xqrinX4zmgvV3PLU++M/ec/cu1IvLfvPdy/4f4gtog97ryLtHs/vr4fGuvY57pnolJ2yu25VyKp\nXfbYPC8aDdxFn/77fspjl0HUYLBA4yfR99QPTBYT4z4Vw78ZjuUHPAfijkgfgQvPUK53e+NszqA5\nLnFiUrEUhtkGxKpiPd6Tab4fAL646wsAwNxBcxnP88Hrp15UVIRHHnkEd95Jzf9mZ2fjs8/8P6/q\nK5n3O65HZRI0b9bx1yf8m/rWEwazAZG1PfFjf3ZBSUKkymQSa1r0dbXeRZ/eKI+rez8qgr3o19Yb\nEaHwn+jPuHmGQyAdAJQ3lDu8px+Y+6/s97jvAW2xZ6RlwDC76eFwd9e7IRKJOHtnnL8ftVzt8FnT\nwUts4ztCvT+7m5awWC3YdGYTntryFABqadXG7I2BbJrPuAsepgUqQhKNihp+K1NMUvdeytYJlMX5\nx4U/vN6n0WBCZAQ30ae9p1fq3W/tbI/BZIZG7R/3vreBzZazjhH1i3Yv8lj+vu734cxTZxzyPTin\n/XX2HktEEsbv/OaUpnTRrdWt3ebjoD0E/VL7YWC7gR7bxxWvoj9t2jQMGzYMBQWUCHXq1Anvvec+\ngjjYKBWOf5KzlVSjr/G6wQ6X3aWExmA2wKSXIznZc7kzT54FLGKYzPwtfUb3/rV1rbV13gXKV/e+\nJtJ9chpn6hqNUCn9J/rL71yOj0d/7Pa81Wq1PaB/yf2FcYAztRe1HMg+DoKp43MdqC2/czn2PLzH\n9l4sEjt81mvuppansbX0Q70/n3iceWOY/Op8LD+wHB8dpjL5eVq7H2q484K1jW4LgNrGtrzWf39P\nSit2O+dtOL0BDTe8jUgVt77Mdc7aaLJAo/aTpX9t8DvjJuat1uMj4rFg1wJbbn37zW6Y2HD/BnSN\n74oImfuVQ87PA3feZPv4nI6x7vOw0N9TQmQCdk3b5bF9XPH6qZeVlWHChAmQSKg/SiaTQSoNjdSf\nTDjPi1qsFrz919u294lLEzFl0xSHMs5fmDc3jz8xmA0wNsq8in7XhE6AUY0qne+WPi1OntzyNXX+\nc+/HqBUwWthZ+vWNRkT6UfS9sSlnU1PQFawOoku78L68+0tW9+IafZsYmYj+bfvb5ioBx8+aju5n\na+mHen9WyVT46u6mFRRiPfX3vb33bYdgPSGTpfgbd+79cV3Hoe7VOpwV/4SN1gf9Vn/bZMpy9CbO\nv+ZSngCuS/bs+wOb36HRZEYUx7TdbHnjjjfw9r/exg2tb2A8r9PrsGDXAryz9x1sOrMJ5yvPu71X\nwfOuHtdj049h9WhqnwPaUnfWHXcrSkQQ4bY2t3n9G2hjwTmIVwi8ir5arUZ5eZObc//+/YiODkwE\ntS84R5ufLD6J//zRtKVlo6kRdUbHdSW9k3oHpG1sGL9hAiwp+6BxTb3ughgSlFfwEH0r1ek8ueVr\n61mIvtHLTm9uiNFwEH19cEW/qLbIIduX/e8sIcJxSZS3JWRJ6iRY53Kffz/46EHbdfaftUQsQafY\nTri1za2s7hMO/dl+6aFSxixUdIBlqGK/XNjdgFgkEnm0INli8tJNO6ZqIC693mseELov89nTgWmb\nW2f8aemP6jwKL/Z/0W0/nLdrHsxWM6RiKWPSp9SoVAxuPxiAY44Mml5JvZASlQLrXKvDnHz5S+XI\neYq6n6cB6d5HqJgCT4OjtJg0nH7ytF/21vD6qS9btgxjxozBhQsX0K9fP0yZMgUrVqwQvCFC4fxF\ne0rY0S2eWtLx+qDX0fia4w+VzUYz/qCg9irrsiJIWC+RcXc9wOyW76DtAACob/A+qFA0Ui5KzpZ+\npAJmkR5mFuOWBr0R6ojgif6r21/Fsn3LbO+Ly5qmJSZeNxF9kvrY3nNNhuILzt/Z2afPuk1M4kw4\n9Gd796gmiN87H8Z+17TLoLeEYNNTViGq3veMa97W+MfEANbaROjqPQ+yzSb+os+0za09JhMVV+Xv\nJXvelrmZLCbG7yVGGYPBaYPdzre7I1YViy7xXQD4viz8+VufB0AN6v21L4xX0b/xxhuxa9cu/PXX\nX1i9ejWys7PRq5cw6QD9gfMXXXctbar9ciua5XdSbnyr1QqF1HGu69lfn/VTC4VDLBKjvJJHIJ9V\nZLuPM6efPI1H4j5HXaNnE8JqteJ89Ge4I/YhzpkOFVI5JHIDdO5j4mw0GIwBefi7i7Z1nj8+cqJJ\n9B/u/TCOTG+K8ueyWY+vcPWq2BMO/dn+M4yOjEDr8+x22buxtfv1+H7dH56Bbeeagoq9iWivxD6w\nmHwXWtp5484dLBIBCqkCJeWeY2hMBgFE30vMVHU1IFHVQa3wb3ZNNmvbDxUccjm29cGteG3ga9C9\nzCxA+XcAACAASURBVOLBxED1y9XQqpgTatn/ru1fd4rtBADo37Y/AO7xUVzw+s2uWbMGIpHI5oo4\ncoR6uD300EN+axQfnK2s02drAQDqRWrUvejoTqF/2GO7OO77HS4Y5SW4Ul4Ot9s1ecFT4JdSqkSC\nVoWGHM+iT0eid4juxLl+hVQBc5vdKK6oh1br+QHQGCDRPzb9GNoub+uxzBt/vgFc84gzuemDYelz\nYd26dSHfn5PUSWgf0x55VXmIkEVgasYEvJa/2Ot1rTWtgULq9dx+izF/b9NgwWA2QCVWubnSv3iz\n/JJi1TCCZTo7BpYdotbH73jINVkUjUom9yr6ZgPVTj6DSm+b21RWAuLIcsRH+HfrcDai//3p712O\n0fu4+Dp4d5cB895u9+KB6x8AQK3tvymFitGZddssdI3viv+74f98qo8rXj+VQ4cO4dChQzh8+DD2\n7NmDefPmITPTe77xYOE8B/Pr0aYUqM8/71g2Iy0DR6cfdfvlfnvCNeuZP2HyRnhjUyGPaQiL546d\nECtHvZddQEwWE0RmOWb2ns25elp4DuYf9VpWbzIiSu1/0U+NTsW39/D73ulpI39CP1gHtB3A+dpw\n6M9ikdi2EZFKqsLokZ6/ezpXgf2DvkuS4+BNiERWvuLNcm4VGwGjhyV33vj0ArWczFOQaGWrTPxw\n/guP9+Fj6feJpBJCefuc1576GsaoXK9r2PkSiME3FzaO34h7ulH79M4ZNAd3plPLZpcOWxowwQdY\nWPrO+19XVVVhwoQJfmsQXzrHdYbldQvEC6jOX9e6ycW2Zw/Q5t+puFJDbd4iFok9BvFtyN6AB3v6\nL6LWGfUiag4pSXwdq/JppuHQGLlb2DQiQxQ+G+p+nXNSvAqNXubnjGYjYJHBl1gwOvDsxf0T8VBG\nvseyemNgRB8AHrj+ASzbt8ynfO11r9YFZG8HrVKLjLQMlw122PDBBx/YXodyf9aqtJh12yzc3vZ2\nKLysMDj82GEkvJPgIPqD0gY5lAmke/9ooeNA1tvUV+u4CFgiirDl7BaM6jzK53pVUveeDJUlAbl1\nhz1eb2ikPmfnHBVsGJ86C0dztnpdVbHyDJWIylNbhYDOikczMf0xfHdutV/rDAc4h09GREQgLy/P\nH20RDHeW++n7RUiOao0fx/+Io9O9W5dsolD9wVNtPmVVLl0+AJUNFT7XYxEZMLDjzW7Pt4pVwYgG\nGD0E/JosJljNMsR4z9brAv09leiZN7Wwx2A2IjpAog8AX4/znqCJyX0YIYvwS8StMwqpwifBdybU\n+/PSYUtxd9e73X6mt7e9HQBsrmLaLT2m8xiX+W0ue6rzJa/K8TP19ptIiKGmt4pqynjV6xybZM8d\nonnoaB7j8Xq9nuqTlQ3cd/8Z1HYwlHWd3A6uzpSegXaJFrUmyqPh791Ob297O/Sz9UhSU9OfXVLY\nZTkNBfhspOYNr0+nMWOafiQWiwXZ2dkYP545/Wg4oDfpkRaTxmqZnvPe6YEiKZGdpaiJUKBY55vo\nWyyAVWxAXIz7utQKFWSqBpSUACkpzGUaDSbALGW1xJAPRrMR0ZrAiT6b+cBQ3rjJE3SfDqf+7E40\nF96x0MGip783JmszkO59Z9eyt99KhJyyeiVG/+2IGBsjw7ki9yP4s+Vn8btxHgCgxsCcHtYTUVGA\nxSxxa+kfKzrmsLdJIAbHcokcs26bhRd/fzGkd1d1ht550x94/dRnzZrVVFgqRbt27ZCamurhitDg\n63Ff25LwaJVaVDZSI9caQ43bpRjRimiHKG3n9fyBIiWJXUZATYQMJ9Xv4kLlU7YldmyprQUg1SNC\n4b4jqGQqmOKP4eMDn2DhPY8ylimvMkIEKcR+3sXBaDZCGxU4kXUOZEqLScPFqosOx449fixg7RES\nuk+HU392ZxXab2jy7T3fom9yX2zK2YSerXq6lA2kpc82WQsNPVgxNvDboMUTsdEy1Oe5/wze3P2m\n7fV1ieymGO2JigIsJjHrpElC7hznick9J+PF318UJB9CINC9rING4T8ryqvoZ2Rk+K1yfzK552Sb\n6Ns/GC5UXkC0knkCuurlKojmN3XOQC/xoUlpxW5Eqr6WH7vWUMu5jqoqKyAxenSxRcgiYBUb8ebJ\nx9yKflmFCRLvPyNelNRUwKy+7HanMn9g/0CKUcYg75k8h98G4H7L3FAnHPu0O6vQ3p1NR0Y3vNZg\nG7SN7jwam89uBhDY/szV0geAmOIxqKrxnDyHD7ExUtTr3d9fKqI+487Kfvh3n39zvn90NGAxi4Ma\nMMkE/dvpl9oPB/7vAG759BaXMpOum4R1p9YFummM+FPwAQ9z+mq1GhqNhvFfVJT/XFBCM7j9YJel\nadEK91Fn7wx9x/Y6WGk+tRp2lr5ITnkifHEzl1UaAYvU42ibzZKa8koTJCL/WuBDvx4KxJ2DQhpA\nS99uSRw9FRSuSzuBpv4MICz7szvRZ9q6VCqW2izrj0Z+ZDs+8EthNy7xBN2vOkkHwzDbgITIBC9X\nAHKJDLpa/4l+fKwMDR5En26zXObbcj21mnLvG03Mz81A5K9ggv7tyMQy3JxyM+Nv5t5u92LzpM2B\nblpQcPvEr62tRU1NDeM/HZtsKiGCUqq05San8RTs8kK/F2yvgyX6bOeeJHKqA/vitiytMEBs8Ty4\n8DQ4ojlbfBn6CP6BYJ4+65K6EgD+D/yxx34wRH++myZsClj9QkP3ZwBh2Z/tRf/TMU2Brt6mtezn\nRp2nZ/wJLXDPd/iS9e9WIZVDV8duAypf0MaI0ND+B7iLEaMtdJHEt2kQsZjqN7V1obUnAv3bof9n\nCpLrltANozqP8ik9drjBelKlpKQEly9ftv0LFxQSBXZM3YFnb6Ey7Dmn2/WE3hCcH6+nQYk9MjnV\nOX0R/fIqAyTwPLhgMzJfeG4c57qZ8JSjwGqh2hHIwDn7OX16QBJq6375EG792V70uyVQeRCiFdFe\nB8iRMv8FRHlizDoqWDI5if2UlEImQ029/yx9OvnP+iNbmM/TefklvrdBIhZDVxOa7n168JUem25L\nwEPjr5S3oYhX0c/MzESnTp3Qvn17DBo0CGlpaRgxYkQg2iYISqkSSeokLBu+DK8NeI2VoL7cn8ri\nFWjR10qoEHn2lj4l9r7MoVVU672KPhsaLdyjfJnw9DdYr6ULDmT0rb17n54Lth8EaeR+Xq7gR8Kx\nP9sP+OjXbAalcokccnGTO7e6sdqvy6GcSU5i7ypXyuSoqffd0n+k2/Mez9OiPmnzaMbz35z4hnoh\n9j3gUSKWoCbELf29j+zFqSdOAQAGtRuECzMvBK1twcCr6M+ePRv79u1D586dkZeXh+3bt+OWW1wD\nIUKRjfdvxFtD3gJAuZ0WDl7I6rpF/1oEAIg2p/utbUyIzNSAhK240W64Bj33TlpRbYBUxF9ENVY3\na/k4Yr8jmTM1RmqZTyAD52j3/q1tbsXdXe92OU/nyA5HwrE/2w/C6P7BxvMiEolw4d9NCaZilsQE\ndHe+5NbsRV8ll6O40XOSKk/0bdPH43m2eUesIt9FXypxb+kHy1NGe+3o/6MUUbZg7usTr0d7bfug\ntCtYePU9yWQyxMfHw2KxwGw244477sAzzzwTiLbx5t7u9/p87f2KT3Bat0/A1njHZAYgYb9+1XzN\nrV9Vw72TVuoMkIn5i35r/R0YFstfNAxm9xZOo4VaneDPTSicoR8QWVOzGL1D4Rz0E4792T7GQiaR\nITEykfUy1WSnPWiu6Lwng+KDfXyKXM7eq5Av/hNFOA1gPqf6zOZrdcg8Z89kOz3maQDuDak49Ob0\naY+Qyw6szxe43RinOePV0tdqtaipqcGAAQPw4IMPYubMmVCruW05GI60TpKgShfYuSmzidu61f/c\n/h8AgM4X0a8xQC5mFzsAwG3wT4NBj3g1//3YPe3zbUXgHyK0yDANNJRSZUAHIEITrv257EUqW51c\nIsfZGWfxx5Q/WF0XyKDx4tpivPBbUzAwlwQ0fdWuHiU26Gqo/qE3e04mZr8Mz9PyRU990RtSicTW\nHrfoNSiY6fs+A77i7GlorWnNGMnf3PGqMnfccQd0Oh2WL1+OO++8E+np6fj5558D0bagkpwkgS7A\noo/GaMy7jv1a0fiIeKhLB6PaB9GvrtVzmiOvdZMKoMGohzaK/eDBHXsu7+F9DyGhRZ1pt7HdD+8O\ndHMEJVz7Mx2IJZfIEa2M9jlrmT/dzL+c+wXv7X/P9j5GyT4/9ejk/4NK345zneVVVP+n8xS4w34V\ngSdvBx9LXyZjEcinqEF0ZPhkx2tueBV9o9GIYcOGISMjA7W1tZgwYQLi4uIC0bagkpQoQX2DBXp9\n4Oo0mMy4oV1nTtfIJFLU1HEbnFitVuTiFyik3jteyQvUcrndOacZz+vNjYgVQPTpREpMyC3R+Jfq\nRd51cIEWBqZgsfYx4T0HGK79mXZPh3L6Yz5Z5rRRcpjBPZCvotIMkUnFKhcAzX0b7nN7jk/mQrlU\ngmpvlj7A6tkjJN0TunP6fJozXn+h8+bNw+nTp/Hhhx+isLAQAwcOxJAhQwLRtqAil4mhiCvG+fPW\ngET7niw6A2PcMbTmEO0LAA3qbLx39klO15yvPI/TrWZDIfPe8Wj35KpjHzCeN5j1iIv2XfTplRKe\nMIirUS8p8LkOISmaVYS4iPAQSXeEa3+2t/T54M8kMXxEPzZa5pPoXy2vAsTcBv6e9hXh496XS8Xe\n3fsIbHwOAJx+8nTYpOH1N6x/oYmJiUhKSkJcXBxKS0v92aaQQCKWoKH1dgzL7IYeH/Xwe30vb3sd\nAKCUc+sMjfIrKDZwW3JCz+clRCR6LUuLfm098+jfYNUjLsZ30adXSnhCZJFjWvs5PtfhC0qpknG+\nz9N+5eFEOPZneqqF70Yt/nTv8xH9uBg5LCLuoj9+bxqsYm7XORsy87Oaggf5uPdzLX/gZ5V7LwIh\n+Hj9hX700UfIyMjAkCFDUFZWhk8//RQnTpwIRNuCCv2Auar/B2fKzvi9vuprmbiY5pCFhk5L3DW+\nm9eynkTfbAbM0CM+RphgGHfbeUoMsUiOD+y6eJlEhobXPEdDhyvh2p9pCz0Qu7P5ir3ob7qV2w6Y\ncVo5rJIGzplATVb2Il30OHVv59Tk83bNs73mY+kDgFGsY5wiCFYaXoIjXkU/Pz8fy5cvR3Z2NubP\nn4/u3VtG5qJA/UCtVisMZgP+KssEwD3RTg/LJJ/qBIDoCO9iTT9g6xpcO/GE9ZOB5MNQK1Sc28DE\nBweZpxAsMCIhLnTnccONcO7PRbOKfArgG9VpFNBIBdUFyr1/XUduy8EStHJAYsIjmf8ndLNsxMdT\nf7vZ4n5gwcfSp5m9Y7bLsdK68PAoNXe8iv6iRYvQu7f3veebG57SwgrJqr9XQbGwyT3eOY5bIN/E\nyNWQWrnNVVmuiX6M2rtY03Nv9Y2uov9D7rcAgFhVLKf63eHO7WqBCa3iiegLRTj3Z1+nVzY/sBnt\nspkHlUJi/xtu08ZDQQZUSqqvHS3w35bNkmuOxAgJ8zLbl9v9hB8n/Mi7niV/LXE5NuOXGbzvS+BP\nYDY0DkNqDMKkl/WG/dKZbrJhnIOUYqIlsIKbd6CugSofqfBeF225lImy3ZYRKsEF03yoaL4IUFYj\nNiZ0XbqE8CA5gfJsBWpOX+njrFeCUpgsl+6IvTwVJqMIC3YtcDk3pvNYjO7MnKaX0Dwgou8Gnd5x\n5zHRfBEOXT0keD3263hVKu5fhzZaAgtH0a+qpqx2LrvW1UScRHYps/CrpMK49z25XeUB3GGP0Dxp\nk0R51Pzp3ucblR53Yh46a24QqDXMxIrb43TVQczNmutyrhXPONUN4zL53YDgd4Ii+hUVFRg6dCg6\nd+6MYcOGoaqKOTtTWloaevbsiT59+uDmm28OaBuZtpU9Xcq8Vp0P9oIZ6YPo+2LpV+qoOTuh1jsL\n9RD1ZIEFcltdAjfCoT8DQGoyJfruBq9CwNeLoJTLUctj0x02REW695rxFf328d69FHfFvcSvEgIv\ngiL6ixcvxtChQ3H27FkMGTIEixcvZiwnEomQlZWFo0eP4uDBgwFt4/S+03HksSMOx7hG1bLB3h04\nN+N1ztdro8WAiFsuATqDH1ch3ZXn30x0ngYPfJZCEfxLOPRnAEhLpaaz1p1ah9Mlwg/gAf6/0wiF\nHLWN3ERf1dCRU/kojXvRj+S5E7FG4T2l8/C2ZElfMAnKkzQzMxNTp07F/7d359FRVGn/wL+9Jens\nCVnIxhYIIWQDImE3LAEhgMgoMud1BPHnvKKI6LA5zgzwExhRnAEFjQuiry86iorwGxZZNC5ABmRV\n2QKyBEIwkD3ppLf7+6PtTnc63V3VW1Wnn885OaeX6uqHkKeeunVv3QsAs2bNwhdffGFzW28ug2lO\nKpEiNdoymTwRi+lyoF6Ku9MG8f58ZKQE0Et5jfqv/a2lz/fWpyd2P85re76osPsmX8hnAOiZ0jZg\n9nLtZY98h6tXvQKULfj85j/4faY+Ha8M4j6VckS7om/emHH1ol1ogOOiHxvl+gyexHmCHGVv3bqF\n+N+uI8XHx+PWrVsdbieRSDBu3Djk5eXh7be9txymUfvL3+3vbXWFTq/D9nPb216Q6p26Rz8iAgCT\n2V1Ao73aBvde3ncXKvq+yVfyOS6mrdi5MtWsLfnv5GPKR1Nc2kdV1E7en9HotAgP5X4CHxVuue2d\n5ju8v9OW2GDHU93GRVPRF5LHhkQXFhaisrLS6vVVq1ZZPJdIJDbPjg8ePIiEhARUVVWhsLAQ6enp\nGDlypEfi7Uj7lrA7Wyml10sx7eNp2Dhpo+k1Z1oJEREAZBqsK11nWnXPkapGw6QhXC/vF/Upws4y\n/gcjvtr3hxpbIMGM5swWWmfI50ZN2x05njjBPHLD9S4LrbyO1/bnbp9Dc+KXiAhb6Hjj30RGyAGz\n87I7KvcVfS7HlPgYKvpC8ljR37dvn8334uPjUVlZia5du+LmzZuIi+t4OtiEhAQAQGxsLO677z4c\nOXLE5kFi+fLlpscFBQUoKChwOnaj9iNx3dmnbzzouDoRhrEPbumBpZyL/jt1DwLgfnl/6wNbEbza\nMBdAbUstIoMikVvs/nu92x+Ijb+b7rKhbv8uf1FSUoKSkhKX9+PNfPZELgNATnyOW/bjUEs4/jjM\n/op3tkyQvYiPMJXz9nO2G5bL5dMXHx1pWZhVGu/OPBmqFNcVRl/hrlwW5ObnqVOn4v3338eSJUvw\n/vvvY9o063Wkm5ubodPpEBYWhqamJuzduxfLllnfYmJkfqBwl/ZFyJ2X940nFK8cfsWl/TjTBydh\nMjCJjvPlfaVCiSmqT/D/lDOwYM8CvDftPZy6dYr/F9twdPbPuOu9/lYtRON0oAG0CqfT2hfNFStW\n2N7YSe7OZ0/kMgB0Ce6CQdqncUy+Hh/++CGm9uVeXPmQMSXenPKGU5/tHZaFsNpunLdnekPONOu5\nr0/fNdpyMq8WbQvidYNwb9A/bXzCvVxdMMlfuSuXBelEXbp0Kfbt24e0tDR89dVXWLrUsNJaRUUF\nioqKAACVlZUYOXIkcnNzkZ+fj8mTJ2P8+PFChGvizsv7xhOK8vpyAMDYBO+MaGWMQQIpukh7Iis+\ni/PnEmMNTYm6Vn6XH7lI72pYQ1yntSz6xhZIYADN2S1mvpTPURGGvPv454/dtk+dXocl+9quskkC\nbK9g50hEmIzXoFyVWm2KgfN3hFpeXldpVWAtYbi7h3u6WnphHADbK/nRanfCEqSlHx0djf3791u9\nnpiYiJ07DX3HvXr1wsmTnpuO0hnOtPRrVDVQKpRWK7aZX0VQHP4zPv9kVfuPekSrrhVgUrya+gsS\neaxhM7R3Bt48aWgVuJtxbe3mJstz0Kpmw1zdQUFU9MXMl/I5OkoK/DbD9hfnvsC0dOurEo5M/3g6\n5ufPR0GPAgCGE+GXDr1kel8ndX4K74hwGXQ8uhFbtIarYQ/0f4DzZ9S61nb7aIG6OQjduF9gsGtW\ndDHW/lqIkNUhODjnIIalDLN435m1E4j70HBpHvi29LV6LaJfioZylfWMdeaD1gIlYQgPdzk8Thpa\nGyDThRoGAPKQlWYIcM/FPfjx1o+m1xcPc32iDePYgvp2Mx8bF+gIonE/xE2io9oOeTO2znBqH9vO\nbcNXl78yPW8/1odJnB/7ExEuhZ5HS1+tMRR9PgMT25+4qzQqtDQq3Vb042Jl0P525eFmw0337JS4\nDRV9Hvi29BUvWPaZj3h3BI7fPG61Ly6zWLmLRq8BdApERjre1lyv7m3/luzibNPjNYXWC2vwZezL\nr2+wPNg1qQ2XB6mlT9wlPKztkOfKCP74kHgc+OUAMjZmuHWAb2S4jFfRT1Xyn9lwbM+xpseL9i5C\nXZOhpZ+YyHtXHYqNlUKnM/xO+K4aSjyPij4PrvTpN2uacbD8IA78cgCAZR9c/24JLsfGlU6vA9PL\nebf0AxWe7wlqamj7jmpVNYo+mgQAkMup6BP3kEldK/rGAq9UKLH/l/04e/ssr/50R/hOqx2FVPSr\nep7Xd/SM6ml6vPbwWhw4+wPCQ2WQuynF42PbxiWYnxAF6WOwOMQzMyES7mjpMh5cOaPvud6QaIv3\nL8ai4YtwpfaK6b3