{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# SYDE 556/750: Simulating Neurobiological Systems\n", "\n", "Accompanying readings: Chapters 4, 5" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Temporal Representation\n", "\n", "- In the previous lectures, we covered representation of a vector space by a population of neurons\n", " - We converted a vector $x$ into neural activity values $a_i$, and then converted those back to the original value $\\hat{x}$. \n", "- What happens if $x$ changes over time? \n", " - I.e. if we have $x(t)$, how do we get $a_i(t)$?\n", " - Seems pretty easy:\n", " - $a=G[\\alpha e \\cdot x + J^{bias}]$, so...\n", " - $a(t)=G[\\alpha e \\cdot x(t) + J^{bias}]$\n", " - where $G[J(t)]= {1 \\over {\\tau_{ref}-\\tau_{RC}ln(1-{1 \\over J(t)})}}$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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yW7WN18Y45rCpZNebqI8x22onu96waC50OHhyPHcxrM9yNcpfCFwdEScDV5fP\nl2sCr42IpwNnA/9d0iE9+98WEaeVPw4mtl+anqjTnB+9XmXN+bYHNVZQroByDnBZ+fgy4BXLD4iI\nWyPitvLxD4D7gSOSldAsgcnx2mhmKK7yqqRcAeXIiLinfHwvcOSuDpZ0BtAAvtuz+b2Svinp/ZIm\ndvHa8yVtlrR527ZE83GZrdH0RG0kM5S5BXcbrqKBBRRJX5R00wo/5/QeFxHB0pSIK55nPfDHwOsi\nojtA4B3AU4EfBw4D3r7a6yPikoiYiYiZI45wgmPDZapRH9EMpe1uwxU0sDsaERtX2yfpPknrI+Ke\nMmDcv8pxBwF/DbwzIq7pOXc3u5mX9DHgrX0sulky0xM15lqjlaF0FoMdC4vuNlxBuaq8NgHnlY/P\nA/5y+QGSGsBfAJ+IiCuW7Vtf/iuK9pebBlpaswEpMpTRCijdiSG9uFb15AooFwMvknQbsLF8jqQZ\nSR8pj3k18FPAr0q6ofw5rdz3J5JuBG4EDgcuSlt8s/6YbtRojliVV/f9ei2U6slyRyPiAeCFK2zf\nDLyhfPxJ4JOrvP6sgRbQLJGpiTqzI9Yo3+2E4G7D1ePJIc0ymhofxQzFy/9WlQOKWUZTE3WarQ6L\ni6t2dKycuYUigE6N2ISYo8ABxSyj6fJb+twIrcHSreJzhlI9DihmGXW/pTdHqKdX972623D1OKCY\nZdTNUEapHaVb5TXtKq/KcUAxy6g7WnyUenq5Ub66HFDMMuoO7hulDKXbbXjSAaVyHFDMMup+Sx+l\n0fJLGYrbUCrHlZhmGXWrvJrz+TKUiOCfv/9Qsmq3W+9/lEZ9jHrN32erxgHFLKPpbhtKxgzlhrse\n5hc+/E9Jr7nhkMmk17M0HFDMMpoagjaU+x6ZB+B9r3omxx+eZvnjDYekW2bZ0nFAMcuom6HkHIfy\nyNwCAM8+8TCOPtQf9Lb3XIlpltG68TGkvG0o28uAcvDkeLYyWDU4oJhlJInpzGuibJ9boDYmDvBA\nQ9tHDihmmU1lXhNl+9wCB62rU6xXZ7b3HFDMMptq1LKOlN8+t+DqLusLBxSzzKYa9ewZigOK9YMD\nillm0xP5M5SDHFCsD7IEFEmHSbpK0m3lv4euclynZz35TT3bT5B0raQtki6X1EhXerP+mmrUaWZc\nD8UZivVLrgzlQuDqiDgZuLp8vpK5iDit/Hl5z/bfBd4fEScBDwGvH2xxzQZneqKWvduwA4r1Q66A\ncg5wWfkf6ISSAAAMEElEQVT4MuAVa32hiq4oZwFX7M3rzYZN0YaSJ0OJCAcU65tcAeXIiLinfHwv\ncOQqx62TtFnSNZK6QeNJwMMR0f1KtxXYsNqFJJ1fnmPztm3b+lJ4s36abtSYzdQoP9vq0FkMBxTr\ni4GNZJL0ReDJK+x6Z++TiAhJscppjouIuyWdCHxJ0o3A9j0pR0RcAlwCMDMzs9p1zLKZbNSX1ghJ\nzaPkrZ8GFlAiYuNq+yTdJ2l9RNwjaT1w/yrnuLv893ZJXwFOBz4DHCKpXmYpRwN39/0NmCUy3ajR\n6izSai/SqKetNNjedECx/slV5bUJOK98fB7wl8sPkHSopIny8eHAc4GbIyKALwOv3NXrzfYXU+WU\nJ3MZ2lGcoVg/5QooFwMvknQbsLF8jqQZSR8pj3kasFnSNygCyMURcXO57+3AWyRtoWhT+WjS0pv1\n0XS5amNzIX07SjegeByK9UOW2eAi4gHghSts3wy8oXz8j8Cpq7z+duCMQZbRLJVuhpJjcOMjzlCs\njzxS3iyzpQwlQ0+vpSqvKQcU23cOKGaZddeVz5GhbJ9bYExwQMNT19u+c0Axy2wqc4Zy0OQ4Y2Oe\nut72nQOKWWbT5bryORbZ8ih56ycHFLPMulVeOebzckCxfnJAMctsuhtQnKHYfs4BxSyzyYxtKI94\nLRTrIwcUs8wa9TEatTG3odh+zwHFbAhMZVgTxVPXW785oJgNganxWvIMpdnq0PbU9dZHDihmQ2Bq\nop68DcUTQ1q/OaCYDYHpRi35SPluQDnEAcX6xAHFbAhMNerJp693hmL95oBiNgSmJ9IvA+yp663f\nHFDMhsBUo558YKMzFOs3BxSzITA9UWM2cbfhRzx1vfWZA4rZEJgcz5OheOp66ycHFLMh0G1DiYhk\n1/TU9dZvWQKKpMMkXSXptvLfQ1c45gWSbuj52SHpFeW+j0v6Xs++09K/C7P+mWrUiYAdC4vJrulR\n8tZvuTKUC4GrI+Jk4Ory+eNExJcj4rSIOA04C2gCf9tzyNu6+yPihiSlNhuQ7pooKQc3OqBYv+UK\nKOcAl5WPLwNesZvjXwn8TUQ0B1oqs0ymMkxh74Bi/ZYroBwZEfeUj+8FjtzN8ecCf7ps23slfVPS\n+yVN9L2EZglNN7qrNqbNUDwGxfppYN07JH0RePIKu97Z+yQiQtKqLZGS1gOnAl/o2fwOikDUAC4B\n3g68Z5XXnw+cD3DsscfuwTswS2dqovivmHL6lUecoVifDSygRMTG1fZJuk/S+oi4pwwY9+/iVK8G\n/iIiFnrO3c1u5iV9DHjrLspxCUXQYWZmJl0XGrM9MJ14kS1PXW+DkKvKaxNwXvn4POAvd3Hsa1hW\n3VUGISSJov3lpgGU0SyZ7qqNqTKUuYUOCx1PXW/9lSugXAy8SNJtwMbyOZJmJH2ke5Ck44FjgK8u\ne/2fSLoRuBE4HLgoQZnNBmbnuvJpMhRPu2KDkGWIbEQ8ALxwhe2bgTf0PL8D2LDCcWcNsnxmqU1N\ndBvl02QoDzcdUKz/POeC2RDoZigPzbaWsodBunf7DsABxfrLAcVsCEyO16iPiT+86lb+8Kpbk133\n0KlGsmtZ9TmgmA2BsTHxf147w+0/nE12zYMnx3na+gOTXc+qzwHFbEi84Kn/ghfkLoTZPvBsw2Zm\n1hcOKGZm1hcOKGZm1hcOKGZm1hcOKGZm1hcOKGZm1hcOKGZm1hcOKGZm1hcOKGZm1hcOKGZm1hcO\nKGZm1hcOKGZm1hcOKGZm1hcOKGZm1hcOKGZm1hdZAoqkV0n6lqRFSTO7OO5sSd+RtEXShT3bT5B0\nbbn9ckleds7MLLNcGcpNwM8Df7faAZJqwIeAlwKnAK+RdEq5+3eB90fEScBDwOsHW1wzM9udLAEl\nIm6JiO/s5rAzgC0RcXtEtIBPAedIEnAWcEV53GXAKwZXWjMzW4thXgJ4A3BXz/OtwLOBJwEPR0S7\nZ/uG1U4i6Xzg/PLpY5J2F8hWczjww7187f5sFN/3KL5nGM337fe8Nset5aCBBRRJXwSevMKud0bE\nXw7qustFxCXAJft6HkmbI2LV9p6qGsX3PYrvGUbzffs999fAAkpEbNzHU9wNHNPz/Ohy2wPAIZLq\nZZbS3W5mZhkNc7fh64CTyx5dDeBcYFNEBPBl4JXlcecByTIeMzNbWa5uwz8naSvwE8BfS/pCuf0o\nSVcClNnHBcAXgFuAP4uIb5WneDvwFklbKNpUPpqg2PtcbbafGsX3PYrvGUbzffs995GKL/xmZmb7\nZpirvMzMbD/igGJmZn3hgLIGq00BUyWSjpH0ZUk3l9Pi/Hq5/TBJV0m6rfz30Nxl7TdJNUlfl/S5\n8nnlp/aRdIikKyR9W9Itkn6i6vda0m+Wf9s3SfpTSeuqeK8lXSrpfkk39Wxb8d6q8MHy/X9T0rP2\n5doOKLuxmylgqqQN/MeIOAU4E3hT+T4vBK6OiJOBq8vnVfPrFB0/ukZhap8PAJ+PiKcCz6R4/5W9\n15I2AG8GZiLiR4EaRc/RKt7rjwNnL9u22r19KXBy+XM+8OF9ubADyu6tOAVM5jL1XUTcExH/XD5+\nlOIDZgPFe72sPKxy09xIOhr4aeAj5fPKT+0j6WDgpyh7R0ZEKyIepuL3mmLc3aSkOjAF3EMF73VE\n/B3w4LLNq93bc4BPROEaijF+6/f22g4ou7fSFDCrTvVSBZKOB04HrgWOjIh7yl33AkdmKtag/Hfg\nt4DF8vkeTe2znzoB2AZ8rKzq+4ikaSp8ryPibuAPgO9TBJLtwPVU/153rXZv+/r55oBijyPpAOAz\nwG9ExCO9+8pBpZXpZy7pZ4D7I+L63GVJrA48C/hwRJwOzLKsequC9/pQim/jJwBHAdM8sVpoJAzy\n3jqg7N5qU8BUjqRximDyJxHx5+Xm+7opcPnv/bnKNwDPBV4u6Q6KqsyzKNoWDimrRaCa93srsDUi\nri2fX0ERYKp8rzcC34uIbRGxAPw5xf2v+r3uWu3e9vXzzQFl91acAiZzmfqubDv4KHBLRPxhz65N\nFNPbQMWmuYmId0TE0RFxPMV9/VJE/DIVn9onIu4F7pL0lHLTC4GbqfC9pqjqOlPSVPm33n3Plb7X\nPVa7t5uA15a9vc4EtvdUje0xj5RfA0kvo6hrrwGXRsR7Mxep7yT9K+DvgRvZ2Z7wnyjaUf4MOBa4\nE3h1RCxv8NvvSXo+8NaI+BlJJ1JkLIcBXwd+JSLmc5av3ySdRtERoQHcDryO4gtmZe+1pN8BfpGi\nR+PXgTdQtBdU6l5L+lPg+RTT1N8HvBv4LCvc2zK4/k+K6r8m8LqI2LzX13ZAMTOzfnCVl5mZ9YUD\nipmZ9YUDipmZ9YUDipmZ9YUDipmZ9cXA1pQ3qwpJT6KYUA/gyUCHYuoSgGZEPGcA1zwduCAi9mmy\nQkkXUJTx0v6UzGx17jZstgck/TbwWET8wYCv82ngooj4xj6eZwr4h3KKFbOBcpWX2T6Q9Fj57/Ml\nfVXSn0m6VdLFkn5Z0tck3SjpR8rjjpD0GUnXlT/PXeGcBwLP6AYTSb8t6TJJfyvpDkk/L+n3yvN+\nvpwyh/KaN5frWvwBQEQ0gTs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "import numpy\n", "\n", "n = nengo.neurons.LIFRate()\n", "\n", "x = numpy.zeros(100)\n", "for i in range(10):\n", " x[i*10:(i+1)*10]=numpy.random.uniform(-1,1)\n", "\n", "figure()\n", "title('$x$ value changing over time')\n", "plot(x)\n", "ylabel('$x$')\n", "ylim(-1,1)\n", "xlabel('Time (ms)')\n", "\n", "figure()\n", "title('Firing rate changing over time')\n", "plot(n.rates(x, gain=1.5, bias=1))\n", "ylabel('Firing rate (Hz)')\n", "xlabel('Time (ms)')\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Unfortunately, that formula for $G[J(t)]$ is an *average* firing rate over a long period of time.\n", " - What does it mean to be firing at 10Hz for 10ms?\n", "- We need to model what's actually happening to that neuron over time " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Leaky Integrate-and-Fire neurons\n", "\n", "- Pretty much the standard computationally efficient neuron model\n", " - Simple\n", " - Produces spikes\n", " - Limiting case of other more complex neuron models\n", " - All parameters map onto known properties of real neurons\n", " \n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "\n", "- Bilipid cell membrane acts as a capacitor\n", "\n", "- Flow of ions through the cell membrane ion channels is a resistor\n", " - This is the \"leak\" current\n", "- Resistance and capacitance together give $\\tau_{RC}$\n", " - $\\tau_{RC}=R C$\n", "- When voltage passes some threshold, neuron emits a \"spike\"\n", " - Very fast, sharp response that's pretty much the same each time\n", " - Spike at time $t_n$ modelled as $\\delta(t-t_n)$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Neuron recovers over a short period of time\n", " - Refractory time $\\tau_{ref}$\n", " - During this time the voltage is reset to some resting level\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- As an RC circuit with a nonlinearity:\n", "\n", "\n", "\n", "- Typical values\n", " - $\\tau_{RC}$: 0.02 seconds\n", " - $\\tau_{ref}$: 0.002 seconds\n", " - Reset voltage (a.k.a. resting potential): -70mV\n", " - Firing threshold (a.k.a. threshold potential): -55mV\n", " - NOTE: we normalize this so that reset is at 0 and firing is at 1\n", " - This does not affect anything about the behaviour of the model\n", " \n", "- For lots more info, see Unit 2 in [this online course](http://www.saylor.org/courses/bio303/)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The LIF RC circuit\n", "\n", "- Let's ignore the spiking elements for now, so here's the circuit\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Useful physical laws\n", "- Kirchhoff's Current Law\n", " - Currents at a point have to add up to zeros\n", " - Current coming into the neuron has two paths\n", " - $J_{M} = J_R+J_C$\n", " \n", "- Ohm's Law\n", " - Formula for current through a resistor\n", " - $ J_R = {V \\over R}$\n", " \n", "- Capacitor\n", " - $ C = {Q \\over V}$\n", " - $ Q = C V $\n", " - Change in these quantities over time gives\n", " - $ {{dQ} \\over {dt}} = C {{dV} \\over {dt}} $\n", " - Rate of change of charge is current\n", " - $ J_C = C {{dV} \\over {dt}} $\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ " \n", "- Applying these laws to RC circuits:\n", " - $ J_{M} = {V \\over R} + C {{dV} \\over {dt}} $\n", " - Then solve for change in voltage with input\n", "\n", "$$\n", "\\begin{align}\n", "{{dV} \\over {dt}} &= {1 \\over C}(J_{M} - {V \\over R}) \\\\\n", " &= {1 \\over {RC}}[R J_{M} - {V}] \\\\\n", " &= {1 \\over {\\tau_{RC}}} [R J_{M} - {V}] \n", "\\end{align}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### LIF RC Circuit Behaviour\n", "- If we solve the general ODE, we get a convolution:\n", "\n", "$\n", "\\begin{align}\n", "V(t) = \\frac{R}{\\tau_{RC}} \\int_0^t e^{-(t-t')/\\tau_{RC}} J_M(t')\\; dt'\n", "\\end{align}\n", "$\n", "\n", "- I.e. the voltage right now (at $t$) depends on all past current input, $J_M(t')$, where each input is weighted by a function that exponentially decays as it gets further away (in the past) from the current time (a kind of memory).\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- If $J_M$ is constant:\n", "\n", "$\n", "\\begin{align}\n", "V(t) &= \\frac{R J_M}{\\tau^{RC}} e^{-t/\\tau_{RC}}\\int_0^t e^{t'/\\tau_{RC}} \\; dt' \\\\\n", "&= J_M R (1-e^{-t/\\tau_{RC}}) \\end{align}\n", "$\n", "\n", "- How long does it take to get to threshold?\n", "- How long between spikes?\n", "- Firing rate? \n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- How long does it take to get to threshold?\n", " - $ V_{th} = J_MR(1-e^{-t_{th}/\\tau_{RC}}) $\n", " - $ t_{th} = -\\tau_{RC} ln (1-{V_{th} \\over {J_MR}}) $\n", "\n", "- How long between spikes?\n", " - $t_{th} + \\tau_{ref}$\n", " \n", "- Firing rate\n", " - $a = {1 \\over {t_{th} + \\tau_{ref}}}$ \n", " - $a = {1 \\over {\\tau_{ref}-\\tau_{RC}ln(1-{V_{th} \\over {J_MR}})}} $\n", "\n", "- Simplify by assuming $V_{th}=1$ and $R=1$\n", " - $a = {1 \\over {\\tau_{ref}-\\tau_{RC}ln(1-{1 \\over J_M})}} $ \n", " - This is the rate approximation of the neuron\n", " \n", "- But we can't assume a constant $J_M$ in a real brain!\n", "- It will definitely change over time (since $x(t)$ also changes over time)\n", "- So we need to do a computer simulation of the differential equation explicitly\n", " - $ {{dV} \\over {dt}} = {1 \\over {\\tau_{RC}}} [R J_{input}(t) - {V(t)}] $\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Spikes\n", "- When simulating the LIF neuron, we need to monitor threshold, as that when the 'spike' occurs\n", "- A LIF neuron treats all spikes the same, and just 'pastes' them in \n", " - As opposed to simulating the nonlinear differential equations that describe the actual voltage changes" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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Fkj/5ch6bmc3zVSICGdpCpYDX6deNIC7kWlmsFrGWWhMpYahKaUrs7FRqFawm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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "from nengo.utils.matplotlib import rasterplot\n", "\n", "model = nengo.Network(label='Spiking Neurons')\n", "\n", "with model:\n", " stimulus = nengo.Node(0)\n", " ens = nengo.Ensemble(1, dimensions=1, \n", " encoders = [[1]],\n", " intercepts = [-.5],\n", " max_rates= [100])\n", " \n", " nengo.Connection(stimulus, ens)\n", " \n", " spikes_p = nengo.Probe(ens.neurons, 'spikes')\n", " voltage_p = nengo.Probe(ens.neurons, 'voltage')\n", " stim_p = nengo.Probe(stimulus)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(.5)\n", "\n", "t = sim.trange()\n", "figure(figsize=(12, 8))\n", "ax = gca()\n", "ax.plot(t, sim.data[voltage_p],'g')\n", "rasterplot(t, sim.data[spikes_p], ax=ax)\n", "ylim((0,2))\n", "ylabel(\"Voltage\")\n", "xlabel(\"Time\");" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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SEWRzaqurN6O8qLXcFgwQEXGRpDrwioh4USGtqYCmZ8nupl53BtHPWeagifrc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\n3kZJn5P0o/znhCGveQ/gYb3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4dyCnk0+zsPfCSx9ccJS2IkIj/OYK7Od9P7P3jONmo4QUHX+woDHG8H+//B/vrnyX9jXb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\n0dgNYykfUZ57a9+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from nengo.utils.functions import piecewise\n", "\n", "x = dict(zip(np.linspace(0,.1,10), np.random.uniform(-1,1,10)))\n", "\n", "with model:\n", " stimulus.output = piecewise(x)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(.1)\n", "\n", "t = sim.trange()\n", "\n", "figure()\n", "title('$x$ value changing over time')\n", "plot(t, sim.data[stim_p])\n", "ylabel('$x$')\n", "ylim(-1,1)\n", "xlabel('Time (s)')\n", "\n", "figure()\n", "title('Firing rate changing over time')\n", "plot(ens.neuron_type.rates(sim.data[stim_p], gain=sim.data[ens].gain, bias=sim.data[ens].bias))\n", "ylabel('Firing rate (Hz)')\n", "xlabel('Time (ms)')\n", "\n", "figure(figsize=(6, 3))\n", "ax = gca()\n", "rasterplot(t, sim.data[spikes_p], ax=ax)\n", "ax.plot(t, sim.data[voltage_p],'g')#, drawstyle='steps-post') #if want to see exact timing\n", "ylim((0,2))\n", "title('Voltage and spikes over time')\n", "ylabel(\"Voltage\")\n", "xlabel(\"Time (s)\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "- Let's try a sine wave input" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "text/plain": [ "(-1, 2)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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PgpENwQfWx2iuy2qs2LhKz9+De8UzKjOJxxfkM/WfC7j51VUs2V6B1tr33FuM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\nYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#have to run previous cells\n", "\n", "with model:\n", " stimulus.output = lambda t: np.sin(10*t)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(.6)\n", "\n", "nengo.utils.matplotlib.plot_tuning_curves(ens, sim)\n", "\n", "t = sim.trange() \n", "figure(figsize=(10,4))\n", "plot(t, sim.data[stim_p], label='x')\n", "ax = gca()\n", "ax.plot(t, sim.data[voltage_p],'g', label='v')\n", "ylim((-1,2))\n", "ylabel('$x$')\n", "xlabel('time (s)')\n", "legend(loc='lower left');\n", "\n", "rasterplot(t, sim.data[spikes_p], ax=ax.twinx(), use_eventplot=True)\n", "title('Voltage and spikes over time')\n", "ylabel(\"Voltage\");\n", "xlabel(\"Time\");\n", "ylabel('$neurons$')\n", "ylim((-1,2))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- So this is how we're going to model neurons over time\n", "- Weaknesses of this approach\n", " - These are \"point\" neurons (i.e. we're assuming the body of the neuron is just one infinitessimal point, rather than having lots and lots of compartments, each with its own RC circuit)\n", " - Assumes R is a constant\n", " - Assumes $V_{th}$ is a constant\n", " - Assumes no adaptation (it's harder for a neuron to fire after it has recently fired)\n", " - Doesn't consider nonlinearities at the input\n", "- Each of these could be added\n", " - Adding these increases computational cost\n", " - Not going to worry about it now\n", " - But we should make sure everything we do would also work with more detailed neuron models\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ " \n", "### The time vs. rate-coding debate\n", "\n", "- There is a standard ongoing debate in the neuroscience literature about whether neurons use a \"rate\" code or a \"timing\" code\n", "- Rate code\n", " - The important thing is the firing rate over some window of time (~100ms)\n", "- Time code\n", " - The *precise* pattern of spike generation carries information\n", "- The NEF gets rid of this distinction\n", " - Some people call what we do rate coding, some call it temporal coding\n", "- The important thing is how to do the decoding usefully ... in short:\n", " - 'Slow' decoders will seem like a rate code\n", " - 'Fast' decoders will seem like a time code" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Temporal Decoding\n", "\n", "- So that's what happens when we allow $x(t)$ to vary over time\n", " - We keep $J(t)=\\alpha e \\cdot x(t) + J^{bias}$\n", " - Feed that into the neuron model $G[J(t)]$\n", " - We get out a sequence of spikes\n", " \n", "- How do decode this?\n", " - How do we get an estimate of $x$ given that sequence of spikes?\n", " \n", "- Can we stick with linear decoding?\n", " - Let's consider a case with 2 neurons\n", " - For simplicity, use the same $\\alpha$ and $J^{bias}$, but use $e_1=1$ and $e_2=-1$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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Udpm3e9fn/X4NKeidz0cIFyxkXFzV9U04tAzm94T4y1anEm7GET8lrwAvKKVO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\nHXC8cpQLuHGH7ZYdL6AOUNu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jO5bkI62rt+aLG78gKTWJy4ZdRkLSft+RREREclxuuUG3KzDROZeWads5zrlYoDvwspmd\nd6yBZnZz4EvB0tTU1JzImu8dTjlMpwmdeOWrV6hQpAK1StekYHhB37EkH2pYviGL+i6idKHSfLd9\nBbsO7fIdSUREJEf5LPubgUqZ1isGth1LV466hMc5tznw8ydgLn++nj/zfkOcc7HOudiwMG+3KOQb\n+47so/mo5ny49kNebvEy1UpUA3QjrvhTtXhVvrzpSwpHFGb1ztW89vVrviOJiIjkGJ9lfwlwvplV\nNbMIMgr9X2bVMbMLgeLAokzbiptZZOB1KeAyYM3RYyVnbT2wlSYjmvDVpq8YGz+WAY0G+I4kAmQ8\ncfeimIsoGVWSO2feyf2z78c55zuWiIhItvN2qts5l2pmdwCzgFBgmHNutZk9Dix1zv1e/LsCY92f\n/8tcA3jbzNLJ+MLybOZZfCTnbdizgeajmrP94Hamd59Os/Oa+Y4k8ichFkKtMrW4osLfee7L59hz\neA9vXv8moSGhvqOJiIhkG6/XtTjnZgAzjtr28FHrjx5j3EKgTraGkyz7btt3tBjVgpT0FD7v/TkX\nV7jYdySRYzKMN69/k5JRJXl6wdMkJCXwbod3iQiN8B1NREQkW+gidjkjC35bQOv3W1Mksghzes+h\nRukaviOJnJCZ8dQ1T1GsQDHunX0vCUkJTOw8UTeRi4hInpRbZuORIDT7p9k0f685ZQuX5cubvlTR\nl1zlnsvuYUjrIXy8/mNajmrJ/iOamlNERPIelX05LTN+nEHr91tzfsnzmddnHpWLVvYdSeSU9W/Y\nnzFxY1i0aRFXv3s1OxN3+o4kIiJyVqnsyyn7cO2HtB/bntplavP5DZ/rYVmSq3Wp3YWpXafy/c7v\nuWrkVWw/uN13JBERkbNGZV9OyfjV44kfH0/D8g2ZfcNsShYs6TuSyBm77vzrmN59Oj/v+5mrRl7F\ntoPbfEcSERE5K1T2Jcu2J26n26RuNK7UmE96fkKxAsV8RxI5a66qehUzus/gt/2/0XREU5LTkn1H\nEhEROWMq+5Il2w5uY+2utTSt0pSZPWZSJLKI70giZ12TKk34uOfHbD6wmeXblpOcluQ7koiIyBlR\n2ZeTemvpW6zbvY4SUSX4qNtHFIoo5DuSSLa5vPLlzOo5i+S0ZJZtW87G/Rt9RxIRETltKvtyQu98\n+w63Tr+VklElqV26FlHhUb4jiWS7xpUaUzemLilpKTQZ0YRf9/3qO5KIiMhpUdmX4xq5fCQ3T7uZ\nltVaUqt0Tcz0fxfJP6Ijo7mo7EXsPbKXpiObqvCLiEiupPYmx/T+yvfpM6UP15x7DR90/kBFX/Kl\nIhFFmN1rNvuO7OOad69hy4EtviOJiIicEjU4+YsJqyfQa3IvmlRpwpSuU3TpjuRrDcs3ZGaPmWxP\n3M41717DjsQdviOJiIhkmcq+/Mnk7yf/Mb3mtG7TKBhe0HckEe8aVWzE9O7T+XXfrzR7rxl7Du/x\nHUlERCRLVPblDx/98BFdJnbhbxX+xozuMygcUdh3JJGgceU5VzKl6xTW7VpHi1Et2H9kv+9IIiIi\nJ6WyLwB8uuFT4sbHcVHZi/i4x8eaR1/kGJqd14yJnSeyfNtyWr3fioPJB31HEhEROSGVfWHRxkW0\nH9eeC0tdyCc9P6FogaK+I4kErdbVWzMmbgyLNy2m7Zi2HE457DuSiIjIcans53Mrtq+g1futKF+k\nPJ/0/ITiUcV9RxIJevE14xnZfiRzf5lL3Pg4ktOSfUcSERE5JpX9fGz9nvW0GNWCQuGFmN1rNjGF\nY3xHEsk1etbtydut32bm+pn0/rA36S7ddyQREZG/CPMdQPxITkui2XvNSE1P5fMbP+ecYuf4jiSS\n6/Rv2J+9R/Zy3+z7KBlVkleve9V3JBERkT9R2c+HUtNT+G77CnYX2M2c3nOoUbqG70giuda9l93L\nzsSdvLDoBUoVLAW08B1JRETkDyr7+cyBpAOs2L6SIymHmdZnGg3LN/QdSSTX+0+z/7D78G4e++Ix\nLitUmwpFKviOJCIiAqjs5ytJqUm0G9uOg8nNqVWmNk2qNPEdSSRPMDOGtBnCnsN7WLxiPeEh4b4j\niYiIALpBN99Id+nc8OENzPllDheUupCSUSV9RxLJU8JCwhgbP5aikUVZu2stM3+c6TuSiIiIyn5+\n4Jxj4KyBjF89nuebPU9MIc26I5IdCoQVoE5MHQpFFCJufBwLNy70HUlERPI5lf18YPCiwbzy1Svc\ndcldDLp0kO84InlaqIVSN6YuFaMr0mZMG9buWus7koiI5GMq+3nc6BWjuefTe+hcqzODWwzGzHxH\nEsnzwkPC+bjnx4SFhHHd6OvYdnCb70giIpJPqeznYbN/mk2fKX1oWqUp77Z/lxDT/9wiOeXc4ucy\nvft0diTu4Pr3r+dg8kHfkUREJB9S+8ujlm9bTsdxHbmw1IVM7jKZyLBI35FE8p3Y8rFM6DSB77Z9\nR6cJnUhJS/EdSURE8hmvZd/MWprZOjNbb2b3H+P9G81sp5ktDyz9Mr3X28x+DCy9czZ5cPtl3y9c\nN/o6ihUoxsweMylWoJjvSCL5VqvzW/Hm9W/y8fqPuXX6rTjnfEcSEZEgYGbDzGyHma3KzuN4m2ff\nzEKB14FmwCZgiZlNdc6tOWrXcc65O44aWwJ4BIgFHPBNYOzeHIge1HYf2k3LUS05knqEz276jArR\neriPiG/9G/ZnY8JGnpj3BJWLVubhJg/7jiQiIv6NAF4D3s3Og/g8s38xsN4595NzLhkYC7TL4tgW\nwKfOuT2Bgv8p0DKbcuYaR1KP0HZsW37Z9wvTuk2jZumaviOJSMBjTR+j90W9eWTuIwxfNtx3HBER\n8cw5Nw/Yk93H8Vn2KwAbM61vCmw7WpyZrTCziWZW6RTH5hvpLp0bP7yRhRsXMqrjKC6vfLnvSCKS\niZnxvzb/o9m5zeg/rT+z1s/yHUlERPKBYL9BdxpQxTlXl4yz9yNP9QPM7GYzW2pmS1NTU896wGDx\n78//zbjV43ju2ueIrxnvO46IHEN4aDgTO0+kdpnaxI2PY9nWZb4jiYhIHuez7G8GKmVarxjY9gfn\n3G7nXFJg9R2gYVbHZvqMIc65WOdcbFiYt1sUstXwZcN5esHT9Kvfj3sa3+M7joicQHRkNDN6zKBE\nVAlaj2nN5oRj/tMlIiJyVvgs+0uA882sqplFAF2BqZl3MLNymVbbAt8HXs8CmptZcTMrDjQPbMt3\nPv/5c27+6GauPfda3rj+DT00SyQXKF+kPB91/4iEpATajGlDYnKi70giIpJHeSv7zrlU4A4ySvr3\nwHjn3Goze9zM2gZ2+4eZrTaz74B/ADcGxu4BniDjC8MS4PHAtnzlUMoh4sbHUb1kdSZ2mkh4aLjv\nSCKSRXVj6jI2bizfbf+OHh/0IGNiMRERyS/MbAywCLjAzDaZWd/sOI7X61qcczOAGUdtezjT6weA\nB44zdhgwLFsDBrGU9BRW7lhJRHQE07tPp2iBor4jicgpur769bzU4iUGfDyA2MhOnFv8XN+RREQk\nhzjnuuXEcfLmRex53JHUI6zasYrktGSmdp1KlWJVfEcSkdN058V3sm7XOiZ9uZGo8CjfcUREJI8J\n9tl45Ci/T7GZkJTAhaUu5JKKl/iOJCJnwMx45bpXKF6gOD/u/pHPfvrMdyQREclDVPZzmYfnPMy4\n1eM4t/i5lC5Y2nccETkLwkLCqFW6JlHhUcRPiGftrrW+I4mISB6hsp+LjFk5hqfmP8VN9W6iUnSl\nkw8QkVwjNCSMOmXqEBEaQev3W7Pr0C7fkUREJA9Q2c8llmxewk1Tb+KKylfwZus3fccRkWxQIKwA\nH3b5kE0Jm+gwrgNJqUknHyQiInICKvu5wJYDW2g/rj0xhWKY1HkSEaERviOJSDa5tNKljGg/ggW/\nLeDW6bfinKbkFBGR06fZeILc4ZTDtB/bnv1H9rOw70JKF9J1+iJ5XdfaXVmzcw1PzHuCi2IuYkCj\nAb4jiYhILqUz+0HMOUe/af1YsmUJozqOom5MXd+RRCSHPNr0Udpf2J6Bnwzk0w2f+o4jIiK5lMp+\nEHvuy+d4f+X7PHnVk7S/sL3vOCKSg0IshPc6vEet0rXoMrELP+7+0XckERHJhVT2g9TUdVN58LMH\n6Vq7Kw9e8aDvOCLiQeGIwkzpOoUQC6Hd2HbsP7LfdyQREcllVPaD0MrtK+nxQQ8alm/IsLbDMDPf\nkUTEk6rFqzKx80R+3PMjPT7oQVp6mu9IIiKSi6jsB5mdiTtpO7YtRSKK8GGXD4kKj/IdSUQ8a1ql\nKf9t+V+m/zidhz5/yHccERHJRTQbTxBJTksmfkI8Ww9sZV6feVSIruA7kogEiVv/disrtq/guS+f\no06ZOvSo28N3JBERyQV0Zj+IDJg5gHm/zmNYu2FcXOFi33FEJMi8ct0rNDmnCX2n9mXJ5iW+44iI\nSC6gsh8k3vn2Hd765i3ubXwv3et09x1HRIJQRGgEEzpNoFyRcrQf156tB7b6jiQiIkFOZT8ILN60\nmNtn3E7z85rz9DVP+44jIkGsdKHSTOk6hf1H9tN+XHuOpB7xHUlERIKYyr5nyWnJxI2Po0KRCoyJ\nG0NoSKjvSCIS5OrG1OW9Du/x9eavuX367TjnfEcSEZEgpRt0PXI4Vu9czb7wfSzqu4gSUSV8RxKR\nXKJDjQ7864p/8eT8J/lbhb8BF/mOJCIiQUhn9j1av2c9CUkJDG83nLoxdX3HEZFc5tGmj3Jdtev4\nx8x/kJCU4DuOiIgEIZV9T4Z+O5QtB7ZQKboSnWt19h1HRHKh0JBQRnccTeWilVm9czXJacm+I4mI\nSJBR2ffgq01fcduM2yheoDjnFq/qO46I5GLFo4ozuctkUtNTVfhFROQvVPZz2LaD2/64Ibdm6ZqA\n+Y4kIrlcnZg6XFjqQhKSErj747t9xxERkSCisp+DktOS6TShE3sO72Fyl8mEhej+aBE5O0oXLE2l\n6Eq8sfQNRiwf4TuOiIgECZX9HDRw1kAW/LaAYe2GcVFZzZwhImdX1eJVuabqNdzy0S0s3bLUdxwR\nEQkCKvs5ZPiy4by+5HX+eek/6Vq7q+84IpIHGcbY+LHEFI6h47iO7Ezc6TuSiIh4prKfA77e/DW3\nTL+Fa8+9lmeufcZ3HBHJw0oVLMXkLpPZeWgnnSd2JjU91XckERHxSGU/m+1M3Enc+DjKFS7H2Lix\nuk5fRLJdg3INeLv128z9ZS73fXqf7zgiIuKRmmc2SktPo/sH3dmZuJOFfRdSsmBJ35FEJJ+44aIb\nWLJ5CS8ufpHY8rF0q9PNdyQREfHA65l9M2tpZuvMbL2Z3X+M9wea2RozW2Fmn5nZOZneSzOz5YFl\nas4mz5pH5j7C7J9m83qr12lQroHvOCKSz7zY4kUur3w5faf2ZcX2Fb7jiIiIB97KvpmFAq8D1wE1\ngW5mVvOo3ZYBsc65usBE4D+Z3jvsnKsXWNrmSOhTMG3dNJ6a/xR96/elb4O+vuOISD4UHhrOhE4T\nKFagGHHj49h/ZL/vSCIiksN8ntm/GFjvnPvJOZcMjAXaZd7BOTfHOXcosLoYqJjDGU/Lhj0b6DW5\nFw3KNeC1Vq/5jiMi+VjZwmUZ32k8P+/9mT5T+uCc8x1JRERykM+yXwHYmGl9U2Db8fQFZmZaL2Bm\nS81ssZm1z46Ap+NwymHixscRYiFM7DSRAmEFfEcSkXzu8sqX83yz55m8djKDFw32HUdERHJQrrhB\n18x6ArFAk0ybz3HObTazc4HPzWylc27DMcbeDNwMEBERka05nXPcNuM2VmxfwUfdP6Jq8arZejwR\nkay6q9FdLNy0kPtn38/fyv+NJlWanHyQiIjkej7P7G8GKmVarxjY9idmdi3wENDWOZf0+3bn3ObA\nz5+AuUD9Yx3EOTfEORfrnIsNC8ve7zb/+/Z/jFg+gn9f+W9and8qW48lInIqzIyhbYdSrUQ1ukzs\nwtYDW31HEhGRHOCz7C8BzjezqmYWAXQF/jSrjpnVB94mo+jvyLS9uJlFBl6XAi4D1uRY8mNYsnkJ\nd868kxbnteDhJg/7jCIickzRkdFM6jyJA8kH6DyxMylpKb4jiYhINvNW9p1zqcAdwCzge2C8c261\nmT1uZr9r8l10AAAgAElEQVTPrvM8UBiYcNQUmzWApWb2HTAHeNY5563s7zq0i/gJ8ZQrXI7RHUcT\nGhLqK4qIyAnVKlOL/7X5Hwt+W8ADnz3gO46IiGQzr9fsO+dmADOO2vZwptfXHmfcQqBO9qbLmrT0\nNHp80INtB7fx5U1f6sFZIhL0utfpzsKNCxm8aDCNKjYivma870giIpJNvD5UKy94/IvH+WTDJ7x6\n3avElo/1HUdEJEsGNx/MJRUu4aYpN7Fu1zrfcUREJJuo7J+BGT/O4PF5j3NjvRvp36C/7zgiIlkW\nGRbJhE4TiAiNIG58HInJib4jiYhINlDZP00/7/2Znh/0pF7ZerzR6g3MzHckEZFTUqloJcbEjWHN\nzjXc/NHNvuOIiEg2UNk/DekunfgJ8TgckzpPIio8ynckEZHT0uy8Zjx+1eO8v/J9thzY4juOiIic\nZbnioVrBZsPeDSxL/papXadybvFzfccRETkjD17xIIs2LeLbVespElHYdxwRETmLdGb/FO1I3MGW\nA1u4t/G9tLmgje84IiJnLMRCeK/De0SGRbJ65xp2Ju70HUlERM4Slf1TsHbXWn7YvY6ikUV58uon\nfccRETlrSkSVoFbpmqSkJdNrci/SXbrvSCIichao7GfRoZRDxI+PJ8RCqVm6BuGh4b4jiYicVYUj\nilCtxPnM2jCLp+c/7TuOiIicBSr7WeCc47bpt7Fm5xpqlK5BRGik70giItmiXJFydK/TnUfmPsLn\nP3/uO46IiJwhlf0sGL58OCO/G8nDTR6meIHivuOIiGSrt1u/TfWS1ek+qTtbD2z1HUdERM6Ayv5J\nrNi+gttn3M41Va/h31f+23ccEZFsVziiMBM7TSQhKYFuk7qRmp7qO5KIiJwmlf0TSEhKIH58PMUL\nFGd0x9GEhoT6jiQikiNqlanFm9e/yRe/fsGjcx/1HUdERE6Tyv5xOOfoP60/P+39ibHxY4kpHOM7\nkohIjupdrzd96/flqflPMfPHmb7jiIjIaVDZP443lrzB+NXjeerqp7jynCt9xxER8eLV616lbkxd\nek7uycb9G33HERGRU6SyfwxLNi/h7ll3c/3513PPZff4jiMi4k1UeBQTOk0gJS2FzhM7k5yW7DuS\niIicApX9o+w9vJfOEztTrkg5RrYfSYjpr0hE8rfqJavzTtt3WLxpMQ/MfsB3HBEROQVhWdnJzC5z\nzn15sm25nXOOG6fcyOaEzczvM5+SBUv6jiQiEhQ61+rM/F/n8+LiF7m88uV0qNHBdyQRkXzDzEoD\n/YEqZOrvzrmbTjY2q6etX83itlxt8KLBTF03lReav8AlFS/xHUdEJKi80PwFYsvH0mdKH37a+5Pv\nOCIi+ckUoCgwG5ieaTmpE57ZN7NLgcZAaTMbmOmtaCBPzUP55W9fcv/s+4mrEcedF9/pO46ISNCJ\nDItkfPx4GgxpQKcJnfjypi8pEFbAdywRkfygoHPuvtMZeLIz+xFAYTK+FBTJtCQA8adzwGC0M3En\nXSZ2oWrxqgxtOxQz8x1JRCQoVS1elZHtR/Lt1m8ZOGvgyQeIiMjZ8JGZtTqdgSc8s++c+wL4wsxG\nOOd+Pa1oQS4tPY2ek3uy69AuFvdbTNECRX1HEhEJam0vaMs9je/h+YXPc0XlK+hWp5vvSCIied0A\n4EEzSwZSAtuccy76ZAOzdIMuMMLM3NEbnXNXZz1jcHp6/tN8suEThrQeQr2y9XzHERHJFZ66+ikW\nblxI/2n9qV+uPheWutB3JBGRPMs5V+R0x2a17P8z0+sCQByQeroHDRaf/fQZj8x9hJ51e9KvQT/f\ncUREco3w0HDGxo+l/tv16TShE1/1+4qC4QV9xxIRybPMrC3w+5Ne5zrnPsrKuCzNxuOc+ybT8qVz\nbiCQq6er2XJgC90/6E6N0jV46/q3dJ2+iMgpqhhdkdEdR7N6x2rumHGH7zgiInmWmT1LxqU8awLL\nADN7Jitjs1T2zaxEpqWUmbUAyp52Ys9S01PpNqkbB5MPMqHTBApFFPIdSUQkV2p+XnP+deW/GL58\nOMOXDfcdR0Qkr2oFNHPODXPODQNaAtdnZWBWL+P5BnCAkXH5zs9A39MIGhQenvMw836dx3sd3qNm\n6Zq+44iI5GqPNHmELzd+yW0zbqNh+YbUjanrO5KISF5UDNgTeJ3lGWWyVPadc1VPJ1EwmvHjDJ5Z\n8Az9G/SnZ92evuOIiOR6oSGhvN/xfeq9XY9OEzqxtP9S35FERPKaZ4BlZjaHjJPvVwL3Z2VgVi/j\nKWBmA83sAzObZGZ3mVmue5KKc45ek3tRr2w9/nvdf33HERHJM2IKxzA2bizr96zn5o9u9h1HRCTP\nsIwbSxcAjYAPgEnApc65cVkZn6WyD7wL1AJeBV4LvH7vlNMexcxamtk6M1tvZn/5dmJmkWY2LvD+\nV2ZWJdN7DwS2rwvcQ3BSSWlJpKSlMKHTBD31UUTkLGtSpQlPXvUkY1eNZcuBLb7jiIjkCc45B3zo\nnNvqnJsaWLZldXxWr9m/wDl3Uab1OWb23SklPYqZhQKvA82ATcASM5vqnFuTabe+wF7nXDUz6wo8\nB3Qxs5pAVzK+dJQHZptZdedc2omOme7SGdZuGNVKVDuT6CIichz3XX4f83+bz7LV64mOPO1poUVE\n5M8Wm9nfnHNLTnVgVs/sLzOzRr+vmNklwJenerCjXAysd8795JxLBsYC7Y7apx0wMvB6InBN4FcZ\n7YCxzrkk59zPwPrA551QWEgY8TXjzzC2iIgcT4iF8F6H94gIjWD1zjXsO7LPdyQRkbzgKmCRmW0w\nsxVmttLMVmRlYFbL/iXAQjP7xcx+ARYBTU/lQMdQAdiYaX1TYNsx93HOpQL7gZJZHPsXEaERpxlV\nRESyqmTBktQsXZOk1CT6TOlDxm+gRUTkDFwHnAdcDbQBWgd+npRl5R9hMzvnRO87537NysGO+sx4\noKVzrl9gvRdwiXPujkz7rArssymwvoGMLx6PAoudc6MC24cCM51zE49xnJuBmwEiIiIaJiUlnWrU\nExsemOK0z/Sz+7kiImfKx79PmY758uKXuXvW3QxuPpiBlw48a5/r9XPOZPzpjD3d453quOze/1TH\n5LZ980OOnMhzupl8jDvJWDM75Jw7aw9yMrPKx9runPvtZGOzes3+k865Xkcd9L2jt52izUClTOsV\nA9uOtc8mMwsjY07R3VkcC4BzbggwBKBQoUI6vSQikkMGXDKAeb/O477Z99GoYiMaV2rsO5KISG41\nnf9/5lUBoCqwjoz7V08oq5fx/OmDAsW74all/IslwPlmVtXMIsi44XbqUftMBXoHXscDnwfuSJ4K\ndA3M1lMVOB/4+gzziIjIWWRmDGs3jMpFK9NlYhd2HdrlO5KISK7knKvjnKsb+Hk+GfeqLsjK2BOW\n/cD0lgeAumaWYGYHAuvbgSlnGDoVuAOYBXwPjHfOrTazx82sbWC3oUBJM1sPDCTw8ADn3GpgPLAG\n+Bi4/WQz8YiISM4rVqAYEzpNYEfiDnpN7kW6S/cdSUQk13POfQvEZmXfE17G45x7BnjGzJ5xzj1w\nNsId9fkzgBlHbXs40+sjQKfjjH0KeOpsZxIRkbOrQbkGvNLyFW6dfivPLniWB6940HckEZFcxcwy\n3/gUAjQAsvTr0qxesz/TzK48eqNzbl4Wx4uISD7294Z/Z96v8/j3nH/TuFJjmlZp6juSiEhukvnB\nJalkXMM/KSsDs1r278n0ugAZ1wl9Q8b0PyIiIidkZgxpM4Rl25bRdWJXlt+ynLKFy/qOJSKSKzjn\nHgMws4LOuUOnMjZLN+g659pkWpoBtcm4bl9ERCRLCkcUZkKnCSQkJdBtUjfS0nWrlYhIVpjZpWa2\nBlgbWL/IzN7IytiszsZztE1kFH4REZEsq12mNm9e/yZzf5nLo3Mf9R1HRCS3eBloQcYU9DjnvgP+\ncon9sWTpMh4ze5WMuT0h4wtCfeC7U44pIiL5Xu96vZn36zyenP8kl1W+jJbVWvqOJCIS9JxzG80s\n86Ys/Xo0q2f21wA/BJbFwL3OuZ6nlFBERCTg1VavUqdMHXp+0JON+zf6jiMiEuw2mlljwJlZuJn9\nk4yp60/qZPPsh5nZf4AngJsCy8tAOzMLP8PQIiKSTxUML8iEThNISkui66SupKSl+I4kIhLMbgFu\nByoAm4F6gfWTOtmZ/eeBEkBV51wD51wD4FygGPDCaccVEZF874JSF/BOm3dYuHEhD36mufdFRI7H\nObfLOdfDORfjnCvjnOvpnNudlbEnu2a/NVDdOff79fo45xLM7FYy7gYecPqxRUQkv+tSuwvzf5vP\nC4te4PLKl9Puwna+I4mIBA0ze/gEbzvn3BMn+4yTndl3mYt+po1p/P8NuyIiIqdtcPPBNCzXkN4f\n9uanvT/5jiMiEkwSj7EA9AXuy8oHnKzsrzGzG47eaGY9CczzKSIiciYiwyKZ0GkCAJ0ndCYpNclz\nIhGR4OCcG/z7AgwBooA+wFgyLq0/qZOV/duB281srpkNDixfAP8Abj2D7CIiIn+oWrwqI9uP5Jut\n3zDok0G+44iIBA0zK2FmTwIryLgEv4Fz7j7n3I6sjD9h2XfObXbOXQI8DvwSWB53zl3snNt8RslF\nREQyaXdhOwZdOojXl7zOuFXjfMcREfHOzJ4HlgAHgDrOuUedc3tP5TOy9FAt59znwOenHlFERCTr\nnrnmGRZtWkS/af2oX64+1UtW9x1JRMSnQUAS8C/goUwP1TIy7q2NPtkHZPWhWiIiItkuPDSccfHj\niAyNJH58PIdTDvuOJCLijXMuxDkX5Zwr4pyLzrQUyUrRB5V9EREJMhWjKzKq4yhW7VjFnTPv9B1H\nRCRXU9kXEZGg07JaSx664iGGLhvKyOUjfccREcm1VPZFRCQoPdr0Ua6qchW3Tr+VxJTEkw8QEZG/\nUNkXEZGgFBoSyvtx7xMdGc3qHatJc2m+I4mI5Doq+yIiErTKFi7L2PixHEo9zLrd6zjGQ91FROQE\nVPZFRCSoNa3SlKrFqrAjcQdDvhniO46ISK6isi8iIkGvctHKlIgqwT8+/gffbv3WdxwRkVxDZV9E\nRIKeYdQoVYMyhcrQaUIn9h/Z7zuSiEiuoLIvIiK5QnhIxgO3ftv/G32m9NH1+yIiWaCyLyIiuUbj\nSo35z7X/YfLaybyw8AXfcUREgp7KvoiI5Cp3NbqL+Jrx3P/Z/cz5eY7vOCIiQU1lX0REchUzY1jb\nYVQvWZ2uk7qyOWGz70giIkFLZV9ERHKdIpFF+KDzBxxKOUSnCZ1ITkv2HUlEJCh5KftmVsLMPjWz\nHwM/ix9jn3pmtsjMVpvZCjPrkum9EWb2s5ktDyz1cvZPICIivtUoXYNhbYexaNMi/vnJP33HEREJ\nSr7O7N8PfOacOx/4LLB+tEPADc65WkBL4GUzK5bp/Xucc/UCy/LsjywiIsGmU61O3N3obl79+lXG\nrBzjO46ISNDxVfbbASMDr0cC7Y/ewTn3g3Pux8DrLcAOoHSOJRQRkVzhuWuf4/LKl9NvWj9W7Vjl\nO46ISFDxVfZjnHNbA6+3ATEn2tnMLgYigA2ZNj8VuLznJTOLzKacIiIS5MJDwxkfP57oyGjixsfp\ngVsiIplkW9k3s9lmtuoYS7vM+7mMp6Ic98koZlYOeA/o45xLD2x+ALgQ+BtQArjvBONvNrOlZrY0\nNTX1TP9YIiIShMoVKcf4+PFs2LNBD9wSEckk28q+c+5a51ztYyxTgO2BEv97md9xrM8ws2hgOvCQ\nc25xps/e6jIkAcOBi0+QY4hzLtY5FxsWFnY2/4giIhJErjjnCp5v9jyT107m+YXP+44jIhIUfF3G\nMxXoHXjdG5hy9A5mFgFMBt51zk086r3fvygYGdf76yJNERHhrkZ30blWZx747AE9cEtEBH9l/1mg\nmZn9CFwbWMfMYs3sncA+nYErgRuPMcXmaDNbCawESgFP5mx8EREJRmbGO23e0QO3RMSbjfs3+o7w\nJ16ua3HO7QauOcb2pUC/wOtRwKjjjL86WwOKiEiu9fsDty5+52I6TejE3BvnEhEa4TuWiOQDR1KP\nEDc+zneMP9ETdEVEJM/J/MCtQbMG+Y4jIvmAc447ZtzBki1LfEf5E5V9ERHJkzrV6sTARgN5bclr\nvPvdu77jiEgeN+SbIQxdNpSHrnjId5Q/UdkXEZE867lmz3FVlau4edrNLN2y1HccEcmjFm1cxJ0z\n76RltZY81vQx33H+RGVfRETyrLCQMMbFjyOmcAwdxnUgOT3ZdyQRyWO2HdxG/IR4KhWtxPsd3yc0\nJNR3pD9R2RcRkTytdKHSTO4ymV2HdrF6x2rSST/5IBGRLEgnnU4TOrHvyD4md5lM8ajiviP9hcq+\niIjkeQ3KNeCdNu+wP2k/G/Zs8B1HRPKIDXs2sOC3BQxtO5S6MXV9xzkmlX0REckXetTtQcXoimw+\nsJkRy0f4jiMiudy2xG1sPrCZgY0G0rV2V99xjktlX0RE8o3zip9HsQLFuOWjW1iyObimxxOR3GPp\nlqX8sPsHihUoxnPNnvMd54RU9kVEJN8wjFqla1G2cFk6ju/I9oPbfUcSkVxm28FtdBjXgYiQCGqW\nrklYiJdn1GaZyr6IiOQr4SHhTO4ymd2HdtN5YmdS0lJ8RxKRXCIpNYm48XHsObyH2mVqExES/E/n\nVtkXEZF8p365+gxtO5R5v85j4KyBvuOISC7gnOP2GbezcONCRrQbQeGIwr4jZYnKvoiI5Evd6nRj\n0KWDeG3JawxfNtx3HBEJcm8seeOPJ+R2qtXJd5wsU9kXEZF869lrn+Waqtdwy/Rb+Hrz177jiEiQ\nmvvLXAZ8PIA21dvw+FWP+45zSlT2RUQk3/r9Cbvli5Sn47iObD2w1XckEQkyP+/9mfjx8VQvWZ1R\nHUcRYrmrPueutCIiImdZyYIl+bDLh+w9spcO4zpwJPWI70giEiQOJh+k/bj2pLk0pnSdQnRktO9I\np0xlX0RE8r2Lyl7EqA6j+GrzV/Sb2g/nnO9IIuKZc44bP7yRVTtWMTZuLOeXPN93pNOisi8iIgJ0\nqNGBJ696ktErR/Pcl8H9kBwRyX5PzX+KSd9P4j/X/ocW1Vr4jnPagvspACIiIjnowSseZNXOVTz4\n2YPUKFWDdhe28x1JRDyYsnYK/57zb3rW7cnAS3P39Lw6sy8iIhJgZgxrO4zY8rH0+KAHK7av8B1J\nRHLYyu0r6Tm5J7HlYxnSeghm5jvSGVHZFxERySQqPIoPu35I0QJFaTumLTsSd/iOJCI5ZPvB7bQe\n05royGg+7PIhUeFRviOdMZV9ERGRo5QvUp4pXaewPXE7cePjSEpN8h1JRLLZkdQjdBjXgZ2JO5na\ndSoVoiv4jnRWqOyLiIgcQ2z5WEa0G8GC3xZw6/RbNUOPSB7mnKPv1L4s2rSIdzu8S8PyDX1HOmt0\ng66IiMhxdKndhTU71/D4vMepXaY2ufs2PRE5nifnPcn7K9/nqaufIr5mvO84Z5XO7IuIiJzAI00f\nIa5GHPd8eg+7D+/2HUdEzrIdh3bw8NyH6VW3Fw9c/oDvOGedyr6IiMgJhFgII9uPpG5MXdbsXENi\nSqLvSCJyliQkJ7B211oaV2rM/9r8L9fPvHMsKvsiIiInUSiiENO6TSM0JJQV21ew9cBW35FE5Axt\nStjEqh2riAiNYHKXyUSGRfqOlC1U9kVERLKgYnRF6pSpQ2p6Km3GtCExWWf4RXKrg8kHaTOmDWnp\nadQpU4cyhcr4jpRtVPZFRESyqEhEEWqWrsmybcvo8UEP0tLTfEcSkVOUlp5Gzw96smL7CmqWrkmh\n8EK+I2UrL2XfzEqY2adm9mPgZ/Hj7JdmZssDy9RM26ua2Vdmtt7MxplZRM6lFxGR/KxkVEleafkK\nU9ZN4Z+f/NN3HBE5RQNnDWTKuim81OIlSkaV9JLBzCqZ2RwzW2Nmq81sQHYdy9eZ/fuBz5xz5wOf\nBdaP5bBzrl5gaZtp+3PAS865asBeoG/2xhUREfl/d1x8BwMuGcDLX73Ma1+/5juOiGTRy4tf5r9f\n/5e7G93NPy75h88oqcAg51xNoBFwu5nVzI4D+Sr77YCRgdcjgfZZHWgZt0lfDUw8nfEiIiJnw+Dm\ng2l7QVsGfDyA6T9M9x1HRE5i0ppJDJw1kI41OvJC8xe8ZnHObXXOfRt4fQD4HsiWR/b6Kvsxzrnf\npzLYBsQcZ78CZrbUzBab2e+FviSwzzmXGljfRDb95YiIiBxPaEgo73d8n3pl69FlYheWbV3mO5KI\nHMeijYvoObknl1S8hFEdRhFiwXPbqplVAeoDX2XH52fbn9TMZpvZqmMs7TLv5zKeP368Z5Cf45yL\nBboDL5vZeaeR4+bAF4alqampJx8gIiKSRb9PyVkiqgStx7RmU8Im35FE5Cjr96yn7di2VChSgald\npxIVHuU70h/MrDAwCbjLOZeQHcfItrL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#assumes has done %pylab inline \n", "import numpy as np\n", "import nengo\n", "from nengo.utils.matplotlib import rasterplot\n", "\n", "model = nengo.Network(label='Two Neurons')\n", "\n", "with model:\n", " stim = nengo.Node(lambda t: np.sin(10*t))\n", " ens = nengo.Ensemble(2, dimensions=1,\n", " encoders = [[1],[-1]],\n", " intercepts = [-.5, -.5],\n", " max_rates= [100, 100])\n", " nengo.Connection(stim, ens)\n", " \n", " stim_p = nengo.Probe(stim)\n", " spikes_p = nengo.Probe(ens.neurons, 'spikes')\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(.6)\n", "\n", "nengo.utils.matplotlib.plot_tuning_curves(ens, sim)\n", "\n", "t = sim.trange()\n", "figure(figsize=(12, 6))\n", "plot(t, sim.data[stim_p],'g')\n", "ax = gca()\n", "ylabel(\"Output\")\n", "xlabel(\"Time\");\n", "rasterplot(t, sim.data[spikes_p], ax=ax.twinx(), use_eventplot=True)\n", "ylabel(\"Neuron\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "- Can we still decode $x$ using a sum of activities?\n", " - $\\hat{x}(t)=\\sum_i{a_i(t) d_i}$\n", " \n", "- Let's use exactly the same technique we did before to find $d$\n", " - $ d = \\Gamma^{-1} \\Upsilon $\n", " - $ \\Upsilon_i = \\sum_x a_i x dx$\n", " - $ \\Gamma_{ij} = \\sum_x a_i a_j dx $" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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RtSdi7yZGDe7I7acN5NP5G7nvk4V1ZVZfIxzrgp6asj3u19sW5+2Qty6LXm71e3fycClK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\nJpozoKQjKZgzUL/ugZ0KePG7VXw8Z33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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import nengo\n", "\n", "model = nengo.Network(label='Decoding Neurons')\n", "\n", "with model:\n", " stim = nengo.Node(lambda t: np.sin(10*t))\n", " ens = nengo.Ensemble(2, dimensions=1,\n", " encoders = [[1],[-1]],\n", " intercepts = [-.5, -.5],\n", " max_rates = [100, 100])\n", " temp = nengo.Ensemble(10, dimensions=1)\n", " \n", " nengo.Connection(stim, ens)\n", " connection = nengo.Connection(ens, temp) #This is just to generate the decoders\n", " \n", " stim_p = nengo.Probe(stim)\n", " spikes_p = nengo.Probe(ens.neurons, 'spikes')\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(.6)\n", "\n", "t = sim.trange()\n", "\n", "x = sim.data[stim_p][:,0]\n", "\n", "A = sim.data[spikes_p]\n", "\n", "gamma=np.dot(A.T,A)\n", "upsilon=np.dot(A.T,x)\n", "d = np.dot(np.linalg.pinv(gamma),upsilon)\n", "\n", "xhat = np.dot(A, d)\n", "\n", "figure(figsize=(8,4))\n", "plot(t, x, label='x')\n", "plot(t, xhat)\n", "ylabel('$x$')\n", "#ylim(-1,1)\n", "xlabel('Time');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- What if we add more neurons?" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "c:\\users\\terry\\py3\\lib\\site-packages\\matplotlib\\cbook.py:637: IgnoredKeywordWarning: \"color\" keyword argument will be ignored\n", " IgnoredKeywordWarning)\n" ] }, { "data": { "image/png": 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BRhHslbtWYkPtBv7/bCPxLbEWx7G1FolnIr4x0pjyOLKx09z04U2YNm8aVuxc0WrZTBH7\n3Vy/uU11850al3vi22FJqgpUoSHSgE11m3I1LIIgCKITMQzjAsMw9jIMw2MYxhDDMJ42DKPOMIyp\nhmGMMQzjBMMw7NlrckZeRbxTknyiaxHTYimtGYxj5x6LOV/M6ZD+GyON+LTiU8trzNrilb3QDA2a\nocGAAd3QUR8275WaYOsWtLbYaXyyLyPhVtFUgfpwPZ8opIzEp/DEp4rEt+aJZ6ks09lpslnYuqZq\nDQDkdJImRq9f/f7VrOqyMed7k6Vc2GmyyY5EEARBEHbyHYl/FsBJeR4DkYaYFmtVwDVEGlAbqu2Q\n/o+bexx+9uzPLIKTiR8xEg+YkXUmipkITkcqO41u6EmTACbG00XiV+9ejeZoMxRNwa6WXTBg8EkF\nX9iqa1lF4pM88Zlmp3Gw0xiGYRXxGUxG2Fj9bn+rZTNFHDs7PxnX7SKR+Fx48/mTIJVEPEEQBJE9\neRXxKZLkE10EwzBaFfGGYUDVVUvGlVyytmYtAKtYEu00opVGtKowMcuY9808XLr4Ustr9uw0qq4i\npsWwYN0CjHxwpKUNi53GQfxquoajnzkaDy17HN/t3Mkj91//UIvt24GGgHl+moMq/7fYtx0eiW+j\nncYpEi8+TQAyi8SzSZFH9rRaNlPE85etCO5qkfj2LA5mbVAkniAIgmgLPXphK9E+mHBNtUgSSAiy\njhDxYrTVIuLj4/LJPkTUCP+/ZmhcFLNINmPJtiWYv3Y+nj7jaUiSZGmTCeM/v/9nrN69GieOOgkh\nJYQv1zRDbSjGzp3AmzvNPvZU+9BYqeC4p4CGBvNPUxMQ1oPQ/hzBX/7RiL/8WAHMMvudflatuazl\n0hAwDHjoYRXwhYHDzPdnzgrjqm1ASYn5p7TU/NM0ohnoD9TURTFvHjBggPmnMdD27DRcxLsz3+xJ\nfIKQKT/U/YBhZcN4P3ZE4ZutCO4ykfgcLGzldhqKxBMEQRBtoMuLeEmSfgvgtwDg9XrzPJqfFkwo\npovEMzHDvNi5ZHNDYtFjqki8aKcR/eb2SHxICSGmxVAXrkPfwr4IBIAN38eFeWMEl10GvFqwBY3+\nH/DZ/KOBo4FpJyoA08JH6MDJQKjZB4+kQJaB0aOB8nKgrAzQ/CE8DODon0UxbFoFXooH2H9//R4c\n4gP+Vh3CdhWYfLyKgB7G10oBVEQweVoEoxuAlpbEn+pqYIvWAvQH6puiuOgi4UDOigAHA3fdo+CD\nKDBiBDBypPln1CgjrZ1GnPwA2dlp2DlevXs1RpWPQllBmWP5YCyI8f8ajwdPehC/PfS3jmVyEYnv\nwL0zMiInnvgs9ikgCIIgCDtSviNakiSNAPCGYRjjWitbVFRkBIO5F4sdjaIpcEkuyC4530PhfFbx\nGcb0GYOBxQOtb8w91fx71ptojDSi/J/lkCBB+6vGI9girMwa3yAcPOBgYNabrXcu9JGuTE2wBgPq\nVgIAav5Ug35F/QAASyuX4ti5x2KFux8iagSPHnAKFqxfgNrra/Hqd6/it2/8FpcefCmerq+CrgNf\nH/ImLv3gdHwTfgOHffMFftizGU2f/RIYtAofXfYzQHfj/CebEJ0xHYFeX+IgfRZWeR7CQ6N/wEV7\nroHPCzw0bipuWDIbk4ZMgqqrWOHuZzmGLQ1bMOqhUbhy4pUYUDQAx350FwDg+9Pm4HeH/Q77PrIv\nNtZtxFWHX4WqQBWu/f59xLQYVp/4d1w36bqkY69oqsCIpvXo4++LL86qRXW1Ke5HrB+JgFGD31fd\nBN/yW7BtG9DIEtF4QvjoZnNc5wQPxuWez3HAAcD++5t/NFcIK27vh0HFg7BP8Ec8e+azuPjgi5P6\nFo+r7919UReuw5KLlmDyiMn47G+lGF42HMOvdV6LvqN5B368bx+M7DUyZZklW5dg6vNT8ZFRiEHF\ngzD2Tz+kvg6EcRkw4Kp8GwDw8cUf42cjftZqHfFYcskHWz7AtHnT0L+oP6r/VN2mNj7Z9gkmPzcZ\n1x91Pe6edneOR0gQBEG0F0mSQoZhFOV7HKnI98LWnwTTX5iOGz+4Md/DsHDaS6fh4eUPpy3DIvEG\njKTINqMjd9AULTH2XVoBM0+8AYNHQwMhDRs2mVHN9z8NYMVXwKefAYceCnyz3owor9n/ZDRNnYk/\n/OMb3H5HvB1ZR1UVcMDBIWhyAAdONJ88nDBdQVkpUFAASC6zbKmv1PGpA7OxRNUoKpoq4HaZD7lq\ng+aCX3t2Go/L9JinisKy441pUYwdCxx7LPCLXwAFftMS84vzYlizJmHpWb0aeHJuYlxBrQn33AP8\n6lfAhAmmVeeoo+OZckLmZCwcy9wTr+gKYloMuqGn/ayZlz9dcEC00GTjbRfL5nuTpZxmpyE7DUEQ\nBNEG8p1i8iUAywDsI0nSjnhi/B7HtsZt2Na0Ld/DsBBSQkm+cTui7zqVpYZZI8QdTXOFmH5RFEus\nL8OQYBgGVn9tvjd6rIoHHjXr1Da1oLAQGD4cWLQIOOTwuLfbY9pMLr/MjcnHa/H2DBiGgbAahgED\n1YFqy7GJfZYVlDlOaJhIj2pRVDZVwu/2wy25sSe0x/I+W3zLnsqk2uwpVQ57Ng7xs+nVCzjkEOCE\nU8xxSZDQb2gTgkFg/XpgwQJg9mygV2+zzcYG87b/w9UqJk4E/vhH4JVXgBohIc+7P76LWz+61WKn\nYRMOHak/a3adpCsjntdsngQ6rZEIxALoc3cfy74Af/vkbzjphY5NepUTT3wW+xQQBEEQhJ28euIN\nw7ggn/13Foqm5G2L+1SoutpqBNAu4gdjcFIZHokXIuUfbf0IT65+EvPPnu9owckUMUqtaCo2bwY+\n/hh4abkGDAYCLS7AB1Tu0IBRwOW/U1E/PIyXq4CJRwcwDiUAgJG/AP7xL+vCWzGrDWDNsMM2t3JK\na1nqLXUU8Sw6H9WiaIw0wiN7oOoqT73J3meReFmS4ZJceG/Le+hb2BfXHHmNpT0m8GJaDIZh8PPI\nRLzT9cTG5ZW9aIo0wetNWGlmzADqwzq+/ScweJALCAGTpypQPwf+9S/ggQfMNpZfYXr8b62bizXh\n13j0WxTx6YR3c7QZnlbKtDkS7yDi68P1qA/Xm5tGjTLfW1ezDutq1gHlB2XcdrbkIhJP2WkIgiCI\n9kB2mk4gpsVSZhPJB0wItiYexDGn2jyIR+L1ROR1ydYleHndy+0+5qgahU8yrWhHHaNi9GjgN78B\nVq42BW6hXwIkA1OnmWOYfb2GEaOcs9PYs+fEtJjFFhJRIzzqvDuw23JsQEJUtxqJV6OIalG4JBc8\nsgd7QnugGzoXwJqhIaSE4JJccEkurNi5Ajd+eGOS6FWNhDh0ilw7nVs2UfDJPrTEWpJsL3xBsMe8\n7U85TcHHH5vZdT7/HLjrLsDvB2prgeUbtyKmJ66PL1eoqGvOTMS3VkYUvllF4gXBzyZVTmI6rIY7\nXBizz6Q9k3Oy0xAEQRDtgUR8J9DVRHymEcCM7DQOkXgmJrM9Zk0Dli8Hbr0VWLVGg6IriFbtDQA4\n6BAVjz4KbNgAvDjf7MtfYF6+ih7jxyVu9iSKPvvOqDEtZhF+ETXChTjb6MkpEl/mKzO94Ta7iGin\niagRU8S7PKgN1VosM8xOw0Q867suXGc9F4IAF0Wek52GwSPxbjOLk30iw46B9cuOz+sFjjoKuOEG\n4MBxwNFHA+V7b7HUvfOfKg6aEJ8gBXR8/TXgpL9Zn5nYaSRIacvZES1b9jzt4kQnpIQ6XBjnMjsN\nReIJgiCIttAjRPysd2Zh1juz2l0mm3LZlFV0hYuMbNpvz9jScdl7l2HkwJHOQmfWmzybRzae+ClS\nCMYlbwBICFpRWFnGLvQRDAL//a+5AHPAAODII4G//x34zYaHMEUK4bjxIwEA996n4ve/B/bbD9Dj\nYvT/Rk7EFCnERZB9sydX5dv4ff/hljHxcWsKNEPDFCmEKVLIjMTbhL6iK3ysTECW+koBAE3nz7dk\nPREXtkbUCO4ZOxn373sCaoO1lr7ZROOesZNxYUkiTeP2pu2Wz+B3/Yby/4oib1Z5f0yRQo7pIQOx\nAKZIITwx7gwAZuYgEd3QMUUKYfGk3yaOz86sNxG48GU0xPZYXr7pFgUzZ0UxRQrhsG+PxiGHmGkt\nr74a+PBDQIk31RxtxhQphLvHpM4cw4T3GQUy/t+wg63dp7rGZ72J6nOf4f+1i2hLJF4Jm08+hOss\nqbl23kvsGEYMHNGmdma9MwtPbXgKQOYpJjviuymX5XJRpj3vd8R76d5vS5v5bCvbPrJpJ1fjz8Ux\ndfT56qhz1ZGfTy7byfd1n+sxZPp+V6VHiPiuTleLxDMLQ1Z2mhQbPomRePvGT6msBg0NwLx5wM9/\nDvTta2Zdeecd4OSTgfnzTTvHPU9WAgAOGWGKeCbQpz4/Fd9UfwPA9H4DiUi1pmuIaKYgYpHtx1c+\nbhmTeGx2O429jD03vSzJKPYWA3DOQ8/ajagRFMgF6OPvg7pwXbKIV8Lwu/3cew8A25u383N28WsX\nY8XOFfw9cbLFBJ+jnSY+kRhQPMDxmNnxsjzxqaLIWxu3Jr22z74qfvcHs+8zz47h6aeBgw4C/v1v\n4IQTgH79gAsvBD5f2ZxyfAx2nfjd/qwi2eL1lFbEq2EoutIhi63t/QPtWNQdf5JBdhqCIAiiLXT5\nzZ66O4ZhLprsUiI+rh5aEw+iaGotEg+YItLr9zraaVTVFOcnnggsWWL+f/Bg4LLLgLPPBo45BnAL\nV+P2SlPU7l1u2mk0XcOO5h1YsnUJ/G4/APA0jU6ReCaySn2l3JPudrn56yxdIqMl1pIkxux2GtmV\nWsSLC1sjagQF7gIUuAsQVaOWlJSarvH3xXPHIvGbGzbj+W+eB2DaXnRDt5xHdqzp7DTlBeVJ42fH\nAABulxuyJKecZG1tSBbx4sJW2avg8fBERE6KYM9La/H++8DixcDrrwN79jQDRwMffxbDK4Y5MfP7\nrW2xfv2eLEW8wxoFJxEvTqgK3AUZt58NFl9/Gzee4vch2WkIgiCINkAivoNhwqNLifi2ROJTLWzV\nrF7kcn85F1HNQQUL3gFefBFYP870UMtbzHSHZ58NHHYY4ErxLKiyqRISJAwvM+0wYjYZNm57JF70\nxDMGFA3g4vOqw69Cqa8Ut31yW5KVpD5cn3xsthSTmUTimZ2mwF0Ar+yFAYPnTmdjjGkx+Nw+/pos\nyTwSL7bLRLz4ObFjTWWnAYDe/t4Akq85Nklhi25T7di6pWFL0muiiFc0BSt3mZtwFRYCZ55p/tE0\n4OxnWvC/XUBNXQznnAMUFwNnnQWcdx4wfbrpv2efo9/tz2phaMaR+PhELqpGO0zEZ5Mm8/WNr2Nw\n6WBM2GuC5XV+H1IkniAIgmgDZKfpYJiQ6kopJlkEsLWJRTaeeMAUsqoK7Kw2Be3hRyo4/3xg1Soz\n6n7oocCmTWYWlFHj6rBq91cp+65sqsTA4oEo9BQCMEUa64uJHmYLYSJXM7Qkf3H/ov5cYI/sNRLn\nHXAePzbRTtMQbkg+Ns0a+XVJrlZFfFgN8wgwm2SI3nS2aRJ7igAAw8qGcREvnmc+aRFEXrpIPIv4\nl/vLHcuw45VdMjwuT+pIfONWlPpK0bewr2UsbByWJyyCeJZloLiPOf6p02P44APg/POBN98ETj8d\nGDgQuPJKYPO29kfi+cJWhywx7LPI1GveFrKJxF/77rWYs2xO0usUiScIgiDaA4n4DoaJiy4Vic/Q\nTpNNdhoAuHNOCMOGAWs3mmLyxFNjWLIEqKwERo0yo7IsbfyNH9yIw/99OD6r+Myx3V2BXRhcOpjv\nfCpG4pk4YyKZjVO00zBEEV/oKeR1FE2xCLGGiIOI11PbaeyZX5gfnZ0nJxHvklxm3ncY8MpePHna\nk7j9+NsxtGwoKpsqLfUvPuhizJluCj9R5KXzxAdiARS4C7jdKF0kXrQW2dlQuwGjykdhQNEA/pol\nEu9gA2Kw8St6DFOnAk89BVRVmUL+pJOAZ54BHnzYrF9f7Uco0jGeeMB63hRNwbD7h2HR+kUZ95fp\nWFqLxEfUiOOEItP7kCAIgiCcIBHfwTAhJQqqxkgjBt47MKUw7miytdO4JJejnSYYBN55PyFmnn0x\nhEMPBYbU2CqEAAAgAElEQVSMNEXzLX9VMGWKGaG1w4TWL1/5pWNEOKyEUegptIh4Vi4bO43P7bOI\neI/s4ccmpsV0tNNoWdhpVLMPtgBYFPHs3BV7i/kkwyN7cNmhl+HmY2/G0NKhXAyza+Ivx/0F4weM\n52MFzM+N22ls50w3dKzavQrlBeVJkxsGO15ZklPaaZoiTfi04lOcsPcJfIEsYAp30U7D2Nyw2VKf\njV/s2+sFTjnFXLRcVQWcebZZf9sPhVi1RsUppwD/+U8iw40TP9b/iG2N2/j/U4l4wzAs1iZGQ6QB\n25u3Y0PthtSdZEE2kfiYFnMU6pnehwRBEAThhJTNZiv5pqioyAgGg47vVcy8CAAwfN7zKevno4z8\n6B0Yev9Q9C/qj+o/VQMAlv18GjbVbcIxry3BqN6jsmq/tb5TvS++vrl+M0Y/PBoje43Elmu2pKwz\n75t50K+6BR6XB8//ZjTe+dU7AIA1a8xdPo997yJovj245IK3AQAvnfI+zp94AhZMGYuIFsW+8xfi\niCFHOI7j1nNceO6b5wAAP171I0b1HmUZx1FPH4UibxHmvF6ENVVrMPCZJ1HkLcKxc4/F2D5jsalu\nEz5aeSwqmirw+5P2IKSE8MHMD3D1O1fj/y2MQNFVXDK1Er/Y/xe4+ZibMeHJCVj57cko9ZVi7D4L\n8Ngpj8Hv8WPW4ll49sNhGFY6FMdP/Nwy1qdOfwrT7v8UAHD3+SVYsH4BvvndN/jgtKMwts9YTHr1\nfV52xqIZWLRhEZ79cBgAIHLfzXBJLvz2jd/is9VTsLlhM248M4Z+hf2wtmYt5kyfg+smXYeKmRdh\nS8MWTD9iOaK3RPHYV4/hqrevwqZN5yOkhHDwAf/DBzM/wNS9p2LrzJn4tOJTXDK1EpOGTMK5+5+L\ns/Y9CyPLR+KLs6bih/of0XLv9Zg0ZBIOe+ow/O/8/2H8Pxbxc7q2ei3G/2s8Fp27COqVN6G3vzem\nv7XccsxfnX0SNuz5DmNefAmPrHgEL617CQBw59Q7MXnOh9hYtwmPX7QXVuxcAQMGnjjtCZz4wFLe\nx4QnJmBN1RpMGjIJT7zbH7JLxv4v/9fSx60f3Yq9b30Wvbx9cPkxBjxPr8GOHabd5qVRF2GvQcA+\nC63X4qSnJ+GqebVQdAWXTK3E/Sfej2uPvBbv/PgOqi+9HINLBuGEN5chokbgv918ErH+u7NR5Cmy\nXPOzJ83GvdPvTbonANNudPXbV+OPk/4IzzV/c7wnWL1tTRWYfKh5bWy9ZitG9Brh2CYA9LqrFw4f\nfDjem/me5f3HvnoMV751JfYq3gu7Zu9KWd/ed7r3O7tMR5dtS/lc1+/o9giCMOmoe6s97UqSFDIM\noyinA8ohFInvYJwi8Ubc1pBqYWF7CMQClgizE9lu9iS7ZESUGF54wdwUaMIEM0Vkv77AiBGJSWBh\nqRkB1dJsSMQQ0x+yHVJFoloUPtkHKe6/0QwtyU7jir9nicQrYXjikWjAjBqzvlwuGRLb6EhXLJ54\np89C0RTo8Sgrs9OU+ErM/9t2Q7Wnc/S5fTwirsXHXegp5OW8whg9sheqriIQC/BItluS4YLEzwWQ\nuG4AoCpQheveuw57P2Rm76kL16HIU4grJ16ZMhIv2mkkyQXdYQK/J7wHXpcHRww+IslOowvXLfPL\nb653jsQruoJN9Zss0XOxLQmAxy2h3wAV27aZdpvDDgMqKoHlX5oe+jffNBfLAuaTEkdPfPypAAtG\niHYqe/YhIPkJisjOlp14bOVjePfHd1OWYYjBj9bWu8S0mOO9xq6hbL37iq6iLlTXekGCIAiiR0Mi\nvoNxEvFMPOV6sWtMi2H17tXYKeQfd8JpwaRIRI3gFwt/gfW16wEAmuLC51/GMHMmUFcHPPAAsGsX\nsO++gL8wIZSYQGWbMaWbpITVMLfK7G5JFvExLQav7IUUF7IWO0183Ow9Nmlhdhpx0aiqq3xcsuTi\nkwK7nYadE9YmYC6uXVrxGZpjLTxPfJGnyNKn/dgZop2GlS3yFHG7jzhGOT6xCMQCaIm2wCt7LTu6\nsuMVRam4w+tHWz+Cbhhwu9yQJCkjO40ECYbDbqnBWBClvlLILhmje4/mx2sR8fGNsoD0dhpN1/iE\nTkTRFUiSCxIkqLoKWTbtNq+/bm72NWw4sHIlcNppwN57A7ffDgSjVqGbZKOJT7bEz8Ei4uMZguxr\nGUR4VhstCt3Q09pkDIfdY1ORyk7DzmG2dpqNdd9j5qszs6pDEARB9DxIxHcwfFt4y0K4jonEt0Rb\noMNAtJXIXmviYXP9Fvz3u//i3x+ZdhElJqO4LIb33gO++w645hqgVy+zrBiRDCkhGIbBhZt9knLO\nwnP4BCOkhDCq3LQSOUbi1Sh87kQk3inFJBO54nFF1Ai8ckIgK7oQiRei2/aFrezfYkaWrY1bocNA\nRAmbnniXDNklwyW5kiLxYi54wCbi42ULPYVcKIqReNllLhpgkXi2Kyw7PibGRVEqrqdYvHExDEPn\n5VOKeCE7jSRJjgsydcOAKz6eyw69DN9d+R1kSbaIeFGUphPxuqFbxC5D0RRIkCBJUtI1UuADRo4w\nF0P/5z/A2LHALbcAO6us16qTFx6AZU2E+KQhk0g8i4hH1Si+qf4GWxzy5TNEgZ9OxJsTGc3xXmtt\nMp2KmBpDRVNFVnUIgiCIngeJ+A6Gp5jUFS40mADIdSSeCZTWMuGkEg+xGPDcc8CZ55qCNKiaWVXK\nSmSMGKVg2rTkvO6imAnGghYRZR/HB1s+QEtc5IWVMIaUDoHH5bHsXMrgdhoxEm9LMSnZRDyz0/hk\nHwrjGVrExa5y3EbCxma105jnRFzMyc6nbujQDI2LZFmS2xaJ9yYi8RYRLwkiPpYQ8WwCwwSgk/0F\nMMWnbhi8vLh4V0S007jgLOINQ+cTHa/sxdCyoXC73Ka1SJh8srbF1JyibSQh4pP7UHQFLknikXgn\nPB7gnHOA998Hvv8e8BZaJ6bffa9B19NH4g2HSHw6Ec8+G5ZNJmJbJC1isdOkmYyn2yeCXX+aoSVN\nCtOhGZrjQmyCIAjip8VPQsTXBGvy1rf4481+0PWOisTHo42Zini2Nb2impHPESOASy4BNNkU8f7e\npkDzyHLKNsXocEgJWUSUfbMk80mBzssWeYswsHigYySe22kcIvF2TzzvT1MQ1aJwu9w4fPDhmDxi\nstUTL5nyVJbkZDtNfELVv6g/f80u4pnYll1yciQ+llkkno3dIzwtaC0SzyYtTJSy3PmMqBaNi+9W\nIvGinUaSHO0iOoykyRFLRylG4p3EqbipFRfxDn2IkfhM8sTvsw8geawifv7LKvbbD3jnfVskvhVP\nvDhGO3Y7jX0HX5FMI/Hs/KSz07A+M0UzdNSH61tNbUkQBEH0bHrMjq1Oq45fnbMagVgAF8cmY8OV\nG7BvBiuT7e28Omc1AODnsyekLJOunYqKT/lriqbgzQfWYctB1+BPnnOxJEUkPl376d4LxAK4ZGol\nRvceDcM2brGeKEBn/OlzvDJ4CYyCUZjmA+bOBZQRQZz+smkRuWRqEBeMOxqxXckbMw2f9zxe/fIB\n4N0lABIi/pKpZs7zlwSBF4gFYMDAU5cMwyvnPY/wI/vA7/bj4p1/hXu3GzjLOsaoakbivY/ehUse\nHo3nBE88E1Cb/m8mLnntYl6HWVq+vOFU/OyYG+CZNx1RNcpFfO9/P4p+Rf3gvf0/UPSEneaSqZWm\ncI7CspiTnc8506+BvnsVF9u3n+vD6N5DcJJwLlgf7NiXuQu4yJpzYS98tG0NZniO5OWZ0B4+73lU\n7VgOPP0GgrEgmqPNKPGWYPi851EbrAXuXcgFXuT+/4dLnpyAAd4BlslSTIvhlrMNHNh/NE6FVcSz\nc7pm9xpUNJoWDJfkwj0XlKLEW4LTALzz4zuYOnIqPLIHV53cgPPHnYjpwrF5ZA9UXcWrv5+AR776\nAuWxcv6eoiu8j61x+0mBuwBRNYqLjt+JQwcdirNgRdVVrDnkj+jj7wNVv9by3vB5z0PTNbz1w1s4\nefTJ3PYT1aL83ALAGWep2P0C8PwLCp4/sxL76hNxWK01Ev/DbRfh0HHnA3COxLNxs3u84AxzohBR\nI7hsehUmDRmJ05DM8HnP4843fges+pIfj71NBhfxWtTs5+Br+T0p1ouqURR6Clv9bhk+73kcfu8A\nxIIxvDJnJVySbPluchrD2uq1eGLVE3jo5If4xFAs4/Qd59ROKuzH1Rr2895avUy+k9Ox+mDzGhue\nUenW22/PeDItm+tymZbNx/iorZ9uuaTyGXzntOmaz+a7LMO2uwo9PhIf1aIwYKAqUJWX/sVIJc/3\nzew0OY7EM4HS2rF+tykhHl5p/jOMkp3AiE/x3nvAiScCQSUhdLyyF17ZmzISb98pU4xIi++x/OlM\nkIaUEAo9hfC5vYg5RCFZJN5psydxbCLs+AvcBQDMCLKiKzzCyiLYHtmTZKdhXu6JgyZiv777wePy\n8OhtWAnzHVsBM9+7fYFkSAnxCDobAxtfIBaALMl8h1nAurBVzD0vRuLtEXV27liGHHaMUTXKz5dY\nT7y+Jjw5ARe+ciEAM/LPoutrq9fi5BdPxls/vMX7EMfJ+hA3exKFsJjD/q6ldwEADuh3AIJKEAYM\nR8sYs9O4JMnxHvho20c4df6pWL17teW4Rcbuq2L5cuD6G8xr4vtNCoYPBx54NBGJF6PfPBKfbmEr\n2yRKjSKqRtNmjRGPK50tzmlhO0O8/rKJxLN7TMngKQYATJs3DY9+9SiqA9UZ90EQBEF0fXq8iGfR\n0HztmCr+wNsXKGaz5XwmMHEViAV4hpioGuX+2WXLzIwfv/5NQjwM3c/8YWdZSADrIk0m4lMJFSbC\nSrwlae00TCQzYRVWwvC7/fDKPkQdPpuoZi5sZSJe07UkwWcXm+z4/R7TD88iyGxM7HU2KWHnn+1w\nKkHCtUdeiw1XboBH9vD2ImrEYqcp9hZbhKxhGAgqQZQXJCLUoohvibVYjoWNgVHkLeLjF0W8z+2z\nnDP2d4k3IeL7+PsgqkX5kwuxbVFgi8iSDI/L3OyJpYBku8qKkwEGF/GadcdWv9vP+1hauRRPrn4S\nNxx9A6aMmMLPuaIrCMQC2NG8g7en6AokuFJ64pnPno3JSUyrugpJAkbsbdY/boqK884D3ng3IeIr\ndgoiPgNPPOsnqAShGVrSxmGW/o3kRdFOZGqnyTTNpLiZlZphEIAds3j9EQRBEN2fni/ikV8R7+SJ\nNzooxaQ1Qmq2fe8Xc3DAg4di6lQzx/uXXwKXXJoQHQ3RPQCsIkKMpmcaiS8rKENQCSbZPBhs11J7\nJN4re6HqikXk6IYOVVeTIvH28yX6yoGEUGOinC3IDCkh+GSfJXuLmCaRRcILPYWJxaGuhIgPq2Yk\nntlpSnwlSdFo3dBR7k+IeJ+cyBPP0kaySQAbA6O1SDw7Z+xvVh4Aevt7I6bFLOKbpZBk55+JYYZL\ncpk7tmoKF9css1AqEa/YPiM2DtYH2wlVzFMPmNfHHZ/dgePmHmd5TZJSe+LZNcT+dhK4YlpRACgo\nVDF3LjDnwcT1d+vfozjnHDNdpeiJT+UlZ09s0k0exGNgZCTi459dVaAKox8anVQv0ww1ETUiLIzP\nLAiQEP25DRoQBEEQ+aXHi3g9RbrDzsLJTpNuYWt9uB47m3e2qS+7sKyrBx5+bjuqgruxYQNw773A\ntm3AeRckfsyZuNEMjZ8jsR2Py5NexOsKXJILxd5iBJWgJYrvaKdRozAMA2E1DL/HzwVfVaAKr3z3\nChrCDbwvn+xrt52GReLFxaAelwcxPWGnGVZm7rLKIvUAkiLxuqGnjMSzY+7t781fs9tpxGNh7TNE\nEd8SbbEsbPW4PFzgMVEp2nZ6+3sn2WlYrvjqQDWk2yQ8suIRy3mSXYlI/Pbm7QDMiQo7vykj8TZR\nW+wtNhf96hoqmirgdrkxqGSQVcTrCmqDtagOVltek5A6Ow0TnWK2GBFvfHMsIDnVZGFZInp+/PQI\nPvwQmDgReP3dxHWeyrrC+mMTTnGRrB2n9KRO2CPxYTWMzQ2bzdSTbbDTiPdXpqK8o+x7BEEQRH7p\n8SI+73YaPdlOky7F5B/f/SPOePmMNvUlCsvvNsWwbi0QiIYguWPYssXA7NlAcXHybqMM0U7A8Mpe\nU/SmicR7XB6UeEvQEm1p3U6jJbzGLBIPABvrNuKchefghW9f4IJHtKCIKSbFsVmOX7HZaVwenmJS\nFPEsEq/qKmRJxqF7HWrWcwsi3uXhk62wErakmCzxlljytLMnF70KevHX7CJefKpgH7tP9kGWZDRE\nGhBWwxaRLk6guJ0m7on3u/0o9BTy1I7MfsPqsRzuf/34r5bzJEuyYySe9WM/r+w8Ool4wLyuK5oq\nMKR0CGSXnBSJj+kxhJUwomoUb2x6I26FkSBJLsd7gF1/qSLxfrc/acdW9n/x+ptyQhSVlcAddwC1\nzQkv/NIVzpYa1k9GkXjhWkwnjsV73oBh2SPCkp0mw0i8Zc1JlqKcIvEEQRA9ix4j4sc/Ph7PrHkm\n6fUuZafhW8SnjsRvb9qOjXs2wjCMrFLIGQbw7fcJcaIihn32AU46PQwDBtY3rELvf/bG7pbdST/m\nTHxyEZ+NnUZX4JE9KPGVoCXW0rqdRsgWU+gp5MK4NlgLwHwyIIrJVJF4CVKSx9fRThPf7MkeZWcp\nJmWXjEMHmSJeXBAsRsojWsRip+lV0AuNkUb++ewJmZakQcWDeB17nvh0nnhJklDsLeapNkUR73P7\n0BxtRnO0OWGn8ZjiuchbBK/sRVSLJtlg0n1mLsnFo+tMxIeVcEoRny4SD8RFfGMFhpcNT6rPcsob\nMPDf7/6L0186Hd/VfmfmiY+nuWSTpYrGCixcvzARiVecI/EF7oKkCDy7t8ToeVSNorQUuOkm4Mjj\nEiJ+2qktOP10YNUq63lhddlTo7Se+LjdSxyDE9admnXLbs0WO02GkXjx/spWlJOIJwiC6Fn0iJVO\nhmFgbc1afL/ne8vrP589AY+ueBR4u+2Pktubasi+sPXnsw/Fsy/fBmx0jsQ3RhoRVIK4ZcktuGPp\nHQjeHEzKC27ns8+Av/wF+MQXAA73Ae4oCi9ahSuOPw1vzjd/9NfVrENDpAEVTRVJP+b9CvuhMdLI\nRYvTwlYDhkXIisfHIvG1wdqU2WnESDzrx+/2Y5+ZBfj13Nl4KPwQAFNIMUHjk328PzFPOWBaQkSP\nOeCwsNXlcbTTiAtbxUi8eI2I2WPCbMfWeH/lBeVm3vuYaX1h4n94r0QSO5/blxRtt9hpXFY/f7G3\nGLtbHES87MO/1/wbX+78Etceca3l/WJvMXxuH0JKCLqhJ4l4NnGyI9ppxEg8O++pRLxdaLInAoqu\noKKpAsePPD6pvqIlNoZi56k2VIuP938eJ40+CViSEMT3LbsPj3z1CGZPms3HBDiLeLsnXozES5Dg\nc/ss4w1pCRH/h9kBvHgfcNhhwBlnALfeOgETJgBfffgfAIkJZ2ue+AJ3gWWBtBOiiD/+ylH4y5Jn\ngZXxSLzehki8cG9WHbccV089M6N6QGoR397vuLbW76x6Xal8pmVzXS7TsvkYX6oyC267EQBw3q13\nZVyuPW21pb905ZzKtka+ro98XpfZlu+osm0p3xXoEZF4ezROJF2Kt87AyRPPxuk0sWiImJk57lh6\nB4DkTYREli8Hpk8HjjsO2LgROHpKCwaWlaO3vzf2hE0PMhNCTOCGlFDSbqN9C/sCgGMKQSbi7cfC\nYJH4Ul9pUiRePD7REy9G4pm4rgvX8fE5ReI1Q7OIEFmSkyYUjikmNcX03wtWGa/s5SLK7XJjXP9x\nScdlicTHs9OwpwZsASvLosLE6YheI3j7LsmVJKrF8dqFcpG3iO9ca4/EA+YkbMm2JZAg8c+r2FsM\nn+zjTyDEbD1e2cvPuZ3W7DSiLQdoPRIfjAWxq2UXj8SL507RFX6914XMzzgQC8AjeyxPWQDTUqUb\nOmpDtXxMgFVMu11unnVIrMv+ZtapAncBArEAvqv9DoD5hKfMVwYAuODiFmzdCvz978CnnwKHHgqc\ndx6wu9bsh523iBpJ+TRM1VV+TYnfO7qhY+Wulfz/4j0TVaP8nhAXVgNZeOKF7wNxt9xMoEg8QRBE\nz6JHiHj+w+ggitNte94ZOGWnsYt5EfsPs11wP/jlg7j/7cU4/XTgyCOBNWvMBaubNwPDxwZQ7CvG\nwOKBXFiyqDcTemElnPRjznYpTeWJdxLxYSWMSxdfip0tOx098S7JlTI7DbMt+D1+HjVnaTDDatji\niWfRb7snnuU6F2HjZmKWib2oavWLM48/s9Ow90RhbYnE27LTMPsRm3DxSHxcxLJJhCUS7069sBUw\nBTET1KKIZ8IXAOavnY/jhh9nEfFe2csXJ2caiWcLZquD1fz6CKvp7TSKrqQU8VsatkA3dGc7jRCJ\nZ58xYJ5fdo7ZffBD/Q8AkHTtiv16XB4+qQAS9xQX8Yq5YNon+/Di2hdx4OMHoipQhZZoC/Yq2QuA\nOYkoKwNuucVc6P3XvwJvvgk896LZn7gbaypxregKv3bF++ntH97GxKcmYnO9uR7BPokXv6vEepmm\nmBQnyfWR+jQlHcacp8X9BEEQRMfQM0S8plj+Fsl3JN5pYSsX8bZJh27olgWTgFUgbNsG3PL6Q7hu\n3tP4/HNzwd7WrcDs2UBhoSlOir3FGFA0gGcDcYrEO9lpgIQn2O6JZ4JTPIfratZh7tdz8cGWD7gn\nvjnajKAShNvlht/td7bT2CLxLJqZKhIvSRJkSU5KMSlLyXYa1i4T5Ux8pvKLq7rKhfXu2bux/Y/b\neRlRZDvZaYDEAsjdgd0o85WhrMCM9DqKeDm1Jx6wbiA1pHQIf90u0C8YdwH/N4vEs882ScSnisTH\n7TSicEy7sFVOsbA17s1n4ptl+XHyxAOJzxgwPxsxEh9VozxnPduUyCkS75E9/HpgdVk/ABBS2SZi\n5loCzdCwpWELWmItGFRirllgE1oAKCsDbrsN2LIF2PfAZCGdKkONGIkX7yc2UWFPEyyReC1q+a5q\n08LW+ES12FtsmRSlQnySQJF4giCInkXPEPG2aJzlvTQCvzNwstOkisQ3RZosUUBWpq4OuO46YJ99\ngEA0jEFjarFli7lgrziRMjwh4osHJAkhJgZDSigpO02/IlPEZxKJ1w0dtcFaHqGMqBEeiVd0BQ3h\nBhR6Ck27hminESPxgieeRTNZxDmsWj3xQMLOIX6+LsmVZKdhx8rGyzzx9l1ImZVE0xMbOA0sHsif\nSLC6DL7ZU7w/JzvNwOKBvA9x3OJ5bE3EM4aWDoWdi8ZfBI/Lg3P2P8cq4t0+vlbAnp3Gfi0x2MJW\n8f+tReKZ0BZtSWzMP9b/CCCxJkCsrxs6v64skXibnYZF8wHwCajTwlYWiWfXcJKdJr6JmPh5VzZV\nIhALYK/iRCTeTv/+wPgJyYL9n/dFEHRwtKm6yq9d8Tpn1y7rw26nEScdmq5BgmSp1xpsgj20dGhG\ndpq2pKS0s6Vhi2WzLoIgCKJr0CNEfKrItvhal7DT2Lzw9vHaN+UBgEcfVzFqFPDgg8CvfgWU9Qmj\nsO8e9OplRhS/rvqal2UifmCRYKeJC6FMIvFOnniP7OGiTNEVvLT2JYx8cKRFQLBIPABUBatQ5ClK\nyo7CIvGqrvL2RU88E3hO3mwmIu12GnskngkcUUQzO4dd4Ip2Gicskfi4nYZ54p3sNAOLB/I+WCSe\n5WtnxyKO12lhK2DuwMp2cBX557R/4otff4G+hX352Nh5Fo/L6d92mCeeMbr36LSReNETzz5nccws\n6szy5NvrMyFpt9MwEa/oCjbVbeLv1QRrAJhRdSA5Ei/aaZwWtjJPPIMteGeR+FS7tjplo/nnnDBG\njQIeewxQhNtV0RTHSDyLqDuJeIudJp6dhl3/mUbi2UR1cOngjCLx4tOYtor4UQ+NwpiHx7Spbku0\nBROfmohvqr5pU32CIAgiNT0iO43TQtGaJ74FAMRGZm6nYXX6Xz4+o34zKa9oChZGH7SMIVUk3nhh\nFxZGH8QM3zX8tTn3qzj9OOCm2xpxxMGlOOX//R2ugCkmH/3qUdz2yW0I3BSA7JIRiAUwrGwYfvXt\nVBwVGIlgLJhkp2GLPNmYZviu4ZF4np0mLoYXRh9En619UHWQxMe9pWELgkoQtaFa3sbtrme4j3tb\n4zb0KeyD23f9AeXf9gZOM49DFBONkUYsjD6Ifq+q8P/e5omP5xNfGH0Qw9/wAlcnRKSYnebp5n+g\ncKHVLsKOVZu3AzWuanj28Zib+6hRLixrnvgW19VeiKv73GGx07D3APPzFF9nkfgbt16Mmie+RfnF\nw/lxAKad5t/Nf4c+z9ykSxSQXtmLF0L3oO/mflg5bIfldbHP4oGmIGaWFPZeZb/lcP1qMHr7eyeJ\n5Cu+Pwtu2YM5mAMgMXmpeeJb/K3qCpyI5XDC93I9ZrQch/txP/xuP0b0GoHGSCM/76PfKgISlyDc\nLjdCSggRNYIXQvcgrIYxw3cNF/FsglbgLkDNE99i33CZpT92Pf3fjt8hqkUww3cNPLKHTyRUXcWm\nuk2WaxJIjsQvij4Er+rFHWVzHUV8zRPf4urqc3HrkH9Z7vfv9piLW8//ejImRodgcyxhpxGJqJGk\nMbzwcgRP3g5ceSXw0EPAPfcAR+z6Fv/YdSXuG/WSZQxAIqI++q0i1HzyLWKHp7DTxPPEvxC6B4qu\nYHcGkfiaJ77FEc3m9dG3sC/W16xPWxYAms5OXMfpMnSl+i5jEfh0nv1034PbGrdh5a6VWL17NQ4a\neFDKNjJpi/hpkWlGl0zK5apMNuWyLUsQbaFHROLF6BajJdaMrQ1b0maC6QzS2mlsY2JiwB1O5Bt/\n5jkVLyxqxrS3h2DR+kXQoUM1TH94daAaETVieYTPFjsCsCxctNhpbItl7ZH4oBIUdv908ahxTItx\n4WZlFSwAACAASURBVCqKco9s2mkAYHP9ZvQr7GfmABdEt7jIkrXBLDEel8cSiWfH44pfnrIr2RMv\nSRK3IjB4vXjEnAnxoBK02CtckBKReClFJN4hxSQks78SXwlckstip/G6vLxfu4g3xySlXdjKou+i\niAcAn1yAwaWDLa+xNmWXDJckJb0OmJ9bKiRIvN6IXiNQ6Cm05Im313W73HxDKfHJBYvKM485O26X\nrT6LxKu2FJ6inYb56kXsnniP7IEUv2ZSbfakGZrpiRc+77XVa+PnxwNASh2Jd/C/7zsujI8/BhYv\nNvdiOOMMYM3aEDTdcFzYys4hs/ukzU4j2LkyXdjK2u3l65XRd5q4xqYtkfgPt3wIAPz+zhb2vZOp\nXYggCILInB4h4p1E8Z7QHlQ2V3IR21F2Gs1Q06aBdFrY6uTTX78e2Lw1vnX8zlP46wcfomJ3y24E\nlaDFcrAntCcpn3UgFkCxpxieuJjb1bIrySLjaKcpSrbTDCgaAMAUn6InnvUpigOPK2GnaYm1oF9R\nP0hwwTAMnvtcLM/ELxN7fo+fW1NEb7YUF5rMA23f7Mku4hmsXSbEg7GgTeBKSQtb7SSlmNQ13ptL\ncqHMV4aGSAMCsQDfkVVKK+ITPnRZkpOELotq20W8E1zESzKf6Iivm/0lzs26K9bh14f8OtGABH7u\nmIgX7TQu23llkXjWp33MzdFmy0JVSbLWZ/eHOHm0L2zd0bwDXtma2jJJxLs8fJMvHoE3rGJe03W+\nVoDBIvFFniK4JdnRtib2Y39Nkkzxvm4dcNsDFWguWYGIFsLa1ckpJpkthh1ryoWt8ew0bFKU7jtE\nRDN0+GQfz1HfGu210yzZtgQAMLbP2KzrAonvHfHcNkeb+QZpBEEQRNvpESLeSRSznRGdvKmZ8sp3\nr2DR+kVpyyytXIrRD49O+X7aFJO6gj17zEf1Bx0EhKLmj+zq+/+KNy54g5dhAlfM7rEntMeS8QUQ\nI/GmAK1orODlM81Ooxs6QkqIL/KU4HIU8WJkXYzEs/ZckmRmBLlvEFbuWommSBO3gzARxQShuFgy\npIT48YgRdbsnHpCSxGKiTkL8Aw6ReMmViISm8sTbU0wammXSUO4vR0OkgS8g9rq98Qi3y1HES0iI\neCe/ejYino1NdsmWqLkoXKX4re2TfTig/wE8o475XuLcDS0dikJ3oePkSeyPXT+yMOlhY26KNlmO\n2QXnSLy9Te6J1xTsatmFQmFXXSA5xaRH9vAnGqk2e9IMDcXeYst4AKDMV4YibxEKPYWWdSRO/aV6\nzeMBppxVyS4vbN9q9vHehyoC8eA+izg7ReLtnnjN0Hj2JXtWqlTohsZ36s3kO629kfjPKj7jY28L\n7LoRPf+z352NM1/OfJMqgiAIwpmeIeIdFooy/zR7nCsK/MqmSr7wMx33fHEP7l12b6vl0rUV02Jc\njNrtNCtXqxg9GnjiCeCKK4Bhw80f2QGl5Ra/MItci9Gr2lCtJRIf02KIaTGLnWZr41ZeXswTL2an\n8ck+HkWPqBFuKWAiXozEK5rCBXiqSDwAbqdhAujjbR8jqkV5dpDGaNxO4zLPi7ibqmjrsIh4w5qd\nxtSZySLenoWGnUOrwM3ATiNE4lVdNcckiNvygnI0RhpR2VQJICHMWZSUIdpp2ITBbqUB2hGJT2Gn\nYa/z3WstfUpcBA8pHQK/x2+NxDvYaZgYcwvni03cmqPNlmO2TwLEtQwMj5zIE6/qKnYHdlsmc4A5\noVv8/eJ4lN7Ls86kW9iq6RqKPcX8OmDn9ZhhxwCQUFpQhpW7VjouJHWy09ij8+JE+hc/90IyXPj0\nMxVjxgBPPw1E1LidxikSr9o88fHsNG6XO2MRrxma48LxVIiT7bZk6GIBhEztPna4iBfsNLWhWr6x\nGUEQBNF2eoSIZz9mosjjIj4uXmN64gdv5qszcfXbV7faLtskJhUGksWJHUVXuFCMaTEYBhCKmmP5\nfJmCSZOAb78FHn4Y0CUVEiTzsb9gNWg1Eq9F+Y9lia+EC7atDQkRzyPxqjUSX+Ir4QIsokZ41HRA\nsWmnkSRbJD7+eL5FWBxoj8T3L+rPI8EA8Nr3rwEAX9jWEG6w2GH8HlskPv6DL9pp7JF4M5qcfL5F\nIZsqpaMkubidIaWdxpY9JqSELFOGXgW90BBuwLIdywAAxfHj97lTifjMIvFO6SVTHaPLZbXlOHni\nmTC2vgdE42JzSOmQJDuNXYS7XW5+H4hPLpiPvzUR74QYiY+oEdQGa+GVrRl8drXswlkLzsLTa55G\ngbsAY3qPwQH9D0gv4uOReDZpO3jgwQCA44YfB8CMyEe1KFbtXpU0Jiehahf24uZb5WVueN0ezLxE\nwd57A7/5DfDCS6kj8VEtmpSdRopP7ppjGYp43fT8e2UvdENPShdrp712Gjb+tnranew0qq5aNq0i\nCIIg2kaPEPHOdhprJF78Ma0P11sEsROGYaAqUJU2QhZTW4+EmZF4U5hs36lg+nQgGDbHOe0kBW+/\nDey/v1lW1RW4XW5IwiJIMRIvCojaYK1le3j2Y1nsLYYEczGqJRIvLGxlP+YuyYUSbwmPWobVMG+n\nf2E8Eg/JstkTt9OIC1tdHssuo/2K+lkixF9s/wIAMGHgBACmnUa0vYgRWNHWkWSn0Wx2GqdIvBBx\nFwW61U4Tj8Sns9PYouWBWMDRTvNpxacY138cF/0+2ZeUzhIwRXU6ET9pyCRM23saDhxwoON4RIaU\nDjFTUXoKrXYa2zECiQmSRcRDQlSL8Lb8bj9iWow/ObHbYUT7iluY3LCJRyAWsHyG9vpOiHnid7bs\nhAEDPtlr+TzEFIoF7gJIkguu+CZfLFWpdWGrwe0m7FxMHTkVsiTjxFEnAgDK4tfp55WfAzDTWS5Y\ntwCAee1JtrHbhb34NIxNRPoPVLF0KTB/PhCMmGK3vlFDLNZKJD5u0XJLmUfidUNHkbeIX5+tLW5t\nr52Gi/gMU2DaYZM/sb6iKxmvASAIguhIrn776lZt012ZnpFi0sFO89CYhXjlu1cwJmrmN7bna3d6\ndN7/8vFQdRUTnpiAmeNnIqJGLBFnO5WnK5gx95qU77O+/tz/QWys3wDpkb+hfC3gOiYGHcCAQdYf\n4EfHvoKVu1biLFzhGImvD9fz1Hf/F/o/iydeFPH9Lx+PWx67EMHGxA8li3yx7DTn+a5FWUEZhnqH\nQpIkFLgLzEh8/Me1f1F/zPBdg+sPux7ny+fzcyjaadhYzpbPTrLT3DbiMXy07SMA5jb2frcf+/Xb\nD4D5iP6K8r+h+nLTT26PxEfUCGb4ZqNhlnncTLSJIuTPA+7Dl5d+CdgyePlkH09P51mTiLYyEdv/\n8vF44MOXEfvCtNOIQl9Ma2ePxAdiATy5/+t48WzzXJQXlKM2WIsdzTtw0fiL0P9Us+5xi47D4YMO\nt/Q7w3cNbjvyNox2jU5qm/XZH8B7M9+z9JkqzV6/on7Y82dTTC5cvxD4T/Ix/uX1R4HVzpH4wlmj\nEKnYBbwMHD74cO4Rb4o04TLfn7DrIqvVQTxHHx/zPW768Ca4XW5L9J39u//l480nQA8lj1tMnep2\nubkQ3d5k7pS77bQo/vzB/YDD/LrAXcDPh3uBG19XfY0+d/fB/v3MGbBmaPBfsjdm3HUw7vHew8dz\n8uiTMXvSbPP6vNxsa++H9sZXu74CABz0r4NQFajCKWNOQUSN4A+9/8E3mwKSffJ14Trc6LsHAHCt\n61o+wZQk4IILgDfcUczfAJy142X4H3sVh9zwPK+b5InXNdwxfC68sheBqHPGHJH+l4/H35+7BkV6\nkeXpmN3/z8oCQPM7c/lr6US807WmGzqvky4S3//y8fjlK7/E+KXjccMxN1jeSxeJNwwj6akNpZZ0\nZu5c83OcNWtWp9TPpnymZXNdLpOymbSVqzIdUa4jy7alfEe1kU9e+PYFNEQacO4B5+Z7KG2iZ4h4\nh0g8i/w4eeIVXXFcxAaYEbo1VWu4cGmJtjj+2ABodRdDTQN+3BrDj9sLgH4SDjsyhrf/a6DvI9aM\nGoyGSAPfSIgJPUVTEpF44emB3RPPxseiowOKB+CTbZ8kjSmshLmNxCt7ufjmIl5JiHggecdWFoG3\ne+KZqIuoEfQr6pcUyd6v335cUDZGGi2RW9ETL7Ytbtqk6Vqrmz2x8TIskXhbdJxF9ltLMcm8xzEt\nZilbXlDOPw9m1QCAhecudByPuGNruo2YsqW1zZ64J16YOMiSjNP3OR3Grebib3b+2QRNPFf2uuz6\nFK8LwDkjTzpEOw1bV7BXyV7cllXmK7P4ucX2Wb2YFuMTAHH8xd6EJ75vYV/LBJO91hxtRlgJ8/Us\nQSWIsBLG0NKhqA5W82s5yRMvPA2TXeamWRYbn8sMFhw1OYi+YeC1ZTHgcAmQDERsO7aytRqlvtKM\nPeLBWBC9/b0t92Q6RNuKeP/8a+W/cMywYzCu/7iUdZ2+T1OxtHKpYxknT7yqqzBgIKJGLBN4giCI\nziaiRizf692NHmGncUoxyX58uSdei2HJ1iVoCDdA0ZSUC7WYf3tN1RoAZhTZnl3jjU1vIKpGuYjv\nW9g3qZ0VK4AjjwTWboih0GcKnuNPUFDSyzqZEGkIN6Dcb2YRcYrEi6nxqgJV/Ada9MRzEV80ICkf\nPJCw08gu2VzUGhdNfrcfYSVsicQDppBmgqEl1sJ/jO3ZaYDEQsd+hf2SItnj+o/j4rA+XG/ZldS+\noJEdJ+uXRTtFsSRLsqMVRhSg4kTCsuA1PraIGmnVTsNEK2Bd8Dmq9yh+rMePPN6xDfEYfILf22lh\na1sRj8vJxuMUibcvXGVCyn7eGeJkiGW5abeIF+w025tNIT6oZBAX3PZ7yknEA9a1GRYRHz8XLH2q\niE/2IaJG+L0OmE8hDBj882Z/25/Y7QnvsdRhuwIzeIpJOYBXXwVOPSMGl2pe648/FUUoYs1OI0sy\nSn2lGdtpQkqIZ6cBWhfxYTXMJ2ns/jEMA3946w949utn09ZlbRe4C1r1xAdjQccyqUQ84Jy1iCAI\norMwDANhNdyqvbor0yNEvNNmT+LGRYApOqfPm45n1jxjRuId7DSGYWDxxsUArI+excWtWxq24PSX\nTsdr37/GRbwoQmtrzQVuRxwB7NwJ7D9OwSEHeuFzJyK6fNy2SHxNsIane3QS8YxCTyG2NGzh/7fb\naQBgYPFAx3MVUkLQdNNGUuwt5mKlwF2AiBbhE4M+hX3w+KmP45fjf8kFQ22wlrdjj8QD5iJZCZIl\nUsg4oN8BXHAGYgFLykN7NK4x0mgR6U6e+FSReFHUplrYyv4dVsOtLmwVRbzY32UTLkPNn2pQ9acq\nR6Fo78vn9nVIJN5JuIv/dvLE2ycuTOSxiVlaEe/PkYi3ReIlSBhQNIBPBPsU9rGUF9sXxy/eT2z8\nRZ4i7Nt3X4ztM9ZxkyKf24eoFsXn2z/nrzH/vV3Ep4vE14RqLItsAVg2XgOA/nvFMKDcHEPlzhh2\n7Dav4eagwu/DEm9JxiI+qAR5dhqg9YwzISXEz4H4FEAzNMfvQBF2bku8JRZrTap+HCPxSrKdho2Z\nFrcSBJFP2HccReLzjNOurPYf34ZwAzRDQ1AJpozEVwersbVxK0+FyHCK9jVFm7CzZScA80LQNODR\nR4GxY4HnngOuvx7YuBHo1TfGt5hPEvG2SHx1sJpvsuS0sJWxd/ne2Fi30XKsTpF4J1gk3u1y48nT\nn8StP7sVQMJOw35YCz2F+N1hv8Pe5XtzQVsbSoh4cWLD3i/1laJPYR9uMwCAkb1G4orDrsCMA2ZY\nBCfLGQ84R+Ltthh7JJ7t9mpHrCc+DXCK0IeVcKspJi0iXuhPkqT4At70t1De7TTu5BST9mO222ns\nT1FEEc/Oh/iEBnAW8XablIiYYrKyqRJ9C/uaWY5SROLFNJWpJl5iJP7SQy7Fxj9sdLTB+WQfomrU\nImLtIp5lgHHyxLPvh5pgDTwuD99wCrDu2QCY3w1+jx+yJOOKP0ThLzLv+Zv/oqC2TrVE4o343hZO\nvPb9a2iONqMl2oISb4llF+V0hNUwP6fs/uHrY9T0IpqL+Hj9qBrFJ9s+wZTnpiQlEQirYcdIvNPC\nVh6Jp8WtBEHkEfb9TpH4POOUYvL/s/fd8XFUZ9fnzuzu7K66bVmSq9wA4y4bbHp7MaYHSAKYUEwv\nCc28Hz1AMDU4lLyhBBLTA4TENCd0k9BMseWCsbFxw7Zs2ZZVVtL2ne+P2efunZk7uytpJRuzxz/9\nLO3M3LlTdubcc8/zPFaSTi94Ci6TeeLp5TahaoLpc1ElEwNESYlvC4cxaRLw618DEycaKSPvvx8o\nKjL2R6plNB51VOJbI61oj7bz1I7plPi9e+9tUrFkdhonJZ4KF6lMxcGDDubBpj63z8gTnzwvIrHm\nSrxA4nWkCIdop6GZBCIZvf298ejxj6K6tNqkkpOiC9jJXlOoyZZlxppikqqeWjPUOGWncVLiMxV7\nKtFKTPvsKEQ7DfXHSpK7ApOdRpXYaSRKvM1OI8QquBW3NMUkQfTEi8chzqbQvsSMRQQ6h2LF1vq2\nelQVGcS42GNsYyXxYjYkF5OTeBrs0nfACaTEi6TTSuI1VYPP5ZMq8RRMu61tm81OQ99vkcTT99+l\nheErNNYtLo1i/YY4FnyuItxSLLXtETa1bMIpL5+CF5e9iEAkYKoFkZHER4P8OlgV8ExKuKjEA8Yz\n9fNNn+Oj9R+ZrH10jjriic9m/3nkkUce3Ql6djWFmjqVvWt3wJ4R2Cqx01wxMIhgZRVmLtsCIFW0\nJBKP8BzNVgSjQcweU4WBJTvwr9Wpz0XVWXwBbmgySPwd+xRCu3A6+vZ9ET//uakmEKLxKNyq2wiQ\nTESw9tvLMXuM0S+RlFLlTyLfYgq5i/u1INw3dSz79NnH1O9QLIRAOIDZY6qw6bur0W/SK3wwYAUp\n8bftXYiFi6ZjYs2LAAwlNRgNmpR4AFi4aDo/V6KdRsShni+xcNF0HDv8WD7gIZIh2hm2r7meH3sv\nr12JL/IU4fa9C1HgqcPKHXYSL16zC/s1YeGi6VAVlc8sxBIxE1nVtv+R709GcIPRIM7ss9l0Hgii\nEj97jEEw16RR3Rcumg4AtnZEO41a/xBmj6nCWwG7Eu+0faZ1rHYaWsejGgNRmSd+8eJfAWC8HVGJ\np/XEfYkqvuiJVxUVs8f2A3QdSxSz3YWBoVgrxtbWrfz8zVy2BX38fVDfVm+y0wDA1YNjWLhoOoq0\nAQCAPj6DxDMw6NA5aVy4aDqO8q3CU5LzIyrx6c6n1+VFOBZGKBbifbOSeK/Ly78TqfOhoyHYgIlV\nE7GheQNmT52NG96/QWqnuWm4cS2iiSg8qocPHOgZdfXMKGZ/GMf2lS5U7piH2WOqUN/UgsK+9gEI\niQX1rfWIxCOYrH6CwkYjZicrJd5ThNljqjAk8gaA6/kxZWun+c2gMJr7ViEcD3P1XCTlYmyOFa2R\nVsweU4US7w/8s6544rP5nnQF3d1+Z9HVzB8d3b4j62e7bq7Xy2bdbNrK1TrdsV53rtuZ9burDUJP\nf//Ed0BjsDGtNXZ3xR6hxMvsNNYqkTz4NamGU8VEETQq87uNQDSeoSZiJ/EfL2hHXUNSjWIJ7Lc/\n8ItfwFaAiJQ4t2LYaRLClLk46KAsGTI7jXXAYSXxoieectJnstNY1VaZnYZAOcdFJV4EtXXjITfi\nnv+5B4DZYpNaL3W7iUo8qbhksbGScSLq4vkiBZ6UXSLpIlkXj9Fkp0n2zcgLLi9MJPXEO6j26SDa\naag/3WWnEUkxEW9up0kej5ifnyAGtsr6Ru2qTOUqN51PJdmWVzWnOfSoHqkSTw9JMbBV3AcN+kiJ\nH95rOO8bwamYFK0jBk3LoKkGoRZVdhmJ97l9CMXNqRETegJVRVVY/ZvVOGnvk2zZaUiNTugJ6LrO\nv/+aqplSTMb1KIpLYzhumoqSIuO+OvToFrzxhr2/m1sM2x5lsFEVlZ+DTHnig9GUnYZmzzqqxNN3\nLBwLc+ItnjtO4tMo8abnXiLvic8jjzx2PUQh48dqqdkjSLxI0AmyUu+AoRZR1hbrVDlZSTTVgxKt\nBEPLhgIwK/HLVxkvnrc/aAM8lNtZh6LI/aykxJGdRqzyalLik7mprXaaYDRoG2zIlPjWSCsU4eUu\n2mlEshRLxIyUlFYil7QO0ItVtEdQARwnJV5GhLnFRkjvJ9o4ZJ54kcRbbTFx3ZxikvZJx0bri9uJ\n/ZLaaaJpSLzME98ZO42SstPQvrojO42maiZya/Wli5VjrRADW63pJYHUORaLDIlFrADYcpV7VI80\nqJTIuVtxm84DJ/GaObB1bIWRN9xMVuXXjAJbM9ppkp74cDwMV7IP9ACnmQarEg8A0bhB1nv7UkG3\nfrffNMgX1eiEHjfZaUQlnrLTFPhUDOpvHLu3OICTTwZOPBFYl6rTxsl7Xavxv4up/DuZjRJf4C4A\nGOs8iU8OXsPxsJSwZ1LiAUAXnsd5T3weeeSxO0DkgD/W4NY9gsTLij05kXjxxWUl8fS3wlRcd+B1\nuHzS5QAMT3wgAFxzDXDr74ztD5m6E2CplHQiORcRiUc4YYnEI6bgNXHQQXYaqxJP6jcRHpWpXJ0k\nkCdeJJnlBeVgYPCoHhvBCkQCUiU+GAsiGA2agjABQ/lkYNjWts3420KiZMRQZqcRq7iK2WmIRBJx\ni1uUeJmdhqY8iGAQmTVVJhWVeImdJpqIOqq6MiX+kMGHSNdNh55S4q1tOnniZQMROv8t4Za0SnyB\nuwAqU/l9BaSuqfUe+/X+v8Yv9rUXzyASL3rixX0cMOAAHDTwIAwrM1J4jiofJTlq+YBZtNOkA1lb\nQrEQ3y/d29Q/r8tr88TT80XMnDOkdAjW7FzD/xZJdVwg8ZrLSGtJAgLNBLoUF7+HH/1LCx54AJg/\n36jiPGsWEA6nSDwp8qqi8vOeTZ54n9sHBsbVcBIrnGplWI+FzpGTEs8tNhIlngY4CQmJzyvxeeSR\nx66EicTnlfhdB1mxJycSL/owrS8xUt0UpuCWQ2/BhTUXAgA+XxTAPiN1PPTMOhxwmLF9QYXx0if1\nOOGQWUJU4kQ7jaZqNiWegXG7ASfxSfWbSKjP7UOpt9RkVQjFQmiNtprsHi7Fhd7+3jzLhoiWcItN\nyxTtNNZsMQB4pg4Gxq0wtJ6MCPO0k54slPgk0RQVTmuqSLudxgC307gkdhrh9jZlrTEp4emV+MrC\nShR6CjG0bChOHXmqdN10ED3xXInPZWCryz54Ef+2euJlAy5ZELMIuhcLPYVgjMGtuvl5JiXemib0\n7qPuxvF7Hc//pnuTvO5OdprJAybjk/M/4fdY/+L+AICrJqeqvVpnpqj/jaFGMDDp/SuClPhQLAR3\nGhJPA1va59rGtWBg2Kv3XrytEb1GYEPzBiytX4q/L/87wrEwPzfxRNxkpxGVZ4rLURUVarIP7fEW\nzJwJrFxpqPG33gqMGQMsXJ1U4k12miyV+GgQPpcPrCtKPEsp8ek88VZRRNd1wU4jzEAmv8f5PPF5\n5JHHroTIAfNK/C6EWOxJ13XEE3HHdG3ii8sa2EUXlIjOts1+QFfw3MsBxA69CbhqKCYcZUS8Erkm\nMipOF+u6jvVN640+xQU7TSJlpynwFNg88X38fWwZTHaGDK8ukStSPAeXDIbKVE5IDCXefDkrCytN\nJJ4yrQTCgbR2GllqQGqj1Ftqs79ka6cBGCf8Jk+8y07inZR4IhTcE58kh3ResvHEO6n1IkSP9sR+\nkzCwZJB0vUwQs9PQrnKaJ16124jEffCKrTSTI/H1iwPCtEp80mvuVtypQQHkSjytRyCiKtppzCTe\nPLAZWjYU4yvH44ABB0C/TcdD0x7iy6wxIqKnv8BT4HhNCdkq8VVFVVjdsBq6rmNr6xY0h5rw/KnP\nm2bChvcajoSewLjHx+GXr/4S4Xg4NaNksdMQoQVSudpVpsKVvCYUFD5gAPDKK8A77wCJBPDe53Wm\nPhqZmbJT4qnYEwPjz8RO22liHbPThGIhTt5lSnzeTpNHHnnsSuSV+N0EoqId1+NpqwuKLw4nOw2D\ngvvuA0aNYkCkEIf8TwuCY/4EIJUpgl6oMiV+1n9nYcjDQ/D6ytdTdhpLYKvf7TeRkfq2elNGGSIX\n9OJ3WQIVB5cORom3hCvorZFWG0GrKKgwkXiyhrSEW+R2mmgQ7bH0JL6isIITRiIrLEs7jbiuTIkX\nP3NKMcn7xiyeeJmdBnI7jUgunegerSPziHcEJjsNdoGdxpXZTqO5NFPWGSvoXBQkA77FQk/MwU4D\nmGc8XMn9ioGt4nWw5n4v9Zai9pJajKkYY2vXSuJp382h5oxWGnH9lnBLWhJ/zLBjsKF5A1bsWIGm\ncDO8Li+mj5luastqbQtGg3wwalLiXZpJeY7GBTtNMmXm00uexvx18/k6U6cCy5YBfYYaNhpS0snS\nRO04Qdd1qRLf0ew01L9QLNShwFY+aGEMCcEClbfT5JFHHrsDZLVCOgLG2EDG2HzG2LeMseWMsauS\nn/dijL3HGFud/L8sU1udxZ6RYlJ4kVHg5sxlW1A29kmUjQUal17El5uUeImdZuayLei3cxaCntU4\n5pgR+KJXMYaPCODjxYa3kwJQ6aVf5i3DzGVbMG3A7fDWrsZ1vbfhtx/9FgDw18V/RTAWhObS4HP7\nsKN9BxIVt2BW/Qb4RvhRv/Qi9Lm/D1474zXUt9abMsoQuWiPtmOW73for/QHcBwnvCfvfTL6+vti\n3up53BP/952DMa/qDqB2NeZOGIET9zoR65rWYd7qeQAMYrSheQMCkQDuYg9iIpuIucn90WAgGE2V\naT+ldjXA7sDcCSPgmd8PANC3oC92tBul5weVDEIffx88ot2PYlbM2wLMVVzFtv67agoAM2Gn/b2t\nHoU1bDAal16Eo4eO5stVpnIl3jfqj3DFo5jb9CbOm/Yi1I+MlISaS0PZ2CfxH20g365i+P2YQIGK\nVwAAIABJREFU+Y4RBEyk85Ta1WgJpXzuHwZrcFbNX0z3wSm1q1HfalgmNFWzpbs6pdaYjZk7YQT/\nzGmdSYKdpnzYfZj5zr64dKLb1oYspVamdU6pXc3t4XR8tM6WVW8BAJ4JjsLbtatx14CUnYbWEduv\nKqpCY6jR1s4ptauxJWj40rkSr6aU+D9t9KGu6kaMiOyFqy39p3tg5rItGLzfyygb24L9+o3C/v33\nx5i+Y8xxF1XXYVZgGL93nTCL3YGF+kIAZ/LPiJQ3hZo4iZ/F7jCOTdIGDeiCQ+7APUofrPn2NE5Y\ny3xl8Lq8KPIU4djhxwIAzlm+FZvCM3F0/D1cbmnLSuI9Ix9Cq7cUM7/8BeaNeQqR+DXcTiNmd4om\nDDvNJ96TsFUdjteX7Q1gC9qj7aiprMGcxXMQuiUEnw+IeuuAJD8uG/skzlm1Px7fVwPwJiLxCP6z\n/j84/JnD8c1l32BU31QMQSQeQenYP+NfbAg2r34SP9tnIs5A9kr8PdvKUDb2SdQXxTHzv5fizdFh\nqepOn0UTUST0BJ/JJBJ/n3I3EnoCVybX70qKSfE7IPseAsYAY9Sjo/Cn4/6EacOndbr9PPLIo2fR\n09+/UCyEWex3AIBftH/VmSZiAGbqur6IMVYEYCFj7D0A5wH4QNf1exljNwC4AcD1uem1GXucEu9U\njZUgvjhMUykNwNMvGH/HYwpGjwbmzgVKfUXY2LKRr7clYORqp5dYSok3potX7zReLEcOORJvfPcG\nYokYjh9xPEq0EjSHmgV1S0F7tB0NwQZ8s+0bbG3dalLi6UVIMwcu1SA8pKxeWHMh/nLyX3jAXGuk\n1aZCXjXlKjw07SGbEh8IywNbSWmz+puBlKpaUVDBSVChpxAfnPMBir32VIJiASgRtK0YMErH5FSc\nyaW4EE/EEY1HeQpNUpStdhoxeFZUgp2KQDmljaR2cqXEi8WecqnEg4GTRNl+6T4iQu10vFSF1NqO\nsQvjXND95VbcNi++zGtvqhKb3O/g0sH44sIvMLBkoOk6iIHOmUAkkLaXkfh0oL4bqVYV02yFR/Xg\n7bPexhX7X4GBJQMxpu8Y1AXqEIlHcPDAg21t9fH3saXSpOOm77tH9cDn9pmKxlF2GsaY6bu4ZOsS\nPL7wcYTjYei6jrZIG8+6Q2hvc+Hk443z3haO4E9fGbOEtVtrccuHt+Cbbd8AMNsDxaJURLqDsWDa\nKrH0TBMrttLzSKbEA2Z7DwW1ulSX2ROfgxSTDy14yFQATERDewPWNq5F7ZbaTrefRx557Pmg55iq\nqJ2y0+i6vkXX9UXJ3wMAVgDoD+BkAM8kV3sGwM9y0V8Z9ggSb6qCmrCTeNFCINppgtEgdB144QVg\nn32ALxYaL71JExX0ThaMLNKK8OG6D/k2lM+dwEl8UhKlDBnnjz8fAHDY4MNwyOBDUOotRXM4ReIV\noU9NoSbsaN/Bq50Chk3Bpbj4i46qVFptC16XF+F4GIFwwJHAWEl8W7TN5mMv9BRCh44d7TvS22kK\nKqRBpE7rmz3xBoEq1opNBI4GDSpT4E0SKnFgZvbEG7cskUJrnniRTKYbFBCc0kayNF7vjkC0u1Cf\nc0riYba3WPdL91k6Ow0AXjFV1jcimWSnuXjixTh1n1Mt7UpIvMQuI95bIskXB3WZQIPdIaVDAJgr\nzlIf00G8bxWm8D7RgPOw6sPQt6AvAODy/S7nz5ODB9lJPGMMI3qZlWBKK9oUajJIvOKB3+03kU7K\nTmMdIIkKd2ukFVtaDdFAfDZMqlFx3DRjH7fcFsGiDauM/aoe3PXxXTjwLwcCSJFkRVGN75BuDH7E\nGch0ggcRfBqkhOOp7DQyT7z1c1Li3YobOnQekNxVT7yu67jmnWuweOti6XI6h2JtgTzyyCMPK+hZ\n6FbcplTBnQFjrBrABABfAKjQdX1LctFWAPLCPTnAHkHiRTuNTIkXi7+ISvyGuiCOPRb41a+A4cOB\ni69IXlA1dVqKPEUmFcnqtycSXxfYjCVbl/AXx6kjT8VZY87C7KmzARhBpU2hJk5OVSW1jx3tOxCI\nBGxqpFtxp0h8kgRZVXJNFZR4d3oSLwaTWt3gtKwuUCcl8fRCryiskAaRWiHLTkPbWI9zWNkwDC0b\nigJ3AcZXjsMlEy/BRTUpC5ToiSeSTmTUmieeOZB4a7Yb2e8i/B4/hpQO4USxsxhbMRajykeht793\nKmg5h3niAePYrOR7eK/hqC6tRkEWeeKBlBIv6xsRTSLIvz3stzhl5CkZ2xXPbalWijJfmWO2oo6Q\n+OqSagRvDnJ/PX0n4nq8Q0o89YG2l2176aRLMbRsKHr7e2Nk+Uhpe9OGTzPZw9yqhcSrHls+ebLT\n0Lnddt02rLhihandplATvt/5PQCYYgO8HgVPPmbsI5aIYE2jMfu3ZafRfiASwModK7Fiu9GeyhRT\nUSqRdKdTw7kS70kp8bJMNOIzVWazoaDlcDyMhJ7g7bZEWrCuUUiInyWcis7xPsTyJD6PPPLIDHqO\nuRRXxiQB6cAYKwTwDwBX67reIi7TDfLkPOXZRewZJF600ySitgArUZ0T1Z/fXBPCp58Cf/wj8Mkn\nQEmvkEH2BH5LwQ4/20c+G0Iv7+ZQM5pCTWhob0CxVgyf24fnT30eE/tNBGCQlEg8wqfURUWUMtmY\nSbZxY9ELkpN4S/o8zZXKTpNJie/lTRENq52GjqO+tV5K4mlKv29BX8eMKCLk2WmMbUTCAxjBjmuu\nXAO/xw/NpeHxEx7Hz/f9OV/uUlyc9ChWJd5qpxEunqgEW4mb1Y5jhd/tx9qr1posTp3BEUOOwDeX\nfwOvy9s9dhoYx2a9FgOKB2DdVevgdRvnJV12GiBF4mXqKA2MZJVQ05F4mk0CjPtrbMVYx/13hMSD\npfK4A+bZkqxIvEmJZyklXrMXpwKAgSUDMbrvaMcB0KwjZ+HNM9/kf7sUI2sUzbx5VA/8LvN3iuw0\nFKDtc/uwV++9TNacplATvq77GoAxowckrx9LXc//vTECeAyyfPMdqXfHmf84Exe9eVHyGBU+EAay\nJ/EUCMvtNBlSTAJmJT6VZ9645qFYyBSU/Oq3r2LoI0NNNqNs8EPzDwCcM0txJT6cJ/F55JGHMyiw\n1aW4pHUusgFjzA2DwL+g6/o/kx/XM8aqksurAGzrem/l2CNIvMlOI1HixRe7OJU8ckwQ334L/PrX\ngKoay6xKNxGXR6Y9Ik2lKFYZBYD1zeulhKTEa6R35GniBDKzrmmdqS2CS3GlPPEOSrzX5UVrpBXh\neNiRhHASL7RvPRZSx3Xo0jzbjcFGAGY7TToySsr6gOIBps8LPYU8A0i2EL9gZA+xKvIdsdOApUij\nkxLfHbCmD80VZHYa2TpAZjuNzBdIZElGkDMp/HSs2aR97CjouyCSeKfvgAhxfQUpT3w2AwAniORb\nYQpKvCU2JV5Eyk4D03YTqybyv4nE7917bwwsNgK2VYs96ofA93z90qqUXWfF9pXY0Lwh2a4q9cQD\n6Qs+kWJOx9YebecE2dFOE7eTeDFFpTWzEABHb7sTNjQZx+VW5Pc89a2j7eaRRx4/LVD1eoUpnVLi\nmfFi+wuAFbqu/0FY9AaAc5O/nwvg9S531gF7RnYaixJPJJ6y0gyuHC/d7qLLgxiYSmaCUCwEr8tr\nynbw0mkvob6tHgNLBqJIK7KpRkSMdy65ENFEFGv6jJSSePpse9t2NC69Gb+ouRgrk8toStlqM3Ep\nLjSFmtC29CI8eEktJsDu0dZUjftmCz2F0sweMhI/ouHPmHvsO/xvcRaACIfYFlWalNlpZPs8csiR\naLmxhZM7WufriocdCadTVhKX4uJkY1TT03hr1VtQxxnfD7Fia+Pii3DRiU8CMFRLUitdisvWj2Ef\nl6Ah2CAltemyo2Sz3GkdUYnvbBuy5ft8arfTWNdJVSNWbMuAlBJvLXgxd8IIvLXqO3wCSP3mbtWN\nxqUX4Z79Fkj371bdCMaCeHrfvtxnnul4sl1HpsSTdzxdWzRgaFx6EW6d+ge8lhwMWK1fHekXEd3G\npRfh0pPn4B5vKba3b0coFkKBpwDuuHngRkr8yexT3DFhKv/8kWMfwQdrP8DV71yN5nAzvqr7CkdU\nH8HbL/nhLsw96TtOhhdtXcS3/cVZLXjoC+P3cDz1DLzt7Pdx3TfGdPGc2jmmQNnXVr6GMX3H4NgR\nx9qO6XT3Qly39DoUHW3EAYkp2JwCW0VyT4OGYxPzMXvpbISPWCcl8YFIAE8vfhrTx0zPapaKBicD\ntj6MuSedbVue98T/eHD6E58DAF6+5IAOLe/o507LctVONseS7Tp59BxCsRAiK6/G2KFHY3Wa1ORp\ncBCAswEsY4xRkM5NAO4F8Apj7AIAGwD8MicdlmDPIPGSFJOAEBDZLg92oxcdIRgL2lTo/sX9edXI\nYq3YROI9qocTGxpIrG1ci8kDJtv2RYWWyM8pWhMaQ4bKbbXTuFU3n9Imgm/tn9fl5cQrk52mxFti\nFH2BblOgxQGEzE5DELPTZFJPZerspH6T0m4jg8pUrgrS8Tt54mUBrDJiQIMqJ3tHd6DIU4SxFWMx\ntmJsTts9cOCBqC6tTrtOpuw0/YqMFKKyXLnWYk8irEXInPabawsRkLpPxe+EGADqBNFOo7m0jHaa\nbCAq8ZqqodRbilUNRsBpRUGFbYaDiKb1eozuOxqaquHqd67Gt9u/RV2gDpP6TeJ9o4EG5Ypfs3MN\n3zYQkdtSfljrg0tx4cvNX2Le6nmma3HTBzdhfOV4KYknZYr2TbNxYv+BzEo8nRurnYbw3w3/xWXz\nLkO5v9xU5dcJpMQ73XN5T3weeeSRDYKxILwuLzyqp1NKvK7rn8C53MxRXepcltgjSLyTnabEU4qG\n0A58s6gAGG7fzlaxNWq304go0UqwCZv43wXuAhuRDcfD6ZV4IvESVVOmxFu3l3niKW97JhLvdXlR\n4ClAa6TVTuIlSrwMJk98msDWXEKayUbITkOeX2ufeMEmST9pUNWTdhq36saSS5fkvN2/nvzXjOuo\ninGeHANbk3YacVaLwEm85J61VoZ1Wt4dJJ6+C+J3IpPaD5gHn6K3vit2GlHF11wGiV+y1bjWFYUV\n0poUgNzeRN/1+euNwk+T+k1KVRBOEmrGGNyq2zTosqaiJFx4ng+V57ux02WsKz4v43rcMVCU1vO6\nvFCZyqtHA9kp8XwQIATGyopTUQG9bPPGkxLvVNQvr8TnkUce2YDcFxRb+GPEHuGJt9tpkg/xeoOo\njaiWK/Gyiq3pUgqSokQv3kJPYVqVV4TVEy8jyrLAVoLf7UexVmxbx+vycqtLJhKvqRonYlbyUKwV\nc4KXjsQXeApSdpou5lDPFiYSb1Hi1WT6PJnqTscj66f1Wv4U4FE9jsdL9864inG2ZXRu03niHZV4\ntfuUeJknnjLWpIM4qPO6vLwdJztNNlAVlX+3NFVDiVbCyWTfgr6275Q4W2gFPSsoz/mIXiP4/Spe\nA4/q4d99AI4Boqed5EfdJpdpXbE/29q2SfPFR+IRbkXTXJppwNARTzz12UmJp9ob6dJdiiAS77R+\nXonPI488sgG5LzxK55T43QF7BokX1J3NW6K4/w/Gw13TDTI9uUZO4m3qmMROI4JepL39Rln1Ak+B\nVOUt1SQkXjOTeJk1wUmJZzCyfMw/dz6unmKuiynuPxOJ96gevo6VPChMcVT7rcgmT3wuYR3MAGYl\nXiTxImFnjMGtuKUEks5DT9ppdjXEXPUyfHv5t5h/7nzb53SurANIIJUTPZ2dhoF1y2BJ5onvqBKv\nqRrPHNMVEg+kng+kxBMqCipMpNnn8pmKjFhBgbD1bfXwqB6UF5TztsU+0n1N18eJxD9wjw/jx1pm\n3rTe/Hcq8mYFBeUCyZgTBztNW7SNf/9MnvikuCLmmZeR+LrWOt6PbEB2GkcST8G38XDWbeaRRx4/\nPZiU+M554nc59gwSLyjxZ/4qiuXfGQ/uyeMN4uxUAMZqp8lWiafsKh1R4umzukCdyVdO8Lv9NsVY\nVJcZY6ipqrFlsBH7O6hkkLTfRLTSkXggNYiQKfGLLl6Ed3/1LgBk7YnPFdIp8S7FBZWptiw14ray\nwUa687Cnwq24He00ADCyfKSUqE+smoi3znwLh1cfbluWjRJP968MtZfUYuM1G6XLMoHu046SeHF9\nUYnvip0GSD0fPKrHTOILzSTe7/ZzAcFpcEPbDygeAIUpjko87VdTNVM2FjEDlM/lQ3lv831ev663\n6e8tgS0mkg5YSLxFibfaaejZIVPixYqvROJ/f/Tv8crPX+H7puWZEIqFeAxRJiUeyKvxeeSRhzNC\nsRB8bl+nPfG7A/YIEt/cGoESN17EI0dFcf3NxsO9NDkt7fRytr4EMnnirSRe5ok39msn8YWeQk6g\nRvQeYSuqIys7zz3dacgyEVSX4nIm8cKLmGYAZAogETgZiZ9QNQFHDzsaAGzZabobMk+8mC/eyU4D\npEikFV0lbD9GpLPTpANjDMfvdbx0AJBNYGs6K834yvG2NKTZgu4F8Tvb0cBWr8ubk8BWQFDi1ZQS\n73f7UegptJH4dHYawEzigdT9KirxYkE1zaVxT/yRQ47ElftfydfzuX22540P5jSvt86/FcP/ONz0\nIrMp8SHnwFZ6dqTzxIdiIS649C/qj6OGGnFflF0rG9WcqsBa9yVC7FuexOeRRx5OCEaNwFZN/fF6\n4n/UMmQ4DNx7L/DN1ihQUgD4gph1TxRL6pOBrV5nJZ6B2ew0oVgorZWELDFEFJyUeNqvaX+MoUQr\nQWOoEcN7DbflCpcpoNkUByLyNKR0iCMhyMZOA6RX4kVkkyc+l5Aq8YKdRlXUVKpJyWyGbBBE5yFd\nsZs9DZnsNJ2B5tKgMtUx973TICoXkAW2phuEE0x2GpfGt8+lnYaeFRUFRrEwk53G7eOqdqbiV5Qf\nXmEK7jziThwz7Bi+Dp3XIq0IO4M7uRL/xAlPoFgrxm8/+q2xP5fP9n0/9rDeeOXb1N9vfvsO2vUm\nrNi+AuMqjbgIqxJPXnSP6rEp8XScaZV4wU7jVt38O7i9bbttWycEwkZV2l6+Xnkl/seAOclsQzPm\nSRe/fMkBxjpz5Ou87JmV/G1elz53WpardjDneLzsgeNx0nl4+ZL0yx23z6NbEIqFUOItgUf1IJqI\nQtf1jDVNdjf8aJX4zz4DamqA228Hisui6F9uvCRjQsVWepGS+iwqiUVakV2JT6YbcoJNiXfyxDtU\nnyRyP7xsOL9RqE2rTQYQ0iemUbyJkAwtG+q4TjaBrWIfMhGhnrbTiESHZ6cR7DRplXjFndZOI6tQ\nuqfCraa303QGF9ZciGdPedbxwZdJie8KZIGt2cApsDVXdhpRiSd7j81OkyY7DWAn8QBwy6G3YL/+\n+/G/OYlPKvHka9fUVFVkGrhZSXwfv9lO064bZPftxansSZFERDrT0svXyxbYKlPio/EoFKbwYxft\nNC7FBY/qgVtJpdHNRokPRALJ/vdxXF+cTciT+DzyyMMJFAdJXObHaKnZpSSeMTaNMfYdY+x7xtgN\n2WzT0mJUWD34YCAQAObNAyr6RVDoJRJv5In3qB6usBFxJVIPGC9cWdq3bAJbRTsNpe4T4UTi6fPh\nvYbzl3j/IiMHvcxOk40ST4REfNlbkWslfpfaaaxKvMVOI/PEp7PTECn4KaCzdpp0GFo2FNPHTHdc\n3p1KvMwTnw1sga05ttOInviKQrsS3xE7zcCSzN/rIq3INjBxKS6Uecv498W6nyKtCG7FbZtBufmR\nJbjrLiAatdtpCL19vXn/dV1Ha6TV0RPvUT38+oRiIZ6EQJbxKJvpbLLT9PH34VVvrcjbafLI48eJ\nlTtW8tm2ngDFQdJzLk/iOwDGmArgTwCOBbAvgDMZY/um2yYeB0aNAh59FPjNb4Dly4HjjjMUH7Ho\nUigWgqZq/OVBSrxIros8RTkJbAVSLzjqg6MSnxxEDO81nKtmVEiqs3YaIqHpfMVimr+0JD6NJ14E\nz06zKwJbLUo8BbXywFZLn9yqO62dRvTY7unwqJ6cK/GZ0K1KvCQ7TTYQ+5OrPPGAPDuNzE7jd/t5\nukdHO41m9sTLIGansVqEAOM5Rd8X6/fd7/bD7/ZjUMkgU996j1qCW24BJk4E6neY7TSEMl8ZJ8r/\n2fAftEfbsV8/Y4bA6okXZ8JEO42MxGelxIdTSjy1aUXeTpNHHj8+6LqOKU9NwR8+/0PO224ONWNj\nsz2BAgW20jMqT+I7hv0BfK/r+lpd1yMAXgJwcroNwmEdhRXbMO+jbbj57m0IKtvQHGpGNBHlLysq\n9kRpg4DUi0Ik18VaMQKRAH/g67puTK10MLAVSL1MB5cOtu1HhKjEk42DKmVKA1vVzIGtVCglG8VO\nc6W302Ttid+VxZ4yKPFWwuikxJP/+adG4ns6paZbdduCKnOFztppFKZwBdoU2JorT7yqceucE4kn\ndMROYwWd1yKPXYkHkiQ++X2xKu5E4isLK7nlp29BX8TLF+Ppv2/D9kAT/vNJBPWbPWhrS33XGRhK\nvaX8ufnoV4+izFuGc8adA0CuxNPz64p/XYGXl79s6o+Yalck8bK89UDq+0pxSTLiH46H+WA1HYlf\nWr8UaxvXOi7vDOKJuGPf88gjD2eE42E0h5uxObA5521PfmoyBj1kT/wRjAbhVVNKfDgeRn1rPZ5e\n/HTO+9Bd2JUkvj8AcWi0KfmZM9xBrDyxAsfNr0DFA8ZP2X1l2NSyib8Yo4koQnGDxNPLbN/yfXHF\nflfguBHH8aZ6+Xph0ZZFGPf4OHy+8XMU3F2ASDySlhAQeR9YPBAuxcV9p/SSGtFrBBSmSP3tgPHi\nqSysRIm3BJWFlQCAKf2nwKW4+MteRDZKPL2AR5WPclynyFPEvak0oJF5mGnqX7QdyUAERSw1350Q\nLU4l3hK4FTe/3gXuAhR4jB8GZgtiLvQUSvtJg57q0uru6/huhiJPUcYBWnfss6vk2AlEdOn6juwz\nMuttxYJlx444FncecSdG9x3dpf708feBylT43X7+rCAl3YnEO9lp+hb0BQNzzDgF2D3xBCLIVUVV\n/BzRfuhclXpLUeotxaCSQZwQnzbyNDQEG3De8gpsPa8MGPEv1Nd5MHo0sHVHMs7IWwKvy4tQLITm\nUDPmrpyLGeNnyD3xiajJ1ggALy570dQfk51GGACc/8b5OP3V023HLHrirfvj7cTCKPIUwaN6TCT+\n2SXPYtCDgxBPxFEXqMO4x8dh2CPD8JdFf5GfYAkuefMSnPHqGdJluq6j5s81+O3832bd3p6Mk/52\nEr5v/H5Xd2OXg93BsGzbspy1d/7r5+O8187LWXsivt3+Lfx3+bG+aX23tJ8OVOdCzILVEXxd9zUK\n7y7E2sa16HN/H7y16i2+7LuG7wDAVjFaZqc57/XzMOP1Gfh+54/j3t3ts9Mwxi4GcDEAqG4Vjxz3\nCF8WCAdwwweGlZ7baeJRtIRbuE90SOUQ3PnFnfjbCX/Dkwuf5Ns+MPUBuBQX3lz1Jmq31nJ/fDpP\n/GHVh+GtM9/CoYMPxQfnfICxFWMBGC/TIZVDwLwMH5zzgaMSf9vht+Gy/S4DAMyYMAOVhZU4bsRx\nGNV3FG9LRDaBrZSxYvKAyY7rnD3ubIwsH4lirZi/NGUvv1+O+iUqCyvTqvoAMHXYVMybPg+j+joP\nHHKJk/Y+CU+d+BTcqhsHDzoYH577IR+03HnEnWgON2No2VCM6DXCZkt69mfPSr3ONVU1ePdX7+KQ\nwYf0yDHsDvjTcX/q8cj7+4++32ZbyxUmVk3EvOnzcFj1Yfj0/E+xd++9s95Wc2kIRALwurwo1opx\ny6G3dLk/5084HxMqJ/BB5ftnv48DBh4AwPxcoeJSgLOdZsaEGRhXOY4XlpPB6okfUjkEDIxf4weO\nfoAr1/QsGVo2FA8c/QCmDJiC/frthzJfGS6fdzkA4I7D70BNVQ2aQ8247r3rMKRyCAoHtCP8CbB8\nYQmwFzDroIewYPv7CMfDWNO4BrFEDAcNOggKU+BSXJyIz3h7BlY2r+RK/CczPsHU56fyIFYnO82M\nt2cAABZsWiA9ZqsSf+1/roXX5cWcaXP4OuF42MiapKh8xnPG2zOwrmkdNrZsRGOoETvad/D1f2j+\nIXXek/sX2xOxfPtyBCIB6Xrfbv8WS+uXchEkU1u5Wqc7l3dl2+8avsMZfYowpm9fyLbm2zpkZJnx\n9gygqq+tbafPjYXzjOVvz7AvT+7H1GfLvtP1Ke2yKkNMc7qKJ5e6cFhVmvPgdDzW/gJYvXM1EnpC\nuizTtpmWr9m5BsFYEBubN6K6tLrL7XdkHeJgYj2KjrSxZucatEXbcNX8q1BcUoyl9Utxwl4nmNbZ\n2rqV85sZb89Aea9yw06TFEHCsTB/xmxu2YzhvYY77m93wa4k8ZsBiGxxQPIzE3Rd/zOAPwNAQUGB\nfvl+l/Nl8UQct8y/BbFEzKTEN4eaUaKVYMqAKSj9ttQU2EkY2Wckjhl2DN5c9Sa+2/Ed/zydnUZh\nCo7fy0gFdejgQ/nnmqohgQQ8qkdaEIcfYPEArsw5tSUiGyXe5/bx/O1OKPQU8n7R9HUobp+G9rq8\nmDpsatq2qF/irEZ3o8BTgAtqLuB/HzzoYP47WZgA4IghR9i2HVMxxrHdTOdtT8PefbInublCuqxJ\nXQVjjN+HBw48sEPb0sC4o1acdCjWinFY9WH8b8qDDhhkXVONqoDZ2GmKteK0zxLArMR7XV4gbM7A\nNaRsCP+dniV+t5/3i1JJDisbhr17743ygnJcWHMhEnoC179/PQDA7VLw5RLg/816DI/+uRG3/99Y\njL7pY4T0EK+cOrjE+A5acy3rus4tPwcNOgjDyoZhVcMqU3+sSnwBjOfThqYN/Dx9uO5D/Oyln2HD\n1RtsnngiMyLC8TA0VYNH9Zgq0dK6De0NpqxUYrFAWq92Sy0mVE2wtR2IBBzT0s5bbZAeX9q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Mnjve2j23DB6xcgHAvzqe9wLJViUgS93GOCnYZIfGuklXtuRRJPRDoUC5nIrZVIEPnhdpo0Snwv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\nc3B5DlEjXrwWDObiV845Fn+yGNOHT5fnAMyKNFLEJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import