{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# SYDE 556/750: Simulating Neurobiological Systems\n", "\n", "Terry Stewart\n", "\n", "Accompanying readings: Chapters 4, 5\n", "\n", "\n", "## Temporal Representation\n", "\n", "- In the previous lecture, we covered basic representation\n", " - take a vector $x$ and convert it into a bunch of neural activity values $a_i$, and then convert 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", " - $a_i=G[\\alpha e \\cdot x + J^{bias}]$\n", " - $a_i(t)=G[\\alpha e \\cdot x(t) + J^{bias}]$\n", " - where $G[J]= {1 \\over {\\tau_{ref}-\\tau_{RC}ln(1-{1 \\over J})}}$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import syde556\n", "import numpy\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(syde556.lif(1.5*x+1))\n", "ylabel('firing rate (Hz)')\n", "xlabel('time (ms)')\n", "show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Unfortunately, that formula for $G[J]$ 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": {}, "source": [ "## Leaky Integrate-and-Fire neurons\n", "\n", "- Pretty much the standard 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", "\n", "\n", "\n", "\n", "\n", "\n", "- bilipid cell membrane acts as a capacitor\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", "- 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", "- 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/)\n", " \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The RC circuit\n", "\n", "- let's ignore the spike for now\n", "\n", "\n", "\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", " - $J_{input} = J_R+J_C$\n", "- Ohm's Law\n", " - Formula for current through a resistor\n", " - $J_R = {V \\over R}$\n", "- Capacitor\n", " - $C = {Q \\over V}$\n", " - $Q = C V$\n", " - ${{dQ} \\over {dt}} = C {{dV} \\over {dt}}$\n", " - $J_C = C {{dV} \\over {dt}}$\n", " \n", "$J_{input} = {V \\over R} + C {{dV} \\over {dt}}$\n", "\n", "${{dV} \\over {dt}} = {1 \\over C}[J_{input} - {V \\over R}]$\n", "\n", "${{dV} \\over {dt}} = {1 \\over {RC}}[R J_{input} - {V}]$\n", "\n", "${{dV} \\over {dt}} = {1 \\over {\\tau_{RC}}} [R J_{input} - {V}]$\n", "\n", "\n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- What does this look like?\n", "- If $J_{input}$ is constant (and we'll write it as $J$ for simplicity)\n", " - ${{dV} \\over {dt}} = {1 \\over {\\tau_{RC}}} [R J - {V}]$\n", " \n", " - $V(t) = JR(1-e^{-t/\\tau_{RC}})$\n", " \n", "- So how long does it take to get to threshold?\n", " - $V_{th} = JR(1-e^{-t_{th}/\\tau_{RC}})$\n", " - $t_{th} = -\\tau_{RC} ln (1-{V_{th} \\over {JR}})$\n", " \n", "- So how long between spikes?\n", " - $t_{th} + \\tau_{ref}$\n", " \n", "- Firing rate\n", " - $a = {1 \\over {t_{th} + \\tau_{ref}}}$ \n", " - $a = {1 \\over {\\tau_{ref}-\\tau_{RC}ln(1-{V_{th} \\over {JR}})}}$\n", "\n", "- Simplify by assuming $V_{th}=1$ and $R=1$\n", " - $a = {1 \\over {\\tau_{ref}-\\tau_{RC}ln(1-{1 \\over J})}}$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spikes\n", "\n", "- But we don't want constant $J$.\n", "- We want it to change over time (since $x(t)$ also changes over time)\n", "- So let's do a computer simulation of the differential equation\n", " - ${{dV} \\over {dt}} = {1 \\over {\\tau_{RC}}} [R J_{input} - {V}]$\n", " \n", " " ] }, { "cell_type": "code", "collapsed": false, "input": [ "import syde556\n", "reload(syde556)\n", "\n", "import numpy\n", "\n", "x = numpy.zeros(100)\n", "\n", "v, spikes = syde556.lif_spikes(1.5*x+2) \n", " \n", "figure()\n", "title('voltage and spikes over time')\n", "plot(v+spikes)\n", "vlines(numpy.where(spikes>0)[0], 0, 2)\n", "ylabel('firing rate (Hz)')\n", "xlabel('time (ms)')\n", "show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ZM9XP0l+wABgxAvD2tu18tdUXVpMIO3bsgK+vLypWrIgKFSqgQoUKqGhuOrCL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\nxVtBuuGRyrVueCX64IH45SY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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "import syde556\n", "reload(syde556)\n", "\n", "import numpy\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", "v, spikes = syde556.lif_spikes(1.5*x+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(syde556.lif(1.5*x+1))\n", "ylabel('firing rate (Hz)')\n", "xlabel('time (ms)')\n", "show()\n", "\n", "\n", "figure()\n", "title('voltage and spikes over time')\n", "plot(v+spikes)\n", "vlines(numpy.where(spikes>0)[0], 0, 2)\n", "ylabel('voltage')\n", "xlabel('time (ms)')\n", "show()\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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REQGtVmvxOQqFotXvZ05LSzP9rlarobbT+W0iDDoKBGKJwQB07cq7FUQkWq3W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\n5I4CoQm9HlAqebfiHqWS/zE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Zmbwcfvedssuighte6nb+PJ+yuW3bovy2/DU/LcjMBD75hN/DcPy49CNllEPe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\nePQIaNTIOjFZS2FbDllZvEu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CBCg5EEIIEfh/RitiPS8bT+cAAAAASUVORK5CYII=\n", "text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Let's try a sine wave input" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import syde556\n", "reload(syde556)\n", "\n", "import numpy\n", "\n", "dt = 0.001\n", "t = numpy.arange(600)*dt\n", "x = numpy.sin(10*t)\n", "\n", "alpha = 1.5\n", "bias = 2\n", "J = alpha*x+bias\n", "\n", "v, spikes = syde556.lif_spikes(J) \n", " \n", "figure(figsize=(8,4))\n", "plot(t, x, label='x')\n", "plot(t, v+spikes, label='v')\n", "vlines(dt*numpy.where(spikes>0)[0], 0, 2)\n", "ylabel('$x$')\n", "ylim(-1,2)\n", "xlabel('time (s)')\n", "legend(loc='lower left')\n", "\n", "show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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J9ZyP3FzRZL5kiajN7/NUY/EbACwHVX50QGHx0CALR4J7QhLspGuT7ltICMEGm74CYREh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\nw2JKnrEk/KZg0ici0gPNmok5/RcvAi+9JHqmr7wCnD0rOzLDUV4OrFs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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "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", " \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 coding\n", " - The important thing is the firing rate over some window of time (~100ms)\n", "- time coding\n", " - The *precise* pattern of spike generation carries information\n", "- We don't find this to be a useful distinction\n", " - Some people call what we do rate coding, some call it time coding\n", "- The important thing is how to do the decoding...\n" ] }, { "cell_type": "markdown", "metadata": {}, "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 $G[J]$\n", " - We get out a sequence of spikes\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 $e_2=-1$\n", " \n", " " ] }, { "cell_type": "code", "collapsed": false, "input": [ "import syde556\n", "\n", "import numpy\n", "\n", "dt = 0.001\n", "t = numpy.arange(600)*dt\n", "x = numpy.sin(10*t)\n", "\n", "alpha = 1.5\n", "bias = 2\n", "J1 = alpha*x+bias\n", "J2 = -alpha*x+bias\n", "\n", "v1, spikes1 = syde556.lif_spikes(J1) \n", "v2, spikes2 = syde556.lif_spikes(J2) \n", " \n", "figure(figsize=(8,4))\n", "plot(t, x, label='x')\n", "vlines(dt*numpy.where(spikes1>0)[0], 0, 1)\n", "vlines(dt*numpy.where(spikes2>0)[0], -1, 0)\n", "ylabel('$x$')\n", "ylim(-1,1)\n", "xlabel('time (s)')\n", "\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 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", "collapsed": false, "input": [ "import syde556\n", "\n", "import numpy\n", "\n", "dt = 0.001\n", "t = numpy.arange(600)*dt\n", "x = numpy.sin(10*t)\n", "\n", "alpha = 1.5\n", "bias = 2\n", "J1 = alpha*x+bias\n", "J2 = -alpha*x+bias\n", "\n", "v1, spikes1 = syde556.lif_spikes(J1) \n", "v2, spikes2 = syde556.lif_spikes(J2)\n", "\n", "A = numpy.array([spikes1, spikes2]).T\n", "d = syde556.decoders(A, x)\n", "\n", "xhat = numpy.dot(A, d)\n", "\n", " \n", "figure(figsize=(8,4))\n", "plot(t, x, label='x')\n", "plot(t, xhat, label='x')\n", "ylabel('$x$')\n", "ylim(-1,1)\n", "xlabel('time (s)')\n", "\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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rbrbeS3qzqV9PZT0X93R7/0bhDRb5fCR7eOPD7M2db7rZlv+ynA1a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\nCIIgwoT/B3Is8JPwKO9DAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- What if we add more neurons?