J2SNcDY0zrV4LppPxbunznb2Pr76aGVA3tvVxVDZa3xNOiKvMT9z5Lo7TrGlG\ntcowx8WjOx41ve7O1mxUhOHOGs4xqbRQBrq2yM+Hl9cB3QHgA5f2YxQfK4Mu2HBZ3+KYqZehe7x7\nVuQkzqOWPg96F1r6vzb9anrMGMOMT9v6E/MHObkGpxN0TAe9Vsa7pd++6Etqe6LsiatuiytUqUR9\nvdl0oGZjHjy5FCrxL+Z52KhuxLNfPmt3++M3j0OtM4yQf3LXk0j5Z4rVNu6c3S8qUgYGPbgealQt\nOigDxdV2iwhrOwkxP8nS6XWIj3XtBIW4joo+D7W17rllzzgq3SiV33oZLlG1asH0coQ6niLbQvt7\n6FnkZfSOddPIHwDBQVLUmRd9s+/z5FKoxL/8adifLJ7/s9T+vemD3hqE4h+KAdgelNa+6Ff+yfmr\nVMogKSDRQcVxvhxVqxZKpbgKqVzWFs9D2x7CxiMbUddSBx3ToWucuGL1R1T0OXhuxHMAgKrb7in6\n3121XK3OmzWtrl4HKWRe/U4uQoKlqG5su9Xp0zOfAgBkLAgrR68UKizSyWTEZvD+zNN7noZGp0FK\nuHUrH7Au+vGhzq9PK5PIAEULym46PnFgjKFSew7BQeIqpO0n/Zq3ex4i10RCDx0SuoorVn9ERZ8D\n4yISVbfdM0r3/q1tE/HEyXq7ZZ9c1TXoIJOI63IgACiVElxInY8b9TcAAH/9+q8AgAHSP6BvTF8h\nQyMEASsD8M6Jdzp8r6G1ocPXnWEcZ7Dhh3UOt91+fjsuB32B8/pdLn/v3d3vdnkfRmGBYUi9ubSD\nd/ToEkVFX2hU9DkwThvprpa+uRNzLri8j4W9PkBY4wBO29bWayHnOYDJG1qkhi6P7ee3W7weEiLc\nUqzEv208stHxRgAGv8P/tjlbjCtt/troeBGcuhbD7JiNzPVBr+/e+67L+zAXHdrBrHuBjZDLqOQI\njf4HHNg+czvu63cfAODOHe4F6HbzbU7bJSa6fp29T5dUNISesLgjwJa6Bh3vUcve8NMdw/wFh64c\ntXj9m8aOW1eEeNq83fO8/p3G8SuqVseDA5UKw6RfMicK6cWnLmLh0LaV+dy9zHbXqI5HCovx2ONv\nqOg7MLXvVNNc0T8lcFvFrkZVg9iXrZeD/dfv/uXW2IzCwwyX640T/9iz7dpbaA2+5JE4XGE8Sdpy\n5j1sPrFZ4GgIEZZO47g4KuWGon9PCvcpeI1So1OxckzbWBl3L4KT2bVfh68br2QQ4Yivc1eEzP9Q\nGXM88K79NJfdSreioTYQK3/SApnujy/yt6LPZfKg/dXvOP2/LoEEDAwTe09E8eRi53Zig/nv7Ltr\nbQMdN03+H7d+DyG+QKPm1h6T16bhz0P/r1PfoZApOnzsDr2TI4Hr9r+TCINa+hyYX5KqdNB9Vt9a\nj8R/WM5nuXnR/Tj1yRTcO82yKOcn5bslvqgI7ySSfplhIGOUMgrdItx3ux5gOS3x5pNtLf3uUW6a\nG5SQ33w+43OhQ3CIaazX62hPrVMDv2bynmjLyHxGwkCZexe46JViHX83BbdxR8SzqOhzYH7pK+Vt\nudUtd+aa1NYrbI0ZA6SkAAMHWr5e+n9K3RJfeKih6a7RemfQmzsnI3FkeLfhXvsu4h/cfcLqbqPZ\nSuhbHS8/26JRQ6tWIIzHapkdOf34abevfJcYZ30SERhEg3LFgIo+B3Kp3HR/r47p7Padt7ZbttKc\nK3P326OQGYo+1wk9XPHYwMcwJ3eO2/crgQQBEuvWQfsliQlxlTPTacvLC2y+137pWFeFBAVA1apx\nuF1dkxoKaQCkLhzF2TKGrPgs53dgg1Jhnbe0WqY4UNHnyLz42Jshzt568z0ie7gzJBPjFLlNzZ4/\nk35ryluY0HuC2/d77Zlr+GKS44GIhLiK72qZANA70npSn7KnygDA5qQ9zgpRytGidnw1rb5R4/YB\neO7SJbiL1WvDurunO5O4hoo+R+aD+ezNBa/SWDa3N9/b1j89KHEQ2DKGdRMcT7zBh/F2m8Ymxwez\nYHV3PBy/1q3f7w7J4ckoyO7peENCXMS3pS9tjsezk6ZZvd472jCxlruXjw1VKrgV/SY1AuXiLPrB\nimDky//b9Dzjwrt4veh1ASMiRlT0OTI/UPBp6c/OnW21zdNDnkb5M+Vui8040LCJQ9GXqMMxLGGc\n277bnYIUlgew1ya49w4BQgDLbrauAb0s3tMzvdVSuQoWhh7dDY87Wo7XuH1eYh4e7P+gy/GFhcjR\nonZ8eb++SW2VM2ISH9v2u8pJi3FqKWPifvS/wJF50ddpbRf9X8ptX943lxye7HJMRsYrDw2NnVyf\ncwAAGM9JREFUjlsHOqZBZJg4b5tpfzI1Z9AfBIqEdGbmudyqtnzvke2PoPdrllNjL0nYZ3qcGGZ9\nN4mx2+6ZIc/gX/e7PhdHeIgC9YHnHG7XqFIjKEC8RT8xwVBeZP+8icX3ThY4GmJERZ8j8wNFRYXt\nor9nX1vR3ziJ2zSe7lLd1Ohwm1blVUR76RY/Z5Q93nZzL03kQTzB/OSypdWyVX+4/LDVzJZP/lcP\n0+PSR0txX/p9pue1S2qxZtwaw37dtAT0bf0vaIr51jTNri0NzWoEB4g3lwPkhvxdsagrcnNFtsKX\nH6Oiz9G09LY+vfJyCS7XXLa6de1/T2/Bx7WLTM9nZs70SmzRymgAQFWT/al/r9ZeBZOrEBkh3jmZ\nUuPaWlLGAYqEuNOQ5CGmlRvVGsv+feMgv++vfQ8AkDAZ4uLa3k8KT0JCaILpeURQhGnCmbBAF++d\n+41xlLu9O4EAoKlFDWWgeFv6xvx9/nmBAyEWqOhztLxgObLjswEAV67q0OvVXnjzhzeh0+tMfXov\nfvUaNJE/mz5jLMaeppApMB5rUdNif5EOnd5wgIsMF28L2rwVRn2AxBOkEilG9xwNANBDh5s3294z\n9vcvK1kGAFjajdsKdhefuoiiPkVuiW/1+OWAOthhv35zqwYhQeIt+jT7njjRUZWH4388jsFdCnH1\nuqEjsFHdiKGbhqLoQ0OyV99u+yNfNGxRh/vwlJjgLqhV22/p1zergcZ49IkT9+QkRvYGTBLiCuOl\neEWAFkfN1ngytvRDJYa1M0YMM5wgG9ffMN/GXGp0qtv+XgMVCkhUsaipd1T01aIu+nSlTpyo6PMg\nk8pwd9og3Kk1XHarVlXjaMVRfHP1G2g0wK1mQ5Ph8UGP46XCl7waW3xYDBp09lv6NXUayNQxXoqI\nEPEyFmhJQAu++qrtdWNL/+Y1w0RRwUGGoj8sZRjOzztvsY0nySQK3K5V291GpVYjVCneou/ulfuI\ne1DR50mpCED3XoZkfOmQobDr9Dq8v+MS9BGG1euEmDAjPiIKzazG7jbVdWrIJZSIhAxMGIiXC1+G\nVtKM/fvbXje24suuGqbTNg4mlUgkSOuS5rX4ZFCgutZ+S1+lViMsWLz5TJf3xYmKPk+B8kB0S7Uc\nYKPVa/HBJ20j52823mz/MY+LDg+ERm9/4E9NvRpyiXhbBoR4S4AsAAu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"text": [ "" ] } ], "prompt_number": 49 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- The computation we use for decoders is close to what we're looking for\n", " - we want to feed in some amount of current $J_j$, but all we have are a bunch of activity values that we can added together\n", " - so we find a weighted sum that closely approximates the desired $J_j$ " ] }, { "cell_type": "code", "collapsed": false, "input": [ "weights = numpy.zeros((N_i, N_j))\n", "for j in range(N_j):\n", " J_desired = alpha_j[j]*encoders_j[j]*x+bias_j[j]\n", " weights[:,j] = syde556.decoders(A_i, J_desired, noise=0.1, dx=1.0/len(x))\n", "\n", "J_j = numpy.dot(A_i, weights)\n", "A_j = syde556.lif(J_j)\n", "\n", "xhat_j = numpy.dot(syde556.add_noise(A_j, 0.1), d_j)\n", "\n", "figure(figsize=(8,4))\n", "subplot(1,2,1)\n", "plot(t, x, label='$x$')\n", "plot(t, xhat_i, label='$\\hat{x}$')\n", "legend()\n", "xlabel('time (seconds)')\n", "ylabel('value')\n", "ylim(-1.5, 1.0)\n", "title('first population')\n", "\n", "subplot(1,2,2)\n", "plot(t, x, label='$y$')\n", "plot(t, xhat_j, label='$\\hat{y}$')\n", "legend()\n", "xlabel('time (seconds)')\n", "ylabel('value')\n", "ylim(-1.5, 1.0)\n", "title('second population fed from first')\n", "\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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EvdCfu/MNLLz3YXRQtZ9w1EL15ZAJ/ZSUFBQWFtreFxYWIjU11aGMWq22vR49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"text": [ "" ] } ], "prompt_number": 50 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- The basic trick is that we can use the algorithm to find decoders to find decoders that approximate value other than $x$\n", " - We just replace $x$ with whatever we want\n", " - $ \\Upsilon_i = {1 \\over 2} \\int_{-1}^1 a_i x dx$\n", " - $ \\Gamma_{ij} = {1 \\over 2} \\int_{-1}^1 a_i a_j dx $\n", " - $ d = \\Gamma^{-1} \\Upsilon $\n", " - Notice that we don't even have to recompute $ \\Gamma^{-1} $\n", "- So consider finding the weights for the first neuron in the output population\n", " - compute the desired current for each $x$ value: $J = \\alpha e \\cdot x + J^{bias}$\n", " - find the decoders that give that $J$ value\n", " - repeat for the other neurons" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A shortcut\n", "\n", "- Let's simplify the solving a bit\n", "- First, get rid of $J^{bias}$\n", " - Assume that the neurons are getting some constant background input at that level\n", " - this value never changes, and it's randomly chosen anyway\n", "- Now, the desired input current for each neuron $j$ is $J_j = \\alpha_j e_j \\cdot x$\n", "- We want $J_j = \\sum_i a_i \\omega_{ij}$\n", "- We already have the standard decoder that gives $\\hat{x} = \\sum_i a_i d_i$\n", "- So what if we substitute in $\\hat{x}$ for $x$?\n", " - $J_j = \\alpha_j e_j \\cdot x$\n", " - $J_j = \\alpha_j e_j \\cdot \\sum_i a_i d_i$\n", " - $J_j = \\sum_i a_i (\\alpha_j e_j \\cdot d_i)$\n", " - $\\omega_{ij} = \\alpha_j e_j \\cdot d_i$\n", "- In other words, we can get the entire weight matrix just by mupliplying the decoders from the first population with the encoders from the second population\n", " - Instead of optimizing each set of connections individually" ] }, { "cell_type": "code", "collapsed": false, "input": [ "weights = numpy.outer(d_i, alpha_j*encoders_j)\n", "\n", "J_j = numpy.dot(A_i, weights)+bias_j\n", "A_j = syde556.lif(J_j)\n", "\n", "xhat_j = numpy.dot(syde556.add_noise(A_j, 0.1), d_j)\n", "\n", "figure(figsize=(8,4))\n", "subplot(1,2,1)\n", "plot(t, x, label='$x$')\n", "plot(t, xhat_i, label='$\\hat{x}$')\n", "legend()\n", "xlabel('time (seconds)')\n", "ylabel('value')\n", "ylim(-1.5, 1.0)\n", "title('first population')\n", "\n", "subplot(1,2,2)\n", "plot(t, x, label='$y$')\n", "plot(t, xhat_j, label='$\\hat{y}$')\n", "legend()\n", "xlabel('time (seconds)')\n", "ylabel('value')\n", "ylim(-1.5, 1.0)\n", "title('second population fed from first')\n", "\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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SlwmE4BPSWfaSkpIcMj9dvnyZdT1lRkYGpyVoBEJ7p0uXLrh48WLA6yV9mUAQFm/7ckhr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\n5FV48uGH0Dfe/MGHfvEQ+sT3waNfPhrw2OJilNA36L0e19RigNLH3fx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"text": [ "" ] } ], "prompt_number": 51 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- In fact, instead of computing $\\omega_{ij}$ at all, it is (usually) more efficient to just do the multiplying\n", " - saves a lot of memory space, since you don't have to store a giant weight matrix\n", " " ] }, { "cell_type": "code", "collapsed": false, "input": [ "J_j = numpy.outer(numpy.dot(A_i, d_i), alpha_j*encoders_j)+bias_j" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 52 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- This means we get the exact same effect as having a weight matrix $\\omega_{ij}$ if we just take the decoded value from one population and feed that into the next population using the normal encoding method\n", " - these are numerically identical processes, since $\\omega_{ij} = \\alpha_j e_j \\cdot d_i$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Spiking neurons\n", "\n", "- The same approach works for spiking neurons\n", " - Do exactly the same as before\n", " - The $a_i(t)$ values are spikes, and we convolve with $h(t)$\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Other transformations\n", "\n", "- So this lets us take an $x$ value and feed it into another population\n", " - passing information from one group of neurons to the next\n", "- What about transforming that information in some way?\n", " - instead of $y=x$, can we do $y=f(x)$?\n", "- Let's try $y=2x$ to start\n", "- We already have a decoder for $\\hat{x}$, so how do we get a decoder for $\\hat{2x}$?\n", " - two ways\n", " - either use $2x$ when computing $\\Upsilon$\n", " - or just multiply your standard decoder by $2$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import syde556\n", "\n", "dt = 0.001\n", "x = numpy.linspace(-1, 1, 1000)\n", "A = syde556.Ensemble(neurons=25, dimensions=1)\n", "B = syde556.Ensemble(neurons=23, dimensions=1)\n", "decoder_A = A.compute_decoder(x, 2*x)\n", "decoder_B = B.compute_decoder(x, x)\n", "\n", "x, X = syde556.generate_signal(1.0, dt, rms=0.3, limit=5, seed=2)\n", "\n", "spikes_A, x_A = A.simulate_spikes(x, decoder_A, tau=0.01)\n", "spikes_B, x_B = B.simulate_spikes(x_A, decoder_B, tau=0.01)\n", "\n", "figure()\n", "t = numpy.arange(len(x))*dt\n", "imshow(spikes_A.T, extent=(0,1.0,-1,1), aspect='auto', interpolation='none', cmap='binary')\n", "plot(t, x_A)\n", "plot(t, x)\n", "title('population A')\n", "\n", "figure()\n", "imshow(spikes_B.T, extent=(0,1.0,-1,1), aspect='auto', interpolation='none', cmap='binary')\n", "plot(t, x_B)\n", "plot(t, 2*x)\n", "title('population