{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# SYDE 556/750: Simulating Neurobiological Systems\n", "\n", "Accompanying Readings: Chapter 6" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Transformation\n", "\n", "- The story so far:\n", " - The activity of groups of neurons can represent variables $x$\n", " - $x$ can be an aribitrary-dimension vector\n", " - Each neuron has a preferred vector $e$\n", " - Current going into each neuron is $J = \\alpha e \\cdot x + J^{bias}$\n", " - We can interpret neural activity via $\\hat{x}=\\sum a_i d_i$\n", " - For spiking neurons, we filter the spikes first: $\\hat{x}=\\sum a_i(t)*h(t) d_i$\n", " - To compute $d$, generate some $x$ values and find the optimal $d$ (assuming some amount of noise)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- So far we've just talked about neural activity in a single population\n", "- What about connections between neurons?\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Connecting neurons\n", "\n", "- Up till now, we've always had the current going into a neuron be something we computed from $x$\n", " - $J = \\alpha e \\cdot x + J^{bias}$\n", "- This will continue to be how we handle inputs\n", " - Sensory neurons, for example\n", " - Or whatever's coming from the rest of the brain that we're not modelling (yet)\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- But what about other groups of neurons?\n", " - How do they end up getting the amount of input current that we're injecting with $J = \\alpha e \\cdot x + J^{bias}$ ?\n", " - Where does that current come from?\n", " - Inputs from neurons connected to this one\n", " - Through weighted synaptic connections\n", " - Let's think about neurons in a simple case" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### A communication channel\n", "\n", "- Let's say we have two groups of neurons\n", " - One group represents $x$\n", " - One group represents $y$\n", " - Can we pass the value from one group of neurons to the other? \n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Without worrying about biological plausibility to start, we can formulate this in two steps\n", " - Drive the first population $a$ with the input, $x$, then decoded it to give $\\hat{x}$\n", " - Now use $y=\\hat{x}$ to drive the 2nd population $b$, and then decode that\n", "- Let's start by first constructing the two populations\n", " - Stimulate them both directly and decode to compare\n", " \n", "" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "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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hmjxbboIQkFJ2ALeghH4LsFBKuUkI8XchxCyt2a+FEJuEEN8Dvwau146tAu5B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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import nengo\n", "from nengo.dists import Uniform\n", "from nengo.processes import WhiteSignal\n", "from nengo.solvers import LstsqL2\n", "\n", "T = 1.0\n", "max_freq = 10\n", "\n", "model = nengo.Network('Communication Channel', seed=3)\n", "\n", "with model:\n", " stim = nengo.Node(output=WhiteSignal(T, high=max_freq, rms=0.5))\n", " ensA = nengo.Ensemble(20, dimensions=1, neuron_type=nengo.LIFRate())\n", " ensB = nengo.Ensemble(19, dimensions=1, neuron_type=nengo.LIFRate())\n", " temp = nengo.Ensemble(1, dimensions=1, neuron_type=nengo.LIFRate())\n", " \n", " nengo.Connection(stim, ensA)\n", " stim_B = nengo.Connection(stim, ensB)\n", " \n", " connectionA = nengo.Connection(ensA, temp) #This is just to generate the decoders\n", " connectionB = nengo.Connection(ensB, temp) #This is just to generate the decoders\n", " \n", " stim_p = nengo.Probe(stim)\n", " a_rates = nengo.Probe(ensA.neurons, 'rates')\n", " b_rates = nengo.Probe(ensB.neurons, 'rates')\n", " \n", "sim = nengo.Simulator(model, seed=3)\n", "sim.run(T)\n", "\n", "x = sim.data[stim_p]\n", "\n", "d_i = sim.data[connectionA].weights.T\n", "A_i = sim.data[a_rates]\n", "\n", "d_j = sim.data[connectionB].weights.T\n", "B_j = sim.data[b_rates]\n", "\n", "#Add noise\n", "A_i = A_i + np.random.normal(scale=0.2*np.max(A_i), size=A_i.shape)\n", "B_j = B_j + np.random.normal(scale=0.2*np.max(B_j), size=B_j.shape)\n", "\n", "xhat_i = np.dot(A_i, d_i)\n", "yhat_j = np.dot(B_j, d_j)\n", "\n", "t = sim.trange()\n", "figure(figsize=(8,4))\n", "subplot(1,2,1)\n", "plot(t, xhat_i, 'g', label='$\\hat{x}$')\n", "plot(t, x, 'b', label='$x$')\n", "legend()\n", "xlabel('time (seconds)')\n", "ylabel('value')\n", "title('first population')\n", "ylim(-1,1)\n", "\n", "subplot(1,2,2)\n", "plot(t, yhat_j, 'g', label='$\\hat{y}$')\n", "plot(t, x, 'b', label='$y$')\n", "legend()\n", "xlabel('time (seconds)')\n", "ylabel('value')\n", "title('second population')\n", "ylim(-1,1);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- So everything works fine if we drive each population with the same $x$, let's switch to $\\hat{x}$ in the middle" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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t4SslHytiJgaklG3AjahBvwV4R0q5SQhxjxBittHt90KITUKI9cDvgauMfSuA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Have to run previous cells first\n", "model.connections.remove(stim_B)\n", "del stim_B\n", "\n", "def xhat_fcn(t):\n", " idx = int(t/sim.dt)\n", " if idx>=1000: idx=999\n", " return xhat_i[idx]\n", "\n", "with model:\n", " xhat = nengo.Node(xhat_fcn)\n", " \n", " nengo.Connection(xhat, ensB)\n", " \n", " xhat_p = nengo.Probe(xhat)\n", " \n", "sim = nengo.Simulator(model, seed=3)\n", "sim.run(T)\n", "\n", "d_j = sim.data[connectionB].weights.T\n", "B_j = sim.data[b_rates]\n", "\n", "B_j = B_j + numpy.random.normal(scale=0.2*numpy.max(B_j), size=B_j.shape)\n", "\n", "yhat_j = numpy.dot(B_j, d_j)\n", "\n", "t = sim.trange()\n", "figure(figsize=(8,4))\n", "subplot(1,2,1)\n", "plot(t, xhat_i, 'g', label='$\\hat{x}$')\n", "plot(t, x, 'b', label='$x$')\n", "legend()\n", "xlabel('time (seconds)')\n", "ylabel('value')\n", "title('$\\hat{x}$')\n", "ylim(-1,1)\n", "\n", "subplot(1,2,2)\n", "plot(t, yhat_j, 'g', label='$\\hat{y}$')\n", "plot(t, x, 'b', label='$x$')\n", "legend()\n", "xlabel('time (seconds)')\n", "ylabel('value')\n", "title('$\\hat{y}$ (second population)')\n", "ylim(-1,1);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Looks pretty much the same! (just delayed, maybe)\n", "- So now we've passed one value to the other, but it's implausible\n", " - The brain doesn't decode and then re-encode\n", " - Can we skip those steps? Or combine them?