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import syde556\n", "\n", "import numpy\n", "\n", "N = 50\n", "dt = 0.001\n", "t = numpy.arange(600)*dt\n", "x = numpy.sin(10*t)\n", "\n", "encoders = numpy.random.choice([-1, 1], N)\n", "intercepts = numpy.random.uniform(-0.9, 0.9, N)\n", "max_rates = numpy.random.uniform(100, 200, N)\n", "alpha, bias = syde556.find_alpha_and_bias(intercepts, max_rates)\n", "\n", "A = syde556.activity_spikes(x, encoders, alpha, bias)\n", "\n", "d = syde556.decoders(A, x)\n", "\n", "xhat = numpy.dot(A, d)\n", "\n", " \n", "figure(figsize=(8,4))\n", "imshow(A.T, extent=(0,0.6,-1,1), aspect='auto', interpolation='none', cmap='binary')\n", "plot(t, x, label='x')\n", "plot(t, xhat, label='x')\n", "ylabel('$x$')\n", "ylim(-1,1);\n", "xlabel('time (s)')\n", "\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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3vmmYaMo2obPUqSi1TMbDddcBhqGu0+91e+FwR/XRV+DDF+e/du61mHT5JKwp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vpz3z43qklixb0HyMmpSvd6jaUkR5QiWFW3eX50Xzj7wZ0+LbxUESztm8vnpEI7IfRi2TAMESAQ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\nYAlr1wI/ylIBGY7JebhCX0v8PXEK5GsNP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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "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's 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": {}, "source": [ "## Temporal filter\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", " - $h(t) = e^{-t^2 / {2\\sigma^2}}$\n", " " ] }, { "cell_type": "code", "collapsed": false, "input": [ "import syde556\n", "import numpy\n", "\n", "dt = 0.001\n", "sigma = 0.007\n", "t_h = numpy.arange(200)*dt-0.1\n", "h = numpy.exp(-t_h**2/(2*sigma*sigma))\n", "\n", "figure()\n", "plot(t_h, h)\n", "xlabel('t')\n", "ylabel('h(t)')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "t = numpy.arange(600)*dt\n", "x = numpy.sin(10*t)\n", "\n", "alpha = 1.5\n", "bias = 2\n", "J1 = alpha*x+bias\n", "J2 = -alpha*x+bias\n", "\n", "v1, spikes1 = syde556.lif_spikes(J1) \n", "v2, spikes2 = syde556.lif_spikes(J2)\n", "\n", "fspikes1 = numpy.convolve(spikes1, h, mode='same')\n", "fspikes2 = numpy.convolve(spikes2, h, mode='same')\n", "\n", "\n", "A = numpy.array([fspikes1, fspikes2]).T\n", "\n", "\n", "d = syde556.decoders(A, x)\n", "\n", "xhat = numpy.dot(A, d)\n", "\n", " \n", "figure(figsize=(8,4))\n", "plot(t, x)\n", "vlines(dt*numpy.where(spikes1>0)[0], 0, 1)\n", "vlines(dt*numpy.where(spikes2>0)[0], -1, 0)\n", "ylabel('$x$')\n", "ylim(-1,1)\n", "xlabel('time (s)')\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", "ylim(-1,1)\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", "ylim(-1,1)\n", "xlabel('time (s)')\n", "\n", "show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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kH3k10qzpeikp0LcvDB8OddMf9CuE0yheXJWV7t0bbt7UOxrjZTaYb2/sXup7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\nWYcI7UNm52n+/Pn4+/tTs2ZNGjduzKFDh3SI0j5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xhCgj3Vy70WbgLn7+Gfbu1TqNEKIo5fL0vqIofHfwe/6z5hPu2iZQ26469nb2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\nzHTqV61fptmk6AshzJpzDWd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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "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": {}, "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", "$\\hat{x}(t)=\\sum_i{a_i(t) * h(t) d_i}$\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", "\n", "$\\hat{x}(t)=r(t) * h(t)$\n", "\n", "\n", "\n", " \n" ] }, { "cell_type": "markdown", "metadata": {}, "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", "collapsed": false, "input": [ "import numpy\n", "x = numpy.random.uniform(-1,1,500)\n", "plot(numpy.arange(500)*0.001, x)\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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dvXpva50Y/7Zt2+yUU06xE0880WZnZ+0lL3mJfexjHxsLN0q1yretLfCPRnUF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\nrUjGP2mpxyzceMqAEH5hweyrX602gpBHzTvyj7j57VEe41dACrH32OZ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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Maybe that's a bit too random\n", "- Real signals don't change that quickly\n", " - how do we get a random signal that doesn't change quickly?\n", " - i.e. a signal with a limit on its maximum frequency?\n", " \n", "\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy\n", "import syde556\n", "x, X = syde556.generate_signal(T=1.0, dt=0.001, rms=0.5, limit=10, seed=4)\n", "plot(numpy.arange(1000)*0.001, x)\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- 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\n", " \n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy\n", "import syde556\n", "T = 1.0\n", "dt = 0.001\n", "x, X = syde556.generate_signal(T, dt, rms=0.5, limit=10, seed=3)\n", "freq = numpy.arange(1000)/T\n", "freq -= (T/dt)/2\n", "\n", "figure()\n", "plot(freq, np.abs(X))\n", "xlim(-500, 500)\n", "xlabel('freq (Hz)')\n", "ylabel('$|X(\\omega)|$')\n", "\n", "figure()\n", "plot(freq, np.abs(X))\n", "xlim(-50, 50)\n", "xlabel('freq (Hz)')\n", "ylabel('$|X(\\omega)|$')\n", "\n", "figure()\n", "plot(numpy.arange(1000)*0.001, x)\n", "xlabel('time (s)')\n", "ylabel('$x(t)$')\n", "show()\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Dh/DEE08gJSUFv/rVr5CRkYG6urqgF0sUTvqHBZERDKlbaenSpVi/fj0yMzPh9XpRUlKC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\nU+X1MzIycObMGQA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q0Y3z4YeBri7ghhuAP/1JXVtJnpDmnANFG8OBTCdaS1knTAA2bADuuUf6xO90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\n7/f+fOTIEfzwhz+Ey+VCcnI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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "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 need to constrain $X(\\omega)$\n", " - This constraint is that $X(\\omega)=X(-\\omega)^*$\n", " - (the complex conjugate: the real parts are equal, and the imaginary parts switch sign)\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "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)\n", " - $E = (X(\\omega)-R(\\omega)H(\\omega))^2$ (added up over all time)\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": {}, "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", " - but we're already using $A$ for the matrix for activities of neurons so let's avoid re-using the letter\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy\n", "import syde556\n", "T = 1.0\n", "dt = 0.001\n", "x, X = syde556.generate_signal(T, dt, rms=0.3, limit=10, seed=3)\n", "t = numpy.arange(int(T/dt))*dt\n", "freq = numpy.arange(int(T/dt))/T - (T/dt)/2\n", "omega = freq*2*numpy.pi\n", "\n", "plot(t,x)\n", "xlabel('t')\n", "ylabel('$x$')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 27 }, { "cell_type": "code", "collapsed": false, "input": [ "alpha = 1.5\n", "bias = 2\n", "J1 = alpha*x+bias\n", "J2 = -alpha*x+bias\n", "\n", "v1, spikes1 = syde556.lif_spikes(J1) \n", "v2, spikes2 = syde556.lif_spikes(J2)\n", "\n", "r = spikes1 - spikes2\n", "\n", "plot(t, r)\n", "plot(t,x)\n", "xlabel('t')\n", "ylabel('$r$')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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JLFy4kIULF7psW7ZsWdfnO+64gzvuuMPvfohII7hl9CW6pqea9d095Yw0Kk2MNLwdG1uD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\nNJxEWqIYlT6K3ZW7PRumHyDdMtK3ygy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"text": [ "" ] } ], "prompt_number": 32 }, { "cell_type": "code", "collapsed": false, "input": [ "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", "\n", "figure()\n", "plot(omega, np.abs(R))\n", "xlabel('$\\omega$')\n", "ylabel('$|R(\\omega)|$')\n", "\n", "\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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dClx4Yfq1QYnGrl3yIe4y+666yjwMykZd1RTRoD6NgDFZlluG6oFYu9be90KH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\nhBOAU0+1XzuJhi5tMTxVr156qxqwR2J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"text": [ "" ] } ], "prompt_number": 31 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Now we can find our optimal filter\n", "\n", " $H(\\omega)= {{X(\\omega)R^*(\\omega)} \\over {|R(\\omega)|^2}}$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "H = (X*R.conjugate()) / (R*R.conjugate())\n", "h = np.fft.fftshift(np.fft.ifft(np.fft.ifftshift(H))).real\n", "\n", "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", "show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "fspikes1 = numpy.convolve(spikes1, h, mode='same')\n", "fspikes2 = numpy.convolve(spikes2, h, mode='same')\n", "\n", "A = numpy.array([fspikes1, fspikes2]).T\n", "\n", "d = syde556.decoders(A, x)\n", "\n", "xhat = numpy.dot(A, d)\n", "\n", "figure()\n", "plot(t, x)\n", "plot(t, xhat)\n", "show()\n", "print 'RMSE:', numpy.average((x-xhat)**2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ukeWeGzdKkteTcVJxQ7Es1zthyf8dkkL/d5Rs14u9/gXp+ncfke16cnnssd6v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\noaOBP3z3h9Nea+1q5c7P7+TTI5/yeU4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"text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "RMSE: 0.00133916386085\n" ] } ], "prompt_number": 19 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Testing how well it generalizes\n", "\n", "- if it's a good decoder, it should work for other inputs too\n", "\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "y, Y = syde556.generate_signal(T, dt, rms=0.3, limit=10, seed=1)\n", "\n", "J1y = alpha*y+bias\n", "J2y = -alpha*y+bias\n", "\n", "v1y, spikes1y = syde556.lif_spikes(J1y) \n", "v2y, spikes2y = syde556.lif_spikes(J2y)\n", "\n", "fspikes1y = numpy.convolve(spikes1y, h, mode='same')\n", "fspikes2y = numpy.convolve(spikes2y, h, mode='same')\n", "\n", "Ay = numpy.array([fspikes1y, fspikes2y]).T\n", "\n", "yhat = numpy.dot(Ay, d)\n", "\n", "figure()\n", "plot(t, y)\n", "plot(t, yhat)\n", "show()\n", "print 'RMSE:', numpy.average((y-yhat)**2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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kYk6+Tt4U1w6PHn9qcSpXj7qfu9ZoV0rNzIQ779T+d4r/FJ7bY9ox/gZRxuhR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\nVFKLU3VqfzS3BDuNp0HDX30V6BxIQX0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"text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "RMSE: 0.00524624605476\n" ] } ], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- It's 5x worse on a different signal\n", "- Not bad, but could use some improvement" ] }, { "cell_type": "markdown", "metadata": {}, "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", "collapsed": false, "input": [ "x2 = numpy.zeros_like(x)\n", "r2 = numpy.zeros_like(r)\n", "\n", "x2[400:600] = x[100:300]\n", "r2[400:600] = r[100:300]\n", "\n", "figure()\n", "plot(t, x)\n", "plot(t, r)\n", "vlines(0.1, -1.5, 1.5, linewidth=3)\n", "vlines(0.3, -1.5, 1.5, linewidth=3)\n", "\n", "figure()\n", "plot(t, x2)\n", "plot(t, r2)\n", "show()\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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0NTc5ki/cFQ4GpprvcPlhAMC2c9tQU1/j08fKukoAwPJNaxE/A/gmvxMOlBzw\nOs79JeLXVzae3ij6IYcBiBLreCN7LUYOVz/2iLAINDU3oZk1e/2vdjxq/0vbAHDxykVsLVmLuXHA\n+pOinOoa6jz9BYCoCcCK/UBsLrzKy+uToybvS9cuAQB2Fu5EecMGnAlvxLGyg+K+gp240nAF5bXl\nHnlJstpduNszzqSxtbd4LwBgX/E+RHWKQn1TPSL6FOIagHUn1iEyPNIzXuWy0pKLdP4OlR3C2ty1\n2PED0Hk0PHKSy6TqahXW5q7FyQsnAQCbz2xGQ3MDAOB45XGszV3raW9t7locqxSfzrfmbUXBpQJU\nXRUn9Dee3ohrjddw8cpFT14A+KHsB3H7xFr0iewDAEibcRDbG8QytfWtsavnr5z3KguIPm6X4PKS\nmfxY9xTvAVpklV/VOoMtjYuymjKv63F3oahrDpYe9KnrfN15rM1d6znvpy+eBgBsOr0Jfbv2Refw\nzjhacRQAcLTiqE/5ZtbsKV9eDnx9UJTVXz7IRkL3fAxN7IxOfcWXGU5dOOVVXn5N1jbU+pxLSb4A\ncKVRXDFxf+l+L1mdrSgFANz62yxMn9GA7GJ4xtfG0xvRObwzWA+G8bcOgBUEZsOf8fnnnyMrKwtv\ntrxH/+GHH2L37t14WXrrBsBtt92GJ554AjfeeCMA4JZbbsHzzz+P8ePHe3dEEBA2NgUxMUC3bkCf\nkX3Qd2TrsgFfnvgSDAzXx12PmO4xaGhqwFenv0JCjwSMGTAGgDhgAODWYbcCEE/e+pPrxX4Muw0M\nDMXVxdhfsh/jY8cjTAjDgO4DsK9kH4qri4ETABhw/fTrsad4DwZ0H4AJcRNQUVuB3UW7kd4/HYN7\nDcahskM4d+kcZg6diepr1dhZuBOj+o3CkN5DvPpwtOIozlw8g5uH3Iz6pnpsO7cNqX1TkRyd7JUv\ntzIXJy+cxE2Db4IgCMjOy0ZydDJS+6Z65Tt14RSOVx7HlEFT0DmsMzaf3YwhvYagX7d+qK2vxZGK\nI5gcPxl9uvZBXlUeDpcfxsSBE+ESXLhc2hc1dY041ykLADBx4ET079bfI9+iy0U4UHoAcVFxKN5b\nLO7snoTEIb2QVy/KKy4qDiXVJdhXsg9jB4xFfI94rDuxDj0698C0wdOw7sQ6dI3oirT+acgpykF6\n/3RcunbJI6vcylzkX8pHZlImahtqsaNgB0b2G4mk3km4eOUithdsBwBkJGRiW3ZnzJ4NrDspHv+M\nITMQGdEfVmpkAAAgAElEQVT6nYDqamDPHuDmm8XtmvoaL7kpkcvxauNVfH3mayT2SkRa/zSU1ZR5\nlM7spFsRHg6U15Z75MMYQ0VdhWdbnlZWU4YB3Qd4rNSymjIUXi5ESU0J5qXMw84dLvRLKkE1ilFc\nXYy5KXPhElxYd2IdunfqjozEDBwsPYiCywWYNXQWLl27hF2Fu5DWPw2JvRKx5ewW1DbUesb06dNA\nUf0RXA47i+tir0NsVCwA4NLVS+gc3hldwrt4+hHTPcbn/7qGOjSzZnTv1N0n7VrjNVy4cgH7SvYh\nqXcSUqJTUFNfg96RrW9xy/sNiCHCG06Lsp00cBL6desHQFRSpTWlnusVAHYU7MCFKxcwIW4CYrvH\noqi6yHMtxkXFca9h+bmZlzIPgiCgvLbcM766hHdBTPcYVNZVeuQW1SkKPbv0RLgr3Ks+6Vjl12X1\ntWrEdI/B5WuX8W3+txjWZxj6R8ah6qKA6gvdkN9ZLN/v4q1AtzJ0ZTG4iFO43Pk4IkqmoHe/a0hL\njIEQccVzPY7qPwplNWXo1aUXNp3ZhME9ByM9Jh1NzU0ory3HvpJ9GNRzEEbHiHdw6VqN7xGPsQPG\nouoikLMHqE/0loVHHtv3oFtxN8RFxSGhRwK+efcb825pZoOdO3eyWbNmebafffZZtnTpUq88ixYt\nYitWrPBsDx8+nJWWlvrUBYBt385Y//6MlZT4tpX2ShqDu7W7l65eYnCD/Xr1rz37Mt7N8MrT0NTA\n4Aa7+/O7Pfs+PfIpgxvsn4f/6dn3i89/weAGgwsMAPvyxJcMbrCcwhzGGGMbT21kcIO9ue9Nxhhj\n/7b23xjcYJW1lWxr3lYGN9jLu18Wj8MNNujvgxhjjP3+q98zuMHyq/LZvuJ9DG6wpd8t9eTr8nQX\nxhhji7csZnCDHS0/yo5XHGdwg/35mz8zxhjr/mx3zzE9v+15BjfYnqI9rOBSAYMb7D+y/oMxxthL\nu15icIN9l/8dY4yxV/e8yuAG++bMN4wxxu6+m7FX3rrM4AZ7YPUDPvKtb6xncEOUBdDy9yd2+5Pe\n8lp1bBWDG+yjQx95juPm9272/D/l7Snsq1NfeeS1aO0iBjfYhboL7OF1DzO4wcprytm2/G0MbrB/\n7PoHY4yxXQW7GNxgf93xV5adzdjkycxTZ9SzUT79bWxkrHt3xi5eFLdPVJ5gcIP9cfMfffIyxljc\nX+M8ciy+XMzgBnts/WOe9BEveY8vO/z805976rrrLsY++ICxX678JYMb7FrjNc9xTXtnGmOMsV+v\n/jWDG+zS1Uts85nNDG6w1/a8xhhjbMFnC7z69ZvfMHbTs79jcIMVXip0pL9y8qvyGdxgv//q99x0\nuMEWfLbAa99PnnmDwQ226fQmz77dhbsZ3OK1JDH7w9lex/LJ4U8Y3GCfHvnUq/6kfyR5ttflrmNw\ng73//fueffLxJfHF91sY3GBp973CEhMZ691b/IMbrPMfBrOFCxlzuxl77z3G7nr7PxncYAfzz7LS\nUsa+/56xF94/yOAGi1vwNOvenbGZMxl74QXGXG6Xz7hY+t1SBjfYF7v3sf/6L8aioxn75cPe1yNj\njJXVlDG4wR798lHPvgt1FxjcYIvWLvLsq7lWw+AGu++L+9i33zLWrx9ja9cyNufDOdwxCTfYHZ/c\n0bptQY3b8vFPmDABJ0+eRF5eHurr6/HJJ59g/vz5Xnnmz5+P998XF/fYtWsXevXqxXXzAKJP99e/\nBh5+WN/fL816a4VpevLIZsh55ZR1KPN4fjn7eW0o6xUgaPZXnqZsy2h9Pn1UpO/dC1w33kDdXv07\niqJC7fp5yPNwj41znPLtH34A0tNVqwcgrkw5Zgw83wjWkpuRY61v0C1mCeUqnXbGCSBG9PTooT/2\nrWLkulIyPUPMe/o05zozOE5U83DOlbzc1avAn/4E/OpX4r4bJgnYuFH8pOhJ0eOFXr3EOaH6euCr\nr4Ct2WLeG38kID0d+MUvgPXrxX3z5gqorBTz/f73AK9rUl8GJQh49lmxHZdL3Hf8uODRXVq6xksn\ntewrKRbwk58AH30E3Npq5PsFW4o/PDwcy5cvx6xZszBy5EjceeedGDFiBF5//XW8/vrrAIC5c+ci\nKSkJycnJWLRoEV555RXNOv/8ZzFa49NPtds2cqFzBw1P8NL/DD755ek85cdXmL7lrCp0o/Vp3Qgu\nXQKKioDhwwzU7dW/Uygt1a6fh5qCV7shKOs/fFhf8QPAddfJFL8JhcU71gY/Kf6EBKCgQFtuRscJ\nIE7u9upp/CZnFkPXlSItsou4/fprMqVncpyo1c813lryFxUJmDBB1Bf/+6a4b8J1AlJSxE+K9hGn\nIdCli2hQPvOMqFTvablJHDkioLwcOHwYeOkf4r4hiYInakrv+KV+REcDzz0r/p+TI2DuXPEGraVr\neDey7GwBK1eKb6f7G9sfW58zZw7mzJnjtW/RokVe28uXLzdcX5cu4jogd9wBzJwp3q15BMTi11BO\nAOASXJ7JqmC2+PftA8aOBSIiDNTt1b/TKCvl1y8dNw+5TOT98Ow3YPEvWKBavYfx44GsLEX/DShD\neT8kGur127NCfDzw9ddAb+6NFV790LohSuTnA9OCzOKX8lZWCMjKAuTqwOg40aubpyhffMGFl34P\nLFwIbDtn4sZvUCFbKX/PPQL67heNkt89qa5rpPyMAS+8IP4/a6aAqVN1m3eEoHxzd/Jk8VX9J59U\nzyMNGvnAUg4g3qDhlfP8z+CTxivjpcA0FKE8P69dJ/Np/Urx+zyFJ8E/jlp07apy7AYsQmU/eTdM\n3+M1Z/Hv2weVetSR90PC364eq+dVfq6qqsSX1iIj9c+BVYzIUc1QWrTIhccfF79BYMbVo2yLd73K\n69m9W9z36CMC7r0XEARz519LB9gtHxHmwn/9F7BjB7B+fUsEU4HL8yQkL3v4sLj8yLp14rHF9A+c\nOg5KxQ8Azz0HfPGFGM8NaCh1k4Nf09WjzKNhlUq/ej5IKc2IlaFn8Vl19UiKX+tiVJNn7ADt+nl9\ntOPqqaoSxKiuPj5d9CE1VXRhXbqkb7HpuQ+cdPXI6/W4ejj9MzJO5HXl54sx/C7OOXCs7xZcPVKZ\nKTcK6NsXeOMN3zStcoZcPS15cnKAZcvE/1NT1S1pXjtqdWqV59ZnoPywYcDaNeL/2dkCUlOBRx4B\n/vqiuO/zzwXMmAHMnw9kb7H+lGWVoFX8vXoBf/sbsGiReFEqX+rgCd/Iix9GyundZLwUG+cCVa7x\noubq8eTTuPDlfbPq6tnf8ujJs3SVKGURF6tdv7IMA1NV8Go3BHn95WUujByp3SeJ8HDxyeDQIX2F\nxZWjn1w98rb69xct9aYm9XxGXYJ5eUBiorql7ARGXB7KtFYrVsD//A+weDFQeV57nHi1pXK9yf8X\nIOD0aeD224En/lPfiNLCjKuHN/aMlg9rmfBdeI+ADz8EkpOB6mpx34QJAgoKgH//d6BTBP8Jzp8v\nkAat4geAO+8UX8//7//2TbNi8W/YADzzjJj/6acFfPcdP5+uNS1XbBrWl57Fz2tPawBbsfhragSU\nlooWiJmLQyI2Vrt+HnYs/ooKcXLOKOnpwA8/mLzwOQrHX64el0scw1pvQGueV9nxSG/tWn3aNYKV\nuuV9HTUK+Nd/Bf76ond9mm1p5Wmpu6bahTlzxJvKjTfqW9xymHKxNI5szRy30fKthpaA668Hfvc7\n4C9PifuShgjo1Em9Pj2Ux2SWoFb8ggC88gqwbJmvRWZGWA0NwD33iGuLTJ4s5p88WcCddwL/+7+c\ndvWsaR2Lv7X/9hW60frUbgSnTgoYM0YMf7RyUccasPhVj0fRTyMWf0W5gORkfn08PIrfzIWrkFld\nHdDMscidIiEBqNX4IIvRcZKfDy+L3y+uHgt1K2X/pz8Bx46aGyd6dS9bJuBnPxM9ALxy/rL47ZQ3\ne4PwefLxw41dIqgVPwAkJQH/7/8BRcXe+81c6F9vEn/37wcybxHzz7xFwNatogVRXMSv27OtYp22\nB4v/RK6AceP4x2GEgXHa9fOwZfGXB97iz88HIjoZb9Ms4vLMBvqjM06CxeJXU1BS2chI4KkWy/bC\nBWPjRK3+5mbx/9hYAU8/rV7OHxa73fJ2bhD+JugVPyAqfisWv/TZvuho8aPd3bp5l0tJAd5/H/hO\nsdiXqjJVbLeHcM7cXAHS6hhWFEZcnJTXu6y/wjnLLSj+w4d9+6eFMmImLw/oFKFRwCbit3fV0zXP\nq+x42ovFD8BjbCx9zqW6fLZehBhjwPKXxbRHHhYgdYk3Bjuixe9P2oXi79RJ/HIUIEZwAPrhnBcv\niu8BAMCkSaKvlVduxozWuiU6Ujhn7nFXq+K3cFH36C7WU1MdmHDOC+cFJCUZ7h769hUtzJJi6+Gc\n/rb4ExKA2hr1dKPhnJLFb+QcWMVOOCfvWrx2TcCSJSr1qFw7Uv1/+Qtw5HBLmGR4a5u84w+WcE4r\n+9qCdqH4AaBbN/Ek3323GCGhdZe8cEGMj21ZFw7yLLxy0lIGQIx3HjXfvsy65D52cp4YjFgJehaf\nFVdPcZHgiZKx9Bgv873z6uf10Y6rp2dP/TcnlaSni6/KK/uldlxKmTlt8StlqPYlLiPjRPqtrha/\nStavH/8cONZ3G2OE15+n/yLggw/EJ2uj5QSI0UHvvw+8+KKG1WzQVaPnutUqz63PhiWv+eRv4SnL\nKu1G8UuhTVeuAI89xl/LR8pzyy3A9OliOKgSnuAju0qVPeqVx1NG7QYgeCszZT/0XD2BCOccMqQ1\nesAIaiF3ZWX8+pVl7IZz8l5i0QtrS08Hjh/TVlha4Zx5ec5a/Mr+iq4e/Y99AOqKwePmEdQtZScw\n8lSoTONZ4FKePtEC1q0DHn8cKCkxFs55/ryAF18ENm4Uy/vUzSnnL1ePnXBOMzcYQP1bIv6g3Sh+\niZUrgQMHgLs46/ZfaPkowU9/CrzwAsAbA9oWzSIAXfStabli07B29Cx+Xp80LQIDlqGyP/KXXKwg\n973z6tcqY8Xij+lvvr/p6cCxY/r98vRPIbO8PJi6OZpFL6pH7eYu35Z/gMWfPmErdetZsSNHAps2\nAdLH+SSfv3IsSTK6VCV+ZCcpiX+TM2vxt3U4p9UblBYdOpyTR69e4ton0pudWVlifOzEia2r8T35\nJF/pA3qCPwDgX/StaR2L39OWAwrdaH1qNwLbir+lHi2LX62MJYs/Rl0+aqSnGwsf9NSnkFl+vn8n\nd/v3B67xvw/jg57Fr5XHCazUrangWn5HjwZuaPmU5tSp4js1jY1iWl2dgLfeAtLSxPQhSa3zblqu\nxUBY/HbKa90gjOCPG7tEu1P8gPgpsv/5H/H/uIHio/QzzwATJ+mX1b6zvwvgXl2foHzgGVn/pi0t\n/pFOWfxl3vUaiurRcAmoybRvX/P9HTkSOHPa+IUr78eVK2IgQLjt5QrVCQtr/Wi8HmrjJJgsfmWa\nloKTj5PIlu/oPPKIGEb949vFtJ/9VMCqVaJPH2h949Wrbo4lzX0KMHLj1+ivvy3+YKFdKn45o9PF\ncM/MTHUrX472rPoqABNRWeHts1QrI1fAwRbV09wk/g4fbu8US/WVlahHmyhRk4lcnmr97mdB8UdG\nAvEDTUT1yPpx7pzoivH3tdmtm7F8PlE9aH0qkSx+I+fAKoaiepSKX+Ma4PXx7rvFNXdWrRTT1n/p\nwrp18KxMKS/DO1atfcEe1RMsBF+PVFC7a/IerYzUwy93FcDn2LSJP7A1H+c0HvvULHmeta5myevV\npyxXWCD+do00pxzUrDktV4/yfy9XD88q0nD1WFH8ADBypLZ1xZWjIHjWv3ESXh+kqDRePr2xAygs\nfk45pzDi8lB9IuYdh8o4AVrX8Q8P49cnb8to3WrzDLxtI+X1ntC1yht5etfqpxZ2b/rtRvGrzXDL\nJzkMLdLGOWne5VYiO5t/8Unb8jZ5Pkgj0Tpe+TQUutfEn4EbhLT/7FlrysEnqqelvuYmAVVV2scr\n/S/PozYJpexv9WXxN6q7+ageABg1SlthceUIwUuhOgWvv926GozqURlzXj5+A+42q1hxT2i6O1XG\niVdbWjcZnkLl+f395OoxGnnlhKuHonr8iL5F8w3OnOJffNy7tIb15YTv3mh9ynJnz+hfVEaQ6ouJ\nEcSvChmwNg3lUfS3qEhSZtb6mzZKv02ftgUBp07BZ20gf9Ctu7F8auPk0iVA+mKpEavcKlbqtqr0\nrIwTtXJm+m3G4vdH+WAg9BS/7oCsx+QfeacZeYz0l0I3Wp+ynPT9U7vuAKm+2AGC9+fkDLgClHm8\nnpQU/ZUUv9ULJz3dxIUrk9nJkzC1RIRVumlM7mqGc7b8DhrU+va5PycNzShs5bYRNwu3LRVXjLzu\n9hjOqYVdaz7kwjntYuTOfPN0bWtaTjCu1VNfD+TlOWvxDxggukV4F6ISQ8s6KC3+Qo3jNnAxJQ4W\n81ypM26xAQiY4u8eZSyf2jhJTNTP4wSOWfxOjxO9m0EHtPj9cWOXCD3Fb+DOPKVlvW/phRKjSlsr\nLZAW/6FDvl/OsoqqxW/AIjRiyXks/kJ7F44UAlhcYrw8Y8CZM8DQoZaaNEWUUcWvIl+5O6rNLX7l\nebVoAauOE55ChXbdgbTYnbD425qQU/xGQqx6RIlpu3cLumW0Jtr8Gc6pHHzytN27gWEpzoSSSeVj\nB7iQn28vnJNXr/RbWKBv/RnpZ0mR8eO9dFlcudVoqKUdpDeDL17Uzqe2SJv85uRPiz8Q4Zx65eRl\n2ks4p5EnnGCiffQS6gqBZ0UaqUernLS9bZt3G1pltR771Cx5nrWuZsn71KfSJwECcnKA4cOtKQc1\nWcTGert6eMfrc6yyfvq0o+h/oU2LX/nk4JPOGRvnK80tAW24L5y2pEnrs2d98+mNHUCh+P04gWjk\npqJq8etZ6ipjS22/vC2jdRuZZzDjqtF7QvfZZ3CeQ6teI9gdA+1G8QcunLM1z7bv+Mo1GMI5fY5L\nlrZ7N5A63Lc9I6jJIi5WfXLXiXBO6b0DnsVk5lvK0iSxkToqzzO/KH5eW5Ic5IrfTDin3NVjd2JP\nCysuCwrnlOXnnBuj54vCOf2IIYumJc+VK+IHnjX98ypWi5l2rcwFqKVduiSgqAgYPNieBa3sW3S0\ngJoa4OoV/eM1IhP5sVRXi+u265XR7Kdk8RcJqh/+UHK+MjChnHLkip+Hr5Eh7jfzjYJAY9Xnbnac\naJUz4/7yx+RueyP0FL+JyaspNwJffaU9KLSsHa0wPbU+Gb1BKNuQ0n44JH5xS3ob0u7gbPXDChg0\nCCgtVbfMJQzNA8iOJT8fiB9o70Yl1de9m3izNkLl+cBE9MjhKX6tcVLXEqVkdK2fQKDqstG4Pnio\njROeO5QXzml0rR7Vp04HnxjMQuGcAcaMxT91qiAqfotWuNF2nbT49+0TcMMNzgxOZd8GDQLKSg3I\nz8TNVYA4d5CQoP9UpdnPlvoS4sWoJiNUVADDhxvL6xRmLX7pi3PBjFUL2tQ44c2N6ewzQzBa/P6s\nP+QUv5HZeyntxilAdjbQ2KAR1cOxSMy2ayWqRy1t9y4XbrrJuQWi5PWIFr+B2GsDMpHXm58PJMTb\nW3hMqi8h3oWDB42VuVQFDBtmqTnL6Cl+5XmTlrIIJtQmQI1a4FrllGV4sf5a+6yOd7tRPe2NdtNz\ntQFkOqpHwzpR5ukbLSA5GTh40Nsa0J1o4vkgDVhFPFePnhWlbOvAfgE33mjdKlGThQABgwcDJcXq\nffAcg0wmaopcfix5ecCgQfasKKlcYqKAvXvV0+X06SMgwg/r8Gs9keXltfrtjYyTy5fU6/InRp6I\nlXn1JneNltO17k1O7qrdqLh9UfZR4wlU73g19xnopxZ2x4BlxX/hwgVkZmZi2LBhmDlzJqqqqrj5\nEhMTMXr0aIwbNw4TJ0603FHHono4J03tc4OAuNzzju3eg4K79ADU69NrV8vVY3aeIClJQM+e1h99\n1WQhuXpKS7SPV/npRT3/quTqGZSg/pRgJlpraJIYzqpslldHzAD/RE1oRfVERQGlper5jLh6/BnV\nY6QN5ZjiWeBGrgu1yV3DBpOOUWQGtfJGP73oyd/Ro3qWLl2KzMxMnDhxAjNmzMDSpUu5+QRBQHZ2\nNg4cOICcnBzLHXUKs37FW26RhXVq3M31Bpy/JneVaZNvUH9isILS4i/mWPyqZUxM7nosfpuWTO/e\nQOfOomWth7ToWSAZMkTb3aM8b5c4Fn+wYdYCVqYZHSda5eyO90BP7rY1lhX/mjVrsHDhQgDAwoUL\n8cUXX6jmDYSFYhQzk7sCBEyZAhw/rj4ojKw3oteuk5O7N9zgncfpyd2SEnXLXMLsWj35+a0WvxMT\nWtdfL37oQ4+Y/rabMs2QIeIyEWrI5c1YO57cFZwfJ5598K27I07u+hPLir+srAwxLSZTTEwMysrK\nuPlEq/kWTJgwAW+++abV5hzDjMUPAF26ANeNt2aFWwnn1Ow7py2pjYZ6cd/UKf6z+OPjgYpyA/Iz\ncXOtrxfEJYf7O3OjYmCYOFFb8Ut2SNxAW01ZYvhw4MQJRX9UxklRERARHnzKRc01Y9SXrVeO5+PX\nmzg2434x674x2m8ztHU4p+aXRjMzM1EqOSRlPPPMM17bWpN427dvR2xsLCoqKpCZmYnU1FRMlb6x\npsDtdnv+z8jIQEZGhk73zWPK4m/JM2WqgO+uOq+0zfRJr61DP4j7onv7z+Lv3Bno1VNAhU69Zm6u\n5yvFG0qYxnsHZm9eEycCS5aopxcUiL89e5qq1hFSU4FVqwCM4qfL5X30qLiWUF3gumcJo4EIRsqp\n5tGb8O2AFr9q/WeBo4ePwn3UbbluTcW/adMm1bSYmBiUlpZiwIABKCkpQf/+/Ofm2NhYAEC/fv3w\n4x//GDk5OYYUv78wE84pkTHNhec2+i+c0yhadezNcQFRvnmcDOcEgLhYl6j4DVhyRmRcUSGGiRp5\n6csoEycCBw4AV6+KT2xKpKeBtrClU1OB3FyoKn65vI8eBXr3FlAYuO4ZQi1KhsI5A8QQYOSIkXD/\n3A0AWKJl5ahguefz58/He++9BwB47733cPvtt/vkqaurQ3V1NQCgtrYWGzduRHp6utUmHcGUldGS\nZ1TL91yl785y8+o85jphJWhZOtJKosr+OOnqAYC4OBOWnIGnqopyce5A62Zh5rFYgIAePYBRo4Bd\nu/h52jLGYNgw8RsActTGydGjYshpsKEcU0bX6lFLM+LqsTO5q3aj4vYlQK4eI+1ojXu7BpJlxf/E\nE09g06ZNGDZsGL755hs88cQTAIDi4mLMmzcPAFBaWoqpU6di7NixmDRpEm699VbMnDnTVoftYsXV\nI7kh9u7RcNPYcPUYRW1w5ua2foBE2R8nXT0AMDBO/3iNyESqr1xS/A4/Pt98M/DNN/w0tRtCIOjW\nDejXTz1dLu9jx0RXT7Cj6epxaJzo1d0RXT3+RNPVo0V0dDS+/vprn/1xcXH48ssvAQBJSUn4/vvv\nrffOD5id3JXnzckRgIe88xp1UfjL4geATz4BMjIErJS340+L/5Jza/WUlwmYMt65G5XEzTcDbjfw\n1FPe+2trgf37AcxwpBlLpKYC51TSPMfPBBw5AoyIFoCigHXNEGrXB+/cWVqrR0eh8yKGKJzTHO3m\nzV2nMGXxK/Lu2eO78qMTk7tG4bXFAKxYAcy4OcAWv4VJO55Lo7zMPxb/lCnA0aOAMtjsu++A665z\npAnLpKaqp0nHX1UlQBCAyCBanE0NzSgbpyZ39W4GAVTGHcHiDz3Fb8Pi7xEl+KwDozXgjIZzGoXX\n1rlzDFevAmmjFJa+nyz++HgTj/AKmfC+LVBW5u3jdyKcEwAiI4F584DPPvNOX70amDPHVhO2US4M\nxxsnZ88IGDkScAWhclG7obfncE4zODFW2zqcM/QUvxmLX6FEJ04UoPRutbXFv3078G//BrhcwW/x\n8/KUlwlISNAuY/Xm9fOfAx9/7L3v88+BO++0VJ1jjFKJ6AFajzU3V8C4cQHqkE06QjinGdo8nNMB\nQk7xWwnnlLYnT3JBGeFqNJzTicHC6/vhw8ADD6iHcTodztm7l/hbU61/4zQi4y5dXOjWzdlwTonZ\ns8WlG/bsad03ahQwZIhjTVhi7Fjxl2e0SXLIPe7CddcFpx+5I4ZzWiEYz41RQk7xW/ErSr/XXy9g\n506gsYmT1+RjrhV4Vs2ECQL69lV/SnHa1SM9WUhLN2iWMfBU5XljV+NmYTacU6JTJ+DPfwYefhho\nahT3/fnPhqvyG9KLY1da3sziuSyOHxNExd8OXD0dIZzTDE6ck3YbztlesePq6RElIC0NKCxozWt0\nrR6nOX5c/M28RfxVu1k57eqRtktLnFmDZUCMszcqJQ8+KE7mlpWL2zff7Gj1tqiu8d3niXYqFzQn\ngYMJLVdPe1mrJ9QIPcVvY3JXEARkZnqvrtgWA+7qVeCXvxT/j4ri98NfFr+0La3SyS2jIhPexTtg\ngLM3Kp++CMBrrwFxcY5W6wg1PMXfcvwpyQLCw4NTkZkJ57Q0ucsZJ3rWfUeItAkkoaf4zVj8HGs3\nMxM4I1f8bTDgfvIT34+EB9riL9FS/CZurv62+IOZ6su++6TjHze+/cgh1MI5OwKhp/htWvw33ABc\nvMhPU2I2ZGvvXqDlBWg8/wJw771A/TVx+913gf/9X/H/QYOADz7wbiPQFn9RkXlLjhfOKVn8vDxW\n8OfHK5ympla0+nnhnBOvD94bYaiHczoxxiicM8CYieqRBpO8TEQEMDSpNa8yjxWkj5fdcYc4IQmI\nvvtp0wBpHG/eDEhNvPYafD4ZGKioHum3WEvxG5CJlBY7QL9/waj8nCAqSnyhTE79NVEe140L3ktT\nTVGb9bmrjRNuBI9gbF97/g6uEgrndBAzrh7PtsKaGJ7qm9dq/HlubmukycmTrUsMjBsH3H9/643g\ng5kTlo8AABBzSURBVA+AB+7XP55AuXoM+fgNPFXFDtDvn9WonmCnVy9xPSF5n3fsEP/v3j14XReq\nUT0mfe5q40TXn88pp/nUQVE9PoSe4rcRzintTx4q5rt0iW99GIUxMcrkJ3eI25KSt0KgXT2V5S40\nNPDLGJHJ1avib5++ivbakeK2S3RvYM0aeF3eX6zij71gRkvpOrWmE+9m4ORaPaFG6Cl+Exa/mhKV\nFPS6dfYGXP014A9/AKZnmC6qi78t/n79xC9EccuoyES+XdiyyLwrhK/TqCigqal1PaErV4BVq5w5\nb4HE6ASskXJW66bJXXOEnuK3ObkrR7kOjFlcLuCxx+zVoYa/Lf6BAwWcU1li0shFqFY2pBCAf/1X\nYG/Lm8Vvv+07qRuMiozCOds/oaf4zVj8KtauxJYtQEWF+T5I68dE2HDt6OFviz9+oPiRdG4ZAxch\nKX6RRx8FSlssfrcb+Mtfglfhq0HhnO2P0FP8Dlr88+cDH36o3hZvcqa83FkrX20CyN8Wf7wFi1/e\nV7WywRBqF0i6dgV+9jOxzx9/DIwdE/w+fgrnpHDOdofdcE45DzwAvPWWufaXPQ/8x3+YK2MH27P/\nKuGcAw1Y/FoyNmPxB6Pyc5IePcTfGTP4ii7YCMZwzo4IhXM6iBPhnBLTpomTc0brAQAw4PHHDXbW\nAGqDw6lBo+bqGZTgUlXeRtZgMaP4O2o4pwTPclXbDgbMhHNaWavHaDin0ZsjhXP6EnqK34FwztZ8\nwH/+p7F2paWB//AEEBZmpsdti6qrJ968q0cuc72yhEh7kIfTrh69PDSRa5/QU/wWBpvWQPvFL8Rf\n+ZrvSqqrgbvvFv/vr/Gh7WBEzeJPiLc+ucsYVMsSHYNAh3MS5gg9xW9hclcLKab/2eeAa9f4eRYs\nAG65xXCVQYWaxd8jSrD8wllpaatfm9AmGJWbmT4FKpyTMEfoKX4zFr+JgZU8VIzJliP5/xsbgZde\nMtfPYEHN4hcE8Vu5VjhzBhgyxJHuEUGKP8M5CfuEnuJ32OKXeOop4MQJ8f9r14AvvwT+/t/i5MzK\nlb6LqjmF2gSQU2GNaha/AAGDB5urS+rT2bPqij8YQu0CjeYkXhAqPDN98kc4p4TRc03hnL6EnOI3\nEs5pxYcYGSkuuAUAFy8AL7wATJ0qbnfrZq2vwYBaOKddiz8pST8f0f6xEs4pJ1RCNwNNyCl+M5NO\nZu+qkZHi74BYIDsbmDTR/4O1rcI5XYLLsuLXsviDIdQu0Dj99OlvjPTJyLWjGs7JCQu1c17bazin\nZnkK5zQH+QzN4aSrR6pDS/ET3gTjOPWXUeHZb1CpBaNs2guhp/hNuHHao7/YaWhyl7CCkWuHjLC2\nI/QUPw02U2hZ/FYVf1kZkJDgSPc6PO3V1WOoHgPhnIR/sKz4P/30U4waNQphYWHYv3+/ar6srCyk\npqYiJSUFy5Yts9qcY5iy+G3OnHcEtCz+2FgxT7PGshU84uL8F+VEBAdGrh0ywtoOy4o/PT0dq1at\nwrRp01TzNDU14dFHH0VWVhaOHj2KFStW4NixY1abdISO+G1Of8KL5vGktYjwyhVjdUmP/1puHnKv\neROMStFpH7/PIm0GnyhorFgn3GrB1NRU3Tw5OTlITk5GYmIiAGDBggVYvXo1RowYYbVZ25ixMmhg\nGZNXnUHFL0GhnMZpr64eI9eOWqhmMN7sOhp+NXuLioqQIHPmxsfHo0jte30Bglw95jDih71SZ64u\nLYufLvqOQSBcPTRWrKNp8WdmZqK0tNRn/7PPPovbbrtNt3InrZWJcRNxvu68z/7hfYd7/h8/YDx2\nF+72yTOq3yifPskHTVq/NG6bncM7e21369TNp02JXl16AQBSolMwLnYcACCpt69pG9M9BgAwaeAk\nRHWOAgDE94j3yZfQU7xhThk0BRW14me++nfr75NPaqN3ZG+v/T06qy+Gk9pX/WlNLitA/eIMc4lL\njEYgEpGXxOON6hSF8QPGe/J069TNS1YpfVLE35TWepT97tvV++vrE+Im+OzTYlBP/ozzjxJ+hMPl\nh732DY0e6vlfbXxZYXT/0fjnkX967RvV31uu3Tt198iKdz6ksTGszzCfNHm//cWQ3up355ToFK/t\n7p26++SJjIj02TduwDhsOr3Js81dhwcCxg4Y61O2U5jvwlBdI7r67FOO++ToZEyIm+C1T+vYYqNi\nvbZvGnwT6pvqvfYN6D5AtTzvmk+OTvbZxzuvynEwNmasl7zkpPdPV+2DEQRm06ydPn06/vrXv2L8\n+PE+abt27YLb7UZWVhYA4LnnnoPL5cIf/vAH344IAhYvXuzZzsjIQEZGhme7mTWjmTUj3NV6r2po\nakC4K9wzcIzkkfZFhLXOLjLG4Ap3Ac2t28o88m3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"text": [ "" ] } ], "prompt_number": 112 }, { "cell_type": "markdown", "metadata": {}, "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 should do some sort of smoothing of the data\n", " - Let's go with a Gaussian" ] }, { "cell_type": "code", "collapsed": false, "input": [ "sigma = 0.1\n", "window = np.exp(-(t-0.5)**2/(sigma**2))\n", "\n", "x2w = numpy.roll(x, 300)*window\n", "r2w = numpy.roll(r, 300)*window\n", "\n", "figure()\n", "plot(t, x)\n", "plot(t, r)\n", "vlines(0.1, -1.5, 1.5, linewidth=3)\n", "vlines(0.3, -1.5, 1.5, linewidth=3)\n", "\n", "figure()\n", "plot(t, x2w)\n", "plot(t, r2w)\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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0NTc5ki/cFQ4GpprvcPlhAMC2c9tQU1/j08fKukoAwPJNaxE/A/gmvxMOlBzw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\nakC4K9wzcIzkkfZFhLXOLjLG4Ap3Ac2t28o88m3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"text": [ "" ] } ], "prompt_number": 113 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- So we're going to take our original data ($x(t)$ and $r(t)$) and shift it around, multiply it by some other function (the Gaussian), and then add up the results\n", "- There's a word for that\n", "- This is actually a pretty common mathematical operation that we've already used\n", "\n", "$H(\\omega)= {{(X(\\omega)R^*(\\omega)) * W(\\omega)} \\over {|R(\\omega)|^2*W(\\omega)}}$\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# original code\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'))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 114 }, { "cell_type": "markdown", "metadata": {}, "source": [ "How well does this work?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy\n", "import syde556\n", "T = 1.0\n", "dt = 0.001\n", "\n", "x, X = syde556.generate_signal(T, dt, rms=0.3, limit=10, seed=3)\n", "y, Y = syde556.generate_signal(T, dt, rms=0.3, limit=10, seed=1)\n", "\n", "t = numpy.arange(int(T/dt))*dt\n", "freq = numpy.arange(int(T/dt))/T - (T/dt)/2\n", "omega = freq*2*numpy.pi\n", "\n", "alpha = 1.5\n", "bias = 2\n", "J1 = alpha*x+bias\n", "J2 = -alpha*x+bias\n", "J1y = alpha*y+bias\n", "J2y = -alpha*y+bias\n", "\n", "\n", "v1, spikes1 = syde556.lif_spikes(J1) \n", "v2, spikes2 = syde556.lif_spikes(J2)\n", "v1y, spikes1y = syde556.lif_spikes(J1y) \n", "v2y, spikes2y = syde556.lif_spikes(J2y)\n", "\n", "\n", "r = spikes1 - spikes2\n", "R = np.fft.fftshift(np.fft.fft(r))\n", "\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'))\n", "h = np.fft.fftshift(np.fft.ifft(np.fft.ifftshift(H))).real\n", "\n", "\n", "fspikes1 = numpy.convolve(spikes1, h, mode='same')\n", "fspikes2 = numpy.convolve(spikes2, h, mode='same')\n", "fspikes1y = numpy.convolve(spikes1y, h, mode='same')\n", "fspikes2y = numpy.convolve(spikes2y, h, mode='same')\n", "\n", "A = numpy.array([fspikes1, fspikes2]).T\n", "Ay = numpy.array([fspikes1y, fspikes2y]).T\n", "\n", "d = syde556.decoders(A, x)\n", "\n", "xhat = numpy.dot(A, d)\n", "yhat = numpy.dot(Ay, d)\n", "\n", "\n", "figure()\n", "plot(t, x)\n", "plot(t, xhat)\n", "title('original signal')\n", "show()\n", "print 'RMSE:', numpy.average((x-xhat)**2)\n", "\n", "figure()\n", "title('new testing signal')\n", "plot(t, y)\n", "plot(t, yhat)\n", "show()\n", "print 'RMSE:', numpy.average((y-yhat)**2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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4sefvjzwCt9/esxXmxIlwzMqZzTYF/65du0hISCAmJgYPDw8WL17MijMe61u5\nciU333wzAJMnT6a+vp4Ke+5JJ/RJkiC/dT+Togce5umVHKmnprsUk/z3UIdkX9FxYgNG9vlehjoD\nc8gxduxpl7XN2vZK9MHy9fgTNBra3Cpk/c3kuNFAgOScGT1n+v2vkpCyrubJ759zdinnJbMZ7rsP\n/vUv2L4dXngB5s6FK6+EFSvgd7+DV6z8hcum4DcYDERFRZ38WK/XYzAYBj2mtLS0z+vl59tSjTCQ\n8nIwRexnWuzQgj8mRI93eCn9/K+yu/zGY6Rrk/t8z8fDh3DlSDYclPcGb6OpUpblGnqNCNGgVJVT\nVyfbJSmoMRLi6ZwZPWcKC4NLvJ7gX/vep7TRSf9QzkNNHU38/acXSX5sMSuaH+Xz1WUkJp5+jELR\n0/N/4w3r2rAp+AeaC34q6YwuT3/n3Xxrt9jowU6ys8FdP/iMnl76AD2eYQanLMglSVBlPs60pL6D\nHyAtdAK7DLtlbbdVWUlipHzBb49lG0obDGj9XKPHD/Db2yLxPvErXt35mrNLOUu3uZujVUf5Pv97\nvjn2DSuPr2Rz4WYOVRyivLmcbnP3oNfIy4N/vmpiyW21XHBxDZOndnP55bB0KRw4IH/NB8sPkvZm\nGv/+YS9tBy7nsitbmPnvMWzI29Dn8dau1+RuQ43odDpKSn4eBy4pKUGv1w94TGlpKTpd3/9w97WM\n49JLr2TKFAWzZ89m9uzZtpQnnGLfkRY6fQsZFT5qSMfrA/RIqlLy88HR/xsMBpDCjjE+pu+hHoBZ\nSeN4Zqt8W0SazdDlWUlylHzBr/ZTY/Ipp7xcIiVFnlk4FW0GZga7TvBfdBEEPXwvb++ewhOzH8fX\nw9ep9dS31/PpoU9ZcXwF24q3EamKJCowCpWnCgmJhvYGattqqWyppLatliDvINT+aiL8Igj3DafL\n3EVFXRPFlY1UN9XR6V4DXo34xKhwi1fQampC7RlPQfMUXr37WpI9LuGlv3kwadLgtQ2moK6AeZ/O\nY0nwP/jq74vZvh2ion7JDUVXc/WXV/PFNV8wJ3YOmZmZZGZm2tSWTcE/YcIEcnJyKCwsJDIyki++\n+ILly5efdsyiRYt47bXXWLx4MTt27CAoKAi1Wt3n9ZJvDWDLt+58eu9fbNrsWjjbttxDaNTJeLp5\nDul4fYCeds9Spwy/ZWdLSIGFxAXH9XvMzJFpPB74EXV1EBxse5vV1RL4VcqyJHMvHw8f3CUf8oz1\nzEGGIoEp0ivCAAAgAElEQVS6biPx4a4x1AM9Pc4Hfh3P0hNT+ezQZ9w+/nan1FHRUMfN/3qaTbUf\n4FawgI699+Je+l86glQokyAqGVJSYNSonj9qNZglE9WtNeSWVbDtQCU7j1Sxb6cnTTUq5kxTccW8\nEC6ZEUKYXzBuyp6nx7vN3WRXZfNj0Y98FvMMx8rvZu7Dj3BDym28/HcPvL2tq7+po4lFny/il1GP\n8vG9i9mwAXpHyGdEz+Dzaz5nyX+WsP3X28/qFC9dutTyBiUbrVmzRkpKSpLi4+Olv/71r5IkSdJb\nb70lvfXWWyePueeee6T4+HgpPT1d2rt3b5/XAaTShlLJ53G1dO3vd9palnCG+MWvS/PfvG3Ix5vN\nZslzqa90zS8b7FhV3555uVLyejxkwGPq2+ol5WN+0patJlna3LanQVI+6i/LtU4V9NhI6aEXs2W5\nlslskhSPe0j//qJdluvJpblZkgIyNkpJ/0iVzGazw9t/6JMvJeWDEZL+N3dKr39slAoLJamzU5La\n2iSpoECS1q2TpFdekaQ775SkGTMkKSREknx8ev7r7S1JKpUkzZwpSX/+syRt2SJJJgv+Sf1U/JM0\n4705UtCDY6WEmXulY8csr99kNkmLli+SFn92u6TWmKVvv+37uH9s/4eU/ma61NTRdNrr1sS4zcEv\nl97iX9vykeR+1wQp+6g839CCJJnNkuR5zf9Jz2x81aLzol5IkjIukie0LHHNb3dJuqfGDnqc32Mj\npGVv5MrS5r++yZF8HoyT5VqninlylnTDI5tkuVZ5U7nk/kiotG2bLJeT1R8fMEuhf0mVvs//3mFt\ndnR1SmMfu0ty/0O89MY3u4d8ntksSU1NklRV1fNfW5nNZunD/R9JqqciJJ9L/yIt/7LTovMf3viw\nNO3dmVLK6A7pn/8cuJ1bvrlFuvqLqyWT+ed8tCb4Xe7J3bsuuJFItSe3/vNfzi7lvFFRAabw/cxK\nHGfRedFBeorqDIMfKLPc6iKiVDGDHjfCM50dBfLM7Mktq8RPId/4fq8wbzWGRnnm8hubjCiadA7b\nctES996joH3z/by41TEPdDW3t5Hw2FUU1BWS86d93PWLCYOf9P8pFODv3zMrSY7nIRQKBTeP+RXH\nf3eAsQt3c/PmC7jtTyfoGsJSRp8c/ITPDi2n4+OvmXexJ/fdN3A7by18C0OTgWU/LrOpZpcLfqVC\nyQeLX2K371IOZdlhCcZh6ODhLqSwbDI06RadFxemp9mt1OH77xqai0gIjx70uNERaRytkSf4i6or\nCZJxuYZeGpWGqlZ5pvWUNBjortM5/andvsTEwGUjfklm/jYK7LyXQ3tXBylPL6KjMYD8Z1YQowmw\na3tDpVVp2XrXGp6++mY+9ZrGqF+9TVlZ/w9xbMjbwB/WP0Dg6m+ZnBbOSy8N3oaXuxf/ve6/fHDg\nA57b+txZMyaHyuWCH+DCkZNJCEjn12+85+xSzgubjmQRIEXj72lZ90YfoCdA59i5/GYz1JqKGK0f\nPPhnJKVjNB2WpV1DfSVhMi7X0CsqSCPbsg0nyox4dkTi5SXL5WT3+MN+sP9W/vHT63ZrwyyZmfq3\nX9FQGcDRZz4mONDDbm1ZQ6FQ8Oc597D/vi20JL9D7COLeOX9irMehPziyBdc/8WNKL/6D4umpPLa\na0OfmqlVadly6xa+zv6au1ZbtxKCSwY/wFuLn2Sf77MczJL36czhaEfxHhJ9J1p8nj5Aj5eDH+Iq\nLwe30CKSIgYP/tkpabQHHqKx0fZ2K1sq0ajkD345l204UW4gUOk6UznPNGoUzPS5h/f3fkhLp/wb\n0AD8+uOnySo2svuhzwgJdhv8BCdJVadQ+Nh2llyUzgP5owla8lsuf/Arbn7pI0Y+dSm3fPwYvv9d\nzwdLp7NsmeXz8fUBenb83w4env6wVfW5bPDPSZpIomqM6PXL4ETLbibrLQ/+SFUkyiADJQ5csqeg\nANxDi4gOGjz4k8OTIKCU/UdsH4uq7agkKkT+4E+M1NDmXi7Lsg1FtQbCvVw3+AGefTAGU8F0Ptj3\nqezXXnFgMx9nv8WHC79kZLyV8yYdyNPNkw9ufIbjD+zkl1eFkO+3nG2V64hrv5pPLjhE4faxXHqp\n9dd3V7oP6fukz3Otb9b+3lryBBe9cyUHDt/OmDTbf781mWDdOjh8GFJTe1a5c3PdToMsJAmqPPYw\nL+0Wi8/VqrSYfMod2uPPz4cuv0KiAwf/B+3h5kFgdxKbs7OYNc3yH2ynajRVEaeeYtM1+hIdokHh\nX059ve3PGxibjANumekKxoyBsZ33s+y7+7hn8h1Dfrp/MBVNVSz+8kaudvuAGy53wZscA4gLjuOt\nxU84u4zTuGyPH2B24kSSAjK47TXbN3zIyYEJE3oeta6p6fnv3LnIMkzgyoqN7ZiCj3LhqDEWn6v1\n19LuXubQHv/R/AYUShMhPiFDOj7KM509Jbbd4JUkaFNWkqSTv8ev8degUJVTLsNoT1W7gegQ1+7x\nA7zz8ByqqxR8c2iTLNczS2Zmv3ILIcYb+GzpfFmuOdy5dPADvH3DExxUPcfOPdbP8Ckq6ll24Pbb\nYedO+Nvfev6bmAiLF+P0TcXtafWew/i1J+Hr6WPxuWp/Nc1SJSWljltA6UhpEWEe0UPuKaaGp3O8\n3rYbvNXVoPSXd2XOXuF+4Zi9aig12r7Mab3ZQJLG9YN/9GgFU93u409f/VOW6/3x65fJNdSS+fgy\nPFzrXu45y+WDf2b8JEaGpPJ/r39g1fkNDbBwITzwANx99883UdzcejYzqKyE987j2wiZObuJcrNu\nGMTTzRN/jwAKK2pkrqp/BdUGdKqzN1/pz5SYNMrMtvX4jUZQ+FcS4Sd/8Lsr3fE0h5BjqLLpOh3d\nHXQqGknSnxtrmXz0hxvJ79rO2r1ZNl1nc+4uXt33PC9NW05inEh9ubh88AO8tfgJjoY9y6bNnRad\n19UF11zT09v/5e1VfJX1FQ9vfJjrvrqO+Z/O58YV1zPvsTd59KkmWuwzCcHpDlXtIT1s6A+3nEnr\nr6W0oUzGigZmaDISHTL0cey5Gek0+x3CbLb+17biUhMmz1rCfO0TqiqFmrwK28Z6jE1G3Nu16HXn\nxLcscVF+zA/4I7d+8JTVv1E3tDdw+UeLmV7/FvfdFCNrfcPdOfGvaGbcFFLVydz00gdDehoOeoZv\nfnOXRH3Eao5OvJjE1xL4+NDH+Hj4cFXKVfx28m+5LPEyjnVupOVX6TzymnwrPbqSYmk7FyZNtvp8\nXaCGNvcyhzzEZTZDg9lIvHrowZ+i14Ck5FCB0ep2c0pq8ZQCcFfaZ65DsIeGohrbHuIyNBmQGl3z\nqd3+/Pv391CjymTZu5YPxUmSxII3b0eRu4BVL1xlh+qGN5ee1XOq95f8lQvqFvLsK1fz+AOD98z+\n+OwxPve7hbhxbfxh3EN8m7wKH4+zx7lvyriJF/y+4uEfL+W3NTuJC7VuepQrqmyuot29jIUT0qy+\nhlalJUhfRmkpJCXJWFwfqqvBI8TIiKCh16tQKAhoHcOGQwcYE2/d+HdORRkBSvslariPBmOZbT3+\n4jojprpIZNwnxu6CfP25d9yfWLb6EX41bxXRFnxrPbryVXbn5bDp/o9RqexX43B1TvT4ASboxrMk\nbTF/3fMAR470f5xZMnPLG6/yStN0Hr3sVxy66wBL0pb0Gfq9/rzwWnTFf+Cqj35t9SPQrmj1ka24\nlU1DF2n9nFWtvxZ/bblDZvYYjeAZarB4yqLOPYOdRQetbrew2kiYl/2CXxeoobLVtuA/ZjTga9Kd\nc9OPn7vyPgLjcph77wo6hzhSuy57Gy9sf4Zl6f9hxlTXn69/Ljpngh/g1SufJij9Jy564F99bmdX\n0lDC+Jfn8dnhz1ix6CcemXv3kGeHPHbRH8irKuG7/O9krtp51hzZgq57htW79EDPdETPEMdM6TQa\nQRFgRKeyrOc+KiSD7Brrg9/YZETrb7+54SNCNNR12Rb8eZVGgt1cf0bPmbzcvfj8xjcpTb+PxbfW\nDrqH81FjEb/45HouM/2LB+/ofz8GwTbnVPCrvFRk3rGS5smPkP7rNygs6plm2NHdwas7X2PUK+PI\n2TiLzF9t5bKplo1LXHeNO6aNT/PEpqfsUbpT7CrfQkbQDJuuoVVpUajKHPIQl9EIXd6WP6Q0OTqD\nUpP1++BVtll2Q9lSCRoNzdg61GNA7XsODfCf4sK4Odw+7Voyw5Zwy20mOvqZmX2ksJxx/5jLmNY/\n8d/nFzq2yGHmnAp+gOSwZPbftwXF2A+JfyUR3UNzCVkWxSMfrSL2x83s+8djXDDV8lsXQUEwS30l\nxyryya7KtkPljtXU0YSx6yizEmx7olXrr6XL2zFDPSWGbjrcqlH7971DW39mjU6mxa3E6vVhGsxG\n4iPsG/xdnuVDHuroS3mLAX3Audfj7/XigufJGGNic9AtTJ/Vxe5Ttks2meDlz44w5rWpTPG+me0v\n/xblOZdM55Zz8subFJZI0WM7+fam/7Ao4g/c5b6b/121ngMbRtl0A/LaqzxQl93Ce/vO/Yn920u3\n49s4jvRU25a60PhraFWWYXDAsvz5FZX4u4VaPLsmJckDqpM5VDHAzZ9+dHZCu4eRkXacLhMZoMEt\n0LZN12s6jcSGnbvB7650Z/WNKxkzpZGKyyez4HeriEsvZ8Klhwm4+kH+nD2bP41/mh+eelSEvgOc\nM7N6zqRQKFgwdgwLxlq+FEF/fvELuP/pG/kyfh4vXvKibOuMOMOmgk105cwiNdW262hVWuq7yyhz\nwFT+oloDYTGWB7C/P3g3ZLD52EGmRlk2dbW8HNyDy9AH2i/4Nf4aJL+eZRt691G1hCRJNGIgSXtu\nDvX08vXwZcXib1h+ZDlvRf6NI+VH6XIL5vqYS1k6bz9RgVZ8cQSrnLPBbw+hoTBGn0JBlzf7y/cz\nTmvZjlWuZPXx9bgVvIpGY9t1VJ4qUEiUVjYDMmxXNABjk5FIf+vCLVI5hp/yLR/nNxgAlX1v7gZ7\nByO5t1Js6GDiRMt/A6tvrwezB/FR9v36O4JCoeCGtBu4Ie0GZ5cyrIlfqs4wf54CbcMvWHl8pbNL\nsVpFcwUFdQWkh062aUYP9Hyjav011HSUDTojw1ZVHdbfZE0OyiDLipk9pQYz3V4VaPxt/Ak5AIVC\ngY85gpwy68Z6jE1G3FrOrYe3BNcmgv8M8+ZB9U+XsSZnjbNLsdqGvA3EKy8kY7Q8a5toVVpUkWVU\nVspyuT51d0MTRuIjrBvHnhSdQWnnYcySZQvKHS+twotAvNztu61VgJuGvErrZvYYmgyYGiJF8Auy\nEcF/hnHjoOnoFLIqs2nsODfXbF6ft56AynmMHi3P9bQqLYG6cruO81dWgleYkagg69JtzMhglJ3B\n5NflW3TecYORYDf7J2qop4bSOuuCv6DaiNSgs3k9f0HoJYL/DG5uMHeON1FuE9lWvM3Z5VjMLJnZ\nkLeBlkPyBb/GT4NPhH1v8BqNPcs1WLvRSFISuFWMZ49xj0XnFVSXEe5j/409NP4ayputC/7jZQYC\n0Nk8bCcIvUTw92H2bPApn0NmYaazS7HYgfIDBPsEk7snxuYZPb20Ki0ewWUYrV8HbVBGI6CyfLmG\nXnFx0J43ie3Fuyw6z9BoRB9k/+DXBWmoarcu+POrDIR4iHEeQT4i+PswcyaU75zJj8U/OrsUi63P\nXc+0iHn4+/fMUpKD1l8LKvv3+Du9rO/xe3qCunsSWwssC/7KjmKSNfZfmC82XENDt3XBX1JvINLC\nZSwEYSAi+PuQkgKdReM5WH6ILtMQ14F2Eevz1hPdLd8wD/QMU3R52XeMv9jYQZey0aY18UeHjie7\n9sCQ/5+1tUG7dyGp+hir2xyqRI2GVqV1m66XtxmIDRXBL8hHBH8fFAqYNUVFqDKWw5W2bevnSE0d\nTewt24t7yWzSrF+J+SxalZZWN/v2+PMqygh006BUWP9PMjU+kABpBFlVQ9v1qaQEPCMKiQ2yf48/\nOlSDQlVBba3l59Z3GxipFcEvyEcEfz9mzQK/+knsMlg2dOBMPxT+wCTdJE5k+cna49f6a2k02XeM\nv7jOSISPbeE2ciQENg/9/1lxMUiBhcQExdjU7lBo/DUoA8otXvqiy9RFm6KG1BjL1i8ShIGI4O/H\nzJnQkD2J3Ybdgx/sItbnrmde/DyOHEHW4A/zDaO5ux5juf2GvcqaDeisHN/vlZQE5pKhB39eYRdd\nXhXoA4a+x6+11P5qzD7llJRYNtZT3lyOW0c4MSPEQ/aCfETw9yM9HZqPWz5LxJnW563n4th5HDsG\no0bJd103pRvhfuFUtFRgtuz5qCGr7jQSE2p78NcdmcROw84hHX+kuBQVGjzc7L+Jt7+nPwqFgryS\nZovOMzQZkBp0jBhhp8KEYUkEfz/c3GBSTBr59fk0d1r2zeoMebV5tHS14F2fTmQk+PnJe32tSotv\nRBk1NfJeF6CrC9rcjMSG2zatMjIS2osyKKovorZt8MH0E5WFqL1ibGrTEiqFhuNGy2b25FQYoFE8\nvCXISwT/AC6Y4kGwKZkjlZYv9+to6/PWc0n8Jezfr2D8ePmvr/HXEKi3zw3e8nLwCjcSFWjbGL9C\nASMTPBgVMIUtRVsGPb6ooYgRgY7bYznUS0NBlWXBn11iQCUe3hJkJoJ/AFOmgKIig4Pl1m/r5yjr\n83rG9/fu7Vl2Qm6R/pH4aexzg9doBPdg6+fwn2rkSBhhnsXmos2Dt9t+gtGRCTa3OVRqPw2GesuC\nP7fSQJinmNEjyEsE/wAmT4baoxkcLD/k7FIG1GXqIrMwk7lxc9m3z07Br4rEM9Rolx6/0QiSvxGd\nDDtMJSWBT+Xgwd/WBi0+R5kSn2Jzm0MVFayhwsJN14vrxMNbgvxE8A8gNBTCTensKHTtHv/20u0k\nhiQS6hPO/v0wdqz8begCdKCyX/B3esrT409NhfrsiRyvPk5De0O/x+Xlgbv2KKlqxwV/vFpDXadl\nwV/RaiBGPLwlyEwE/yCmJaRztPaQxcv9OtL3+d9zcdzF5OX17B0cZv3Dr/2KVEXS5W2wS/AXGpuR\nlF0EegXafK20NMg+5MUk3SS2lfS/yN7RE510+xeSGJJoc5tDFR2qwexbQaMFi77WdhtI0ojgF+Rl\ndfDX1tYyd+5ckpKSuOSSS6ivr+/zuJiYGNLT0xk7diyTJk2yulBnmT0pFGVXAEX1Rc4upV8/Fv/I\nzOiZdhvmgZ7gb3WzT48/r9JIkFukLFtdJib27Ko1LXI2mwo29XvczpxcAqQRdl+H/1RalQav0HJK\nS4d2vCRJtLgZSIsWwS/Iy+rgf+6555g7dy4nTpzgoosu4rnnnuvzOIVCQWZmJvv372fXrnNnTnyv\nqVNBUZnBwQrXHO7pNHWy27CbaVHT2LkTJk60Tzs6lY4Gs9EuN3dL6o1E+Mqz+qS7e884fyILBtxM\n56DhKFE+jhvmAVD7qVEGDD34GzoakExujIxV2bcwYdixOvhXrlzJzTffDMDNN9/MN9980++xkjUr\nU7mI0aOhsziDXUWueYN3r3EvCSEJBHkH8dNPcMEF9mkn3C+cFlM9xooO2a9d3mJEHyDfssNpadBV\nPJ7atlryavP6PCan6TCp4TKtWz1EGn8NJp9ySkqGdnxxfc8cfvHwliA3q4O/oqICtbpn/RC1Wk1F\nRd/7iSoUCi6++GImTJjAu+++a21zTuPuDgmqdH484Zo9/i3FW5gxYgZtbXD4sP16/EqFkgg/NWVN\n1q0wOZCaTiMxYfIGf9YRJQsTF/LtiW/7PKaM3Vyc4tihxwi/CNrdK8kvGNr9ooP5Bjw7dPj42Lkw\nYdgZMPjnzp1LWlraWX9Wrjx9I3KFQtHv+Oy2bdvYv38/a9eu5fXXX2fLlsEfrHE1F/z/G7yuaEvx\nFmZGz2TPnp4ZLb6+9mtLFxCJe4iRfm7nWKW9HTo8jSSEyzeOPXp0zw/By5IuY9WJVWe9X14u0RWx\ni/lpjg1+L3cvfJQqjhUNbYnOw0UGApVifF+Q34ArP3333Xf9vqdWqykvL0ej0VBWVkZERESfx2m1\nPY/hh4eHc+WVV7Jr1y5mzJjR57FPPvnkyb/Pnj2b2bNnD1K+Y8yflMi/9hlo6WzBz1PmtRBsYJbM\nbCvexruXv8tH38K0afZtT6fSUarvucEr1xICZWXgHW5AFyDfryoZGXDwIMyNu4TbVt5GRXMFav+f\nV7dctzsXD6U3OhmHl4Yq3EdDbnk5MPjUqxNlBtQ2rlgqnH8yMzPJzMy06RpWL/m3aNEiPvroIx58\n8EE++ugjrrjiirOOaW1txWQyoVKpaGlpYcOGDTzxxBP9XvPU4Hcl06d6oNiYxJHKbCbr7TSWYoWs\nyixCfUPR+GvYtg1uvNG+7UWqIvHV9EzplGsROKMR3ILkmcPfS6fr2ZGr0uDHL0b+gs8Of8Yfpv7h\n5Psrs9cTJ82VrT2LagvUkFVbDgy+fGp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ZfjlrL13LTVNuGu6yZKWy6jlYJoJ/qNS0mFCYg/Hzc7wNjUpDYOTIX56529LD\nc/vu5o/jX0Dl4zXgcbdMuwVdmB9dE97ifcc7yCeVz7M/Z8nYJU61IYLfARYLXPVbK82THiMz7CF+\nXPEjC+IWDHdZsgt215FfK27wDpWqRhMBnmqnxua1Ki1+muoR3+N/6IOPcesM5slrTrx2lUKh4OUL\nXsaU/CgPP9Xg8FpZJ4vOnk6+zfuWS8Ze4lQ7Ivjt1NUFl64oZUv0PALO2MSOG3YwPmz8cJflElpf\nHWVNIviHirHFhNrHseUaDtP4afAKHvk9/jf3v8LK5D+hVA7+KZmsSeY34y/Fc/4TrFkzBMW50A9F\nPzA+bDxalZ079RxDBP//dFm6yDfls6dyDxk1GZQ0ltDc2YwkSUDvvNkfs38h/vY7+W70JO5cPI8t\nv0sl3N/OHTNOIdFBeqrbRfAPlXonFmg7TKvS4hYwssf4P96+mzZqeOrai20+5/G5j1OvW8szr5fT\n5djDrk6paqnipq9uQv2cGs2LGh784UE6e+zfOOHzQ84P88BpPqvHKllZl7uO1b+sZmvJVkJ9Q1H7\nqOno6aCls4WGjgbM3WaCvINo7mhFaozmjKDL2fbHTKLUIzfwD4sN1fFtyWfDXcZpo7HTRFKA8z1+\nq2821bkyFXUSemT9q8zxvQUfb6XN52hUGlZOu5EPSp/mX/96g+uvd2GBx9hXtY9F/1nEVROuIuuW\nLMw9Zm7/9nZ+88lv+O/S/+Kh9LCpHYvVwle5X/HArAecrsnpHv+GDRsYO3Ys8fHxPPfcc/0ec/vt\ntxMfH8/EiRPZt2+fs5d0iiT1roHz3Mc/Yngumbu+eIIk63I+m1XKhgsK2bDkF365/iD7ri1l2wUt\nvKhuJ+rrLGI+aWDdghx2P/v0aRH6AEk6Ha0K0eMfKq09DUSonQx+lYYuj5Hb4y+qrSVH+pq/XHOD\n3efeM/MemvUf8eSrJUM2w6fQVMz8f17MzJa/0vjJ8zx+bzifvR3Dwwmf0WXp4s8//tnmtn4u+xmt\nSkuMOsbpupzq8VssFlatWsWmTZuIjIxk2rRpLF68mMTExL5jvvnmG/Lz88nLy2PXrl3cfPPN7Ny5\n0+nC7ZWZCatXw0cbSmk5808QuYczav5KZMslHPhBQWoDNDRAYyM0N4NKBVotpKR48sT9YSxYAO6n\n2e9HZ8To6PIWwT8UrJIVs9SILsT2h/76o1VpaVNU0zMMY/wdPR089MNDbCzcyEz9TJ4+72mCnbxn\ncaw//vvbC3xcAAAgAElEQVQtdC1XMDHB/nZDfEO4dcYf+EfhU3z++RquuELW0o4iSbDmvQZu238B\nmtL7GR3/GwyToacHcnJg9ZWedHu+x45lZ7DAcCnnxp85aJtyzOY5okDH/fzzz9KCBQv6/v3MM89I\nzzzzzFHHrFy5Uvrwww/7/j1mzBipurr6uLacLGVApaWStHSpJIWFd0jnPfqUFPR0sPTI5kek9q52\nl1xvJLFYrBIP+Ug1Dc3DXcqQslqt0g1f3iDFvxIvpZWnDck1G8wNksfDgdK77zrXTrYxWzK8FCfp\n9bKUZTOr1Sot/3S5dMl/LpF2V+yWbl53s5T0epJU314v2zW6erokj/sipVc/2e9wG/Xt9ZL/E6Ok\npJkFktUqW2lHaWiQpAUXdUiqVbOlZe/8sd9jrFZJ2rlTkqZc/57kcUuK9P6/LCesx2K1SLq/6KSM\nmozj3nMkO50a6qmoqECv1/f9W6fTUVFRMegx5eWu70VKErz9Nkya0kNP0vv43zce34Sd/PKH3Tw6\n51F8PEbY4h0u4OamwL1dx/7CisEPHkFe3voOn25LR5N/L7/74nqs0gCbJcjIZDbh3u34w1uHaVVa\n6jt7h3r+Ny9hSGws2Mjeqr385/L/YC2fStD2N9B3LWDpJ8tk+/69uP4L3JpiuHnJRIfbCPYJ5s6z\nbqUy7gm7dsGzVWEhTJ1mpTj5eubPDOGD617o9ziFAqZPh7R//Ja4OIk/f/QBc+ZAXl7/7e4o20GA\nV4BsMwidCn6FjROOpWP+C7T1PEd1dMDvbuzi4S/ewufeMdRHv82bi/7OV1d+Jcv42OnE16Ijs/T0\nGe6RJImHv/kr50rPEFBwAw11PqzLXefy65rMJhQdji/XcFiAVwBdli68VO00NspTmy2e2PoEj895\nnE8/9OGSS3qHRds+f549+838dbs8C+W8vONVLtfd1repkaP+eNZdWOPW88BfDsn64VhYCHPnQuxN\nDxMcW8S/L39/0Kf43RRuvHX5X7HOfZCLl5g588ze1X2P3Zjpo4MfsXzcctlqdWrUOjIykrIjnuws\nKytDp9Od8Jjy8nIiIyP7be/RRx/t+/ucOXOYM2eO3TXlFZk5795/UDfmeWaeM45H5q7l7Kiz7W5H\n6KV205FXc/oE/783pWO2tPPh0+dSVaUg8ZrreW/Mf1g8xrWb3JvMJqxtaqd7/AqFoncnrugaampG\no1bLU9+JZBmzKGwoZIL75ZxzF2zbBomJYLG4c9nv3+bB72Zy2bhFjFYbHL7GttwD1HYX8vz1zm8/\nGuQdxENz7uWJ4gf54YfPmSfDiuc1NXDeeXDW7X9nj+fH/Lz8Z5tHFWZGzWRa5DQsES+zffv9XHst\nfPEFvPMO6PXQY+3hk6xP2HLdFgBSU1NJTU11rmC7B4eO0N3dLcXExEhFRUVSZ2enNHHiRCkrK+uo\nY9avXy9dcMEFkiRJ0o4dO6Tp06f325aTpUhWq1V64evPJOXdeinp8UuktPLdTrUn9Jp2/wPSwqef\nGO4yhkzKn56Sznzitr5/L7y8VvJ5LEDq7Ol06XU/SP+P5LZsqdTa6nxbKW+lSBMv+lnavNn5tmzx\n8I8PS3d/d7d05ZWSdMwtPqmzU5Iilz8ljX9qkVPXmP7UjVLyrU861caRzN1madSTemnChT87Pdbf\n1iZJKSmSdMUjH0uRL0VKBaYCu9vIrcuVRj03SqptrZW6uyXpySclKTRUkt57T5I+zvxEmvn2zAHP\ndSQ7nRrqcXd357XXXmPBggUkJSWxbNkyEhMTWb16NatXrwbgwgsvJCYmhri4OFauXMkbb8i/k1R7\ndztzX72W+zc9wCMT3ufgw18wLXKq7Nc5HekCdFS0nB49fosF9jVv5MbZF/S9dv2yUDxbEthVvsul\n165uMuHW4dw6PYdp/DT4aYZuSuf6vPVMVi1i40a45Zaj3/P0hG8f/hNZtTms3fm1Q+3XtZnY3fop\nT10u31pY3u7ePLvwUfIN9/PDD46P91itcO21oJq4kS1+t7L+qvUODSfHj4rnqglX8fiWx3F3713m\n/bvv4Pnn4Q9r/8b1SXc5XGO/7P6ocBFHSylvqpAiHk+WfH57tbR1R5vMVQl/XP2lFP6ni4a7jCGx\nM61bUjzkJzWYG/peM5kkyfPCe6WHvn/Epdf+4xdPSgFLHpSlrRu/vFGac/eb0t/+JktzJ1TRXCGp\nn1VL99zXLd1998DHLX/we8nvIYPU1mX//6O/e/sZSX39tbLPwum2dEu6p8dL8Zd87HDb998vSUmX\nfi2FPh8qbSvZ5lQ9xjajpHlBc1Q7n2euk9T/Fy9pwrulzz/v/zxHsvOkWrKho8e+FZRyqktIfP4c\netKXkfXke8ya4euiyk5fYyN0NHN69Pg/Ts0kUKE7agMdtRpi3Gfx7cHtLr12VaOJQA955rz3Ltsw\nNAu1bcjfwPmx5/Pxh+5cffXAx731wDysZSnc8kH/SygPpMvSxX8KXmXVlD/KvrGMu5s7H1y5muLE\nO1i9tsHu8//5T3h31ycYz7yBdVetc/peYohvCO9c8g7LP13OgeoD5NTlsOq7lXx07ev89xN37r4b\nVqwAo9GpywAn2Vo9N31903EzgAayIS2fCX+ZTbzpNgrefRCD4TTYbmgYJBt0mD1Oj+D/IXsXycEz\njnt97phpZDXusfm/TUfUNpsI8pYn+DUqDVafoVmo7afSn4iyzsbXF5KTBz5OpYLnz3uJf+X8nWzj\nAHMW+/Fq6of0VCdy3wrHp3CeyCzDWVyScBl/3PhHmppsP2/bNrjtvdexLLidjdd+R0pkiiz1XBh/\nIc/Oe5Z5789j2lvTeHzu48yPnc/MmbB/PwQHQ1ISvPIKdHc7fp2TKvgPGQ/x3Pb+l304rKUFbn7k\nIBd9Moel4Q+x5/U7UKmGqMDT0LjRIVjdW2jvMg93KS5ltcKhll0snHD8Hqbnpmigy598U77Lrl/f\nbiLUyQXaDtOqtHR6DE2P/+eyn6nbfxaXXz74Vo+3XqNDX3I/V7y9yqYPUUmSeDb1L1wS9idZ7n0M\n5J2rnsEzZgeL