B')\n", "\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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KYgBX+fJC7Pv1E+u9vCAx0f3s/tu2iYFbKcHCzOMO9n1HccjGn5uby5gxY/jj\njz8IDw/njjvuoE+fPjRu3Nhsv7vvvpuVK1cWWt7W+K3cuNEaf3+YPVu0Is6fF3FqLFu77sqVK6bW\nDgjRf2HNC2w8u5HNT26mYaWGxm3jOo5j+eHl9F7Um897fc6AJgMKLLt6dTGtVUt0qikUJc1bbwmv\nu/nzRQNk2zax3vL3WZDwS6R9Pzxc9At4eYkBX6NGibcCd0HGHqraYT331C77Zh5wsMW/Y8cO6tev\nT+3atfH29mbIkCGsWLEi3372hgvYlriNtDQh9Lt3C1OPv7972/4suXIFo7kK4J2N77AtcRubnthk\nJvogOpsGNhnIb8N+47nVz7HyaMF/js2bix/Lxo3w++9i3ciR0K2bs69CobCOtO2fPy86bBNuZQDM\ntogcULGiaAAVFA1BjnFJTIQXXjD59EuhdReEWUsjveq6Uo3P40wcEv7ExERqyDgCQEREBImJiWb7\nGAwGtmzZQsuWLenZsyexlsP3dGyN38revcfMzDt+fpCWZv2Pw2Aw5PM40SM9T/TbvG65FHjcylzu\n6elp7NXXz+s9WAqagumPzcNjIHFxQvg1TWPl0ZVM/HkivzzyC4G+gTZjCLWq2oqLn1xkxMoRxCbH\nFhhryM/Pk7Aw0Xns7S0CYP3xh22vF3m9ejw9PfPtX1AMF72Hj367Nc8gy7goRZnqv8/iHqevoyPr\nLae27k1h+xfVLGDL68ZgMBQYj0Z+z/pt+mfYnntr65r0z2Furlj31lsf07696ZisLPP9/Pw0jh8v\nOF6WFH5/f6hZU+PyZbEcEFD49215Xyy/U/15LX/L1sqwdv1y/127gEpH8TL4UL9S/XznKella/NF\nxSHht+ehbt26NfHx8ezbt4/nn3+eftKgZ4WElQng/RHZ2ZOADYAQ/rLS4tc00bMVGAjJN5IZ+etI\nDD8ZqOpftdBjDecM/Pu+fzPghwFk5BTNXUcfrE2hcCWmNkBlszg80qtHT8VCXMxff11MO3YU+8oW\nv75D2B04cgSos44uNe7BQOnb9zds2MCkSZPIy8tjUlEi3elwSPjDw8OJl+Ozgfj4eCL0TwMQEBBA\nhVvRmHr06EF2djZXbDi73/343VD3boKCJgHRgGgVNGpU+je7KHh4wCu/vcKjzR/FEG9/3Z+IeoKm\nlZsyOWayXfvL1+u77ipOLRWKomMKDFiZypXF3MsvazRoUPSymjUTUy8vqFQJTpwQy+7Wn5ecDH1f\n3MBDrdy+RPcMAAAgAElEQVTDvh8dHc2kSZPw8PAoHeFv27Ytx48fJy4ujqysLJYsWUKfPn3M9klK\nSjK+quzYsQNN0wjVG8F1dAi/EyL+5uWXoUcPiI3VjK0AGQOnLLA9YTvr49YzKXpSkY+d1XMWX+/9\nmt3ndtu1v87SplC4HFObrQY1a4o5C1+OIuPpKVr8sr/AnZK1ZGZC+k2NLec23BYDtyQOefV4eXkx\na9Ys7r//fnJzcxkxYgSNGzdmzpw5AIwcOZJly5bx+eef4+XlRYUKFVi8eLHN8tqE3Qk1pjFunBgO\nrmkwcya8+iokJZmHeHU3TIP/NF7+7WWm3jsVf5+iv7NW9a/KjK4zGLNmDBqFd4rXrasGcilKhoQE\nyMgwEBgI167VoW5d4XrpaJgVKfwAXl4a6enu84afnAzBkYcI9A2kRtBt1MrS3ARAO5GQovGmn5ad\nm61pmqbl5eVpmqZpbdvmadu3m5b1WFtX0DYPD498y3I//bzl/ram8jxpaZoGN7Qfdv2mNZ7VWMvJ\nzbG6nz3rcnJztKgvojRDM0OB+8XEaNqvv2pa27aa9tRT1u+B3F9/XZb3wHK7wWCwuU2/vaD7K7f9\nU6euwNp3WZxtRZ3K43fs0LTIyDxNNMn2G8u397m2tq5p0zxt3jyx7bPPNO299/K0oUOLdn/tfcYL\nukd69PV89VVNaz36U23EihHGdZbnKelly/niyLhbCf/Jk5rm/WITbXfibuN6Dw8PrXt3TVu9uuCH\n0t51+puYl5en5eXlmW2z3F+KnJzm5uYa95X77NypaQZDey00NE/r8nUX7dt93xb4oOqPtaynZN2p\ndVrtj2trN7NvWt1PTjdv1m79EK3/OVmey/Kabd0jy3X6/fX3wHKqP/Z2m+opSESKur+9FLWRY882\na1j7o/Dw8NB++UXTevTQtPXrNe3kyfxl6hsMBd07/X6WQrZ6tXiWs7Lsr698Hq09o/Y+t5bI57h2\nbU27b14/zdDcemOnNJflfHGE361CNqSmQkBqe7YmmGePDwhwP99eyY4dIvSspm3CUHsjidcSGdxs\nsMPl3lPnHppWbspXe74qcD99bCNnJHVXKGyRlARhYWKEbp06rjnH/fcLc8+XX4pxPKVNUnIuuy/H\nQFxp18S5uJXwX70KFW/eybaEbWbr3Vn4//c/OefNzaiZjOs4Di8P5wQ9fbvL27y7+V0yc2zHXzbP\nYlTG4lsoygya5sMbbwjhdyUeHmLU73//K8K2lCY3bkBelb+pHlAdww336XdwBm4l/OPGQbh2Z74W\nv78/pKWVUqUKwTiUIfg0mVW2MrTFUKeVfUf4HTSv0pyv935tcx/z8VkFjI9XKByiGZcuYXThdCXl\ny4vRsjpP8VLh4kUo3+TP2yIapyVuJfy7dkGEb2MupV/i4o2LxvUBAcIMtHFjKVbOBh7yDradQ8WE\nx6jg7dwM0hPvnsiMv2aQlWvdn1WmYxS42cgXxW3BpUugaTsL3U9DIyYuhhmbZjD2f2N5e/3brDm+\nxuaza4ty5UQYh9IW/pQUyK25jq51upZuRVyAWwk/QFgVD9qHtzcz99y4ARMnGrj77lKsmA0MBsAr\nA6LmUzNptNPLbx/RnoYVG7LowCKr26tVE7Z94UuthF/hfGSuWbA+GlfTNH449AM8Dy+sfYHLNy9T\nK6gWeVoe0/+aTr1P6zF391y7Y3aVKyeeaenXX1pcTs0kveJW7q7thsLjIG6XgWv8eAOf7hd2/j4N\n+5CTk8O4cabtmmbAYDCFi7CWNamgddZidBSUoUfGqZFTGeNHZv2ZPh1o+gOca0P7SFOcbstsYHr0\nGYMs97e27pU7X+G131/jsZaP2SzX3x+2bj1gVvecnJx85yrqPdKXJdHfg4Ku1db2sjrVU1DGp6Ls\nv3GjyEdrT0ifomQzs3ebNSzrmpEhpsOHm0IzyG2pGak8vuJxTl45ybqx66ymJdx9bjejV43mx8M/\nsnjgYrPYT9YyYfn6iuPtbfHL59HaM1qc51au231hB/4ZjQguF2zz+5OxguQ1eXl5GX93tva3d1kf\nOwwKjzFUFNyqxT95sghw1iGig5md/733xMjdChXcK27PwYMwYQIQ9RXsHknz5q45T/d63cnT8vjj\n1B8293HnfpB/Anl5hY8uz87WhzwQ3H23+yfUkaN1IyJ0pk3g3PVz3PnVnVT3r87Op3fazEXbpnob\ntozYQoOKDej8dWfOXy/4guV9TEoyBXIrDRZt/5Mq6beffR/cTPhlR2X78PbsOrfLmJ3Kw0PE7wgM\ndC/vnpgYIPg0VI6F4z2N8fKdjcFg4OU7X+bDbR/a3MffX/SDLFnimjooCmbixMJHsFapAq+8YlqW\nlg93D0dy4YKY6oNBnk09S5evu/BYy8f4T6//4OtV8MV7eXjxyQOfMKjJIB747gGuZthWdJmIpUcP\n+OUXR2tffA5cX8fpP5Xwuxwp/CHlQ6gRWIMDSQfMtl+4AKtWlULFbFCtGtByIX3rD4FcH4KCXHeu\nR5s/yt4Lezl08ZDV7f7+IgXekCH68BGKkuLvv82Xs7OFV4ieq1fNU3LKUBvulnHKkh07xFQK/9WM\nq/T4rgej2o7ijU5v2F2OwWDgX13+RXTtaAb8MIDcvFyr+8m3+mrVxPz48SL0eEmSlpUG1f4m51Sn\nkj1xCeGWwg9wZ0R+t06AZ54pwQoVQm6uBi0XMK67MHzWreu6c/l6+fLcHc/x4VbrrX5/f+GFAPDI\nI66rh8I60mydnS3s9StXCp/3mzehVSv45hux/dgx074yGJk7vcVa49CttoanJ2TlZjHwh4F0rdOV\nV+96tchlGQwGPuwunuGJG6wn2fXzEx285cuLezRjhvDrL0k2nfkLzrXh7Ted66XnLriv8NewLvzu\nxMHUrQT6eXNnrbbk5WkuDyI3qu0ofjzyo5mrq8Tf39TC/Osv19ZDkR/5lnXypJgmJYnpsWOwb59I\nVygTl0i7tRR+d+ybOXcOGjaEnTtF/StU0IiOhlf+9wrlvcvz0f0fFbtsTw9PFg1YxDf7vuG3k7/l\n2/7HH7B5sxB/eY9c2aiyxs/7/8A7oSuT7YuQXuZwO+GXWWXujBCePbKzSNNEhh7LHJ72elUU1evB\nVs+/3iVtY+pCItOFp43l9oIyD+kpbD/9ukoVKnF181Xm7JqTLxuTvz8cPQo1a4KPj31eC8W5D/Zi\n6bpn7ZqKM2+JI1mILLHX3RDMs78B/PHHekB8ByCiOoLJBFSxosm0U7lyfSC/8Bd2Lba2O3IPrN1n\ng8FARMRQjh2DwYPFuitXICn0R1YdX8XChxbiYfAwO0Z6nBT0PMupl5cXVfyqkDg7kWd+fYZrGdeM\n5wWRU/qOOzwpXz6/uayg67X3mbb8nvXLsuy569aSffgB47L++7bMiqWJmGeA8CLy8vJyStYt6R0k\nl61p0IQJE6zei8JwK+HXJ2BoXLkxyTeSSb6RbFwXHCzsoZaeEaVBVm4Wu9KX0ij70RI9r2GHgdm7\nZqN5mj+8f/8Ne/YYqFGjdD0hnMXZs6ZOxbKBEAiZP0JON28W0xs3xEfkJBKdQfKPwD1NPSIYz+nT\nQmzOpccxetVoFg1YRHC5YKecwXDKQNc6XXnjT+v9BOXLm1w6S/KtKD41HvyS4FybkjtpCeNWwq83\n9XgYPGgX3s5sIJeHh/jhuMOr8Rf/W8eNsw2p7FOzRM9rSDbQrEozaGK+ftQoMa1c2b0SWdjL5s3m\ngb/q1oVOZapfTTy88k/30iXRct126/FdvVpkmAoPBxDCuWeP2OaOnbuaFmpM8vPUM7kM/XEo4+4a\nR7vwdk49zwfdP2DF0RVsOrMp3za98H/0UcnlnVhzYg2c7A6a894m3Q23FX6w3sEbEOAewv/inGUQ\nO9DhJBTFYWz7sWjtNbNXvp49xbR8eTGVaRnLCj/+CGfOmF7L8/IMxuTb7sLRo+JP9exZkZlJIr4G\nkf9SCv/ixcLv/fRpsbxtm7g24fIrWvzDh4tt7unOGUqLFmIuvfnH+Hj68NKdLzn9LCHlQ5jZbSYv\nrH0hn5dP+fLiXktsZGx1OmtPrIUTPXj++ZI5X2ng3sJvpYPXHSJ15uTlQMMVEDugVIS/R2QP8IXN\n8ZuN66QpMy9P/GDcsRVZENZGabpbmOlGjWD6dNGSL1cOFiwQIbn1z6PezFalSv4Bh+HhoGkP0quX\naV2m7eCrpUgo9eoBFY/ya+q7fNXnK6Nd39kMbjoYP2+/fMEIy5eXneTCXa0kTJh5hrv4ae86ONmV\nTz5x/flKC7cWfsuBXOAewh8TFwNXa0NqrVI5v4fBA8MOAx9v+zjftsBAYQ4rK+aevDwxctXaG4o1\n4c/M1IfCLnn0rfN9+0RgQemqCfmFX88bb8hYNz1YvRruuQfgvNsKf63audDvCUbUnUSdEBcF4Ed0\nnH7ywCdMWDeB1IxU43r59mowvE779iXUdxURBZcj4Ya/XWE0yipuJ/z62BT6gVyyR7u0hd9gMLA0\nVph5QNhtLbdD0WMI2btOTlNjUlkft56zqbp3YSAkRAh/abf4Lb0prF0TwNSpBqpXNw8FIJHCP326\nwWjeW7cOHnjA5AufkJDjtJAH9ngu6R1KwsPF/jNnCnfH6tXF6Onu3UXFpfBLN9+gIOGgEBpaFRCJ\nRrp2rWoU/qVLcwp0XLCM71TYenuwFfulVq27OBz0CeT68HbP0XbHM7Ln2bWcGgwG2lRvQ6/IXkzd\nONW4TUaeXbZsDiEhJuF35Hotr9NyuVn/8nDiASCgwOvRH5Obm2vm0aT3xpEeOV5eXkVa1p/P0mNK\nf+533nmnWPfA7YTfkg4RHcw6eEtb+HPzcvn5yE94nxhAt27QppQ6/v19/Hm85ePM2jHLuO655+CJ\nJ8qWqUf6u1uz32qaKR6SjBApf/zyD/ehh3BZqAzLuoBo8VeuLNyKr12D2rWFHTo93UBWlqjfsGFi\nX2vCHxQEV66IH+7lyyI2VVaWGAcwYICBxETXX0th5ObCucyj/HRpOh/f8xXBQSUjE1Pvncr8vfOF\nVw3i7VVO9cLvSuJ9hX3/dsfthd+ygzcgANasMX+9Lkk2x2+mSoVq+N6oz2+/wcsvl049AMa0G8P8\nvfPF8HJg1ixhh5amnkPWozu4DV9/bfLUkC16S/POplvOHnLEtuzsk39sUhxczTXhak5KihDvGzdg\nyhQRTwbgjjs0o/DXumUBbNVKTIUnj2jtB9/yhJR/CiEhwnwlXVfdIQjhseO5GB4awcS7J/LiY/VK\n7LzVAqrxdOunmRIzBTAX/uBgcW9zckyNBWdzOuU06R4XIKG9a07gRri/8Ft08Pr7wxdfwOOPl1y9\n9CyLXUavOqXTqWtJnZA6RNeOZsG+BWbry5cXfv3NmpVSxaywceOt2Ea3OH0annzS5PUiBU/vspeW\nBn/+Keb//lv88OWbgTSPlMT3MGoU/PyzmD9/3vzPJiJCvIFu2IBR+GULv21bMZV1li1+gC5dxDQ0\nVFzLrFsvbikpws1z5EiXXpJVYmLg11/hjZ8/JTTYk+faPVfidXi94+v8fPRnjl0+ZrxXAQEm4f/w\nQ6hWzTXG95+O/IR/Ym/QPNm61c08C5yMWwm/fgCXpEnlJmYDuaztU1LkaXksP7yc+2uUjhunNV5s\n/yKfbP+EPM1kHK5QwRQ6wF0Cth09Klq1suUsA3/Jlrs031kO0NO37l57zbS/sztET5821cmSOXMw\nenicP49ZML7y5UVjJEO7Rkb1P4gP+4J5x6YwecMUvtj7MW/M/4VRr4rmfFAQwlMG8acHQviXLROh\nxwHuukuI29y5zr2+woiNFUnUew8/zi9XpzGikuu8eAoipHwIL3V4ibfXv221xX/mjGlfZw/k/OnI\nT+QefIgLF0zhNW5X3Er4vbzyd7xYDuTSC8Hu3SVZO9iesJ2QciHUrNCoUOF3RpgEa+ssp51rdsbP\n24//nTC5ulSoYLKJp6biFiQni/pKgZf1kyYeuT4pyTzFZkqKqeP3yy9Npp4vvoB33wUoWuvv8mVz\n33DJypXwn/8Iwe3c2bReioucmgl/QCKb8z6g3bx21PwkHO6eAtX24OGVQ05eDqdSTrHXZzYj9zeB\n0S1YfuHfVK4tHuBOnYTYVqliyBeWIC7Oet1tdT47kpBD0qkTYMiDvk+ixUygcVhkocfYW5eiJLgB\n0ZjZeHYjR1LFCLeAAAPBweL7l3/8WVmio12fHcwRktKSOJB0gJux91G5cuHhTqyFqsjOzjaGb5HL\nOTk55Obmomka2dnZxnVyXi7Ljz5UA5gnY5HbLetSHNxK+G2FHNHb+ZNNERyM9t+SYlnsMgY0HkBm\nZsmYGOzBYDAwtsNYPt5ucu0sX14IGZgidpY2586JaWamGKz16adiWQq/nDZtavpemzQRQv3jj6Zy\nZKfu4sXw5psm98px40TntiW//QYf67xeX37ZZIPXk54u4sKcPi2C3EnzjPQYEoHKxB9TdqU90P9R\neLY5yRxm2r3TuPL6FTK/2EjeirlM7foOU+6Zwqc9PmXNo2s4OyYZVs3mXNZRWs5rwstrX+Gmx0Ua\nNzY9RwsXipDa8h6VCu1mgUGD7c+XmtMCgJ+PH+M7jWfC+rc4elS0+K9dE8+y7NuTHb0xMc4558qj\nK+lU9QHCw3ytepjdbrjVJVawEQFV79kzZozwXAFcHg1Tj6ZpLD+8nIFNBrqV8IMYALM/aT+xybGA\neSv/0iX38OnXt9QGDjQJq7Tt67LxMWeOCC0dHCyE31+XSjg5WbwZyv4CaZ754AOYPRu++078Uezf\nL/5AvvkGXnrJdH7z5PTm9UtONp1r507xZqB/xgLrHIOHB7ChWh+4EAWfnOLRgC/pVq8bPp4++PhY\nT6Ho7+eJIb4T8x78igOjD5CVm0XT2U35YtcXGDzEq0SfPuItJiDA3IRRUiOwc4NOijeWFfPpeq8n\njRqVzHlt8UybZzhy6QgXfMXrnxyZLhu88i3JWabMn478RBu/h4wd8bc7biX8lpE3JR0iOhgHcg0a\nBPPnC3tkSdqvd5/fja+XL82qNHM74ff18mVUm1F8ul00o2UHaZcuQvRs/aGWJLJOmZmixT1oEDRt\nfY3Uqr9CpxnQazT0fRIeHEVi3WmcCViCFhhPdra5WCcnC08Y+cdh6eI3dCgMGACvviquv74IhJkv\nUcrOnUJoJVL45R9EerruzcAvCXo9S3LvjpDYjjHacdjyKmQEc+edhV+7wSA80fz9oXpAdT7r+Rnr\nh6/nm33fMOH4PRAYT2CgaNmmp5t3cPv4iHECffsWfp7iEns4l2vRT8KmN+FyA5cmFLIXXy9fJkdP\n5s0/30TTNJo0gbfeEttCQkxvYs7QgEvpl9gSv4WamT1LtDFZmpQJ4Q8pH0J4YDgHLx40rouIKNkY\nJ9LMYzAY+Phj2x2BpcWotqNYcmgJl9MvG+9LUJApSFhphz+QYnblisY5/19I79ebwz3DyWnzMd6B\nKXCxGZztSHXP5uCTxkEWs7tNG3ixLp+ffBUitgHiIqQLpMTbO39HnzQtyXsh3yzkffj2Wxg92tRZ\nePOmufDfvAn4pMHdk/F8oQnklKPp+iOw+XUqBoohpUOHYnee5fvvN38baFalGZuf3MzQOx8g9M22\n/HL0FwwGYd6KFS9u7Nsnpq+9ZjLduYJhc94FDLBtLIBbCD+IrHOpGamsOi7S7skGTO3azhX+pYeW\n0iOyB08NCzA6H9zuOCz8a9eupVGjRkRGRvKedE2w4IUXXiAyMpKWLVvyt2XTS4f+ld6SOyPuZGu8\nya3T17fkhF/TNJbFLmNgk4HMnSvsy489VjLntpcw/zD6NuzLvD3zjPdF/xCXdmC7mzeB2ht4fHN7\nPO57m4FNBtBp6wVY8AcV9/wbdj7H9i9GcGD+c7wTPYNP7/qJ7vuTYPHPBFXwo+YLj+M9tgl0+IjA\nMPPRXg0b5j+fNJHIP4i0NGFOkvdGvkXUri2m6ekm8ccjh5/OzoXnG0Cloyzrvgv+9yEBXhUBkzA6\nmgrAw+DBxHvfZOX//ciYNWN444836D/AZPOS4wAkly+L/gpHvVmuXxcd2QBPT9nKHu9Pqbv3W2M0\nSuliW9p4engy7d5pjP9zPHlanrHxEBBgGvfgDFPYtwe+5ZGmQwFu28Qrljgk/Lm5uYwZM4a1a9cS\nGxvLokWLOHz4sNk+q1ev5sSJExw/fpy5c+cyevRom+VVqGA7GYblQC4fn5LrBNuftJ88LY9LB6KM\n/tUfWUlAZG8iD1sJKiyn1hJE2FoG4Q3xn53/ISNL/Bqk3bxGDUo10uX1zOvsr/UM9BtOo5SX6XZq\nN4+3epxynuIVT/7h168v3BsnTBCRK319DJDUgoldJhP36mG6Zc6F6rvZe3ddeGgY1NpI7Toafn7m\nYwTA9GxIsRgwAFq0MLXoLe9HejpgyGNP+s94PNeCrdcXw/e/wPLv6Rct4tSUKyf2DQoSeWDHjHHO\n/elYsyO7n9nNtoRtrPTrC77Wm50xMcJ0t2CB1c128/PPou5XM67y5ZVH4dc5PN7fZOP4/nvrx9nz\nfBf0zBanzD4N++Dn48eiA4uM352fn/Na/KdSTnH88nGa+HYnIkIE3bOG5W9TevZYhlWQyGV9kiaD\nwYCHhwceHh54e3ubLXvdGsSUm5uLh4eHWTIWuSzLcEbyIYeEf8eOHdSvX5/atWvj7e3NkCFDWLFi\nhdk+K1euZPit+LPt27fn6tWrJNkYelfQ9VgO5CrJFr8w8wzk/vtNX2xISMmcuyhEVYuiXkg9wrv9\nSIsWJuGvWLHkQtpacvDiQaLmRJGTl0Pgd/vxOTaE6tXEY+fjI/aRJj7Ljle53d9fPPC16Aw/fsuI\nGyfhfGtqjB6F99jGXG7wAZdvJpsdKzu49V5NsbHWhd/glcX2zG9gdHNOVJ9Klb0zabX/Tzjfxux7\nlkHDQkNh2jTTAC1nUKlCJX4f9jut6tYg5LUO9H3iRL59ZEvcWlaqopCUBBhy+b/l/wdHe8ORfsbv\n4M478/+JliYGg4EZXWfw9oa3eeyJLKZOda7wf7v/WwY1GUTKJe98QfVuZxwS/sTERGrIbA1AREQE\niRbBRqztk5CQUORzNanchJSbKSReE+WXZIt/2eFl3FttgNk6d43c92L7F7kc+RF792rGH0XVqrBo\nUcnXZcWRFdw15x7+1Wky1XfOJ6RCEHFxoj5gGown//AtB+dJk4ZcL72TqgZWhG0v8WPXQ8zv9yUZ\nQfvJGhUJQ/pC6y/B/7yx09fyD08K/6WULKi5CXo+By+HczboW8rHfEr2f3ZSI6Mnq3410KCBuchK\n4ZfmIWfj7enN/P6fM63P82xu2BHq/Gn88wPh3+/vn/+5P3xYBK6zlytXgK5vkZGTAb/NBEzOCgW8\nkJca0bWjiQyN5K/0L3nrLWEZkMLviKknJy+HeXvm8XSbp7l50/T9/hOwEiTBfuwdPGDvoINJkyYZ\nX5Gio6OJjo42bvMweBBdO5p1p9cxrOUwfH3FQJ9nn3VtvJbY5FhuZN2gWq5zMw+5ij4N+zB+3Xh+\nP/U7ubndARE0zOJFzOV8vvNzpm2axvU5q8iu1o6MDGEiOXtWBDkDk6Db8pu2FLi33hLeQMeOiWV/\nfwNta3aiY3InlnyZApGrocGv0O01uBkKF6LY51sLOlYBzQO8MljvHw+PHyMmfA/UjYTD/WHeTrha\nm473wR+HoGVL4fUTFGQeRqRBAzGt6eKka6PvGE24b2P6XhpCyInXSPr5ZcDAhQvi3Jb35eefixaq\neq/Hl9D0Bxb130HVx8WXIP9gbLm7ljbTu07nwe8fZHjL4QQH+xnzNzjS4v/12K/UCKyBz5VWZUr4\nNU1j0qRJDpXhkPCHh4cTr8ugER8fT4SFP5TlPgkJCYTbcJbVC7817q1zL+vihPD7+AgXuZkzRbAs\nV7H00FIGNB7A+fOmOu3d67rzOYqnhyeT7p7EhHUTyMntBhgIDXV9ZMMuXaB/fxg7FmbvnM17m9/j\nz6EbafRKXVJTha29cmVRDykusqVvy5vL0pRXv774yHy28g8kJQXICKFh1qMcXf4oeORCyAmo9jdJ\ngQnCHRMg14fss1FULz8Ij7/aknDC3F4n3waaNhXTv/4ybbtyRTQwunUrGVfe+xtGw7ztZD4zEAZt\ngxXziYsLIDw8/30pihnvh0M/sMlzIiyMocI7lYzrfXyECUjeU3ejdbXWdK7VmQ+2fkBo6NucOSO+\nB0eEf/bO2bTKfpamTeGnn8qO8BsMBjPhn1yMHmmHTD1t27bl+PHjxMXFkZWVxZIlS+jTp4/