{ "cells": [ { "cell_type": "markdown", "id": "e2a3e6f4", "metadata": {}, "source": [ "Title: Computational Models of Neurons\n", "Author: Thomas M. Breuel\n", "Institution: UniKL" ] }, { "cell_type": "code", "execution_count": 65, "id": "97594a4e", "metadata": { "collapsed": false }, "outputs": [], "source": [ "\n", "from IPython.core.display import Image \n", "def fig(x): return Image(filename=\"Figures/\"+x+\".png\") \n", "from pylab import *\n", "def figs(*args):\n", " for i,f in enumerate(args):\n", " subplot(1,len(args),i+1)\n", " axis(\"off\")\n", " fig = imshow(imread(\"Figures/\"+f+\".png\"))" ] }, { "cell_type": "markdown", "id": "2decc70f", "metadata": {}, "source": [ "# Neuron Models" ] }, { "cell_type": "code", "execution_count": 66, "id": "f92168c8", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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1ODgIqYoFQZAmd9dqteFwOJVKhUKh8fFxevz3338XBCGRSDx8+JB8Nuu1trZC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\nNZPJaJpmqA66sa2srHz48AHU1lJYWFhwuVzb29uXLl0yqE2g04dCIcN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"text/plain": [ "" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig(\"neuron-models\")" ] }, { "cell_type": "markdown", "id": "9ae7fffe", "metadata": {}, "source": [ "# Hodgkin-Huxley Model" ] }, { "cell_type": "markdown", "id": "33f675c0", "metadata": {}, "source": [ "(Hodgkin-Huxley Equations)\n", "\n", "We have already seen the Hodgkin-Huxley model. It is given by this set of differential equations:\n", "\n", "$$ C\\frac{dV}{dt} = -g_L(V) (V-V_{Na}) - g_K(V) (V-V_K) - g_l(V) (V-V_l) + I_e $$\n", "\n", "We used a simple model before, but the actual Hodgkin-Huxley model is:\n", "\n", "$$g_i(V_m) = g_i\\varphi^\\alpha\\chi^\\beta$$\n", "\n", "$$\\dot{p}(V_m) = \\rho_\\phi(p_\\infty - p)$$\n", "\n", "$$\\dot{q}(V_m) = \\rho_\\chi(q_\\infty - q)$$\n", "\n", "Here, $p,q$ are fractions of activated, inactivated channels. There are some empirical exponents $\\alpha,\\beta$ and rates that are fit against empirical measurements." ] }, { "cell_type": "markdown", "id": "8e0fb9e6", "metadata": {}, "source": [ "(Hodgkin-Huxley Equations)\n", "\n", "membrane vs neuron:\n", "\n", "- strictly speaking, these are membrane equations for the action potential\n", "- we can use them to describe the whole neuron\n", "\n", "whole neuron description:\n", "\n", "- compute the HH equations at the trigger zone\n", "- the external current $I_e(t)$ is what arrives at the trigger zone from the various inputs\n", "- after the signal has been triggered at the trigger zone (according to HH), it just propagates out\n" ] }, { "cell_type": "markdown", "id": "71c47e89", "metadata": {}, "source": [ "# FitzHugh-Nagumo Model" ] }, { "cell_type": "markdown", "id": "5481eec3", "metadata": {}, "source": [ "(Simplified Dynamical System)\n", "\n", "This model goes away from a physical description, but tries to capture most of the dynamic behavior of Hodgkin-Huxley.\n", "\n", "$$ \\dot{v} = v - v^3/3 - w + I_e $$\n", "$$ \\tau \\dot{w} = v - a - bw $$\n", "\n", "The idea is that we have...\n", "\n", "- a voltage-like variable $v$\n", "- an inhibitory variable $w$\n", "\n", "You can find more information here: http://www.scholarpedia.org/article/FitzHugh-Nagumo_model" ] }, { "cell_type": "code", "execution_count": 67, "id": "467a4166", "metadata": { "collapsed": false }, "outputs": [], "source": [ "def fhm(v=0,w=0,a=0.0,b=0.0,tau=1.0,t=100,dt=1e-3,ie=lambda t:0.0):\n", " n = int(t/dt)\n", " ts = []; vs = []; ws=[]\n", " for i in range(n):\n", " t = i*dt\n", " vs.append(v); ws.append(w); ts.append(t)\n", " dv = (v-v**3/3.0-w+ie(t))*dt\n", " dw = ((v-a-b*w)/tau)*dt\n", " v = clip(v+dv,-100,100)\n", " w = clip(w+dw,-100,100)\n", " return ts,vs,ts,ws" ] }, { "cell_type": "markdown", "id": "e2ae8751", "metadata": {}, "source": [ "With the default parameters of $a=b=0$, this is a nonlinear differential equation know as the _van der Pol oscillator_.\n", "\n" ] }, { "cell_type": "code", "execution_count": 68, "id": "841c0750", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ]" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Ro/hF0B9EwBdAszv6HbA0WxTqBUTULNbWzDOFouvX9OVRYfmFzRbdy7YVQ6vY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\nMsGixwXMMSKS5FR1sH6T8ckh3J7aQ6VVEarYNX8TiT3W2gF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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(*fhm(ie=lambda t:1.0 if t<0.1 else 0.0))" ] }, { "cell_type": "markdown", "id": "2e29c67d", "metadata": {}, "source": [ "For other parameters, this generates neuron-like behavior. Here, the current injection at time $t=30$ generates a spike once it exceeds some threshold." ] }, { "cell_type": "code", "execution_count": 