nengo\n", "from nengo.utils.matplotlib import rasterplot\n", "from nengo.dists import Uniform\n", "\n", "model = nengo.Network(label='Decoding Neurons')\n", "\n", "N = 50 \n", "\n", "with model:\n", " stim = nengo.Node(lambda t: np.sin(10*t))\n", " ens = nengo.Ensemble(N, dimensions=1,\n", " max_rates=Uniform(100,200))\n", " temp = nengo.Ensemble(10, dimensions=1)\n", " \n", " nengo.Connection(stim, ens)\n", " connection = nengo.Connection(ens, temp) #This is just to generate the decoders\n", " \n", " stim_p = nengo.Probe(stim)\n", " spikes_p = nengo.Probe(ens.neurons, 'spikes')\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(.6)\n", "\n", "x = sim.data[stim_p][:,0]\n", "\n", "A = sim.data[spikes_p]\n", "\n", "gamma=np.dot(A.T,A)\n", "upsilon=np.dot(A.T,x)\n", "d = np.dot(np.linalg.pinv(gamma),upsilon)\n", "\n", "xhat = np.dot(A, d)\n", "\n", "t = sim.trange()\n", "figure(figsize=(12, 6))\n", "ax = gca()\n", "plot(t, sim.data[stim_p],'b')\n", "plot(t, xhat,'g')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\");\n", "rasterplot(t, sim.data[spikes_p], ax=ax.twinx(), use_eventplot=True, color='k')\n", "ylabel(\"Neuron\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- What's happening here?\n", "- At a given instant in time $t$, only a very small number of neurons are firing\n", " - If no neurons are firing at that instant, $\\hat{x}=0$\n", " - There are usually only one or two neurons firing at any given time\n", " - As $dt$ gets smaller, the problem gets even worse\n", "- What can we do? " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Temporal filtering\n", "\n", "- We want a spike to contribute to other points in time\n", "- So we want to convert a train of spikes into some continuous function\n", "- Convolution:\n", " - $\\hat{x}(t)=\\sum_i{a_i(t) * h(t) d_i}$\n", " \n", "- What should we use for $h(t)$?\n", " - Maybe a gaussian?\n", " - $h(t) = e^{-t^2 / {2\\sigma^2}}$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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sZ6mZtsjMpf7YXGzW0uuUsZ9F5iXrE7QkEzQ31JNqTbKxs4kNnY1ctLr5vLss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\nwkJERIr6/54QvuXcYZTKAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "dt = 0.001\n", "sigma = 0.007\n", "t_h = np.arange(200)*dt-0.1\n", "h = np.exp(-t_h**2/(2*sigma**2))\n", "h = h/norm(h,1)\n", "\n", "figure()\n", "plot(t_h, h)\n", "xlabel('t')\n", "ylabel('h(t)');" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "c:\\users\\terry\\py3\\lib\\site-packages\\matplotlib\\cbook.py:637: IgnoredKeywordWarning: \"color\" keyword argument will be ignored\n", " IgnoredKeywordWarning)\n" ] }, { "data": { "image/png": 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qlrbV2p5CZBHJbaWKlKJ+2XqkpKfSb2I/3D3oSCJybBcCX5rZKjNbZGaLzWxR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\nUfafZ2bfmlmamXULImOkyMG5usvMlpn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UVyuNnPy7MS7A4yxrJ7TrA8fiwGyHCopCNMTJgeb2HS8AkgxYR9VfcAOyvYSj\n+cxfvocJPYO57rzOVgpMiMZTSvHClH74e7gwb9EOistM1r1h2ASjomBKZTXC0kKj9kBtXQRVgntD\n+QljETAhmrOTD46SDJybMuKNfsuaRjvXoKTcxNyvduDj7sz8q/ui7LRQhRB18fNw4eVp/dmfeYJn\nfom37s1CRxn/j+KWGu/3/GTUb4+4+OznVbXIZVg5PiGaKn03uPmCV/0Wq7MmSQasISPBaBWo54f6\ns78ksC+jkJemRtHW09XKwQnRNCPCApg9uhtfbDzEqngrlit2doNekyB+GZw4Dls/MQYIVg0urE1V\ni1y6JAOimctIMFoFmsEDoF2TAaXURKVUolIqSSn1UA3771FKxSulYpVSvymlulTbZ1JKxVS+ltk2\n8rPQ2sj26tns81tCOp9tOMgtI7syukeglYMTwjLuvbAHvdp788A3sWQUWLFc8fC7jK6Ct4bA4Y0w\nYl7dvzhdPY114dPjrBeXEE2ltZEMNIPxAmDHZEAp5Qi8BVwM9AKuUUqd/qeyA4jWWvcDlgLPV9tX\nrLXuX/m6wiZB10fBUSjJrVcykFFQwgNLY+nZ3psHJkbYIDghLMPVyZHXr+nPidIK7l8Sa73phoER\ncPF8o5BQv+kw6Mb6nRfcR7oJRPOWn2aU1W4GMwnAvi0DQ4AkrXWy1roMWARMqn6A1nqN1rqqruhG\noH6d8PZUz9GhZrPm/iWxFJZW8PqM/lJuWLQ4YUFePHpZL/7Ym8mn61Osd6Mh/4AHU2Dy++BQz/8n\nQb0gK8lYMEyI5qiqG6sZ1BgA+yYDHYHD1d6nVm6rzS3A8mrv3ZRSW5VSG5VSV9Z2klJqduVxWzMz\nM5sWcX2c/As+ezKwYH0Kf+zN5NFLexIu0whFC3XdeZ0ZHxnEs8v3kHiswN7h/C24l9GakLnH3pEI\nUbOTs86axyJ0LWIAoVLqOiAaeKHa5i5a62hgJvCqUqp7Tedqrd/XWkdrraMDA23QJ5++Gzzbgbt/\nrYckHM3nueV7mNAziOuGdqn1OCGaO6UU86f0w9vNiXmLdlBSbuXphvVVVZZYugpEc5W+G7w7Qhs/\ne0cC2DcZSANCqr3vVLntFEqpCcAjwBVa65Orlmit0yq/JgO/AwOsGWy9pe82ip7UoqTcxLxFO/Bu\n48z8q/vJNELR4gV4uvLC1Cj2HCvg+RWJ9g7H4N/NWPwlfbe9IxGiZulxfyetzYA9k4EtQLhSqqtS\nygWYAZzS8TdPAAAgAElEQVQyK0ApNQB4DyMRyKi23U8p5Vr5fQAwArD/I0BFmdEseZa/4OeW72Fv\neiEvTZNphOLcMTYiiBuHh/LxugOs3WuD7ri6ODhCYKQkA6J5Ki+BzMSzPjjamt2SAa11BTAHWAkk\nAIu11ruVUk8ppapmB7wAeAJLTptC2BPYqpTaCawBntNa2z8ZOL4XzOVGudQa/LXvOAvWp3Dj8FDO\nl2mE4hzz0MWR9Aj25N4lO8kqrGHpYVsL7i3dBKJ5ytwD2tSsWgac7HlzrfUvwC+nbXu82vcTajlv\nPVDzJ649Vc1rruEvOK+4nPuX7qRboAcPTmweA0aEsCQ3Z0demzGASW+u45Hv4njnuoH27QYL6gUx\nC42CRWdby0AIW6v6rGjXz75xVNMiBhC2GMd2gaMrtA07Y9d/lu0mo6CUV6b1l9UIxTmrZ3tv7r2w\nByt2H+Pb7WcMAbKt4MopW9JVIJqbY3Hg7A7+Xe0dyUmSDFhSepxRQMLx1AaXX3Yd5bsdadw1Loyo\nEF87BSeEbdw6qhtDQv35z7LdpOUW132CtQTLGgWimUqPM1qu6ls3wwYkGbAUrY2WgdMGhGTkl/Dv\n73YR1cmHO8ee2WIgxLnG0UHx0rQozFpz3+KdmM1Wqk5YF88g8AiEo7H2ub8QNTGb4Vhssxo8CJIM\nWE52MhRlQafBJzdprXngm1hKyk28PL0/zo7yxy1ahxB/d564vDcbkrP4eN0B+wXSaTCkbrHf/YU4\nXdY+KMmDTkPsHckp5NPJUg5vNr6GnHdy05ebD/F7YiYPX9yT7oGedgpMCPuYGt2JCT2DeX5lInvT\n7VSdMGSI8cv3RJZ97i/E6Q5vMr6GSDJwbjq8CVx9IMBYcCjl+Ame/imBUeEBXC9VBkUrpJTiuav7\n4uXqxN1fx1BWYbZ9EFXJubQOiObi8Caj6mANA83tSZIBSzm8GTpFg4MDFSYz9yyOwdlR8cKUKBwc\npMqgaJ0CPF35v8l92X0knzdW77N9AB0GgIPT309jQtjb4c1GktrMqs9KMmAJJfnGiOXKp5D31iaz\n/VAu/72yD+183OwcnBD2dWHvdkwd1Im31iSx/VCObW/u3MaYy13VjSeEPRVlG8XpmlkXAUgyYBmH\nNwEaQoYQl5bHK7/u5bJ+7ZnU/2yLMArRejx+eS/a+7Thnq9jKCqrsO3NOw+FtG2ynLGwv0Mbja/V\nxpY1F5IMWELSKnByo6T9YO7+Ooa2ni48fWXzmjYihD15uTnz0rQoDmYX8ewvCba9ebexUFEMh9bb\n9r5CnC5pFTh7nDLrrLmQZKCptIZ9/4PQUby4+hD7Mgp5fkoUvu4u9o5MiGZlaLe23DqyK19sPMTv\niRl1n2ApoSONyqD7frXdPYU4ndaQ9Ct0Ox+cmt8idZIMNFV6HGQnk9x2NB+tO8D1Q7vIIkRC1OLe\nCyOICPbigaWx5Jwos81NXdyh+1iIX2YUfBHCHo7sgNxDEHGxvSOpkSQDTbVrCVo5MiemM6FtPXj4\nElmESIjauDk78vL0KHKKynj0hzi0tlF1wj5XQ34qHN5om/sJcbpdS8HBGXpebu9IaiTJQFOUl8CO\nL9jtOYw9+UafqLuLXReCFKLZ693Bh39N6MHPsUdZtvOIbW4acYlRB2TLR7a5nxDVlRUZK2hGXmLU\nGGiGJBloih2fQ1EWz2aN5s6xYQzs3Dz/koVobm47vzuDuvjx2PdxHM2zwWJGrp4w4DqI/x6y9lv/\nfkJUt/1TKMmFIf+0dyS1smsyoJSaqJRKVEolKaUeqmG/q1Lq68r9m5RSodX2PVy5PVEpdZEt4wbg\nxHHMa/6PbfQiv90w5o4Pt3kIQrRUjg6Kl6dFUWHW3L8k1jaLGY2YC44usPIRYzCXELZQmAF/PA9d\nz4cuw+0dTa3slgwopRyBt4CLgV7ANUqpXqcddguQo7UOA14B5lee2wuYAfQGJgJvV17PZvTP92Iq\nzuc/FbN4ZfoAWYRIiAbq0taDRy/txV9Jx/l840Hr39CrHYx9BPYuh79esf79hCgrgiU3QXkRXDy/\n2VUdrM6en2BDgCStdbLWugxYBEw67ZhJwKeV3y8FxiulVOX2RVrrUq31ASCp8no2s9L/Oh4ou5Ur\nJ15EeLCXLW8txDnjmiEhjI0I5P+WJ7A/s9D6Nxx6B/SZAr89CYtnGSO8ZYaBsLTyEoj/AT4YBwfX\nwRVvQlBPe0d1VnWOdlNKvQb8S1t+2G9H4HC196nA6WWZTh6jta5QSuUBbSu3bzztXJuW+/uzxIW0\nbmN5aXioze6ZkpfCjowdpBamkluSS4mpBLM2Y9ZmtNaYtAlNw/6aFA3LVFUDM9uGXL+hsTTkcGv+\nnA2+tpX/zOvL2cEZX1dfgtyD6BfYj15te+GgbPt8oJRi/tX9uOjVtdzzdQxLbx9u3VY2BweY/D4E\nhMP6N4wxBG4+4BMC7v5GPQLlUO2lGv40Z4suiEbdoxHnNPg+trhHI+5jq3uUFxlL2WcfAHM5+HWF\nmYuhx4WNuL9t1WfoewGwTCk1Q2t9orJ//nGt9Qgrx2YRSqnZwGyAzp07W+y6xZ4/kOy2lvlbtjNn\nwBy8XKzXOpCYnchLW19iw9ENADgoB3xdfWnj1AYH5YCDckChTn6tr4YmDg0+3oq/FBsSS0PjaC7X\nbqiGxlJmLiO3JJcKbZQHDvMNY97AeYwJGWOF6GoX5O3GM1f15Y6F23lrTRL/mtDDujd0cIQxD8GQ\n2bDnZ6NUcWG68Uu8tBC0ufKl//6+wQlZIxI4m9yj4ac0+KRGJa/N9c+rgec4tTFaACIuhi4joPt4\ncGwZM8zqjFJr/ahSaibwu1KqDCgEzhjs1whpQEi1950qt9V0TKpSygnwAbLqeW5V/O8D7wNER0db\n7DfxvIHz8HT25OvEr9l8bDMfX/Qxfm6Wn02w6egm5vw2B3dnd+YNnMe4zuPo4tUFRwebDpEQ5yit\nNelF6Ww8upFP4j7hrtV3cV/0fczqPcumcVzStz1XDejIG6uTGBsRRFSIr/Vv6u4PA683XkK0cqqu\npwml1HjgUYy0qj1whdY6sck3Nj7c9wLjMT7ItwAztda7qx1zJ9BXa32bUmoGMFlrPU0p1Rv4EmOc\nQAfgNyBca2062z2jo6P11q1bmxr6KTYc2cBdq+9iQNAA3rvgPYs2sx4tPMrVy64m2COYDy78gIA2\nARa7thCnKzOV8dCfD/HrwV95d8K7jOho28a/vOJyJr66ljYujvx81yjauEjCK0RTKaW2aa2j6zqu\nPp9cjwCPaa3HAFOAr5VS45oYH1rrCmAOsBJIABZrrXcrpZ5SSl1RedhHQFulVBJwD5UtEpUJw2Ig\nHlgB3FlXImAtwzoM44HBD7Dx6EZ+Tv7Zoteev2U+FbqC18e+LomAsDoXRxeeHfks3Xy68dSGpygz\n2ahccCWfNs68ODWK5MwTzF+xx6b3FqK1qzMZ0FqP01r/Vfn9LoypgE9b4uZa61+01j201t211s9U\nbntca72s8vsSrfVUrXWY1nqI1jq52rnPVJ4XobVebol4GmtKjyn09O/JWzFvYTJbJieJz4rnt0O/\ncXOfmwnxDqn7BCEswM3JjQeHPMiRE0f4dt+3Nr//iLAAbhweyoL1Kfy177jN7y9Ea9XgNm2t9VGM\npn1RyUE5MLvfbNIK0/gj9Q+LXHNhwkLcndy5tue1FrmeEPU1rP0w+gb05cs9X9pu7YBqHro4ku6B\nHty/dCd5xeU2v78QrVGjOri11jaoH9qyjAkZQ5B7kEWepk6Un2Blykou63aZVWcpCFETpRTTI6Zz\nIO8AOzJ22Pz+bs6OvDK9P5kFpTzxQ5zN7y9EayRl8yzEycGJiaETWXdkHXmleU261prDayg1lXJp\nt0stFJ0QDTOhywRcHV1ZkbLCLvfv18mXu8aF833MEX6OPWqXGIRoTSQZsKCLQi+iwlzB2tS1TbrO\n6kOrCWoTRP+g/haKTIiG8XD2YGTHkfx26De7dBUA3Dm2O1Ehvjzy/S4y8kvsEoMQrYUkAxbUJ6AP\nfq5+rD+yvtHXKDeXs+HIBkZ1GmXzanBCVDe602gyijJIyk2yy/2dHB14eVoUJeUmHvgm1m5JiRCt\ngXzaWJCDcmB4x+GsP7K+0b+44o7HUVheaPM53kKcbkQH49/gurR1douhe6AnD1/ck98TM/ly8yG7\nxSHEuU6SAQuLDo4muySbg/mNW4Vte/r2k9cRwp6CPYLp7NXZLoMIq7t+aBdGhQfw9E8JpBw/YddY\nhDhXSTJgYf0DjX7+mMyYRp2/M3Mnod6hViltLERDRQVGsTNzp12b6B0cFC9MicLZUXHP4hgqTLLK\noBCWJsmAhXXz7YaXsxc7M3c2+FytNTszd9IvsJ8VIhOi4foH9SerJIvUwlS7xtHOx43/XtmH7Ydy\neW9tct0nCCEaRJIBC3NQDvQN7NuoZCC1IJXskmyiAqOsEJkQDVf1b7Ex/54tbVL/jlzWrz2v/LqX\nuLSmTd8VQpxKkgEr6B/Yn6ScJArKChp0XlXXgiQDorkI8w3D3cmdmIzGdXsBFJYVWqyb4ekr++Dv\n4cLdX8dQUm6X5UiEOCdJMmAFUYFRaDS7ju9q0Hk7M3fi4exBmG+YlSITomEcHRzpG9CX2MzYRp2/\nMGEhoxaN4pb/3UJxRdMLl/q6u/D8lH7syyjkpf81efFUIUQlSQasoFfbXgAkZjfsl1VidiIRfhE4\nOsjSraL56BXQi325+yg3N2ydgMP5h3lx64sEuAew5dgWPo//3CLxjIkI4rqhnfnwrwNsTM6yyDWF\naO0kGbACXzdfgtyDSMypfzKgtSYpN4lwv3ArRiZEw/Xw60GFuYIDeQcadN5XiV8B8OUlXzK602gW\nJiykwlxhkZj+fUlPQtt6cO/inRSUyGJGQjSVJANWEuEX0aCWgaMnjlJYXkgPvx5WjEqIhovwiwAa\n1tJl1mZWpqxkZMeRBLoHcmXYlWSXZLPl2BaLxOTu4sRL06I4mlfMkz/GW+SaQrRmkgxYSYR/BCl5\nKZSZyup1/L6cfQDSMiCanVCfUJwdnNmbs7fe5+zN2UtGUQYXdLkAgFEdR+Hm6GaxJb4BBnb2444x\nYSzdlsrK3ccsdl0hWiO7JANKKX+l1K9KqX2VX8+osKOU6q+U2qCU2q2UilVKTa+2b4FS6oBSKqby\n1exW9Inwi6BCV5CcV7850ftyjWRABg+K5sbZwZkw37AGJQPb0rcBMDh4MABuTm4MCBrApqObLBrb\n3PHh9O7gzcPf7iKzoNSi1xaiNbFXy8BDwG9a63Dgt8r3pysCbtBa9wYmAq8qpXyr7b9fa92/8tX4\neU9WUtXcX99foHtz9tLeoz1eLl7WDEuIRgn3C29QN8GOjB2092hPe8/2J7cNaT+EpNwkjhcft1hc\nLk4OvDq9P4WlFTwoixkJ0Wj2SgYmAZ9Wfv8pcOXpB2it92qt91V+fwTIAAJtFmETdfbujKuja71/\nge7L2SddBKLZivCLIKskq14f5FprtqdvZ0DQgFO2DwwaCBiLcVlSeLAX/744ktV7MvhsQ+PWBBGi\ntbNXMhCstT5a+f0xIPhsByulhgAuwP5qm5+p7D54RSnlaqU4G83JwYnuvt3r1TJQbionJS+FcF9J\nBkTz1MO//i1dqQWpZBZnMih40CnbI/0jcVAO7M7abfH4Zg0PZWxEIM/8kkDisYYV+xJCWDEZUEqt\nUkrF1fCaVP04bbTr1dq2p5RqD3wO3KS1rlqh5GEgEhgM+AMPnuX82UqprUqprZmZmU39sRok3Dec\n/bn76zzuQP4BKnSFtAyIZqsqUa3Pv+ftGcbKm1UtAVXcnd3p5tPN4i0DAEopXpgahbebE3O/2iHV\nCYVoIKslA1rrCVrrPjW8fgDSKz/kqz7sM2q6hlLKG/gZeERrvbHatY9qQynwCTDkLHG8r7WO1lpH\nBwbatpch3C+czOJMcktyz3qczCQQzV3bNm3xd/MnKTepzmPjjsfh7uRON99uZ+zr3bY38VnxVunb\nD/B05YWpUSSmF/Dc8j0Wv74Q1nY0r5iyCvusymmvboJlwKzK72cBP5x+gFLKBfgO+ExrvfS0fVWJ\nhMIYb2D5Rw0LqJoZUDVToDb7cvbh5OBEV++utghLiEYJ8w0jKafuZGBP9p6TXQKn6xPQh+ySbI6e\nOFrDmU03NiKIG4eHsmB9CmsSa3zGEKJZKik3cePHW5j9+Va73N9eycBzwAVKqX3AhMr3KKWilVIf\nVh4zDRgN3FjDFMKFSqldwC4gAHjatuHXT1UyUNfT1L7cfXT16Yqzo7MtwhKiUcJ8w0jKTcKsa39y\nMZlNJOYkEukfWeP+PgF9AKwybqDKQxdHEtnOi/uX7JTphqLFeG75HhLTC5g1PNQu97dLMqC1ztJa\nj9dah1d2J2RXbt+qtb618vsvtNbO1aYPnpxCqLUep7XuW9ntcJ3WutAeP0ddgtyD8HLxqvNpal/O\nPhk8KJq9ML8wiiqKzvpUf6jgEMUVxbUmAz38euDk4MTu49ZLBtycHXltxgDySyp4YOlOmW4omr3V\ne9JZsD6Fm0aEMjYiyC4xSAVCK1JKEe4bftaWgYKyAo6eOCrjBUSzV5Wwni253ZNt9NVXLdZ1OhdH\nF7r7dD95nLVEtPPikUt6siYxk0/Xp1j1XkI0RUZ+CfcviSWynRcPTqw5ibYFSQasLMw3jH25+2p9\nOqlKFGRNAtHcdfftDpx9DExCVgLODs41Dh6sEukfSUJ2gtWf2G8Y1oVxkUE8u3wPe47lW/VeQjSG\nyaz519cxnCir4M2ZA3Bztt+KtZIMWFmYXxgFZQVkFNU8mGlvtjFvW7oJRHPn5eJFO492Z23pSshO\nIMw3DGeH2se/9Gzbk+ySbDKLrTvVVynF81P64e3mzLyvYmS6oWh23v1jP+v3Z/HkFb0JC7Jv9VlJ\nBqzsZNNqLb9AE3MS8Xbxpp1HO1uGJUSjnG1GgdaahOwEerbtedZr9PQ39lu7qwCM6YYvTTOmGz77\nS4LV7ydEfW1NyeblX/dyeVQHpkWH2DscSQasra4ZBYnZxshrY5akEM1buF84yXnJVJgrzth35MQR\n8krz6OVf83iBKhH+ESgUCVm2+XA+v0cgt47symcbDrJ8l3WmNArREHlF5cxbFENH3zY8c1WfZvH7\nX5IBK/N18yWwTWCNZVxNZhN7c/bKeAHRYoT7hlNuLudQ/qEz9lV9uNc2eLCKh7MHnb0726RloMoD\nEyOJCvHlgW9iOZxdZLP7CnE6rTUPfhNLen4Jb1wzAG+35jGlXJIBG+jh34OE7DOfgg4VHKLEVFLr\nNCwhmpuqxDU+O/6MffFZ8Tgpp5PrGJxN1SDCs8kvy+fVba+yIG4BJnPT+vtdnBx48xpj4aQ5X263\nW5U3Ib7YdIgVu4/xYGWCWt2J8hN2mworyYAN9Avox/7c/RSVn/pEUrWiYYR/hD3CEqLBuvt2p41T\nmxrXF4jPiqe7b3dcHeteNyzSP5K0wjTySvNq3G8ym7h91e18FPcRL217iee3PN/k2EP83XlhSj92\npubx/AopVyxsL+FoPv/9KZ7zewRyy8gzK87euvJW5q6Za4fIJBmwiT4BfTBr8xlV1/Zk7zFWN/Tp\nbqfIhGgYJwcnerXtxa7MXads11oTnxVfZxdBlapBhLUt8b1s/zJiM2N5duSzTI+YzqLERSTnJjct\neGBin/bMGtaFD/86wKr49CZfT4j6Kiqr4K6vduDTxpmXpkXh4HDqOAGzNrM/bz8dPTvaJT5JBmyg\nqgTrruOn/gJNyE6gu093KUMsWpS+AX1JyE6g3FR+ctuxE8fIKc2pcyZBlaqusZq6CrTWLExYSIRf\nBJd1u4w7+t+Bo3Jk8d7FFon/4Ut60ruDN/cu2UlabrFFrilEXZ74YTf7Mwt5dXp/AjzPbD07euIo\nxRXFJ+t52JokAzbg7+ZPJ89OpzStmswmdmbuJCowyo6RCdFwfQP6Um4uJzHn76f6qmWL+wf2r+20\nU7Rt05b2Hu3PSJDBWLcgMSeRaRHTUErh7+bPmJAxLD+wnHJzeQ1Xaxg3Z0femjkQk1kz96sdlJtk\n/ICwrsVbDrNkWyp3jQ1jRFhAjcdULQ9eNQPN1iQZsJG+AX2JzYw9+T4pN4kT5ScYEDzAjlEJ0XB9\nA/oCp7Z0bUvfhqezZ4NmxvQP6s+O9B1nDJhauncpbZzacEnXS05uu7zb5WSXZLPhyIYmRm8IDfDg\n2cl92XYwh5d/PXOmjxCWEn8kn8d+iGNEWFvmTaj9/0fV9HNpGTjH9QvsR3pROqkFqQBsOroJgIFB\nA+0ZlhAN1s6jHUFtgtiWvu3kti3HttA/qD+ODvUvpzogaAAZxRmkFaad3FZUXsTyA8u5KPQiPF08\nT24f2XEkvq6+/Lj/R8v8EMAVUR24Zkhn3vl9P2v2yHLHwvLyS8q5Y+E2fN2deW3GABwdaq8nsD93\nP0FtgvB28bZhhH+TZMBGRnUaBcAfqX8A8Hvq74T5htHBs4M9wxKiwZRSjOw0knVp6yg3lZOcm0xK\nfgqjO41u0HXOa3ceAOuPrD+5bWXKSooqirg6/OpTjnV2dOaCLhfwR+oflFSUNP2HqPTE5b3o2d6b\nf30dI/UHhEVprXlgSSyHc4p5c+bAGscJVLc/d7/dWgVAkgGb6eLdhW4+3fjlwC8cO3GM7enbGRsy\n1t5hCdEoYzqNobC8kHVH1rE8ZTkA40LGNegaXX260tGzI3+m/nly27f7vqWrT9cax9Jc0OUCiiuK\nWXdkXdOCr8bN2ZF3rxuIWWtuX7hN1i8QFvPRXwdYsfsYD02MZHCo/1mPNWszyXnJkgy0FjMiZxCb\nGcv0n6ajUEzpMcXeIQnRKCM7jaSDRwee2vAUH+/6mDGdxhDsEdygayilGBsylnVH1pFdkk1idiIx\nmTFMDptcY3nW6HbR+Lj6sOrgKkv9GAB0aevBq9P7E5eWzxM/7K77BCHqsO1gNs8t38OFvYK5ddSZ\n9QROl1aYZteZBGCnZEAp5a+U+lUpta/yq18tx5mUUjGVr2XVtndVSm1SSiUppb5WSrnYLvrGmxw+\nmX6B/cguyWZ2v9nSRSBaLGcHZ+4bfB85pTm4Obkxd2DjCqVM7TGVcnM5H8R+wEtbX8LL2Yurwq+q\n9Z7jQsbx++HfKTOVNSX8M4zvGcycsWF8vfUwizafWWpZiPrKKizlzoU76ODbhhemRtVr3YH4LKOi\nZ1X9DXuwV8vAQ8BvWutw4LfK9zUp1lr3r3xdUW37fOAVrXUYkAPcYt1wLcPV0ZVPJ37KL1f9wu39\nb7d3OEI0yQVdLmDZpGX8fNXPhPs1bgnubr7dmNR9El8kfMGGoxuYO3AuPq4+tR4/MXQiheWFrDm8\n5ox9WmsyizJrXESpPu6+oAejwgN4fNludqXWXBlRiLOpMJmZu2gH2UVlvH3tQHza1K+GzO7ju3F2\ncLbrOjX2SgYmAZ9Wfv8pcGV9T1RGmjUOWNqY8+3NycGJEG/7L1cphCWEeIfg6+Zb94Fn8diwx3h8\n2OO8OvZVZkTOOOux57U/j3Ye7Viyd8kp2w/kHWD6T9MZt2QcFy29iC3HtjQ4DkcHxWszBhDo6cpt\nX2wj54RlWx/EuW/+ij2sS8ri6Ul96NOx9qT2dHFZcUT6R9q1AJ29koFgrXXVWqLHgNo6G92UUluV\nUhuVUlUf+G2BXK11VfqfCtRav1EpNbvyGlszMzMtErwQwnJcHV2Z2mMq4zuPr/NYRwdHrom8hk1H\nNxGTEQMYJY1vXHEj6UXpzBs4Dw8XD+787U5S8lIaHIu/hwtvXzuQzIJS5n0dg8lsn0VjRMvzQ0wa\nH/x5gOuHdmHa4Po/8JnMJnYf332yUq29WC0ZUEqtUkrF1fCaVP04bVQcqe1/XBetdTQwE3hVKdXg\n0RVa6/e11tFa6+jAwMCG/yBCiGZlRsQMgtoE8ei6R1mYsJCbV96Ms4MzCyYu4Na+t/L+Be/j4ujC\ng38+eErJ5PqKCvHliSt6sXZvJq9IQSJRD7uP5PHgN7EMDvXjscvqtz5HlZT8FIoqis7dZEBrPUFr\n3aeG1w9AulKqPUDl1xorfmit0yq/JgO/AwOALMBXKeVUeVgnIK2m84UQ5x53Z3deOP8FckpyeG7z\nc7TzaMenF39KVx9j1HY7j3Y8OfxJ4rPieTf23UbdY+aQzkyPDuHNNUn8FHvEkuGLc0zOiTL++fk2\nfNu48Pa1g3BxatjHalUlzz5t7ZsMONV9iFUsA2YBz1V+/eH0AypnGBRprUuVUgHACOB5rbVWSq0B\npgCLajtfCHHuGhg8kOVXL+do4VG6+3bHyeHUX2XjO49nUvdJfLTrI8aGjD3lqWvDkQ2sTFmJr6sv\n1/a8lkD3M1sMlVI8dWVvkjILuW/JTkLbejSoD1i0DhUmM3O+2k5GQSmL/zmMQK+6l+8+XUxGDF7O\nXoT6hFo+wAZQp9cFt8lNlWoLLAY6AweBaVrrbKVUNHCb1vpWpdRw4D3AjNGC8arW+qPK87thJAL+\nwA7gOq11aV33jY6O1lu3brXKzySEaF4KygqYvGwyZrOZ18e9jkbz2vbX2Hh0I57OnpRUlODt6s0n\nF31CN99uNV4js6CUK978CwX8MGdko37Zi3PXMz/H88GfB3h+Sj+mRTd8YLjWmou+uYjebXvzythX\nrBAhKKW2VXa3n/04eyQD9iLJgBCty96cvcz+32yySrIA8HX15R99/8H0yOmkFqRyy8pb8HLxYsnl\nS3BzcqvxGnFpeUx5dz19Oviw8B/n4epU//UXxLlr6bZU7luyk1nDuvDkpMY18SfnJjPph0k8NvQx\npkVMs3CEhvomA1KBUAhxzurh14PvJn3Ho+c9yuPDHufnyT9zQ+8bcHV0pbtvd54b/Rwp+Sm8vuP1\nWq/Rp6MPL0yJYuvBHB7/fvcZqyyK1mfzgWwe/jaWEWFtebSBAwarW3lwJQrF+Z3Ot2B0jWOvMQNC\nCP80rxcAABkkSURBVGETfm5+TI+cXuO+oe2HMj1iOl/Ef8GFXS6kf1D/Go+7PKoDiccKeHNNEpHt\nvbhpRN0lZsW56WDWCf75+VZC/N15e+YgnB0b90xt1mZ+Sf6FQcGDGlzK2xqkZUAI0ardM+ge2nm0\n44n1T5y1zPE9F/RgQs9g/vtTvCx53ErlFZdz84ItaODjWYPxcW98kaA/U/8kJT+Fq3tcXffBNiDJ\ngBCiVXN3dufxYY+TnJfMC1teqPU4BwfFazP607O9N3d+uZ24NClZ3JqUm8zcuXA7h7KLeO+6QYQG\neDThWuW8uv1VOnp25KLQiywYZeNJMiCEaPVGdhzJrF6zWJS4iE93f1rrcR6uTnx842B82zhz84It\nHMkttmGUwl601jyxbDd/JR3n2av6cl63to2+VoW5gifWP0FSbhL/Pu/fODvYrwRxdZIMCCEEcPeg\nuxnfeTwvbn2ReavnsS9nX43HBXu78fFNgykqM3Hzgi0UlDS8yqFoWT766wBfbjrE7WO6M7URUwir\nJGQlMGv5LH5M/pE5/ecwutNoC0bZNJIMCCEExroHL57/InMHzGXzsc1MXjaZ21fdzo6MHWccG9nO\nm3euG0hSRiF3LNxOuclsh4iFLSzbeYSnf07g4j7tuP/CiLMeW2oqpaSi5IwZJ3tz9nLv7/cy7adp\npBamMn/UfP4Z9U9rht1gUmdACCFOk1uSy9eJX/Plni/JLsnm+l7Xc/fAu89YVe7rLYd48JtdzBgc\nwv9N7luvtetFy7E+6TizPtnMgM5+fHbzENyca64xEZMRw5sxb7Ll2BbM2oyHswdhvmH4ufmRWpBK\nUm4S7k7uXNvzWmb1nnXWZbotTYoO1UCSASFEQxRXFPPy1pdZlLiIgUEDeXnMy7Rtc2p/8YsrE3lz\nTRL/mhDOvybYbz16YVnxR/KZ9t4GOvi6seSfw2ucOWDWZt7Z+Q7v7nwXfzd/rg7///buPDyq+lzg\n+PdNSAIhkIUkQGIgrGFJGjA0oJQq1ooWBXxQHqRCvS7c1rpU5VZRa2vpvfWKetVbr4W6AFVcaxWw\nrVWkIpssMewqBEhIDCZkJfsy7/0joyQ6IWNIZiaZ9/M8eZhzzm/OeedlMnnnnN/5/WYTGhTKF5Vf\ncKj0EBV1FUT1jOKChAuYPmT6WU/33R7uFgM2zoAxxrSiV49e3DfpPs7tfy6/2vwrrnn7Gp686ElG\nRY36qs1dl4wkv6yGx987RFTvYBacl+i9gE2HOF5cxXXPb6dPzx6svD7dZSFQWlPKvZvu5cO8D5k5\nbCb3TryX0KBQL0TbMazPgDHGtOGyIZex8tKVNGoj17x9DY/tfIyCqqaxBkSE/56dwsWj+/PrNft5\nK9MmUe3Kiivr+Mnz26mpb2Tl9ekMDO/VYruqsj5nPbPXzmZr/lbun3g/SyYv6dKFANhlAmOMcdvJ\n6pM8kfEEbx5+kwAJIDUmlYkDJ5I+IJ2kiGRuWpnJruwSnvnJBC5MivV2uOZbKq+pZ96ftvHZFxW8\ncMNE0odEtdi+48QOHs94nD2FexgaPpTfT/k9Y/q1fzhiT7A+Ay5YMWCM6Qg55TmsPbKWTbmbOFB8\nAIc66BnYkxERSWTlh3CqKohZqcNIioklrX8aY/uNtc6FPq6qroH5z25nT24py+dPYOqo08XcicoT\nPLzjYd7NfpfY0FhuTr2ZmcNnfmPqbF9kxYALVgwYYzpaeV05O0/sZPuJ7Xxa/CnHT+VRUFGKSg1I\n0+fryMiRLE5fzIQBbX4mGy+oqW/khpU72JpVxB/mncuPUgZ+tW17/nYWfbCImsYabky5kQVjFrQ6\nw6UvsmLABSsGjDGekFtSxZxlW6hsKOOmaTWsyV5JfmU+C8Ys4PZzbyc4MNjbIRqn+kYHP/3zLtZ/\nUsCjV6cyO+0coKlvwKoDq3hs12Mk9k3k8amPMyS8601QZVMYG2OMl5wTGcorC8+nd2AEz/49hocn\nvcDcpLmsOrCKa/92LcfKjnk7RAM0NDr4xSuZrP+kgCWzkr8qBMrryln0wSIe2fkIPxj0A1ZPX90l\nC4FvwyvFgIhEici7InLI+W+kizZTRSSz2U+NiMxyblshIkebbXM976gxxnhJQlQoLy2cRM+gQK5/\nfjdXJd7Gk1OfJL8ynznr5rBq/6ozzpJoOld9o4PbX8nk7T353PujUcyfNBhV5Z/H/snsNbN5P+d9\n7ki7g0cveJTeQe2flKir8MplAhF5GChW1YdE5B4gUlXvPkP7KOAwcI6qVonICmCdqr7+bY5rlwmM\nMZ529GQlc5dvpaFReWnhJMLDqvj11l+zOW8z0b2iuWLoFUwbMo2kyKQu0SGtO6hrcHDbSx/zj/0n\nuPeyUVw2Ppj1Oet58/CbZJVlMTxiOL89/7ekxKR4O9Sz5tN9BkTkU+BCVc0XkYHAv1S11UGfRWQh\ncIGq/ti5vAIrBowxXURWYQVzl2/D4VBW3ZDO2LhwtuVv48WDL7IpdxMN2kDPwJ4MCR9C3+C+9OrR\niwAJ+OonIiSC6F7R9OvVj7iwOEZGjiQ21G5dbE15XTmHSw6TXZ5NYXUhJTUllNSWcKruFLUNdRw4\nUUJpVQ1xkUHUcpLS2lIAUmNSmZM0h+lDphMY4Hro4a7G14uBUlWNcD4WoOTL5Vbavw88pqrrnMsr\ngPOAWmA9cI+q1rby3IXAQoBBgwalZWdnd+RLMcYYtxwprODaZz7iVG0DK/7tu6QNbrqHvai6iG35\n29h3ch9Hy49SVV9FdUM1DnXgUAeN2khZbRnFNcUt9pcUmcScpDlcOeJKn5kG15sc6mBDzgZeOPgC\nGQUZOPT05FG9g3oTGRJJWFAfjhfXUVblYHhMOAmRfYjuFU1KTArpA9IZ3HewF19B5/B6MSAi7wED\nXGy6D1jZ/I+/iJSo6jf6DTi3DQT2AHGqWt9s3QkgGFgOZKnqb9uKyc4MGGO8Ka+0mh//aRtflNfy\npwUT+N6IaLefW++op7i6mOOnjrP35F7eOfYO+4v2MzR8KA9NeYjR/UZ3YuSek12eTcYXGQRIAONj\nxzOo76A2n3P81HHu33Q/GQUZJPRJ4LIhl5Eak0pi30QG9B5AcGAwZdX13LRyJzuyi/nPWSnMm9j2\nfrsDrxcDZzzot7hMICK3A2NVdWEr2y8EFqnq5W0d14oBY4y3FZyqYcGz2zlSWMn/zhvPtLGuvjO1\nTVX5IPcDlmxdQkltCfek38PVI6/usoMbHT91nKU7lrLh+IYW6ycOmMjN427m3P7nfuM5qsprn73G\nIzsfIVACWTRhkcvBgArKa1jw3HayCit4bM44rkiN69TX4kt8vRhYChQ160AYpaq/bKXtNmCxqm5o\ntm6gs5AQ4H+AGlW9p63jWjFgjPEFpVV1XPf8DvbklvLgzGTmT2r/6enSmlIWb1rMprxNzBg2g19N\n+lWXGhRHVfnLob/w8I6HCZAA5o+Zz+VDL6fB0cAHuR+wav8qimqKmBI/hRtTbiQ1JhWAHV/s4KmP\nnyKzMJNJAyexZPISBvT+ZmF17GQl85/7iKKKOpbNT2PKiBhPv0Sv8vVioB/wKjAIyAbmqGqxiEwA\nfqqqNzrbJQKbgQTV0xeAnH0IYgABMp3PqWjruFYMGGN8RVVdA7eu/pj1nxTw7xcM5e5powgIaN+3\neoc6WLZ7GU/vfpqkqCSWfn8pieGJHRtwJ8iryOPBLQ+yNX8rEwdMZMnkJQwMG9iiTXVDNasPrua5\nfc9RXldOSGAIqkqdo46onlHcfu7tzBo+iwD55p3ymcdLuXHlDhodyop/Syc1wfNTCHubTxcD3mLF\ngDHGlzQ0OvjN2v28sC2Hy78zkEeuTqVnUPt7sW/M3cjiDxdT3VDNvFHzuHbMtS6/LXtbYVUhqz9Z\nzYsHX0QQ7ki7gzlJc1z+Qf9SRV0Fm/I2sffkXgQhJSaFKfFTWp0tcN2ez7nr1d3E9g3h+evSGR4b\n1lkvx6dZMeCCFQPGGF+jqizfeITf//0TJgyO5Olr04jpE9Lu/RVWFfJ4xuOsO7IOgOToZMb2G0t8\nWDyRPSMJDggmKDCIkMAQAuWbhYerPgeCe2csvrwDovmdEI3aSEVdBaW1pRRUFbC/aD+ZBZkAXJJ4\nCXem3UlcWMddw1dV/vD+YR599zMmDI5k2fw0+oW1P59dnRUDLlgxYIzxVev2fM6i13YTGRrMH69N\nO+tT2nkVebx1+C22fL6FrNIsKurbvJLa6UICQ0iKSuL8uPOZPmR6h1/KqKlvZPEbe/nrx3lcOT6e\nh2anENKje4wX0F5WDLhgxYAxxpftyyvj3/+8i8KKWn5/ZcpXY+WfLVWlvK6c8rpy6hrrqGuso7ax\ntsW9+ADKN/8efJu/ESJCoAR+9W+ABBAogYQFhxEREkFoj9BOu9shp6iKn724i/2fl7PokpH8fOrw\nLntnRUdytxiwsS+NMcZHJMeHs/bW7/HzFzO467Xd7M0r494fjSa4x9lNIyMihIeEEx4S3kGR+pb1\nB7/gjleaLj08s2ACF4/p7+WIuh6btdAYY3xIVO9g/nxDOtdPHsKKLceY/fQWjp6s9HZYPqmh0cHS\ndz7hhpU7SYgKZd2tU6wQaCcrBowxxsf0CAzggSvGsGx+GjnFVVz+5Ie8kZHr7bB8SnZRJXOWbeWp\nDVnM/W4Cf/nZ+Qzq5/rOAtM2u0xgjDE+atrYAaTEh/OLVzK589XdbPyskAdnJBMe6r9zEagqL+84\nzpJ1BwgMEJ6YO46Z4+K9HVaXZ8WAMcb4sLiIXrx00yT+8P5hnnz/EJuzilgyM5lLk31v/IDOVlBe\nw71/3ct7Bws4f1g/Hrk6lbiIXt4Oq1uwuwmMMaaL2JdXxi9f38OB/HKmpwzkNzPGntWYBF2Fw6G8\nuD2Hh//+CbWNDn45LYnrJw9p94iN/sTuJjDGmG4mOT6ct26ZzPKNR3jivUNsOnySRZeM5Jr0QfQI\n7J5dwA58Xs59b+7l45xSzh/Wj9/NSmZojH+OJtiZ7MyAMcZ0QYcLTnH/m/vYdqSYpP59eOCKMUwe\n7v6UyL6uoLyGR//5Ga/tOk5EaDD3Tx/NlePjbeyAb8kGHXLBigFjTHeiqryz/wS/e/sguSXVXJgU\nw10/TCLlnK47nsCpmnqe23SMZRuzqG90sOC8RG69aDgRocHeDq1LsmLABSsGjDHdUU19I89vPsYf\nP8iirLqeH47pzy8uHsHYuK5TFJRV1fP8lqM8v/kYZdX1XJY8gLsvHUVidG9vh9alWTHgghUDxpju\n7Mtv1c9sOsKpmgYmD+/HDd8bwoUjY322s11OURUvfJTNSx/lcKq2gR+O6c9tF43o0mc3fIkVAy5Y\nMWCM8QdlVfWs3p7Dyi3HOFFew9CY3sz9bgKzxsUT27ent8OjvtHBpkMneWFbNu9/WkCACJcmD+Dn\nFw5nTFxfb4fXrfh0MSAiVwO/AUYD6arq8i+0iFwKPAEEAs+o6kPO9UOAl4F+wC5gvqrWtXVcKwaM\nMf6kvtHB3/bms3LLMTJySgkQmDIihpnj4piaFEtkb89dh290KBk5JazJ/Jy39+ZTXFlHdFgI89IT\nmDdxMAPCvV+kdEe+XgyMBhzAMmCRq2JARAKBz4AfArnADuAaVT0gIq8Cb6jqyyLyR2C3qj7d1nGt\nGDDG+KuswgreyMjljYw88stqCBBIGxzJ1FGxpCdGkRwfTs+gjpvuV1XJLalm25EiNh46yYeHCimt\nqqdnUAAXj+7PzHHxXDAy5qwnYTJn5tPFwFcHF/kXrRcD5wG/UdVpzuXFzk0PAYXAAFVt+Hq7M7Fi\nwBjj7xwOZW9eGesPfsF7Bws4kF8OQHBgAMnxfRkT15eh0WEMiw1jUFQo/cKC6RPSo9Vb+hoaHRRX\n1pFdXEV2URXZRZXszStjT24ZxZVNJ2xj+oTw/RExXJAUw0WjYgkLsSFuPKU7DDoUDxxvtpwLTKTp\n0kCpqjY0W28DUxtjjBsCAoTUhAhSEyK485IkTlbUsiu7hIzskq9O45fXNLR4TnBgAOGhQQQHBhAQ\nAIEi1DY4KK+up7KuseX+BYbHhnHRqFhSzwknbXAUowf2sfEBfFynFQMi8h7gavDs+1T1rc46ros4\nFgILAQYNGuSpwxpjTJcQHRbCtLEDmDa26eNaVSmqrCOroILckmqKK+soqqyjtKqO+kbFoUqjQ+kZ\nFEDfnkH07RVEZGgQCVGhDO7Xm/iIXnbqvwvqtGJAVS8+y13kAQnNls9xrisCIkSkh/PswJfrW4tj\nObAcmi4TnGVMxhjTrYkI0WEhRIeFMNHbwRiP8eXybQcwQkSGiEgwMBdYo02dHDYAVznb/QTw2JkG\nY4wxprvxSjEgIleKSC5wHvC2iLzjXB8nIn8DcH7rvwV4BzgIvKqq+527uBu4U0QO09SH4FlPvwZj\njDGmu7BBh4wxxphuyt27CXz5MoExxhhjPMCKAWOMMcbPWTFgjDHG+DkrBowxxhg/Z8WAMcYY4+f8\n6m4CESkEsjtod9HAyQ7aV3dg+WjJ8tGS5eM0y0VLlo+WOjofg1U1pq1GflUMdCQR2enO7Rr+wvLR\nkuWjJcvHaZaLliwfLXkrH3aZwBhjjPFzVgwYY4wxfs6KgfZb7u0AfIzloyXLR0uWj9MsFy1ZPlry\nSj6sz4Axxhjj5+zMgDHGGOPnrBhog4hcKiKfishhEbnHxfYQEXnFuf0jEUn0fJSe40Y+vi8iGSLS\nICJXudpHd+JGPu4UkQMiskdE1ovIYG/E6Qlu5OKnIrJXRDJFZJOIjPFGnJ7SVj6atZstIioi3bpH\nvRvvj+tEpND5/sgUkRu9EaenuPP+EJE5zs+P/SKyulMDUlX7aeUHCASygKFAMLAbGPO1NjcDf3Q+\nngu84u24vZyPROA7wCrgKm/H7AP5mAqEOh//rLu+P9zMRd9mj2cA//B23N7Mh7NdH2AjsA2Y4O24\nvfz+uA74g7dj9aF8jAA+BiKdy7GdGZOdGTizdOCwqh5R1TrgZWDm19rMBFY6H78O/EBExIMxelKb\n+VDVY6q6B3B4I0APcycfG1S1yrm4DTjHwzF6iju5KG+22Bvozh2W3PnsAFgC/DdQ48ngvMDdfPgL\nd/JxE/CUqpYAqGpBZwZkxcCZxQPHmy3nOte5bKOqDUAZ0M8j0XmeO/nwJ982HzcAf+/UiLzHrVyI\nyM9FJAt4GLjNQ7F5Q5v5EJFzgQRVfduTgXmJu78rs52X1F4XkQTPhOYV7uRjJDBSRDaLyDYRubQz\nA7JiwBgPEJFrgQnAUm/H4k2q+pSqDgPuBu73djzeIiIBwGP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IZFc7H6CU8rS9bgkMBGpY9OxcXlqwnZ1Zh3l9TCxBPrZ94gtsuxXKMIFwdqHd\nwFplJATVDOkSwqQBbcnZvRGLazP7vVxHJxFmbq7/OIUQZ8S0ZEBrXQXcB/wKbAPmaK2TlVLPK6WO\nrg54FfABvjlhCWFXIEEptQn4HXhJa+30ycBfuw4xfeVeJg1oy6DO1YYsjm5dLMMEwtkdXVGQdfI/\nt8eviKa3ZwbbrG3ILak6+d5WscazrCgQwum4mfnHtda/AL+ccO6Zaq+H1nDfSqBH/UZXtwpLK/nn\n3E20D27OY8Oij79oKzgkwwTC6QV1BBc3yE4GRh93ycvNhR7u+/i+pBdTv9/Ce+N7H19N0ycYWoTD\nwSTHxiyEOK0GMYGwMXh2XjLZxeW8OabXybsRFqSBlx808zcnOCFqy83D2IXQTs8AxZm4leUT1qUv\nC5Mz+W6DnY2JWvWUngEhnJAkAw7wy+aDfL8xg/sv7khshJ0v/LxUGSIQDUdIzHHLC/9mqz9w/oBB\n9GsbyLPzkskoKD2+TVisMd+g4ogDAhVC1JYkA/Wl6CCkLiM7v5gnv99MbBs/7h3S0X7bvD0QaHdl\npBDOJzQGCvdB2QnbGGcZEwNdW3Xj9TGxWLXmkTmbsFqrVScM62ksPbQlDkII5yDJQH1IWwnvxMGM\nq8l9/0osleW8cUMv3F3t/M9tqYSCdAiSZEA0ECG26oLZ248/n5UMfhHQLICIQG+mXN2NVXty+XRF\n6rE2YTKJUAhnJMlAXSsvhm9uAb9wkjreRdfyTXwak0iHYB/77fPTQFukZ0A0HCFdjefsE37dZ245\nrgzx6Pg2DO0ayiu/7mBnVrFxskU4eAdJMiCEk5FkoK6tmgaHMzkw5C1u2DGErZ6xxB+YZfQA2JO3\n23gObO+4GIU4F/6R4OFrfPkfVVUOh3YeV2xIKcVL1/XA19ONf3ydSEWVFZQyJhFmyooCIZyJJAN1\nqbIM1n6EtdMw7lvmgrurIuzyh1DFB2H37/bvybUlAzJMIBoKpSA8DvavO3Yua4vRw9Xq+MqDLX08\n+e+1PUg+UMT/ltoKFYXFGqsRqlUxFEKYS5KBurR5DpQcYl6zUWxIL+CFUd0J6DkcvPxhy1z79+Tt\nAU8/o+tUiIYi4jxjjkD5YeM4fc2x8ye4rFsrRvdpw7TfU9iQnm8kA9bKk4cZhBCmkWSgrmgNq96l\nNDCGRxJacFXPMEb2CjfWZUdfCTsX2h8qyNsNQe2NX1tCNBQR5xk9AfvXGsfpq4zhgxat7TZ/5uoY\nwvya8dAVfqKBAAAgAElEQVTXiZS26mO7Z7WDghVCnI4kA3Vlz++Qs42pJZcS5OPJv0dV6y7tPMxY\nhmXvP365u2W+gGh4ogaAmxfs/M3o7k9dBlEX1Njc18ud18fEkpZXwn/+KjK2M05b6cCAhRCnIslA\nXVk1jcNugXxU0JtXro/F39vj2LUOF4Orh9E7UF1lmbFeW1YSiIbGozm0Hwzb58PuJcaumzEjTnlL\n//ZB3H5BO2auTiczoDekrQCr1SHhCtEgrHgHNs4y5U9LMlAXMrdAymLeKxvKDf07Hr8JEYCnD7S9\nEHYsOP58zjbb3u/dEKLB6X2zkczOHgveLY2k9zQevqwLXUJ9mbYvCkpy4eBGBwQqRAOx/jMjuTaB\nJAN1oGL525TgxTK/kTwxPNp+oy5XGPMDDlXb+vXohi2tGtSeS0IYugyHHmPArRmM+B+4eZ72Fi93\nV964IZZfy2KwotA7Fp72HiGaBK2h6ECN827qmyQD5yorGbfkucyuGsJzNwzE26OGjSA7DzOeq/cO\nZG421msHtKv/OIWoa0rBdR/B05kQPbzWt3Vr7cfEofGstnTlyPqvjP8ICtHUleRBVZlRmMsEkgyc\nC63J++b/KNTelJ3/EL0jA2pu6x8BoT2OTwb2r4XWvcBF/m8QTctdgzqwIeByfI6kk5tsTreoEE6l\nyLbLZ1PsGVBKDVNK7VBKpSilHrdz3VMp9bXt+hqlVNtq156wnd+hlLrckXEfVbTyYwIPreVLn5uZ\nPCz+9Dd0GQb7VhsZYEmeMUzQ7qL6D1QIJ+Pqohhx030c0n5kz3sOq0UmEoomruiA8dzUegaUUq7A\nNOAKIAa4USkVc0Kz24B8rXVH4E3gZdu9McBYoBswDHjX9n4Oo3csxHvR4yy39uSy8Y/Z34ToRJ2v\nMCYMbv8Zdi8FNLQbVO+xCuGMIkNbsqf7A3StSGLT7KfNDkcIcxXtN56bWjIA9ANStNZ7tNYVwFfA\nyBPajARm2F7PBS5RSinb+a+01uVa61QgxfZ+DrP7r2/Yao1g75CpdArzr91NreOMveCXvw5/vQn+\nUdCmFj0KQjRSfa97iNXeQ4hLmcaRGWOgcL/ZIQlhjqIDoFzBJ8SUP3/aZEAp9bbtC7iuhQP7qh3v\nt52z20ZrXQUUAkG1vLdefRP2EO+0eZ2bBvWs/U0uLnDJFMhPNWq5X/APcHFoh4YQTkW5uNB+8ize\nVONxS/0DPbUfrPvY7LCEcLyiA+AbZtp3Qg1T349TDMxTSo3VWh+xjc8/o7UeWM+x1Qml1GRgMkBk\nZGSdve8Tw7tRUdUVF5czzJO6DINJv0BlKXQaWmfxCNFQhfg3p8u1T3PJl/HM8v+KqJ8fBldP6D3B\n7NCEcJyiDNMmD0ItkgGt9dNKqXHAH0qpCuAwcNJkv7OQAURUO25jO2evzX6llBvgB+TW8t6j8X8I\nfAgQHx9fp2uYPNzOcpSlbYPIo4RwmOE9wljUK45LN7VkfZQLvgsfN4oY+ZkzfiqEwxUdOG4LcEer\nzTDBJcAdwBGgJfCA1np5HfztdUAnpVQ7pZQHxoTAeSe0mQdMtL2+Hliqtda282Ntqw3aAZ2AtXUQ\nkxDCJM+O6EaQrzd3Fk1CV5XD8tfMDkkIx9AaCjPAr41pIdTmp+1TwL+01oMxvpC/Vkqdvu7oadjm\nANwH/ApsA+ZorZOVUs8rpY4WOf8ECFJKpQAPYeuR0FonA3OArcBC4F6tteVcYxJCmMevmTuvjY5l\nZa4PCYFXwYYv4Mih09+45Vv4fNTJ5b6FaChK86Gq1NRhAqXPsPqXUioM+FZrPaB+Qqo/8fHxOiEh\nwewwhBCn8Oy8ZFas+otFno/CZf+GAffX3DhzC3w4GKyVRlnk+9YZBb6EaEgyt8D7A2H0dOh2TZ2+\ntVJqvdb6tMvWznjQW2t9ELjkrKISQojTePyKaKwtu7BZdcGSMP3U5YrXfmDsCDr5T+OX1aavHBan\nEHXG5IJDcJZ1BrTWpXUdiBBCgLGZ0Zs39GJm5WBc81IgfZX9hhVHYMv3xi+p1r0g6gLYMtexwQpR\nF0wuRQyyN4EQwgn1bONP5IXjOay92Le0hroDW+dBRTHE3WQcdxoKOdvhcI7jAhWiLhRlgHIBn1am\nhSDJgBDCKd05tDurml1EYNrPZOfmntxg40wIbA+R5xvHkbZpTDX1JAjhrIoOGImAa21K/9QPSQaE\nEE7JzdWFmCvuojll/PDl+xw32TlvD6T9Bb1uMrZSBqPct6sn7FtjTsBCnC2TCw6BJANCCCcW3vNi\nipu1oVv2z3y5Nv3YhcQvjW7V2BuPnXPzgJCuRqlvIRqSogOSDAghRI2Uovl5NzPQNZlP5y9j76Ej\nYLVA4mzocMnJFQpbdTeWaZ3hkmkhTHO04JCJKwlAkgEhhJNz6XUjWrkyyfUXHpqTiGXL98Z2r30m\nntw4tAeUHILDWY4PVIizUVYIlUdML70tyYAQwrn5R6Jib2Scy2Ja7P+Dw79MgZadocuVJ7cNjTGe\ns7c5NkYhztbfNQZkmEAIIU5t6LO4+gQz3eMVmpceYM/5Lxpbgp8oqKPxnLfboeEJcdacoOAQ1G4L\nYyGEMJdPMNy+hJLEuUxe5knWnx781NOCl/sJe7/7hoG7N+RKMiAaCCcoOATSMyCEaChahOF90f3c\nPnoUu7IP8/pvO05uoxQEdoDcFMfHJ8TZKMoAlJHImkiSASFEgzK4Swjj+0fy8V+prN5jpxhRkCQD\nogEpygCfUHB1NzUMSQaEEA3Ok8O70jaoOQ/P2URxWeXxF4M6QH4aWCrt3yyEM3GCGgMgyYAQogHy\n9nDj9TGxHCws5bmfth5/MagjaIuREAjh7CQZEEKIs9c7MoB7Bndk7vr9/JqceezC0RUFMlQgGoKi\nA6avJACTkgGlVKBSapFSapftOcBOm15KqVVKqWSlVJJS6oZq16YrpVKVUom2Ry/HfgIhhDN44JJO\ndGvdgie+20xOcblxMrCD8SzJgHB2ZUVQXmR6wSEwr2fgcWCJ1roTsMR2fKIS4GatdTdgGPCWUsq/\n2vV/aq172R6J9R+yEMLZeLi58NYNvThcXsVj3yYZmxl5B4KXvyQDwvk5SY0BMC8ZGAnMsL2eAYw6\nsYHWeqfWepft9QEgGwh2WIRCiAahU6gvT14RzdLt2Xy+Ks22vLA95KeaHZoQp1a433huwnMGQrXW\nB22vM4HQUzVWSvUDPIDqlUT+Yxs+eFMp5VlPcQohGoCJA9oypEsw//llGzsyi41kIHeP2WEJcWqF\n+4xnvwhz46AekwGl1GKl1BY7j5HV22ljk/IatxhTSoUBXwC3aK2tttNPANFAXyAQeOwU909WSiUo\npRJycnLO9WMJIZyQUopXR8fSwsuNB2ZvpMq/nfEf2qpys0MTomaF+0C5ml5wCOoxGdBaD9Vad7fz\n+BHIsn3JH/2yz7b3HkqpFsDPwFNa69XV3vugNpQDnwH9ThHHh1rreK11fHCwjDII0Vi19PHk1dGx\n7MgqZt4+L0DL8kLh3Ar3G/MFXI2dAQ4WllJRZT3NTfXDrGGCecDR/UcnAj+e2EAp5QF8D3yutZ57\nwrWjiYTCmG+wpV6jFUI0CEO6hDBpQFtm7rTtWZAnQwXCiRXuB782AJRVWpj06Tomf5FgSihmJQMv\nAZcqpXYBQ23HKKXilVIf29qMAS4CJtlZQjhLKbUZ2Ay0BP7t2PCFEM7q8SuicQs2ag0cPmhn/wIh\nnEXBPvA35gu8tGA7O7KKmTigrSmhmLJrodY6F7jEzvkE4Hbb65nAzBruv7heAxRCNFhe7q68cOMg\nit73Zl3COi4epDE6EYVwIlaLsS+BXxuWbs9i+sq93DKwLUO6hJgSjlQgFEI0Ol3CWlDh1xb3wr3M\nWLnX7HCEOFnxQdAWijxb8c9vkohu5ctjw6JNC0eSASFEoxQUEU205yFeXLCd7ZlFZocjxPFsNQbe\n3VjOkYoqpo6Lw8vd1bRwJBkQQjRKKqgDwZYsAj3hwdmJlFVazA5JiGMKjBoDiw548tyIbnQM8TU1\nHEkGhBCNU2B7lLbyzhVB7Mgq5sVftpkdkRB/2793JwC9undnTHwjLjokhBCmCmwPQL8WBdx+QTs+\nX5XGgs0HT3OTEPWvsKSShE2JFNCCKdf1dYoJrpIMCCEap6O7F+bt4dFh0cRG+PPot0nsyysxNy7R\npGmteezbJEIr9+Me0pEWXu5mhwRIMiCEaKyatwQPX8hNwcPNhak3xgFw35cbTKvyJsTMNeksTM6k\nR7NDNA8zb/XAiSQZEEI0TkpBcGc4ZBQeigj05tXre7JpfyGvLNxucnCiKdp2sIgX5m/l0o4++JRn\nQ1B7s0P6myQDQojGK6QrZB+bODisexgTz4/i479SWbw1y8TARFNTUlHF/bM34tfMnVcu9jFOBnU0\nN6hqJBkQQjReITFwJAcOH9ux9InhXenWugUPf7OJjIJSE4MTTcmUH5PZnXOYt27oRUBpunHy6LwW\nJyDJgBCi8Qrpajxnb/37lJe7K9PG9cZi1TwweyOVFpk/IOrXnHX7+Gb9fu4f0pGBHVtC7m7jQqAM\nEwghRP1rFWs8H0w87nTbls158doerE/L541FO00ITDQVWw8U8a8ftzCwYxAPDu1snMzdDb5h4Olj\nbnDVSDIghGi8mgeBfxRkbDjp0ojY1tzYL5L3/tjN79uzTQhONHZFZZXcM2s9/t7uvD02DlcXWz2B\nvN1ONV8AJBkQQjR2rePsJgMAU66OoWtYC/7v60SpPyDqlNaaR79JYl9+KVPH9aalj+fRC3Bop1MN\nEYAkA0KIxi6yPxSmQ0H6SZe83F15f3xvrFpz96z1sn+BqDOf/JXKwuRMHh8WTd+2gccuFGVAaT60\n6mFecHZIMiCEaNzaDzae9/xp93JUUHPeuqEXWzKKmPJjssPCEo3X+rQ8XlqwnctiQrn9wnbHXzy4\nyXgOi3V8YKdgSjKglApUSi1SSu2yPQfU0M6ilEq0PeZVO99OKbVGKZWilPpaKeXhuOiFEA1KcDT4\ntIJdv9bY5JKuodw3pCNfJ+zjq7Un9yAIUVu5h8u5d9ZGWvs349XRsSfvO3AwCZQLhHYzJ8AamNUz\n8DiwRGvdCVhiO7anVGvdy/YYUe38y8CbWuuOQD5wW/2GK4RosJSCmJGw8zcoLaix2T8u7cyFnVry\nzLxkNu8vdGCAorGoslh54KuN5JVU8O5NvfFrZmffgYObIKgTeDR3fICnYFYyMBKYYXs9AxhV2xuV\nkWZdDMw9m/uFEE1Q7FiwlMOGGTU2cXVRvD02jmAfT+6auZ78IxUODFA0Bi8v3M6KlFz+PbI73cP9\n7DfKTHK6IQIwLxkI1Vof3Us0EwitoZ2XUipBKbVaKXX0Cz8IKNBaV9mO9wPhNf0hpdRk23sk5OTk\n1NRMCNGYhfeGjkNh+euQv7fGZoHNPXj3pt7kFJfz4NeJWKzacTGKBu3HxAw+Wp7KhP5RjOkbYb/R\nkUPGBMKwno4NrhbqLRlQSi1WSm2x8xhZvZ3WWgM1/YuL0lrHA+OAt5RSZ1y7UWv9odY6XmsdHxwc\nfOYfRAjROFzxivH8yWWQsqTGZrER/kwZEcOynTm8KQWJRC0kHyjksW+T6Ns2gH9dFVNzwwMbjeem\n1DOgtR6qte5u5/EjkKWUCgOwPdut+KG1zrA97wH+AOKAXMBfKeVma9YGyKivzyGEaCSCOsAtC6BZ\nAMy8FhY/C5Yqu03H9YvkhvgIpv6ewvykA46NUzQo+UcquPOL9fg38+Ddm/rg4XaKr9W0leDiBuF9\nHBdgLZk1TDAPmGh7PRH48cQGSqkApZSn7XVLYCCw1daT8Dtw/anuF0KIk4R2g8l/QJ9J8NebMO8+\nowjMCZRSPD+qG32iAnjkm01syZAJheJkVRYr983eQHZxOe9P6EOwr+epb0hbYRTBcrLJg2BeMvAS\ncKlSahcw1HaMUipeKfWxrU1XIEEptQnjy/8lrfXR3UYeAx5SSqVgzCH4xKHRCyEaLvdmcPXbMPgJ\n2DQbEmfZbebp5sr74/sQ4O3B5M8TyCkud3Cgwtn9PWFwVHd6RfifunFZEWSsh7YXOCa4M2RKMqC1\nztVaX6K17mQbTsiznU/QWt9ue71Sa91Dax1re/6k2v17tNb9tNYdtdajtdbyr1QIcWYuehSiLoAF\nj0PBPrtNgn09+ejmePJKKrh75nrKq6RCoTDMXb+fj5anMvH8KMbE1zBhsLo9v4O1CjpeWv/BnQWp\nQCiEaJpcXGDUNNAWWPBojc26h/vx6vWxJKTl88wPyWg7wwqiaVmbmscT3yUxsGMQT59qwmB1O38F\nTz+IOK9+gztLkgwIIZqugLYw+HHY8Qts/6XGZlfHtv67QuH0lXsdFp5wPmm5R7jziwQiAr15d1wf\n3F1r8TVaWQbb5kP0leDqdvr2JpBkQAjRtPW/B4K7woLHoOJIjc0eurQzQ7uG8sL8rbLlcRNVWFrJ\nrdPXoYFPJ/bFz9tOhUF7di6A8kLocV29xncuJBkQQjRtru5w1RvGzoYLHrO7ugDAxUXx9thedA1r\nwb1fbpAVBk1MpcXKvbM2kJ5Xwgfj+9C25RmsCFjzIfhHQfsh9RfgOZJkQAghogbARf+EjV/Airdr\nbNbc041PJ/XFv5k7t05fx4GCUgcGKcyitWbKvGT+SjnEi9f04Lz2QbW/efdSSF8J/e8GF9f6C/Ic\nSTIghBAAg5+EmFGweArMvhGy7G9nHNrCi09v6UtJhYVbp6+juKzSwYEKR/vkr1S+XJPO3YM7MLo2\nKweOKi2A+Q8ZvQLxt9ZfgHVAkgEhhABjdcH1n8IlU2DvX/DeAJh5PaSvPqlpdKsWvDe+NynZh7ln\n1gYqLVYTAhaOMG/TAf798zau6N6Kf17W5dSNS/JgfwLsXQFbvoPPhkPhPrjmA3A7TUEik6mmtEwm\nPj5eJyQkmB2GEMLZleTBuk9g7QdwJAf63wtDnwU3j+Oafb0unce+3czYvhH899oeJ+9dLxq0lSmH\nmPjZWuIiA/j81n54udfQzZ+2EhZNgf1rjz/v2xpG/s/YJMskSqn1tj1+Tsk51zgIIYSZvANh0D/h\n/Hth0TOwehoc2ABjvgCfYxue3dA3kn15pUz9PYVWfl7839DOJgYt6tLWA0VM/mI97Vo256MJ8fYT\nAasFfn8Rlr9mfPFf/DSE9jCqXHr6QKuexgTVBkCSASGEqImHN1z5GkT2hx/vhY+GwNgvj9uC9uHL\nOnOwsIy3Fu8isLkHN5/f1rx4RZ3Yl1fCpM/W4uvlxoxb+9lfQngkF76/E1IWQdwEY1dMD2/HB1tH\nZM6AEEKcTo/rjR0PrRb46GL47V9QdBAwNjV6+boeDO0aypR5yfyYKJuoNmR5RyqY+NlayiotzLi1\nH2F+zY5voLVRQOj9gZD6J1z5Boz4X4NOBEB6BoQQonbCe8Odf8Li52DlO7BqKrTpB+0H4dbuIqaO\n6c3Ezyt5eM4m/Jq5M7hLiNkRizNUVFbJzZ+uYX9+KTNvO4/Oob7HN9j7l7H19f510LILjPsawmJN\nibWuyQRCIYQ4U7m7Ielr2LUIDiaCtoJbM6pCe7AspzkZZZ4MjetIWGgYRJ0PrXuDTC50aiUVVUz4\nZC1J+wv4cEI8Q6KrJXOFGbDwcdg2z5gbMPhx6HWT05YWrq62EwglGRBCiHNRWmDsU5+6DDK3YMlP\no7QoD29KcMH239fQ7saYctuB5sYq7CqrtHDbjHWs2p3L1HG9Gd4j7NjF1GXwzSSoLIULH4Lz7zMm\nCDYQsppACCEcoZm/sQFN9JUAuAIF+SUMe38l7hX5zLown9ab3oHpw40vkkuecfo1503J0TLDK1Jy\neX107LFEQGtjKGjRMxDUCcbOgpadzA22HskEQiGEqGNtAryZfecAyj0CufKvtmy/bgn0vcP4cvl4\nKBxKMTtEAVRZrPzf14ks2Z7NC6O6c12fNsaF0gKjN+C3p6Hr1XDHkkadCIBJyYBSKlAptUgptcv2\nHGCnzRClVGK1R5lSapTt2nSlVGq1a70c/ymEEKJmEYHezJ7cHy93V8bNSGJHnykwdjYU7ocPLoJV\n06Cq3Owwm6xKi5UHv07k56SDPDk8mgn9o4zegOQf4L2BsH0+DH0ORs8AT9/Tv2EDZ8qcAaXUK0Ce\n1volpdTjQIDW+rFTtA8EUoA2WusSpdR0YL7Weu6Z/F2ZMyCEcLTUQ0cY++Eqqiya2ZP707lZMcy7\nH1IWg08o9LwBul9rFKtpABPSGoOKKisPzN7IwuRMnroimjt6KGO5YOIsyNlubGk9chq06WN2qOfM\nqScQKqV2AIO11geVUmHAH1rrGos+K6UmA4O01jfZjqcjyYAQooHYnXOYsR+uxmrVfH5bP7q19oM9\nf8CaD2DXb2CtArdmENwZvPzAvbmxw51SoFyNiog+oeATAn6RENoNWoSd9u82WaUFkL0NclPgcKZR\nXvrIISgrxFpVzq6D+RSXlBLl70ZwZSa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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "from nengo.utils.matplotlib import rasterplot\n", "\n", "model = nengo.Network(label='Decoding Neurons')\n", "\n", "with model:\n", " stim = nengo.Node(lambda t: np.sin(10*t))\n", " ens = nengo.Ensemble(2, dimensions=1,\n", " encoders = [[1],[-1]],\n", " intercepts = [-.5, -.5],\n", " max_rates = [100, 100])\n", " temp = nengo.Ensemble(10, dimensions=1)\n", " \n", " nengo.Connection(stim, ens)\n", " connection = nengo.Connection(ens, temp) #This is just to generate the decoders\n", " \n", " stim_p = nengo.Probe(stim)\n", " spikes_p = nengo.Probe(ens.neurons, 'spikes')\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(.6)\n", "\n", "t = sim.trange()\n", "x = sim.data[stim_p]\n", "d = sim.data[connection].weights.T\n", "\n", "fspikes1 = np.convolve(sim.data[spikes_p][:,0], h, mode='same')\n", "fspikes2 = np.convolve(sim.data[spikes_p][:,1], h, mode='same')\n", "\n", "A = np.array([fspikes1, fspikes2]).T\n", "\n", "xhat = np.dot(A, d)\n", "\n", "figure(figsize=(8, 4))\n", "ax = gca()\n", "plot(t, sim.data[stim_p],'g')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\");\n", "rasterplot(t, sim.data[spikes_p], ax=ax.twinx(), use_eventplot=True, color='k')\n", "ylabel(\"Neuron\")\n", "\n", "figure(figsize=(8,4))\n", "plot(t, x, label='x')\n", "plot(t, fspikes1*d[0])\n", "plot(t, fspikes2*d[1])\n", "ylabel('$x$')\n", "xlabel('time (s)')\n", "\n", "figure(figsize=(8,4))\n", "plot(t, x, label='x')\n", "plot(t, xhat, label='x')\n", "ylabel('$x$')\n", "xlabel('time (s)');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Better, but how can we improve this?\n", " - Different shapes for $h(t)$?\n", " - Different $\\sigma$?\n", "- Is there a general solution?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Optimal filters\n", "\n", "- Let's try to find the optimal filter for a particular special case\n", " - Two neurons\n", " - Same $\\alpha$ and $J^{bias}$ but different $e$ (-1 and +1)\n", "\n", "$$\\hat{x}(t)=\\sum_i^N{a_i(t) * h(t) d_i}$$\n", "\n", "- Since there are two neurons and they are opposites of each other, we can assume that $d_1=-d_2$ (i.e. they both contribute equally, but oppositely)\n", "\n", " - $\\hat{x}(t)= \\sum_i{a_i(t) * h(t) d_i} $ \n", " - $\\hat{x}(t)= a_1(t)*h(t)d_1 + a_2(t)*h(t)d_2$\n", " - $\\hat{x}(t) = (a_1(t)-a_2(t))*h(t) d_1$\n", " - $\\hat{x}(t) = (a_1(t)-a_2(t))*h(t)$ (since we can roll the constant into $h(t)$\n", " \n", "- Let's call $a_1(t)-a_2(t)=r(t)$, for *response*\n", "- In this case, it's a difference of spike trains\n", "\n", "$\\hat{x}(t)=r(t) * h(t)$\n", "\n", "\n", "\n", " \n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Random inputs\n", "\n", "- Can't just optimize for decoding a sine wave\n", " - Needs to work for any random input\n", "\n", "- What do we mean by a random input?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/plain": [ "(0, 0.5)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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e+4nr1HvDnQqXC6m6z3jHJU073n4T0kaRZcwO9/Gg53oiohcT0Z1EtJaI3qpc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/CebUcVFukUxZuHBvBPbzsBQDGRSF65dP/0Dnz/Q1uxuG+qtZyq2OMfrO9CoIYL53RnQoieGvDB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\nQEBAgBWBUAQEBAQEWPH/ASc26L6lT+4TAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "x = np.random.uniform(-1,1,500)\n", "plot(np.arange(500)*0.001, x);\n", "xlim(0,.5)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Maybe that's a bit too random\n", "- Many signals don't change that quickly\n", " - How do we get a random signal that doesn't change so quickly?\n", " - I.e. a signal with a limit on its maximum frequency?" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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97KV29I9P4Q8f3A5tiqd/LeTaNWUoMGjxyJF+XNqQWt1uNurwBHD9WvFPXywV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\n8O7tNSl938hkCE+eHMS7t9fAoFPP0r6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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from nengo.processes import WhiteSignal\n", "\n", "dt = 0.001\n", "max_freq = 10\n", "\n", "model = nengo.Network('White Noise')\n", "with model:\n", " sig = nengo.Node(output=WhiteSignal(period=1, high=max_freq, rms=0.5))\n", " \n", " sig_p = nengo.Probe(sig)\n", "\n", "sim = nengo.Simulator(model)\n", "sim.run(1.0)\n", "\n", "t = sim.trange()\n", "x = sim.data[sig_p]\n", "\n", "figure(figsize=(8, 4))\n", "ax = gca()\n", "plot(t, sim.data[sig_p])\n", "ylabel(\"Output\")\n", "xlabel(\"Time\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- What is this doing?\n", "- Generate random Fourier coefficients and convert back to time domain\n", " - Randomly generate coefficients from a Gaussian distribution\n", " - For $\\omega$ values outside of some range, set to zero" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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OBgwaa0nUMAq5DN7w0nW4Z+fBtuG15YguqWbAsM8xwSuoS8otegdkGD984gDO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\nqeqDInLZqNvTCwaMLqjqG4K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s4o82NeFXH7oelzRV4Z8fO4wr/+Vp3Ph/n8Xvjo7h02/owZ9eraz4rlg+evta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\nAHLtKh+mE2nsnzONtedsEACw2cAMpD7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "T=1.0\n", "dt=0.001\n", "signal = sim.data[sig_p][:,0]\n", "\n", "sig_freqs = np.fft.fftshift(np.fft.fft(signal))\n", "\n", "t = np.arange(int(T/dt))*dt\n", "freq = np.arange(int(T/dt))/T - (T/dt)/2\n", "\n", "figure()\n", "plot(freq, np.abs(sig_freqs))\n", "xlim(-500, 500)\n", "xlabel('freq (Hz)')\n", "ylabel('$|X(\\omega)|$')\n", "\n", "figure()\n", "plot(freq, np.abs(sig_freqs))\n", "xlim(-50, 50)\n", "xlabel('freq (Hz)')\n", "ylabel('$|X(\\omega)|$')\n", "\n", "figure()\n", "plot(t, signal)\n", "xlabel('time (s)')\n", "ylabel('$x(t)$');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Things to remember\n", " - $X(\\omega)$ values are *complex numbers*\n", " - When we plot $X(\\omega)$ we actually plot $|X(\\omega)|$\n", " - Since $x(t)$ should be real (i.e. no imaginary component), we expect $X(\\omega)$ to be constrained\n", " - This constraint is that $X(\\omega)=X(-\\omega)^*$\n", " - (i.e., the complex conjugate: the real parts are equal, and the imaginary parts switch sign)\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Finding an optimal decoder\n", "\n", "- $\\hat{x}(t)=r(t) * h(t)$\n", " - $r(t)$ is the response of the two neurons combined together\n", " - $r(t)=a_1(t)-a_2(t)$\n", " - $h(t)$ is the filter we are trying to find\n", "- How do we find $h(t)$?\n", " - Convolution is annoying; let's get rid of it\n", " - One nice thing about convolution is that it turns into multiplication when you do a Fourier transform\n", " \n", "$\\hat{X}(\\omega) = R(\\omega)H(\\omega)$\n", "\n", "- We want to find $H(\\omega)$ that minimizes the error\n", " - $E = (X(\\omega)-\\hat{X}(\\omega))^2$ (added up over all time/frequency)\n", " - $E = (X(\\omega)-R(\\omega)H(\\omega))^2$ (added up over all time/frequency)\n", " \n", "- But, we know that our signal $x(t)$ can be written in the frequency domain as a sum of sine waves (that's the Fourier transform)\n", " - We've already computed those for our signal $X$; that's how we made it in the first place\n", " - So, we can write our error in terms of different frequency values $\\omega$\n", " \n", " - $E(\\omega) = (X(\\omega)-R(\\omega)H(\\omega))^2$\n", " \n", " - Now we can take the derivative and set it equal to zero to do the minimization\n", " \n", " - $H(\\omega)= {{X(\\omega)R^*(\\omega)} \\over {|R(\\omega)|^2}} $\n", " - Note the complex conjugate that appears there\n", " \n", "- So now we can find $H(\\omega)$ given the Fourier transform of our signal $X(\\omega)$ and the Fourier transform of the spiking response $R(\\omega)$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Notes for comparison to the textbook\n", "\n", "- Here we're using the convention that lower-case letters are for time-domain functions and upper-case letters are used for Fourier transfomr\n", " - $x(t) \\rightarrow X(\\omega)$\n", " - $r(t) \\rightarrow R(\\omega)$\n", " - $h(t) \\rightarrow H(\\omega)$\n", "- The textbook uses $A(\\omega)$ instead of $X(\\omega)$\n", " - $A$ for amplitude\n", " - This has caused confusion with $A$ as the matrix for activities of neurons, so I've switched it here\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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Gtg3qsLLh6WFf7SpJfIrpAwai78ZxSrR5/8+H/gwAuOPiO6RZV3X5IySCn17z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\nfxsx98eH94uTJH0Pa/pR37/+++O355bPxWM3P5adfYQVa/qO+T+tlXI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "from nengo.processes import WhiteSignal\n", "\n", "dt = 0.001\n", "max_freq = 10\n", "T = 1.0\n", "\n", "model = nengo.Network('White Noise')\n", "with model:\n", " in_stim = nengo.Node(output=WhiteSignal(T, high=max_freq, rms=0.5))\n", " ens = nengo.Ensemble(2, dimensions=1,\n", " encoders = [[1],[-1]],\n", " intercepts = [-.3, -.3],\n", " max_rates= [100, 100])\n", " temp = nengo.Ensemble(1, dimensions=1)\n", "\n", " nengo.Connection(in_stim, ens)\n", " connection = nengo.Connection(ens, temp) #This is just to generate the decoders\n", " \n", " stim_p = nengo.Probe(in_stim)\n", " spikes_p = nengo.Probe(ens.neurons, 'spikes')\n", " dec_p = nengo.Probe(ens)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(T)\n", "\n", "r_plot = (sim.data[spikes_p][:,0]-sim.data[spikes_p][:,1])*dt\n", "r = sim.data[dec_p][:,0] #properly scaled r\n", "signal = sim.data[stim_p][:,0]\n", "\n", "t = sim.trange()\n", "figure(figsize=(8, 6))\n", "plot(t, sim.data[stim_p],'g', linewidth=2)\n", "plot(t, r_plot,'r')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\")\n", "axis('tight');" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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lAveK6vK5FidE79veUz2qXVE3DMMIQLmlENWhc+UhDjVOk0Inc4vilgEzdLuF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\n3wo3fWO4tENDgbaCMbhLu1YYbqVT12X8dUo8Ivq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "freq = np.arange(int(T/dt)) - (T/dt)/2\n", "omega = freq*2*numpy.pi\n", "\n", "X = np.fft.fftshift(np.fft.fft(signal))\n", "R = np.fft.fftshift(np.fft.fft(r))\n", "\n", "figure()\n", "plot(omega, np.abs(X))\n", "xlabel('$\\omega$')\n", "ylabel('$|X(\\omega)|$')\n", "xlim(-200,200)\n", "\n", "figure()\n", "plot(omega, np.abs(R))\n", "xlabel('$\\omega$')\n", "ylabel('$|R(\\omega)|$');\n", "#xlim(-200,200);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Now we can find our optimal filter\n", "\n", " $H(\\omega)= {{X(\\omega)R^*(\\omega)} \\over {|R(\\omega)|^2}} $" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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KGpIZaYw0mqWn5hbqHJ+YYd+2ZEFjuJin4WBuoflJdVFVqrXYk/2Bi/3zM46c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\na48Gq2fMbKuZ3Wtmz/r/jvW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Qx941xRbHmDkEyiIQXreTpNnRrQP/19xNOOmeqVixtTqBQvj8HGEFEz2WVsvY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\nZlt6wiGCpyrT6M8c2hPPf+cUfO/MI9C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W9Pg3T8b3zjoCpw3pgb4JnvMiN2SMCSIqB/AX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\n", 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qPKRAcO9qCSV/NfPCgA9bAYxnsoxngr3Ow1+oOagtSqRAcO9qCaWBgO9rBZNn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\nh4iIVE3JQ0REqqbkISIiVVPyEBGRqv1/6wwfwnZomRwAAAAASUVORK5CYII=\n", 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POEsOkBZNfAQlHm7RvLOlkOa2Tq49JafH179/YgapseG8tvawR99XBTcNNIOM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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Rmag = R*R.conjugate() #=np.abs(R)**2\n", "#Rmag[(Rmag.shape[0]-1)/2 + 1] = (Rmag.shape[0]-1)/2 #set zero DC term\n", "H = X*R.conjugate() / Rmag\n", "h = np.fft.fftshift(np.fft.ifft(np.fft.ifftshift(H))).real\n", "\n", "figure()\n", "plot(omega, np.abs(X*R.conjugate()))\n", "xlim(-200,200)\n", "\n", "figure()\n", "plot(omega, np.abs(Rmag))\n", "\n", "figure()\n", "plot(omega, np.abs(H))\n", "xlabel('$\\omega$')\n", "ylabel('$|H(\\omega)|$')\n", "xlim(-200,200)\n", "\n", "figure()\n", "plot(freq*dt,h)\n", "xlabel('t')\n", "ylabel('h(t)')\n", "xlim(-.5,.5);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Does this new filter work?" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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1M2PRUk1LGff/yR8jZIaT9HHrZnUurMkk2LVtOwBKERf0A9EkXrMm/npVa1d7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\nZWFrAG1m6NorKFM2br3OTHkDRTrHP+tEK70MXkr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "RMSE: 0.00624025\n" ] } ], "source": [ "fspikes1 = np.convolve(sim.data[spikes_p][:,0], h, mode='same')\n", "fspikes2 = np.convolve(sim.data[spikes_p][:,1], h, mode='same')\n", "\n", "A = np.array([fspikes1, fspikes2]).T\n", "d = sim.data[connection].weights.T\n", "\n", "xhat = np.dot(A, d)[:,0]\n", "\n", "figure()\n", "plot(t, signal)\n", "plot(t, xhat)\n", "show()\n", "print('RMSE: %g' % np.average((signal-xhat)**2))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Testing how well it generalizes\n", "\n", "- If it's a good decoder, it should work for other inputs too" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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9pj1QNHg1/hkGb+1QbMr0T+pLGodYCTWvjT/AVcvS+dHNy9lW2sK3/3FI1wJogkv9Qfjd\n+fDB74c8fVMU5J4LL34duhrCu76xaD8NQA0ppE/S+GcmROGR0GjKUDue/XygVxcy6rzGP9npbbs8\nHY2/j/gssFhVk7gQMud6+0yFO9blUNvRx6/eKCUzIYp/3bwo3EvSzFX2PwYDffCFHZC8ABx2FQN3\n98P96+HtH8P1vwz3Ks+mvZIuk404czxm4+R8xqxEFSaqtQ+Q7dvZ3wMR/lUJzyTqO/owGQQxXach\nNn1q3TzPRAhv+wsd9gkLX7l8IbevyeZXb5Ty5K7QDFPQzEM6qiExXxl+gEirKvBJKoK198DeR5SE\ncKbRXkGDIZ2MhMnF+0F5/uCNl9/yB7WzdXZ23a23ewu8WsuGqnMDQVqJksGGMPIQEOMvhLhKCHFC\nCFEmhPjmKM/fLYRoFkLs9/58OhDXDSS+hnAXLkrh288c5q0TTeFekmau4bCrea+JeaM/f96XlHzw\nF0th90OhXdtEdFRS6Ukmc5IhH4Asr/Gvbe8b6oPTOjuTvvX2PjITItX6AxHy8ZFaot4fnXWBO+cE\nTNv4CyGMwP3A1UAJcJcQYrSytyellKu8P3+c7nWnzEDfmJpas9HAbz5yDsXpcfzLY3s5XGv365S1\nHX08uauKv7xfwSndRVQzFv/8IvQ0wXlfHv35hFxI8fbJf/5fQ7euiXAPIO01lA4kT1rpAxBpNpIU\nE0Fth0Pd4SCgpSzw6wwB9XYHRTFOJcsMpOfv+1IMYegnEJ7/eqBMSlkupewH/grcGIDzBp6WMvhx\nLvxyGTi71S2Wo1Pdgvap7H2sxcSf7l5HYnQEd/9pF9VtvWOerrqtl6/9/QAX/ORNvvH0Ib77zyNs\n/vk7/Pbt2XlLqwkix56HY1vg0n+D/E1jH3fj/w09nikFUfYahPRQ7kpWXu8UyEyIUq2QzVFgzZmV\nnr+Uknq7g5KIRrUjKZDGf4nahrACOhDGPwsY7krXePedya1CiINCiKeEEKHvYlR/UMnq3N6Crr/f\nDT8rhh/nwP+eA3+4ZPDQ1PhIHr5nHQNuDzf/ZjtvHGscoQJq6+nnBy8c5bKfvcOWA3Xcs6mA1796\nEe9+4xKuXp7BT14+rvsHaYYYcMBL31B67nO/OP6x2Wvhq8cBAUf+EZLlTYhX5lkzBY2/j6yEqKGm\niskLZqXWv7Wnn36Xh0JRr3YkBzDsE21Tlb4hVPyESu3zHPCElNIphPgs8DBw6ZkHCSHuBe4FyM3N\nDdzV7TXw2O3K67jlKXjsNqjeCQs3Q/pyOPg39Y3rUyBIyQIr/O2z5/KlJ/byqYd3U5weR0lmPC2d\nfXSe3sMSTvPD3AQuvPw6UouGoly/unMVDXYH33vuKJcWpxIX6V/rW80cZu/D0FkDN90PRj/eD/EZ\nkHceHN0CF5+VQgs97RUAVHlSJy3z9JGZEMXW0maklIikhVD9mLrz9rM76EzAp/HPcteAMULN7g0k\nqSUh1foHwvjXAsM9+WzvvkGklK3Dfv0j8D+jnUhK+QDwAMDatWsDl/be9SD0tsBnt6ms+me3qdij\nT2qWkAtPfVLdCQC4B8DVx+Lrf8VzX/oYf99dw3v7DrPsxF+4x/038H1+64G//BSW3w43/C+YozAZ\nDfz7dSXceP97PPRuBfddHsBbQ83sY8AB234OeZug4CL/X7foKnjtu8pxsWZPfHwwaa/EI0zUkzTl\nsE9WYhS9/W46egdITFoA/d2qpiE+I8CLDR6+CV42RxXYCsFgDOwF0krggwfA7QJj8P3yQIR9dgEL\nhRAFQogI4EPAluEHCCGG/w/fAIRW0NpRqeKMvkq6jBUjNcYLLodN98GqD8Oqj8C6T6mii9PbsJS+\nxEcrvs1vmz+uDD8oqd59B+G+A3Dh1+HQU/DEh8CjuoSuzEngksUpPL6zEpeuGp7fNB6G7gZYf+/k\nvNyFV6ht6WvBWddkaK/AHpGOMBhJjZui8fd+adR29A2FS2ZZ3N83wSumqyKwSh8fqSXgdkJbeeDP\nPQrTNv5SShfwReAVlFH/m5TyiBDi+0KIG7yHfVkIcUQIcQD4MnD3dK87iQWq+OJ43lNkPGz+Plz9\nE7j6x3DlD1SzpcNPwZMfgeoPYMPn4PLvqeMj4pRcLzFfJfCu/xWUvw2P3Ag7fgvAh9bn0tjp5J2T\nzUH/EzUzGJ90LzF/cq9LWazuSEtfDfiSJk1HJU2mNNLiLBinOFs2K0ENdanr6BtKlLbOLsVPnb2P\nKKPE2HE6sEofH6mhbfMQkHsLKeWLwItn7Pv3YY+/BXwrENeaxKLg1X9TcfyGg8q4T4ZLvgNVOyB3\no4q/Gs3Q1QjHnoML/t/IY9d8Ak69CUefhYptsOR6Li3OxBYTwZYDdVy2JC1wf5dmdtHlTQ7Gj6aB\nGAchlPe//3FwOdXQj3DRXkE1G6ZU4OUjc7jnvyRPtbSYZXLPBruDVXGdCMdAYJU+PlIWgzAo47/0\npsCf/wzmboXv8efh/f+DPX+CzHNg479M7vWFF8HF31BbX5IuLg0+8wYUX3P28Zu/N/R432OYjQYu\nWZzK2yeadehnPnPiRYjLnFrf94VXwkAvVG4P/Lr8xdkNva2UDyRNuqHbcGwxEUSaDcrzNxhU2GS2\nhX06HKyI8hZ/BsPzN0epXEKIPP+5afw9Hnjrh0O/33h/8BMoifnw6TeVR3DiBQAuW5KKvW+AvVUd\nwb22ZmbSfEKFA9fdowzeZMk7Tw0IP7014EvzG6/M86gjcbBNw1QQQpA5y+WedfY+lph9Gv8gxPxB\nhX5CJPecm8b/6LPq2/Oib8DHt0x/zqa/ZK9RH9hOdat/wcJkjAbBOyd1q4j5iGfnH3AbzPyocQN/\n2VE5+bGhllh111qxLTgL9AevzLPclTItzx98Wn+VNCVpofpicTmnucDQ4PFIGjsd5FOnevgHYojL\naKSWqIRv/9jFpYFi7hl/j1t1RkxZoox/4STkdYEgNk1NPXK7iIs0sywznl2nQzuhRxN+Bpy9OPY8\nwfMD63j0UC/fffYwdz6wgy7HJMeGFlyoBr7U7gnOQidiGkNcziTLV+ULKpktPUM5kRlOS4+TAbck\nfaAmOCEfH2klgAzJzIO5Z/w7KlWc9OJvBl6H6w/xGYAEuyp6Xl9gY39NB06XHhY/n3j+7w8R7enG\neM5HOfy9K/ntR87hcK2dr/39wORmRhRcoLZ/OKsmMjTU7cNliqGduGl7/pkJUTR3OdUdkM9zDvHo\nwqlS771jSeyrDE6y14dvqlcIQj9zz/jbCuFLe2DJDRMfGwzyvH1bTr0JwLp8G/0uDwdr/GsSpwkA\ndfvgvV+H7fKHauxYT/wduzmF6278EEIIrl6ewTeuWswrRxp56fAkBrbkbBh63Bfi3JHHA8efp8m6\nHBBkTLHAy4cvZ9Bgd0BUoto5W4y/vY9YerE4mgPb1uFMbAVgigxJ0nfuGX9QsripJNgCQfIiVfbt\nLc5Zk6fe5Pt10jc09LTAAxer6tjnvwq/OVf9NB0P2RL+8NJ2LjQeJHLtR0bcfd6zqYDi9Dh++OIx\n/0eGmqPgY8+qxzW7g7DacehuhIFeDsVdiNkoSI6ZntzU19q5rqNvaPbtLDH+dR2OoZ4+wfT8DUYl\n+dTGfxbi02effgdcTpJiLWRYIzlcpz3/kPD6fw493v2gkuk2HQ1Z0nRPZRtpFVsw4cGy5qMjnjMZ\nDXz9ysXUtPfxwsFJxLqz1yn9d/UHAV7tBHSooUanXUmkWyMxTLHAy4fP+Nd09EFMstrZ1Titc4aK\nhk4Hi03eO7ZgxvwBlt4C2euDew208Q8OBReqvEP9AQCWZlr9ng2gmQaNR9WYxNUfg2W3wSeeh3vf\nUQVFDYdCMiXpwW3l3GHehjtr7ahG4pLFqSxIjeWBreX+x/4tsZC2FGp2Bni1E+A1/iccidNO9gKk\nWS0I4fX8o5PUFLNZUuVb19HH8sgmEEZILAjuxc7/ClwS/JpYbfyDQe65austzlmaGU95Sw+9/a4w\nLmoe8PaPVOuNzd+H2x5UyVIh1Hbvw/DkR9X8hiDR1Ong6NHDLKQa44o7Rj3GYBB8+vwCjtZ3sqti\nEiGPnA0q7OMJoXDAq/E/2B0/pQleZ2IxGUmJtSjjL4QKkbbMkJkFE1Bvd7DI2KDaupgiwr2cgKCN\nfzCITVFxwar3AViWZUVKOFYfPMMz7+moVlXdaz95tgb7zsdUX6YTL8Gjt6qq1SDwt93VpMoW9cs4\noYEbVmUSE2HkqT2jT5QblZwNqhNmCFv+0lGFjEmhqktOq7XDcLISo6jzaf2TF82aQq/29nY2Orap\nBpFzBG38g0Xeuao3kMfD0sx4AI7UaeMfNHY/qLbrPnX2c6YIdSt96x9V6OTw0wG/vJSSf+ytZVO6\n9+4uNn3MY6MjTFy7IoMXDtb7fzeYvU5tQxn376jCFZfNgFsGxPMHzqjyXag6njpmdkjU7ZEU9exV\nvwQ73h9CtPEPFrnngqMDmo+TYY0kMdrMUW38g4PbBfsehcXXqOKhYXg8kn1V7eypbMddfINql+AN\nZwSSI3WdlLf0cElKl9oxQZ/6W8/JpqffzStH/JR9JuZDTCpU75reQidDRxXdUaohXSBi/jA00UtK\nCcmL1c4Z3uCtucupKntBdfGdI4Rqktf8w+ep1e1DpJWwMDWOsiY93D0onH5bVVWvvGvE7tZuJ59+\nZDf7vDLb4vQ4no9JxxSEJOOWA3WYDIKl7W8qpYZPxz4G6wtsZFgjefFQAzev9mNYixCQdQ7U7Q3Q\niifA4wF7Ne3JarzpdDX+PjKtkfS7PLT29JOcvEjtbDmpWqPMUOrsfRSKevotNiIm+H+dTWjPP1jY\niiAidlDxU5Qaw6lmbfyDwqGn1fCdhZsHdzldbu7+0y6O1nXyo1uW87PbV1Jvd/B83zLk0S2q4VqA\n8Hgkzx+o4678LozNR2GMZO9whBBcuTSdrSeb6XH6GfrJPEfFyIOYtB6kuwHc/dQbVDvyQHn+mcO1\n/ol5YDCHpJXBdKjvcFBoqMeVWBTupQQUbfyDhcEA6SuGjH9KLO29A7R2z45GVrMGl1PNWCi5fkTP\n+9++fYpDtXZ+9aHV3LU+l1vXZPPQ3ev4j74P0RiRA/+4VxWEBYA9Ve3U2R18LHqnkgIuvdmv1121\nLB2ny8NbJ/xs/Jd1DiChfv/UF+svXplnlScJi8lAYnRgZlFnJQ4z/kazqsif4UnfensfhaIOU8qi\ncC8loGjjH0wyVip9ucfNgtRYAE4194R5UXMMew30dw211UDFaH/79imuX5nJVcuGEq9r8hK555Jl\n3N31BTy9bfDi1wOyhOcP1BFpggVNL8GCy4YKmCZgXb6N5NgIXva33UPmOWpbG4LQj9f4l/YnkZkQ\nhQjQoPXBQq/2YUnfGS73bG9tIkV0Yk5bHO6lBBRt/INJxkoY6IHWMopSlPHXcf8A85p3YFzckJH/\n8/bT9Ls9/OvlZyszPndxIZ3xi3gi6kNw5B9Q9vq0Lu/xSF450sg9OY0YOmth+cQhHx9Gg2BzSTpv\nHW/yr91zTJJKaIci7u/r498TP+2GbsOxRpmJjjCOlHu2lYN7kt1OQ4j03pmIOaT0AW38g0vGSrWt\n209WQhSRZsOMiPv3uzw8uqOSlw/XT67D5ExDSqXth8FeMd1OF4+8X8nVy9Ip9H7hDsdiMvLFSxfy\nvdbLkQionl7V7P6aDho6HdwesR3MMaNPeRuHq5al09Pv5r0yP0NQmeeoxnXBpqMKYlKp7JQBi/fD\n0FCXwdbOyYvA4xqcGzATsdi9A9W18df4jU/NsON+DAZBYXLsjPD8v/H0Qf7t2cN87tG9PPZBVbiX\nM3WGFzylqFvyFw/V0+Vwcc+msUvwb1uTTUpCPO0GG9hrp7WElw83EG10k9f4GhRfCxExk3r9xkIb\n0RHGycX9O6pUuCuYdFQhE3Jp7HQMzt8NFFkJUdTZhxl/mNGhH2tPBW6MSm47h9DGP5j4RkfWH4Du\nJgpTYjjdEt6Y/76qdp7ZV8vnLirigoXJ/OTl43ROdsDITMEXsvnqMdX9Enh6Tw0FyTGD3VRHI8Jk\n4GPn5nHaZcNZuVPVCUwBKSUvHa7n3oxyDI4Ov1Q+Z2IxGdm0IJm3jjf7dxfmi/v/YumkrzUpOqpw\nxGThkYFfl1l8AAAgAElEQVRT+vjITIiitn3YOEeYsca/3+UhbaAae1T20CzvOYI2/sHm/K+qbctJ\n8pKiqevoC+tA97/sqCQu0sSXLl3A/3dlMV0OF8/snZ73GzbKXldj7+IzAahu6+WD023csjprwgTl\nh9bl8ChXY2k/CR/8dkqXP1rfSXVbH7eYt0N0MhReMqXzXFqcSm1HHycb/bgrzFw99DhYITuPBzqq\nsVtUoVqgNP4+shIiae3pV3mOSKuqhp6hip/GTtXKuS8+yM3cwoA2/sFm7T1q23KSXFs0Lo+k3u4I\ny1IcA25ePdLI1cvSibGYWJ5tpTg9jucO1IVlPdNioE+1zygamnD1wiHVJvmm1VkTvjwhOoLIlbfx\npmcN8s0fQNvpSS/h5cMNGARkOcogf9PQnd4kuWRxKgBvHvcj9GOJhet+qR63T37NftHdAJ4BmoxK\n458ZBM8fGBb3n7mKn/r2HvJFIx7b3Ir3gzb+wSc+S7UUbikjxxYNQFVb8Iczj8a+qg66nS6uKBlS\nxlyzPIPdle209fSHZU1TpmY3uPsh//zBXa8eaWBZVvzgv/NEfOzcAr7dfzcD0gDP3TdpT/qlww1s\nKEjC2NMEceO3cxiPdGskJRnxvOWP8Ych778uSHp/r8yzVqYAan2BZGioy/AGbydD0nJ7snTUn8Ii\nBoiYYzJP0MY/+BgMKq7p9fwhfMZ/R3krBgHrCoa6Xm5aoDTpH5S3hmVNU6byPUAMts9u6nKwr7qD\nzUvGbqh2JiWZ8WTnLeD3xjvV8J3GI36/tqypi7Kmbq4rjlN1BnH+X3c0Li1OZU9VO/ZeP/IvqSVg\njAhesdfRLQCcciURE2EkPjKwXWB8nn9th/dzkLxINXfr9vPLL4T0N6rqY2vOkjCvJPBo4x8KkhZC\naykZ1ijMRhFW478004o1aihxtSLbSnSEke2nZpnxr3gX0pdBVAIAbxxrQkq4YmnapE7zsXPzeK3L\nG8/t8F/59NIhVZh1TZT3CyN9xaSueyaXFKfi9ki2ljZPfLApQn0BBMvzr9kJtiIO96WSEcACLx/p\n1kiEgFqf5+9VatF8LKDXCQSuDqWqikzOD+9CgoA2/qEgeSG0V2J0O8lOjA6L8e93edhX3cGGgpG9\n7s1GA+sLbLw/mzx/lxNqdkHeUMjntaONZCdGUZweN6lTXbUsHWe012v3s9unlJJn9teyvsBG4vEn\nVI/3wosndd0zWZWTQGK0eRKhn1VKRRaMUEl7BeRvor7TEdACLx9mo4G0uMihmH+aV7nUGMJZBX7i\n6vJ+LqJs4x84C9HGPxQkLwIktJWTY4umOgzG/2RjF/0uDytzEs56bk1uImVN3XTNFsln7V5wOVSS\nFZXI3n6qhcuXpE3aS7WYjGxet5xSTxburT/3K/RwsMZOeXMPH1/khlNvweqPjhjUPhWMBsFFi1J4\n+2Qzbo8/ks/VqmV4oIuj+ntUh9SEPOrsjoAne31kJgwz/rGpSi0VykE1/tLXTr+IgAj/8kizCW38\nQ0HSkJY51xYVFs//qHeKWIl3sMxwlmVbgVk0bKbyXbX19vPZW9mOY8DDBQv966lzJh/emM99ri/h\n6bPD058C1/jJ72f21RJhMrC5Z4sy+mvuntJ1z+SS4lTaevo5UNMx8cEZq9Q20NW+7erux2XNo6Xb\nGXCZp4+sxOihoS4AaSUz0vibnO30mazhXkZQ0MY/FPiMf2spubZoOnoHsPeF1ss+WtdJdISRgqSz\nK1CXZ6k396GamT1RaZDK7Srm7R3XuK2sBZNBsKEwaUqny0yIIrt4Hf/FZ+D0VvUFMMas3H6Xh+cO\n1HHt4lgsh55QHTynmez1cfGiVIwGwZvH/Aj9BCvp672TaDVnIGXgZZ4+MhMiqe9w4PHd5aSWQNNx\nVWMwQ+hxurC5W3BGpoR7KUFBG/9QYIlVUsDWU4OKn1CHfo7U2VmSEY/BcHZYJDnWQqY1kkO1s8D4\nezxQs0fNtPXyXlkLq3MTiLVMXZXy8XPzeaTvPI4suQ+ObRmz589Lh+tp7enn8wkfgLMTNnxuytc8\nE2u0mTV5ibx+rHHig4OV9PXWDtSgvtCC5vknRNHv9tDS421xnlqimiAGYcraVKm397HQUIszYUG4\nlxIUtPEPFYkF0F4RFq2/lJLj9V2UZJwd8vGxNMvK4bpZYPxbS8FpH5yU1t7Tz6FaO+cvmJ53dl5R\nEoUpMfyitkTtGCWWLqXkwXdPszgpgoUnH1RfQNlrp3XdM7l8SSrHG7pGhkTGIhhJ37ZyiLRS41RG\nP9CtHXz47igGtf6+pO8MCv00NjWTIdogpTjcSwkKATH+QoirhBAnhBBlQohvjvK8RQjxpPf5D4QQ\n+YG47qzCpox/doIy/nX+fLgDRHO3ky6ni6KUsZuOLU6Lo7K1F6fLj9bC4aRmt9p6jf/75a1ICecv\nnFrIx4fBIPjSpQvY1uQdCHPiRZX8HMbO020crLHz/dw9iK46uPhb07rmaFy2RElV3/TH+89YFfik\nb1s52AqpsyuPPBhqHxga6jLY48dnYGeQ8e+rUzLeqKySMK8kOEzb+AshjMD9wNVACXCXEOLMf61P\nAe1SygXAL4CfTPe6s47EfOiqJ940MLKfeQgo9w6QGa3FsY+FabG4PZKKlvDUIPhNzS41stGbR9lW\n2kKsxcTK7LNVTJPlhpVZ5KbaeMx8qwr9/HQxPHw9dDUgpeRnLx1kQdwA6yv/ALnnTVveORqFyTHk\nJ0Xzhj+Sz0xv0jeQcX+f8e/oIyHaTMw0QmnjcVaLB0usmlXQdDwo15sKnkZVd2DNnV4Nx0wlEJ7/\neqBMSlkupewH/grceMYxNwIPex8/BVwmAl05MtPxtoMV9uqR/cxDwJDxH9vzX5iq9PEnG7tCsqYp\nU7NbDfs2qLfuu2XNbCxMwmSc/lvZaBD8+/UlfKfrVh4u+SPkrFMJ4Ip3OfD4v/G35pt4KvK/EX1t\ncPVP1FD1ACOE4LIlaWw/1Upv/wTdRlNL1AzcQMX9Xf2q0M1r/IOV7AWIjzQRazGNDG/FZULPzKny\njW4/Ti+RmJPmXlM3CIzxzwKqh/1e49036jFSShdgB866TxdC3CuE2C2E2N3c7Eel42zC1wu87TSZ\nCVHU20Np/LuJNBvG/TAXpsRgEFA6A+YNjEl/DzQdGQz5VLX2Ut3WN2WJ52hcsDCFj2zI5T/2RvNI\n7g/Uzqc/xarS/wMgoasUNnweMoLnDV5WnEq/y8O7pRMMeDFZlEQyUJ6/vRqkB2xF1Hb0DXrnwUAN\ndYkcafyjk6Bn5hQb2npKqTblDToac40Z9VdJKR+QUq6VUq5NSZlj8qpEr/fQXkGmNXKotD0ElLf0\nkJ8UM6rSx0ek2UheUgylM9nzr9unjFOWSrJuK1MOgq8/UaD4zxuWcvmSNP79pdO8K1dyzJPLL6O+\niDRGKHnlZf8e0OudyboCG3EWE2/4I/nMWKU8/0Akfdu8E6u8nn9WkJQ+PnLPLHiMtkHvDDH+UpLl\nPE1L9NxU+gAEIqBXC+QM+z3bu2+0Y2qEECbACsyQ/+UQEZOsxvy1V5CZcBkt3U6cLjcW0/QqQ/3h\ndEvPuEofHwtSY2e251+zS229Cpv3ylrIsEaOm8ieCmajgQc+toZ/HqjlxYr7WZASy+c25CJ6P6/6\nz5uDaxTNRgMXLk7hzRNNeDxy3C9tMlfB3oeVRHK6k6a8xr87JodORwsZQfT8AXJtMWw/1YqUUlVm\nx6ZCb4sKP5kignrtifB0NmCli56ERWFdRzAJhOe/C1gohCgQQkQAHwK2nHHMFuAT3se3AW/KWT08\ndgoIoT6c7RWDt9MNIejr3+/yUNXWO26838eitFgqWnrod82cQpsR1OwGWxFE23B7JO+VtXL+guSA\nNx4Dpf65eXU2P7x5OfecX0Ck2QjWbLBMrnfQVLl8SSrNXc6Jay98lb61ARjq3lYOEXHUDShhQDDD\nPgB5SdH09rtp7vZq/dOWqXm+M0DxY688oB6kBXliWhiZtvH3xvC/CLwCHAP+JqU8IoT4vhDiBu9h\nDwJJQogy4KvAWXLQeYHP+Hvlc35puadJdXsvbo8kf5TK3jMpSI7F5ZEhWdeUaDg42Mv+cK0de98A\n5wcw3j+T8FX7vnykYfwDfcbpqU9O2JZiQtrKwVZArdcpCXrYJ0nJnitbvaGfwTkFIRhQPwHdVSqP\nEp0zN5U+EKCYv5TyRSnlIillkZTyB959/y6l3OJ97JBS3i6lXCClXC+lLA/EdWcdXq2/z/jXhyDu\nX+PVUfs+aOOR7z2mIsxzhsekuxni1dCUd8tUMvS8orlp/BNjIjivKImXDtWPP9vXZBl63Hhoehcd\nJvOE4Hv+Podk0Pgn5kNkAtQF4C5mmngajtAoE8jImHgq3GxlRiV85zyJ+eDqI92obuVDIfesaVcf\nrOzEiT/Ied4PY0XrDDT+/T3g6lOKEODd0haK0+NIibNM8MLZyzXLM6ho7eVY/QRJ+H/xtqKo3jX1\ni/W1Q2sZJOZT19GH0SBIjQuu55+VEIVBQJXv/SaE8v5ngOcf1X6CE56cwaljcxFt/ENJQi4AkT11\nJMdGUBcCuWdNex9mo38f5OTYCGItpiFPbCbR45U9RifT1+9mT2V7QCWeM5ErStIwGgQvemcTj0nK\nYjUutGb0fkR+sV1JWUlbRl2Hg/T4SIzjJZoDQITJQGZCFJXDFT9Z50DTMTWjOVy4XST2nqbK7M31\nzFG08Q8lVq8oqqPSW+gVmrBPZkKUXx9kIQR5SdEz0/P3tTCwZvHB6Vb63R7OXzjH5MBnkBRrYWOh\njRcnCv2Aqn2YjudvVxOrWH4btR19IfN41fttmPHPXK2SvpMYqRlwWksxy37aYueu0ge08Q8tCV7j\nb68m0xqaKt+a9l6/Qj4+8pNiZmbM31fIlL6Sd0tbiDAaWJ8/96YrncnVyzIob+nhxET1FznrwV4F\nXRMkiMei+TgUXgJCqOreICd7feTaYobCPjCU9A2EemmqeCume5KXh28NIUAb/1BiiVMJrY5q0q2R\nNHSGxvP3NZPzh7ykaGra+xhwzzC5Z/0BdecUk8S7ZS2szU8kKmLu3pL7uHJpOgYBLx6awKhnr1fb\nMVpRj4vHA80nILUEt0fSYHcEPdnrIz8pmvbeATp9U+Tis1T78+odIbn+aLhr99IjLUSmac9fE0gS\ncsBeTVp8JF0O18T9W6aBY8BNc5dzsIOiP+Qnx+DyyJD2HvKLuv2QsZKmLgfHG7rmrMTzTFLiLKwv\nsPH8gbrxQz8ZK1T18VTi/h0VKpmeWkxzlxOXR4bM+Of55J6+hoJCQN55UPl+cOYT+8FA9R4OywKy\nkkJT0xEutPEPNQl50FFNWrxSqTR2OoN2KZ9ef7JhH2BkHDbcOOzQdgoyVrG9TBWGXzDN/v2ziZtW\nZVHe0sOB8SatmSyQsXJqcf8m1b2S1JLB90yoYv6+TrPlLcMqy/POg666wM8n9ge3C3PzYQ55CshJ\nnHtze4ejjX+osSrPP90rUQxmla9P4589iTfxjNT6N3j165mr2FbaQkK0maWjzCKeq1yzIoMIk4Fn\n9taMf2D2epUbmWyxl8/4pyweNP6hC/vEYDQIShuHGf/c89S26v2QrGEEzccxup0c9BSSY5u7Mk/Q\nxj/0JORAfzfpFvUhawxi3H8yGn8fKXEWoszGmaX48SbgZPoK3i1rZlNR8vj9buYY8ZFmNpekseVA\n3fitN3LWg8sxeZ180zGw5oIlbrDRmm/caLCJMBnIS4qmbHhPqZRiiEqEivdCsoYRPHAxACcMRUFt\naT0T0MY/1HjlnulSdaQMrvHvw2QQpMX7r9wQQpBjixq8a5gR1O+HuEyOdkXS2OnkokXzJ+Tj45bV\nWbT3DvDOyXFanedfoLYVWyd38ubjkKomaVW19ioHIITJ9AUpsZQ2DVMzGQyQt0nNUghl3L+7CTwq\n8SxsRXPewdDGP9R4Oy9G175PrMUUVMVPTXsfGQmTL9bJSYwO+YD5cak/AJmreNPb4viS4tQwLyj0\nXLgohaSYCP4xXugnJgnSliuj6S+ufmg5CalLADVbOlRev4+FabFUtvaOvKvJXqekq84QthivUgqj\nR823U5A6t5O9oI1/6Elfrr4AKt8jNd4SVM+/wd43pQHcOTYl95wRjVedXdBSChmreON4EytzEuZ0\nS4exMBsNXL8ykzeONWHvHRj7wIILoeoD/ytkm46Cu3+wO2g4jP+CVNVQsHJ4qDEuXW17QjjUqWoH\n0hTJD3uupyA5sG3CZyLa+IcaISB5MdhrSI+PDKrap6FTlelPluzEKLqdLjrGMzKhouEwILEnlHCg\npoPL5qHX7+PWc7Lpd3t4/lDd2AcVXAhup/96f19+IHMV/S4P9fY+ckLt+Xu97BFx/1jv/3O3H4Ps\nA0XVdhypq+j1mMaddz1X0MY/HMRnQmct6fGRQVP7SClp7HSSYZ2K8Vcf/ur2GRD68Vb2bu3OQkq4\ndB4b/2VZ8SxKi+Xvu8cJ/eSdB8IIp9/x76T1+9WAmsQC6jr68MjQJXt9FKXEIgQcaxgW4on3dtNs\nLQvNIvraof4ADQlrALTnrwkS1izobSUjVtDU5QhKeKW9d4B+l2dSyV4fPonbjEj61u2H2HRerJCk\nx0fOK4nnmQghuGNtDvurOzg5VruHyHg16az0tYlP6HZB6esq5CMEVSFW+viIijBSlBLLkeGDa5IX\nQXw2nHgpNIuoeBekh8OR5wBQqI2/JijEZwNQGNHBgFvS1jPNIRyj4BsQnz4Fz9932z8jkr71B3Cn\nr+DtE81cXpIalKlds4mbV2dhNgqe3FU99kHF16rBNx3jHAPw6negswYS8wDCZvwBlmdZOVw3zPgL\nAUuuh7I3wBmC0aKn3oKIWHYMFJEQbSYxJrxjJEOBNv7hID4TgGxDG0BQFD++RPJUPP/4SDPWKHP4\nwz79PdByglOmBfQNuLluRWZ41zMDSIq1cPmSNJ7ZVzu25r/4OrXd/r/gGientPcRtS24CFBf9hEm\nA6lhSKgvy7LS2OmkqWvYZ2HJ9Sp/UebHXcx0KX8b8jZxvKmPRWlzX+kD2viHB6vy/NO8M+ybgpD0\nbbCrc04l5g8q6VvdFuawT8NhkB7e6MggJc7CunnQxdMf7liXQ1tPP68fGyMZmlSk6kl2/h6euGv0\nY1xOkB5YegssuxVQnn9OYlRY9O3Ls6yAGs85SO5GiE2DA08G9+Jtp6HtFJ6CizjR0MWSdG38NcHC\n6/nb3GpASTA8/4ZOB0IwZVlkTmJ0+D3/ejVE+4kaG9cuzwj6cJHZwoULU8iwRo4f+sn0DnY/9Ya6\ngzqTyvdUNfCKO1SIBTVOMdRKHx8lmfEIAYdqOod2Goyw+qNQ+sqYISyPR/L4B1Xc8fv3ueuBHTy7\nr3byObTjLwDQkHEZ3U4XxRnzI6+kjX84MEdBlI0YZwNCBKe/T4O9j+RYC2bj1P6Lc2xR1IZb61+/\nH4cliSpXAteuyAjfOmYYRoPgtjXZbC1tHrv76jU/g1ivVr698uznT74KRouShqKM6OmWHgqTwyNx\njLWYKEyO4UBNx8gn1tytqnz3/Pms1wy4PfzL43v59jOH6Ha4aO528pUn9/Nfzx+b3Pv2+AuQtpzD\nvQkAFGvPXxNUrFkYO+tIirGMjHMGiIZO55Q0/j5ybNE4XR6au4JXhzAh9Qc4KQpJj49iTW5i+NYx\nA7ljbQ5SwlN7xpB9xqXBHQ+rx51n1AVIqbzpggshQqlaGjod9A24KUwJn8plfYGNXRVtuD3DDHdC\nLiy+Gnb9UXV3Hcb3nzvKS4cb+PY1xbzw5fN59SsX8slN+Tz03mke3THKF95odDer2QHF13K8oQsh\n0DF/TZCJz4bOOtLiLUHx/BvtjikpfXzkhFvrP9CHbDrG1u4sbluTPef7rEyWHFs0mxYk8bfd1Xg8\nY3i5Pq18w8GR++v2QVu5UgV5OdWsFDVFYSxu2liYRJfDxbH6zpFPnP9VcHQMhmcAdpS38pcdldyz\nqYB7LyxCCIHBIPjutSVcsjiF/3rhGFX+tCU/+qzKfSy5juMNneTZoomxmAL8l81MtPEPF9Ys6FRV\nvg3BSPhOVN1bfxCe/syYbQB8nUDDlvRtr0RINyc92dyxNic8a5jh3LE2h5r2Pt4vbx39AGs2FF4M\n7/4COqrUxK4Xvw4PbgZTJCy7ZfDQU97q2qLU8Hn+GwqSAHj/1Bl/T8YKtfXG/R0Dbr71j0Pk2qL5\n+pWLRxxqMAh+eMtyjELwgxePjn/B934NL35N9UNKX87Ruk4Wz5OQD2jjHz7iM6Gvnew4aApwwrev\n3429b2Bsz9/VD7+/AA79DQ4+OWrzrMEq3zBp/T3dqqdLemY2uUlze6jGVLlyaTrWKPPYiV8h4Nqf\nq8cPXgl/vgZ2PqAGpJfcqCp7vZxq7iEu0kRKbPj6JqVbIylKieHtk00jnzBZICZF1SQAv3qjlNMt\nPfzw5uWjdh/NsEbxxUsX8MqRRnZVtI1+sfZKeO276vHqj9DW009Fay+rcuZPeFEb/3DhK/Qyd9Da\n04/T5Q7YqRsm0vgf/OvQ4+fug58vhZOvjDgkKsJIcqwlbFW+J06rmO15KxZPcOT8JdJs5KZVmbx8\npGHsZm9JRfDxf6q7gOGx/033jTjsVHO3t81CeMNrVy5NZ0d5G+1nFj5mrIIj/+TEyWM8sLWc29dk\njzvK855NBSTHRvC/b47RHmLbT4ceL7+dfVXtAKzOTZjunzBr0MY/XFhVPDbXrN50gdT6+3IIo2r8\npYQdv4W0ZXDB1+CqH6sKz7/fDS0jPyg5tqiwxfx3Hz0JwMZlc3uI9nS5Y10O/S4Pz+6vHfugrHPg\n06/BVw7C/zsBH3sG0paOOKS8uSesyV4fVy/LwO2RvHr0jIH11/wP0uPC9OSHyY9y8J1rl4x7nqgI\nI5++oJCtJ5vZX32GgqjtNOx/HM75BNx3AGKS2VfVgdEgWJFtHf2EcxBt/MOFV+uf4Sv0CqDiZ9zq\n3uqdqo3vhs/BZd+FjZ+HDz8JRjO8/h8jDg2X1v9UczfOxpO4DBYirekhv/5sYmmmlWVZ8eNr/ocT\nlw5Fl47Y1ekYoKHTEdZkr49lWfEUpcTwlx2VI+WatkKeK/4x2a5qXjR9jYTu8gnP9dGNeSREm/m/\nN0uHdkoJL39LDbu/+JuD8zX2VLZTnB5HdMT8SPaCNv7hw6vESHKr2LavIjcQ1Hs9/7Ni/h1V8NAV\nYDCpmO/gWjJh0VWDRVU+cmxR1HU4cLnHGR0YBB589zTLjRXItGVgnD8fxqly59ocjtZ3jqyOnQTH\n61XOp2QGFDcJIfjU+YUcru1k+7DE7+FaO1/dk8zP8+7H4myFY89NeK5Yi4l7NhXw+rEmSo/uhd+c\nBy/8Pzj5Elz8rUEHrLffxZ7Kds4rSgra3zUT0cY/XHiTWPH9gR/n2NjpIM5iIvZMydqWL6mtOUZ1\nfxxOfCZ01StFiJfsxGjcHjn4ZRIKWrud/GNPFSuNVZizVoXsurOZG1ZlYTEZ/Pf+z+Cot6Hakhlg\n/AFuOSeLrIQovvvsYdp6+ilr6uaeP+8iOdbC5+68WbV8aDgADYfg8NOqHfOZuF2w/wnuXhlDsaWN\n5Kdvh6YjsPtByFip7ni97Chvpd/t4cJ5Nh5Uu1XhJD6LiN56IkyGgBr/BruDtNHi/V3eOOpN94+6\nFjwuNTrPeyvs0/rXtIduwMejO6pIczcQ6elRH1LNhFijzFy9LJ1n99fynWuXEGme3PzdY/Vd2GIi\nSIufGRPSIs1Gfn7HSj720E42/fhNBtwe4qPM/PXeDarbZtoy5fn7vP9L/g0WX6W8+vgsuPKH8PSn\nofJd4hds5umIPQz0OxmIy8I80A23/1mFOb1sPdlCpNkw73pHaeMfTuKzEO2nSQvwOMdRNf4DfdB6\nSqk8llx/9osWXKa2B56Ei78BDPX1r27v5VyCf0vsGHDzlx0V3JPVBi1o4z8J7liXw7P763j5cAM3\nrc6a1GuP1ndSkhEfdqXPcDYUJvGPz5/HEzuriI8yc/d5+UM5rDv/AlXvK4ny3++G3Q/B2z8C6QZT\nlBpkM+D9PJW9RqQ1l7uc3+G8pHi+edVisBUOXsfl9vD8wXouWJgy6S/N2Y4O+4QTaxZ01pIWFxnQ\n5m4NdsfZyd6aXeAZgLxNo7/IVqgSgXsfAY+SnWYmRGEQUBMirf+z+2pp6e7nxtRGlZBLLQnJdecC\nGwuSyLVFTzr043J7ONHYRckMHJKzLMvKD25ezjeuKh75fo6IgQWXw9KbVfvq3hbVA+jib4OrD+Iy\n4N63YdNXoPASjJ95g3PP3cTvT8ZwROaPuMa20hZaup3cek52CP+ymcG0PH8hhA14EsgHKoA7pJRn\nBeCEEG7gkPfXKinlDdO57pwhPgscdnKzJfsaAjPQxe2RNHePMr6xcjsgIGfD2C9e9RF4+lPqiyJ3\nI2ajgQxr1OCQj2Di8Uj++O5pSjLiyew7oaSIprk/UCNQGAyCO9Zm89NXT1LZ2kNekn+yzfKWHvpd\nHpZkzNLK1pt/B+4BiLapoS/WLNWi2hwFm783eNgXLkrk6T01fOeZwzz9+fMGO8T+aXsFSTER83I8\n6HQ9/28Cb0gpFwJveH8fjT4p5Srvjzb8PryKnwURdho7AzPOsaXbidsjz4751+xSnnTUOEUsC69Q\nHvcwJUWuLTokxv+dk82UNXXzmQvyEXUHVFGPZlLctiYHg2D8Gb9nsL9KaeB9/fRnHZY4ZfgBLLGq\nBbQ56qzDrNFmvntdCfurO/jZqycAePVIA1tPNnPvhYVEmOZfEGS6f/GNgLd1IA8DN03zfPMLb6FX\nnrmN3n43XU7XtE/pK/AaEfOXUs3CzVw9/osj41UvmGPPqdcQOuP/h23lpMdHcl2OE5z2ideqOYt0\nayQXLUrhqT01fstz91S2kxBtDlsr51Byw8pM7lqfy2/ePsWN97/HFx/fx7KseO7elB/upYWF6Rr/\nNKDrplUAABcPSURBVCllvfdxA5A2xnGRQojdQogdQogxvyCEEPd6j9vd3Nw8zaXNAryef6Z3nGMg\nevz4cgcjjL+9RsVFM/3wpouvg45KaDwMQG5SNC3d/fQE4ItpLI7U2dl+qpW7N+VjbtivdvqzVs1Z\nfGh9Lg2dDt443jTxwcDuyjbW5CbOi66pQgj++6ZlfOOqYqSUXL8yk0fu2YDFNL8SvT4mNP5CiNeF\nEIdH+blx+HFSxSzGilvkSSnXAh8GfimEKBrtICnlA1LKtVLKtSkp80BzG5cBCJI93oleASj0ahit\nwKveZ1D98KYXXqG2p94EIM/bVC2Y3v8ft50mJsLIXetz1VqNFkgZv3xfMzqXFaeSaY3kkfcrJjy2\nvaefU809nJM3f5qZGQ2Cz19cxJYvns/P7liJbR4Mah+LCY2/lPJyKeWyUX7+CTQKITIAvNtR3Q0p\nZa13Ww68Deh7elAJzdhUEgbUP1sg5J4NnQ7MRkHS8Dd13X4QxrP6uYxKfAakFKuB1qiwDwTP+DfY\nHTx3oI471+VijTKrtepk75QxGQ18ZGMe75W1UtZ0drfW4bx3SjkdGwvnl75do5hu2GcL8Anv408A\n/zzzACFEohDC4n2cDGwCJmi0PY+IzyK6TxVfBULu2Wh3kBoXOfI2vn4/pC4ZNRE2KoUXQ+X74HKS\nZ1OqEb8GY0yBv+6qwi0ld5+Xr6qL6w/oeP80uXNdDhFGA395f/xpVm+faMYaZZ5XbYw1Q0zX+P8Y\n2CyEKAUu9/6OEGKtEOKP3mOWALuFEAeAt4AfSym18fcRn4mxu4H4SFPAYv4jKjXbK6Ds9ckVTBVc\npPTS1TuxRpuJjzRR2TbKEPBp4nJ7eHJXNRcsTFE9+9vKwdmp4/3TJDnWwnUrMvj7nhrazmyN7MXj\nkbx9opkLF6UMyh4184tpGX8pZauU8jIp5UJveKjNu3+3lPLT3sfbpZTLpZQrvdsHA7HwOYM1WxV6\nxQem0KvhzPGNr3xHbRML/D9J/vkgDHB6KwB5STFUBWGi1zsnm6m3O/jweu+krsnkJjTj8oVLiugb\ncPOHbaN3v9xV0UZLt5PL5qG+XaOYf+LWmUZ8Jjg7yY9z0zjNnv5SSq/nP8z4u71DPoY1spqQyHhI\nX64GW6MUP1Wtgff8H/+gipQ4C5ct8YrE6vZ5k73FAb/WfGNBahzXr8jk4e0Vo3r/T+2pIdZi4oql\nYwn0NHMdbfzDja/QK7Jr2gnfLqeL3n73SJlnywlVBm+ZpI4791yo2Q3uAXJt0dS09+Eea1D4FGjs\ndPDWiSbuWJuN2eh9G9btV186w5puaabOly9bgGPAzc9fOzFif0dvPy8cqufa5Rnzqn+9ZiTa+Icb\nq+opslScpqnLiWcaBrbxTJnnQJ+aVToV2WTuRhjohYaD5NmicXkkdR2BC/08d6AOj4RbfD1VBpO9\nOt4fKBakxvHJTQU8uqOKbaVDdTP3v1VG34Cbe86fRChQM+fQxj/cZK2BmBSW9OzE7ZG09Ew99HNW\ngVdLKSAhZQqjEHM2qm3VjqDIPf+5v47lWdah6VFtp6C/S8f7A8xXNy9icVocX3hsLy8frufxD6p4\n8N3T3Lk2h8Xps7SfjyYgaOMfboxmSFpIok/rP41Cr7MKvJq9t/tTiaHHZ0BCLtTsVkocAmf8TzV3\nc6jWzo2rMod2+qaI6Z4+ASXGYuKhT64jLT6Szz26l28/c4i1+Ta+e53umDrf0QG/mYA1m5i27YCK\nhS9nak22zprd23JCFXfZRi2o9mNdudDVQIY1CrNRUBkgrf8/99UihOq1Mojd24zMO0hGEziyEqJ4\n4cvns+1kC2aTgfMXJGt5p0Yb/xmBNZuI3gYMeKYl92zodJAQbR4aStF8XPXpn2q1bEwSNB3DaBBk\nJ0ZTFQCtv5SSLQfqOK8oidThiemeZjBFql7tmoBjMRm5vEQrezRD6LDPTMCajfC4SBMd0yr0arA7\nRyp9mk9AyuKprysmRRllID8pmtMt0/f8S5u6qWjt5eplGSOf6G2F6GSYQdOkNJq5jDb+MwGrKnIq\nie6cluffOFzj7+pXFbPTMf7xWWo4dl87RSmxlDd3T0uNBPDa0UYANp/phXbWQawuONJoQoU2/jMB\nr9xzUZR9WoVe9fZhs3vbytVA9ukUTPmUN3X7KEqNxenyUDtNueerRxtZmW0dWYjm8ajq3owV0zq3\nRqPxH238ZwJe419obp9yodeA20Nrj3NogleLV+mTPAWZpw+f8a/dw4JUJcksa+6e8ukaOx0cqO44\n2+tvLQWHHbLWTvncGo1mcmjjPxOIjAeLlWxj65SNf1OXEymHafybTwBiesY/KgGSFkLtvkE9/qmm\nqRv/14/5Qj7pI5+o3qm2480X1mg0AUUb/5mCNZs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "RMSE: 0.0503933\n" ] } ], "source": [ "sim = nengo.Simulator(model)\n", "sim.run(T)\n", "sig = sim.data[stim_p][:,0]\n", "\n", "fspikes1 = np.convolve(sim.data[spikes_p][:,0], h, mode='same')\n", "fspikes2 = np.convolve(sim.data[spikes_p][:,1], h, mode='same')\n", "\n", "A = np.array([fspikes1, fspikes2]).T\n", "d = sim.data[connection].weights.T #not needed\n", "\n", "xhat = np.dot(A, d)[:,0]\n", "\n", "t = sim.trange()\n", "figure()\n", "plot(t, sig)\n", "plot(t, xhat)\n", "show()\n", "print('RMSE: %g' % np.average((sig-xhat)**2))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- It's a few times worse on a different signal\n", "- Not bad, but could use some improvement" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Improving the optimal decoder\n", "\n", "- We're only training on a pretty small set of data\n", " - So let's increase $T$\n", " - This helps, but can get computationally expensive to generate more and more data\n", "- There's also a bit of a shortcut\n", " - We've already created a pretty long signal ($T=1.0$ seconds)\n", " - We know the filter should probably decay towards zero\n", " - A spike shouldn't affect values far away from when it happens\n", " - So let's take our one existing signal and chop it up into lots of little signals\n", " " ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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2hsGq8GNHDXyL73Lb1ZfRr7t7Fbn2I3hwUmvdLsu/2YPRfYu49Y39/PW3bvjt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\nXF3lUTG0aX/QisGrHX7i25l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ORK5CYII=\n", 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sig2 = np.zeros_like(sig)\n", "r2 = np.zeros_like(r)\n", "\n", "sig2[400:600] = sig[100:300]\n", "r2[400:600] = r[100:300]\n", "\n", "figure()\n", "plot(t, sig)\n", "plot(t, r)\n", "vlines(0.1, -10, 10, linewidth=3)\n", "vlines(0.3, -10, 10, linewidth=3)\n", "\n", "figure()\n", "plot(t, sig2)\n", "plot(t, r2);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Add up a whole bunch of these with different slices\n", "- But, this introduces some weird edge effects at the beginning and ending of the window\n", "- So we can do some sort of smoothing of the data (as described in Appendix B.3)\n", " - We use a Gaussian because its Fourier transform is local in frequency (unlike a square)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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2hsGq8GNHDXyL73Lb1ZfRr7t7Fbn2I3hwUmvdLsu/2YPRfYu49Y39/PW3bvjt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\nXF3lUTG0aX/QisGrHX7i25l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ORK5CYII=\n", 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sigma = 0.06 #This should be ~3x longer than the neuron memory\n", "window = np.exp(-(t-0.5)**2/(sigma**2))\n", "\n", "sig2w = np.roll(sig, 300)*window\n", "r2w = np.roll(r, 300)*window\n", "\n", "figure()\n", "plot(t, sig)\n", "plot(t, r)\n", "vlines(0.1, -10, 10, linewidth=3)\n", "vlines(0.3, -10, 10, linewidth=3)\n", "\n", "figure()\n", "plot(t, sig2w)\n", "plot(t, r2w)\n", "show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- The last graph can be thought of as one trial, which we perform at every $\\Delta t$ and then average over\n", "- So we're going to take our original data ($x(t)$ and $r(t)$) and multiply it by another function (the Gaussian) in the time domain\n", "- Consequently, in the frequency domain, this multiplication becomes a...\n", "\n", "$$H(\\omega)= {{(X(\\omega)R^*(\\omega)) * W(\\omega)} \\over {|R(\\omega)|^2*W(\\omega)}} $$\n", "\n", "- So we're windowing and averaging in time which becomes convolution in frequency (it's kind of unusual to see convolution in frequency), which gives an efficient method for estimation." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "# original code ignoring DC\n", "H = (X*R.conjugate()) / (R*R.conjugate())\n", "\n", "# new code\n", "sigma_t = 0.025\n", "W2 = np.exp(-omega**2*sigma_t**2)\n", "H = (np.convolve(X*R.conjugate(),W2, 'same')) / (np.convolve(R*R.conjugate(),W2, 'same'))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "How well does this work?" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] } ], "source": [ "in_stim.output = WhiteSignal(T, high=2, rms=0.5)\n", "\n", "sim = nengo.Simulator(model)\n", "sim.run(T)\n", "sig1 = sim.data[stim_p][:,0]\n", "\n", "r = sim.data[dec_p][:,0] #properly scaled r\n", "\n", "X = np.fft.fftshift(np.fft.fft(sig1))\n", "R = np.fft.fftshift(np.fft.fft(r))\n", "\n", "sigma_t = 0.06\n", "W2 = np.exp(-omega**2*sigma_t**2)\n", "Rmag = R*R.conjugate()\n", "Rmag[(Rmag.shape[0]-1)//2 + 1] = .1 #remove zero DC term\n", "H = (np.convolve(X*R.conjugate(),W2, 'same')) / (np.convolve(Rmag,W2, 'same'))\n", "h = np.fft.fftshift(np.fft.ifft(np.fft.ifftshift(H))).real" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- What does this new filter look like?\n", "- How does it compare without windowing?" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/plain": [ "(-0.2, 0.2)" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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frF9pZvkxOJJBd1OpJeExCcvQXLqbvgPcqeIlp48ASwG3g+2IFxHFMYmUz26aGJNwSFiG\n5jJwvRHYKOl84DcptkI2zfxbZoe/kbFxxmNyjCAtpZaEu5ssS9WsJ6Hy1eEi4nHg8ZmOMTuSDI0W\nG8xph8TkwLVDwrJT1dxNkj4xdfEhSS2S3irpVuAD9SnPLHulMYG0xyRamxqQYMgtCctQNd1N64A/\nAW6XdDrwCrCIYsDcA3w5Ih6tX4lm2Sp19yxqSfcUWEm0NTV6TMIyVU1InAJ8IyK+nkzk1w4MRsSr\n9S3NLB8GM2pJQHHw2iFhWaomJL4PnCJpG8WxiCeAxyU9ERF76lqdWQ6U/pFOe0wCisFUGhMxy0I1\ns8CeB3QAH6V4bcTpwOcoBsWuuTyZpHWStkrqlnRthWP+IFnQaLOk787l8c3qYSjDkGhrbnBLwjJV\n1SmwETEMPCypLyI+UdovaUW1T5QseXoTcCmwI3m8jRGxpeyYNRQXN3pzRLwi6bhqH9+sXrIauIZi\nMHng2rI015G4g05zjYhX5vC7FwLdEbE9IkaAO4D1U475MHBT6XHdnWV5MDhS7O5J+2I6KAaTWxKW\npWrWuL5J0lWSLgDms8DvKuCFsts7kn3lzgTOlPQzSQ9KWlehpqsldUnq6unpmUdJZrPzwLUtZNV0\nNz1G8Qrr9wPLJG0BNlNcX2JLRNxZ43rWABdRnEDwfknnTT2TKiI2ABsAOjs7fRGf1VWWA9dtzY3s\n7RtJ/XnNSmYNieQf5AmSVgPnAecD7waqDYmdwEllt1cn+8rtAB5KlkN9Ljmjag3FdSvMMlEaE2hL\neapwKJ3d5JaEZaeaaTlOnmb35uSn/P5XI2Km9SUeBtZIOo1iOFwBvG/KMT8ErgT+m6R2it1P22er\n0ayeMj+7yQPXlqFqupturbC/1M2jZPsW4LZKDxIRhWS507uBRuDmiNgs6XqgK5lA8G7g7UmX1hjw\npxHxclWvxKxOBkfHaG4UzY3ZtCQ8JmFZqqa76eJaPVlEbGLKzLERcV3ZdgCfSn7McmFwdCyTVgRA\nmweuLWPpfzUyO8xksSpdyaLmRkYK44yP+/wMy4ZDwmwWgyPZtSQWebpwy5hDwmwWQ6Pj2bUkWrzw\nkGXLIWE2i8HRMdoyuNoaoK3JS5hathwSZrMYHB1jUQbXSAAT4eRrJSwrDgmzWQxleHbTxJiEpwu3\njDgkzGYxOJLt2U3g7ibLjkPCbBZDhQxDIlky1QPXlhWHhNksBkfGMxu4bvXAtWXMIWE2i0wvpvPA\ntWXMIWE2g4hIpuXI5qMyOXDtkLBsOCTMZjA6FoyNR/YD1x6TsIw4JMxmUJoOI7NTYEtXXPsUWMuI\nQ8JsBqUFh7JY3xqgtSk5u8ndTZYRh4TZDLJc3xpAEm3NDQw7JCwjDgmzGWS5vnWJFx6yLDkkzGZQ\nGjDOqiVRem4PXFtWHBJmM8hDS8Kr01mWHBJmMxhOzirKauAaitOF+zoJy4pDwmwGWQ9cQzGgPAus\nZSXVkJC0TtJWSd2Srp3huN+XFJI606zPbKrSWEBWV1yDB64tW6n95UtqBG4C3gmsBa6UtHaa45YB\nnwQeSqs2s0ry0JJo88C1ZSjNr0cXAt0RsT0iRoA7gPXTHPcXwA3AUIq1mU2rNBaQ1SywUOpuckhY\nNtIMiVXAC2W3dyT7Jkh6A3BSRPxDinWZVTSUg5bEouYGdzdZZnIzcC2pAfgvwKerOPZqSV2Sunp6\neupfnC1Yg6NjNDaI5sbsPiptzW5JWHbS/MvfCZxUdnt1sq9kGfAbwH2SfgW8Cdg43eB1RGyIiM6I\n6Ozo6KhjybbQDY6MZ9qKAA9cW7bSDImHgTWSTpPUAlwBbCzdGRH7I6I9Ik6NiFOBB4HLI6IrxRrN\nDlJcSyLbkCi2JMYZH49M67CFKbWQiIgCcA1wN/AUcFdEbJZ0vaTL06rDbC6GRscm1pnOSulCvuGC\nr5Ww9DWl+WQRsQnYNGXfdRWOvSiNmsxmkuXSpSUTCw+NjmV65bctTLkZuDbLo3x0NxU/ph68tiw4\nJMxmMDiSh5CYbEmYpc0hYTaDXHU3+apry4BDwmwGg3kIiWQcwt1NlgWHhNkMimMSGZ/d5O4my5BD\nwmwG/cNjLGlN9STA11jc0pTUUsi0DluYHBJmFUQEvUOjLGtrzrSOZW3FkDgw5JCw9DkkzCoYLowz\nOhYT/0hnZXkSUr0OCcuAQ8KsggNDowAszzgklibP35vUY5Ymh4RZBaVv7ll3NzU2iCUtjW5JWCYc\nEmYVTIZEti2JYg3NbklYJhwSZhWU/lHOuiVRrKHJLQnLhEPCrII8tSSWOiQsIw4JswomWxLZh4S7\nmywrDgmzCvIycF2swS0Jy4ZDwqyC0j/KSzO+4hqKp+H2+opry4BDwqyC3qECS1oaaWxQ1qW4u8ky\n45AwqyAPU3KULGttYmh0nNExL2Fq6XJImFXQO1TIxaA1TA6ee1zC0uaQMKugd3g0RyFRmr/JXU6W\nLoeEWQXFlkROupvckrCMpBoSktZJ2iqpW9K109z/KUlbJD0u6R8lnZJmfWbl8tXdVAyrA25JWMpS\nCwlJjcBNwDuBtcCVktZOOexRoDMizge+D3wprfrMpsrVwLVbEpaRNFsSFwLdEbE9IkaAO4D15QdE\nxE8jYiC5+SCwOsX6zA5yYKiQ+TThJQ4Jy0qaIbEKeKHs9o5kXyVXAT+e7g5JV0vqktTV09NTwxLN\nioYLY4wUxnPX3eSBa0tbLgeuJf0h0AncON39EbEhIjojorOjoyPd4mxByNOUHOCWhGUnza9JO4GT\nym6vTvYdRNLbgM8Db4mI4ZRqMztInmaABWhubKCtucEtCUtdmi2Jh4E1kk6T1AJcAWwsP0DSBcDf\nApdHxJ4UazM7SJ7WkigpTs3hloSlK7WQiIgCcA1wN/AUcFdEbJZ0vaTLk8NuBJYC35P0S0kbKzyc\nWV315awlAclMsJ7kz1KW6icgIjYBm6bsu65s+21p1mNWyYEczQBb4paEZSGXA9dmWSt1Ny3PUXfT\n8rYmj0lY6hwSZtPI28A1eOEhy4ZDwmwaEwsO5Sgklra6JWHpc0iYTaN3aJRFzY00N+bnI+IxCctC\nfj4BZjmSp8n9Spa1NTEwMkbBCw9ZihwSZtPI01oSJaVrNvp8GqylyCFhNo08rSVR4qk5LAsOCbNp\nHMhhd1NpRlqvKWFpckiYTaN3aDRX10hA+UywbklYehwSZtPI68A1OCQsXQ4JsykiIlmVLm8h4TUl\nLH0OCbMp9vQOMzQ6zolHL8q6lIMcv7yNBsGvXh6Y/WCzGnFImE2x+cX9AJx74lEZV3KwRS2NnN6x\nlC1JfWZpcEiYTbF55wEAzjlhWcaVvNa5Jy5n84sHsi7DFhCHhNkUW146wCnHLs7ddRIAa09Yzkv7\nh9jXP5J1KbZAOCTMptj84gHOPXF51mVMq9QFtsWtCUuJQ8KszIGhUZ7fN5C78YiSUnht9riEpcQh\nYVam9A19bU5bEiuWtHDiUW0el7DUOCTMypRCIq/dTQBrTzyKLS85JCwdDgmzMptfPEDHslaOW9aW\ndSkVnXvicrb39DE4MpZ1KbYApBoSktZJ2iqpW9K109zfKunO5P6HJJ2aZn1mm1/cz9oT8tuKgGJX\n2HjAU7vcmrD6Sy0kJDUCNwHvBNYCV0paO+Wwq4BXIuJ1wN8AN6RVn9mLrw7Svacv111NMNkVdv+2\nnowrsYUgzZbEhUB3RGyPiBHgDmD9lGPWA7cm298HLpGkFGu0BeoXz7/C5V/7GYuaG3n3+SdmXc6M\nVh29iN87s4Mv/+QZvvS/n2Z8PLIuyY5gac5gtgp4oez2DuCNlY6JiIKk/cCxwN5KD7ptdy+X/PV9\nta30COJ/PmY2Nh68OjDK/sFRTj5mMbd/+I2sWZm/K63LSeJb7+/kCxuf5Ov3Pcu3/99zHLukhbaW\nxpl/r4rHnc/v25EpX9NcVknS1cDVAMtPPJ2zc96HnDV/uCtrkFixuJnjlrfxvgtPZsWSlqxLqkpL\nUwN/+Z7z+J0z2nli535e7hthuFB5IHvWLwuzHBD+unHE+UmVxykinf/5kn4b+POIeEdy+7MAEfFX\nZcfcnRzzgKQmYBfQETMU2dnZGV1dXfUt3szsCCPpkYjonO24NMckHgbWSDpNUgtwBbBxyjEbgQ8k\n2+8F/mmmgDAzs/pKrbspGWO4BrgbaARujojNkq4HuiJiI/Bt4DuSuoF9FIPEzMwykuqYRERsAjZN\n2Xdd2fYQ8G/TrMnMzCrzFddmZlaRQ8LMzCpySJiZWUUOCTMzq8ghYWZmFaV2MV29SOoBfp11HUA7\nM0wfssD4vZjk92KS34tJeXgvTomIjtkOOuxDIi8kdVVz9eJC4Pdikt+LSX4vJh1O74W7m8zMrCKH\nhJmZVeSQqJ0NWReQI34vJvm9mOT3YtJh8154TMLMzCpyS8LMzCpySBwiSZ+WFJLak9uS9FVJ3ZIe\nl/SGsmM/IOmZ5OcDlR/18CLpRklPJ6/3f0g6uuy+zybvxVZJ7yjbvy7Z1y3p2mwqr7+F8jpLJJ0k\n6aeStkjaLOmTyf5jJN2b/O3fK2lFsr/i5+VIIalR0qOSfpTcPk3SQ8lrvjNZMgFJrcnt7uT+U7Os\n+zUiwj9z/AFOojjl+a+B9mTfZcCPKS4E9ybgoWT/McD25L8rku0VWb+GGr0Pbweaku0bgBuS7bXA\nY0ArcBrwLMXp4RuT7dOBluSYtVm/jjq8LwvidU55zScAb0i2lwHbkr+DLwHXJvuvLfsbmfbzciT9\nAJ8Cvgv8KLl9F3BFsv1N4KPJ9seAbybbVwB3Zl17+Y9bEofmb4D/yMGLPq4HbouiB4GjJZ0AvAO4\nNyL2RcQrwL3AutQ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8cqaNiiMhKsztUHwiKEg4Jz2RtYWWoIw7XEtQAKq6HFjeruw+r+164KudnJvWSbUd3nyi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\noIwxxgSk/w/5/BgeqlwUwAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure()\n", "plot(omega, np.abs(H))\n", "xlabel('$\\omega$')\n", "ylabel('$|H(\\omega)|$')\n", "xlim(-500, 500)\n", "\n", "figure()\n", "plot(t-T/2, h)\n", "xlabel('t')\n", "ylabel('h(t)')\n", "\n", "figure()\n", "plot(t-T/2, h)\n", "xlabel('t')\n", "ylabel('h(t)')\n", "xlim(-0.2, 0.2)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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+1TcwRXEglQCU85VkgqUeEuazJaeK1Ch/QoZ56h2V0105LgK7hI1ZF1wFFG2Hhmr9AlMU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\nrZf2vArDIlS3ewVGTIQ7VkNrM7w0H3a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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "spikes1 = sim.data[spikes_p][:,0]\n", "fspikes1_1 = np.convolve(sim.data[spikes_p][:,0], h, mode='same')\n", "fspikes2_1 = np.convolve(sim.data[spikes_p][:,1], h, mode='same')\n", "spikes_1 = (sim.data[spikes_p][:,0]-sim.data[spikes_p][:,1])*sim.dt\n", "\n", "sim = nengo.Simulator(model)\n", "sim.run(T)\n", "sig2 = sim.data[stim_p][:,0]\n", "\n", "fspikes1_2 = np.convolve(sim.data[spikes_p][:,0], h, mode='same')\n", "fspikes2_2 = np.convolve(sim.data[spikes_p][:,1], h, mode='same')\n", "spikes_2 = (sim.data[spikes_p][:,0]-sim.data[spikes_p][:,1])*sim.dt\n", "\n", "A1 = numpy.array([fspikes1_1, fspikes2_1]).T\n", "A2 = numpy.array([fspikes1_2, fspikes2_2]).T\n", "\n", "d = sim.data[connection].weights.T\n", "\n", "x1hat = np.dot(A1, d)[:,0]\n", "x2hat = np.dot(A2, d)[:,0]\n", "\n", "t = sim.trange()\n", "figure()\n", "plot(t, sig1)\n", "plot(t, x1hat)\n", "plot(t, spikes_1, 'k.')\n", "ylim(-1.5,1.5)\n", "show()\n", "print('RMSE: %g' % np.average((sig1-x1hat)**2))\n", "\n", "figure()\n", "plot(t, sig2)\n", "plot(t, x2hat)\n", "plot(t, spikes_2, 'k.')\n", "ylim(-1.5,1.5)\n", "print('RMSE: %g' % np.average((sig2-x2hat)**2))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- It's a bit better on the original signal\n", "- And is 'less worse' when tested on a different signal\n", "- What about higher frequency inputs? Or lower frequency?" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n", "RMSE: 0.0719121\n" ] }, { "data": { "image/png": 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8Fyj654V4+osAnwKI7yiGuMyQnOSpcSoZzGdWomCb6q3QXhX0WDVtSiGPdbc9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\nzRVAkvo+zjlT1X8qDJFAJ6vb+cfxGu7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "in_stim.output = WhiteSignal(T, high=10, rms=0.5)\n", "sim = nengo.Simulator(model)\n", "sim.run(T)\n", "sig3 = sim.data[stim_p][:,0]\n", "\n", "fspikes1_3 = np.convolve(sim.data[spikes_p][:,0], h, mode='same')\n", "fspikes2_3 = np.convolve(sim.data[spikes_p][:,1], h, mode='same')\n", "spikes_3 = (sim.data[spikes_p][:,0]-sim.data[spikes_p][:,1])*sim.dt\n", "\n", "A3 = np.array([fspikes1_3, fspikes2_3]).T\n", "\n", "d = sim.data[connection].weights.T\n", "\n", "x3hat = np.dot(A3, d)[:,0]\n", "\n", "t = sim.trange()\n", "figure()\n", "plot(t, sig3)\n", "plot(t, x3hat)\n", "plot(t, spikes_3, 'k.')\n", "ylim(-1.5,1.5)\n", "print('RMSE: %g' % np.average((sig3-x3hat)**2))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- The decoder works better if it is made for the right range of frequencies\n", "- What does this tell us about rate vs timing codes?\n", " - Doesn't make much sense without thinking about the signal properties\n", " - These methods can account for both kinds of codes and smoothly vary between" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Optimal filters reconsidered\n", "\n", "- So we have now found the optimal filter to apply to the spike data to decode out information\n", "- Note a limitation: we've only done this for the case of 2 neurons!\n", " - But we could use the same filter for many more neurons\n", "- Recall what this windowed filter looks like" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/plain": [ "(-0.2, 0.2)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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8cqaNiiMhKsztUHwiKEg4Jz2RtYWWoIw7XEtQAKq6HFjeruw+r+164KudnJvWSbUd3nyi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\neH4T339xC2lJUSy/ex63X5B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ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure()\n", "plot(t-T/2, h)\n", "xlabel('t')\n", "ylabel('h(t)')\n", "xlim(-0.2, 0.2)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- What is this saying?\n", "- Every time a spike occurs, when we interpret the data we should replace the spike with this shape\n", "- What does this mean?\n" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figure(figsize=(8,4))\n", "vlines(dt*np.where(spikes1>0)[0], -1, 1)\n", "plot(t, fspikes1_1*d[0], label='filtered spikes')\n", "ylabel('$x$')\n", "ylim(-2,2)\n", "xlim(0.2, 0.4)\n", "xlabel('time (s)')\n", "legend();" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- If we're analyzing the data after the fact, this is fine\n", "- But what if we're just sitting here observing the neural activity and wanting to know what's being represented right now?\n", " - Notice that the blue line (the filtered value we're using for decoding) starts going up *before* the spike happens\n", " - The filtered value is using information *from the future*.\n", "- This means that when we look at $\\hat{x}$ this way, we're getting a better estimate of $x$ than it is possible for other neurons to get\n", " - (assuming neurons aren't psychic)\n", "- What could we do instead?\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Biologically plausible filter\n", "\n", "- We're looking for something that takes a spike and turns it into some smooth signal\n", "- Instead of coming up with the optimal filter, is there anything from neuroscience we could use instead?\n", "- What actually happens when a spike occurs?\n", " - What is the input to the next neuron that occurs when a spike happens?\n", "\n", "\n", "\n", "- A spike causes a vesicle to release neurotransmitter\n", "- The amount of neurotransmitter causes current to flow into the next neuron\n", "- The neurotransmitter is slowly reabsorbed\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- What is the current that goes into the next neuron thanks to a single spike?\n", "\n", "\n", "\n", "(image stolen from [here](http://www.zoo.utoronto.ca/berry/zoo252/l9/lect9.htm))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- So other neurons don't get spikes as inputs\n", " - They get these post-synaptic currents\n", " \n", "$$\n", "h(t) = \\begin{cases}\n", " e^{-t/\\tau} &\\mbox{if } t > 0 \\\\ \n", " 0 &\\mbox{otherwise} \n", " \\end{cases}\n", "$$\n", "\n", "- This is the standard simple model\n", " - $\\tau$ is different for different neurotransmitters and different neurotransmitter receptors\n", " - GABA-A-R: $\\tau=10.41 \\pm 6.16$ ms\n", " - AMPA-type GluR: $\\tau=2.2 \\pm 0.2$ ms\n", " - NMDA-type GluR: $\\tau=146 \\pm 9.1$ ms\n", " \n", "- For more complex models, some people use \n", "\n", "$$\n", "h(t) = \\begin{cases}\n", " t^n e^{-t/\\tau} &\\mbox{if } t > 0 \\\\ \n", " 0 &\\mbox{otherwise} \n", " \\end{cases}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dt = 0.001\n", "tau = 0.05\n", "t_h = np.arange(1000)*dt-0.5\n", "h = np.exp(-t_h/tau)\n", "h[np.where(t_h<0)]=0\n", "h = h/norm(h,1)\n", "\n", "figure()\n", "plot(t_h, h)\n", "xlabel('t')\n", "ylabel('h(t)');" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "c:\\users\\terry\\py3\\lib\\site-packages\\matplotlib\\cbook.py:637: IgnoredKeywordWarning: \"color\" keyword argument will be ignored\n", " IgnoredKeywordWarning)\n" ] }, { "data": { "image/png": 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Ji1w87uKYXoivmHgFNgR1HSd0jCx2W2q3kOZM+5caG/GaNGxS4iYVLT1Jhd1lyP0iy1bV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\ncH1xz4ssKFlgqW3BoyUQlGSWcPQ/jvLBjR9Q+e1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HQOUm2P9J0BeE9hy3rlKrhqyRvV5eCEGByxGdZwCUEt/4M9UXTBxXxbq7PiLP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\nqL6I+zfcz/bS7ZyadCr3TLmH5NCOOzEOjQslNEiF3a7s8L0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ei2P2K/LNcWLcRBZPW9zh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KAAAg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\nP8/6Z0gV5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z4PHBc99UtycIh5tUDkcGkkgTZHlYUac/SJmdYuD8z49sGzt7wEAIQYXPM/kQ\nqhy5Mj64uYnlM4o5ddbIief69XNwCHh4i3avywW7mnspznMxK1mr8EkoLfBwxrwyLtvzNbj/xvEt\nvcPDtbxw3ufA3wr1z9jy2tMZLQY0k3LY6CRIxRlsFLEV+mtuZKB4AV9y3cuAv3f8yaV8vrKvfev/\noHXP+OeyQFPXADVFeXhdCQrpzLUV1cBZn1RCBCY86ZlUJRUZMASFP7utdF2BEGUFNrgPRoKqqLN4\nhhrfDDAwcY69otBDZ6IaCshJmuBY9wDbmnq4dnXdqO1VRV7OWVjJI1uPZX2stgZ2N/eyfEZx+rUt\nMVy+ohZ3dACO74Ct946+MxLTNlw6V/0eDNj22tMVLQY0k3K4XX1R5qabJhgWA25wuhm66Ksschyj\n4uhz8U+6F3xBDf155utpvWxSo4tjhco5nx3ZPkmawOdxkud2JI4MzD0H8svhhe9mzegkEpUqTWBH\nzUB4aOT/Z8O3lUXzsqsm3L3c5528gNAUA1k8+b64T4mxi5dVj7vvylW1NHQERiyyNVkhGpXsbelL\nu6VwLJcvr8GDIeif+/fRaYDh4mBvztp+pyJaDGgmpaHDj8floK7EYhivaTP0t47cHtOuV7L6GjbJ\n5aPvi8VXoYoJ9z0OR15PYeXGMroGEhcPjlqbWw0busjw1i9IPDRFCEFVkTdxZCC/FC75inJX3P3I\nxPvZSO9ASA0psiVNENM9kF8GN9wLtadMuHulz5O4tRCMz4DMqivjC/vaqC3OY3EcS+0LFlcZ++ip\nd9mkoTNAIBhhhc1iYE5FAW4RYYdnNfQ1w6s/HblzOE3g1mIgBi0GNJNyuMPPnFTaCu/7ANzz/pED\nfjhGkQPC4eDeUmOoT+uu+M+xzjD7OfKacjC0SCgSpblnYPJ85FhfgYu+BP/SpoTBJFQWTmBJHMua\nj0D1SnjqX4w2xsxim+EQjG79TIJynydxqyVkvcMiHInycn07Fy6pihuOnl1ewIIqHy/s066I2WR3\ncy+A7ZEBImGcRHkqsJjQkncq35KeJnVfbKeQ07Anz0H9ylRDiwHNpBxuT7GTINgPx96ETXeq27FX\n3waRGWv4pet6uPJ78Z/DY1zF7XoEvr8IOg9aWkJz9yBRyXgr4ld/CgdfGLk9Rqio35M7kVYVehO3\nFoI66Gz4tjLwsallMhH2WhEPTVo7EUtFoZfBUJRAMME46ixfkW0/2kPfYJjzl1ROuM85CyvYfLgz\nsYGUxlbUbFi6AAAgAElEQVR2N/fiELC4xp6ZJ8MYn6sh6eKFeZ9VLcOPfXHUfTgnSRNEQieVB4EW\nA5qERKOShk4/81LpJDC/YM9+Q7UIxn4JDRZUFfLv/VczuOaW+M/hcAIC2vZCoAMe+aylPHNjl9FW\nODZN8OJ34cGPgr999FotXAGbVE6WJjBZcCGsuBZe/D60Z7avvdOvrnRs8xlIUhhBzHyCRKmCLLdb\nvml4358xr3zCfdbOLcMfjGiL4iyyu7mPBVWF5LnTdMkci/F9dnu8PHrErSJ9e/8Cu/88QZogzufw\niS/B/5wDg732rm2KosWAJiHH+wYZDEWtzySQUn0hV71PheWe+FLcE67ZoXCofYI+XyHUFzZk3H/4\nJXjz7qSXMeIxMCZNEA4qcfF4nKsFi1QVeukKBAlFkkhjXPldNQnxkc+klPZIFnNiYZkvxW6CN++G\n+z6oDpLm7IgkqUjGhTDLaYItjd3MKMmjJoGd9to5Sii8eaQrK2tKl7a+IX750kH+sq15Yre9KY7Z\nSWA7xudqXk0pz+9tI7z+k1BzCjz2BfW9B/WZdrhG7T+KvhboboCnv2r/+qYgWgxoEmJ2Esy3Ghkw\nlXbVUrjwC7DrIdj+oNrmio0MqOc92JbA9CP2RDT3XHjqX5M2I2rsCuB0CGrHngQiQVUcuOMPsOcv\n42sGLFBZ5EXKSYbzmBTVwBXfUjUQb/7G8mslS2e6NQOHX4E9f4aXfjB6dkQSJOVCmOU0wdbG7kkn\n4s0uz6ey0MubDVNfDLT0DHLNT1/m3/+ym0/d8yZfecj+sd+ZpncwxNHuAZbPKJp8Z6sYn6sldZX0\nDITY1NQP7/yRKiY0vUtc3pGLjXgeIOZnc/NdcOCv9q9xipFTMSCE2CCE2CuEqBdCfCnO/f8ohNgl\nhNgmhHhWCDE35r6IEGKL8ZOdEu2TkAZzWqHVmoHYk+u5tykr3/qnR7YZmJGBg4lausyrSOGEq3+i\nctgPfyqpK+umrgHqSvNwOWM+6tEIyAisu1ldLfz5H9VBIva1LJBUWDyW1R+Esvlw4FnLr5UsXYEg\nXpeD/FTDr+b/3wv/CY1/syQGTCOmxJGB7KUJOvqHONIZmFQMCCFYO7eUzdMgMvCFB7fSMxDiT39/\nDrdesIB73zjCEzvsmeWRLepb1Xd+cXWaYmDfk/DEl0cfD4zP7+K6ctxOwbO7j8OsdXDOp6GnUe1j\nftcnMsCKBKH2VKhYpNKTQyd2+ihnYkAI4QRuB64EVgA3CCFWjNntLWCdlPJU4EHguzH3DUgpVxs/\nV2dl0Schhzr8eJwO6kotthXGigGnG979C3Dlj2wzKPC4qCvJ4+BEaYLY/Z0eqFiorqwPPAuv3zHp\nMtTo4jFCxlybuwCu/R/lT/6C8dGawGY3EeaVcFKRAVBXI3nFGT0RdvmVFXHKRi6RIJTOgcIaCLQr\n8ZQkw2mChDUD2UsTbG1S9QKTiQGANXPKaOgIJP9/mQNeqW/npf3tfO7yJZw+p4wvXLGUJTWF/NdT\n+6ZVuuCAIQYWxWn1tMTuR9Wx4NWYSadGQXB+Xh5nLajg2d1Gi/PF/wLVxmnGTAlOZIAVCUFeCVxz\nhxIQz38nvXVOcXIZGVgP1EspD0opg8B9wDWxO0gp/yqlNK2hXgdmZXmNJz0N7cqwx2m1rXDs1L/K\nxfD276krcc/oL/+CqsJJIgOe0c+17hZY9g5lRnTsrYTLaIznMRArVGacCpd/Q3U+xL6WBUYm9SVR\nRGiSYW/+Tn+I0nSKB800yrWG4GrelvRDCzwu8t3O5NIEWbBo3t7UixBwysySSfddWaf2MVvepiK/\nfvUwlYVePny2CpS6nQ7+/qJF7G/tn1atkfVt/XicDmana0NsiupnvwlH/mZsG6kBunRZNQfb/eoY\n486D990N5/8TFNUa+0zwXTRHdc85E2pWQkd9euuc4uRSDMwEGmNuNxnbJuIW4PGY23lCiE1CiNeF\nENdO9CAhxK3Gfpva2qbPF2WqcLgjxU6CeFP/1nwYPvnKSG+vwfxKHwfb/RNbwcaG80BdWV/9EzVB\n8IGPTmiNOxiK0NY3NL540Dx4mFGAMz8BSzaoYiK39QNTuU89j6WryQx783cFgpSnWjwII0WDCy+G\nd/wQ3vtrSw8v93kSvx/DkYHMi4E9Lb3MLS/A53VNuq+Zv56qYqC1d5Dn9rRy3dpZo+y1rzp1BmUF\nbv741tEcrs4aB1r7mVdZMDqFlwqRISieCaWz4cGbIdAZ0zHg4dLlNQAj0YHKxXDpV9VxxNhnwjSB\necxx55/wxkTTooBQCPEhYB0Q24w+V0q5DvgA8EMhxMJ4j5VS/lxKuU5Kua6qqioLqz1xkFIqMZDK\nTIKYL+NkLKjy0TcYnni4TWyawKSgHK67U4Xv/nhr3HbDpi41unjW2MhAOMabHNRB4bq74OanUhID\npfluHMJCzYD52hk8uHSlO744Ehp5v9d9FFZOqLfjUlnooT2ZmoEEMw7sYm9LH8tqk6tYryj0Uluc\nx65jU1MMPLGzhUhUct3a0ddNbqeDq06dwdO7WugfSuDvMIU40OZPP0UA6rOaX6a+w/5WeOCmmEif\nm9nlBSytKeKZ3cfjPz5RmiD22HOCGxPlUgwcBWbH3J5lbBuFEOIy4CvA1VLK4bijlPKo8e9B4Hng\n9Ewu9mTkeO8Qg6FoaoZDFqrzF1SpA8KEqYKxkQGTOWfBxf8P9j8J7fvGPWzYY2BcZCDO2jwFMGvt\npGuNh8MhDNc9q5GBDIoBf5rji80QaYpUFHoTpwlqTgFfNTz2eejPXMRuIBjhUIefpbXJF6mtqCtm\nV3Mv7PijKhybQieBp3YeZ0GVj0Vxiu6uWlXHYCjKy/unvqXyUDhCQ4efRVV2iAHDIXPmGnjnj+HQ\ni/Dn29R9RvTv0uXVbGrooicQ5/9you9irNlWDgZrZZtcioGNwGIhxHwhhAe4HhjVFSCEOB34GUoI\ntMZsLxNCeI3fK4FzgQn8bDWpYk4rTC0yECdNMAELzI6CiYoI40UGTMxioND4qWNNnRMYDlmIWiSL\nCotbrRnIzEkmEpV0D9hQM5CC54JJ+WTzCQrK4Yb71OyK+26A0EDKr5WI/a19SAnLrIiBGcXUt/YT\nfe121f75l3/KyNqs0jcY4vWDHVy+oibu/evmlVHkdfHCvta4908lDrcHiEpYaEdkIHaQ1uobVPeS\n6VRqbL90eQ2RqOT5eO+N0z1BmmBsZECLgYwgpQwDnwaeBHYD90spdwohviGEMLsDvgcUAg+MaSFc\nDmwSQmwF/gp8R0qpxYDNmG2FSdUMHH4ZfnQaHH1T3R7Oy09+QqorzcfjciSIDCQQAwlyz85Dz/Os\n9/NUDRwYfYcFoZIsk578xi0uc1caPQMhpITydMYXR0JpRgZUzUDCkcCz1sK7fwZNm+APH4OI/eHt\nPYab4DILxjYr6ooJRyV9XqPA7M3fZDR6kSybDncRjkouXBw/3el2Ojh3USXP722b8qOYzemQC22J\nDIRGf5cv/Zpq3QXwqGPX6tmlVPg8I3UDsUwYGQiOHL90miCzSCkfk1IukVIulFJ+y9j2VSnlI8bv\nl0kpa8a2EEopX5VSrpJSnmb8+6tc/h0nKofaA7idghklE7u2DdO2F7oOw/+9C1p2WEoTOB2C+RW+\niV0IzZNSPGGRwLzG1bGHheIY4u5rRtv/pmEwNBEVPm8KBYSZEQOdw+6D6UYGUn98pc9LMBKlb7L8\n9Ypr1MyGPX+Ghz5p+xTDPc195LkdzBk7myIBS2pUFMEfiIlWhBK0vmaJ1w924HE6WDO3bMJ9zl1c\nSXPPII2dmYm02IXpMWCPGBjzWXU44O9fgw/cD1XLAHWMuXhZNc/vbR3vFOr0QP/x8Z+92IiDjgxo\nTmYaOvzMLk+y2tdUzQ4X3H0NtGxXt5M8oSyo8k3sQpgwMjCxGOg3D+bRCPzmndBxYPRaLfjtT0ZF\nodWagQlCkzbQbcfEwjTFQFJeAyZnfRIu+VfYfv+IO5xN7G/tY1F1oaXW2LkVBbgcgoHBmBPqFLgq\nfO1gB6vnlCb08T9jnhIKGw93ZmtZKVHf2s/M0nzyPTbMJIj3WXXnw5IrRjoGgMuWV9M7GGbT4TGm\nUivfpY5Xf7x1dHRKpwk0GsWhdgtthWbo/cN/VMOFnviyum1BDBzpDMT3948t4hl3X/w0gZSSQMCo\nI7jpEaXy77rSctQiWcp9HnoGQsnNJzBfO9ORgXRrBtIQS0lZEsdyweehbo1yO7SRg21+y1efbqeD\neZU+hoZiRk3n+ETQOxhix9EezlpQkXC/JdVFFOW52NQw9cWALZ0EkPSI7fMXV+FxOpQbYSxn/p1K\nLex4EP5wy8gE01iRkUHxPlXQYmAqEBqE+29SefcpgpSSho6ABTFgfIGqV8BHH4cSo1EkSUe/BZWF\nhKOSI53jCwFHugniPNcEkYFOfxAZCRLFAbWr1JocLrjr7XDw+dGPtQHTkrgr2ehABsXA8PjiXKYJ\nkrEkHou30NYD7mAowrGegWHLayssqiokPIXEwOaGLqISzpo/8dRFUJ0t6+aWsXHs1e8UIhqVHGy3\nWwxM/ln1eV2ctbCCZ/fEqRs4/x/hbf+uZqj87j0w0KUMsXRkQJNVehrVh/DXV028T99x+Mla2HRX\nVpbU1jfEQCjCvMokc62xaYKKhXDLk3DZv0Hl0qQePj/RwKIC42rIH6eIawIxcKQzgJsw0hQS1cvg\n5ieVUdFL/2U8No0CuzFUWD35ZfBKwxxfXG4lMtB5EG4/C3Y+pG5bHE40FktpAhObD7iHO/xIOdK6\naoVF1YVEwjFryfFV4dbGboSAU5OwVF43r5z61v4pa6nc3KsmoZpDytImEkr6ouOy5dUcavcPFzCO\n4pzPwLt+Bg2vwc8vVttGzS+Ymu+nXWgxMBVI5kPWfUTZYf75Nvjz5zJSeR2LWcw310pkwOkdydEV\n18F5t41zG5yIhZWFxuvG+ZJe/P9g3vkqtzeWCdIERzoDeAiPjiaUzoZbnlL97QBe+0anWp5PkOHI\nQJ7bYS0f214PbbuVYcvTX4PwQFpiyXKaAGx/T0xhuSCVyEB1IW7CRM15Gjk+EWxv6mFRVSGFSbgo\nrpmj6ga2NWXe0CkVLHUpjWXr72HfU6O3WfDEuGSZ+u6PSxWYnHY9fPhP6ngLKuUJOk2gyRLJHGjM\nfeaeC5vuzOjEOxjxGEh6dHGaV5IlBW4qfJ74kQFfJXzkz0pcjGWCyEBjZwAPIRxj894F5fC5nfCx\nZ1UEwybMNEF7sic/pwei4aQmL1qlyx+0FhWAkfdvwUXwyg9BRkGkfnjwupwUeV05Lao0W1VTuQI1\nxUDIaTw2h2JASsnWph5OnTV5VABUayTAzinqothopAKtdHgM8+w34J73wl8+r9KrYCmlNausgGW1\nRTwTr8XQZP75qhthwcUw5xy1TUcGNJlgKBzh9r/Wc9kPXmD9t57hvx7fPvmDzA/i6g+ofwd7MrdA\n4HCHaiusK02irRCSLuJJRMKOgolIkCYodktEvIOEy6PGmdqImSZIPjKQual9XYGg9XoBcx0b/lPN\nfYeRuo8Usd5hYXNkoN3PjJI8CjzJRadiWVDlw0OIAWF8/nN4VdjcM0h7/xCnzpp80BJASb6buRUF\n7Dia2WNEqjR0BHA5kmxZHktkSE3S3PgL+MUlcHzXeJ+BSbhseQ2bG7qGu27iUrUUbnxIDSmCjIr3\nqYIWA1mmbzDE9T9/ne89uZfqIi/nLa5kx5Ek7EPNg5EnO1cqh9v9zC6zMEQkzYIzUEWEB+OlCRIx\nQZqgoSNAiRdb6wISYc4nsJQmgJEuDBvp9KcwlyB2yuTaj8CXj6p/02BSS+KxOD0jldw2cLDNn1Lx\nIBiTFx1R+qWRZsrhVaEZ7k9WDACcUlfCjmNTUwwc6Qwwsyw/tQFFkaBKF37wQeUN8LMLlAeEhWPP\npcurlRvhXgtGUlkcuZ0rtBjIIsFwlL/7v81sb+rhjg+u4Z6Pn8UP3rea7797+fA+Zj5tHOZJwxz/\nm2kx0BGwZkNsUZ3HY36Vj/b+ID0DFq7CEqQJij0y6cKidHE4BGUFnomHLY2l2Bg0c8/7oXmrrWvp\nCoRSjwyY76e3cFSPdipUWHZltC8yIKXkYFt/WkVqec4I3ZHci4HtR3twOQTLLbgorpxZTGPnQHwv\n/hxzpDOQWooARpwxF18On3pjpI6oIHGXRSynzSqlstAz8eCieCTwMzlR0GIgi/zkuf28eqCD7153\nKm9fNWN4e0XeyEH3H+/fSjQax0rU/BAORwYy9yVXbYV+5loZUBRJb7ANjBR6TehEGI84X9KhcITm\n3kGKXNLW9sHJsDSfYMW1aqhK+3742YXwyGeUT78NdPqD1q2IM+HKWOihw/K8BnsOth3+IL2DYRZU\npt6+5iVEZ8j8fOXupLq3pY8FVb6EZkNjOaVORRF2TsHoQFpiINYV0FcB7/mFEgXrbkn6KRwOwcVL\nq3lhX5s1XxCIOxDtREGLgSyx42gPdzx/gPesmcW718wafWfMAXBzQxePbjs2/gmymCZo7RsiEIxY\nC7FGgmlfhU86vTAeDiMfHHOwPto1gJRQ6IpkLU0AI378SeFwwNqb4DOblQPflnvh8S+mvYZwJErv\nYCqRAXN4k43tloZFc1xxGw8bCwhNQTl/sshAJKwmE/7tZxAcLUJdhOmN5j4ysLu5j6VJjmA2WWkU\nEe5qnlpFhD0DIboDIWsXGibRCMjIeMFatVRNHbXApctr6BsMs/FQkuZMdatVVPaXl8EDH4HW3ZZe\nbzqgxUAWkFLyjUd3UVbg5qvvWDF+h5gDzfIZxXzvyb0MhSPx9zHTBGH7c80mh9tTaP1Jc7ANqOpi\np0NYKyIUYtwVpWlcVOCMZjUyUOHzWiuYA8gvVd78c86yJTIwPKTIqhgI2z+8qaLQQ1RCd7JpHxsj\nA2bF+qSf4Z5GNYjo8S/Cf6+E5741/P/glGEC0iwgzI0Y6BsMcbR7wNLURVD1GpWFHvYd78vQylIj\nrU4CG6eNnr+4Eo/TkbirIJbZ6+G27XD+P8H+p+GOs+B374X9z5wwRYVaDGSBZ3a38sbhTm67bAkl\n8cK3MQeaf96wlKauAR7eciz+PllIExxOpQ/YhgJCj0sNlLFeRDi68MwUA3mOOFcRGcTy5MJYbJpi\naLoPWh5fnIGxzsNGTJbaLUNgw8S9pi41V2DSbhjz7z7706qN7MXvwg+Ww+8/jCMawk9uuwnMk/nS\nGmtiAFR75L7jFr9LGcb8bs5OSQzYl8ryeV2cvbCCZ/ccT37CY0E5XPqvShRc+CU4tkW5Ff50Hbx5\nd9pryjVaDGQYKSU/eHofCyp9XH/GBK1aMSeBCxeVs6y2iDtfPjT6Qzo8XMerQuMZvFJJ2FYYDqqW\nnt+9F976LQQ6R9Znw5d0fmUK7YXeItj4S7j3A7D9QZpa2vB5nLgJZzcyUGhxPkEsNl0Vp+Q+CCOv\n7bDehjcRI94LVtst0z/xNnUFqCn24nVNkmc3/+7ZZ8IN98CnN8GZn4CGVwDopnj0flnGHMG81GJk\nANT0xfrW/ik1zrihY2pEBgAuW1FDQ0fAumAqKIeLv6z8St79S9XV8MhnbRGxuUSLgQzz4v52djf3\n8omLFk7cShNz8BPREDefO589LX28drBjZJ/YMK7Tm1kxkKitcKALjm6GQy/Cw5+C7y+Gu69V7og2\n5JsXVKpRxknnmQE+9AdYdzMcexP+cAuf3/Z2fu39HqL7SJbTBMZ8gkT9yxNhU758ZHxxCgWEsQ6S\nNmBaEltvt0z/s93UNcCssiROOGOvNisXwxXfgn/cDTc+zPMlV6vtodyMBN7b0keh18WssnzLj11c\nU0T/UJhjPYOT75wljnQGKPd5KMpL4VhhdlTZVNdyxcoaHAL+Eq9GKxlcHjj1vXDe5wA57R0KtRjI\nMP/7/AFqi/O4dvXMiXeKPfhFgly9uo6SfDe/39gYs91Uxd6MW2MmbCs01/r278HH/6rCqz1N0NcM\nvqq0X3tBVSFD4SjHeiwcfGtWwpXfgc/tgo8+zsOOy5nHMfC3qorjLFHuM8PiqYgBeyIDKY8vtimy\nE0uF+X4k21FguxhI4gQ6UeGkywsLLqK8ooZBvGq08k/XKyvw7Q9Cb4onEIvsaeljaW0RIgWRtsQY\nBDSV6gaOdPrTaCu0t+OluiiPsxZU8Oi25vSiJxn0DMkmWgxkkO1NPbx2sINbzpuPx5XgrR4lBkLk\nuZ2887QZPLmzhb7BUMw+QnllZ9Aac9K2wmFzmjyYuQYu/zf4zCa4bQe847/Tfv0FiQYWTYbDwWDd\nmXwx8EF+t/4h+OwWuOLbaa8pWSxfCcdiV5rAnFhoOU2QfmvoWMoK3AiR/TRBJCo51p2sGEh8gplb\nWcj7ot9CXvp1KJ0D2x5QY25/sBy+vxTuuR5e/u+MiHMpJXuae1NKEYBKEwDsn1JiIE2PAbBVtL7z\ntDoOtfvTs24eFgM6MqCZgHs3HiHP7eD96yexdQ2PjgwAvGfNLAZDUR7b3jyy3emJqZ7PzAdv0rbC\nia6kSmer3H2ajIiB1AqfhifVVRdB+XzIs28Y0WSYaQLLHQWg3k8b3Pe6/EHy3U5LPemALQWgY3E5\nHZTmu60VEAI89w147Q7Y85hq4bJYrX28d5BwVCaZJkjcRTGvooBtwTraVn8SPvQg/PNhFRHb8J9q\njkPbbnjm66qYzGaO9w7ROxi23ElgUubzUFnonTJFhKFIlGPdg6m1FcJol0yb2LCyFpdDxG/nTpYT\nxJ3QvmqhFBBCbAB+BDiBX0opvzPmfi9wN7AW6ADeL6U8bNz3ZeAWIAJ8Vkr5ZBaXPikDwQiPbjnG\n21fWUvzC19UsAV+lCqUXVKrwdYFxOxjzZTU+UKtnl7Kg0sfDW47x/jPmjA7j2lR5Ho9J2wozYE4T\nS1Whl0Kvi4NWjIdiSGdSXboMTy60YsFrYlMdSKc/ZD1FABlJE4DqKEg6UjJ7PdSdDrseUcWpJud/\nXlVxJ4nZSZBWmsBgrvE5augIUF2Up6ZwzlyjfgAOvQS/eQeE7c/Lm101C1MYwWyypKZQRQae+xYc\nflmN8DZ/fNVQMhPmX5T0dNF0ONY9QCQqU+skgIwce8p8Hs5bXMlftjXzpQ3LUkrHDPuraDGQGkII\nJ3A7cDnQBGwUQjwipdwVs9stQJeUcpEQ4nrgP4H3CyFWANcDK4E64BkhxBIp5Zjm/Nzx5M4W+obC\nXL+qAB74Kbh96iokOsno4b1PQNlchNPDx+cc58GtbfQcdFPSfzwrs7UnbSvMQKguFiFEagOLDNKZ\nVJcupQUehEg1MmBPtKc7EEy+eNDfDn0t6rUHujJi0GTJkrhqKdz6vKrKDnRC12G4532qHsUCTV2q\nYj2lAsIxmFM7D7f7OWNeHMvbDOaLh42T0hC2S2qKuH9TIzL6IGKgG/xtcPCvowedvf93sPwd6S53\nUsxOgrkpuw+a/1f2fk7fcWodn39gK1sauzndGP9siRMkTTCpGBBC/Ai4Tdrfn7IeqJdSHjRe5z7g\nGiBWDFwDfN34/UHgp0JJt2uA+6SUQ8AhIUS98Xyv2bzGifnbz5TSnoAZh7u4qmQD62auVhs2/Aes\nuQkGu8HfAYF29cX0t8NAJ/QchU2/gif+efg5bgBucKNiIwClc9W/GUwTTDqtMJKZL2QsCyp9bDzc\nldJjD7alPqkuXZwOQXmBxUl9ww+2J9rTGbAwpOgXl0B3w8jt2lPTfv2xVBZ62d1iMR8rhIqc+SpU\nmsfi+5K0xwCMbtmNw8yyfJwOMSySx+HK3IngUJufPLeD2uIk/o6df1LpCgDhVOOnhYP3FF/Ar4MX\nEwkN4Vp6JVx7h9onNKhmYtz5NhjKjkuh6TEwJ900gc0XIm9bWYPnjw4e3dqcohgwjoUZNILLBskc\nMfuAR4QQ10sp/UKIK4CvSinPTfO1ZwIx5fI0AWdOtI+UMiyE6AEqjO2vj3ls3HJ9IcStwK0Ac+bM\nSXPJMfQ1K1/5OIQiUdYG9lMwowqHNBS3me/PL1M/LBr/wPM+p76Y4SGIBJHhQT5/70bml7r59IWz\nocJ4jNMNPUdUKHWoDwZ71eMGe1TKYfWHYPFlKf1Zk04rnCTHagcLqgp5aMsxBoIR8j3Wct8H2v05\niQqYlPs8dKbTTSBlWu19Xf4gs5O5IgYIdMCSK2HVdeq1MyAG0jJiAsNQytpBNmmPAZhU3LqdDmaV\n5XPYuKqNu77Y57GRQ+1+5lX4cDiS+Dw0vKo6HFZcCzKqbHuP/I0FHc8DFxMNjRkx7s5TdT4ZWns8\njnQG8Lgc1BQlIW46D8G236tjW7APhvqVWyTYfuwpznNz4dIq/rL9GF+5ajnOZN7vWE6QIUaTigEp\n5b8IIT4APC+ECAL9wJcyvjKbkFL+HPg5wLp16+yLblz2dfUTh58+vY/3vbyBBeUea2H10tGFhgIo\nPa2aH7/WwE2LLhvpzfVVwv6nVJ+/idunCvgC7eqRKYqBQ+3+xNMKM5wmgJgiwvZ+VtYlP7bVnFSX\nsI0zw5T7LA7nMXF6AKn819PI33b6g8nXDESCUL1ciYEMEWvE5E5lZG0KbbRJewxAUlebcyt8E08T\nzWCI+FC7n2UzkiwejAQhv1wN7jF58Ba8TZsBkPEKRLMc3j7SEWB2WX5y4uaNn8PrdxjHtUJlw+4t\ngiUboGqZ7Wt71+kzeXrXcV6pb+eCJRZbpE+iNMGlwMcBPzADuFlKudeG1z4KxJ79Zhnb4u3TJIRw\nASWoQsJkHpsTolHJg5ub+IDbi88ZTdvz/YqVtfzq5UO8uK+dq041Jh2+55fQfQS8xeoL4i0eOYHc\ncXbKClW1FQY4e2GC3vwspAnM6undzX2WxEBb/xB9g+GcRgZSCotDTEXyUMpiQA0pCieXJpAyIx0E\nYzEtibv8QaqTCXePJYX6mKauAU6fU5rczkmI23kVBbzV0IWUcnyBWYYqyUORKEc6A1y5qja5B4Tj\nnxKh9wwAACAASURBVOydMoTX5YhfIJrl8LaltsLQgCpw/EL86KvdXLq8mtICNw9sbkpBDJwY3QTJ\nSPWvAP8qpbwIuA74vRDiEhteeyOwWAgxXwjhQRUEPjJmn0eAm4zfrwOeM2oXHgGuF0J4hRDzgcXA\nGzasKW1eO9jB0e4BCvLz1IcjzTzXmjmlFOe5eH5vzECNvBKoXQVlc5U1ZuzJI416gpbeQQZCkcSV\n+BnuJgCYX1lIntvBLou9v3vTsG61CzXGOMU0AaR1QDEHApUnU0CYgSmF8ai0akk8FotdFpY8BiBG\nrE/8PswpL6BvKExXIM73ypmZSvKmrgHCUZn8fJBIcPzf4HQjIiHmV/pwROMMEstieFtKyZHOAHOT\n/nsy090yEV6Xk2tOq+PJnS30JDtYy2T4MzC9awYmFQNSykuklC8bv28HrgT+Pd0XllKGgU8DTwK7\ngfullDuFEN8QQhgeoPwKqDAKBP8RIz0hpdwJ3I8qNnwC+NRU6SR4YFMjxXkufPkF6gOd5kHX5XRw\n/uIqXtjXlpxLVhqdBvWtRitTdYJWpiykCZwOwbLaYsuz2E0xsMziuFc7Kfd56A6ECFudTxBbiBYJ\nqRxwe72lp+gatiJO4v8mC6IORtotU0qdgOU0gSWPAUg6TQDETxWYj7PBIyKWQ+0Wu2ImSgNEgsyv\nKMBNvMhA9sLbXYEQ/UPh5NsK44mbDHPd2tkEw1Ee3WrRc+AESRNYTuJJKZuBS+14cSnlY1LKJVLK\nhVLKbxnbviqlfMT4fVBK+V4p5SIp5Xqz88C471vG45ZKKR+3Yz3p0jMQ4vEdLVy9ug6H26uUog0H\n3QuXVtHaN8Tu5iScxNKIDBwwxMCihGIg82kCUPPYdzX3WrIJ3d3cR3WRN7U+e5sYdiG0Op/A/Hz8\n6e/guwvgritH14QkwfBcgmTSBFkSA2aaIKVoCRif5+SFhCWPAUhK3JomOWY1/Oj1ZSZEfKhdvdb8\nyiQ9BuKNEHd5IRxkYYX6P4iIMeknh1N1HmQhMmAKqaTbCrOQwhrLKTOLWVZbxAObm6w98CRKE4xD\nSpmbqR1TnD9vO8ZQOMr71s0euUK3QwwYOawX9rVNvnMaLWoH2vwU5bmoKozfZgVk7SSysq6EvsHw\n8ME9GfYe72XZjNxFBSDGeMjqya/IqAdp2wsr3wU1q1SniAW6rFgRZytNUJhumsCauE3aY0BKaNoM\nh19SbXiOiTsPzDx3Q7yOggyF2g+191OS76Ys3sjzeMSNDKhjwYJytb0nGKdwL4OeJbFYbivMcpoA\nlMfJdWtnsbWx25qF89jPgJTQuBEe+wL88FRlojUN0HbENnL/piaW1RaxambJSHjThoNuTXEey2cU\nj64bmAiLV1Kx1Lf2s6i6MLELVxbSBAAr6tRJPdlUQTgSZd/x/pStW+1ixIXQ4gF20WXw+f1qLOrV\nP4bKRZYP0sPji6dQmqA4z43LIZK3JB6Ly9rJalKPgUAnvPIjuH09/PISaHwD1t2S8Dnz3E5qir2T\niAF7Q8SH2v3Mr/Ql74g3UZogGmJ+qYoIdAzEibJlSwwY713Sba85SBMAXHv6TNxOwb1vNE6+s4m5\nzv5WePWn8JO18KvLYPNvlI9Hy7bMLNZmtBiwiX3H+9ja2M11a2epL7CNkQGAi5ZWsbmha2Rw0US4\n0kgTtPVPbn2apTTBstoinA6R9ACRwx1+guFozsXAyKQ+iwdYIZRFrHnwT8Ge2IwMlCZzNZklMeBw\nCMrS8RqweLKa0GOgbS88+g/wgxXw9FehoALe+WP4/D646vuTPu/cch9HOuPUDDgc4HDZHxlo81uz\n1I6XJjBuzzOCZa3xgmwWxVaqHOkMUF3kTd43JAdpAlDdQBtOmcEDmxsJBCdxizUx1/nEl+Cpr6jW\n72tuhy/Ugyt/2pgRaTFgEw9sasTlELzrdKPH3anydXYddC9cUkU4KnmlviPxjikq/d7BEK19Q4nF\nQMcB2PfkyOtkkDy3k4VVvqQ7CkzRkMviQUhzcmEsKaR7uvxBfJ4khxRlKU0AhiVxyjUD1gY4xfUY\niIThZxfC1vvU/PlPvAI3PwFrb4L85FoQ51QUxK8ZgPHRuPAQ7PijulJMgYFghGM9g9ZsiONGBpQw\nLXWp96/VH6eoNUuRgQar0wrjiZsscePZc+kbDPPIliQLCQtr1NCqdTerz9YtT8HpH1LumRl0i7Ub\nLQZsIBSJ8qe3jnLp8urhgqnhg/mw3Wl6J881c8rweZy8XD9J3UCKX+6ExYP9bSr/dft6aNoEF3xx\nQvtWOzmlroStTT1JFRFuaewm3+1kSU3qQ13soCyd+QSxpPD/2BkIUpqsFXGWIgOgrrZS7yawniYY\nVzwYHoTwAFz0Zbj6J1B7iuVlzCkv4HjvEIOhOE1LZkowGoUt96gw8YMfhU13WX4dGJkPMt+KX0Zc\nHwF1WwTV87X0J1h7hmnsDFizIc5RZABg3dwyltUWcfdrDckVMLs8cOPDaoT72M9WBofK2Y0WAzbw\n1z2ttPcHVeGgic1pAo/LwdkLK3hpf3viHVP8ch8wBgMtjD0ARULw8g/hx6th469gzY3wD1vgkq9Y\nfv5UWDO3jPb+oYmvyGLY0tjNqpklE9soZwmnQ1Ca76Yz1ZOfictr+f+xy5L7YHZqP0BFS9JLExhr\nDXTCQ38Pv7wsbrRgQo+B4dG3KZgeGSTuKPBC6y741eXw0CdVmNjhgtDkn9t4HJpscmg8JvAZAIan\noh7rTyIy0HMUHr0N9trXoDUYitDSO2gxMpA7MSCE4MNnz2VXcy9vHkltRsowadRwZRstBmzg/k1N\nVBV5h6v+gZGDmI1XYOcvrqKhIzCxNSoY6Yk4H76eownDlgfa+nE7xcgXtmkT/PwieOZrMP8C+NTf\nlPItStIRzQbWzVNDQzZNMrQoGI6y81gvq5N1ncswKRsPxZLCFUVnIJScxwBkrfYDzPkEaUYGdj2s\nIlNbfgdNG0dP3TMwPQZmlo5NE6SfEpm0o+DQi8oV9F0/g4//FdwFKV8RpjStMJHdsBEZOB6IjI9s\nOD1KWEWj8Pr/qPd4810qzWETTV0DSDkiqJIiRwWEJteunkmR18XdrzVMvnMishR5sQMtBtKktW+Q\nv+5t5d1rZo6+KnUZitDG3Oz5iysBEkcHxuaozC/5j09Xin8C6lv7mVfhU3/DkdfV1VegE66/B264\nFyoXp71+qyypLqIoz8WmhsRiYHdzL8FwlNNmTQ0xUOHzpt5KZ2IO6LHgs9AdCFJupRXNfJ0MU1no\nxR+McyJKBqdHhfjvvxGK62D9rWp7nKutCT0GbPhbExoPrbkRzvksfGYTnHa9KgJNIzx8sM1PTbEX\nn9eCLXW8NIGZyjPEQFC6xkc2nB7obYK7r1YFcHPOhqI6W0PbjWZb4TSJDAD4vC7eu242f9nWzNHu\nNDrpXdYLgXOFFgNp8ofNR4lEJe9dO3rI0PAVjfFFtOODPb/Sx8zSfF7an6BuIPYg1NcCv323+pJH\nQ2pK3QQcaOsfqRc4vhOQqshq2VVprztVHA7BmjllbG7oTLjflsZugBMsMhAzuChJOv1BC5GBLKYJ\nhl0IU3hPSueoNV76VfjYc1C3Rm2Pc4Ad8RiwXwyUFbgp8sY5mQJc9M/wtm8qm3CTNArzDnf4rUUF\nIHGaoEeZ6IRwcbh9jJhxetQo42NvqQr4Dz6gOi1sPIGZAmpOeZo1EFnmlvPnA/Crlw6l/iRm5GUa\noMVAGkgp+f3GI6yfVz6+8M7pVqYxL31fjR52pl9wJ4Tg/MWVvHqgY2K7W/Mg1PgG/OwCdZX/jv+G\nhZdM+AUPhqMc6QiMWJ+aJwpvbtv0AM6YV8a+4/0Jw8x/O9TBjJI86kpSzwnbSXmhXWKApA/KoUiU\nvmSHFMU+bza6CYyi2pRSBad/GL7cBOf/Ezhdo22bxzDiMTBWDKQfnRNCMKeiIH6aIB4WuyBiUR4D\nFgthE6UJnv0G0YIq9kTnjF//vPOUx8UnX1EV8GlGNeJxpHOAAo9z2IAqKXKcJgCYWZrP1afVcd/G\nI3RbdRQ10QWEJwevHezgcEeA69fPHn+nK0/NFZ91Bnz0CdWPbAPnL66ibzDM1qYJzHjMK8q73g7u\nfPj4c6rlxTlxQdrB9n7CUclSsy0viyHkybhgEvfFaFTy2oEOzllYmbxBS4ap8HnoCgSJRNOYmG1R\nDAy7DyYTGZASDr2gfndbCN2mSHk6kQGHY3TnyvAsgHhpAtXLPq610qbP89yKguGQ96Sk4BMBKtXT\n6Q9a8xgY6lcdE2NPnh7jOWafieMTLxEpqBzuVBjm0n+FD/0ByuaNbLM5tH2k08+c8gJr389IMCsd\nS5PxdxcuJBCMpF47MFGEqLsRHvioEYWdGmgxkAb3vaGGEr191Yzxd67+IFz1A/jwQ1BocSRmAs5d\nVIEQTJwqcBtXx/POVYVMNSvUbad7wqrW3c2qR3+5adgzhcTAKXUlVBZ6eW5P/OLHXc29dAVCnLso\nwdjlLFPh8yAlqV9NwMiBPdbiNAHdxkS98skiA+EhNf/gb/8Lqz+UlVqQYUviPhuqqhM4/v3/9s48\nPpK6zP/vp7uTzn2fk0wyB5kDZmBmmAMEBIZLRQVBLlFBUWB3PVbFRX+urrsrLuqu166u4jWIB4LL\njYoycsk9wNz3TObITO5kcieddH9/f1RV0sn03dVHku/79epXuqu+Vf3t6k7VU8/xeQKWFfqPjfP3\nXFeSy9HuwciMvBjDBFEnD/a1woZ3Ge+14ILJ6+rPgQ88CDc/AQXV1JfmRubZsDnp7UjXYOQNiizS\nIEwARgfU9Usq2PDSIYY8Mea8TD2WzVuMnKwdDxkNydIEbQzESPeAhz9tb+F9K2sCi7yUzIc1txBr\nb/pgFOVkcnptUfAkwuXXGLXUN/6f0d7YIsTJaXdzH5lOx8QJKImCNOFwOIQLFpfz/N72gKGRv+5u\nQwTONZMr04GSeJvzwGTPwNHX4O462PVE0OHjTYpCtS/2DMJvb4Ctv4P1/wxX/M+E4mECKTOPR9xJ\nlRDSYxJQcMh/bJy/5/rSHEa9iuaeCBLKYrygjhsDkWgMdB8yZG879sEN90PDJSfPYdGlE0qEpTkn\newYCYSWv2oDVujiq5ME37jXKIf3PXynk7y5YSNeAh1+/GoN3YGpp4eGX4ReXG15jSKtKA20MxMhD\nbx3D4/Vx/dq6pL/3eaeUsfnoicB9t/OrjOzmqUZICJniXS19NFTmTVRDeD3gyEjKhSIS1i+poHd4\njNcOnZxI+MftLZxZV0xFfnrkC0CcCXMWlov08EtGB8ORXmjZFnS41b44qM7ASD/85lo48FfDWHz7\n55P2/ea6XeRmOmm31TMweV9BNQbAvjCBeUE7EtHddWz15Y0dAzgkAg3/zgPGRWW417jzX3RZ2H3X\nl+Zy/MQQI2Nh7nBDhBSjpb1vhOFRX+Rlha/9BB7/lJHHsO52W+YQL2vmlXDuKWX88NkD9I9EKFFs\n4X8TduAZI6E7vxI+Yuo4pJEGgTYGYuRo1yCr6opYmoIueec1lOE1Y+URE9Iz0DtZxjfFZT1TuXBx\nBfluF7+f0lp0f1sfu5p7ecey5GkfRELMnQv9se5iH74dCkyJawn+79oVrmPh458yDIurfmIYi0mm\nPN9NW99w/DsKEiawNAYCewbsCRNYru7DkeQNBBKN6j4ctjrkYMcAc0tyyHSFODV3HoANlxuiRjc/\nATVnhp8PhmfApwjfCdTGpDfrWEUUJnhjA/zhDlj0Trj+txM5D2nAHZctpmvAwy/+FmVlgeUhOvgc\n/OY6KJ5vGAJWjsaU38g3/7SbDS/GUb0QB9oYiJGvvvc07r/17JS898pIpYn9CVLi0tnTT29fL0ur\n/SoHUqgLHojsTCfvWTGHP2xrnnSB/eXLh8l0OrjS6geRJox7BmIV2oGJC1fRXOPkEabvvOUZCNqk\nqG23cfd4+jWxzykOyvPdNnkGAvSO944y/Nq95DEYxDMwMnnbGJlTlE2GU6KIu/vNcfNv4Hunw67H\nQ27W2B6mrLCvBe670tj3zU9A1fIIZx9GK8EfG1XzLC9KfThjYMv9hg5Kw6Vw7b1xy7fbzYq5RVy8\ntJJ7XjgYXS6Qyw29x+H+D0DpQuM7y6swPLfimBSO6egf4acvNI6rwSYbbQzEQUjrPcHvG5E0sT+B\nPAMj/RR9/xR+m3nXZA9HmnkGAD56zjw8Yz7+56/7ASNz/MFNTbz7jOrxmHS6UGxHmKB2DZxxA9z0\nOBTWhD1Bdw2MkpvpPLlbn4XXE5ccb7xU5GfRHo9xZGGFT6yTqFLw5OdY8NKdrHdsTmiYwOkQaotz\nAncvPGmwX9x975/h0U8Yz4eCa2YopUJrDAz3wK+uhoFOuPH3UHlaVPOfZ7rqD3WEMWamhhQHOo3q\npN1/iOr9wEgeFIGaQN+LxYFn4NF/MJROr70vLaoIAvG5SxfRPzLG9zfuj3wjZ6YR4ssphQ8+FDKP\n696XDjHq83HzOfPsm3QUaGNgmhKRNLE/U40Bnw8evg2nd4iVjv2TW/+mSSavP6dU5HPdmrn84qVG\nNrzYyGd/twUR+Nyli1M9tZPIcDooyHLFFybIr4L3/cgQ3YHAWcl+dA96KAlVx51iA88+z8CUMMGL\n34M37wXALZ6TNQb8x9rw+etKItQasL6v5i3w4E1GQjGE1B5o6xth0OMNXlb4yN8brZiv/xXUrIp6\n7iW5meS7XRF6Bsx5jo3A726Ewy/CsU1Rv+eRrkHmFGYHN1JbdxjqkmWL4br7Jqqh0pCl1QVcv6aO\nX758iP1tfZFtVFgL+dXwoYehYErVmV9uRv/IGPe+dIhLT60M30Y+QaTEGBCREhH5i4jsM/8WBxiz\nQkReFpEdIrJVRK7zW7dBRBpFZLP5WJHcT5B6IpIm9seZCco7EbN87huw28hOb6ZsotsipIXgRyC+\n8u7TWF1fzFcf38lbR7v5j6uWUxPo5J8GlOa54+9c6E+YvvNdAx5KckPcUXlHba9siYbyfDd9w2Ox\nSRL74x8m2Pmo0TtjwQUAlLoJXNljo8BSfWkORzoHw3ezc2Yaip/33wjZxfCBBybPJQAH262ywiAX\ng+NvwbKrDQGxGBAR6styOBTOmLGMAaXgsU/BkZeN5THkERhlhUH+R71j8JvrDa2LGx+YrOCYptxx\n6SJyMp386+M7I+toeMEX4dNbjBDBVPzKve9/7Qi9w2Pcfn6AcUkiVZ6BLwAblVINwEbz9VQGgQ8r\npU4D3gF8V0T89WY/r5RaYT42J37K6UVE0sT+jCu3mSfR5+6GFTfyh4zLyHZOKdlLwzABGLkDv/34\nWTx4+9k89/kLuWJFeuUK+FOam0mXHaV0FmFkTbsGwvQl8KXW21NuGptxewcsJc/WHcadcu0auPJH\nAJTlBKmOsFE3o64kh76RsXFdh+DzzISBNhhoh+t+BYVzJ88lAGHLCr0eyIxPJMrQGojAMzDmMTL7\nt94PF37JuFDHoKh4uDNEWeFwD/QcgXM+bdxBTwNK89x85pJFvLCvgz9tbwm/gUjwsIdpdA15vNzz\n/EHWzS9hZfujRsVPCkiVMXAFcK/5/F7gyqkDlFJ7lVL7zOfHgTbAPvWeac64NPH+ENLE/lgnwvbd\n4yfRgUu+RfuwIkumlMukWQKhPy6ngzXzSgK7g9MIW/oT+BNGxCZsX4JUhwkKjBNiW9zGgPm7fPV/\njZPsNfeOy2aXZQcxBoZOmNvG//nHk/DCVRRYF4D3fM9w6QdKfJxCY0c/bpeD6oIgrnIbvsN5pTk0\ndQ8xGuqcYTWHeur/waJ3wHl3xCSiNOgZo6N/ZPyYnYS1vzQODQTiQ2fVs6ymgC8/uj2+/3GXYXT9\n4qVG2vpG+MqqEXjyDtj0c/smGwWpMgYqlVLN5vMWoDLUYBFZC2QCB/wW32WGD74jIkH9oyJyq4hs\nEpFN7e1RZN9PA85rKKdvJIQ0sT/WSeT/Pmb0Wr9mA9tbhxlRGbiYagykZ5hgOlGal2lvmCBMAmH3\noCe0+mCKDTz7PAPWZxSjTLKwBq/D+Fwlga4pPceMvII5q2wRsbHq5cPeXa+7Da76qdHFEIw7REfo\nkr3GjgHmlebicATzcMT/Hc4rzWXM1GQIinWM86vgyv81JKHD5KwE4ki4ssI0UjqNBpfTwX9ecwY9\nQ6N85dHtse/ImYnHM8z/PnuAyxfncdrLn4G8SnjP9+2bbBQkzBgQkadFZHuAxxX+45QReAkafBGR\nauA+4CNKWbJNfBFYAqwBSoA7g22vlLpHKbVaKbW6vHxmORbCShP7Y/3Dde43lOcKa9na1MMoTpy+\nKf/kaRommE6UmP0JfPH0J/Bn6sl4/0boNySah0e9DHq8aZ1AWJFvGgPxVhRkZBu12hd9BU65CIC2\nASMPoXjqLYHPB4/cbnz2q39qi8hSXaTCQxVLTy7jdLlDutoPdoQpK7TDM2DuP2TeQF658T7XbJgw\noGIoNwxbVpjEzpl2s6SqgE9f1MATW5t55K1jse3EmcmB5m76R8b4euYGQ1Hy6p+kTHkxYcaAUupi\npdSyAI9HgVbzIm9d7AMKz4tIAfAk8CWl1Ct++25WBiPAL4C1ifoc6UxYaWJ/rH+4Mz8CS98DwJam\nE2S5sxHfqHHitEjDaoLpRkmuG69PBVaJjAX/BML9Gw0ls2fuAibEjYJ6Bnw+8I2l9Dstyc1EBNp7\n4xQecjjhU2/BeZ8dX9R0YpgR5aIwc4rr++X/hsbn4Z3fCJzAFQNZGU4qC9yRCQ9NZar2gHcUNrwb\nnr2bMa/ROTRovoBN32FEno1VN8FndkLtar+5Rx8msDwDQXMGktg5MxHcfv5C1swr5osPbWN3S2/U\n2w94HbSe6OWbSw5QuO8hOP8LUP+2BMw0MlIVJngMuMl8fhPw6NQBIpIJPAz8Uin1+ynrLENCMPIN\n4vDVTG9CShP7s3C9IUF72dfHF21pOkFZkVlS6O8d0GGCuLFFktgfq259uAce++TEMvz7EgQzBlLf\na8LldFCa67ZHa2DKHX5T9yAeMijI8PPCdOyDv34NlrzbaINsI3UlOZFJEk9laifDl/4bDr0ALdto\n6h5izKeCewZs+g7L89zkZDpDaw04nCc3V3OFTmANxJGuQfKzXMGFsKZpmMDC5XTwgw+sIi/LxW33\nvRFVCKx3eJSDXaPUOHt4f6sZxjrvcwmcbXhSZQzcDVwiIvuAi83XiMhqEfmpOeZa4O3AzQFKCH8t\nItuAbUAZ8LXkTj99iFiaOL/SaE5jZiM39wxxtGuIqpIpbYs7D0DLViiqT+CsZz62SBL7Y8ma/vUu\nQ9EMxuWJrfbFpcGMgTQ56dqmNTCFpq4hRnGS5zI9Az4fPP5pI6Rw+bdt78FQV5LL4UiEh6bif3fd\nsR+evdt47h2l0bxTD6oxYLnUHfEZAyISWUXBVKZ6BhpfgI3/FnITq5IgaOviaRwmsKgoyOLHHzqT\ntt4RPvSzV+kJV2WC0Ufjjge20D8mNKhDyPAJI3SbwtJfSJExoJTqVEpdpJRqMMMJXebyTUqpj5nP\nf6WUyvArHxwvIVRKrVdKLTfDDh9USvWn4nOkA5Y0ccQlhiavNRpKaHPLzNreMbOu+InPGEp1FwSq\n9tREyoQxYNPFz+mGjr3w+k9g7ccht3z85BzWM5AmJ92EGQPdQ3glA5cyP+fmXxkiOZf8u2EE20x9\naQ6tvSPRayZYYQKfz+gV4cqCkgXgHaGxPUzrYhsNuoi7F/rj79UY7jUSkV/8XshNjnYNhm5QNM3D\nBBar6oq558NncrB9gOvueZljIZIzvT7FFx/ayp93tjK33JTXOe9zUatJJgKtQDjNsaSJ/7Y/Cmli\n4JWDXeRnuagqMY0Brwe2PQiNzxnJWfnp1fxnumFJJNsaJhjqMoyA9f88SXcgbM5Ampx0y/MSZAyc\nGMTnMBMs+9vhz1+G+nNsDw9YWBe4o9HmDbjcRqhny28NY+WyrxlNqLyjNHYMUJDlmug66fMZxrmF\njW3F60tzOdo1hDea5Fb/fIdn/wP6W4wcBl/gEkWvT9HUPRS6QZEvPYxUOzivoZyf3byaY91DXP79\nF3jozaaTju+xE0Pc9PPXeGBTE5+6qIHaeYuM3hIpDg9YpNYvobGF8xrKeXpXG4c6BsazhcPxamMn\na+aV4HCZRsRQF/z5n40OaKs/msDZzg6Kc42Ttm3CQ5Zo1GVfNwRg/Ny23QMeHAKF2WFis3G6mOOl\nosDIGVBKBXcdx0BT99BETsUzXwNPP7z7O0ZJXAKwEuIOdw7SUJkfZrQfzgxD82DjvxpiSSs/BDse\nhuFeGjsGmF+eZxwXpeC/V0LNanj/z4xtbfYMeLw+mnuGAnd5DITLbWjst+6EV38EmXnGcfZ6wHFy\nTWdL7zAery948iCkjcfKLs5rKOeRT5zDHQ9u4bMPbOG7T+/j/EXlFGZnsLe1j2f3tIPAN68+nWvX\nzAXftw2DKk2aMmnPwAxg/ZIKAJ7c1hxmpEFb7zAH2wdYN79kQhzl+f+E/lZ45zeNBCJNXLhdTvLd\nLvs8Aw2XwZqPGXK0MKnUq2vQQ3FOJo4n/3EiudCfNDnplue5GfWq8Op9UeA1a+Ylww2t2+HNX8Ka\nj0N54npWRCw8NBWnGw7/zfg/u+w/jFwG06g72N7PfMulvvNRo8xsu1/etI3GgDX/sA2LJs3d9Lz8\n5SuGyNO62yfPawoTZYVhSiUh5R4rO1lYnsfvb38bP/jAKupLc3j4rWP88Nn97Gzu5Ya1c3n2jgsM\nQwAMYzVNDAHQnoEZwdySHM6sL+bxLcf5hwtPCTv+r7uNSs7zF5dDl/mPuOMhOO2qyeVEmrgoybNR\nhXDFDcbDwk93oGvAw1lZh4x+8JUBWtqmyUm33E9rIKRaYhS09Q0z6lU4XZnQsROyiuD8f7Jl38Eo\nzskg3+3iSCxJeADLr4W5a8aX+cZGON4zzILyPOM73fivxjr/79LGMMG8MrN7YecA55o9TsLP6rsY\n6wAAIABJREFUPcPIWWndbuRiZJgKoMGMATPBMrRnID0SW+3G6RAuP72ay0+vDj84jdCegRnCe8+Y\nw+6WPva0hO+m9fSuNmqKsllcmT/xj+jMhIv/JcGznF2U5GbSaVcC4VRcEy1yu/pH+LvR+4zlgU7O\naXLSHTcGbMwbaOo2krVcmaar+vw7Ey7aIiLUleZE7xlwucGVPfn/zJnJqMc4HgvKc+Gt+6DroBHS\nUX4JijZ+h5X5WbhdjugqCqwEwsI6WHtrWHnlw52DuBzCnKIQUsNp4rHSGGhjYIbwruXVOB3CY1tC\nq2ENj3r52/52Ll5aYcQnrTDB2luheF7iJzqLKM3NpNPOZkX++OUMLOh5jWWeLcaFJpBKXMs242+K\nlM0sKhJiDBgXZFdeKZQsNEIpScDqXhgV599pNi3ya8rjcuMbNY7HwiInPPsNmHuWIQw25necbLxw\nOhxCfWkE3Qv9sS7+F/+L0UvAahjlP8djb4DHMDAOdw5SW5yNyxniEjOey6Id1OmANgZmCOX5bs45\npYyH3zwWsnHRC/s6GB71cdFSs+Rq7jpD+er8oIrOmhixvVmRP5Yx4PPx4cENdGVWGxeQqfrx3lF4\n7ptQfQbUnZ2YuURIhdmApyVeFUI/mroMz4Dzyh/AR59KWgy2riTXKGmMJiO/bh00XDx5mTMDn1kV\nckrjr40s/Yu/ahjp3ilCYGBbLXrUWgMLL4TTrzdCiea8jXmZczz2JvxkPWy5H4DDXQPBGxRZpInH\nSmOgjYEZxI3r6jjeM8yfd7YGHfPQm02U5mZy9sJSY0FmLlz4RcgqSNIsZw8luW66Bz2R9T2PFtMY\nULufYAmNvFx3G7jzJt+pAWz+NZw4DOu/bLv4TrTkuV3kuV209NhoDHQPUZHvJquo8mTVvARSV2Jk\n5Mdt2DjdiHeEhkJFxsvfNRJF688+uReAzRfOeaU5HO4cjLx3xrKr4aofT1RoWB5Fa47PfcP4O9KL\nUorDHWE0BkCHCdIMbQzMIC5eWsnckmx+8WJjwPUd/SM8vauVK1fWkBHKfaexhbK8TEa9it7hsfCD\no8VseuN9/r845KukZe7lJzcz8nnhb9+FOSvhlIuD7yuJVBVm0WqnZ+DEIDXFyW9nHXH3wnA4M3D4\nRvlo1jOG1LQl9jVV8a/XDP9lRFgKGIb60lxGxny09sX4XVgXcK8Hjr8Fe/9kvB7z0D04St/I2IRn\nIIgWgZ1JkZr40VeEGYTTIXzkbfN5/VA3Lx04WYRow4uHGPMpblhbl4LZzT5slyT2x5kBHXtwtWzm\nR973UFKQc/Ld5M5HoLsRzv1syr0CFlUFWTTb6Bk42jXE3Ehr5W0k4u6FYVBONxnKw+UDD8OCC6Bm\nlbHCv8OhUvDyD6FsEVSvCLarqJgXS3mhP5YxMOYxypKzCg15bK9nXN2wviQHXv0x/Fuxoa8wld5j\nxjauEEmGmqShjYEZxgfW1VFTlM3XntjFqF/uQFvvMPe+dIjLTq3ilIq8FM5w9mC7JLE/Tjf4xvDk\nVPKQ9zyKczIn300qBX/7DpQ2GM160gQ7PQNjXh/HTgwxtyT5noE5RdlkOCW27oV+DHgdOEVRMNYJ\n535mYoW/4t/+p6F1G5zzj7YJKcXt2bCMgfZdsPtJQ9vB6QbvyLiBNK80G/5olnkOTLk5GemDt34N\nS9+bVrX2sxltDMwwsjKcfPndp7KzuZe7ntyFUooxr487/28rI14f//SOxImxaCZTmmtKEieiosB0\nrR5q+AgeMgzDw+UG5QPvmNHmuGUbnPPphCnxxUJVQRZtfSPRJd4FoblnGK9PpcQz4HQItcUxdi/0\no3PIOA59pafD/PP93sBtyPX6fIZRV1ALy6+J6738sYyZqCoK/LFyBl76b+O3uPZWs832KIc6BxCB\nuhOvToyfWoL45i9hpAfe9qnY3l9jO7qmYwbyjmVVfPSc+fz8xUZ2t/Qy5PGypamHf79ymSFsokkK\nJXk2tzH2J78KcivYXn0VsN/0DPjVfr/4XcifA6dfZ/97x0FVYRZen6Kjf4TKgvjcw0fNssKQ+vcJ\npK4kJ7buhX60Dwv1gOfsT08O5Vjf5fE3jT4Gl95l6x200yHMLcmJwzNgzq/rIKz4oNEQypSEPtI7\nSHVBFpmv/3BivL8x4B2FV/7X6B9Re2bsH0JjK+lzy6CxlS+/eylffveptPaOMOjx8u1rz+BDZ+m2\nxMmkNJE5A+ffCZ94jfYRw54vzcucqP0+/hYcegHW3ZZ2Ltgq0wCwI2/AKisMqXKXQOrNjPx4qkVe\ndJ3Nf/luoHjl+yavGL/z/r6RNLjyg3HMNDDzSnNj9wxYvzWAs/9hYpnpGTiroMMIb8w9y1jnbwzs\nfBR6jsLbAkhna1KG9gzMUESEW86dzy3nzk/1VGYtWRlOcjKdiQsTZBfTNdCC2+UgO8M5cbf2yg+N\nE/OqD9v/vnFSVWhqDfQMw9z49nW0exCnQ6guTE0C2rzSXPqGx+gc8Ix3qYyWt/ryaS29kc85p/QD\nsWLyux6HVTdBdlGcsz2Z+tIcXjnYGVvjKOu3tvAiqDx1Ypl3hCNdg/xTwZPGb3DdbXD0lcnGwGs/\nMVo3N1xmzwfR2IL2DGg0CcQQHkqQJDGG16EkN3OymuTuJ4268BQrDgZiwhgI3vM9Uo52DVJdmBVa\n5S6BNFQaIbd9rf0x7+NAez8LywOI81jGgPIZ8fgEMK80l0GPl/b+GH6fBTWw4EJY/6WJZS43Y55h\nxvo7OfPEU3DGdVAwx1hn6V+07jCMg9UfTatcFo02BjSahFKa505MzoBJ96BnvGphQrxFwdrkyPJG\nS0lOJplOBy298RtIR7tTU1Zo0VBhtC/e3xa+H0ggBkbGONo1ZPQImYr1Xc47b+LO22YmKgpiCBVk\nZMGHHzFanls4MxgcGuIq59/I8A3D2tsm6xEAbPq54TFYcWOcs9fYjTYGNJoEUppISWKM5MSTjIE5\nqyafpNMIh0OoKHDb5hlIRVmhRWWBmzy3i/1tsXkG9pnbLaoKYAxkmt6CdbfFOr2wTGgNxCmcZOF0\nMzI8xHXOZxisWAlVyyYbAyP9sOV3cNr70tJrNdtJiTEgIiUi8hcR2Wf+LQ4yzisim83HY37L54vI\nqyKyX0R+JyLplSWl0ZgktD8B0D3gMSoJYKKt7NqPJ+z97KC6MCtuGd/hUS9tfSMp9QyICKdU5I1f\n1KNlr9lhNKBnoOFSuGYDLL48jhmGprY4G5dDYvMMBMKZSX7XNhY7mnCceZOxzApdjXlg++/B0wdr\nbrHn/TS2kirPwBeAjUqpBmCj+ToQQ0qpFebjvX7LvwF8Ryl1CtAN6F+XJi2xOhcmpD8BEzkDgKFg\n957v2VqPnggqC7Li7k/QlOKyQouGOIyBPa19ZGU4An+GzBzjDjqBcXWX00Ftcfa4YmD8O8wka6yX\nQbLIWvF+Y5l/ueumn0PlMqhdY8/7aWwlVcbAFcC95vN7gSsj3VCMtNf1wO9j2V6jSSYluZl4vD76\nR+zvT+AZ89E7PDZewkhGNpx5c9prvVuegXgMpKNmWWEqwwQAp1Tk0d43wonB6L0/e1v7aKjIx+lI\nnVS00b3QPs8AwEtZbwe36e0YL3d9E5q3GJURaSKNrZlMqoyBSqVUs/m8BagMMi5LRDaJyCsiYl3w\nS4ETSinr7NoE1AR7IxG51dzHpvb2dlsmr9FESiL7E1j7LI2xrC1VVBVmMzzqo3twNPzgIIwLDqUw\nTAATFQWx5A3saeljUaAQQRKZV5rDoc4BezxXpjGwo/KKiWVWmGDrg+BwGVUumrQkYcaAiDwtItsD\nPK7wH6eMX2GwX2K9Umo18AHguyKyMNp5KKXuUUqtVkqtLi9PXotTjQZMMSASo0LYYZaEleVNr5SZ\nWrPL4LHu2JMIj3YN4nY5KM9PrSFkVRREGyroHvDQ1jfC4qrUKoLWm1oJ8RhmFp6i+bzpOwVn3dqJ\nhZaXaqTHyIPILY37fTSJIWGiQ0qpoD1TRaRVRKqVUs0iUg20BdnHMfPvQRF5FlgJ/B9QJCIu0ztQ\nCxyz/QNoNDZQYvYn6EqA8JBlDEw3z4BlDDR1D7K8tjCmfRztGmJuSU70Yjk2U1OUTVaGI2qtgb2t\nRvJgyj0DZYZn5VDnwETuSYzsXf55rn52HT+s8PtM/kqFaSaNrZlMqsIEjwFmuik3AY9OHSAixSLi\nNp+XAecAO01PwjPA+0Ntr9GkA4mUJO4wDYzp5xkwLkBNcXgGjnQNMrc4tfkCYJRKNlTks7ulN6rt\n9pjGwOJAZYVJpN4sL4y5R4EfB9r7UTgm9z+xPANZhbDoHXG/hyZxpMoYuBu4RET2ARebrxGR1SLy\nU3PMUmCTiGzBuPjfrZTaaa67E/isiOzHyCH4WVJnr9FESCLDBJ3jYYLp5RkozM4gP8s1XhEQLUop\nDnUOjF/IUs1pcwrY2dwbVdx9x7FeinIyxns1pIra4mwcAoc64k8iPNBudCu0xIwAI1kwuxiWvd8Q\nKtKkLSnpTaCU6gQuCrB8E/Ax8/lLwPIg2x8E1gZap9GkEzmZLrIyHAmRJO4c8JCV4SAn0xl+cJpR\nW5zD0Rg9A+19RvOtBYFkfFPAaXMKuP/1oxzvGaamKDJvxbZjPSyvKUx5mMPtcjKnKNsWz8DB9n7m\nFueQlTHl9/ixjZBfHff+NYlFKxBqNAmmNNedkGZFHX0jlOa6U35BiYW5xdkxewYaTcW8eWniGTh1\njpH3sONYT0Tjh0e97G3tY1lNbPkSdhNX90I/DrYPBDbQShcaugmatEYbAxpNginJzUxMNcGAh7IU\nZ9PHSm1xDk3dQzGVtFnGwPyy9DAGllbnIwI7myPLG9jT0seYT7E8TYwBoxVzfJ4Bn09xsKOfheWp\nrY7QxI42BjSaBFOalxhJ4s7+EcrizABPFbXF2Qx6vDGVtDV2DpDpdDAnQpd8osnJdLGgLJcdxyMz\nBraZHoR0MQbmlebSPThKTxzlhc29wwyP+tImdKOJHm0MaDQJpizPPV4GaCcd/SPjCYrTDf/ywmhp\nbB+grjQnpcp9U1lWU8i2psjCBNuP9VCYnTF+DFKNlfAXjyzxwXajtHJBmfYMTFe0MaDRJJjyfMMY\n8Pns60+glKKz3zPtKgks4ikvPNQ5kDb5Ahar6opp6R3m2Inwn+eNw92smFuUNrke88xwSzzGwAFT\ndGmh9gxMW7QxoNEkmPI8N6NeRc9Q/CpvFj1Do4z51LQTHLKoMe+Kj3ZF5xnw+RSHOgeZX5ZeCWln\n1huNVzcd6go5rnvAw762ftbOT58WvvWmlyVa4SR/9rT2U5idkXJFSE3saGNAo0kw1gmy3cZQwXQV\nHLIozM6gIMsVtWfgeM8QnjEf89PMHb2kKp/cTCdvHO4OOe5101hIJ2PA7XKyoCyX3WZL5VjY09LL\n4qr8tPF2aKJHGwMaTYIZNwb67DMGpqvgkD91pTkcjtIzYInjzEszz4DL6WBlXTGbDoU2Bl5r7CLT\n5eD0GGWYE8Xiqnz2tEanomihlGJvaz9LUqymqIkPbQxoNAkmEcaA5RmYrgmEAPPL8mjsiM41bY1P\nl7JCf86sL2Z3S2/IcNDrh7pYMbcItyu9hKIWV+ZztGsoplbbTd3GdqmWVtbEhzYGNJoEkxDPwMD0\n9wzML8ulqXuI4VFvxNvsa+snz+1KuYxvIM5rKMOn4IV9gVuldw142Hash7MWpF/nPutCvq81+lDB\nHjO8oD0D0xttDGg0CSbf7SLT5bC1vLCj34MIFOdMX8/AwvJclDKaDkXKnpY+Girz0jI2vbKumOKc\nDDbuCtiElef2tuFTcNGSiiTPLDxLqgqAiQt7NOxJkw6MmvjQxoBGk2BEhPI8t81hghFKcjLTqtY+\nWqyadKtGPRL2tfWzqCI9LzpOh3Dh4gqe2dOGN0AZ6dO72ijLc6eN2JA/tcXZ5GQ6Y0oi3N3SR01R\nNvlZGQmYmSZZaGNAo0kC5fluW6sJOvtHpnWIACaSAA+0R1bf3tE/QteAh0Vp7I5ev7SCE4Oj41UD\nFn3Do2zc1cplp1XiSEMDzuEQGirz2RtTmKBXhwhmANoY0GiSQHm+vZ6Bzn7PtE4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XAAAC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\nHG0MaDQajUYzy9HGgEaj0Wg0s5z/D+SOs+wv3pHNAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "in_stim.output = WhiteSignal(T, high=10, rms=0.5)\n", "\n", "sim = nengo.Simulator(model)\n", "sim.run(T)\n", "sig = sim.data[stim_p][:,0]\n", "\n", "fspikes1 = np.convolve(sim.data[spikes_p][:,0], h, mode='same')\n", "fspikes2 = np.convolve(sim.data[spikes_p][:,1], h, mode='same')\n", "\n", "A = np.array([fspikes1, fspikes2]).T\n", "\n", "d = sim.data[connection].weights.T\n", "\n", "xhat = np.dot(A, d)\n", "\n", "t = sim.trange()\n", "\n", "from nengo.utils.matplotlib import rasterplot\n", "figure(figsize=(8, 4))\n", "ax = gca()\n", "plot(t, sig,'g')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\");\n", "rasterplot(t, sim.data[spikes_p], ax=ax.twinx(), use_eventplot=True, color='k')\n", "ylabel(\"Neuron\")\n", "\n", "figure(figsize=(8,4))\n", "plot(t, sig, label='x')\n", "plot(t, fspikes1*d[0])\n", "plot(t, fspikes2*d[1])\n", "ylabel('$x$')\n", "ylim(-1,1)\n", "xlabel('time (s)')\n", "\n", "figure(figsize=(8,4))\n", "plot(t, sig, label='x')\n", "plot(t, xhat, label='x')\n", "ylabel('$x$')\n", "ylim(-1,1)\n", "xlabel('time (s)');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- What about with more neurons?" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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1ouW2P9raZFqLHY8iH7HhzKfS8l76Jyr1Ai5YMtzeFFV1XLKMzy3zXOR0op4s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\n2WHWd49eVKe1SUenXG8rJsaXaO38Mwch5IvRvIOhMEca28VsLgjWKrn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from nengo.dists import Uniform\n", "\n", "with model:\n", " ens = nengo.Ensemble(40, dimensions=1, max_rates=Uniform(100,200))\n", "\n", " nengo.Connection(in_stim, ens)\n", "\n", " dec_p = nengo.Probe(ens, synapse = 0.005)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(T)\n", "sig = sim.data[stim_p][:,0]\n", "\n", "t = sim.trange()\n", "figure(figsize=(8,4))\n", "plot(t,sim.data[dec_p])\n", "plot(t,sig);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- What about different neurotransmitter time constants $\\tau$? " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## A detail\n", "\n", "- Notice that we find our decoders in two different ways\n", " - [Here](#decoders) we found them using activities directly\n", " - With Nengo, we just computed decoders using the non-spiking version of the neurons\n", " - Then run the model with spikes, filter the data with $h(t)$ and decode\n", " - You could filter all the spikes first and then invert the resulting A matrix" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Why does this work?\n", "- Consider a single neuron with a constant $x$\n", " - When we found decoders using a rate mode, the firing rate was $a$\n", " - When we use spikes, we get $a(t)$, which is a sequence of $0$s and $1$s\n", " - If the rate neuron is a good model of the spiking neuron, then the firing rate (the sum of $a(t)$ divided by the total time) should approach $a$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- But what about $h(t)$?\n", " - It should just blur $a(t)$, pushing it towards this average\n", " - But this will only happen if $\\int_{-\\infty}^{\\infty} h(t)dt=1$ \n", " - Otherwise $h(t)$ will scale the value as well\n", "- So this trick only works if we normalize $h(t)$\n", "- It acts like an infinite amount of training with constant inputs\n", " - With more complex neuron models, there may be \"memory\" effects where the past history of the neuron doesn't end up averaging out like this\n", " - For those neuron models, there is no rate approximation anyway\n", " \n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- The filtered spiking neuron model gives some sort of variability around the ideal $a$ value\n", " - This can be treated as noise\n", " - We can find the variance of this noise (see Appendix C.1)\n", " - But we're already making sure decoders are robust to noise\n", " - So we don't have to do anything (except maybe slightly increase the amount of noise the decoders are supposed to be robust to)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" }, "livereveal": { "scroll": true, "start_slideshow_at": "selected" } }, "nbformat": 4, "nbformat_minor": 1 }