/u8dm44/eKiHBS+vInjh6+z6/XbO0J4haz1XJ19N9Z+qaby/kesn/bqokEoFf/0r\nbNkCX38NEybAf//r2DVOquCP2/MlL259jX/t/fSo1yUJ9u2DBx+EqOl7+af1PP560bP8666bTot9\nRYeTys8Nt7ZIDpaN7Ie48vJA0u7jvMQpx72XkgJS2TTSKna77PqNnSY0Ti7QdpjGT0ObwvU9/rr2\nOqpaqziwcTwLbNiOQqGAD++8g5yqCv61d/DF/976+RMa6pW8evtCGaodmL+XP5tu/IKffe/nvjXf\nn/DYbemlTH75PGKn5ZN++w6XPRekdFMO+AxAUhJs3Aivvopdv6Uc6aQK/inxkUT//BXX/Oc2Ri18\ng6nTJCZOhMBAuOI3Evus76G4dgH/vuoNbp9zggFFQVbeXTrSi0f2cM/efRas6hwSQxKPe0+vBw/j\nNH7Mdl3wt/SYCJdp0r1GpaGpx/WzenaW72RS6HQK8pVMP/4XpX5Nn+bB/O7XufWru2jtah3wuC5L\nF/dufJBF3s8THu763t1Uw1j+Mf8zXij4LX/819vH/UbSbenmnk9eZc4HU7ko/kL237Peqa0PnaVQ\nwPz5OLzK6Em17Ng998A990zmUM02Lv/oCrr5gPkRVxCklviu9DPKzA2kXv4DyZoTDCYKsgtAR3bl\nyA7+reklqLxC8PfyP+49hQLGjTqD3aUvuuz67ZIJfYh8Qz11HdV01fYOYbm5qHu3p3IP6vZpzJ4N\nHratLAzAO/83m+i7zuHW//6ZtVf+rd9j7v/6RdpLE3jj6fNkqnZw1517NsquVK5fdzUfFbzBjTMv\nQxsYzP6KbD448DGdpcn8Zd4P3HHlhCGryVVOquA/LFETR/qqPXx+6HNSi1Pp6FRwx/Q7WDJ2CUo3\nJ5/XFuwW4qmjsG5kB39a4SFiUpIGfH9qdBJrWw+65NqSJNHhZiJaI0+P39/TH4tkwU/dismkIiRE\nlmaPk16TTnvxcs4/x77ztFp4YubfeHjvDGbEjufmlBuPen976Q5e2/037h7zC+FDvAL6NQuTmDlm\nD9c+/h1P7/oRr8BSuo2jOV+/mVcfGYvBMLT1uMpJGfzQO9XqN+N+w2/G/Wa4SzntRah0lDeP4J09\ngNzGLJbpjx/mOWzmeD2rD7VhMptkX2rY3GMGqxK9Vp6FAxUKBVqVFmVUDTU1rg1+71+e5szL7T/3\nnltD2HTVN/zp6zm0dDVw15l34qH0YEvxFi5au5T4g2t5/FP94A25QMxoN3569wLa2y+guhrCw8Fn\nhK3peFKN8Qsnp2i1jhrzyO3x19RAV2AWKTED9/gnTFDg3pBEljFL9uubzCbcOp1fmfNIGj8NARGu\nu8Hb2tVKVWsVhXvimDzZ/vMVCvh0dQJJO3bw0lcb0L0UxbjXJ7Don78l4If32Pj6BcO+/4WvL8TE\njLzQBxH8gg0StDoarSM3+LOzwTPiEONCBw7+hATorkziQKX8wV/fbsLaJnPwqzT4hbnuBm9mbSZ6\n70QmjHPH29uxNgICYMuX0Vxj/YG2V38i74V/cv6hQvZ+vIAB1nEUZCKCXxjUhCg9bcqRHPwSnQGH\nSAwdeKjH0xNCpHFsz5N/nL+83oSiU42vjA+ea/20eKirXdbjT69JR9WezJmDbxx1Qn5+8OKL0FQc\ni7lgCp9+5IlWK0+NwsBE8AuDGmcIo8fDRJela7hLcYlfcqvxdPMadOw+IWgc6VXyB39JrQlv6yhZ\n29SoNLgFuK7Hn16TTmdpMjOOf9DZIUolTq+zL9hOBL8wqHCtElrDKa6vHO5SXCKjvJBI38EfxEkO\nT6LELH/wl9XV4+cm7w1jrUqLxcd1Pf6M2gxq0ycw5fjn3YRTgAh+YVBKJXh26DhQXDb4waeggvpi\n4kJGD3rclDg9ZmszzZ3Nsl6/stGEv7vMPX4/DZ0eruvx5xhzaS0ZS2ysa9oXXEsEv2ATlVVHVtnI\nG+fv7ASTtYjxusGDPyFBgWdrrOxr9tQ016OWaYG2wzQqDW24ZlZPc2czzZ0tTDBEuOzhMMG1xI9N\nsEmwu458o/zBn1aRxtnvnM1fd/xV9rZtkZ8PKl0RscGGQY+Nj4ee2njZg7++3USIr/xDPY09rlmo\nLbc+l2DiOWOiWCjrVCWCX7CJ1kdHaYO8wd/R08FV/72K5eOX89KOl9haslXW9m2RnQ0eYUWMDhq8\nxx8aCoqGOA6U276ssC0aO01oA+Uf6qnrqMFYJ2GxyNo0ufW5eLYkMNE1KyULQ0AEv2CTqCAdVe3y\nBv+HmR8SPyqeVSmrePLcJ3nmJ/s26ZBDXh50+xUzWj148CsUEO4Zz4FSeXv8zd31hAfJ2+NXefau\nVR4Y2kp9vaxNk1OXQ0e5CP5TmQh+wSaxYTpM3fIG/3sH3uPGSb3rtCwbt4zdFbspbSqV9RqDKSjq\noc2tgqjAKJuOjw2KJ7de3h5/u2QiKlTe4FcoFGj8NIyKkn+cP6cul/rcMUw49dcqO22J4BdskqTT\n0eImX/A3dTSxu3I3FyVcBICPhw8Xxl/Iutx1sl3DFocqygnyDMNT6WnT8RN0cVR2yNvj73QzYQiT\nd6gHem/wumLZhoyqXEIUCfgfv5CpcIoQwS/YZFy0li53I90WJ/Z7O8K20m1Mj5yOt/uvz/svSlg0\n5MFf1FCEIXDwYZ7DJsVG0CG1yDalU5Ikuj3qiY2Qt8cPvTd4fcPkvcErSRKFjblMio6Xr1FhyIng\nF2xi0HugaA+lqkWe7uOPRT8y1zD3qNfmjp7L9rLtWKwy340cgMUCNV3FjNHYHvwxMQq82uSb0tne\nbQZJgT5c/pXANH4aPILk7fFXt1bjZvVm0lh5lpAWhocIfsEm/v7g1qrjUIU8wz2bizdz7uhzj3ot\nxDeEcFU4mbWZslxjMOXl4BtRRNwo24PfYACrUb4pncW19Sg6RrlkBUitSovCX94ef1FjEd4dMYwd\nK1+bwtATwS/YzM+q44AMWzC2d7eTU5fDlIgpSBL84x+walXv1MqZ+plsL9suQ7WDKyoC7/AiDEEG\nm8+JiICumjgO1chzg7ewyoRHj/zDPNDb47f4yNvjL2oowlI3WgT/KU4Ev2CzUe46smXo8afXpJMY\nmoin0pPHHoM33oBRo2DuXEhUDW3wo7ZtDv9hSiWMIl62ufzFNSa8ZF6g7TCNSkOnu7zLNhQ2FNFW\nPpqEBPnaFIbeSbsDl3DyiVDpKKp3Pvj3Vu1lknYSBw/C3/8O6emg0fS+98PaGeRPG5r5/EVF0OFV\nZNMc/iPp/GLJrVsrSw3l9fIv0HaYVqWllWpkui0DQGZFEX7d08WMnlOc6PELNjME66hodT7491Xt\nY3L4ZJ5/Hu6889fQv/deSPs2gYqmSlq7Wp2+zmDyijoxK+qI9Ldv14+EkFjK2wpkqaGywUSAh+uG\nehp75O3x59TY9xuScHISwS/YbEyEjvouGXr81XvRe0zi669h5cpfX/fzg+uudSewO5GMmgynrzOY\nnOoSwrx1KN3sWwg+SRdJq8VEe3e70zXUtphQe7luqMdorsbUINHTI0+bZa1FJEYY5GlMGDYi+AWb\nJRucf4jLKlnJMmaR+cMEliyB4GM6u8uWgbl4Ivur9zt1HVuUNBURE2x/7zVmtBLfLgOFDYVO11Df\nXk+In2t6/CpPFUqFkmBtC0aj8+31WHtotFQwJda2p5yFk5cIfsFmUxIi6PaqcmqefVlTGcE+wXzx\nsYply45/f9o0oGYiqdkHHC/UBmYzNCuL7JrDf5jBAMqmWApMzg/3NHSa0AS4Jviht9cv17INZU1l\neHRpGJ/o5XxjwrASwS/YLFLjBR1qCqprHW4jtz6XKN8Eiorg3HOPf1+hgPOSJrKjyLXBX1wM/vpi\nYuy8sQu9wd9VE0tBg/PB39JjIjLYNUM90HuD1z9cnrn8RY1FSKbRjBnjfFvC8BLBL9hMoQDvTj2/\n5Dk+3JNnysO9OYELLgD3AeaUXX52MpU9GVglq8PXGUxREXhp7JvDf1hEBHRWx5JjdD7426V69KNc\n2OP30+AbJk+PP7u6GEvdaKLESM8pTwS/YJcAdGSWOh78ufW5tBQlMHfuwMdcMFeNtW0U2TXOj6EP\npKgILAGOzVBxc4Mw91iyqpwP/k43Ewat64Jfq9LiHiTP3rt7i4oY5T5a7Lo1AogfoWCXUC8duTXO\nBX/xLwnMmTPwMWo1qMyJfL3zkMPXGUxxMbR72j+H/zBDQCyFjc4FvyRBj2c9cRGuG+rR+GlQ+Msz\npTO7uohofzGVcyQQwS/YRRego8SJnbgyq3Lx64rHYDjxcXGBiaRmZjt8ncEUlLXSrWhD46dx6Pwx\nmtHUdpTSY3V8nmRjowTeJtk3YTmSRqXB4i3PUE9JcxGJ4SL4RwIR/IJdYkN1VDu4E1eXpYuqtjLm\nTY4Z9Ngp0YlkGV3X488zFhPuG41C4di+sXEGb3wlDWVNZQ7XUFTZjMLqddTS1HLTqrR0uMtzc7eu\np4gpMSL4RwKHg99kMjF//nwSEhI4//zzaWxs7Pc4g8FAcnIykyZNIiUlxeFChZPDhGgdph7Hgr+o\noQivTj3z5g6+6cm5yWOp7nZd8Je3Fjk0o+cwgwG8252b2ZNXacSzJ9Th822h8dPQKjnf4zd3m+l0\nq2f6uAh5ChOGlcPB/+yzzzJ//nxyc3M577zzePbZZ/s9TqFQkJqayr59+0hLS3O4UOHkkDJWR7t7\nOZJk/7nZdbl0VZ14fP+w85IT6Q7MpqrKgQsNoqMDWtyLGKt1Lvglk3Nz+YtqjPhKrg1+rUpLQ7fz\nPf6ihhJo1pM01r6nnIWTk8PB/9VXX7FixQoAVqxYwRdffDHgsZIjKSGclBIjI5FUFVRW2T/VcltW\nLr7mBPT6wY8NU4XirlSyaaeMC838T2kpqHTFjHZgKudh0dFgrnSux19SZ8Rf6eIev0qD0VxDc4tE\nV5fj7aTlFeHRNloszjZCOBz8NTU1aP63upZGo6FmgC6FQqFg3rx5TJ06lbfeesvRywknCR8PH9yt\nKvZk1dl97o6cXMZpbd+yT6Mcy6YD8g/3lJSAR5jjM3oAwsN7gz+3zvHgr2gwEuzl2uD39fDFQ+lB\nSEQztY4/d8cvBcWMchPj+yPFCZdlnj9/PtX9DA4+9dRTR/1boVAMeJNs+/bthIeHYzQamT9/PmPH\njmXWrFlOlCwMN39Jxy955VwyL8yu83Lrc7lx3BU2Hz82JJFf9mYDJ5j074CSEsfn8B+mVEK4Zyw5\ntY4Hf02rkTCta4Mfeod7PKOrqK4ORKdzrI2syiKixFTOEeOEwf/9998P+J5Go6G6uhqtVktVVRVh\nYf2HQHh4OAChoaEsWbKEtLS0AYP/0Ucf7fv7nDlzmGPLYLAw5EK9dBwsKwcm23yO1Qr15LHkHNt3\n8Jgek8jftrqgx18q0eZRSIx68NlFJzI6KJY9zQVIkuTQ7KA6cy2Jga6/WaoL0NEWXk5NjePbZpU0\nFTFTY/vPW3Cd1NRUUlNTnWrD4Y1YFi9ezNq1a7nvvvtYu3Ytl1566XHHtLe3Y7FY8Pf3p62tjY0b\nN/LII48M2OaRwS+cvKKCdBQctG9mz869reBTz9QEGwb4/+fM+LE8q9qAyXT8Kp7OyC0zoRzthtrH\nuQ3D4/VB7JU8MbYbCfOz77cfgKYeI/pRE52qwRb6AD1FoWVOzeyp7S5i8mjR4z8ZHNspfuyxx+xu\nw+Ex/vvvv5/vv/+ehIQEfvzxR+6//34AKisrueiiiwCorq5m1qxZnHHGGUyfPp2LL76Y888/39FL\nCieJBK2Oyhb7gv+z1HzUUhxuCtv/k0sKTUSpOUSmzHuv59UVEunrXG8fem/wBlgcn9nTJhmJ0bh+\nqCcqMAoCy5ya2dPqUcTMcSL4RwqHe/zBwcFs2rTpuNcjIiJYv349ADExMezf7/p11YWhNSFax+qe\nH7FasXndltSMXOKS7duoNTooGotXPbsPtHDOOfJNJylvLWKyA+vwH8tgAM/03pk9Z+rPtOtcSYJO\npZH4SNcHvz5AT4/fbqqrHDu/sr4Zya2DSQmur1UYGuLJXcFucWE6lMHllJTYdrzFAgerc0mJs31G\nD4Cbwg2tRwI/58q3dIPFAiapkKRweXr8FmMs+aZ8u89taAD8jOjUQxD8gXraPRwf6tmaXoSXeTRK\npWNPOQsnHxH8gt10ATrc1eVk2Lg74r594BWRx6Qo+3r8AGOCk8iolu8Gb2Vl73LM8SHOB7/BAG1l\njs3lr6qSwNdIqO/Q9PibJMeHetLyiggWUzlHFBH8gt0i/SPp8i4nPd22B/NSU8E7MpeEUfYH/7TR\niZS2H3LoSeH+9M7hL3RqDv9hkZHQXBJLfr39wV9c2YZCocDP08/pOgYTFRiFsauMikrHvomZFYXo\n/Jz/oBROHiL4Bbv5e/njqfRk76EGm47fvBnavB0L/qnRiRB6iHLn93gHeoO/J8D5qZzQu5GM1iuW\nPAeCP6/SiLd1aMbMA70DUbopKDc2OvQBWtRYxJgw0eMfSUTwCw4J99ORXjx4Gnd3w9Y99bgpLQ4N\naySFJqHUZtk8rDSYwuIeOjzKiQ6MlqW92LBwWrtaaOlsseu84lojKsXQ3SzVB+rx0ZY59PRuTWcR\nk8RUzhFFBL/gkJgQHaWN5XR2nvi4tDQIH5dHQki8Qw85xQXH0eldyr70QS5ko0MV5fgrw/Byl2fD\ncEO0G6OUoylssG+3sDKTkSDPoQv+qMAoRo0uo7TUvvMslv9N5UwSQz0jiQh+wSFRQTo08eUMNlt3\n0yaIm+HYMA+Ap9KTUA8Du/LzHDr/WHl1RUT6ytd7NRhA1WX/Dd7K5io0vuGy1TEYfYAef12ZzTOx\nDisuliCoiHERosc/kojgFxyiD9ATFlfOzp0nPu777yEoJpeEYMeCHyAhOJGDtVkOn3+k8rZCYkfJ\n13uNjgZls/0PcRnNVUQGDm3wu48qtbvHvyOzBnfJD5WnyjWFCcNCBL/gEF2ADl9tObt2DXxMczPs\n3w+dKsd7/ABTo5Mo6ziE1f6VoI8iSVBnzWNCZKxzDR3BYIDumji7e/wNPVUYRg1h8AfqkQLs7/Gn\n5RYRrBDDPCONCH7BIVGBUXT7FZ+wx795M8yYAQWNzgX/JF0i7tpDdvdWj1VXB4qQXJIjxjjX0BGi\no3undNob/K2KKuK0WtnqGExUYBRmD/vH+DPLC9H5iWGekUYEv+CQuOA4KjryaG5mwKmWn38OixZb\nyTflEz/Kvqd2j5QYkohSe4gsJ0d7SkpAGZbDmFHyBb9eDw359g31dHZCt1cVCRFD1+OPDoymUSqx\nu8df2FBEgpjKOeKI4BccEhUYhbHNyLkL2tmw4fj3u7vh669h+vxyAr0DCfAKcPhaY0PGYvbNJSPT\n4kTFUFhsoUtVSFxwnFPtHMnTE8K8oqlorqDb0m3TORUV4BZYRWTA0AV/VGAUdZ2VlJTbVuNh1Z1F\nTB4thnpGGhH8gkOUbkpGq0cz6dwCvvnm+Pc3b4aYGGjyOMTYEMfXgQfw8/QjyF1DWl6RU+0cKC7B\nVwqV/WlZg96TYM8ISpps606XlkpYfasJVw1d8HsoPYgIiKDNvYS2NtvOqauDHv9CJkaJHv9II4Jf\ncFh8cDzacXn8+GPvBuZHeustuP56yK7LJjEk0elrxQUlOr1mT2Z1DuGe8g3zHGYwQDC2D/fklDbg\nLvng4+Ejey0nEquOJSS+0ObhnpwcUI4qIkaG5S2Ek4sIfsFh8cHx1PbkkZIC//3vr69XVfXO3//t\nb+FQnfM9foApUUmUtGc5tWZPYVMuMYGO32QeSHQ0+HbYfoM3u7wKf8XQ9fYPi1HHEDi6gAIbb0dk\nHuqmx6eqdz1/YUQRwS84LH5UPHmmPG6+Gf7yF/qmWz79NFx7LQQE9Pb45Qj+lKhk3MIPUFbmeBtV\nXax1y0gAABJuSURBVDmM17qmx0+D7T3+QmMVwZ5DN6PnsFh1LN7aQvJsfBZu56FSAt0i8FB6uLYw\nYciJ4BccFh/cG/yXXgpeXvDYY/D++/Dpp/Dww73HyDXUc4b2DNwi9zs8s0eSoNE9h+lxrunxd1bF\nkWvKten40sYyIlW2b0Eplxh1DD0BBeTbuH3A3pIcRgfI//0Shp8IfsFh8aPiyavPQ6HoDfvUVHjl\nld7ZPCEh0GBuoL27nQh/5zcUTwxNpNOniH2Z7Q6dX18P1lEHmREzzulajmUwQGNeEoeMtt2DqOko\nJTZk6IdPYoNjafWwrccvSZDfkMtEnQj+kcjhrRcFQRego6mziebOZiIiAtiy5ej3s+uyGRMyxqHF\n2Y7lqfQkwmMsOwoygRS7z99zqBY3j050ATqnazlWVBTUHIrDraUCc7d50Ju2DdZSEiNmyF7HYGLU\nMdR0FWDJl4AT/0yqqsCqzmGSXv4PSmH4iR6/4DA3hRvjQseRUdP/mskHag6QHJYs2/XGh55BZp1j\nezj/lJuBujtZlg+hY3l7gybUnShVHNl1J94msqMDOn1KGacb+h5/kHcQXh6eVDXWDbqqano6+Ohy\nGRMievwjkQh+wSkTNRM5UHOg3/f2Ve1jUvgk2a41K+4Mynv2OzSzZ29lOlFe8n0IHSs+HrTKJLKM\nJ74JUVEByuASDEHDM1MmLjiO0MTcQWf2pKdDd6BzS20IJy8R/IJTJmoncqC6/+DfW72XyeGTZbvW\nzNhJEL6Xigr7z81vTmfcKNcGv8o8ePCXlkpYVWXDNkUyKTSJkMQsDh488XF7M9roVNahDxj6m9CC\n64ngF5wyUI+/29JNljGLZI18YTs5fDKWkAz2Zdi/KUuVdIAUg2uDX6oZR1bdiYM/o9CIB35Dstdu\nf5JCkvDSDb6j2e7CPKJUcSjdlENTmDCkRPALTknWJJNZm4nFevQ6Otl12egD9LKu467yVDFKGsv3\nmb/YdV57dztt3jnMGz9RtlqOlZAALUVJHKw9cVf6QHEJarfheyBqXNg4Ov1PHPzNzVDRkcuECDHM\nM1KJ4BecEugdiC5AR2Zt5lGv7yjfQUqk/bNvBjPO/yx2Vm6365ydJXvBOI44g7fs9RwWHw9VmXGU\nNZfR3j3wlNOc2iIi/Qwuq2MwSaFJ1FhPHPy7d0PYuEMkhsr/sJtwchDBLzjt7Kiz+an0p6Ne21qy\nlXOiz5H9WueMnkl+5892nbPx4C4Cmmfg7sLJyzExUF7iSWJI0oD3PACKW3NIDBu+QI0KjKKlp4GK\nuuYBF2tLSwOvqHRZh+mEk4sIfsFps6JmsaXk10n8kiSxpWSLS4L/8mkzafTfjtVq+9Se7SU70btN\nl72WI3l6QkQExPtN4ZeqgYeijNYcphqGL/jdFG6MDRlL9NQsDgzw+bRrF7T6ZojgH8FE8AtOOz/2\nfDYVbqLL0gXAvup9eCm9iA92fPOVgSQb9CgsPvx0yLblESRJ4kDjNpKDZspey7ESEiCke+Dgb2qC\nnsAc/r+9ew+K4kzXAP4ggwkqMSLGIEwKuTkwMwyEUUQFYQ13MbUxZ8VzKmvQokyyrmVqT2qz5g8w\nu0VJKtZWolubnCRe1mPYRCOLu0YKj8moERAUEAXjLWgGEBWVVcGSi9/5Y0qI4dYMTDfQz69qqqT7\nY/r1rZlnmp7ur2fPVPYQiv4ZPbzDavDddz3XdXYCR4pb0PywjqdyjmEMfhoyTzdP6Dx0OPTDIQDA\nnpo9eCnoJYdcLAUA0+/G4+8nern7Sy9OXz+NcR1uMPv7OKSWnwoKApyvheNkQ+/Bf+mSADzOQafw\nsXPDNAOeeK6q1+CvqAAmB1QjaJoOmnG8sH+sYvDTsFgVtgqbijfh7oO7+LT8U6wMW+mwbYVOTMY3\ndb3c/aUXBy8dhNv1OOiGPkHogIxGoKnaiIu3LuJ++/0e60vPXoUGT8Ld1d3xxfRjttdsXHcpw7Fj\n6HED+4MHAd95VTBONypTHMmCwU/D4hXTK7h67yrC/yccS2YtGZapmPuyyHcRfmgrwr22ewOOLfyh\nEK1n4hA09AlCB2Q0AjWnn4DOQ9frtQ1F589hukb5M2XCPcNRc6sST7u348zjJ2OhsBDQPFeKcM9w\nZYojWTD4aViMdx6PI68ewab4Tfhryl8dui2z8SlMvLUA+87t63dcU2sTjtcdx/0zcXhOhlPn9Xrb\nXavmzJiLImvPM48qGysRNMVx1xJI5faEG3ye9sHcF8/gH//oXn71KlBZCdQ7FWOedp5yBZLDMfhp\n2EydMBWps1IdfuOO4GCgrXQFdlTu6Hfc7urdiHBPwqyZkzBOhlf6hAmAtzcw64lf4Jvab3qsv9xW\nhmh/s+MLkWCO1xzMmF2K3Fx0zX20cyeQ9MtmXP5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"text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "RMSE: 0.00317380360121\n" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- As expected, it's a bit worse on the original signal\n", "- But it doesn't get hugely worse when tested on a different signal\n", "- What about higher frequency inputs? Or lower frequency?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "z, Z = syde556.generate_signal(T, dt, rms=0.3, limit=2, seed=1)\n", "\n", "J1z = alpha*z+bias\n", "J2z = -alpha*z+bias\n", "\n", "v1z, spikes1z = syde556.lif_spikes(J1z) \n", "v2z, spikes2z = syde556.lif_spikes(J2z)\n", "\n", "fspikes1z = numpy.convolve(spikes1z, h, mode='same')\n", "fspikes2z = numpy.convolve(spikes2z, h, mode='same')\n", "\n", "Az = numpy.array([fspikes1z, fspikes2z]).T\n", "\n", "zhat = numpy.dot(Az, d)\n", "\n", "figure()\n", "plot(t, z)\n", "plot(t, zhat)\n", "show()\n", "print 'RMSE:', numpy.average((z-zhat)**2)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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QRFRUVPaQzkN2dnZYWVlRoUIFKlSoQPv27Tlz5ky+wS+Erk7EnOCZes/k2KbRaPC28Wbq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\nE28MdMPO+Ra7wndxPOY4X3b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Pno1Go0FRlDK79EdBzkV6ejp///03e/fu5cGDB7Ru3Zpn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\n", "text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "RMSE: 0.00246507856803\n" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- the decoder needs to be made for the right range of frequencies" ] }, { "cell_type": "markdown", "metadata": {}, "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", "- What does this filter look like?\n", "\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "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(-0.1, 0.1)\n", "\n", "show()\n", "\n", "h_optimal = h\n", "H_optimal = H\n", "xhat_optimal = xhat" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ynoQ3vnooTqf8XkQDFQOFKEjehrzOnw88UPrroRANVAwUoiB5G/IKJlBiYuRr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\nGChERBQSDBQiIgoJBgoREYXE/wNocFN1ddezWAAAAABJRU5ErkJggg==\n", 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"text": [ "" ] } ], "prompt_number": 137 }, { "cell_type": "markdown", "metadata": {}, "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", "collapsed": false, "input": [ "figure(figsize=(8,4))\n", "vlines(dt*numpy.where(spikes1>0)[0], -1, 1)\n", "plot(t, fspikes1*d[0], label='filtered spikes')\n", "ylabel('$x$')\n", "ylim(-1,1)\n", "xlim(0.2, 0.4)\n", "xlabel('time (s)')\n", "legend()\n", "show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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sLHh6elb5encmAOYyGmV43h07gB9/lCl6H3tMxhH/8kvAzc1imyIijevUCVi+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\nXFyQn59f4+eV3cxdXFzQoUM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"text": [ "" ] } ], "prompt_number": 32 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- If we're analyzing the data after the fact, this is fine\n", "- But what if we're just sitting here obseving 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 $\\hat(x)$) 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": {}, "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", "- What is the current that goes into the next neuron thanks to a single spike?\n", "\n", "\n", "\n", "(data stolen from [here](http://www.pnas.org/content/108/29/12131/F2.expansion.html))\n" ] }, { "cell_type": "markdown", "metadata": {}, "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", "collapsed": false, "input": [ "import syde556\n", "import numpy\n", "\n", "dt = 0.001\n", "tau = 0.05\n", "t_h = numpy.arange(1000)*dt-0.5\n", "h = numpy.exp(-t_h/tau)\n", "h[numpy.where(t_h<0)]=0\n", "\n", "figure()\n", "plot(t_h, h)\n", "xlabel('t')\n", "ylabel('h(t)')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [ "t = numpy.arange(1000)*dt\n", "x, X = syde556.generate_signal(1.0, dt, rms=0.3, limit=10, seed=3)\n", "\n", "\n", "alpha = 1.5\n", "bias = 2\n", "J1 = alpha*x+bias\n", "J2 = -alpha*x+bias\n", "\n", "v1, spikes1 = syde556.lif_spikes(J1) \n", "v2, spikes2 = syde556.lif_spikes(J2)\n", "\n", "fspikes1 = numpy.convolve(spikes1, h, mode='same')\n", "fspikes2 = numpy.convolve(spikes2, h, mode='same')\n", "\n", "\n", "A = numpy.array([fspikes1, fspikes2]).T\n", "\n", "\n", "d = syde556.decoders(A, x)\n", "\n", "xhat = numpy.dot(A, d)\n", "\n", " \n", "figure(figsize=(8,4))\n", "plot(t, x)\n", "vlines(dt*numpy.where(spikes1>0)[0], 0, 1)\n", "vlines(dt*numpy.where(spikes2>0)[0], -1, 0)\n", "ylabel('$x$')\n", "ylim(-1,1)\n", "xlabel('time (s)')\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", "ylim(-1,1)\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", "ylim(-1,1)\n", "xlabel('time (s)')\n", "\n", "show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ccIPZrUiCw65BfGF+TvrR9+cbTif9PXvCfbCHnbtIJdxI+oWFiVfTD4XMIOYH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\nfYDzzw+P4K+6XTsoST/WwXx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B2tj6Y/Hbtd/ItECxSNTQOkMRmxyL5wXPOe02rt4YdlZ2OP7wOOccK+yst198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sDJo2LTvL7G7ZIkoN9S40JSxMxHVLejEhb8v1oGy598uSpQ8wcaKo8PAXfZje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\nE+El8xLOcWIOcX3i4CnzBMAeDH769SeMDhmtlbLW0Vh6XP/GDbbpEGW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"text": [ "" ] } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "- What about with more neurons?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import syde556\n", "\n", "import numpy\n", "\n", "N = 50\n", "tau = 0.01\n", "dt = 0.001\n", "T = 1.0\n", "t = numpy.arange(T/dt)*dt\n", "x, X = syde556.generate_signal(T, dt, rms=0.3, limit=10, seed=3)\n", "\n", "encoders = numpy.random.choice([-1, 1], N)\n", "intercepts = numpy.random.uniform(-0.9, 0.9, N)\n", "max_rates = numpy.random.uniform(100, 200, N)\n", "alpha, bias = syde556.find_alpha_and_bias(intercepts, max_rates)\n", "\n", "A = syde556.activity_spikes(x, encoders, alpha, bias)\n", "h = syde556.psc_filter(t-T/2, tau)\n", "\n", "Af = syde556.apply_filter(A, h)\n", "d = syde556.decoders(Af, x, dx=1.0/1000, noise=0.1)\n", "\n", "xhat = numpy.dot(Af, d)\n", "\n", " \n", "figure(figsize=(8,4))\n", "#imshow(A.T, extent=(0,T,-1,1), aspect='auto', interpolation='none', cmap='binary')\n", "plot(t, x, label='$x$')\n", "plot(t, xhat, label='$\\hat{x}$')\n", "ylabel('$x$')\n", "ylim(-1,1)\n", "legend()\n", "xlabel('time (s)')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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pO6sbYGrS1C6PZ2TsSNvfp7L0O0OwvxD9L6/9ktFxo/Hx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\nhdZcrxqkpARITmaPLzRdQEpwisNtGwz8F0PrEP9APP3GRta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0fWW+pgZIjkCYxFdQU4DM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