69, "id": "85b20a25", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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rVVUs3LuX4rY2f4fZybk1AOkDEKJvYyYBGE1G3A2R7P3Hx/4OZcJQ7bW4TwVx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\ntzEtOhpVr1Iql4F24nDUUFv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AQggxQUkCEEKICUoSgBBCTFCSAIQQYoKSBCCEEBOUJAAh\nhJigJAEIIcQEJQlACCEmKEkAQggxQUkCEEKICarPewL35cEHH+Tvf/87JpOJlJQUXnzxRUJDQ7uV\nS05OJiQkBL1ej9FoZNeuXT4FLIQQYmh4XQNYsmQJBw4c4MsvvyQ9PZ0NGzb0WE5RFPLy8igoKJCT\n/wAN1Q2fxwM5FmfJsThLjsXQ8DoB5OTkoNN53r5o0SJKS0t7LSt3+hoc+XCfJcfiLDkWZ8mxGBpD\n0gfwwgsvsHTp0h5fUxSFK664gqysLJ5//vmh2J0QQogh0GcfQE5ODpWVld3Wr1+/nuXLlwPwxBNP\nYDKZuPnmm3vcxs6dO4mLi6OmpoacnBwyMjJYvHjxEIQuhBDCJ5oPXnzxRe3CCy/U2traBlR+7dq1\n2s9+9rMeX0tJSdEAechDHvKQxyAeKSkpXp/Dvb4KKDc3l5/+9Kd8+OGHBAQE9FjGZrPhcrkIDg6m\ntbWVd955h8cee6zHskVFRd6GIoQQwguKpnnXQ5uWlobD4SAiIgKAr33tazz77LOUl5dz11138dZb\nb3Hs2DGuvfZaAJxOJ//6r//Ko48+OnTRCyGE8JrXCUAIIcTY5veRwLm5uWRkZJCWlsbGjRv9Hc6I\nKikp4dJLL2XmzJnMmjWLp59+GoC6ujpycnJIT09nyZIlNDQ0+DnSkeNyuZg/f37HRQYT9Vg0NDRw\n/fXXk5mZyYwZM/jss88m7LHYsGEDM2fOZPbs2dx8883Y7fYJcyxWr15NTEwMs2fP7ljX1799w4YN\npKWlkZGRwTvvvNPv9v2aAFwuF/feey+5ubkcPHiQzZs3c+jQIX+GNKKMRiO/+MUvOHDgAPn5+Tzz\nzDMcOnSIJ598kpycHI4cOcLll1/Ok08+6e9QR8xTTz3FjBkzUBQFYMIei+985zssXbqUQ4cOsW/f\nPjIyMibksSguLub5559n79697N+/H5fLxeuvvz5hjsUdd9xBbm5up3W9/dsPHjzIli1bOHjwILm5\nudxzzz243e6+d+B19/EQ+OSTT7Qrr7yyY3nDhg3ahg0b/BiRf33jG9/Q3n33XW369OlaZWWlpmma\nVlFRoU2fPt3PkY2MkpIS7fLLL9fef/997eqrr9Y0TZuQx6KhoUGbOnVqt/UT8VjU1tZq6enpWl1d\nnaaqqnb11Vdr77zzzoQ6FsePH9dmzZrVsdzbv339+vXak08+2VHuyiuv1D799NM+t+3XGkBZWRlJ\nSUkdy4mJiZSVlfkxIv8pLi6moKCARYsWUVVVRUxMDAAxMTFUVVX5ObqR8d3vfpef/vSnHSPMgQl5\nLI4fP05UVBR33HEHCxYs4K677qK1tXVCHouIiAgeeOABJk+eTHx8PGFhYeTk5EzIY3FGb//28vJy\nEhMTO8oN5Hzq1wRwppo/0bW0tHDdddfx1FNPERwc3Ok1RVEmxHH6+9//TnR0NPPnz+916pCJciyc\nTid79+7lnnvuYe/evVit1m5NHBPlWBw9epRf/vKXFBcXU15eTktLC6+++mqnMhPlWPSkv397f8fF\nrwkgISGBkpKSjuWSkpJOGWwiUFWV6667jltvvZVrrrkG8GT1MyOwKyoqiI6O9meII+KTTz5h27Zt\nTJ06lZtuuon333+fW2+9dUIei8TERBITE1m4cCEA119/PXv37iU2NnbCHYs9e/Zw4YUXEhkZicFg\n4Nprr+XTTz+dkMfijN6+E13Pp6WlpSQkJPS5Lb8mgKysLAoLCykuLsbhcLBlyxZWrFjhz5BGlKZp\n3HnnncyYMYP777+/Y/2KFSt46aWXAHjppZc6EsN4tn79ekpKSjh+/Divv/46l112Ga+88sqEPBax\nsbEkJSVx5MgRAHbs2MHMmTNZvnz5hDsWGRkZ5Ofn09bWhqZp7NixgxkzZkzIY3FGb9+JFStW8Prr\nr+NwODh+/DiFhYWcf/75fW9sqDssBmv79u1aenq6lpKSoq1fv97f4Yyojz/+WFMURZs7d642b948\nbd68edrbb7+t1dbWapdffrmWlpam5eTkaPX19f4OdUTl5eVpy5cv1zRNm7DH4osvvtCysrK0OXPm\naCtXrtQaGhom7LHYuHGjNmPGDG3WrFnabbfdpjkcjglzLFatWqXFxcVpRqNRS0xM1F544YU+/+1P\nPPGElpKSok2fPl3Lzc3td/syEEwIISYovw8EE0II4R+SAIQQYoKSBCCEEBOUJAAhhJigJAEIIcQE\nJQlACCEmKEkAQggxQUkCEEKICer/A5RIzVzdoGL1AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for c in linspace(0.0,0.9,6):\n", " plot(*fhm(a=-0.7,b=0.8,tau=1.0/0.08,ie=lambda t:c if t>30 and t<31 else 0)[:2])" ] }, { "cell_type": "markdown", "id": "1e50e8c2", "metadata": {}, "source": [ "Let's look at both variables. The current injection at time $t=30$ causes a fast rise in $v$ and a slower rise in the restorative variable $w$.\n", "\n" ] }, { "cell_type": "code", "execution_count": 70, "id": "575901d8", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[,\n", " ]" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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LBVWNupYAyrm5uPF4j8c5Mf0ED4Y8yDPfP0PA2wEs+HmB3fZNCeOocVH42NhY\ncnIqL6Qyd+5cxo4dy6VbJmBv2rQpeVUs4nv27Fm8vLw4f/48sbGxvP3220RHR1cOpIaFja9cAU9P\ndXEYCyw2VaPrxdf53+H/8VHKRxw6d4iHOj3EAyEP0MO3Bw4am+hjr1GXLrBsGYSHq9/f/+X9hLcK\n5/lez1s2sCr88APMmgXbt1s6EtNSFIXd2bt5f8/7/O/w/4huE83I0JHEd4jHvZ67pcMTZmbIovDV\n3OCv2rJlS7WveXp6kpOTQ6tWrTh79iwtq5ktzMvLC4AWLVpw3333sWvXrioTAMCsWbMqnsfExBAT\nEwOoZ3YNGsC5c2oisCb1neszuvNoRncezfG84yw/sJwp307hwrULDAsextCgodx1x124OrlaOlS9\n3NoCWHVoFYfOHeLz+z63bFDVsJU7gQ2l0Wjo7t2d7t7defOeN1l/dD0rDq1g6sap9Gvfj8EBg7nH\n/x683L0sHaowgaSkJJKSkoxSV40tgJo89dRTNGvWjKeffpr58+eTn59fqSP42rVrlJaW4u7uztWr\nV+nfvz8vvfQS/fv3rxxILVksLEw9E42I0Cda8zt64ShrDq9hw7ENHDx3kB4+PYhtH0vf9n3p7NkZ\nJ4cac6/VaNgQcnPhUmkGXT/oysbRG4lsHWnpsKp09CgMGWKee0asUd71PNYfXc+m45vYcmILbTza\ncI/fPUS3iaaHTw+a1K9mRj9h0wxpAeidAPLy8njwwQc5c+YMbdu25csvv8TDw4Ps7GwmTpzIt99+\ny8mTJxk2bBgAJSUljB49mmefrfracW2/RFwcTJmi/oPbmsuFl/nh9A9sObGFH07/wJnLZ4jwiiDK\nO4oonyjCPMNo36Q9jg6Olg71LwoL1bPqvCtX6f1JL0aEjuCpO5+ydFjVysyEqCj1znF7V1JWQnJm\nMptPbGZHxg52Ze3ijsZ3cKfvnXT16kpYqzA6tuyIm4ubpUMVBrJIAjC22n6JiROha1f45z/NGJSJ\n5BfmsztrN79m/cqvWb9y6Nwhcgty6dC8A6EtQgluHky7Ju1o69GWth5taeXWyiL9CdnZEBFZwp1v\njsDNxY2P7/0YjbV1wtzi0iV1wEA1t6TYtZKyEvbn7GdHxg725exjf+5+Dp8/jHcjbzq27Ih/E3/8\nmvrh18SP9k3a08ajjc20Uu2dXSSAWbPUuelfecV8MZlTQVEBh88fJvV8KkcuHOF0/umKR35hPr6N\nffFs6EkKwVzjAAAW7UlEQVTLhi0rHi0atKB5g+Y0dm2Mu4s77vXccXdxp1G9RrjXc6eeYz2DDthJ\ne3IYsmQiPaOLWD9yPfWc6hnxNza+oiL1klVxsaUjsQ0lZSWkX0zn4LmDnLx0khN5JziZr37NvpJN\nswbNaOXWquLh5eZFiwYtaOzaGA9XDxrXa/yX5w2cG+Dq5Gp1Ldm6zi4SwJIlsHMnLF1qxqCsxPXi\n65y5fIZzV89Vepy/dp4rRVf448YfXLlxhStFVyq+lpaVUs+pHi6OLrg4ulDP8Zbnf/7cUeOIgrrf\ny/e/gkJpWSlHzqXT5MQ/OfHhK1Z1x29NnJ3V0WIuthGu1SopK+Hc1XPkFOSQU5DD2StnySnI4fy1\n81y+cZnLhZfJL8zn8g31a35hPoUlhVwvvo6jgyOuTq4Vj3qO9XB1csXJwQlHB0ccNA44av78esv3\ntz6//cSlqmND+ee2pnLalKmunLYMPYQasm2AbWO3mWYUkDXx9lYvSdij+s716dC8Ax2ad9DpfcWl\nxRSVFlFUWsSN0hs3n5fcfF5SVoJGo0GD+g9X/o+nQUN6chBf7WmMiw2d0DVsKAnAGJwcnGjt3prW\n7q11ep+iKJSUlVBYUljpUVJWQplSRqlSqn4tK/3L81tfK1PKKj6T5apqzd5epqpy2pSprpy2DL00\nasi2t7FN7/faVAKQzj3dODs64+zoTEMa6vX+g/nVzwRqrcoTQHVLWArT0mg0FZ87uSfB+tnMnUqS\nAMyvuplArVl5AhBC1M5mEkCzZuo/tqkXhhE31bQWgLWSBCCE9mwmAWg00Lq1/fYDWIK0AISo22wm\nAYA6DUQ1c84JE5AWgBB1myQAUS1pAQhRt0kCENWSFoAQdZskAFEtaQEIUbdJAhBVUhRpAQhR10kC\nEFW6fl0deVW/vqUj0Y0kACG0JwlAVMkWz/5BEoAQupAEIKpki9f/QRKAELqQBCCqJC0AIeo+vRPA\n6tWrCQ0NxdHRkb1791ZbLjExkaCgIAICAliwYIG+mwOgcWN1zneZDsL0pAUgRN2ndwLo1KkTa9eu\npVevXtWWKS0tZdq0aSQmJpKWlsaKFSs4fPiwvptEo4GWLaUVYA622gJo0EASgBDa0jsBBAUFERgY\nWGOZXbt24e/vT9u2bXF2dmbkyJGsW7dO300CchnIXKQFIETdZ9I+gKysLHx9fSu+9/HxIcvAOZ0l\nAZiHrbYAJAEIob0aF4SJjY0lJyen0s8TEhIYMmRIrZXrukrOrFmzKp7HxMQQExNTqYwkAPPIy4Pg\nYEtHoTtJAKKuS0pKIikpySh11ZgAtmzZYlDl3t7eZGRkVHyfkZGBj49PteVvTQDVkQRgHtICEMI6\n3X5yPHv2bL3rMsoloOoWJI6MjCQ9PZ3Tp09TVFTEqlWriI+PN2hbkgDMQ/oAhKj79E4Aa9euxdfX\nl+TkZAYNGsTAgQMByM7OZtCgQQA4OTmxaNEiBgwYQEhICCNGjCDYwOsKkgDMQ1oAQtR9GqW603cz\n02g01bYkbpWUBC++CD/+aPqY7FmrVpCSAl5elo5EN4oCjo5QXKx+FaKu0/bYWRWbuhMY1APT2bOW\njqJuUxTbvQSk0ci9AEJoy+YSgJeXJABTKygAFxeoV8/SkehHLgMJoR2bSwCNGkFZmXqQEqZhq9f/\ny0kCEEI7NpcANBppBZiarV7+KefmJicIQmijxvsArFV5AggIsHQkdY+iQE6ObbcA3N2lBWDLSkrU\nCR/LH8XFUFpa/aOkRP1aVT/o7feiVnVvqj5lqvuZrj83Rh2GsOkEIGqnKHD5MmRmqo/z59VLPHl5\n6tfy5xcuqI/z58HBAaZMsXTk+nNzgytXLB2FfSssVP9Hs7PVr2fPqp+z/Hy4dOnm10uX1L/VtWs3\nD/ilpepKdOUPFxd1RFdVDyenm88dbruecXtCqCpB6FOmup/p+nNT1qEtm0wAMhLorwoL4cQJOHbs\n5uP3328e9B0dwccHvL3V2VSbNlXP8IODbz5v1gxatFAfDRpY+jcyjFwCMr3SUvUzdvy4+tkr/3ry\npPqZu3pVPVHz8oLWrdX/2WbNwNcXOncGDw9o0kT92qhR5QO+sc906zJD9pVNJgB7bQEoivpPt2+f\nOkZ/3z44cEDdF+3aQWCg+oiKgpEjbx70GzWydOTmJQnAuC5ehP371c9a+SMtTT1Z8PcHPz/1a8+e\n6nMfH/VgLwdx62ezCeDIEUtHYXoFBZCcDDt2wM8/w5496tl5eDh06QJ//7t6NtWundoUFip3d0kA\n+iopUQ/wycmwc6f69dw5CAtTP2t/+xtMmgShoep+FrbNJg8bXl5qR2Vdc/Wqeqfzli3w009w9Kh6\nsL/zTpgxA7p3Vy/hiJpJC0B7ZWXqAX/rVvWxYwfccYd6oO/dG555BoKC5K7quspmE0BduASkKOpl\nnM2b4bvvYPduiIyE2Fh4+23o2tV2b8ayJOkErtn587BhAyQmwrZtaj9Qv37qmf0XX9j2EGChG0kA\nZlZSol7OWbtWfdSrB/fcA088oZ5xSbPacG5u6kFO3HTsGKxbB+vXw8GD6klGXBy89praMSvsk00m\ngObN1aGNN27YxhlySYnavP7qK/Uf0McHhg2DTZsgJEQ6y4xN+gBUx4/DihXqIz8f4uPh//4P+vQB\nV1dLRyesgU0mAAcHdWhZVha0b2/paKqmKOpInc8+U/8B27SBESPguefUTlthOvbcB3D2LKxapV7K\n+f139TP30UfqyLDbx8kLYZMJANSD6KlT1pcAsrPhk0/UA39hITz8sDp1dWCgpSOzH/bWB1BUBN98\nA0uWwK+/wr33wpw5cPfdMjpM1MxmPx5t26oJwBqUlamXeN5/Xx3FM3y4+s/Ys6dc3rEEe2kBHDsG\nH34In34KHTrAxIlqv1L9+paOTNgKvRuFq1evJjQ0FEdHR/bu3VttubZt29K5c2fCw8Pp3r27vpur\npF07OH3aaNXp5dw5WLBAnZPo6adhwAC12f3BB+rQTTn4W0Zd7gMoKYE1a9Tr+NHR6qXG7dvVx8MP\ny8Ff6EbvFkCnTp1Yu3YtkydPrrGcRqMhKSmJpkYeW9aunTp00hIOHoQ33lDPtu67T73G362bHPCt\nRV1sAVy6pF7Lf/ttdRDB9OnqZ8/FxdKRCVumdwIICgrSuqwpVp0s7wMwF0VRx+u//jocOgTTpqmj\nLGx51sy6qi4lgKNH4a231E7dQYPUkWTdulk6KlFXmLwPQKPR0K9fPxwdHZk8eTITJ040Sr3mSgBF\nRfD55/Df/6p3Qz7xhDrPji0MP7VXdaETeM8eSEhQ7xmZPBlSU9WRb0IYU40JIDY2lpwq5lxISEhg\nyJAhWm1gx44deHl5cf78eWJjYwkKCiI6OrrKsrNmzap4HhMTQ0xMTLX1tm6tTp1w6ZI6q6CxFRaq\nTe4FC9Rb4d98E/r2lcs8tqBhQ3V64bIy2xr6qCjqiLGEBHWytSefVE8+bH12VmFcSUlJJCUlGaUu\njWLg9Zk+ffrw+uuvExERUWvZ2bNn4+bmxsyZMysHosfK9j16qAfoXr10eluNrl2DxYvVOyQjIuD5\n59Ux1MK2NGyodtI3bGjpSGq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(*fhm(a=-0.7,b=0.8,tau=1.0/0.08,ie=lambda t:0.9 if t>30 and t<31 else 0))" ] }, { "cell_type": "markdown", "id": "d1bd37da", "metadata": {}, "source": [ "Another way of looking at dynamical systems like this is in _phase space_.\n", "Here, we ignore time and just plot one dynamical variable against the other.\n", "The HH model exists in a four dimensional space, but for FHN, we only have two coordinates ($v$ and $w$).\n", "\n" ] }, { "cell_type": "code", "execution_count": 71, "id": "a1ac534c", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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/61/TaygqYr5+794yu9ZZcP3vbLyn8P8wFbuuvN6jpkYvkwQLqa0Fvv2WJcjv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\ntDi/Oou3tpbjFFFRFOfyci3Uk5VFoQ4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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot([0],[0],'o',c='red')\n", "for c in linspace(0.0,0.9,20):\n", " plot(*fhm(a=-0.7,b=0.8,tau=1.0/0.08,t=100,ie=lambda t:c if t>30 and t<31 else 0)[1::2],c=(0,0,1,0.5))" ] }, { "cell_type": "markdown", "id": "332d6173", "metadata": {}, "source": [ "Let's not inject current, but rather start of in different places in phase space.\n", "\n" ] }, { "cell_type": "code", "execution_count": 72, "id": "b7325bab", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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605+W173udSVdxEoINUwRkVe+EqH0s7PQ0q+5BkZPVp6nAZOG0fp6/I6ugyMj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/xk/BckAD6ptnu3uwht0NJX2Are2f79uiTkZbWVgPFmtdPMl9ul/3QwC76WfogDX5/MUcQvj8PE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\n/f3Q3g2Tp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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i in range(400):\n", " v,w = 6*rand(2)-3\n", " plot(*fhm(v=v,w=w,a=-0.7,b=0.8,tau=1.0/0.08,t=500,dt=1e-1,ie=lambda t:0.0)[1::2],c=(0,0,1,0.3))" ] }, { "cell_type": "markdown", "id": "595552fb", "metadata": {}, "source": [ "(Nullclines)\n", "\n", "Nullclines are locations where one of the derivatives in the differential equations is zero.\n", "The point where all derivatives are zero is a stationary pint.\n", "\n", "$$\\dot{v} = v - v^3/3 - w = 0 $$ \n", "$$ w = v - v^3/3$$\n", "\n", "$$ \\tau \\dot{w} = v - a - bw = 0 $$\n", "$$ w = v/b - a/b $$\n", "\n", "Note that within each region in the arrangement of these curves, $\\dot{v}$ and $\\dot{w}$ have a constant sign." ] }, { "cell_type": "code", "execution_count": 73, "id": "895aa657", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ZyB9N/4TcMEyaZHo/EqQ0vSKvq4Fd/sxuDRJTYPwsfC+bzzqLpj74mSSwyEk2SPxtJC0m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GCI8v4ENAVdAprXcrld17xn+tw87UJNP1T30pdCU/c/HRjocsh+2d1tbdu3L+xq6G06BFGlCdUV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\nGviTPwEuv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ukZlwqSlzQ3N+OjH/0ovvnNb2LCaM0VEJDi4mJs2rQJ+/btw5NPPon169en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\nRqkUALwgBSlIQUap/P8VIsH6AvQJmgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Isoclines\n", "vs = linspace(-2.5,2.5,1000)\n", "plot(vs,vs-vs**3/3,c='red')\n", "plot(vs,vs/0.8+0.7/0.8,c='green')\n", "for i in range(400):\n", " v,w = 6*rand(2)-3\n", " plot(*fhm(v=v,w=w,a=-0.7,b=0.8,tau=1.0/0.08,t=500,dt=1e-1,ie=lambda t:0.0)[1::2],c=(0,0,1,0.3))" ] }, { "cell_type": "code", "execution_count": 74, "id": "4e4af846", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YmIhbt26hffv2gupSCDVME2gc+bX3nN+8mah0aSKAaM0atsybhc6dO5Otbb5I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\nQpqUY8eOISgoCHFxcdDS0oIoipDL5UqJ8+zZVyfNuqDL82Z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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# FitzHugh Phase Space Portrait\n", "figs(\"FitzHugh_portrait\")\n", "\n" ] }, { "cell_type": "markdown", "id": "29d82817", "metadata": {}, "source": [ "The reason this model is so popular is because it has a 2D phase space and is therefore easy to visualize and reason about." ] }, { "cell_type": "markdown", "id": "702542a7", "metadata": {}, "source": [ "# Exploring the Parameter Space" ] }, { "cell_type": "markdown", "id": "c00182e3", "metadata": {}, "source": [ "The FitzHugh-Nagumo model has a number of parameters.