ZPn36\n9GHBrd6obdu2ERwcTFhYWLHO17VOV9adXoemacYWihP6OQrkh9gfGNR0kNE9EESL0J0Z1HQQGTkZ\nDJ/6K0uXmuKcuJJNm+CXX0yiP7X+ehqF1QWEK6Vs8YNJ6GWYBlsudLb6cGRnsLS/y3bFgQNiGhrs\nCZcbwsEhsOVVZt7/Pvz+PqybBrtGUyevGynn83fSSFNSr17CNKY3s4SEiGft7rsLuxPOwccHPNNq\n8VjuJsgIgafbsevsQSIi8rf4CxJ+TTP19Xz999e8uPZFel1dDVfqm4U39/EREUPd1YQJ8H639/l0\n+6doQafJyxN9LcU19Ry9dJS9F/ZSL1Pk1ShLLX5n4JDwe3l5MWvWLO6//36aNGnC4MGDady4MXPm\nzGHOnDkA9OzZk7p161K/fn1GjhzJ7NmzCyyzIPNRg4oNyMnL4WTKSWOry5WDk2KTY0nNSKVDRAej\nTbGgH4Zl3fW97/p5uV/2radWH6NDv6wvzzL5REHJKDwMHky5ZwrfJEzgof65JSL8AOcjhOivH76e\nP5fVNa5PSxPiHxoqlqVwyzq98gpYyycxcaJ1/3UpZNJEJIXP21uEom7dWizLH3ITi8T05cuL+lhG\nL/3sM+ExExlpCp9QWhgM4g+yYb1y8Mtc2uW8DsPv4VTEVG5mmaudLeHPzBSCPn5CDhPWTWDKxinE\nPEekO+kAAB+VSURBVB5DQLpouehDntjzFmOPabegZ7a4ZUpqBtXkpQ4v8WuOyP1bsWLxW/wz/prB\nmHZjyM0UrlqFCb9l8hhPT08zjx59MhZ7lvXJWvTLXl5eBS7LeXs9CG3hkKkHoEePHvSQQclvMdIi\npuysWbNwBgaDwdjqT00VQzJdOTBp6aGlDGwyEA+Dh1H43cnjoSD6NuzLzC0zmf/3fHqHP82xY7B9\nO9St66LX+bafExf+HgeHr6duSF2zVum1a8KMIq2AssUfHCx+vI8+ar3ITp1snKqtSdxBBFWT5h8Z\n3wdMeQks//TkD/zbb8195Tt2FB93YeFC8X0FBED/Oo+zY8a9JL/+DPtCl/Dg0Wn0btAbg8FgU/gP\nHYKckEMs9HyGZol+bB2xlar+VY0urq+8YtpX/3bjzrx616t8vq0ZRK5myJCenDkDP/wgwoDYG2Pn\nVMopfjn2CydfOMmUW31f16+rFr9bc2+de1l3eh0PPyySjrgyG9fS2KU83PRhwGSOuOWZ6vYYDAY+\n6/EZ/1r/L3wCU/D1FcLvCpe1z3d+Dp3epfMpIfpgbo64eFH4wIt8s6YW/6JFFCvjVJ065pFZly6F\n9etNy5Y++padsfIH7u7ue336iLeSa9duCXNqTd6IWEOL5Kn8a/2/aDO3DZ9t/4wLGXHIUc0AGTkZ\n/DfmT8asexQev4eI1CGsHbqWqv7CnSozU/RVyHEJUHaE39fLl6/6z6L2c88RHHaNnBwYPNjU4W8P\nU2KmMLrtaILLBRudHs6fd4/QJiVFmRX+Bg3zeOYZ1wn/4eTDXM24SoeIDoAwDSxfDtOnu+Z8riCq\nWhT9GvVjUsxEHn5YuP2BeUA0R/l85+e8u/ld+GY9wZrJvKMX/p9+EmIvs0/JFr+/v2s6Sp9+2jxS\np2UrXgpepVt9m02auNZBwBlIW3a5cgaqpPSld+Lf9Co3g+2J2zkRfSeMq0yT/zSh/qf1qfjvijzx\n3Zvs+LkdfHaM9PXPcybO9FPPyBBvridPisF9UHaEH+D++vfTrW43lqSONd6XnBxhuiosquj2hO38\ndvI3xnUcBwj9kOMCVIvfjakZVJPKfpXZdW4XAQG2OwYdZWmsycwDQvjLYotg6r1T+eHQD9wI2cbB\nW6GOrl8XUSwd5YtdX/Du5ndZP3w9pNQ1umdu25a/AzItzST8BYXmcAYTJpgyWkkSEky5eaWpQ9Z3\n6FD4179cWydHkcHm5PiVaVM9OLrqfr7t/y0h88/B7IMs7PMDqx9dze/dLsK8HdRIfJGKfsEcOmRu\n0srMNI2lkG9D7hR00B4+vP9DjmVu5LjPEkDEzvrlF5G9zBY5eTk8v+Z5pnedTqCv8AFPT4ewMJHb\nuVIl28febpQ54QfoFdmL1cdXExjouhb/0tilDGoyyLicnm7b7dCdqVShEv/p+R/WBz/GqQQRqez4\ncSF2jvDZ9s+Y8dcM1g83mXe8veHUKTH6U/aJyAiXBoNpvIUUnZIkPFy4mo4ebf7MbN0q1rs7/fuL\nVr+vrymIm/SSupluwPNmVf41shmfvN2A1EviQU1ONvWryAbS6tViVLMUOdmJXdaE39/Hn5cjlvJ3\nteeh+i5GjCg8X/HkDZMJLhfMYy1FoC1NE79rb2/xh/HIIyVQcTehTAp/z8ierDq+ioAA1wj/kUtH\nSLmZwp01TDF3i9Pi13s1WPNw8LjVG2Utpoelt0NhywUxoMkAanq250LLsYBmlsymOMzcMpOPt3/M\nxsc3UjekrtF05OtrSpQh7ez33286rls3IV4l5TJ4zz3mYRVee03E7Nc/Mx06lJ1XfC8v8ZFpNdPS\nhHjdvCnMd2vWiCxV8vu9ccM8gF1KinBV3b5ddI5/9hn07i222RtltCg4IzNYQUQGRFH30FwY0g8q\nHi1Q+H899itf/v0lCx5awM10DzIyTF5Psp+pIC9zy4xc+t+z/vcqvW9ctWypFcWlTAp/xxodOXHl\nBNm+F1xi6vlu/3c83PRhs5yjN26UzRa/5JHA/5AXvhXumG2MbFhUVzhN05i0YRLz9swj5vEYagWL\n5rw+rIFsjSYlidfvzz8Xy9KG7OWwH5n9LFkiRM6S0o5U6gj6lvnixaJjW+/ZlpUlwjnLsBLSvAXm\n+QdCQkSgtlq1xJ9xaeayLi7e3nB0RT9Y9w48Hk2il/WUfCuOrOCJFU/w8+CfqepflQYNxJuObMyV\nZHh3d6FMCr+3pzfd6nZj7401Tm/x52l5fHvgW4a1GGZcd+OG8Booy8JfKSAQFq2Eu99hfeKvQNEe\n+IycDIb9NIzVx1cT83gMEYGmEdoy9FJWlrlPuZ+fycWuNFrVHh7WXfzcMcCevXTuDFOnmpYHDxbT\nN94wrYuNNQl/hQomO/6WLaZ9ZJ8BlOyfsTO5du3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9zVn1XS+7rtGUk+M4pKcrzuPjAaGBkCYrQFOcG7tB1Orm+AGFLf8QDGlpUXSi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\n8ey+x4F93+Jht+fBcU+hTx86qs3KAoAahIYCvr6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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- What about a nonlinear function?\n", " - $y = x^2$\n", " \n", " " ] }, { "cell_type": "code", "collapsed": false, "input": [ "import syde556\n", "\n", "dt = 0.001\n", "x = numpy.linspace(-1, 1, 1000)\n", "A = syde556.Ensemble(neurons=25, dimensions=1)\n", "B = syde556.Ensemble(neurons=23, dimensions=1)\n", "decoder_A = A.compute_decoder(x, x**2)\n", "decoder_B = B.compute_decoder(x, x)\n", "\n", "x, X = syde556.generate_signal(1.0, dt, rms=0.3, limit=5, seed=2)\n", "\n", "spikes_A, x_A = A.simulate_spikes(x, decoder_A, tau=0.01)\n", "spikes_B, x_B = B.simulate_spikes(x_A, decoder_B, tau=0.01)\n", "\n", "figure()\n", "t = numpy.arange(len(x))*dt\n", "imshow(spikes_A.T, extent=(0,1.0,-1,1), aspect='auto', interpolation='none', cmap='binary')\n", "plot(t, x_A)\n", "plot(t, x)\n", "title('population A')\n", "\n", "figure()\n", "imshow(spikes_B.T, extent=(0,1.0,-1,1), aspect='auto', interpolation='none', cmap='binary')\n", "plot(t, x_B)\n", "plot(t, x**2)\n", "title('population B')\n", "\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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sOxB7b+5FakaqgyXmcBxL3KM4jN4xGqFzQuExwwNVf6mKYRuHFdqpW4C92DUc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\nv6/8jb41+zpAIg6Hw3FtCr3ibx/cHhdSLiA5Pdn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4OzXphENZh6rbDLu5UnoFn+z/BG/2exOdbnQSvvkG+P57sfzaa+LBrbGXlkpS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\nSjExMdS+fXs6YOx3JhuiEH6lv7k54Ve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"text": [ "" ] } ], "prompt_number": 160 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adding\n", "\n", "- What if we want to combine the inputs from two different populations?\n", " - $z=x+y$\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- We want the total current going into a $z$ neuron to be $J=\\alpha e \\cdot (x+y) + J^{bias}$\n", "- How can we achieve this?\n", "- Let's optimize again\n", " - sample over $$\n", " - find $\\omega$ for each connection that minimizes error\n", "- Can we do this more efficiently?