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### A shortcut\n", "\n", "- Let's write down what we've done:\n", " - Encode into $a$: $a_i = G_i[\\alpha_i e_i x + J^{bias}_i]$\n", " - Decode from $a$: $\\hat{x} = \\sum_i a_i d_i$\n", " - Set $y = \\hat{x}$\n", " - Encode into $b$: $b_j = G_j[\\alpha_j e_j y + J^{bias}_j]$\n", " - Decode from $b$: $\\hat{y} = \\sum_j b_j d_j$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Now let's just do the substitutions:\n", " - I.e. substitute $y = \\hat{x} = \\sum_i a_i d_i$ into $b$\n", " - $b_j = G_j[\\alpha_j e_j \\sum_i a_i d_i + J^{bias}_j]$\n", " - $b_j = G_j[\\sum_i \\alpha_j e_j d_i a_i + J^{bias}_j]$\n", " - $b_j = G_j[\\sum_i \\omega_{ij}a_i + J^{bias}_j]$\n", " - where $\\omega_{ij} = \\alpha_j e_j \\cdot d_i$ (an outer product) \n", " \n", "- In other words, we can get the entire weight matrix just by multiplying the decoders from the first population with the encoders from the second population" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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KcVLKg6SUx0opN+jOfUlKOUL7ezlWnyEQNVVpzjXJB/b1NgFOHz6dyQMmM673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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Have to run previous cells first\n", "n = nengo.neurons.LIFRate()\n", "\n", "alpha_j = sim.data[ensB].gain\n", "bias_j = sim.data[ensB].bias\n", "encoders_j = sim.data[ensB].encoders.T\n", "\n", "connection_weights = np.outer(alpha_j*encoders_j, d_i)\n", "\n", "J_j = np.dot(connection_weights, sim.data[a_rates].T).T + bias_j\n", "\n", "B_j = n.rates(J_j, gain=1, bias=0) #Gain and bias already in the previous line\n", "\n", "B_j = B_j + numpy.random.normal(scale=0.2*numpy.max(B_j), size=B_j.shape)\n", "\n", "xhat_j = numpy.dot(B_j, d_j)\n", "\n", "figure(figsize=(8,4))\n", "subplot(1,2,1)\n", "plot(t, xhat_i, 'g', label='$\\hat{x}$')\n", "plot(t, x, 'b', label='$x$')\n", "legend()\n", "xlabel('Time (s)')\n", "ylabel('Value')\n", "title('Decode from A')\n", "ylim(-1,1)\n", "\n", "subplot(1,2,2)\n", "plot(t, xhat_j, 'g', label='$\\hat{y}$')\n", "plot(t, x, 'b', label='$y$')\n", "legend()\n", "xlabel('Time (s)')\n", "title('Decode from B');\n", "ylim(-1,1);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- In fact, instead of computing $\\omega_{ij}$ at all, it is (usually) more efficient to just do the encoding/decoding\n", " - Saves a lot of memory space, since you don't have to store a giant weight matrix\n", " - Also, you have NxM multiplies for weights, but only do ~N+M multiplies for encode/decode\n", " " ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "J_j = numpy.outer(numpy.dot(A_i, d_i), alpha_j*encoders_j)+bias_j" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- This means we get the exact same effect as having a weight matrix $\\omega_{ij}$ if we just take the decoded value from one population and feed that into the next population using the normal encoding method\n", " - These are numerically identical processes, since $\\omega_{ij} = \\alpha_j e_j \\cdot d_i$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Spiking neurons\n", "\n", "- The same approach works for spiking neurons\n", " - Do exactly the same as before\n", " - The $a_i(t)$ values are spikes, and we convolve with $h(t)$\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Other transformations\n", "\n", "- So this lets us take an $x$ value and feed it into another population\n", " - Passing information from one group of neurons to the next\n", " - We call this a 'Communication Channel' as you're just sending the information\n", "- What about transforming that information in some way?\n", " - Instead of $y=x$, can we do $y=f(x)$?\n", "- Let's try $y=2x$ to start\n", "- We already have a decoder for $\\hat{x}$, so how do we get a decoder for $\\hat{2x}$?\n", " - Two ways\n", " - Either use $2x$ when computing $\\Upsilon$\n", " - Or just multiply your 'representational' decoder by $2$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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RRVaaavMXXWIIN2EhYT7LAonTCS1bKvNMT0vxYn/psrVGRFOfZGUp5+lM97tC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\n9elUftzqoWNeLZk/HwYP1n1js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UXEUiQ8VQe1MsLcXY/WDXRL/haXjqGmJoNvTANMQ1PB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\n0DCKiMFgMBgMhqBhFBGDwWAwGAxB4/8DfAQiSiAIB4oAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "from nengo.processes import WhiteNoise\n", "from nengo.utils.matplotlib import rasterplot\n", "\n", "T = 1.0\n", "max_freq = 5\n", "\n", "model = nengo.Network()\n", "\n", "with model:\n", " stim = nengo.Node(output=WhiteSignal(T, high=max_freq, rms=0.3))\n", " ensA = nengo.Ensemble(25, dimensions=1)\n", " ensB = nengo.Ensemble(23, dimensions=1)\n", " \n", " nengo.Connection(stim, ensA)\n", " nengo.Connection(ensA, ensB, transform=2) #function=lambda x: 2*x)\n", " \n", " stim_p = nengo.Probe(stim)\n", " ensA_p = nengo.Probe(ensA, synapse=.01)\n", " ensB_p = nengo.Probe(ensB, synapse=.01)\n", " ensA_spikes_p = nengo.Probe(ensA.neurons, 'spikes')\n", " ensB_spikes_p = nengo.Probe(ensB.neurons, 'spikes')\n", " \n", "sim = nengo.Simulator(model, seed=4)\n", "sim.run(T)\n", "\n", "t = sim.trange()\n", "figure(figsize=(8, 6))\n", "subplot(2,1,1)\n", "ax = gca()\n", "plot(t, sim.data[stim_p],'b')\n", "plot(t, sim.data[ensA_p],'g')\n", "ylabel(\"Output EnsA\")\n", "rasterplot(t, sim.data[ensA_spikes_p], ax=ax.twinx(), colors=['k']*25, use_eventplot=True)\n", "#axis('tight')\n", "ylabel(\"Neuron\")\n", "\n", "subplot(2,1,2)\n", "ax = gca()\n", "plot(t, sim.data[stim_p],'b')\n", "plot(t, sim.data[ensB_p],'g')\n", "ylabel(\"Output EnsB\")\n", "xlabel(\"Time\");\n", "rasterplot(t, sim.data[ensB_spikes_p], ax=ax.twinx(), colors=['k']*23, use_eventplot=True)\n", "#axis('tight')\n", "ylabel(\"Neuron\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- What about a nonlinear function?\n", " - $y = x^2$\n", " \n", " " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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+XP3PFyywtd16zq00DVG/GUv/WcqQL4bU0uo09ZXCQlVN2yBuu80nadHeRXy3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\nI6O90QFhwiLLy8cv10SzVU6tefwt3m6YGsbW4mfW1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "from nengo.processes import WhiteNoise\n", "from nengo.utils.matplotlib import rasterplot\n", "\n", "T = 1.0\n", "max_freq = 5\n", "\n", "model = nengo.Network()\n", "\n", "with model:\n", " stim = nengo.Node(output=WhiteSignal(T, high=max_freq, rms=0.3))\n", " ensA = nengo.Ensemble(25, dimensions=1)\n", " ensB = nengo.Ensemble(23, dimensions=1)\n", " \n", " nengo.Connection(stim, ensA)\n", " nengo.Connection(ensA, ensB, function=lambda x: x**2)\n", " \n", " stim_p = nengo.Probe(stim)\n", " ensA_p = nengo.Probe(ensA, synapse=.01)\n", " ensB_p = nengo.Probe(ensB, synapse=.01)\n", " ensA_spikes_p = nengo.Probe(ensA.neurons, 'spikes')\n", " ensB_spikes_p = nengo.Probe(ensB.neurons, 'spikes')\n", " \n", "sim = nengo.Simulator(model, seed=4)\n", "sim.run(T)\n", "\n", "t = sim.trange()\n", "figure(figsize=(8, 6))\n", "subplot(2,1,1)\n", "ax = gca()\n", "plot(t, sim.data[stim_p],'b')\n", "plot(t, sim.data[ensA_p],'g')\n", "ylabel(\"Output\")\n", "rasterplot(t, sim.data[ensA_spikes_p], ax=ax.twinx(), colors=['k']*25, use_eventplot=True)\n", "ylabel(\"Neuron\")\n", "\n", "subplot(2,1,2)\n", "ax = gca()\n", "plot(t, sim.data[stim_p]**2,'b')\n", "plot(t, sim.data[ensB_p],'g')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\");\n", "rasterplot(t, sim.data[ensB_spikes_p], ax=ax.twinx(), colors=['k']*23, use_eventplot=True)\n", "ylabel(\"Neuron\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- When you set the connection 'function' in Nengo, it solves the same decoding equation as before, but for a function.\n", "- In equations:\n", " - $ d^{f(x)} = \\Gamma^{-1} \\Upsilon^{f(x)} $\n", " - $ \\Upsilon_i^{f(x)} = \\sum_x a_i f(x) \\;dx$\n", " - $ \\Gamma_{ij} = \\sum_x a_i a_j \\;dx $\n", " - $ \\hat{f}(x) =\\sum_i a_i d_i^{f(x)}$\n", "\n", "- In code:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "f_x = my_function(x)\n", "\n", "gamma=np.dot(A.T,A)\n", "upsilon_f=np.dot(A.T,f_x)\n", "d_f = np.dot(np.linalg.pinv(gamma),upsilon)\n", "\n", "xhat = np.dot(A, d_f)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- We call standard $d_i$ \"representational decoders\"\n", "- We call $d_i^{f(x)}$ \"transformational decoders\" (or \"decoders for $f(x)$\")" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Adding\n", "\n", "- What if we want to combine the inputs from two different populations?\n", " - Linear case: $z=x+y$\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- We want the total current going into a $z$ neuron to be $J=\\alpha e \\cdot (x+y) + J^{bias}$\n", "- How can we achieve this?\n", "- Again, substitute into the equation, where $z = x+y \\approx \\hat{x}+\\hat{y}$\n", " - $J_k=\\alpha_k e \\cdot (\\hat{x}+\\hat{y}) + J_k^{bias}$\n", " - $\\hat{x} = \\sum_i a_i d_i$\n", " - $\\hat{y} = \\sum_j a_j d_j$\n", " - $J_k=\\alpha_k e_k \\cdot (\\sum_i a_i d_i+\\sum_j a_j d_j) + J_k^{bias}$\n", " - $J_k=\\sum_i(\\alpha_k e_k \\cdot d_i a_i) + \\sum_j(\\alpha_k e_k \\cdot d_j a_j) + J_k^{bias}$\n", " - $J_k=\\sum_i(\\omega_{ik} a_i) + \\sum_j(\\omega_{jk} a_j) + J_k^{bias}$\n", " - $\\omega_{ik}=\\alpha_k e_k \\cdot d_i$ and $\\omega_{jk}=\\alpha_k e_k \\cdot d_j$ \n", "- Putting multiple inputs into a neuron automatically gives us addition!" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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DBgyA7bxN3Ke36ANATCPlPF6v9qec4Aln24T9+/dj/fr1in0ulwvVBZ///Tdw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\nzGTd+P70J1Zi+H//i+x6eEU2I9FfvXo1vvzySzidTng8Hmm9ORrRB1i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sQr/sbXmNRxJ9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+z4JNNb7UXJ0yWS5b969Wo4nU589u5nquON3Pt6OHOdyD4zW8rLFwgiRdxBcaA9Rtpecgn7fe65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\nDwDwwQcfg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "from nengo.processes import WhiteNoise\n", "from nengo.utils.matplotlib import rasterplot\n", "\n", "T = 1.0\n", "max_freq = 5\n", "\n", "model = nengo.Network()\n", "\n", "with model:\n", " stimA = nengo.Node(output=WhiteSignal(T, high=max_freq, rms=0.3, seed=3))\n", " stimB = nengo.Node(output=WhiteSignal(T, high=max_freq, rms=0.3, seed=5))\n", " \n", " ensA = nengo.Ensemble(25, dimensions=1)\n", " ensB = nengo.Ensemble(23, dimensions=1)\n", " ensC = nengo.Ensemble(24, dimensions=1)\n", " \n", " nengo.Connection(stimA, ensA)\n", " nengo.Connection(stimB, ensB)\n", " nengo.Connection(ensA, ensC)\n", " nengo.Connection(ensB, ensC)\n", " \n", " stimA_p = nengo.Probe(stimA)\n", " stimB_p = nengo.Probe(stimB)\n", " ensA_p = nengo.Probe(ensA, synapse=.01)\n", " ensB_p = nengo.Probe(ensB, synapse=.01)\n", " ensC_p = nengo.Probe(ensC, synapse=.01)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(T)\n", "\n", "figure(figsize=(8,6))\n", "#plot(t, sim.data[stimA_p],'g', label=\"$x$\")\n", "plot(t, sim.data[ensA_p],'b', label=\"$\\hat{x}$\")\n", "#plot(t, sim.data[stimB_p],'c', label=\"$y$\")\n", "plot(t, sim.data[ensB_p],'m', label=\"$\\hat{y}$\")\n", "#plot(t, sim.data[stimB_p]+sim.data[stimA_p],'r', label=\"$x+y$\")\n", "plot(t, sim.data[ensC_p],'k', label=\"$\\hat{z}$\")\n", "legend(loc='best')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Vectors\n", "\n", "- Almost nothing changes" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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vvvtOP/7447pfv37aaDRa/tZDQ0P1LbfcomfOnKk3bdqkCwoKLrifgQMHnve/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\noEEZ5EoiUT9J8hcNhlIKtw5uGIOMlsT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OnVRLoCiKUv6EOvMaM38A4ANX2BCfuF3ClCVeatdOtQSKoijlj45o9uGEE1It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\n", 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YHLVkWHC2OAOm8MYuimWTa9Ow8Y+WJ2EAJG4wkpvnkharigJuJwMYyfCdzNEP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\nmdD6Ziu2Wl+3ZqjGSCVpjLG0a9LYaN8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X8RkyZHB6/rBhw/jPP/8QADNnzkwAVEo5pDtx4oRpwN9WpkyZogeHbeMrVqxIALrnmClT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\nCbviiitClvF6vVyxYgX/8Y9/kGx1dLNmzQrrN0yKnAnzdJQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "from nengo.processes import WhiteNoise\n", "from nengo.utils.matplotlib import rasterplot\n", "\n", "T = 1.0\n", "max_freq = 5\n", "\n", "model = nengo.Network()\n", "\n", "with model:\n", " stimA = nengo.Node(output=WhiteSignal(T, high=max_freq, rms=0.3, seed=3), size_out=2)\n", " stimB = nengo.Node(output=WhiteSignal(T, high=max_freq, rms=0.3, seed=5), size_out=2)\n", " \n", " stimA = nengo.Node([.3,.5])\n", " stimB = nengo.Node([.3,-.5])\n", " \n", " ensA = nengo.Ensemble(55, dimensions=2)\n", " ensB = nengo.Ensemble(53, dimensions=2)\n", " ensC = nengo.Ensemble(54, dimensions=2)\n", " \n", " nengo.Connection(stimA, ensA)\n", " nengo.Connection(stimB, ensB)\n", " nengo.Connection(ensA, ensC)\n", " nengo.Connection(ensB, ensC)\n", " \n", " stimA_p = nengo.Probe(stimA)\n", " stimB_p = nengo.Probe(stimB)\n", " ensA_p = nengo.Probe(ensA, synapse=.02)\n", " ensB_p = nengo.Probe(ensB, synapse=.02)\n", " ensC_p = nengo.Probe(ensC, synapse=.02)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(T)\n", "\n", "figure()\n", "plot(sim.data[ensA_p][:,0], sim.data[ensA_p][:,1], 'g', label=\"$\\hat{x}$\")\n", "plot(sim.data[ensB_p][:,0], sim.data[ensB_p][:,1], 'm', label=\"$\\hat{y}$\")\n", "plot(sim.data[ensC_p][:,0], sim.data[ensC_p][:,1], 'k', label=\"$\\hat{z}$\")\n", "legend(loc='best')\n", "\n", "figure()\n", "plot(t, sim.data[stimA_p],'g', label=\"$x$\")\n", "plot(t, sim.data[ensA_p],'b', label=\"$\\hat{x}$\")\n", "legend(loc='best')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\")\n", "\n", "figure()\n", "plot(t, sim.data[stimB_p],'c', label=\"$y$\")\n", "plot(t, sim.data[ensB_p],'m--', label=\"$\\hat{y}$\")\n", "legend(loc='best')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\")\n", "\n", "figure()\n", "plot(t, sim.data[stimB_p]+sim.data[stimA_p],'r', label=\"$x+y$\")\n", "plot(t, sim.data[ensC_p],'k--', label=\"$\\hat{z}$\")\n", "legend(loc='best')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Summary\n", "\n", "- We can use the decoders to find connection weights between groups of neurons\n", " - $\\omega_{ij}=\\alpha_j e_j \\cdot d_i$\n", "- Using connection weights is numerically identical to decoding and then encoding again\n", " - Which can be much more efficient to implement\n", "- Feeding two inputs into the same population results in addition\n", "- These shortcuts rely on two assumptions:\n", " - The input to a neuron is a weighted sum of its synaptic inputs\n", " - $J_j = \\sum_i a_i \\omega_{ij}$\n", " - The mapping from $x$ to $J$ is of the form $J_j=\\alpha_j e_j \\cdot x + J_j^{bias}$\n", "- If these assumptions don't hold, you have to do some other form of optimization \n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- If you already have a decoder for $x$, you can quickly find a decoder for any linear function of $x$\n", " - If the decoder for $x$ is $d$, the decoder for $Mx$ is $Md$\n", "- For some other function of $x$, substitute in that function $f(x)$ when finding $\\Upsilon$\n", "- Taking all of this into account, the most general form of the weights is:\n", " - $\\omega_{ij} = \\alpha_j e_j M d_i^{f(x)}$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### General nonlinear functions\n", "\n", "- What if we want to combine to compute a nonlinear function of two inputs?\n", " - E.g., $z=x \\times y$\n", "- We know how to compute nonlinear functions of a vector space\n", " - E.g., $x^2$\n", " - If $x$ is a vector, you get a bunch of cross terms\n", " - E.g. if $x$ is 2D this gives $x_1^2 + 2 x_1 x_2 + x_2^2$\n", "- This means that if you combine two inputs into a 2D space, you can get out their product" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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6WanvanwiEC6EuAlIAP7laF5K+YGUMkFKmdCqVas6X89Qth3QZkDF+eHDD90X\niI6PiOdU6SlS89TtqBHTuOwy+OUX99igsfLaytdo6N+Qx4Y+5lCzqEsXePlla31CUIMgbuh5A7N3\nzSbvVJ7Faaxfr7oz+iIZ+RkUlRVZVhp796rn8HAPGXUGhrUbhr/wt0iKGPY+8ICHjPJhPOk0MgD7\nPKToijELQoixwFPAZVLKIncYtiZ9Dd3CutE8qDlLl5qrC2f2zzgTRgbV5iwVDLfvPKabMrmfoyeP\n8vmWz7m5981EhETY6hEMSkvVnasjpvWdRlFZEV9t+8qmJWaQkOAae12NIVRoX6Px3HPq2f5v1Vto\n0rAJA9oMsIgXGnVPS5d6xiZfxpNO4w8gTggRK4QIBK4D5tgfIIToC7yPchhH3GGUlJI16WsYHK00\nPL75xpz7/HN3WADdW3XHX/jb4hqhoeacpyWnz0c+WP8BRWVF3D/wfqDq3am/v4M3VdA3si89w3vy\n1bavqmTdeUPDotpQOd3WfuVlNCjzNkbFjGJdxjpOFKntguHD1Xhamuf6mfsqHnMaUspS4F5gAbAT\n+FZKuV0I8YIQ4rKKw/4FhADfCSE2CSHmVHM6p5Gal0rOqRxbPMM+hjFsmKuvrghqEESXsC5sOaKc\nRuPG5pwOhruX4rJi3k16l4s6XkT3Viq577vv1FxsLLz99pnfL4Tgqm5XsTJtJVkFWdx7r4sNdgMp\nuSk09G9IdFOVl2KIFL7wggeNOgujY0dTJstYkbYCgA8+MOd8PZPN3Xg0piGlnCul7Cyl7Cil/EfF\n2DNSyjkVr8dKKSOklH0qHped+Yx1x4hnGE7D/s7JCeGSGlM5g8rA1/P7fY2fdv7EoROHeGCgubwY\nP149L1kC99139nNc0e0KJJLZu2bzzjvmXa6vkpKbQocWHWzptkYWUsTZJbg8xpC2Qwj0D7RtUQUH\nw/79au7nnz1nly/iE4Fwd7L64GpCAkNsd5XuyJZyRHx4PPuP7ef4aVWK3quXGjcCeBr38OHGD2nf\nrD0TOpnKkfn5MHCgNYX2TPQM70lcaBw/7FTiUy1busJS95Gcm2yJZxhOo7q4jjfQKKARg6MHs3Dv\nQttYTX9/GivaaVRiTcYaBrQZgL+f2qj21B6tEQzfdmQbAFu2qMpj7TTcx/5j+1m0dxHT+kzDT/iR\nmwvXXAMLF0Jc3NnfbyCEYHKXyfy+/3cKigt48UVzzte6xzlKtzW2TJs185BRNWRCpwlsytpka3IG\n8Pzz6jmCse8SAAAgAElEQVQ720NG+SA1chpCiKE1GfN1CksK2Zy1mUFtzPqM9HT1fKZgpyuwZVDZ\nyYm0aqVqNXzti8ZX+WTjJwgE0/pOA1RRmBHPsBcirAnjO42npLyEpfuX0rMnvPqqGve15kyZJzI5\nVXrKkm5r9AX3Bjn0MzGx00QA5qeYjT+MZlH2vWs0Z6amK413ajjm06w/tJ4yWWYp6vuxQjqoctcv\nVxPdNJrmQc1tabeg0hnLyswPqcZ1lJWX8cmmTxjXcRztmqm2ifZV3Jdffm7nG9ZuGMEBwSxIUTnT\nxl15s2bem3HkCEdChcbfo7fL98dHxNO6SWvmpZg1wobtKSkeMsoHOaPTEEIMFkI8DLSqEA80Hs8B\nbr73dj1GEHxg9EDArImIiXFNe9czYciJbD1iqt0aXzT2irv1gdJSWLRIvV69Gt57z7P2ACTuS+Rg\n/kFu63ubbawuK7ygBkGMjBnJglT1R3XttWrc6P3uK6tHRzUa//ufevZ2pyGEYELHCSzcu5DSctVn\nwL7mxld+B57mbCuNQFTKawOgid0jH7jKtaa5nzUZa+jQogPhjVVZq9E177bbzvAmF9IrvBfbjmxD\nVvw1G4VT7dr5rkz6gpQFXDTrIkJfDSX6jWim/TyN+x/PZtw4WL4chgzxjhTIjzZ+RMtGLZncRcmh\n7d1r9sLo1q125xzfcTzJucnsy9tH8+bWucoFg95KSm4KAX4BtG2q6nJzcsz0VW93GgAT4yZy7PQx\n2w2ifUO1I26pBPN9zug0pJS/SymfBwZJKZ+3e7whpUx2k41uQUrJ6oOrLVtTBp4K8PUK78WJ4hMc\nOH4AMDO5SkthzRrP2FRbymU5D85/kAlfTGB3zm4Sjv2TyB0v8d3273jvZ/VtbB8gfustJd3iCXIK\nc5i9azY3xd9EwwYNyc83G2/FxdW+dev4jipX1z6Dx8BXNJCMdFsjUcSI+YH3xzQAxnYYi7/wZ16y\n2qK6805TL+zgwTO8UWOjpjGNmUKIxZUfLrXMzaTnp5NZkGkLgtsvVT3mNCJUnq3RkOnCC825sjJH\n7/BeHlv4GG+tfYv7B9zP7FEpLHzlTtZ/dAu7/5KKTFXt1BbafZc++KC1T4U7+XzL5xSXFXNr31sB\nVTVsMHJk7avyO7fsTETjCJanLQfguuvMOV9RXE3JTbFsTdk7O19YaTQPas6QtkNscQ0/PzOpwddr\noKSb9tdq6jQeAR6teDwNbALcHBp2La2btGbzXZu5psc1gHX7x5VNl85Ez/CeALa4RlSUGWfxpRTB\nL7Z8wfTV07n3gnt5c8Kb9Otj/ocu/uXMFWGffHLGaacjpeTjTR+T0DrBlsHmrC90IQQj2o9g2QG1\nVJls1whg7VrnXMOVSClJyU2hYwuz37GvOQ1QWVQbszaSVaC8RGvVR4rrrzf75vgiN/10E5d95fL6\n55o5DSnlervHSinlQ8BAF9vmVvz9/ImPiCciRH2JGdsRF17ouRadTRs2JaZ5jKUy3BC58xWnkXki\nk/vm3cfg6MG8OeFNjh2zpgrdfPOZ33/rrS40zgEbszay5fAWpvWZZhtz5ipgRPsRpB1P48CxA5a2\nwVuqFv97HYdPHuZkyUlL5pS7Olo6k4lx1tTbNm1UNXtBATzyiCctqxsr0lYQHOD6PcKa1mmE2j3C\nhBDjgapNBeoRxpfyP/4BDRt6zo5e4b0sGVQtWqiAuK+kCD6R+ASFJYV8MvkT/P382bfv3M9x331Q\n5BZ9Y1Wb0dC/Idf3vN429swzzjv/8HZKQ2R52nKGDoV161Rlsi/ENIx0W0crDV+KB/SO6E1USBRz\nk+cCKuXZiBHax2h8iUMnDpF2PM1hTNbZ1HR7aj1qO2o9sBp4GNUUqd7j7lTbyvQK78Xu7N0Ulapv\nTSGUDMWMGTB7tmdtOxtbDm9h1uZZPDDwAbqEdQFUto3B7bfDlClnP89//qO2ECZMUP9+o0ucsykq\nLeLLbV9yedfLCWnQgpIStcrYvPns760pPcN70jyouW2L6oILlIqxLziN1FxVqOJopRHpQ7eQQggm\nxU1iQeoCisuKAZVWP2SISjJxVwsEZ2Jkgxnq3K6kpttTsVLKDhXPcVLKi6SUK1xtnCc4dcpcor78\nslVh1hP0iuhFmSxjV/Yu25iRGuip7KKa8sySZ2gW1Iy7ejzJn/6kvmDsuw/GxFClx0RJifk6YZBZ\nLp2ba8ZzXCUwN2f3HHJP5TKtzzRat1ZblJW3AUePrts1/P38GdZumM1pgFrJGrUO3kxqXip+wo/2\nzU3RpmPHVJOwBg08aFgtuLzr5eQX5bN0/1LbWOPGKjPuT3/ynF21ZfXB1QT6B9In0vV3uTXdngqq\nKOr7UQjxgxDiQSFEkKuN8wQzZsD06ep1mzM1n3UTvcIrMqjstqhCQtRz5Vx/byI5J5k5u+dw/4D7\n+XBGcz7/HJ591iqf3bChdetv1Sr15fPPN/JpdNVfaHr3pezYUTUjxFV3gjM3z6RNkzaM7TCW7Gy1\n5bLE7NvDkSPWjKfaMrzdcHbn7OZwwWHA3Brx9rhGal4q7Zq1I9Df7FV77Jh3/x1Wx5jYMQQHBDN7\nl7lcNyrzv/zSQ0bVgdXpq+kf1Z+GDVy/l17T7anPgB4o6ZD/VLye5SqjPElxsfnaG5xG55adCfQP\ntKXdAjz+uHr2ZrXUt9a+RYB/AH+54C82Qbu334YdO8xjmjc3ncZLL5n6P0/8tSmvPdqdxfsWk5T3\nW5Vzu6Kw8dCJQ8xPmc/NvW+21SCAyuM3cJY0/tC2SrbN2FKYMUONJyRYpUq8jdTcVEs8A9T2nS86\njUYBjRjfcTxzds+xpar6StpzZYrLilmfud4t8QyoudPoIqW8TUq5pOLxZ6CzKw3zFPbChN7gNAL8\nA+gW1s3WkAlUDUNwsOdk289G3qk8Ptn0CTf2upGIkAiHonwvvABTp0J3pUBfRab6zv530qVlF176\n4+Eq7/3HP8xeCM5i1uZZlMtybulzi8uTDPpF9aOBXwPWZqg821tuUeMlJSrt01tJzavqNHJyrJ0l\nfYnJXSaTcSKD9ZnrAWswf+hQtTL2BTZnbeZ06Wm3xDOg5k5joxDC5saEEAOBlXW9uBBighBitxAi\nRQjxhIP5hkKIbyrm1wohYup6zTMxdy48YWeFNzgNUHEN+5WGEOruzlulJ77c+iWFJYW29qiOePpp\nlaJ5002qT/ONN1rnA/wD+Ne4f7Hn2Ham3F/1Ty029tzkyc+ElJJPNn3C0LZD6dyyM/dXMvudd2D+\nfMfvrQ2NAhoRHxFvcxr29Q0ZGc67jjM5fvo42YXZdAy1Oo2DB5WsjS9ySedL8BN+ti2qSy8151at\n8u5OhPbYguBtvctpDARWCSH2CyH2ozKoRgohtgoharUTK4TwB2YAE4HuwPVCiO6VDrsNyJNSdgL+\nDbxam2vVFPtiK1ABPm+gV3gvMk5kkHfKXD+HhLgui6iuzNw8k76RfW1BucrpsuPGma+FULUwjpRe\nL+l8CaNiRrGszWQGDi6tMp+S4hzF3+Vpy9mds9tWAV65SO0vfzG79TmLgW0G8kfGH5SVl1n+7YcO\neWfaZ2pe1cyp0lJlq686jZbBLRnebjg/71aZFTNmwFdfedioWrA6fTVtmrSxtd91NTV1GhOAWODC\nikcs6sv+EuDSM7zvTAwAUqSUe6WUxcDXQKWvbSYDn1a8/h4YI4TrhKRL7b6XaisV4QocBcP79oUV\nK+D0aU9Z5ZhtR7aRdCiJW/rcYhuzj0Fs3AiffVazcwkhmH7RdHJP5bL7gOOc1MOH62BsBe/+8S7N\ng5pzXU8V5bZ3Gr/+6pptwIFtBnKi+IQlK87AGcF2Z2Ok29pvT23cqORsevb0lFV1Z3KXyWw7so3U\n3FQCAkyRUl9iTfoat60yoOZO4yUp5QH7h/1YLa/dBrAvCUqvGHN4jJSyFDgOuCT8ax8Ei4z0LjkB\nQ87Cfovq4otVFpG9LpI3MHPTTAL8Arih1w22MftttB49zi2nv29UX26Kv4ljOarc+IlKm5h1dRqH\nCw7z484fmdp7KsEBweTkmGm/Bw/CpEl1O391GPL7xhaVPd4YkDVWGh1amLKws2erGOCYMZ6yqu5M\n7qruU40tKl8L6h8uOMy+Y/ssjeNcTU2dRg/7H4QQDYD+zjendggh7hBCJAkhko7W8tvez89MZfU2\nDZ3WTVrTIqiFZaURE6OenR0Qrgvlspxvtn/DxLiJhAWbS7W66ni9NPolGlz8EI2aH+Mf/1DCci+9\npOaMTnq15aONH1FSXsLdCXeTnKwC8t9+qxINol242u/csjPNGjZjbXpVp+GNfR1Sc1MJbxxOk4bm\nnm1Skip+dVZWmSfo0KIDfSL78N0O8w8pNtac96abR0e4O54BZ2/C9KQQ4gQQL4TIF0KcqPj5MFDX\nEqsMwE59h+iKMYfHVDiqZkBOpWOQUn4gpUyQUia0quVfcLNmMGeOet2rV61O4TKEEPSK6GXRoApX\nLT+86o96XcY60vPTubr71UgJY8fCN9/UPUW2XbN2PHx3K04/GMrmwxuJiIAnn1RzRk1NbSgrL+P9\n9e8zOOQGMrZ0oU8fOHlSzbm6Dauf8OOCNhew7tA6wFoc55VOo1LmVE4O/Pab2S7Vl7m2x7WszVjL\n/mP7AfU9YMRptmyBzMzq3+tpVh1cRYBfAP2i+rntmmfrp/FPKWUT4F9SyqZSyiYVj5ZSyifreO0/\ngDghRKwQIhC4DphT6Zg5wNSK11cBi6UL9X+HDVM1EN5YaV25IZNRo3HTTR40qhLf7/ieAL8ALul8\nCcXFkJio9ued0WnwyWFPEtoolEcXPoqUEj8/uKFiB6xPHxVIv+eeczvn7F2zSTuexupHvmDMGPf3\n6x7YZiBbD2+lsKSQ7783q829MSsuJTfFkjn1ww/quXKqtC9iKFt/t12tNnr2VBl9AP/+t5KwmTvX\nQ8adheVpy7mgzQUENXCf967p9tQ8IcSIyo+6XLgiRnEvsADYCXwrpdwuhHhBCGHo+34EtBRCpAAP\nAVXScp1JQAC88op3LrcrN2Rq0cKc8wbFWyklP+z8gXEdx9E8qLnli89eOqS2NAtqxjMXPkPivkSb\nOmnv3mrO0IZ6992aJwZIKXll5SuWbCB30z+qP2WyjK2HtzJ5snKyjzxi1efyBopKi0jPT6dTC/P/\nats29eyNN1jnSocWHUhoncC3O761jRly6b/+qp6XL/eAYWfhVMkpkg4l2UQw3UVNncajWPtp/AI8\nV9eLSynnSik7Syk7Sin/UTH2jJRyTsXr01LKq6WUnaSUA6SUe+t6TV+lckMm+yLEdes8YZGVDZkb\n2H9sP1d1U12A7Z1GUZEqWps3r27XuCvhLjqFduKxRY9RVl5m20qyZ/fump1r8b7FJB1K4rEhj1nG\nly1TwnWjRtXN1ppgbClsyNxgG2vZUqURu3vVcyb2HduHRFpWGjk5SpvL2+J/teXaHteSdCjJliVW\nWdnaG7cM12Wso6S8hGHthrn1ujUVLLzU7jEO6ImKa2jcROWGTGCK3K1f7wmLrPyw8wf8hT+XdVGL\nxMpbLEOH1j2dMdA/kH+O+Sfbjmxj5qaZDLJLGDGcaE2zqV5d+SpRIVFc2cna0GP4cFi5Eha7oS9l\nu2btCG0UanEaRqq3N602HKXb5uZaV7u+ztXdrwawBMTtazZcIV1TV1akKc3YIW2HuPW6tc1AT0c5\nDo2bMBoy2TuNiy9WKYLeEAz/NflXhrcfTstgFWyp7DR69HDwplpwZbcrGRw9mKeXPM3Q0fmcOAH/\n/Ke555yRoYLZUlbfc+T3/b+zcO9CHhzwMNdfY95Sdu3qHBtrihCCflH92Ji10TZmbI16U4GfkW5r\nv9LIy/Nd+RBHtG/enkHRg/hm+ze2MaMNLDgnLudslqctp2d4T0IbqV/Epk3q4WpqqnL7jhDi7YrH\nf4AVgBO7DGhqQq9wawYVKKfh6V4M6fnpbDm8hUmdVFFDaiqWVcCGDaq3tjMQQvDmhDfJKsjiiUVP\nEBKiajcMp3Trrepu/W9/UzIjO3da318uy7np0U00+O8eHh/xML9V6CGuW1f1WHfQL7IfW49stfV1\nGDxYBfUXLXK/LdWRmptKSGAIrYLNYF9OTv1aaQBc0/0aNmVtYne22uMMCDDbDRuim95CWXkZqw6u\nYlhbc2vq8cetApuuoqYrjR3AnorHGuAxKaUX5e2cH1RuyATqg+vpYrB5ySpYMSlOOQ375lB//KGq\n153JgDYDeHDQg/w36b+2vhT2X2CnT6uEBjB7jxh8tfUr0r9/gNLDVuGqyn093EXfqL4UlxWz46iS\n/w0PhwED4OOPrYrLniQlT/UFN8QYSkvhwAGzVqi+cG3Pa/ETfny+5XPb2C23wIgR3rfS2HJ4CyeK\nTzC8vRkEz89XpQOu5mx1Gg2EEK8BLwK3VjzeBCYLIXykI3D9wVFDpq1bVWzDGRpMtWVuylzaNWtH\n91bdycpSYoQGrvojfnHUi3Ro0YFpP0/j2OljNGrkuHBw5EiYVSHin12YzV+mL3R4Pk9lzDkKht95\npyra3Lq1mje5mdTcVEuW2f79qmq+SxfP2eQKWjdpzdgOY/lsy2eUS7NpS9Om3rfSMOIZ9kHw48e9\nwGkA/wJCgVgpZT8pZT+gA9AceN3Vxmms2ORE7OIaRuD0QG3FXOpIUWkRi/Yu4uK4ixFCcMMNVgdm\nVNk7m8aBjZk1ZRZpx9O4+aebkZQzrJokkptvhrIyyV3/u5v8z2Y6PMZTfeA7hXYiJDCEjZlmXMPo\nK2Lfe8RTlJWXse/YPksQ3IiheWp15kqm9p5K2vE0ft//u22sWTPvW2msOLiCtk3b0q6ZqRbpLU7j\nEuDPUkpb7oCUMh+4G3CRKo+mOuJC46o0ZPr4Y/XsqbjGirQVFBQX2LamKmf9uMppgMoaeeOiN/hl\nzy88tvAx2ratPi+yRfhJfvhvtyrjTz7pWSkWP+FH38i+bMgyVxpGNbI3yKRnnMiguKzYFgSX0rTL\n13SaasLlXS+nSWATPt38qW2sWTNVC+UN9VCgaoyWH1hu2ZoC5TSaNnX99c/mNKSjCmwpZRnghZnL\n9RtHDZmMD66nnMbc5Lk09G/IqBhV2FD5jj042LXXv3fAvdxzwT1MXz2dDTnVV2CdyA2BpdYGCX5+\nqg+8p6ua+0X1Y1PWJsrKywD1fxYc7B1ZcZXTbd97D65W2an10mkEBwRzTY9r+H7H9xQUqxTA4mKV\nctuqlXc4jl3Zu8gsyLR95kD1Ajl50jtWGjuEEDdXHhRC3ARU1XTWuJzKDZmMD66nls8LUhcwvP1w\nGgc2BqoGb+2LEF2BEIK3J77NQ4MeYluvS2lz7T+ZfPuZ93X6qDYfLus1fq70i+pHYUkhe3LMBinh\n4V7iNCql2/70kzlXH50GqC2qkyUn+XHnj4C114uzkzpqw+J9qohodKzSnTl0yKzZckcL6LM5jXuA\ne4QQS4UQ0ysevwP3o7aoNG6mckMm44PriS+YrIIsth/dztjYsbaxfu7TTbPhJ/yYPn46P948k4DB\nH/Bzg4qeqZfdSuM/W9u9NGsGv//u4CQepG+k+iayD4aHhys1X0+TkptCgF8AbZsqbVH7PjP11WkM\nazeMDi062LaoXreL3npD/UzivkRimsfYZOrn2Cn2uaMP0NkECzOklAOBF4D9FY8XKiQ9vGDH9fyj\nckOmiAi1vbLQcVKQS1mybwkAYzqYDRWKi5W8xPbt8Msv7rVnSrcppNyXwsq//ZfPN3/Bgjeu4/B/\nvrEcc/y4GWfxFrHHbq260dC/IZsPm6VPoaHqd+qpBAeD1LxUYlvE4u+nloz2d7L1QeHWEUIIpvae\nyuJ9i9mbt5emTa1qyqtWec62svIylu5fyuiY0baxu+1u392RBVhTGZHFUsp3Kh6JrjZKUz2VGzL5\n+am7+zlzYOZM99qSuC+R5kHNbXfKoPZVg4Ohe3e45BL32gPg7+fPkLZDuDH+Ri7qeBGNA6sGVfz8\n1MrMSCLwNA38GtAjvIfFaRhxFkMwz1Ok5lol0b1lS8/V3Nb3NvyFPx+s/wCAO+4w54YOhRdf9EzX\nzE1Zm8g7nWe7UdtcqcTaHRltLmhkqXEljhoyRUSo52nT3GtL4r5ERsWMst2Fgqqq9mYRO0PSOyys\ndg2hXEV8RLyl2v/ll9XzPffgUJjRHUgpq/TRMORh3LF37knaNG3DpV0u5eONH1NUWkRIiFUM85ln\n4Nln3W+XEc8wguCT7Rpk//abullzNdpp+BiOGjIZQoDu7Gu+N28v+4/ttwXj3n4bvvhCfbCGuFc/\nrcYsWgRXXOFpKxwTHx5PVkEWR06qEnb7Cvc1azxjU86pHPKL8i2aUwUFqqPhvn2escmd3J1wN0cL\nj9oC4p06YakFOniwmje6kMX7F9MtrBtRTdSSwn770llSPWdDOw0fpHJDpsmTVZe8zp3dZ0PiXrVL\nOSZWLZMfeMCMEXgiGH4mDEfhzb2se0eq5iDGzYB9xs7YsY7e4XocqdsePKiEHZs0qe5d9YexHcbS\noUUH3lv/HqC2Ne1jh+6WeSkuK2b5geW2z1zl5Bd3rZy10/BBKjdkAhXcdad8c+K+RKJCougaVlUa\n1tvUT7/91rMyKzXBiFXZryA/+MBT1ihScpVMsH1h3+7d9U8+pDr8hB939r+TZQeWsf3IdsAa/C8q\nquaNLmL5geWcLDnJuI7jAKu0iTvFNrXT8EEqN2QCVYm9davZptKVlMtyFu9bzJgOY2widvbY97v2\nBvz9vT/TJyw4jNZNWluC4fb9RzwRgE7NS0UgbKmdJSXqi6o+yodUx7Q+0wj0D+S9pPeqzLnbacxN\nnkugfyBjYsdw771quwxUGrk7Zf094jSEEKFCiIVCiOSK5yoiy0KIPkKI1UKI7UKILUKIaz1hqzfi\nqCGT0YjpnXdcf/1tR7ZxtPCobZlcVmadr2/qp+6icjC8cWNzzhPFm6l5qbRp2sbWf9roJmhvV32n\nVeNWXNvjWmZunsmx01bZhfXr1R3+k0+6x6nPTZnLyJiRNA5szIwZ5riR3OEuPLXSeAJIlFLGAYk4\n7v1dCNwspewBTADeFELU03Kic8NRQyajUjcw0PXXrxzPsG9N+vzz58/2hbPpHdGbHUd3UFJWAli/\nnD3Rya9yuq3xe3a1NIy38dDghygoLrCl3xrk5qpspVdeqXmb4dqyN28vu7J3ManTJEpLrXPu0Juy\nx1NOYzJgKIJ9Clxe+QAp5R4pZXLF60PAEcBDAtbeR+WGTBddpPowuEODKnFfInGhcbRtpqqEjS+T\nGTNUKqKmdsRHxFNcVszuHPUNZH8DULkTojtIyU3RTgPoE9mH0bGjeXvt27ZmWZXZ5WJRJfueNX/8\nYZ07X5xGhJQys+J1FhBxpoOFEAOAQCDV1Yb5Co4aMjVv7vqGTCVlJfx+4Hdbqu3x4xAZqebOty8T\nZ1M5GG4fLnJ3ID+/KJ/DJw/TuaWZkvfQQ+r5fPw9Pzz4YTJOZPDt9m8dzrv6czc3ZS6dQjsR1zLO\nEgCPiXG/4KbLnIYQYpEQYpuDx2T74ypUdKtVzBVCRAGzgGlSSoc7h0KIO4QQSUKIpKPeoPLmBhw1\nZGrRAg4fVlkuriLpUBIFxQW2rSn7ng/n45eJM+nSsguB/oFszjKD4ctUY0LLFqA7SM5JBiCupdnh\n0JCF8ebiTVcxodMEuoV1Y/rq6UyaVPUD5kqnnl+UT+LeRC6Ju4T8fPj6azWelKSSX9yd5OEypyGl\nHCul7Ong8TNwuMIZGE7hiKNzCCGaAr8CT0kpqy1xklJ+IKVMkFImtPJUCzY346gh07BhqjdEqgvX\nY4n7VDxjVKyqSLUP0LpDlrk+E+AfQPdW3S3S94YjdrvTyK1wGqFxVeY8IZ/hafyEHw8NfohNWZu4\n67VENmywzrvy/+TXPb9SVFbEVd2vYupUUy4oNNS1/Wqqw1PbU3OAqRWvpwI/Vz5ACBEI/AR8JqX8\n3o22+QRGQyb7uEZcxee7cl9sZ5K4L5E+kX0IC1bl5/b9Beqr6qk76R3R27LS8JjTqFhp2Ld5NfBU\nl0NP86f4PxHdNJpX1j5LfLx1teHKlcZ3O74jKiSKwW0HW2Inniqw9JTTeAUYJ4RIBsZW/IwQIkEI\n8WHFMdcAI4BbhBCbKh59PGOu9xHgH0DP8J5szDLbhLq6IVNhSSGrDq6ybU0BZGaa83qlUXfiI+LJ\nLMjk6Em1zeopp7Endw9tm7alUYDaizL0rwIDYeJE99riLTRs0JAnhz3JqoOrWHpgMf/+N2ys+Pg9\n/TTceqvzr1lQXMC8lHlc2e1K/ISfJc51XjkNKWWOlHKMlDKuYhsrt2I8SUp5e8Xrz6WUAVLKPnaP\nTZ6w11tJiEog6VCSTU7E0CtyVXXoyrSVFJcV25zGkSPw2GPmvF5p1J3KwXDDabzxBvz4o/vsSM5J\ntsQzDImYO+6wBujPN27rexttmrTh+d+f54EHpK2hF8Ann8Dll1etW6oLc5Pncrr0NFf3uJoHHrB+\ntt2RXu8IXRHuwyS0TuDY6WPszdsLmF/ajzzimusl7kukgV8DW2/iBx6wzuuVRt3pHWHVoDKcxrZt\ncOWV7rNjT84eOoeamVNGD4n+/d1ngzfSsEFDnhj2BMvTlrN0/9Iq8z//DLNnOy8Z5dvt3xLROIKh\nbYfy9tvWOU85b+00fJiE1gmAymgCq+ZTSorzr7d432IGthlISKCKvlVuEHQ+ZtU4m1aNWxEZEmkL\nhgcHu/+OMqcwh7zTeZaVxoUXquepU6t503nE7f1up3WT1jy1+CnbKt+eq66C//yn7tfJKczhlz2/\ncH3P60G6uG/yOaCdhg/TI7wHDf0bsj5TaYg0aAB//auai6ua9FInjp0+xvrM9ZZ4hn2Krbd0wasP\n2AfDhXC/mqqROWVfo5GXB4MGnd9bUwZBDYJ4YeQLrE5fzQ87HWt4LFhQ9+t8ufVLisuKmdZ3WpXs\nrJ09BpQAABrSSURBVOeeq/v5a4t2Gj5MoH8gvSN721YaYG2Oc/iw8661dP9SymV5ldauAMnJMGuW\n8651vhMfEc/2o9spLS89+8EuYE/OHsCabnvsmLXHx/nOLX1uoWd4Tx5f9Dhr/yihb1/rvDPKxT7Z\n9Al9I/sSHxFvSYQYP94zDaAMtNPwcRKiElifuZ7yirrHG24w5+z7GteVxL2JBAcEMyh6kG0sLw+m\nTDHVNjXOoXdEbyUnkl1V0GiTG1JBknOS8RN+xLaItY3l5WmnYY+/nz+vj3udvXl7WVU6gxUrrPPb\nt9ft/BszN7IxayNXtb+b9HRISzPnPF1Eq52Gj9O/dX/yi/JtvQ9iY5VoIDi34ChxXyLD2w0n0F9t\nsF9zjQrO6i8S52NkUBky6Z9/bs65snDTYE/uHmKbx9p+16Cchs6OszK+03gu6ngRL/z+AiflUf79\nb3Pu5Elrw6Zz5c21b9I4oDEvXXE7bdtCQoI5V1mw0N1op+HjVA6GgxINbNvW2qSlLmSeyGRn9k5L\nPOO779SzVrR1Pl3DuloKN7t1M+fc0S+8crptebnenqqONy56g4LiAh7+7WEefNA6d9FF8NJL537O\nzBOZfLX1K27teyunTlUNInm6Il87DR+ne6vuBDUIsjgNUEtYZ1WpGs3s7eMZBuPGOecaGhNDTsRY\nafTrZ8aM7r7btc1/pJQk5yZb4hkFBcpxaKdRlR7hPXh86OPM2jKLhalVlxZPP22+TkurWQ3Hu3+8\nS2l5KQ8MfMDhfEZGba11Dtpp+DgN/BrQN7Iv6zLWWcYbNVIa//aCgrUlcV8iLYJa0CdSVTLl5ppz\nvXvX/fyaqvSO6M2mLDOAMWWKei4shPvvd911swqyKCgusGRO7VFxca9r4+stPDXiKeJC47jr17tY\nuOQUb71lnffzg9dfV2q0X3xx5nPlnsrl7XVvc3nXy21tdiszaZKTDK8l2mnUA4a0HULSoSSLTHqj\nRrB5M/ToAStX1v7cUkoS9yUyKnYUfsKPNWvMDK3HHlMfCI3z6R3Rm6yCLI6cVEJi9jUwruwdXlmo\n8NQpU1XVvv2sxiSoQRD/d+n/sS9vH9/k31/l/0lKePRR9Xrq1Koy6lLCq6/CwYPwr5X/4kTRCZ4f\nqQKTlWufDh+Gf/7TRf+QGqI/8vWAIW2HUFRWxIZMU3rT/o/t008dvKmGpOalknY8zRbPePllc87T\nWRz1md6Ragln1Gu4yznb0m0rYhoXXKCy8KKizq/e4OfKhTEX8sSwJ/hw44eszD1z/9WOHc3VG8Ch\nQ/DEE9CuHbwy7p9MCHmC8X17IYR1i3nVKggPV/VYnkQ7jXrA0LZDAVh1cJVtbO9ec74u8h7GPu3Y\nDmMBa3WyK/t2nO8YciJGXMNdJOckE+AXQPtmqrOPkTra0fFOicaO50c+z6DoQdy/eBqgYlGOyMtT\nCSQLFsCf/wzR0db5eY+8bBECNXB3s6Xq0E6jHhAREkHHFh1ZedDch9q/35yvS1ex+anziW0eS1xo\nHF9+CevXm3NZWbU/r+bMtAxuSXTTaEtcw14W21UOe3fObjqFdsLfzypbcdllrrlefSLAP4Bvr/qW\nJg1DaPt6R+YsdvDNb8esWfDhh2c8xIK3yPRop1FPGNJ2CKsOrqqihdOhQ+2dRlFpEYl7E5nYaSJC\nCG680eqM3JH+eT7TO6K3ZaXR2YxNuyyDamf2Trq16lZl/I47XHO9+kbbZm355fpfyCnKYuzno1m0\nunpZhpp+Lo26q8aNnWCgE9BOo54wtO1QDp88bFO8HTZMjUdGKvHCEyfO/Zwr0lZwsuQkEzpNsNzZ\ntm+vguCvvuoEwzXV0juiN7uyd9kSHIRQNThQu9/n2SguKyY1N5VuYabTiIyE22/XCsbnQv/W/Zl/\n43wy8jO4fe0gLhzvuMHN3LlnP9fWrep3LqXnpNAro51GPWFI2yEAti2q335T/S4aNYItW6Bnz3M/\n5/yU+QT6BzIqdpRF+2bwYOUwWrd2huWa6ugd2ZvS8lJ2HDXzpjt0UM+ucBrJOcmUyTKL0zh+XDuM\n2jC8/XASb06kpKyE5afeB+CeB899ae6pRktnwiNOQwgRKoRYKIRIrniutmxICNFUCJEuhHCC2HD9\npUd4D5oHNWf5geWAchatWpmtOe21a2rKvJR5DG83nJDAEMtS2n6bROM6jLoY+7iG8SXiCqexM1t1\n+DG2p8rKVPaOJ/pQ1wcuaHMBm+7axCXXHIGYxbwbcO4ibd6YoeiplcYTQKKUMg5IrPi5Ol4ElrnF\nKh/GT/gxMmYkifsSLeO17ed88PhBth/dzsROqrenfS9wf++R9q/XdGzRkeCAYEtcw6VO4+hOBIKu\nYV0Bs8Wsdhq1Jyw4jJ/vmc72dZE8NeH2c36/dhomkwGjeuBT4HJHBwkh+gMRwG9ussunGRM7hn3H\n9tniGgAlJeZ8eXnNzzUvZR4AEzqpSiX7hkvaabgHfz9/eoX3cug0brzR+dfbmb2T9s3bExygvqkK\nCtS4twRgfZnurbrz4ugXbT9vPkMm9fvvm6+9JWPKHk+ViURIKY18tCyUY7AghPADpgM3AWPdaJvP\nYhTgJe5NpEN/tfltH4vYv9/cEz8bs3fNpkOLDnRv1R1QPaoNdCzDffSO6M13O75DSokQwuY0arPd\neDZ2Zu+0xDOM7DjtNJxPr17m67Vr1crxs8/U1u8dd0DXrkoU1BsVF1xmkhBikRBim4PHZPvjpMoR\ndZR1/hdgrpQyvQbXukMIkSSESDrqjO4nPkrXsK60btLaskVlX1F6prsbe46fPs6ivYuY0nUKt9wi\nEAKWVWwQfvGFbvnpTnpH9ibvdB7p+epjYL9dYb+KrCtl5WXsyt5lcRpGerXennI+9h0QBwyAMWOU\ncsNTT6mxESPgnXc8Y9vZcNlKQ0pZ7epACHFYCBElpcwUQkQBRxwcNhgYLoT4CxACBAohCqSUVeIf\nUsoPgA8AEhISzts6ZSEEY2LHMC9lHuWyHD/hZ1lpPPccXHrp2WUIfk3+lZLyEq7odgVDP7PO2Td5\n0rge+2B422ZtiYw057KylAS+Mzhw/ACnS0/bguBJSaaCsV5pOI/t21UfGoBvvlHJKr6GpxY/cwDj\nfnUq8HPlA6SUN0op20kpY4BHgM8cOQyNlYs6XkR2YTbrD6nSbfuVxpYtVu2o6vhx549EhkRauvQB\n3HWXMy3V1IRe4Wofw4hrNGoEv/yi5hxJTdSWnUcrMqcqVhr2Ipd6peE8undXDcxAPY8a5Vl7aoOn\nnMYrwDghRDIqXvEKgBAiQQhxDoX1mspMipuEv/Bn9q7ZQNWeGvaaVI4oLClkXso8pnSdgp8w/zze\nfx/++19nW6s5G00aNqFji46WYLghHHjokPOuUznd1j7FWq80NPZ4xGlIKXOklGOklHFSyrFSytyK\n8SQpZZW8NCnlTCnlve631PcIbRTKiPYj+Hm3Wrx1726dP1tgbV7yPApLCpnSdQqLF5vjt93mZEM1\nNaZ3ZG+b2i2Y0vR10RSrzM6jOwlvHE5oo1DKy63V/tppaOzxwti8pq5c3vVyth/dTkpuCl9/DUuW\nmHNr18K991YvePfp5k+JColidOxoxlQ06nv0UZ1m60n6RPQhJTeFE0WqOKNpUzV+6JDzRCN3ZO+w\nbU1lZFhbiurtKY092mnUQyZ3UQlqs3fNpnlzGDnSnNuxA2bMcLxNdeTkEealzOOm+JtITTG9RFCQ\niw3WnJF+Uf2QSFtluOE0/v53GDKk7ucvl+VsO7KN+Ih4oGoPar3S0NijnUY9pH3z9iS0TuCrbV9V\ne8zWrVXHvtz6JaXlpUztPZV77jHHvUUo7Xylf+v+ALY+8PbZb/v21f38+4/tp6C4wOY0KsfBtNPQ\n2KOdRj1lau+pbMjcwJbDWxzOHz9u/VlKyUcbPyKhdQI9wntY+oCfSyW5xvlEhkQS3TSa9Znrz35w\nLTDiJYbTmD/fOq+3JjX2aKdRT7m+5/UE+AUwc9NMoKqMeeWVxuJ9i9m2vYSrox4DTAkJ0E7DG+gf\n1d+20qhMXX8/Ww5vQSDo0aoHRUXw+ONqvFcv1WFOo7FHO416SsvglkzuOpmZm2ZSUFzAY49Z56dP\nV1WpGRnq59eXvwMzdvH4pVfz4Yeqyb1BWZn77NY4JqF1ArtzdpNflA/ALbeYc5W3k86VLUe28P/t\n3XuQVGV6x/Hvb5gFBMQBh+UiDDMKRBDMrraIDMgKmGLNFmJtcEFNZMtoWCsmFTW1bmKta1JWiESt\nuKVrUKxldyVi4i6Ly00ZJbIoLqPITRRHvDBBuXjhUoTh9uSPc2amG3pmDtDdZ7r7+VRNTZ8+b/c8\nLwP98J73Pc87qOcgunbsmjLCfOKJ1N0CnQNPGgXtrivu4stDX/LUW8GtL4nEyW3efRce+Xkdy2Ys\nbHru1ltTP4g8acQv0S/45b316VsAzJ0LjzwSnEseFZ6ODTs3NF2aSl7G2x6L5bn4edIoYKP6j2Lc\nwHE89PpDHDp6iJUrm2tINZo4ER6en37eo/GeDk8a8bu0b+pkeEkJ9OwZnNu37/Tf98DhA3zwxQdN\nSSN5pOGr5lw6njQK3H3j7qN+Xz0Prn6Qrl1h7FiorExtU3/8D2lfe3HwOUJVVXZjdG3r1bUXA88Z\nmDKvMTSsLfjAA+lXw0WxeddmDEubNHyk4dLxpFHgrqq6iqnDpvLAqgeaPnAWLz6hUc2stK996KFg\n29jbbstykC6SRL9EygqqRCJYfjtvXnOCP1WNq+vSJY32uAGQi58njSLw+J8+Tp9uffjO/O+wpn5N\nmx8Gl14a7NcwfnxQ6bQ91vQvRol+Ceq+qOPL/wsmHiTo0eJGydGs37mebh27UVlWCaQmjbKyM3tv\nV5j846AIlHcpZ+mNS+lU2okr5l7Blb8c2Wr7s87KXMltlzmNk+Frd6xteu5MP9hrd9RySd9LmopT\nJicNv6nTpeNJo0gM6zWM9TPXM2vCLBIVw1tt69ey26eR542kRCW8tv21pueSR4FHj57a+x05doS3\nP3ubRN/mZXWZLILoClNc2726GJR1LuOHY37IoQScNaPldr5qpn3q3qk7I74+IiVpHD7cfL5jx2C3\nvYqKaO+3adcmGo41cNl5lwHwu99ldo8OV5h8pFGEOnVqfrx+PQwenHrek0b7VT2gmjX1azh2PFgH\n3Vi8EILKxQsXtvDCNBoXRiT6Jdi0KdjV8Te/Cc6NG5epiF2h8aRRhCSYPj34gLj4Yti6NdjRr7o6\nOD9mTLzxuZaNHjCa/Yf3s2lXsGfoM8+k1oY6lZIitTtqKetcxgU9LmD//ubnv/1tWLkyM/G6wuNJ\no0jNnw9TpjQf/+hH8PvfB+v977gjvrhc60YPCGqhN16iuuii4O7wRi3tk5LO2h1rSfRLIImvvmp+\n3ldNudbEkjQk9ZT0kqT3w+9pFw5KqpD0oqQtkt6RVJnbSIvP8OHBSMS1T5VllfTp1ofX6pvnNZIv\nJ0adDD909BAbd21smgRPngAfNCgTkbpCFddI4x6gxswGAzXhcTq/AGab2VBgJLArR/E51y5JonpA\nNas/Wd30XPIcVdSSIrU7ajl6/CiX978coGmksXFjsLmTcy2JK2lcC8wLH88DppzYQNIwoNTMXgIw\nswNmdjB3ITrXPlUPqObDrz6kfl89kDrSiLpkdtXHqwAYUzEm5XWDBvn9Ga51cSWN3mbWuLjvM6B3\nmjZDgK8k/VrSOkmzJfl2MK7oja8aDwR7oEDqSOOxx2DnzrbfY9UnqxhaPpTyLuVAMNLo3NlXzrm2\nZS1pSFohaVOar2uT25mZAemm70qBscDdwGXA+cCMFn7WbZJqJdXu3r07sx1xrp0Z0XsE5V3KWbFt\nBXDyB/20aa2//tjxY6zevpqxFWOBYPL8ySdP/eZAV5yydnOfmU1s6ZyknZL6mtmnkvqSfq6iHnjb\nzLaFr1kIjALmntjQzOYAcwASicQprB9xLv+UqITxVeOp+bAGM6OsLHXlQlsjjY27NrKvYR9jBwZJ\nY9Wqk7f/da4lcV2eWgTcHD6+GfhtmjZrgTJJvcLj8cA7OYjNuXZvQtUEduzfwXufv3dSqfstW2D5\n8pZf2zifMbZiLNOnww03ZC9OV3jiShqzgKslvQ9MDI+RlJD0FICZHSO4NFUjaSMg4MmY4nWuXZlQ\nNQGAmm01aWuFTZoEM2emf+3Kj1dScU4FA7oP5Nlnm7f8PalkvnNpyE7lbqA8kEgkrLa2tu2GzuUx\nM2PQTwdxYfmFLL5hMQcPBnMT3bqd2C71+MixI5TPLud7F32P+y6ZQ//+zeeOH/d7dIqZpDfNLM2m\n0Kn8jnDn8pAkpvzRFFZsW8H+hv106QJduwabMrXm9frX2dewj0mDJvHRRye+Z9bCdQXEk4ZzeWrK\nhVM4fOwwy+qWNT3XVt2wpe8vpbSklPeXXMP112c5QFeQvDS6c3lq9IDRlHcpZ+F7C5l60VQAnn8e\nzj235dcsqVtC9YBq7vl+8zrd2bNTN19yrjU+0nAuT3Uo6cDkIZNZvHUxDUcbAOjZEy6/vLlNctXb\nd/e8y4adG7juwutS3ufuu4Mqx85F4UnDuTw29aKp7G3YywtbX2h6Lnny+8CB5scLNi0AEwdfm5G7\nAF3B8aThXB67+vyrOe/s83h63dNpz99+e7Ab3/79xk//pQ/li1bxD3ed03T+V7/KVaSuUHjScC6P\ndSjpwIxvzGD5B8vZvnf7SeefeQb69YPu3cXnL/4Ve9ZVN53r1AluvDGX0bpC4EnDuTx3yzdvAeDR\nNx4FgvmJCy6A3unKgCY5la1hnWvkScO5PFfVo4ppw6fxs9qfsefgHiZMgLo6WLas9ddNmpSb+Fxh\n8aThXAG4d+y9NBxr4J4VzfuZ9enTcvsf/zgHQbmC5EnDuQIwtNdQ7hx1J3PXzeW5zc8B0KtX+rZL\nlsD99+cwOFdQ/OY+5wrE/Vfdz+rtq7np1zfx5o43OXL8CPDwSe3OPz/3sbnC4UnDuQLRubQzL0x/\ngZmLZzL7tdlIIl3S6No197G5wuFVbp0rQHsP7Q2SRkN3SkuDfb+rqqC+Hvbsab3UiCtOUavc+kjD\nuQJ0TufwBr6k/cNffhkWLAhKjTh3ujxpOFckBg+Ge++NOwqX73z1lHPOuchiSRqSekp6SdL74fce\nLbR7UNJmSVskPSr5NjHOORenuEYa9wA1ZjYYqAmPU0gaDVQDFwPDgcuAcbkM0jnnXKq4ksa1wLzw\n8TxgSpo2BnQGOhJM530N2JmT6JxzzqUVV9LobWafho8/A04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IEntRvIe9eA97Cd8XxujIselGirQwGgrx45MneWdZGdX6g42UkrV/WMvISyMx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\ndpyflaHjlPEN1Vs4SZ5SqgT4InCfiAy4ybpS6jGlVIlSqiQ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sGPz4I3zxBVdsgRipkZCQwIYNG3S/zLFjx/TIPwtnLKGR00hKUh3hTHI0du7c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\n+OJ73wNOWob/4he/YOLEicyZMye51qiZyjnn2EQZj6X5mDFjAGjcuHH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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import nengo\n", "from nengo.processes import WhiteNoise\n", "from nengo.utils.matplotlib import rasterplot\n", "\n", "T = 1.0\n", "max_freq = 5\n", "\n", "model = nengo.Network()\n", "\n", "with model:\n", " stimA = nengo.Node(output=WhiteSignal(T, high=max_freq, rms=0.5, seed=3))\n", " stimB = nengo.Node(output=WhiteSignal(T, high=max_freq, rms=0.5, seed=5))\n", " \n", " ensA = nengo.Ensemble(55, dimensions=1)\n", " ensB = nengo.Ensemble(53, dimensions=1)\n", " ensC = nengo.Ensemble(200, dimensions=2)\n", " ensD = nengo.Ensemble(54, dimensions=1)\n", " \n", " nengo.Connection(stimA, ensA)\n", " nengo.Connection(stimB, ensB)\n", " nengo.Connection(ensA, ensC, transform=[[1],[0]])\n", " nengo.Connection(ensB, ensC, transform=[[0],[1]])\n", " nengo.Connection(ensC, ensD, function=lambda x: x[0]*x[1])\n", " \n", " stimA_p = nengo.Probe(stimA)\n", " stimB_p = nengo.Probe(stimB)\n", " ensA_p = nengo.Probe(ensA, synapse=.01)\n", " ensB_p = nengo.Probe(ensB, synapse=.01)\n", " ensC_p = nengo.Probe(ensC, synapse=.01)\n", " ensD_p = nengo.Probe(ensD, synapse=.01)\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(T)\n", "\n", "figure()\n", "plot(t, sim.data[stimA_p],'g', label=\"$x$\")\n", "plot(t, sim.data[ensA_p],'b', label=\"$\\hat{x}$\")\n", "legend(loc='best')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\")\n", "\n", "figure()\n", "plot(t, sim.data[stimB_p],'c', label=\"$y$\")\n", "plot(t, sim.data[ensB_p],'m--', label=\"$\\hat{y}$\")\n", "legend(loc='best')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\")\n", "\n", "figure()\n", "plot(t, sim.data[stimB_p]*sim.data[stimA_p],'r', label=\"$x * y$\")\n", "plot(t, sim.data[ensD_p],'k--', label=\"$\\hat{z}$\")\n", "legend(loc='best')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Multiplication is quite powerful, and has lots of uses\n", " - Gating of signals\n", " - Attention effects\n", " - Binding\n", " - Statistical inference\n", " \n", "- Here's a simple gating example using the same network" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Building finished in 0:00:01. \n", "Simulating finished in 0:00:01. \n" ] }, { "data": { "image/png": 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ShGvTRslM6wIy7mPO+jl0COzAQ6MfAuwHRrz2mqqDcu+96rWfjx+3JdzGkvQl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\nyYNM6zsNUNnIBk+c7a+lcRjR7aLpFNTJSoOqUyf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dgz2mEKMRszFXkExBWFWko4/+l4gChosys+loISHGI7NMQfoUhNVEGhS+ofs5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\noCXELusB/J4V2wFkE9GUaL3/WAwKBQB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odgBHsoiGiNRwvGqJyIXAGTG2LSHY8+P+0wTjxo3zcUCPHz+ehg0buo40/P/p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\nvdvbtm0LdIw/8YTPbm5uLn379nWNkLr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with model:\n", " stimB.output = lambda t: 0 if (t<.5) else .5\n", " \n", "sim = nengo.Simulator(model)\n", "sim.run(T)\n", "\n", "figure()\n", "plot(t, sim.data[stimA_p],'g', label=\"$x$\")\n", "plot(t, sim.data[ensA_p],'b', label=\"$\\hat{x}$\")\n", "legend(loc='best')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\")\n", "\n", "figure()\n", "plot(t, sim.data[stimB_p],'c', label=\"$y$\")\n", "plot(t, sim.data[ensB_p],'m', label=\"$\\hat{y}$\")\n", "legend(loc='best')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\")\n", "\n", "figure()\n", "plot(t, sim.data[stimB_p]*sim.data[stimA_p],'r', label=\"$x+y$\")\n", "plot(t, sim.data[ensD_p],'k', label=\"$\\hat{z}$\")\n", "legend(loc='best')\n", "ylabel(\"Output\")\n", "xlabel(\"Time\");" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" }, "livereveal": { "scroll": true, "start_slideshow_at": "selected" } }, "nbformat": 4, "nbformat_minor": 1 }