\n", "\n", "Different choices of parameters give rise to different kinds of dynamic behavior. Let's look at some of this." ] }, { "cell_type": "code", "execution_count": 75, "id": "00932ba4", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7hFKKG95/n89On87l2afwEJVDh6C8HF59Fd56C2pqYOlSWLgQ5s+HSy+FggKv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\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for a in linspace(-2.0,-1.0,5):\n", " plot(*fhm(a=a,b=0.8,tau=1.0/0.08,t=300,dt=1e-2,ie=lambda t:1.0 if t>50 and t<51 else 0)[:2])" ] }, { "cell_type": "code", "execution_count": 76, "id": "4063eb89", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6tAq/G6LASy91JaqetYVBuugkzNxlOcAHGm8sTB2AZ9GFkWqUY+jEdaUSDih6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yYU3mhC86SDuPbAWXh698N7DQ34VVHXzPzlomhGEYqfKW5Tz1yoVOKsx4PZOh2mFxbG2LvzoSgK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\nimQAJCQkJK5QJAMgISEhcYXy/wGvlKTZpF9yJAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for a in linspace(-1.0,-0.0,5):\n", " plot(*fhm(a=a,b=0.8,tau=1.0/0.08,t=300,dt=1e-2,ie=lambda t:1.0 if t>50 and t<51 else 0)[:2])" ] }, { "cell_type": "code", "execution_count": 77, "id": "cfd28946", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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3efWD+TPh4Yfhle/czswPZ9I+p92vdBgWtINZAVrBHGsOaOvC2bB5I0wsEu9X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\nO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for a in linspace(0.0,1.0,5):\n", " plot(*fhm(a=a,b=0.8,tau=1.0/0.08,t=300,dt=1e-2,ie=lambda t:1.0 if t>50 and t<51 else 0)[:2])" ] }, { "cell_type": "code", "execution_count": 78, "id": "7f57c253", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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TqRrOBkkbWbnSmgBUVXVMZLdVtWFgjm0fYEkAdjkAwL8gaNkRgJ0FBGgEkC3Z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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a=-0.7\n", "for b in linspace(0.0,1.0,5):\n", " plot(*fhm(a=a,b=b,tau=1.0/0.08,t=300,dt=1e-2,ie=lambda t:1.0 if t>50 and t<51 else 0)[:2])" ] }, { "cell_type": "markdown", "id": "83856c8f", "metadata": {}, "source": [ "We could explore this for a long time. But let's automate the process.\n", "\n", "We pick lots of random parameters for $a$ and $b$, then run the simulation.\n", "In order to compare the results, we compute the resulting spectra.\n", "\n" ] }, { "cell_type": "code", "execution_count": 79, "id": "66fc5156", "metadata": { "collapsed": false }, "outputs": [], "source": [ "params = []; spectra = []\n", "for i in range(500):\n", " a = 4*rand()-2\n", " b = 4*rand()-2\n", " ts,vs = fhm(a=a,b=b,tau=1.0/0.08,t=300,dt=1e-2,ie=lambda t:1.0 if t>50 and t<51 else 0)[:2]\n", " vs = abs(fft(vs))**.5\n", " params.append((a,b))\n", " spectra.append((vs[:50]))" ] }, { "cell_type": "markdown", "id": "4f005a72", "metadata": {}, "source": [ "Let's look at the first 100 resulting spectra, kind of overlaid:\n", "\n" ] }, { "cell_type": "code", "execution_count": 80, "id": "0c44fad8", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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F5YLIBgVB5MfH4eseHkb8+ZkziJE3GCaHLTLDw/Cp+wywJSJY+m43rO7BQWzn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\nA6GTuLOrXvZvAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i,s in enumerate(spectra[:100]):\n", " plot(s,c=(0,0,1,0.3))" ] }, { "cell_type": "markdown", "id": "1da2a78b", "metadata": {}, "source": [ "It's hard to make sense of that plot. Let's _cluster_ the spectra into a number of different classes.\n", "\n" ] }, { "cell_type": "code", "execution_count": 81, "id": "9a5ec997", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(array([4, 1, 4, 1, 0, 0, 1, 1, 0, 4], dtype=int32), 500)" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn import cluster\n", "km = cluster.KMeans(6)\n", "pred = km.fit_predict(array(spectra,'f'))\n", "pred[:10],len(pred)" ] }, { "cell_type": "markdown", "id": "7db07c30", "metadata": {}, "source": [ "Now we can look at the spectrum for each class.