\n", "- Again, substitute into the equation\n", " - $J_k=\\alpha_k e \\cdot (x+y) + J_k^{bias}$\n", " - $\\hat{x} = \\sum_i a_i d_i$\n", " - $\\hat{y} = \\sum_j a_j d_j$\n", " - $J_k=\\alpha_k e_k \\cdot (\\sum_i a_i d_i+\\sum_j a_j d_j) + J_k^{bias}$\n", " - $J_k=\\sum_i(\\alpha_k e_k \\cdot d_i a_i) + \\sum_j(\\alpha_k e_k \\cdot d_j a_j) + J_k^{bias}$\n", " - $J_k=\\sum_i(\\omega_{ik} a_i) + \\sum_j(\\omega_{jk} a_j) + J_k^{bias}$\n", " - $\\omega_{ik}=\\alpha_k e_k \\cdot d_i$ and $\\omega_{jk}=\\alpha_k e_k \\cdot d_j$ \n", "- Putting multiple inputs into a neuron automatically gives us addition!" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import syde556\n", "\n", "dt = 0.001\n", "x = numpy.linspace(-1, 1, 1000)\n", "A = syde556.Ensemble(neurons=50, dimensions=1)\n", "B = syde556.Ensemble(neurons=50, dimensions=1)\n", "C = syde556.Ensemble(neurons=50, dimensions=1)\n", "\n", "decoder_A = A.compute_decoder(x, x, noise=0.2)\n", "decoder_B = B.compute_decoder(x, x, noise=0.2)\n", "decoder_C = C.compute_decoder(x, x, noise=0.2)\n", "\n", "x, X = syde556.generate_signal(1.0, dt, rms=0.2, limit=5, seed=2)\n", "y, X = syde556.generate_signal(1.0, dt, rms=0.2, limit=5, seed=6)\n", "\n", "spikes_A, xhat = A.simulate_spikes(x, decoder_A, tau=0.01)\n", "spikes_B, yhat = B.simulate_spikes(y, decoder_B, tau=0.01)\n", "\n", "spikes_C, zhat = C.simulate_spikes(xhat+yhat, decoder_C, tau=0.01)\n", "\n", "figure()\n", "t = numpy.arange(len(x))*dt\n", "plot(t, x, label='$x$')\n", "plot(t, y, label='$y$')\n", "plot(t, x+y, label='$x+y$')\n", "plot(t, zhat, label='$\\hat{z}$')\n", "legend(loc='best')\n", "\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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pv/zyi109d2X/3tbBzp0weLDVhsWLRei0rgQEwLXXitdZ4eMjwkfJjkycq/czghUGg0Hp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\nmBVScPRUMQ+2ytopW7dCUJCx+Nyg+6NvmWfUGvdsgENXKssbb4jOzZp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"text": [ "" ] } ], "prompt_number": 102 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Vectors\n", "\n", "- Nothing changes" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import syde556\n", "reload(syde556)\n", "\n", "dt = 0.001\n", "\n", "A = syde556.Ensemble(neurons=50, dimensions=2)\n", "B = syde556.Ensemble(neurons=50, dimensions=2)\n", "C = syde556.Ensemble(neurons=50, dimensions=2)\n", "\n", "x = numpy.random.normal(0, 0.5, size=(2,1000))\n", "decoder_A = A.compute_decoder(x, x, noise=0.2)\n", "\n", "decoder_B = B.compute_decoder(x, x, noise=0.2)\n", "decoder_C = C.compute_decoder(x, x, noise=0.2)\n", "\n", "x = numpy.zeros((2,1000))+numpy.array([0.25, 0.1])[:,None]\n", "y = numpy.zeros((2,1000))+numpy.array([0.1, 0.25])[:,None]\n", "\n", "#x = numpy.array([syde556.generate_signal(1.0, dt, rms=0.2, limit=2, seed=2)[0],\n", "# syde556.generate_signal(1.0, dt, rms=0.2, limit=2, seed=3)[0]])\n", "#y = numpy.array([syde556.generate_signal(1.0, dt, rms=0.2, limit=2, seed=4)[0],\n", "# syde556.generate_signal(1.0, dt, rms=0.2, limit=2, seed=5)[0]])\n", "\n", "spikes_A, xhat = A.simulate_spikes(x, decoder_A, tau=0.1)\n", "spikes_B, yhat = B.simulate_spikes(y, decoder_B, tau=0.1)\n", "\n", "spikes_C, zhat = C.simulate_spikes(xhat+yhat, decoder_C, tau=0.1)\n", "\n", "figure()\n", "plot(xhat[0], xhat[1], label='x')\n", "plot(yhat[0], yhat[1], label='y')\n", "plot(zhat[0], zhat[1], label='z')\n", "legend(loc='best')\n", "\n", "figure()\n", "title('first dimension')\n", "t = numpy.arange(1000)*dt\n", "plot(t, xhat[0], label='x')\n", "plot(t, yhat[0], label='y')\n", "plot(t, zhat[0], label='z')\n", "legend(loc='best')\n", "\n", "figure()\n", "title('second dimension')\n", "t = numpy.arange(1000)*dt\n", "plot(t, xhat[1], label='x')\n", "plot(t, yhat[1], label='y')\n", "plot(t, zhat[1], label='z')\n", "\n", "legend(loc='best')\n", "\n", "\n", "show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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PAl270uM9e4AHD4CoKNo/eswYTg4GgnsQEqsr74MxjfLyKBns20c1lBwdgZ9+ot3funcH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\ni8CECcDp07S/p5sb7RfdsSPw9ttUe4k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hCdhhYaXXplQprtb24AGwahXXyohkk4afH9C6NRAZya5EYiLQtCnfF+A1AvPy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\nLhu6KOUi4n4Xp7VOlJSZRD/5/FREvvWX11NUShR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xViAQlG9KKlvEmIKAycriVoGvLysEabvrSpWAXr3KNm0CgeBfQyiF/zrnzvEx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\nP/R/Zz8/Ls+sLKL8fH233bs5T5mZ/FxQoCs/Fxd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"text": [ "" ] } ], "prompt_number": 158 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Summary\n", "\n", "- We can use the decoders to find connection weights between groups of neurons\n", " - $\\omega_{ij}=\\alpha_j e_j \\cdot d_i$\n", "- Using connection weights is numerically identical to decoding and then encoding again\n", " - which can be much more efficient to implement\n", "- Feeding two inputs into the same population results in addition\n", "- These shortcuts rely on two assumptions:\n", " - the input to a neuron is a weighted sum of its synaptic inputs\n", " - $J_j = \\sum_i a_i \\omega_{ij}$\n", " - the mapping from $x$ to $J$ is of the form $J_j=\\alpha_j e_j \\cdot x + J_j^{bias}$\n", "- If these assumptions don't hold, you have to do some other form of optimization \n", "\n", "- If you already have a decoder for $x$, you can quickly find a decoder for any linear function of $x$\n", " - if the decoder for $x$ is $d$, the decoder for $Mx$ is $Md$\n", "- For some other function of $x$, substitute in that function $f(x)$ when finding $\\Upsilon$\n" ] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }