{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# SYDE 556/750: Simulating Neurobiological Systems\n", "\n", "Accompanying Readings: Chapter 8\n", "\n", "DO ADMIN STUFF: NEW ASSIGNMENT, PROJECT\n", "\n", "jupyter nbconvert --to pdf my_name.assignment1.ipynb\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "\n", "## Dynamics\n", "\n", "- Everything we've looked at so far has been feedforward\n", " - There's some pattern of activity in one group of neurons representing $x$\n", " - We want that to cause some pattern of activity in another group of neurons to represent $y=f(x)$\n", " - These can be chained together to make more complex systems $z=h(f(x)+g(y))$\n", "- What about recurrent networks?\n", " - What happens when we connect a neural group back to itself?\n", " \n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Recurrent functions\n", "\n", "- What if we do exactly what we've done so far in the past, but instead of connecting one group of neurons to another, we just connect it back to itself\n", " - Instead of $y=f(x)$\n", " - We get $x=f(x)$ (???)\n", "- As written, this is clearly non-sensical\n", " - For example, if we do $f(x)=x+1$ then we'd have $x=x+1$, or $x-x=1$, or $0=1$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- But don't forget about time\n", " - What if it was $x_{t+1} = f(x_t)$\n", " - Which makes more sense because we're talking about a real physical system\n", " - This is a lot like a differential equation\n", " - What would happen if we built this?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Try it out\n", "\n", "- Let's try implementing this kind of circuit\n", "- Start with $x_{t+1}=x_t+1$ " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING: pylab import has clobbered these variables: ['piecewise']\n", "`%matplotlib` prevents importing * from pylab and numpy\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "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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DIwDc/W2gmZm1pu6pdF24+5fuPg3YnIsKZlFV1sUUd19d/HIKsFeW65gtVVkX\n+WVe7kqclV8XVaW9ALgCGA18ns3KZVlV18V2Da7JRQjsBSwq83oxW/8zb1lmSTll6oKqrIuk2N51\n8VPgpR1ao9yp0rooHpgxE3ge+EmW6pZtla4LM2sLnOru97KdDWAtU9X/ke8Vd6OPM7ODKptpJoeI\nimSFmR0D/Bjoleu65JK7jwHGmFkv4I/AcTmuUq7cDpTtH6/LQVCZaUB7d883s37AGGD/bX0gF3sC\nS4D2ZV63K562ZZm9KylTF1RlXSRFldaFmR0KPACc4u4rs1S3bNuuvwuPs+/3NbPmO7piOVCVdXEk\nMNLM5gNnAHeb2SlZql82Vbou3H1tSVehu78ENKjs7yIXIfAO0MnMOphZQ+AsYOwWZcYC5wOYWQ9g\nlbsvz241s6Iq66KsuryFU+m6MLP2wDPAee7+cQ7qmC1VWRffLvO8K9DQ3Vdkt5pZUem6cPd9ix/7\nEMcFfu7u2/o/qq2q8nfRuszzbsRpANv8u8h6d5C7F5rZ5cB4IoQecveZZnZpvO0PuPuLZnaCmc0D\n1hG7/nVOVdZF8S/1XaApUGRmvwQOcve1uat55lVlXQC/B5oD95iZAQVeBy9NXsV1cbqZnQ9sAtYD\nZ+auxjtOFdfFNz6S9UpmSRXXxRlmNggoIP4uBlQ2X50sJiKSYLrGv4hIgikEREQSTCEgIpJgCgER\nkQRTCIiIJJhCQEQkwRQCIiIJphAQEUmw/weD/XKjiaefTwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "\n", "model = nengo.Network()\n", "\n", "with model:\n", " ensA = nengo.Ensemble(100, dimensions=1)\n", " \n", " def feedback(x):\n", " return x+1\n", " \n", " conn = nengo.Connection(ensA, ensA, function=feedback, synapse = 0.1)\n", "\n", " ensA_p = nengo.Probe(ensA, synapse=.01)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(.5)\n", "\n", "plot(sim.trange(), sim.data[ensA_p])\n", "ylim(-1.5,1.5);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- That sort of makes sense\n", " - $x$ increases quickly, then hits an upper bound\n", "- How quickly?\n", " - What parameters of the system affect this?\n", "- What are the precise dynamics?\n", "\n", "- What about $f(x)=-x$?" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "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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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with model:\n", " def feedback(x):\n", " return -x\n", " \n", " conn.function = feedback\n", "\n", "sim = nengo.Simulator(model)\n", "sim.run(.5)\n", "\n", "plot(sim.trange(), sim.data[ensA_p])\n", "ylim(-1.5,1.5);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- That also makes sense. What if we nudge it away from zero?" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "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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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from nengo.utils.functions import piecewise\n", "\n", "with model:\n", " stim = nengo.Node(piecewise({0:1, .2:-1, .4:0}))\n", " nengo.Connection(stim, ensA)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(.6)\n", "\n", "plot(sim.trange(), sim.data[ensA_p])\n", "ylim(-1.5,1.5);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- With an input of 1, $x=0.5$\n", "- With an input of -1, $x=-0.5$\n", "- With an input of 0, it goes back to $x=0$\n", "- Does this make sense?\n", " - Why / why not?\n", " - And why that particular timing/curvature?\n", " \n", "- What about $f(x)=x^2$? " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "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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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with model:\n", " stim.output = piecewise({.1:.2, .2:.4, .5:0})\n", " def feedback(x):\n", " return x*x\n", " \n", " conn.function = feedback\n", "\n", "sim = nengo.Simulator(model)\n", "sim.run(.6)\n", "\n", "plot(sim.trange(), sim.data[ensA_p])\n", "ylim(-1.5,1.5); " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Well that's weird\n", " - Stable at $x=0$ with no input \n", " - Stable at .2 \n", " - Unstable at .4, shoots up high\n", " - Something very strange happens around $x=1$ when the input is turned off (why decay if $f(x) = x^2$?)\n", "- Why is this happening?\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Making sense of dynamics\n", "\n", "- Let's go back to something simple\n", "- Just a single feed-forward neural population\n", " - Encode $x$ into current, compute spikes, decode filtered spikes into $\\hat{x}$\n", "- Instead of a constant input, let's change the input\n", " - Change it suddenly from zero to one to get a sense of what's happening with changes" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "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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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "from nengo.utils.functions import piecewise\n", "\n", "model = nengo.Network(seed=4)\n", "\n", "with model:\n", " stim = nengo.Node(piecewise({.3:1}))\n", " ensA = nengo.Ensemble(100, dimensions=1)\n", " \n", " def feedback(x):\n", " return x\n", " \n", " nengo.Connection(stim, ensA)\n", " #conn = nengo.Connection(ensA, ensA, function=feedback)\n", "\n", " stim_p = nengo.Probe(stim)\n", " ensA_p = nengo.Probe(ensA, synapse=0.1)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(1)\n", "\n", "plot(sim.trange(), sim.data[ensA_p], label=\"$\\hat{x}$\")\n", "plot(sim.trange(), sim.data[stim_p], label=\"$x$\")\n", "legend()\n", "ylim(-.2,1.5);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- This was supposed to compute $f(x)=x$\n", "- For a constant input, that works\n", " - But we get something else when there's a change in the input\n", "- What is this difference?\n", " - What affects it?" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "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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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with model:\n", " ensA_p = nengo.Probe(ensA, synapse=0.03)\n", "\n", "sim = nengo.Simulator(model)\n", "sim.run(1)\n", "\n", "plot(sim.trange(), sim.data[ensA_p], label=\"$\\hat{x}$\")\n", "plot(sim.trange(), sim.data[stim_p], label=\"$x$\")\n", "legend()\n", "ylim(-.2,1.5);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- The time constant of the post-synaptic filter\n", "- We're not getting $f(x)=x$\n", "- Instead we're getting $f(x(t))=x(t)*h(t)$\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "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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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tau = 0.03\n", "with model:\n", " ensA_p = nengo.Probe(ensA, synapse=tau)\n", "\n", "sim = nengo.Simulator(model)\n", "sim.run(1)\n", "\n", "stim_filt = nengo.Lowpass(tau).filt(sim.data[stim_p], dt=sim.dt)\n", "\n", "plot(sim.trange(), sim.data[ensA_p], label=\"$\\hat{x}$\")\n", "plot(sim.trange(), sim.data[stim_p], label=\"$x$\")\n", "plot(sim.trange(), stim_filt, label=\"$h(t)*x(t)$\")\n", "legend()\n", "ylim(-.2,1.5);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- So there are dynamics and filtering going on, since there is always a synaptic filter on a connection\n", "- why isn't it exactly the same?\n", "- Recurrent connections are dynamic as well (i.e. passing past information to future state of the population)\n", "- Let's take a look more carefully" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Recurrent connections\n", "\n", "- So a connection actually approximates $f(x(t))*h(t)$\n", "- So what does a recurrent connection do?\n", "\n", " - Also $x(t) = f(x(t))*h(t)$\n", "\n", "- where $$\n", "h(t) = \\begin{cases}\n", " e^{-t/\\tau} &\\mbox{if } t > 0 \\\\ \n", " 0 &\\mbox{otherwise} \n", " \\end{cases}\n", "$$\n", "\n", "- How can we work with this?\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- General rule of thumb: convolutions are annoying, so let's get rid of them\n", "- We could do a Fourier transform\n", " - $X(\\omega)=F(\\omega)H(\\omega)$\n", " - But, since we are studying the response of a system (rather than a continuous signal), there's a more general and appropriate transform that makes life even easier:\n", "- Laplace transform (it is more general because $s = a + j\\omega$)\n", "- The Laplace transform of our equations are:\n", " - $X(s)=F(s)H(s)$\n", " - $H(s)={1 \\over {1+s\\tau}}$\n", "- Rearranging:\n", "\n", "$X(s)=F(s){1 \\over {1+s\\tau}}$\n", "\n", "$X(s)(1+s\\tau) = F(s)$\n", "\n", "$X(s) + X(s)s\\tau = F(s)$\n", "\n", "$sX(s) = {1 \\over \\tau} (F(s)-X(s))$\n", "\n", "- Convert back into the time domain (inverse Laplace):\n", "\n", "${dx \\over dt} = {1 \\over \\tau} (f(x(t))-x(t))$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Dynamics\n", "\n", "- This says that if we introduce a recurrent connection, we end up implementing a differential equation\n", "\n", "- So what happened with $f(x)=x+1$?\n", " - $\\dot{x} = {1 \\over \\tau} (x+1-x)$\n", " - $\\dot{x} = {1 \\over \\tau}$\n", "- What about $f(x)=-x$?\n", " - $\\dot{x} = {1 \\over \\tau} (-x-x)$\n", " - $\\dot{x} = {-2x \\over \\tau}$\n", " - Consistent with figures above, so at inputs of $\\pm 1$ get to $0 = 2x\\pm 1$, $x=\\pm .5$ \n", "- And $f(x)=x^2$? \n", " - $\\dot{x} = {1 \\over \\tau} (x^2-x)$\n", " - Consistent with figure, at input of .2, $0=x^2-x+.2=(x-.7)(x-.2)$, for input of .4 you get imaginary solutions.\n", " - For 0 input, x = 0,1 ... what if we get it over 1 before turning off input?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Synthesis\n", "- What if there's some differential equation we really want to implement?\n", " - We want $\\dot{x} = f(x)$\n", " - So we do a recurrent connection of $f'(x)=\\tau f(x)+x$\n", " - The resulting model will end up implementing $\\dot{x} = {1 \\over \\tau} (\\tau f(x)+x-x)=f(x)$\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Inputs\n", "\n", "- What happens if there's an input as well?\n", " - We'll call the input $u$ from another population, and it is also computing some function $g(u)$\n", " - $x(t) = f(x(t))*h(t)+g(u(t))*h(t)$\n", "\n", "- Follow the same derivation steps\n", " - $\\dot{x} = {1 \\over \\tau} (f(x)-x + g(u))$\n", "\n", "- So if you have some input that you want added to $\\dot{x}$, you need to scale it by $\\tau$\n", "\n", "- This lets us do any differential equation of the form $\\dot{x}=f(x)+g(u)$\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### A derivation\n", "\n", "#### Linear systems\n", "- The book shows that we can implement any equation of the form\n", "\n", "$\\dot{x}(t) = A x(t) + B u(t)$\n", "\n", "- Where $A$ and $x$ are a matrix and vector -- giving a standard control theoretic structure\n", "\n", "- Our goal is to convert this to a structure which has $h(t)$ as the transfer function instead of the standard $\\int$\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Using Laplace on the standard form gives:\n", "\n", "$sX(s) = A X(s) + B U(s)$\n", "\n", "- Laplace on the 'neural control' form gives (as before where $F(s) = A'X(s) + B'U(s)$):\n", "\n", "$X(s) = {1 \\over {1 + s\\tau}} (A'X(s) + B'U(s))$\n", "\n", "$X(s) + \\tau sX(s) = (A'X(s) + B'U(s))$\n", "\n", "$sX(s) = {1 \\over \\tau} (A'X(s) + B'U(s) - X(s))$\n", "\n", "$sX(s) = {1 \\over \\tau} ((A' - 1) X(s) + B'U(s))$\n", "\n", "- Making the 'standard' and 'neural' equations equal to one another, we find that for any system with a given A and B, the A' and B' of the equivalent neural system are given by:\n", "\n", "$A' = \\tau A + I$ and\n", "\n", "$B' = \\tau B$\n", "\n", "- where $I$ is the identity matrix\n", "\n", "- This is nice because lots of engineers think of the systems they build in these terms (i.e. as linear control systems)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "#### Nonlinear systems\n", "- In fact, these same steps can be taken to account for nonlinear control systems as well:\n", "\n", "$\\dot{x}(t) = f(x(t),u(t),t)$\n", "\n", "- For a neural system with transfer function $h(t)$:\n", "\n", "$X(s) = H(s)F'(X(s),U(s),s)$\n", "\n", "$X(s) = {1 \\over {1 + s\\tau}} F'(X(s),U(s),s)$\n", "\n", "$sX(s) = {1 \\over \\tau} (F'(X(s),U(s),s) - X(s))$\n", "\n", "- This gives the general result (slightly more general than what we saw earlier):\n", "\n", "$F'(X(s),U(s),s) = \\tau(F(X(s),U(s),s)) + X(s)$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Applications\n", "\n", "### Eye control\n", "\n", "- Part of the brainstem called the nuclei prepositus hypoglossi\n", "- Input is eye velocity $v$\n", "- Output is eye position $x$\n", "- $\\dot{x}=v$\n", " - This is an integrator ($x$ is the integral of $v$)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- It's a linear system, so, to get it in the standard control form $\\dot{x}=Ax+Bu$ we have:\n", " - $A=0$\n", " - $B=1$\n", "- So that means we need $A'=\\tau 0 + I = 1$ and $B'=\\tau 1 = \\tau$\n", "" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "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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c3lDo6zkWf4yeM3sSHRudZRlOnjsJQEpqCmujbDD9bddv/Lb7N55ZmPUZ79tj\nthMTH8P55PNsPraZ9YfXc/DMQedyHK6aeBXD5g1j8vrJAPwv+n9sO76NhOQEklKS2BGzg/2n9wOQ\nnJrMuqh1pEoqIsKuE7ucy3lg9gP8uuNXL2yNzLzSJiAi84AmGYZ94mHaB7yxTlX43HY4GgSKr0qV\nICbGJ6veEbODV5a9wtR/T/U4zR/7/0AQrq1zrXOYiHDFJ1fQpnob1g7MnMUM+GkAe07tYfF9i4mO\njaZ6+eocizvG+eTzHIs/xuvLX2dWb3t0f+TsEQ6cOcBVNa5i36l9RJ+N5tJKlxIdG02dinU4GmdP\nSJz+z3QevfpR9p/ez/0/3s/THZ+m58yeAOwcspOVB1dyzw/3sGPIDrpM68KL173IxqMbmbhuIpdX\nu5yv/vmKj1Z/xLL7l3H9l9fTsXZH2tVsxwerPgAgvF44P/T5gZC3Q9j9+G6W7VvGuuh1rIteR4OQ\nBgT5BxExK4KGIQ2pHFyZcoHlWLRnEa3DWrPmoTUEvBpgP/sVA9h5Yie/7/sdGSEkpSQB4O9nd9er\nDq6iw2cdCA4IJj4pngV3LyjQd1hUDcPqAuXMBH74AQ4f9mlZSrosMwGw1UEnTuRrmamSSnxSPOUC\ny+Vr/jk75jAtcprHIJCcmsy1X9id/6EnDlGjfA3OJJzhwGl7QmFwQDAAszbPopRfKW5rfBvfb/me\nz9d/DsC6qHVcNekq1j60lqsmXeW27E/WfkKXhl34euPXvLD4BRbes5Cbpt4EwDW1r+GPA38QHBDM\nz31/BuDp355mTdQavt30LYAzADjG1alomzY/XvsxAH8e/JOziWcZ9Msgt/Ve/+X1AKw+tJqwcmHO\n4fFJ8YS8HQJAu0/bcSz+mHOcn/EjYlYEAFGxUew66TrKDwkKYXrkdEKCQjh5/iSf/f2Zc1yqpBJ9\n1mYwkUcieXD2g85gEJ9kHyvaZVqXLLd9bhnJ8lflO8YYKW5lKqm6dYNBg+D224EXX4Q9e2D6dF8X\nq8TatAl697bvbsaNs9VB48fneZmj/xzN0789jYyw/7nElEQOnTnEueRzVAmuQs+ZPZkdMZunf3ua\nVtVa8Vjbxzhy9ggJKQnUqlCLt1e8zfOLnyf++Xh+2f4LN9a/kdAyoew6uYuHf3mYtVFrOZ1w2rm+\n+1rdx+QNk+nfuj97Tu1hy7EtHH7qMGZU9m1NZfzLcC75XJ4/X07K+JfhnsvvYeL/JuJn/KherjqH\nYg9Rxt/+FjXmAAAgAElEQVReD5NxnQF+ASSlJmVazg11b+D3fb/nef1dGnZh/eH1GAw/RvzI0789\nzYr9K3I1b4BfALN6z+KOGXfASBCRfDXY6b2DlEduDcNJSdCypU/LozxkAiEhcPJknpazeM9iUiXV\nWQcOsGTPEkq/VpoGYxvQfEJzRi4dybJ9y1h1cBWT/jeJCWsnsGzfMsLeC6PumLpc8ckVPL/4eQDe\nX/k+vb/rTcOxDfll+y80/qgxi/YscgsAAJM32LrxL9Z/wZ1N7iTmXAzD5g3LsbztarVj/aD1mYa3\nqd4GgLc6v+UcNrPXTNYNXMeB4a7LlzrV6+TsHn+rDZY1ytegc4POxCfbI+q5d83lmWtsG8BdLe/i\nXPI5GoQ0cM43rus4+rfun6kMc++ay7y751GxdEVqlne7RIpNj25i5A0jnf0rB6wE4I0b3wCgc/3O\nHI07ypG4I7Sr2c6tHcAhtEwo3S7txmNXP+Yc1rdFXz7q+hEdanfgjiZ3ZJonL7Q6SOWOXi3scx5P\nzCpbFuLjsxwlIpgMM8YnxdN5SudM09045Ua3YRPWTgDglum3APbIs/fM3s7xkUciubza5UQeieTF\nJS8CcDrhNA/PeRiAysGVebjNw0z830RnvbzDA60f4J5W97B472I+/OtDXuv0GpWDK/Pdlu9YuHuh\n27R/PfgXzas0J0Vsg+u9re7l4JmDLN6zmCn/nkLzCc25o8kdPHjlg4SWCXX7vJse3UStCrUYMHuA\nc1iXhrb65MDwA/gZP979411KlypNl4Zd6FCrA4diD3FtnWv59O9PebLDk0z/Zzof3/YxLau1ZEfM\nDppVacbSfUu5/dLbGTB7AE0qNSHIP4hTz54iJj6G2766jb8O/UXqy6kYY3iiwxOM/H0kAFfVsFVa\n7Wu154ObP2Bgm4E80eEJziWdwxjD8fjjANx+6e3M2zmPikEVOfa0q1rpm03fcDz+OF/931fOYT9F\n/ITpm/+z9jQIKI/cMgFtGC4WMmYCH676kG7nAwk9EUVy3DGqlK0CwC/bf+GX7b+weM9idpzYwcJ7\nFtIotBGj/xzNuDXjMi33/ZXvZ7vetzq/xYtLXsTP+PH3oL+54pMrqFSmEhse3sDMTTPp/V1vHm/7\nOGNXj2XglQPpVL8TFUtXpFVYK0Z1GkWpV0oBEP1ktFs9+o99fuRs4lnKly4PwD2t7iE+KZ7SpUrz\n54E/ubbOtZQNLOtWlnY121HGvwyRRyJpHNqYj7p+xGVVLsuy3M2qNAMgonkESSlJ/LTtJxqENCDu\n+Tj8jK0IearjUzzZ8UkAypcuz1s3vYWIkPpyKnFJcYTXC3cup3GlxgytNJSh7YcCMHHdRLfPUym4\nEovuXWSreNL+PI7P9vv9vzvr86uXr06n+q7sxDHN89c9T4BfAC9c/wI7T+zM9Hnm3TWPhJSEbL+r\nvNI2AeXRrbfCY4/BbbcB994LnTvDfff5ulgl1pYt0KOH+9mgZpTh8YQr6Dn9b3oOqUrN8jVZ89Aa\nGn3UiL2n9uZ7Xd0u7cagNoO4/evbAUh+KRn/V/3x9/Mn6aUkzChDtbLVOPyUPVmgzcQ2zI6YTc0K\nNbNcnhll+Pi2jxl01aAsx+fW0r1LubrG1ZT2L01yajJB/nk7MDl57iQhZUIKVIb8WBe1jiurX4kx\nhsSURAJLefeiS2OMtgko79NMoPhxHB+dTz7Pgl321MAd5w8RnARH447y9+G/eW7Rc84AUKF0BUaF\nu64m7dWsFwCRD0eyc8hOKpWp5BzXomoLEl9MJPrJaGb83wy6XdqN1298HYBSfvZIvmLpis7pHUe1\nAOsGrvMYABwuCbokn5/aJbxeOGUDy+Lv55/nAAD4JAAAtKnRxpkZeDsAFJRWB6nc0SDgc45TRI+c\nPcLcnXPp/5NtpNyTeJTgJBjSdgi7T+7m3T/fdc4T0TyCl294mYYhDXll2SvM6DmDaanTnDuig08c\nJMg/CDPKUDm4MgGlAtyqN/7V4F/Os17m3TWPSsE2aDx29WNujaY5+aHPD3Rt1LXA20B5nwYB5VGm\nTEAbhn0uJfAEdcfUZXDbwc5h8QFQ1ZRjbNexJKUkMWzeMB5q8xDzds7jXw3+BUD3pt1pU6MNfsbP\n7UjUcTS9ftB6qpatmml9V9e8mvl320eA3NzoZufwcbdmblfIzp1N78zT9KroaBBQuaOZgM8ZA4nl\ndpKQksDEdRPp2qgrc3fO5Zw/lElMBSCgVADjb7OnQLYOa+2ct1xgOZpWzvSsJ6dWYa0Kt/Cq2NI2\nAeWRWyZw7pwGgSL25vI3MaMMT85/klRJ5eNNr3PglnZUKF2B2MRY56mO64dvo0zm65eUyhXNBFS2\ntGHYdyb9bxIA7696n/dXuU7h7N2sN6ujVnNdnetIeikJf/wgMdG+9FbfKo80CCiP9AZyRUtEWBO1\nhrByYRyPP87J85mvAi4d04aIFhFMumOS+4gqVeDoUahVq4hKqy4WGgRUtrRhuGhExUZR8317imWN\n8jWIio1yG182oCz9Gg9m8XNv0XlsFguoVg2OHNEgoPJM2wSUR5oJFJ30O/2MAQBgxA0jeLr1W5mG\nO4WF6V1eVb5oEFAeacNw0Tl8NusduOPunmcTz3q+lTS4MgGl8kiDgModzQS8Yvi84dw5I/M58+lv\n8bDsfvtIwyrBVZzD6l1SL/sne2oQUPmkbQLKI2cmkJxse/z151JQn6//nDMJZ/jnyD9c/vHlRLSI\nYMbGGW7TXFvnWpbet5T2tdoDkPhiIv5+/uzenU0mEBYGe/cWbuHVRUkzAZUzR6OwPmS+QM4knOFM\nwhnAPnkKYMbGGRjct6sxhhvq3UBp/9KAvQDMGKOZgCoUeminPHJmAloVlC8iwt5TewkOCKZq2aos\n3rOYNtXb0LZmW/679r/c2vhWLgm6hBZVWtA6rDVvrniTDUeyf/B6tpmABgGVDxoEVM60UThfVh9a\nTfvPbJXOS9e/xKI9i+jVrBf/ueY//HftfwkJCmFaj2nO6TvV70RCsud7xeeYCejZQSofNAgojzQT\nyJ+FuxfiZ/xITk12Dnt12asAfNXjK+cthSuUruA2X5B/UI63R9azg5S3aRBQ2TIGmwnohWI5OnL2\nCDXfr+l8DKLDrY1v5fo61/PsomepVq6ac7jjDp+5le0poqGh9jnQp07BJQW/b78qObzSMGyMucUY\ns9UYs90Y80wW4/sZYzakvVYYY/SJ5RcA5w4nPh6Cg31algvB9V9enykAlA8sz5fdv6RxpcaA69bN\nqS+n8u/L/u29lfv5QbNmsHGj95apSoQCBwFjjB8wDrgZaA70NcZkvGftbuB6EWkFvAZkuPGJKq40\nE8jeL9t/Ydi8YQBEx0a7jRv9r9GcfvY0VcpW4V8N/sXL17/sHJfx4e+5kW0mAFCvHhw8mOflqpLN\nG5lAW2CHiOwTkSRgBtA9/QQiskpETqf1rgKyfw6dKhacO5xz5zQTyOCGL2/g0JlDPLvwWT7860Oq\nja5GucByhNcLd07zRIcn3B42PqrTKA9L85Jy5SAurnDXoS463ggCNYED6foPkv1O/kFgrhfWqwqZ\ns2E4Pl4zgXR2n9zNsn3L+H3f7xw4Y3/6R+OOEn02ml7NenFN7WvYMWRHvo72s5NjJlCuHJw969V1\nqotfkTYMG2M6Af2Ba7ObbuTIkc7u8PBwwsPDC7VcKgclPBM4cPoAtSrUwhjDPT/cw7RIe1rnnB1z\nuKb2Nczd6TqmefTqR3n06kd9U1ANAiXG0qVLWbp0qVeW5Y0gcAiok66/VtowN8aYy4GJwC0ikvlG\n6emkDwLKdzQTsOqMqcOX3b8kvF64MwAAfLPxG97s/CZRsVE5XuTlDTlmAmXLQmxsoZdD+V7Gg+NR\no/Jf1eiN6qA1QCNjTF1jTCAQAcxOP4Expg4wC7hHRHZ5YZ2qKJXghmFJ2+v+tO0nXlv2GsPbDweg\na6OupEgKNzW4iRUPrKBl1ZY0qdSkUMuSY+2SZgIqHwqcCYhIijFmMLAAG1Q+E5EtxphBdrRMBF4C\nQoEJxlaUJolI24KuWxUuZyZQgquDYhPtkfUPW38AYNWAVXyw6gPe6PwG424dR4OQBgCsHLASIbvD\ndO/IsU1AMwGVR15pExCReUCTDMM+Sdf9EPCQN9alfKAEVAcNnzecjrU70qt5LwDOJ59nxf4V1Cxf\nk4qlK3I64TStqrWiXa12znv8p1c2sGyhlzHHTKBFCxgwACIi4JZbCr086uKgVwwrj9wygYoVfV2c\nQjXmrzGsjlpNi6otEIQhc4eweM9iAPq26MvXG7+mWZVmPi5lDplA27bwzDPwxx8aBFSu6a2kVc4u\n8jaBN5e/CcDaqLU0m9CM5hOas3jPYjrX7wzgvMlbUmqSz8oIubyT95VXwqZNhV4WdfHQIKA8Kgln\nB60/vJ7nFz8PQGJKonP4NbWvYcwtY+jZrCd+xo+F9yzkhete8FUxnbLNBMA+aP6HH2Dq1CIpj7rw\naXWQytbF2DC879Q+ygWWo1JwJf675r9u4166/iUeu/ox543eZvaaCUDnBp2LvJwZ5XiKKEDNtOs0\nf/oJ7rmn0MukLnyaCSiP3G4gd5FkAmNWjaHeh/W4aepNfL/le77b8h33t74fgDc7v8ngtoPd7vR5\nwale3b7nGC2UsjQIqGxdDJnAvT/cy5QNU/hk7ScMn2/P819/eD3/9+3/MfDKgVwZdiUAz177LFXL\nVvVlUbOVq0wgMBDmz4czZ4qkTOrCp9VByiO3G8hdoJlAUkoSUyOnci75HN9t/i7T+PB64XRu0Jku\nDbv4oHSFJDQUTpzwdSnUBUIzAeXRhd4w/MHKD1iwawGAMwD8PehvAOpfUh+AmhVq4u/nT5PKhXu1\nrzfkKhMADQIqTzQTUDk7eRJCQnxdihytPLCSDrU7ABCfFM8TC56gcWhjt2laVWtF6supGGNYF7WO\n5lWa+6KohUuDgMoDzQSUR85MICYGKlXydXE8OhZ3jG82fkPHzzvSfUZ3Hpr9EJFHIgHYcWIHjUIb\ncffld7N36F6MMc5bPLep0cbrt3suTLnOBCpUsJnbTz8VepnUhU8zAZUtk5Ro2wQqVMh54kJ2LO4Y\nFYMqElgqkP9F/4/aFWpTpWwVxv41lteWvwbA7G323oWf/v2pc76WVVsy9d8l6Lx5Pz/o1g3uvNM+\nbrL5RZjtKK/RTEB5JAIBsSds9UIxOGKuNroa9/94PwBtJrZhwOwBmFGGMX/Zi7oASplSbvOUDSjL\npNsvjqeZ5joTcEwMsH59oZVHXRw0E1DZKhV7qti0BwjC1xu/Zv6u+QBsPrYZgLOJZ3mi/RNsPLqR\n7k26My1yGqsfWs2ek3uoXr46lYKLb1VWXuQpDr/5JqxZYxv1lcqGBgHlkQiUOnfWPqzEJ+sXPv3f\np/Rt2ZfDZw87h584Zxs9d53chcEgCGHlwtjy2BZEhLdueguAGuVr+KTchSnXmUDlynDDDbYqT6ls\naHWQylap83FFHgREhLF/jSXg1QAG/jKQWu/XovFHjSkb4F6OxqGNaV+rPYDzKt8LqaE3r/L80cqU\nsZnA9u2FUh51cdAgoDwSKdog8MHKDzCjDFM2TGHovKGkSAoApxNOAxCXFOd8spfjyH/xfYtJeimJ\n4IAL94rmvMjT3SCCg+H0aWjSBBISCq1M6sKm1UEqW35eCgIiQuSRSFqFtXIbHhUbRXRsNK3DWvPt\n5m8BGDpvKA1DGrLrpH0SabdLu7Hm0Bom3j6RO5rcQcuqLWletTml/EpRyq9UpnVdrPKcCQQHw9at\ntvvsWShd2utlUhc+DQLKI9sm4J0g8MeBP7jui+t4vO3jNK7UmAOnD/DWTW/RdFxTYhNjiWgRwaqD\nq+hxWQ++3/I9o8JHMX/XfObunMvPfX92W1b/K/oXuDwXqjxnAnv32u6zZ4v1tR7KdzQIqGx5KxP4\nY/8fAIxdPdY57J0/33F2z9g4gz8f+JP6IfX5fsv3dG/anW0x2wq83otJnk4RBdsmsG+f7dZnD+fO\nsGH2GoubbvJ1SYpM8W8TWLcOdu3ydSnybs0aX5egwAqaCcQlxnE07ihgr9zNqGXVls6j/AYhDehQ\nuwNh5cKIfjKaepfU4/2b3+fIU0fy/wFKuuBgiIqy3WfPem+5xsDhwzlPdyHauBH27/d1KYpU8Q8C\nV10FDzzgPiw11b4K0zPPZA4+cXG5OxQ7edI+7/UCJwJ+eQwCB88cJCXVNugOmD2AaqOrMWvzLOeV\nvA7h9cKJfCSSLg270LF2R3Y97trWYeXCAAjyDyrWt3YuannOBCpXdnVv35796aIxMfYW1DlJSnvE\n5qlTeShIOsePw5NP5m/eonDiRP4C5sGDthE+K4mJ0KBBsb29d/EPAgBVM+wI2raFPn1yN+/PP2c+\nMyIx0T6CLzvvvAMTJ7oPK1cOJk+Gbdvg9989z+v4syX59pm03pDb6iARYfGexdT+oDb+r/rz5Pwn\nWRNls6GeM3tyLP6Y24PaW1drDUBgqUD+eOCPwil8SRcW5nq/7z54/HF7BH/unH3/5RfXtG+/nbuH\n00dH2/fYWEhOznuZ5s+H99/P+3zekJoKEyZkP01MTP6CwEsvwRdfZD1u5UrYsweOHcv7cotA8Q4C\njqP9jKdFrFsHC+wtgjl71n1n++ijMHCg7Y6PhzvusNOnt2ED9OiR85dy6FDmYXv2QO/eEB5uj4Yc\nh2Zz57qWFxfn/p5XMTH5O6Vv82bon0Wj6ZgxritHf/4585/3vvvg/vszzZbb6qBtx7fh94ofnae4\nHsE4fs14YuJjqF2htnOYv59tgjr97Gnev9lHO4ILWJ4zAcdTxv7v/+z7gQN22JAh8N57cPvtriP6\noKCcl7dqles/0a4ddO2ah8KkSUx7jvORI67/9xdfwLhxtjslBXbuhH/+cZ9vxgz48MO8ry+9DRvg\nsceyPzjLLggcPeo5mzp2zGYDWXHc0TWrq7dF7LbI6NAhiIiAoUPterPjqPLLJ68EAWPMLcaYrcaY\n7caYZzxMM9YYs8MYs94Y0zq75Z1JSEubHOlTVqnn+fP2vXx5eO451/CffoJJk+xOdKyrEZKjR+3G\njotzpW2rVtkfhKeqpXnz4PXXOZ98Hkn/73P8EEJCEMdpd7feCuPH227Hzt/xpS9ZQuzpY85qkhxV\nrgyDB+f9EYGzZsGXX7oPO34chg+HRYvs57zjDns09o6rUZbvv4fJk9lweEOmRWasDjpw+gDbY9wv\nPnIc8aeXkJJAo9BGbHp0E00rNwVgYreJTO8xnQqlK1zUF3UVGyEh0LIl9O1r+x2/888+swczjmlO\nncr5yXFnz0KHDhBp786KCCxcCIsXu083a5brt5YVRxAIC3NVCz3+uA1Mp06Bvz80bgyXX+4+X//+\nttHWkwUL4Jtvsh534oStDps+3dUPtozpA0JCgv3vZgwCIjZ4VqtmDzB377aZUFyc695MMTHuB403\n3+zazzj2X1kdFP74oytjS2/5cvt5xo51r6Y7dcpur/Qcz5XOLxEp0AsbSHYCdYEAYD3QNMM0XYE5\nad3tgFXZLE/2LpgpkSu+l7veaS8CcvbS+nLZR03FyX4t7t1+fra/c2fbv2KFa9xvv0lyjequ/q++\ncnWDpA4ZIiIiqampsvvEbpHkZLfx/i8hM/6ZIQKS9MzTkurv7zZe4uLs+0cfiXTqJPLss3a527bJ\nuQfuc073/p/vi2zZInLqlC1rfLz8tOVHuWlyZzmx/DfZOv4ViV++xH3ZqanOjz1z00zZ/dl7knr/\n/fLodw9IfGK8pLf7iQdEQOLOxNgBN93kXM65jz4Q2bHDfdk//CB/rZ8j56tWEgFhJG7Lu6nJfolr\n1kaSv5khSSlJ8vGaj6X5+ObCSKT66OrCSGTSuknS6ctOwkjklmm3yH8W/EcYiczZPkcW7looIiJv\nr3hbbpt+m6iCOX1apFy5fMy4Z4/7957xtX27yPvv2+5p00SWL7fdN9zgWsZzz9lho0a5z9upkx1f\nvbrI6tXu4zp2dC/H/Pmu5YDIddfZ4ZdcknW5tm51zQsiZcqIzJkj8tlnImPGiAwY4D7e318kJkak\ndGmRc+dEXn9dZP9+ke7d7fi6de37pk12HsdniY+3/7N9+2x///4ivXqJPPWUne7ECVeZGjZ0dd92\nm2s/1KiRyPXX2+7z5+3wxYvtsurUsf3PPSfy5psiCQkikZH2/zhhgut/HhMjMmiQff/mG9d6Xn9d\n5JVXRF56yTXs3DmRyZOdn93uyvO5D8/vjM4FQHtgbrr+Z4FnMkzzMdAnXf8WoJqH5YmAnKp2ibR9\nEEmtVk0EJLKq/YFu+X6ia0PExrr9aKZHTpek3r1s/2uvOYf/0tj9x7Xr+Ufc+n+vg0hAgOx870UR\nkIS9u9zGt3wYaTOhtQjIonZVZV9FJMUgh+qGioCkzPlFBOR/Q+y6zwUHioC8Oran23L+fX8ZZ3fq\niBEiIK/dW18e6+qa5mxA5j9DasuWkjD1S7dho65HNs75Uvac3COHdm+Q3564U8Zd7Rq/cNGnbtN/\nfHsNSZz5TaZlp3+VeglJ/fNPWTz9ddkRs0PO+FUQAXlqWHNpNLaRMJJsX6/9/prM3DRTbvgi3c5D\neU2+g8C5c/Y7duyMsnq9+GLWw0+etMvo08f2DxrkGte0qcjTT4scO2b7X3kl8/wxMSIffGB3chnH\nNWliA1DFipnHGWPff/zR7qRB5IorMgeMuDi7DhBp3Fjk228ly2AFdj1+fiIDB9rP1KGDHf700+5l\n79XL1T1zpsg//2T7v5Ev0/6bDRvaz7l1q+0PDHSfzlH2Hj3se926Iu+8Y7vvucc13cMPi9x1l6vf\nEXjatMm87oEDRfB9EPg/YGK6/ruBsRmm+RnomK5/IXClh+WJgMQG+sm4q5FfW3TJcsNHV6guE669\nWRL9/JzDqj9h3/dWDJRz/gEev7QZzV3dvXsix8vY7mNl7U7v4W7lnOOPlUG69UUuecb2b6qMLK+N\nxAYg0eVKSXQ5P5l+eYgIdjnnSrmW/Vv9bH446V6L6+VuuqxejLSfQUDi/F3D74hAEvyQP2sFiYB8\n0A55OTz7Ze2v4OpuP8DVfd392e/8GYnsOblHUlJT8rGHUrl15ow92H3kkby/RndfJo88IjK50+cS\nWfe2TN/9maDKWf4m3r1zhTzyiMjmWjarjKzbzTluQaunRED+aGoz0NjSoZnm//mqkSIgr/aOdA6L\nD7T/s5hytT3+FneGdRQBWduwt0zu9IUIyMHQltn+fg+GtpDllz0ke6peLaeCwzKNP16+rsQG2ax3\n6INnPS7H8Vkdr9+bPZzv/2fG19EKDdz6t9S8Mcd5zvsH2+0WUN7zfgBEJH/78GLZMDy4DIxOTOXw\nGniqddaNtwvrRtN73XwCUlO5JK0VIiqtrXF1zUSCkj03/rQ4CsfLwISr4NvmUDqtnbRynG2DeGPh\nWaLLwdi28FNTuGY/tE+wNyprdhwOVYD4AKgUn8KUy1PpF3kSgErnYGq467YIN+2x759f4drMkVUh\n8EX4rYGrPNdmOC05sircdI/7sO2h9n1VTajxsmvmD3+Fb9Kenx6crr33pxkQmAoTrrZtJ//eCqOW\nQsaa2q1pF5EeqAC1053BtvIzV3dcIFky2Hr9uXfNpd4l9fAzxfLndNEoVw4+/xxatMj7q0yX62jR\nAs727M/y//zChHHuv4Ty54+z6dpBbsO2X30X1yUv5oaQSCpznNiQ2lRLdTVClmpxGQAdt35uy5dw\ngsSg8gD8c/2jnK7ckMvjVgLw4reuOn6/UvZ3c0mcqw597kD3s/Wkur0DbJtd33Lvkv6cCa1LzRMZ\nGovT2dLhAWqe2Mi1Wyax9fb/UDE+83UMgf7C1HePkOLnT7vqWV8LcL7MJVx2cKHbsKZn17KvWT4a\nwdPZ2u5eAJKquN/Ztumhxfxz/aPZzls62bYtng+p7hy2FBiZ7lUg+Y0ejhe2Omheuv7cVAdtJZvq\noObPlJdnX75GIiMXCiORhx9vIKdKu0e+Q6896+z2e9l9XNSj92YbWZMN0qun6yg2plGtLKdbH71e\n5jVM6+/YUc4E27aAdzoieyra4QMibJQ+17CuPRpZNifTchoPThf5W9cWRiKVnkb+rubhiObef0uf\nj92PRh7tXVYEZGVNW+bpi8Zk/flGjRIJcGVBjERGPH65s39TZffpf2xi36dc7hq2evwLbtNUetq1\nreIT42XD4Q2ydM9SCXkrRJJSkgrlqFcVgZUrbZ2547vu18+mGiDy7rtuVaoCts47LMzWzYPI7Nmu\ncY5hx4/b97/+stOXcVWBysCBdn0hIZl/tyL2PTxcZNs2kauuch8fHu6qImrZUiQlxe13Ltu2iVSp\nYqt7oqPtsPTVTK+8IrLQtlFJ1aoiM2bY6rETJ0T27nVN56hy+fBD9/X//LN7v2M73ZjuSH78eM/7\nnYfTson0VU2O17RpmZfreJVPd/TftKl9b9jQfVvg++qgUrgahgOxDcOXZZjmVlwNw+3JoWE4/Y6F\nkUiLCS0kvoz9wpOrVbUjZs1ybpzSr5Z233BvvOHxy4ipmZayLl4sHT7tINuOb3M1HIHIC+l2gCKy\n8D+Zv7TnbnTtTB94wX4Jsff1FQE5F3daBGTYzciK2naasCdd86bcfrtzh9p8VDXZdZltsE5Nq9Y6\ntusfWweakOBa52WXOf8kK2sij/zyiKRmVcfq+DOtW+fsD3w1UGTpUmf/V61LiYB0/jxcBCTxOpt2\n39oPueoh5MctP9p1f/yxsyHNUd6P13zs/F5iE2JlxJIRed/xqOJn0CBbZ+TYGQYE2OFTprjvRIcP\nt92vvmobLh317xl/f6++auvqb7/dDrvmGtc4kawbgkXs+0MP2e7x421jq2N8pUqZy12vnsjjj9vx\nqakiiYn2pIvERDvsySdFPv3UNd7BscxevTIP693bvv/6q2t7lC9vp0nfNnDddTYQDRjgGpZVEGjT\nRi7Z8XgAAAlmSURBVOSPP1wB1VHefftEvvtOZNgw94bn4GCRgwdt99ixIj/84BpXpYp9r1ZNpEYN\nkaAgkZo1xedBQOyO+xZgG7ADeDZt2CBgYLppxqUFiw14aA9Im87te16xb4VsPrrZFfmqV7cjduyQ\ng1c0kn/djew6kdaQ+9FH9gjm9Gnb6t62rQhIfO8eIn//LdKggRzs8S877Z497n8CkNTISNtfqZL7\nj3byZNt/880iK1bIik3zZENNG7E3brVnUiS9N1ruHm3Phti8/U/5/p+ZsqSu/fLavNfE9UW+8Yac\niD8hGw5vkITkBEl98snMf4aMP8zWrZ398dd1cI3/5BPnNHGff2I/o4MjmImIHDpkuxcssEdJr77q\nWn6jRnJq+KNy1+fd5HzSeff1p6bK4VWLZOammTZjio8RdZEDe4QsYneczz0nMn267Z8/347/7jvb\nHx9vd9og8vzzmX+/d99td9TLl4uMGOEaHhTk+m3XrGnPknGs+8knXdP9/rsd1q2bSERE5rJ27y6y\napXnz/Gf/9jPcPhw5nGOMjuMHWuHOXbqq1fb4cuX22Ag4joR5YUX7H9KxAZPsA3cBw+KvPee7e/Z\n0+7gHX77zQ4fN86+Jya6l8nPT+T7722gcZRx2TJ7hhHYjMOxrrJl7br27BH5+muRceN8HwS8+coY\nBDJ9cT17OgfN2jzLdVpjQIDIzp3u8yQn22idTuoff0j0yKfdp3N8cQ6DBrmfHuf4MSYnOwdtqZfW\neOw4Iv/gg0xFTp4wXlI7dbLTTJ9uj7DTH5GI2COXyLRGs2bNsv7cbdva7n/+sTtxh5QUe2ZE+lPp\nHN56y/0zgciBA+7TNG0qcsstmefNYEfMjkynj6qLVN++tiokK46DiRUrXMMcpzhmZfBg96Nthxtv\ntKePguu0ShHbP2qUq3/Nmkz/u1wDe9ZPVr7/3o53nGLp0KePPRsIRHbvzjyf479+9Khr2NChWR+8\nOU4vTS8hQWTSJM/bK724OPu+aJGd3rEfy+pgUaSEBIExY0SmTnX7QaSmpsrRs0eznj4v4uNt6uuJ\no44xncPffiHxl9a3PY50uSD+/NN1dJFejRoizzyT9+XFxorMm5f9NOfO2R+mUrnh2Ak6zrMXsW0A\n48dnPf3kyfaanIwSE+2rUyf3I/+MB1NHjthMIT8yZhUZeQosSUl23tOnc7eeY8dse0F6W7e6B4r0\nPv44d0HAISrKZkIOkybZwJtBQYKAsfMXH8YYKW5lypEx8N//wsMP+7okShWulSuhfft8POEmF268\n0f6PmjQp+LKMsVfK5+c+RXPn2vsoFcZnHD8+f3cDyIExBhHJV4H1eQLecOaMzx7GrlSR6tCh8Jad\n8RYUvpKfeyLlVn5uulfINAh4Q/nyvi6BUiq9+fOhTRtflyKz9u1dN/YrJrQ6SCmlLnAFqQ7SSzyV\nUqoE0yCglFIlmAYBpZQqwTQIKKVUCaZBQCmlSjANAkopVYJpEFBKqRJMg4BSSpVgGgSUUqoE0yCg\nlFIlmAYBpZQqwTQIKKVUCaZBQCmlSjANAkopVYJpEFBKqRJMg4BSSpVgGgSUUqoEK1AQMMaEGGMW\nGGO2GWPmG2MqZjFNLWPMYmPMJmPMP8aYxwuyTqWUUt5T0EzgWWChiDQBFgPPZTFNMvCEiDQHOgCP\nGWOaFnC9JcLSpUt9XYRiQbeDi24LF90W3lHQINAdmJzWPRm4M+MEInJYRNandZ8FtgA1C7jeEkF/\n5JZuBxfdFi66LbyjoEGgqogcAbuzB6pmN7Exph7QGvirgOtVSinlBf45TWCM+Q2oln4QIMCLWUwu\n2SynHPAdMDQtI1BKKeVjRsTjfjvnmY3ZAoSLyBFjTBiwREQuy2I6f+AXYK6IfJjDMvNfIKWUKqFE\nxORnvhwzgRzMBu4H3gbuA37yMN3nwOacAgDk/4MopZTKu4JmAqHAt0BtYB/QW0ROGWOqA5NEpJsx\n5hpgGfAPtrpIgOdFZF6BS6+UUqpAChQElFJKXdh8csWwMeYWY8xWY8x2Y8wzHqYZa4zZYYxZb4xp\nXdRlLCo5bQtjTD9jzIa01wpjTEtflLMo5OZ3kTbd1caYJGNMj6IsX1HK5X8k3BjztzFmozFmSVGX\nsajk4j9SwRgzO21f8Y8x5n4fFLNIGGM+M8YcMcZEZjNN3vadIlKkL2zg2QnUBQKA9UDTDNN0Beak\ndbcDVhV1OYvRtmgPVEzrvqUkb4t00y3CnmjQw9fl9uHvoiKwCaiZ1l/Z1+X24bZ4DnjTsR2AGMDf\n12UvpO1xLfY0+0gP4/O87/RFJtAW2CEi+0QkCZiBvegsve7AFAAR+QuoaIypxsUnx20hIqtE5HRa\n7you3gvtcvO7ABiCPdX4aFEWrojlZlv0A2aJyCE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "from nengo.utils.functions import piecewise\n", "from nengo.utils.ensemble import tuning_curves\n", "\n", "tau = 0.01\n", "\n", "model = nengo.Network('Eye control', seed=8)\n", "\n", "with model:\n", " stim = nengo.Node(piecewise({.3:1, .6:0 }))\n", " velocity = nengo.Ensemble(100, dimensions=1)\n", " position = nengo.Ensemble(200, dimensions=1)\n", " \n", " def feedback(x):\n", " return 1*x\n", " \n", " conn = nengo.Connection(stim, velocity)\n", " conn = nengo.Connection(velocity, position, transform=tau, synapse=tau)\n", " conn = nengo.Connection(position, position, function=feedback, synapse=tau)\n", "\n", " stim_p = nengo.Probe(stim)\n", " position_p = nengo.Probe(position, synapse=.01)\n", " velocity_p = nengo.Probe(velocity, synapse=.01)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(1)\n", "\n", "x, A = tuning_curves(position, sim)\n", "#plot(x,A)\n", "\n", "plot(sim.trange(), sim.data[stim_p], label = \"stim\")\n", "plot(sim.trange(), sim.data[position_p], label = \"position\")\n", "plot(sim.trange(), sim.data[velocity_p], label = \"velocity\")\n", "legend(loc=\"best\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- That's pretty good... the area under the input is about equal to the magnitude of the output.\n", "- But, in order to be a perfect integrator, we'd need exactly $x=1\\times x$\n", " - We won't get exactly that\n", " - Neural implementations are always approximations\n", "- Two forms of error:\n", " - $E_{distortion}$, the decoding error\n", " - $E_{noise}$, the random noise error\n", "- What will they do?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Distortion error\n", "\n", "\n", "- What affects this?" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\r", "Building finished in 0:00:01. \n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "from nengo.dists import Uniform\n", "from nengo.utils.ensemble import tuning_curves\n", "\n", "model = nengo.Network(label='Neurons')\n", "with model:\n", " neurons = nengo.Ensemble(200, dimensions=1, max_rates=Uniform(100,200))\n", "\n", " connection = nengo.Connection(neurons, neurons)\n", " \n", "sim = nengo.Simulator(model)\n", "\n", "d = sim.data[connection].weights.T\n", "\n", "x, A = tuning_curves(neurons, sim)\n", "\n", "xhat = numpy.dot(A, d)\n", "\n", "plot(x, xhat-x)\n", "axhline(0, color='k')\n", "xlabel('$x$')\n", "ylabel('$\\hat{x}-x$');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- So we can think of the distortion error as introducing a bunch of local attractors into the representation\n", " - Any 'downward' x-crossing will be a stable point ('upwards' is unstable).\n", " - There will be a tendency to drift towards one of these even if the input is zero.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Noise error\n", "- What will random noise do?\n", " - Push the representation back and forth\n", " - What if it is small?\n", " - What if it is large?\n", "- What will changing the post-synaptic time constant $\\tau$ do?\n", " - How does that interact with noise?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- But real eyes aren't perfect integrators\n", " - If you get someone to look at someting, then turn off the lights but tell them to keep looking in the same direction, their eye will drift back to centre (with about 70s time constant)\n", " - How do we implement that?\n", " \n", "$\\dot{x}=-{1 \\over \\tau_c}x + v$\n", "\n", "- $\\tau_c$ is the time constant of that return to centre\n", " \n", "- $A'=\\tau {-1 \\over \\tau_c}+1$\n", "- $B' = \\tau$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:02. \n" ] }, { "data": { "image/png": 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vo3Xt1lxT9Rqv85v+23QA3vnpHUq/XhqA2b/PBuDJZU9S5906Xu9DKVW0vK7h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\njOP2K6x+/Uv7LWXMlsoczPC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "from nengo.utils.functions import piecewise\n", "\n", "tau = 0.1\n", "tau_c = 2.0\n", "\n", "model = nengo.Network('Eye control', seed=5)\n", "\n", "with model:\n", " stim = nengo.Node(piecewise({.3:1, .6:0 }))\n", " velocity = nengo.Ensemble(100, dimensions=1)\n", " position = nengo.Ensemble(200, dimensions=1)\n", " \n", " def feedback(x):\n", " return (-tau/tau_c + 1)*x\n", " \n", " conn = nengo.Connection(stim, velocity)\n", " conn = nengo.Connection(velocity, position, transform=tau, synapse=tau)\n", " conn = nengo.Connection(position, position, function=feedback, synapse=tau)\n", "\n", " stim_p = nengo.Probe(stim)\n", " position_p = nengo.Probe(position, synapse=.01)\n", " velocity_p = nengo.Probe(velocity, synapse=.01)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(5)\n", "\n", "plot(sim.trange(), sim.data[stim_p], label = \"stim\")\n", "plot(sim.trange(), sim.data[position_p], label = \"position\")\n", "plot(sim.trange(), sim.data[velocity_p], label = \"velocity\")\n", "legend(loc=\"best\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- That also looks right. Note that as $\\tau_c \\rightarrow \\infty$ this will approach the integrator.\n", "- Humans (a) and Goldfish (b)\n", "- Humans have more neurons doing this than goldfish (~1000 vs ~40)\n", "- They also have slower decay (70 s vs. 10 s).\n", "- Why do these fit together?\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Controlled Integrator\n", "\n", "- What if we want an integrator where we can adjust the decay on-the-fly?\n", "- Separate input telling us what the decay constant $d$ should be\n", "\n", "$\\dot{x} = -d x + v$\n", "\n", "- So there are two inputs: $v$ and $d$\n", "\n", "\n", "- This is no longer in the standard $Ax + Bu$ form. Sort of...\n", " - Let $A = -d(t)$, so it's not a matrix\n", " - But it is of the more general form: ${dx \\over dt}=f(x)+g(u)$\n", " \n", "- We need to compute a nonlinear function of an input ($d$) and the state variable ($x$)\n", "- How can we do this?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Going to 2D so we can compute the nonlinear function\n", " - Let's have the state variable be $[x, d]$\n", " \n", " " ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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GhVLKk0KIMcbDcj7wPvCDEKJgTPYbUsqk8l67qlElAeuggkBJxadVUGyHWdoE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\n0DKH97fMoecFyKgGaW7QKulxYAX1ciAlZRj1auj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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "from nengo.utils.functions import piecewise\n", "\n", "tau = 0.1\n", "\n", "model = nengo.Network('Controlled integrator', seed=1)\n", "\n", "with model:\n", " vel = nengo.Node(piecewise({.2:1.5, .5:0 }))\n", " dec = nengo.Node(piecewise({.7:.2, .9:0 }))\n", " \n", " velocity = nengo.Ensemble(100, dimensions=1)\n", " decay = nengo.Ensemble(100, dimensions=1)\n", " position = nengo.Ensemble(400, dimensions=2)\n", " \n", " def feedback(x):\n", " return -x[1]*x[0]+x[0], 0\n", " \n", " conn = nengo.Connection(vel, velocity)\n", " conn = nengo.Connection(dec, decay)\n", " conn = nengo.Connection(velocity, position[0], transform=tau, synapse=tau)\n", " conn = nengo.Connection(decay, position[1], synapse=0.01)\n", " conn = nengo.Connection(position, position, function=feedback, synapse=tau)\n", "\n", " position_p = nengo.Probe(position, synapse=.01)\n", " velocity_p = nengo.Probe(velocity, synapse=.01)\n", " decay_p = nengo.Probe(decay, synapse=.01)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(1)\n", "\n", "plot(sim.trange(), sim.data[decay_p])\n", "lineObjects = plot(sim.trange(), sim.data[position_p])\n", "plot(sim.trange(), sim.data[velocity_p])\n", "legend(('decay','position','decay','velocity'),loc=\"best\");" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from nengo_gui.ipython import IPythonViz\n", "IPythonViz(model, \"configs/controlled_integrator.py.cfg\")" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Other fun functions\n", "\n", "- Oscillator\n", " - $F = -kx = m \\ddot{x}$ let $\\omega = \\sqrt{\\frac{k}{m}}$\n", " - $\\frac{d}{dt} \\begin{bmatrix}\n", "\\omega x \\\\\n", "\\dot{x}\n", "\\end{bmatrix}\n", "=\n", "\\begin{bmatrix}\n", "0 & \\omega \\\\\n", "-\\omega & 0\n", "\\end{bmatrix}$\n", " - $\\dot{x}=[x_1, -x_0]$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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HIDTEargbljQMFS0VduUGq6udX79rryVfqJ6NlPaY9jhZn9Jj050i33v2UCKj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r25PTRee4384LEkP0XC975HIseHH8b2XjuRYZHvEJS6S1HZpu7MCIwm394uL0sZraqi+8aC7LRs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\nkVv73Vo8KxTKE0/oVGeXLrqy/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "\n", "model = nengo.Network('Oscillator')\n", "\n", "freq = 1\n", "\n", "with model:\n", " stim = nengo.Node(lambda t: [.5,.5] if t<.02 else [0,0])\n", " \n", " osc = nengo.Ensemble(200, dimensions=2)\n", " \n", " def feedback(x):\n", " return x[0]+freq*x[1], -freq*x[0]+x[1]\n", " \n", " nengo.Connection(osc, osc, function=feedback, synapse=.01)\n", " nengo.Connection(stim, osc)\n", " \n", " osc_p = nengo.Probe(osc, synapse=.01)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(.5)\n", "\n", "figure(figsize=(12,4))\n", "subplot(1,2,1)\n", "plot(sim.trange(), sim.data[osc_p]);\n", "xlabel('Time (s)')\n", "ylabel('State value')\n", " \n", "subplot(1,2,2)\n", "plot(sim.data[osc_p][:,0],sim.data[osc_p][:,1])\n", "xlabel('$x_0$')\n", "ylabel('$x_1$');" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "scrolled": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from nengo_gui.ipython import IPythonViz\n", "IPythonViz(model, \"configs/oscillator.py.cfg\")" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Lorenz Attractor (a chaotic attractor)\n", "\n", " - $\\dot{x}=[10x_1-10x_0, -x_0 x_2-x_1, x_0 x_1 - {8 \\over 3}(x_2+28)-28]$\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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jr6+7jtr3LVlCXT5WrKAIyIgR1HEkJ4d6VqekkMMcHQ38+9/Ul3rWLDrGa6+R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\nIYdQx7jzTpLEviwmrK0liS4uZjOb0aM5hz7jDN42Pv6Y6uc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8dw1ipSgkuIEZ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\npRI6Ih3jDAsXwoEPr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/8qXustWyQBcupU8WYXhl48VRQlCENLaPfyaIOEj6R2tuAhg0Z3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\nkauvht/9Tjza6slWlNgz9KqOjBgBjY09Q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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "\n", "model = nengo.Network('Lorenz Attractor', seed=3)\n", "\n", "tau = 0.1\n", "sigma = 10\n", "beta = 8.0/3\n", "rho = 28\n", "\n", "def feedback(x):\n", " dx0 = -sigma * x[0] + sigma * x[1]\n", " dx1 = -x[0] * x[2] - x[1]\n", " dx2 = x[0] * x[1] - beta * (x[2] + rho) - rho\n", " return [dx0 * tau + x[0], \n", " dx1 * tau + x[1], \n", " dx2 * tau + x[2]]\n", "\n", "with model:\n", " lorenz = nengo.Ensemble(2000, dimensions=3, radius=60)\n", " \n", " nengo.Connection(lorenz, lorenz, function=feedback, synapse=tau)\n", " \n", " lorenz_p = nengo.Probe(lorenz, synapse=tau)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(14)\n", "\n", "figure(figsize=(12,4))\n", "subplot(1,2,1)\n", "plot(sim.trange(), sim.data[lorenz_p]);\n", "xlabel('Time (s)')\n", "ylabel('State value')\n", " \n", "subplot(1,2,2)\n", "plot(sim.data[lorenz_p][:,0],sim.data[lorenz_p][:,1])\n", "xlabel('$x_0$')\n", "ylabel('$x_1$');" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from nengo_gui.ipython import IPythonViz\n", "IPythonViz(model, \"configs/lorenz.py.cfg\")" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Note: This is not the original Lorenz attractor. \n", " - The original is $\\dot{x}=[10x_1-10x_0, x_0 (28-x_2)-x_1, x_0 x_1 - {8 \\over 3}(x_2)]$\n", " - Why change it to $\\dot{x}=[10x_1-10x_0, -x_0 x_2-x_1, x_0 x_1 - {8 \\over 3}(x_2+28)-28]$?\n", " - What's being changed here?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Oscillators with different paths\n", "\n", "- Since we can implement any function, we're not limited to linear oscillators\n", "- What about a \"square\" oscillator?\n", " - Instead of the value going in a circle, it traces out a square\n", "\n", "$$\n", "{\\dot{x}} = \\begin{cases}\n", " [r, 0] &\\mbox{if } |x_1|>|x_0| \\wedge x_1>0 \\\\ \n", " [-r, 0] &\\mbox{if } |x_1|>|x_0| \\wedge x_1<0 \\\\ \n", " [0, -r] &\\mbox{if } |x_1|<|x_0| \\wedge x_0>0 \\\\ \n", " [0, r] &\\mbox{if } |x_1|<|x_0| \\wedge x_0<0 \\\\ \n", " \\end{cases}\n", "$$ " ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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qPWuW0grUxeV7l9GlbhelZRRj4kS+P3gQ+VUz3t/9voKKCvPNNxxTJ73fzPHo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "\n", "model = nengo.Network('Square Oscillator')\n", "\n", "tau = 0.02\n", "r=4\n", "\n", "def feedback(x): \n", " if abs(x[1])>abs(x[0]):\n", " if x[1]>0: dx=[r, 0]\n", " else: dx=[-r, 0]\n", " else:\n", " if x[0]>0: dx=[0, -r]\n", " else: dx=[0, r]\n", " return [tau*dx[0]+x[0], tau*dx[1]+x[1]] \n", "\n", "with model:\n", " stim = nengo.Node(lambda t: [.5,.5] if t<.02 else [0,0])\n", " \n", " square_osc = nengo.Ensemble(1000, dimensions=2)\n", " \n", " nengo.Connection(square_osc, square_osc, function=feedback, synapse=tau)\n", " nengo.Connection(stim, square_osc)\n", " \n", " square_osc_p = nengo.Probe(square_osc, synapse=tau)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(2)\n", "\n", "figure(figsize=(12,4))\n", "subplot(1,2,1)\n", "plot(sim.trange(), sim.data[square_osc_p]);\n", "xlabel('Time (s)')\n", "ylabel('State value')\n", " \n", "subplot(1,2,2)\n", "plot(sim.data[square_osc_p][:,0],sim.data[square_osc_p][:,1])\n", "xlabel('$x_0$')\n", "ylabel('$x_1$');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Does this do what you expect?\n", "- How is it affected by:\n", " - Number of neurons?\n", " - Post-synaptic time constant?\n", " - Decoding filter time constant?\n", " - Speed of oscillation (``r``)?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- What about this shape?\n", "\n" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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zljNnrBuLMYa7d30rqGzdanxRJSZ4cuSguNvy5UnelZ1nZ6DV3fdHr17kRznV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\n8D9a/hHvfLFX9b2KtjftiJL/0eSde+6BefNg1SoYNKj04y1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "\n", "model = nengo.Network('Heart Oscillator')\n", "\n", "tau = 0.02\n", "r=4\n", "\n", "def feedback(x): \n", " return [-tau*r*x[1]+x[0], tau*r*x[0]+x[1]]\n", "\n", "def heart_shape(x):\n", " theta = np.arctan2(x[1], x[0])\n", " r = 2 - 2 * np.sin(theta) + np.sin(theta)*np.sqrt(np.abs(np.cos(theta)))/(np.sin(theta)+1.4)\n", " return -r*np.cos(theta), r*np.sin(theta)\n", "\n", "with model:\n", " stim = nengo.Node(lambda t: [.5,.5] if t<.02 else [0,0])\n", " \n", " heart_osc = nengo.Ensemble(1000, dimensions=2)\n", " heart = nengo.Ensemble(100, dimensions=2, radius=4)\n", " \n", " nengo.Connection(stim, heart_osc)\n", " nengo.Connection(heart_osc, heart_osc, function=feedback, synapse=tau)\n", " nengo.Connection(heart_osc, heart, function=heart_shape, synapse=tau)\n", " \n", " heart_p = nengo.Probe(heart, synapse=tau)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(4)\n", "\n", "figure(figsize=(12,4))\n", "subplot(1,2,1)\n", "plot(sim.trange(), sim.data[heart_p]);\n", "xlabel('Time (s)')\n", "ylabel('State value')\n", " \n", "subplot(1,2,2)\n", "plot(sim.data[heart_p][:,0],sim.data[heart_p][:,1])\n", "xlabel('$x_0$')\n", "ylabel('$x_1$');" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- We are doing things differently here\n", "- The actual $x$ value is a normal circle oscillator\n", "- The heart shape is a function of $x$\n", " - But that's just a different decoder\n", "- Would it be possible to do an oscillator where $x$ followed this shape?\n", " - How could we tell them apart in terms of neural behaviour?\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Controlled Oscillator\n", "\n", "- Change the frequency of the oscillator on-the-fly\n", "\n", "- $\\dot{x}=[x_1 x_2, -x_0 x_2]$" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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AlTWbNjEqiKZRcN+5k86D69bRLOPgQT7DY8bQ9ljTKNxVr+4+jGn1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\nQH76iUJOunen379pU+c67zt20H1w5Eiahf3sM8dt9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2GnWjX620ZFKd5ds9DKV15RPNGp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "from nengo.utils.functions import piecewise\n", "\n", "model = nengo.Network('Controlled Oscillator')\n", "\n", "tau = 0.1\n", "freq = 20\n", "\n", "def feedback(x):\n", " return x[1]*x[2]*freq*tau+1.1*x[0], -x[0]*x[2]*freq*tau+1.1*x[1], 0\n", "\n", "with model:\n", " stim = nengo.Node(lambda t: [20,20] if t<.02 else [0,0])\n", " freq_ctrl = nengo.Node(piecewise({0:1, 2:.5, 6:-1}))\n", " \n", " ctrl_osc = nengo.Ensemble(500, dimensions=3)\n", " \n", " nengo.Connection(ctrl_osc, ctrl_osc, function=feedback, synapse=tau)\n", " nengo.Connection(stim, ctrl_osc[0:2])\n", " nengo.Connection(freq_ctrl, ctrl_osc[2])\n", " \n", " ctrl_osc_p = nengo.Probe(ctrl_osc, synapse=0.01)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(8)\n", "\n", "figure(figsize=(12,4))\n", "subplot(1,2,1)\n", "plot(sim.trange(), sim.data[ctrl_osc_p]);\n", "xlabel('Time (s)')\n", "ylabel('State value')\n", " \n", "subplot(1,2,2)\n", "plot(sim.data[ctrl_osc_p][:,0],sim.data[ctrl_osc_p][:,1])\n", "xlabel('$x_0$')\n", "ylabel('$x_1$');" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/html": [ "\n", "
\n", " \n", "
\n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from nengo_gui.ipython import IPythonViz\n", "IPythonViz(model, \"configs/controlled_oscillator.py.cfg\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" }, "livereveal": { "scroll": true, "start_slideshow_at": "selected" } }, "nbformat": 4, "nbformat_minor": 0 }