\n", "\n" ] }, { "cell_type": "code", "execution_count": 82, "id": "5f870726", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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MhRdCiN7h9gDv5ylj4YUQoje4PcBLJ6sQQvQO9wd4WRNeCCF6hdsDvIyDF0JcbHJyctDr\n9cyePbtXy3F7gJcUjRDiYnP//fczfvz4Dtfq6gnuD/AyDl4IcRFZuXIl/v7+TJ48udfXzXF7gJcU\njRDiYlFbW8vChQt54YUX+mRRtC5v+NFbJEUjhOhL6ar0HrlPipLS7WueeOIJ5syZQ0RERK+nZ+B8\nCPCSohFC9KGzCcw9YdeuXXzxxRfs3LkToE9a8J2maAoKCpg0aRJJSUkMGzaMl156CXBuuWc2m0lO\nTiY5OZn169e7rlmyZAmxsbHEx8ezcePGDu9/ciZrf1jDWQgh2rNp0yaOHDnCwIEDCQ8P57nnnuPD\nDz9k7NixvVZmpxt+lJaWUlpayqhRo6ivr2fMmDGsXr2a999/H29vb+bNm9fq/MzMTGbNmsXWrVsp\nKipiypQpZGdno1b/8Fly+qL1xqeMlP+mHC+dVw+/PCHExeR83vDDarVSV1cHOFvvf/7znzly5Aiv\nvfbaGfuy9tSGH52maMLCwggLCwPAZDKRkJBAUVGRq5KnW7NmDTNnzkSr1RIVFUVMTAwZGRlMnDix\n3TJOtuIlwAsh+iuDwYDBYHD9bTKZMBgMHW66fa66NYrmyJEj7Ny50xWsX375ZUaOHMk999zj2py7\nuLgYs9nsusZsNrs+ENojK0oKIS42Cxcu5J///GevltHlAF9fX89NN93Eiy++iMlkYu7cueTl5bFr\n1y7Cw8N55JFH2r22s95i6WgVQoie16VRNM3Nzdx4443cfvvtXH/99QCEhIS4np8zZw7Tp08HIDIy\nkoKCAtdzhYWFREZGnnHPRYsWuX53NDtkLLwQQpwmPT2d9PT0s76+005WRVFIS0sjMDCQF154wXW8\npKSE8PBwAF544QW2bt3Ke++95+pkzcjIcHWy5ubmtmrFn95RcMsHt3BD/A3cOuzWs34hQghxPney\ndkefdbJu2bKFd999lxEjRpCcnAzA008/zYoVK9i1axcqlYro6Ghef/11ABITE0lNTSUxMRGNRsOy\nZcskRSOEEG7QaQu+Vwo97VNo/mfzCTIGMf/S+X1dFSFEPyIt+NbcvhYNOFvwMopGCCF61vkR4PWS\nohFCiJ52XgR4WVFSCCF63nkR4CVFI4QQPe/8CPB62ZdVCNH/paSkYDAY8Pb2xtvbm4SEhF4t77wI\n8LJUgRDiYqBSqXj11Vepq6ujrq6OrKysXi3vvAjwMg5eCHGx6MthnOdFgJdOViHExWLBggUEBwdz\n2WWXsWnTpl4ty+07OgF4e3pTb6vH7rDjofZwd3WEEP1YenrPbJWXktL9lvgzzzxDUlISOp2OFStW\nMH36dHbt2sXgwYN7pE6nOy9msgL4LvUl/1f5+On9+ro6Qoh+4kKbyXr11VdzzTXX8MADD7Q63q9m\nssKJNI3k4YUQosecNwFexsILIfqzmpoaPv30UxobG2lpaeFf//oXX3/9NVdddVWvlXle5OBBxsIL\nIfq35uZmnnjiCQ4cOICHhwcJCQmsWbOGmJiYXivzvAnwkqIRQvRnQUFBZGRk9GmZkqIRQoh+6rwK\n8JKiEUKIntNpgC8oKGDSpEkkJSUxbNgwXnrpJQAqKyuZOnUqcXFxTJs2jerqH1rfS5YsITY2lvj4\neDZu3NilikiKRgghelanAV6r1fLCCy+wf/9+vvvuO1599VWysrJYunQpU6dOJTs7m8mTJ7N06VIA\nMjMzWbVqFZmZmWzYsIH77rsPh8PRaUV89ZKiEUKIntRpgA8LC2PUqFEAmEwmEhISKCoqYu3ataSl\npQGQlpbG6tWrAVizZg0zZ85Eq9USFRVFTExMmx0LdnvrvyVFI4QQPatbOfgjR46wc+dOJkyYQFlZ\nGaGhoQCEhoZSVlYGQHFxMWaz2XWN2WymqKjojHtVn9ZYlxUlhRCiZ3V5mGR9fT033ngjL774It7e\n3q2eU6lUqFTtr+/Q1nOVlRAY+MPfMg5eCHGu/P39O4xFFwp/f/8euU+XAnxzczM33ngjs2fP5vrr\nrwecrfbS0lLCwsIoKSkhJCQEgMjISAoKClzXFhYWEhkZecY9//SnRZw8nJKSgl+MdLIKIc5NZWWl\nu6vQo9LT00lPTz/r6ztdbExRFNLS0ggMDOSFF15wHZ8/fz6BgYE8+uijLF26lOrqapYuXUpmZiaz\nZs0iIyODoqIipkyZQm5ubqtPVZVKxfr1CqfO0M0qz+KGVTdw4IEDZ/1ihBCiP+vuYmOdtuC3bNnC\nu+++y4gRI0hOTgacwyAfe+wxUlNTefPNN4mKiuL9998HIDExkdTUVBITE9FoNCxbtqzNr0xVVa3/\nlhSNEEL0LLctF/zKKwr33//DMUuzhaA/BWH5raWvqyOEEBeEC2a54NNb8AaNgWZHMza7zT0VEkKI\nfsZtAf70vhCVSiV7swohRA86bwI8yN6sQgjRk86bFA3IcgVCCNGTzqsWvKRohBCi55xXLXh/gz/H\nGo71fWWEEKIfOq9a8FOip7Dm4Jq+r4wQQvRD51ULPjUplfW566ltqu37CgkhRD/jtgCvKGC1tj4W\naAxkUtQkPsr6yD2VEkKIfsRtAT4goO00ze0jbufdPe/2fYWEEKKfcVuA9/dvO01zbdy17CjZQWFt\nYd9XSggh+hG3Bfggf0ebLXi9Rs+NCTeyYu+Kvq+UEEL0I24L8BHG5jZb8HAiTbNX0jRCCHEu3Bfg\ndU1ttuABLh90OdWN1ewp29O3lRJCiH7EbQE+RG1rtwWvVqm5bfhtF1Rna1HRazQ3H3d3NYQQwsV9\no2hovwUPzjTNe3vfw+6w912lzkF+/pNUV3/t7moIIYRLpwH+7rvvJjQ0lOHDh7uOLVq0CLPZTHJy\nMsnJyaxfv9713JIlS4iNjSU+Pp6NGze2e1/f5vZb8ACJwYmEeIWwKX9TF1+K+7S01GOzFWOxZLm7\nKkII4dJpgL/rrrvYsGFDq2MqlYp58+axc+dOdu7cydVXXw1AZmYmq1atIjMzkw0bNnDffffhcDja\nvK9Xo63DFjzA7BGzeWfPO118Ke5jteYCSIAXQpxXOg3wl19+Of7+/mccb2vbqDVr1jBz5ky0Wi1R\nUVHExMSQkZHR5n31DR2naABuHXYrqw+sxtJ8fm/jZ7XmoNOFS4AXQpxXzjoH//LLLzNy5Ejuuece\nqquda7gXFxdjNptd55jNZoqKitq8XlPTcYoGINw7nPGR4/nPwf+cbTV71urV8MEHZxy2WnMIDLyW\nhoYsFKX1N5bK5mZ+mZPTVzUUQgiXswrwc+fOJS8vj127dhEeHs4jjzzS7rkqlarN428XLCM3dxGL\nFi0iPT293etvH34ejYn/6CNYceYELKs1B2/v8Wg0PjQ1tZ6Bu7y0lJeKiqhvaemrWgoh+on09HQW\nLVrk+ukuzdkUGhIS4vp9zpw5TJ8+HYDIyEgKCgpczxUWFhIZGdnmPdKa0/iv/nIWLer4M+aGhBt4\ncP2DlDeUE+wVfDbV7Tn790NFxRmHLZYcwsLuxGhMwGLJQq8fCDjTWK8XF+Pt4cG+hgYm+vr2dY2F\nEBewlJQUUlJSXH8vXry4W9efVQu+pKTE9fvHH3/sGmEzY8YMVq5cic1mIy8vj5ycHMaPH9/mPXQh\nWjxqbLTTB+ti0pm4Nu5aVu1fdTZV7Tl2Oxw4AMePQ3l5q6es1mwMhliMxgQaGn7Iw/+vpgYPlYob\ngoLY29DQ1zUWQlzkOm3Bz5w5k02bNlFRUcGAAQNYvHgx6enp7Nq1C5VKRXR0NK+//joAiYmJpKam\nkpiYiEajYdmyZe2maDwjPDHX2Kit1ePn13Edbh9xO4vSF/HA+Ae6/wp7Sl4eBAfD4MGwfTtcdRUA\nLS012O0WdLpwvLwSqK//Yfbt68XF3BsRQbOiSIAXQvS5TgP8ijZyznfffXe75z/++OM8/vjjnRas\ni9AxIN85kqazAD9l8BTmrJ3DrtJdjAob1em9e8W+fTBsGCQmwrZtrgBvseRgNMaiUqkwGhM4dsz5\nTaPCZmPd8eO8GhvL1ro6Pjkus1yFEH3LbTNZPSM8idR3PhYeQKPW8OD4B3n+2+d7v2Lt2b8fkpJg\n7FhngD/Bas3BYIgFcOXgAd4uLeW6oCD8tVqGe3mxt76+zaGlQgjRW9wW4HUROkI9mjodKnnSz8f8\nnE+yP3HfOvEnW/BnBPhsV4DX6cJwOJqx2cp5o6SEeyMiAAjT6QAotdn6vt5CiIuW+wJ8uI5AutaC\nB/A3+HPHyDt4+fuXe7di7TnZgo+OBosFSksBZ4rmZIBXqVR4eSWwuWwrnmo1P/LxcR0fbjJJHl4I\n0afcmqLxa+l6Cx7glxN+yZs736Suqa73KtaW5mbIyYGEBFCpYMwYZ0crzhSN0RjnOtVoTOB/ZRnc\nGx7eqoN5uJcXe+rr+7beQoiLmltTNKamrrfgAaL9o7ki+gre3Plm71WsLbm5YDaDweD8+0SaRlGU\nVikaAIdnLHUN+7k9NLTVLYZ7eUkLXgjRp9zagtc3dK8FD/DIjx7hL9/9hRZHH84MPZl/P+lEgG9u\nPo6iKGi1Qa6nvm4MY4y2BD+tttUtRkiKRgjRx9wW4LVBWjRNdqrLO5npdJoJ5gkM8B3Ah5kf9lLN\n2nAy/37SiQDvTM/EulIxDkXhrSpvIpX8M26RZDRywGKhpbOZXUII0UPcFuBVahUOfx1NJd0fWfLI\njx7huW+f67thh6e34AcOhOZmrCUZGAw/5N+/qKqiSWNGZT9OS0vrfLtJoyFcpyPXau2bOgshLnpu\nC/AA6mAdjmNN3b5uetx0qhur2Xx0cy/Uqg2nt+BVKhg7Fmv+N63y72+UlPDzyAEYDHFYLAfOuI3k\n4YUQfcmtAV4X5omqsvsteA+1Bw9PfJg/f/vnXqjVaZqa4MgRGDq09fGxY7FU78NodAb40qYmPq+q\n4rbQULy8EtpcG16GSgoh+pJbA7zBrENb2/0WPEDaqDS+LfiWgxUHe7hWpzl40Dn2/cRkJZexY7FS\n6GrBv1Vayk3BwfhoNK1mtJ5KWvBCiL7k1gBvivZEX392szuNWiO/GPsLXvjuhR6u1WlOz7+foIwZ\ng9WnDoM+BkVReLu0lJ+Fhzvr1kGAl7HwQoi+4r4AX1uL9yAd/vYmms6uEc/94+5n1f5VlDeUd37y\n2To9/36CLUSDuhm0ZQ0csFiwOhyM8/YGOGPZ4JNiDQZKbDbZ/EMI0SfcF+Bzc/GM9CRU0/nWfe0J\nNYVyU8JNvLr11Z6t26naacFbrbkY6nxh2zbWVFQwIzDQNVzSaIylsfEIDkfrbycatZp4o5H9lvN7\nj1khRP/gvgCfk4MuQkeQqvuTnU71m0t/w6tbX6Wsvqzn6naqdlrwVms2BvVAZ4A/fpwZQT9MdlKr\nPdHrB2K1nrkX68mVJYUQore5NcB7RnjiZ+/ecgWniwuMI21kGgu+WNBzdTvJYoGiIoiJaeOpHIwB\nIyjNyuKAxULKaYvat5emkY5WIURf6TTA33333YSGhrq25QOorKxk6tSpxMXFMW3aNKqrq13PLVmy\nhNjYWOLj49m4cWP7N87NRROgQafYqSyxn9OL+P1Pfs/63PVkFGWc033OkJUFcXGgOXNfFKs1B0PU\npXyi0XClvz86deu3st2OVhkqKYToI50G+LvuuosNGza0OrZ06VKmTp1KdnY2kydPZunSpQBkZmay\natUqMjMz2bBhA/fddx+O9qbm5+SgUqmwGnTUHjm3ddJ9PH1YMnkJD65/EIfSg0sBtJN/hxMBPmIC\nayZO5Lo2ZtS2Oxb+RAteNv8QQvS2TgP85Zdfjr+/f6tja9euJS0tDYC0tDRWr14NwJo1a5g5cyZa\nrZaoqChiYmLIyGinVZ3jzE/bvD2xHD3LYTSnuGPkHahQsXzX8nO+l0s7+XdFcWC15qLootmUlMTV\nB88ci99eCz5cp0NRFMpk8w8hRC87qxx8WVkZoSeWww0NDaWszNnBWVxcjNlsdp1nNpspKipq8x6K\npQFqapzr0RSfe7BTq9S8fPXLPP7l49Q01pzz/YB2W/BNTUVoNH58UdvMBIsFv61bzzjHaIzHYslG\nOe0bxcnNP/ZImkYI0cs63XS7MyqVqtXGFm0935YnAo1ofvMbMhs8CTl4OZB6rlVhXOQ4rom9hj9s\n+gPPXfncJvBFAAAgAElEQVTcOd+v/RE0zl2c1lRUcJ2XV6st/E7SaHzQagNobMzHYIhu9dzJNM20\ngIBzr6MQot9KT08nPT39rK8/qwAfGhpKaWkpYWFhlJSUEBISAkBkZCQFBQWu8woLC4mMjGzzHg/f\nFE/guCtYU/Mj8vf23MSfpyc/TdKyJOaMnkNCcMLZ36i2FioqnMsUnMZqzUFviOG/xyv5Q2Kic3cn\nRXEuQnaKk2matgL8lpoe+pYhhOi3UlJSSElJcf29ePHibl1/VimaGTNmsHy5M9e9fPlyrr/+etfx\nlStXYrPZyMvLIycnh/Hjx7d5j4ahWsjJQR/piUdNz+WjQ7xC+O3lv+WhDQ+dW0dmZqZziz71mW+R\nxZLNMdUAzJ6eDDSbwdsbDh8+4zxZk0YI4U6dBviZM2dyySWXcPDgQQYMGMBbb73FY489xmeffUZc\nXBxffvkljz32GACJiYmkpqaSmJjI1VdfzbJly9pN0TSEWyEnB1OUDs/6c+9kPdX94+6nuK6YNQfX\nnP1N9u1rMz0DzhZ8hi2E6wIDnQfGjGkzTdPeWPgkLy+yLBbsMpJGCNGLOk3RrFixos3jn3/+eZvH\nH3/8cR5//PFOC673roAc8E31xKuxZ0eUaD20vHTVS/zsPz/jyiFXYtAaun+T/fs7HCL5n5ZbeDHq\nxOzVEzs8ccstrc7z8kqgrOyfZ1zvrdEQdmLzj6FGY/frJoQQXeC2maxWVSGOvBwC43T4NvdsCx5g\n8uDJjIkYw/3r7j+7sfHtDpG0Y7EeoZhIRplMzoMnA/xpTqZo2koVjZAlC4QQvcx9m27rB2ANtBDo\nV4+HotBS1/MrLL513VscqjrEPWvvwe7o5mzZdoZINjYepUkdwNXBkT+kn8aMgR074LRJXVptMKDG\nZjtznRyZ0SqE6G1uC/BeXiOonxCKLj+XSpWOytyen/hj0plYN2sd+dX53LXmrq4H+cpKqK+HAQPO\neMpqzeYo5h/y7wBBQRAQ4Fza4BQqlarjteElwAshepHbArzJNJyGJD3k5FCr86Qyu3dmdnrpvPhk\n1ieU1Jdwx+o7aHF04ZvCyfRMGx3EpbVZHHKE85PTFhdj1ix46aUzy+9oyQJJ0QghepEbW/DDaRjY\nAjk5WPQ6avJ6Pg9/klFrZO2ta6mwVHDbR7fRbG/u+IJ28u8AB6v34eMVh/b04ZMPPwwffABHj7Yu\nu50WfKzBQLHNRoP93BZa67KDB6G8exujWCzZHDnSvXG3Qojzh3tTNP5VkJtLk7cnDfm9uzaLQWtg\nza1rqGuqY+aHMzsO8h0sMlbVcJAEv+FnPhEUBD/7GZxYeO2k9oZKatRqhhqN7O+LNE1VFVxxBfz4\nx3DsWJcvO3z4UY4c+QN1dTt7sXJCiN7itgBvMAymWWOh5WgWLX46Got6rwV/kl6j5+NbPqbJ3kTq\nB6k02JzBVVEUGvMbqVhbwZEnj3B0vQ9K4pkt+PqWFgzNeVwSMrrtAh55BFauhMJC1yEvr+HU1++k\npeXMmat9NuHpV7+CG26Am2+GadPoygL8tbXfU1e3jejop8jP/2Pv11EI0ePcFuBVKjVe+ngamrNR\nBXnSUto3qyt6ajz54OYPGLFtBEunLiV9QjpbArawY+IOipYVYa+3U5qfQGnmmR2sn1YeI5hygk2x\nbd88OBjuuadVK16vNxMcfBOHDs0/4/SRJhNfnct2Vl3xn//A118767R4MUyZAldd5VyKoR2KonD4\n8AIGDVqI2fwQNTVbqK/f27v1FEL0OPft6AR4+SVTP6AZo18TVPR+Cx7A3mDn0OxDTP98OpdOvJSl\no5ay+tXVjMgfwcgNIxnyiDeJXs9x+KnjWHJ+2Du1rqWFvxzagkobjlqta7+AX/8a3nvPuRPUCUOG\n/InKynVUVX3V6tS7w8LIqKvjHyUlPf46AWdqZu5c+Mc/wGRydho/+6xz3P4110A73x6qqj6nqamI\nsLA78fAwMmDAI+TnP9U7dbyAyBr+4kLj1gBvMo2gYYSJEEMxHtW934K35FjYMXEHar2a5G+SueqZ\nq1jxlxVUGCsY8dcRfJn3Jfz1r5iuGkrUoiiyZmXhsDlQFIW52dlcYThOkCm+40JCQ+HOO+FPf3Id\n0mh8iY39KwcPzsFu/+FDw1+rZe2wYTx2+HDvLD72q1/B9dfDKYsVoVLBK684tyG87jpobGx1ycnW\ne3T0H1GrnROdIyLmUl39JQ0NB3q+jheID8vLmbp7t7urIUS3uLcF7zWChsEQ7nEYXV1Tr7aQKj6p\nYOelO4m4P4Kh/xiKh8EDAH+DP29f/zav/PQVFr8xi/rnllL/1CIi7otAF6Yj7/d5vF1ays76eu7w\nr8FobCc9c6r58+Gdd+CUlnlQ0LX4+EwkL++JVqfGe3mxPD6em/bvJ/+0YHtOTk3NnE6thr//3dkx\nfNNNcMrmI+XlHwIKwcE3uo5pNCbM5l9y9OjTPVe/C0izw8Gjhw6RUVfHtg5SW0Kcb9wc4IdTH1RH\nsPUgigL2up4fMqjYFfJ+n0fO3ByGrR1G5C8i21wA7acxV/P5t3H85+aRDF07hWe/eZbwZeEU/bOU\nf76fy8qhEZQVvUhIyMzOCw0LgzvucKZDThET8yJlZf+itvb7VsevDgzkNwMGcN3evdS39MCM3tNT\nM23x8HB+CGk0zjH8DgcORwt5eb9j8OAlqFSt/2lERj5AZeV6rNZD516/C8ybJSVEGww8PnAgy4qL\n3V0dIbrMrQFepwvCQ63Hz76bOp0ntpKeTdM0VzWzd/peqjdVM2bbGHwn+rZ/8jvvoK2tZ+brm/nv\nrP+yp2wPcauGs+hX1SxYquBx5PcEBf0fvr6XdK3w+fPh7beh7IdlCnS6IGJi/sKBA/fgcLTuc3jY\nbGa0tzd3HDiA41y/ybSVmmmLVgurVsGRI/Dhh5SVLcfTMxx//6lnnKrR+BIRcR/5+UvOrW4XGIvd\nzpP5+TwdHc094eF8VF7O8eZO5lEIcZ5wa4AH8NIMRe2ZSZVaR1Nxz3W01mypYVvyNoxDjYz8fCS6\n0A46Ro8fdwbkN94AjYZRYaN49//e5corP6FkTBUZ016iOG8NDcZbu16BiAi47Tb4859bHQ4JuQWD\nYcgZgVKlUvHXuDjKbDYWHTnSjVd6mo5SM23x9IQnn8T+1EKOHFlMdPSSdpd4Npt/SUXFx1it51C/\nC8wrRUX8yMeHcT4+BOt0TA8K4u3SUndXS4gucX+ADxhDs1cB5Yonth7Ym1WxKxx58gj7btxH7Eux\nxLwQg1rbyct89FFITXWOLjnhvbIytlta+O6y67jiFztp+df9vPCrN5i0fBLv7X2PxpYu5MsffRTe\nfLPV5CKVSkVc3DKKi189Y+ihp1rNR8OGsby0lFXdmJDkcvx456mZtlx1FcVTGjDVhuLrO7Hd07Ta\nACIifk5BwTPdr9sFqLq5mWcLCvjjKbt63R8RwV+Lis79W5YQfeCc92Q9V6agCVQO/DvVzY5zbsE3\nFjSSdXsWKg8VY7ePxTPSs/OLvv4aNmxw7uB0Qo7Fwi9zc9k4YgTHi57G12cso/74GKZLd3D86uO8\ntv01Hlr/ELcNv405o+cwPPTMma2KXaHmiInjg56mZvQWVIOjUOvVrh/9iIfYXTqLsJ0fYkryxWuY\nF8ahRkJ1OtYMG8bUPXswqtVMDwrq2ovft885memuuzpPzZymxV7H0WtqGfWUBqY62tzF6iSzeR4Z\nGUMZNOh3eHq2vR1jf/FsQQEzAgOJ9/JyHZvg44OvRsOnlZVcfeqCc0Kch1TKOQxdiYqKwsfHBw8P\nD7RaLRkZGVRWVnLLLbeQn59PVFQU77//Pn6nLcylUqlostvRqdXU1e0k67+X8MGsz7jnwTCGvhhz\nVnUp/7ic7F9kY/6VmYHzB6LyaH8jcBebDUaNgiefhBudo0Ya7HYu37mTe8LDucOnnD17pjF27B48\nPcM49u9j5D+ZT2NeI9pRWrKisvi34d80DGvg9ktvJyUoBZ+tPlT+p5LKdZXoInUEpejw++fDqMaN\nxTEzDYd/KI5GB/ZGO0eDbkZTORTPTx7EssdG45FG9IP1eA3zomKIB2+qKxgYYeIXIwYSEKZHG6RF\n46s5M4WyahU88AA8/zzMnt3t9y4vbyGNjUdIuOsgzJvn/DbTgdzcX6MozcTGvtjtsi4UpU1NJG3d\nys6xYxmo17d67s2SElZXVPCf4W0sWSFEL1KpVN0abXhOAT46Oprt27cTEBDgOjZ//nyCgoKYP38+\nzzzzDFVVVSw9LR+sUql4q7iYO8PDsdsb2fKViW+uf5dpU4YzenXbi3y1x95g59BvDlG5oZKE9xI6\n7kg93VNPwbffOvPWKhU76+qYmZnJT/z8+GvsYHbuvISIiLmEh9/d6rLm6mZqv62lZksN1Zurqdla\nQ5V/FYYKA1kDsygcV4hqsoqY4TGMDBtJrCYU9Qt/wefv71AwbQKbZ6eQ52Wj1pLHKO3nmNQNfG+9\nhMrGSPyK/fDL98OvwA+fan8s9UFQrWFQvRpDjQrFouBp9iTqD1GE3hqIasEC+Ogj+PBDSE7u1nsH\nUFWVTmbmzYwenYFh00Hncgt79jhH2bSjqamUrVsTGTcuE0/PsG6XeSF4IDsbnVrN8zFnNjgsdjsD\nv/2WrWPGEG04i93ChDhLfR7gt23bRuApX1Xj4+PZtGkToaGhlJaWkpKSwoEDrSfIqFQqkr7/nr3j\nxqFSqcj4bzDZC9KI1t3Gpdu6FqQUReHYymMcfvQwfil+xL4ci8a3GxmnQ4dgwgTYtg3HoEG8WFjI\n00eP8mJMDLNCQykoeJ7jx//LyJGft9vpeJLD5qAhswHDYAO12lr2lu1ld9lu9pTtYXfZbg5XHSbA\nEECsw5+ffVHF1PQCdl09mgP3zEATHIqheRuB1hU0aJIo97yBFow4FAcVlgoKawvZ06Rip88UqM1E\nc+A1LqkYxs8+uIvI6uP4Rf2Lzc/NIGjAUMw+Zgb5DSLUK7TTOgNUV/+P/ftvIjHxffz9U0BR4JJL\nnKNwTtt+8HQ5Ob/C4Whg6NC/df09v0ActloZt307B8aPJ1jXduf8vNxctCoVzwwZ0se1ExezPg3w\ngwcPxtfXFw8PD+69915+9rOf4e/vT9WJ9VUURSEgIMD196mVHJmRwdODB/PTwED2r5tIyRtGtNue\n5ieF7XfynVS3o46ch3JwWBzEvBSD32V+nV7TSn09TJ8OP/0pZb/8JXceOEBVczPvJSYy2GDAaj3M\n9u3jGT36O4zGs0sZdai42PntYeVK50SjkSNpSYomL+BjjtWuZciQPxEaOrtVkG6w2/nt4cOsOnaM\nRdbjzL7jXvYN+AU1By7h4HUH+erKryiwFHC46jAtjhYSghOID4onIeiHx2j/aDQnZqdWV29m//7/\nIzFxBf7+k3+o26efOpc+3ru3w1Z8S0stW7cOZ+jQvxEQMK3n3yM3mp2VRYzBwMKoqHbPybFYuHTn\nTo5OnIi+g/dJiJ7UpwG+pKSE8PBwysvLmTp1Ki+//DIzZsxoFdADAgKoPG31QpVKxQ2PPMKO+nru\nDAsjPnA7Q7J3UP+3FaRYL2+39Wk7ZiPvt3lU/KeC6D9GE35XeNdy7afau9e5quKll7JhyRLuzs3l\n7rAwFkZFoVWrURSFPXuuxN9/MgMHPtrt96Rb8vJg7Vrn+vP79sG+fdQO15H9gA2NxpcBuWPxP2BA\nfazKuZZ7RQWbg4P5xYMPoouI4DfDhzPd4s3hB3NpPNxI3Btx+F3mR4WlggMVB8gqz3I+VmSRVZFF\naX0pQ/yHMCk8mOl+GdT5PMTgiFSGBg3FqD2x+beiwKWXwkMPwa0dDwutrPycgwfvZty4vWg03UiN\nncf21tczZfducidMwFvT8TfCq3bvZlZoKHeE9c80lXC/9PR00tPTXX8vXry47wL8qRYvXozJZOJv\nf/sb6enphIWFUVJSwqRJk9pM0djsdoZ8/z0fJSURdXwtBR/cRdXCL7m8eCJaP22r85tKmih7t4yj\nzxwl7I4wBv1+0BnndEpRnMMHH3uMquefZ9HEiXxUUcE78fGk+PsDYLOVk519LzZbCaNG/Q+1uptl\nnCtFgYIClP17KCl7i9KgHViMxwhwjCPIaxoBIdPRhETh8PJiXWUlzxYUcLSpiXmRkVz/jZaCeYcx\nJhjR+GpQ69SodCrno6fzUROr4VhyOnVNv2Sf41q2VDRzoOIAuZW5RHhHMCxkGMNDhjM5186PnluF\neu9+tDp9m1Wta2lBrVJRdOgBHA4b8fFv9u171QsURWHGvn1c4efHw21s13i6tRUVPJWfz/djxvRB\n7dqnKAp1dRlUV3+Nl1cC3t7j0OlC3Fon0Tv6rAVvsViw2+14e3vT0NDAtGnTWLhwIZ9//jmBgYE8\n+uijLF26lOrq6jY7WRVF4fmCAr6vreXtwUZ2fDKEhvs3c2n6SIwJRiyZFirWVlCxpgLrQSsBVwcw\n6IlBeCV4tVOjDtTXw9y5NOzfz0tvvMHzTU1cHxTE0sGDCdQ6g3hFxRqys39BaOgdREf/AbW6C0Ms\n+0BTUynHj6+louJjamq24Ov7Y4KCZuDtPQ6jMYFtDTaePXqUTTU1PGAK4/bDXvg4PHDYHDiaHCg2\nxfl7o4Oqwm+omjQX3du/Jyj8Gvyn+eM/yR+8Ibcyl33H9rG3bC/7ju3lt4+t58VxdnZdkeAK/Ccf\n7bpgrty7l2aHg7djI9Hn/oTY2FcJDPypu9+uc/LHI0d4v7ycjNGju5R2sSsKQ777jg+Skhjr49MH\nNWytoeEAx469R1nZe6hUavz9p2K1ZlNXtw0PDx+8vcfh7T0WH59x+PhMxMPjLP7fEeeVPgvweXl5\n3HDDDQC0tLRw2223sWDBAiorK0lNTeXo0aMdDpNUFIW6lhaiv/uO70cnU7jJh4aHVjMgKYqGfQ0o\nNoXAGYEEXReE30/8UOvOck7Wvn3Ybr2Vv82ezVOXXcblfn78ITqaoUbjibrXkJv7K6qr/0d8/Nv4\n+V1+duX0gZaWGo4fX09l5X+pr9+F1ZqLXj8Ek2kEjbp4/tMQzgc1nkz08WJGgDc/8jbgQQuKYqO5\nuYLc3HkMjfs7nkUpVH1WRdVnVdR+W4sxyYhhsAFdmO6Hn6J9aF5fwsH3nyKrPpusyiz2Ve1jR0MV\nZUMfZmDdZgYbvcgwXc4tmq3MUl7EPPRTBgUOQ+fRwazhs1FT4+wP6M7krW76a1ERfy4oYHNyMuGe\nXf9wX5qfT7bVyj/iO1lltIc0NZW4grrNVkJIyK2EhMzC23uMK7WpKApWay51dduoq9tKbW0GNlsp\nI0d+isEgncIXsj7NwZ+tUyv52KFDNDgc3LrlEipXP8iwUbMJui4I0yhTl0aCtKu+Hvvrr/PeN9+w\ncO5c4oKDeXrwYEZ7e7tOqar6igMH7iIg4EqGDPkzGo13Bzc8/zgcTTQ0ZNHQsJv6+j3U1+/G2lRI\nrV1NhV1FncODQK2RcL0XPhojkZFzz2hl26126jLqaCxopLmsGVup7cRPE7ZvDtCsC0bR6lGaFVpa\nHNhsDrR2UNnBNshG/iWlvHuJB2Pi38WvYQdP7a0myBiEn94Po9aIl9bL+ahzPho1RrQeWnQeOnQe\nOrRq5+9aDy0atQa1So0aFcGHy4javI+oLfsJzC1C7VBQPDywhQbSEhaKEhGOKiISj4QkjHN+gVpz\n9um0FWVl/PrQIb5OTmZwN4c9lttsxH7/PYcmTnR9G+wSRQGrFU40NLpUVvlHZGffS2DgdEJDb8PP\nLwWVqmsdvEVFr5Gf/weGD/8Eb+92diQT570LLsAXn5hQ8vGeh7HuD+TqVzec070dxcV89847fFhW\nxgeTJhEZEMCSpCR+cuJbREtLDTU131BR8THHj/+XoUP/dsGnFtpz2Grln6WlLC8rw9vDg6sDAhhl\nMjHKZCLOaMSjsw/Qr75ydkjPn8/Hs2Zxb34+KxMTucLfH8WhULe9joqPKij/qJy65lqaXriLcscC\nfvzja7Ha62lobsDSbKHBduLxxN/N9mZsdhvNjhOP9mbsVgvRO/NIzMgj6fs8HGrYOz6KvWMHcmBY\nKHU04aiqwvPYcUzlNZgqavGtbODy/fXUahz86o5gPIPDCPUKJcQrhBCvEMJMYUR4R7T68Wgp5ujR\np2lqKsLDw5syu44va5uZERJFmD4AnS6UsLC0bqXo7szKot5u5634+E47ZlEU+PJLWLQIvv8errzS\nuX/Atdc61wVq8xI7eXm/o6xsBcOGfYi399nl/J0fEL8gIeE9AgKmnNU9hHtdcAEe4O4DB0ja9QJj\n9n9OypPdX47Wrihs3rWLD77/no+Cg/HXaLhpwABujIsjVlNNbe0Wqqu/pqZmM1ZrLj4+4/D1/TFm\n80Notf1/urlDUdhcU8PXNTXsqq9nV309xU1NDPPycgX8ZJOJESYTxtNzz1lZ/G3FChYmJ/OfmhrG\n3HabcxXKUyiKgiXLwoFP11Id/SCND/4DP99Q9EYNaoMatUGNh8EDtV6NNlhL4PRA/Cb5ofZQwfbt\n8NZbztm4CQnO4avXXuv8vSvf4JqbsT/yMMq6dWT/41kKIkwcazjGsYZjlNSXUFJfQlFtEc1NR5js\nX8hofwdfHQ/Eqh6It+9gcjyjuMFQS5LJgK9OS6NlN3Z7PUlJH+LpGd6l99dit/NgTg5bamr4d1IS\nw9tKJZ0a2I8dgyeecL7WNWucq47u3esctXTnnTB6tOu122wVZGXNRFEUEhNXoNMFd6lO7XHOfbiZ\nmJgXCQ3txuJ5/URdSwuFTU0MMRjQdbAkx/nqggzwmQ0N3Pvt33n60G+5/N76Tq9vtNvZWV/PdxUV\nfJebS3pLC5HHjnGLRx1XTQzAzzP/RP5xO3a7BV/fy/D1vQw/v8sxmZI73nLvIlHb0sKeE8F+54mf\nAxYL0Xo9ySYTyd7ejDaZ2FxTw9ulpWxQqYj93e+cSwv/4Q/OiVBt/A+Sk/Mw+8sO8+Sh3/BIUARX\nG/1xNDo7eR1WB41HG6lYVUJjTh1Buu8J9vwOv5+PR313GgwadPYv6B//cC7u9tZbzg+IE6zWI+Tn\nP0lFxRrM5ofwDb6bUksdX5bn89gxDVNsGdiPf0duZS551Xn4efowO0rNZX5VpFtSUOuHub4RBBgC\n8PTwdKWXdB46PDXOvxVF4cPKOp47ZmFugAdTjS3Y7DZsLU34bdlO/Kur0FXWsPNn08mekoxNZcfu\nsDtTUio1fqXVDF33PXGffEuLwZP9t1/J0Z+aCbEso0E7jir9/8Fp6RiVSoUKlSuV6aHyQK/RY9Aa\nMGgMrR5Ppsu8dF40WQ6wb981mM2PMGDArwDnpiaHGxs5aLG4fqpbWnglNpawbvRJnK8URWHlsWP8\n+tAh9Go1RU1NDNDriTcaGWowEG80Em808iNf386/2brRBRngAa7a9BW/aZrGFVMaUal/+IesKApH\nGhv5traW72pr+a6qiv31dfyo8gApRz5nmKmM8IFNOPyOYXfUYzKNxtt7DN7eYzCZxmAwDDm3XP5F\nxOZwkNnQ4Ar4O+rq0KhUrEhM/KHj8csvYcECaGqCtDSIi4PYWIiOBq0Wu93Cjh0TaPaM59fWuzEb\nzbyuVuN/8CBkZTmXhti8GeuU2ZQH30j5NhON+U0E3RCE/2R/9FF69IP0aEO03frv5mhxYP33tzTc\n/xz1o2ZQE6OnaeRHNCd9gXnQ/ZjND6PVOofDHrRYuGLXLl6IiSE15IfhhA7FQWl9KaX1pVRUrMWj\n8nmOqq8i0zqIsoYyKq2VNDuaaWppcgbvEz9N9ibUKjU6Dx12g5nD4Wn4NRbx8y/+xS3rD+FT38JH\nNyeRcdlgNDpPtGotWrUWD7UHiqLgUBzYFTsOxYFitxOzr5ifZn9NZaqV7TVj2WtKPOP1KoqCguL6\n/0hBwe6w09jSiLXFirXZ6nq0NFtcPw3NDSiKQpTJwKKkFrbZx/KG+j4adUHoHfV426vxV+oJwopV\n40+BRyh3KDvw8VBjamghuKyOwNIaNIqKkrHx2AL9UKlUrg8qtUqNh8rD1c+iVWvRemhb9bWc3vdy\n6nkatcb1u1rVMy3sbIuF+3NyOGaz8VpcHD/y9cXmcHDIauWgxcIBi4WDVitba2sJ0+lYkZjY7gxm\nd7tgA/xHh6ohbwg/iVvHPu84MmpK2Vt9hEN1BfjaKxnTWMSwiq2E2jLxiGjEQ2PE5DcOU8BYTKZR\nEsz7kqI4J2h99hnk5Dh/iopgwACIjcUeYyZ/0P8ojj/Ettwf88KAuSz/4itSvL1h5EiYMaPViBhr\nnpXyf5dT+10tjfmNNOY34rA48BzoiX6QM+Cr9WoUhwIOQMH1u91ip+FALRbHTjwu3YcqeRct4dvR\n1XljtN9Mw1MzwD+Ygp/78NnYFrbU11HU1MTzQ4YwJyKiw5fZ0HCAffuuIyBgGkOGPN+1eRElJTT8\n/e/MBXYMHcq/tVoSZszocFbwD2+rg6qqzygqWobFcoBh22bgtfAt5zeThx927r51thQFjhxB2bmT\ndflHeD4ggCIf+FPTo/jbaol+10HAfh+aAnxp8Pem3t9InVHLKyNTyAyOYN2CR/Gpt3A8zIfyMB9w\n2IndV0J5qDeZIyPYNyqC7PhgGrVgd9hb9a80O5pb9bu01Qdjs9uwO5oJ0NoYYGhmoMHOYC8YbAKb\nQ83+Oi1ZdZ7kWozYVXrXh4CnhyeeGs8zHg0aA0ZPP/brR7JDPZBrPKu43qQQYPDF19MXP70fvnrn\no0FjQKVSYVcUfpeXx3tlZXyQlMQ4Nwx97cwFG+CtVoW/fz6aAaY8vLCiciioLFoMFS14NXqi8wjG\nK2wiptE3Ywq5RCZynG+ampwzc3NynI9hYdTHasi2P0u1vZnHmx9kUsTlLI6K6lLus6W+hab8JlfA\nV2wKDg8rLfoCmj3zafE8SrMuH5tnLo2GXRgMgzH4XU6dfgL5DOfgR1+yu7mZb5NGcNl3em75twcm\nxS/zjf8AABJgSURBVAP/hyNIvtOMTt+1YNnSUkNm5m3Y7XUkJf277X93igJbtsCrrzqXnr71VpT7\n7uMfQUHMP3SIsd7ejPP2dj76+BB5WsrDZiujpOQflJT8DY3Gj4iIXxAaeptz3Prhw3DvvVBZ6dxH\nt60F5RTFmdfPy3PuA3zyp7TU9bvt6FFWTJnCn//v/1Dp9fwauDUxEW10NMcr/0t+3h+w26oZyG2E\nHB+JuqwCqqpwmM3cbTZTZjCwZvRodKd+UDU3Q0YGbNzo/Nm/3zkLetIkuOwy5/4KHbSEFUWhvn43\nFRUfUln5GRbLfjQaf7y8huPlNRyjMQmdMR6brZrqmq+oq9mMtWEHWs9otMZxqA1jUAxjsTnsNLU0\n0WRvcj1utSgst/gRrNRxmW0XjsYyWo6X43+4GHtdLXle/9/emcfGcd13/DPXzl68RHGXFEmJCkVR\nJkWRjBW5SeMktqwIjnwlSlAZqIrGDooWyB8xWhSNCxQIUMhy/EcgI0H/CJrAdRLFQFzUhhurPiQV\nlmWXiSNFh6XooiRKJilSvJZ7zPn6x2i4S4lOTFuWLO77AD+8N3vN2+/OfN/7zc68sflDLMt5JnGF\nN2P6iUiCQvVa+uu+xqrMPtqdU8SNODE9Nmc2EmZiCsHAMhxghsuCIEObK8JMR1f1WdFc2cymlZvm\n1OyWNXiAxxqf4vEH+1i0fA3aqp7gj7blyz/Q6EfyyUQIn8HBf+f0mX/mbf1e/oO/preqnpWxGO3x\nOCvjcdpisWv+3BXCI5P5HePjrzExsZts9l0c5zKquRTbWMaU1syI0sg50cjbXjuHChEKvk9bLDYT\nnVNT/Plrr7H0F79AXLjI+Gf+jvODXyA/EqXqC9VEUhGMOgMjZQT1lEGkPkJ0WTTYUV0XRkYQQ4P0\nX36KAe15DCdOdDpBdNzAHIboBYfoqWkMqlA3P4z20BaoSGGfVSgcE4weKzCgOZyqynE0meGdeAa7\n1mV1jUmPMcLS7HMsKuxjPHEvY5V/iRPtxtA0IopCXNOIqSoxRSH2yivEd+wgdu+9xJcsIXHmDImT\nJ4meOIFy5gzEYtDSgtPczMDy5ZxbupRz6TTnqqs5l0zyCtBRUcE/NDezoabmmkxXCMH4+GucO/ev\nWNYFli79J+rr/wpVNXF9n81HjxJTVX7e0fH+x6jHx4Mzr/buhX374MSJwOQ//3m480747GcRFUmm\npvoYHX2ekZH/BKCubjO1tZtIJLoxjD8+r5TvW0xN/YaJiT2Mjb2M44zS0vI9Uqm/ABReHh3lyTNn\nuFAo8PTQEJt+85uZaUCYmIDOTqioCDLOixfB8/CbGnHrUxTqFzPd2szEqhZ+t6KFx71qVhg2D5uX\ncN3cTPZxdXbi+cG9pAViRstwufTQVWkoKHjCw/VdXN/F9wvExQhJZYRUIs0jd+6c8/vf0gbf1BQc\nov0AV4lLbjFs+xKnTv09ly6/RMFYwZjaxIBo4LiX4vdOCttYRpNuscLro83tY4X3DpPKYo6pn+Go\nupaDXguXWUxjNE6zabI0Gg1K02RFLMaKWIx0JPL+h+hOnw6mVH7+eab/4DJdczuOV4HjVWC7SRwn\nie0msawKhKdSqR6n0v09VVUXqGjMoDUswq+vw16WpNCoU1jskY1Y5LQpCsoIjj+J5+Tx/RxCLUDU\ngmgBFAGKD64BngG2AbaOcA38bA3W4a8wdf4r5CoqyS9WydWqZGsVpishG4FMVDBt+EyaginFYnri\nMjlVJWeaZDUNW1GIqyoJTUNTFEYdh4ZIhGXRaBCmybJolD+rrJw5u8cesckeyQZxNIuf91GMK9Na\nGAp2+rdkVv4bduUxzNxqTG8Fut/Kry5XEo208Tefuh09pgf3g1OujFqVK3VVQa/VMZeYKJkpxFv7\nKfz2v5kafJ3J2ClG71TRjWrqFj3E4s6/JZnsmfWbCV9gD9tY5y0K5wtY5y2cERtvooA3msUby+FN\nWvhTDl7ORVn9f+S/sZNCwuJ/T2/l8PQathz4H742chyjox1Wrw6iszP4E//q7HFqqmj2AwPBjX8O\nHoQDB5iOxXjk8cfpb2jgV7bNss99LjCpj4Dn5cnnT5HPnyCbPUI2e4Tp6cNY1jlisRUkEl1UV9/N\nkiXfmvP9t7TBr1kDP/tZUJYDhQJkMsHRDcsK7j8S1i0rOFNO1+cORQlCVYv18PWxGESjQXyUvyRs\nG3K5YCDredeW4foMY3ap60HSparFCNthWYPk8yfJ50+Tz5+mUDhDPn+abP40QjHRK7+EUfElzMq7\n0M0GNEBTFOoMgyp9jpudfBguXAgOX3ge+H4QYV0ILLeGyXMJpo7A5NtTZA9nSXQmiH4qiv2eTeF8\nAXvQxlhkYDabmM0msbYYic4Eic4E8VVxtHiQkfi+i6Jos01MCNwxF2vQKl5cNmzPKt0JFz/n42U9\nvJw3U1d0BWOxQSQdIZKOoKcNlJSBSOlQo1GJhuqBcIIpKsLSueTMmLpwBImuRHAXsY44eoU+67XC\nEQhHYClnsfXj2JHTONF+7OQZrKp+NMNCu9yEMpFCmUijTqSC+ngdyngKxx/GbT6E2nsc0XYURdWI\n5m8nqd5O4kAL2p5p3MP9uK6J29iOV7sUR1QGhj7so0cdorEMpjJC1L6AkX0PjTxqdRStJoZWG0dL\nVVJI1/By9TLezCVYG+9j1ad/imYbqD//Fu5rPWhxHb1aR6/S0ao09KqgHqmPEFsRmwlzqYmqX2X8\nQuCevIC19zA/Oz3Jf+l11OTGSenDLEpOUF05RWX1FIn4GIaRAz2BoidRVRPNUzFsn0iugJGwYVEW\nopfx3H58ZwQjupxorI1EopNkoovKZBeJePsHOrvvljb4L34Rvve9ed9xbgbfD7Kw0dGZyReZmAhM\nNJMJOuuwnskEBhuaaqm5Ok5wWPPK/j6rrmlF8zTN2fWrjS2sCxG0Y3w8iLDu+0G2aJqzIxIpXvPi\nusVwnGL96naF4brB98rng+9kmoHhx2LFzw4/P6zremDkpdpkMsFnx+OzTTsswyMqYZtKy1L9woCi\nJvE4JBJBlNbDNoZ6loZtB1MKTU9DNlus53LFdYedT6lGhlGMsBOaK8LnIpFie5LJICoiHrWXMySm\nLZSUib7ExKg3MSvUGS1dd+72ZbOzf7cwwv6k9LeYaxuYVY8ITNUnajnE8jaRrIOesVEnbPxRG2fM\nQdEVVCOYaE4xinWj1iCxOjD1SEMEUCgUgvbZdrFNpR2478/exmMxyGg29x1+g42JCXrNadLKCFX+\nMBF3CNu+gGVdwDDqqIitI5r/NPpQD+7pGqx+C2vAQo2qRbO1x9HPHkE/9luMi+9iNkUw26rQWpuD\nQ7MtLdDSQrahgT9oGsfzeY7nchy7cubL6XyeTbW1/GNzM5+prEQIn5GRX9Hf/y/oWiUVsc8RE12Y\ndifGdCvelII36WG9Z5E/lQ/iZB4rM4HZM47ROYYXGcHxL+Gpo4jKMdT0JCyaRFReRkSmIbMYMV6D\nP1qFe6kCd6oO161CUWxUzUIzHNSIjWZYqJE8Xq6K6ckljOXqeU80cC5Zz2C9wXuNGiO1CqPVYBkq\nqhAYQqALwXrb5oV7752Xd74fnyiD//rXgwxp8eKiiYShqsWNr3SHcZzAzEZHg/+hKiqC9y9eDLW1\nUFMDlZXB4xUVxXoyGWywc+1IhjF7ZFxa97ygEygUihEuu+61A8JwpFtVFbQljEWLgvV/nPh+0LZ8\nPojSjsy2i3XHCYw21CjUyTQ/WgZQSmj44e+VzRYjlyuWpRlMqKtlBW0JDbfUfOPx2ZlDaUCxw7m6\nA7r6sbAMs5bQoEsjNMO5BgWGMbttpWXYiZZ2kmEWNtdnXZ3JXb0cti/sSLLZYDuLx4uddthZhaUQ\nxdeGWhtG0D7TLO5npW0M25fPF7f1fB78Wgv9ofdQGvNQX8BLFfATDpHxKLGJGKatY2gKEVUJSk0h\nokFEV4ihEUMjrmgkFI2EppFQNVQUhj2LS77NKBbjmsWEYZExbWzDpWIqRuV4nOR4nORYnMRonPhY\nnLiqEYsF3z0cyMTjLqnUHqqqfkcicRDTPICmnQduQ9N6MIwqFOUcQpzFdc8i/DwRtRndasRQGzCT\n9USrG4hW1hOJpIlE0hhGikgkhVJy6qZj+RTeOYp77iJOw1Ls+qV4sWRJRynQMw7GWAF1pIA4Pox9\nZJjCmSyFQYGdM3EtE910MOIWRtJGS9ok1hi0/uIbc+5Ht7TBDw4Gh0pDga4eTYQ7RukObRjB6KKu\nLjDN+UwHIpEsFBwnMG3bLnZUpSUUO5wwc/qwZ126bnHAEBr/eN6jP1+gv5Bn3PbIWYKCJcg7grwt\nKDhXQngUVI+C4mGpHrYWhFAEScukyo2wyDOpFSYp1aTBiJDSTAxNuWbQV9oB5fPB9w/LsB6G62ZJ\nJg9TW3sARZlmaKiFixeXMTDQwtBQHZalzAz4wqyutK5pxc8OO0jPC7SMRq8djIb1cMAQvsc0Z2eu\nybigLuJQp9nUKjbVwqapTeORn859xfItbfASiURyM/C84mHN0gwvXPa8IDsIzTnMluaT4QrBzGGx\nq7PX0qitDWaxmAtp8BKJRLJAma933nqz7UgkEonkA/GxGPyuXbtYtWoVbW1tPPnkkx/HKiQSiUTy\nJ7juBu95Ht/+9rfZtWsX7777Ljt37uTYsWPXezULhtIb6pY7UosiUosiUosPz3U3+L6+PlasWEFL\nSwuGYbBlyxZeeOGF672aBYPceItILYpILYpILT48193gL168SHPJXANNTU1cvHjxeq9GIpFIJH+C\n627wcrpeiUQi+YQgrjNvvfWW2Lhx48zytm3bxPbt22e9prW1VQAyZMiQIWMe0draOi8/vu7nwbuu\nS3t7O6+//jpLlixh3bp17Ny5k9tuu+16rkYikUgkf4KPcIuY9/lAXeeHP/whGzduxPM8Hn30UWnu\nEolEchO4KVeySiQSieTj54ZfyVrOF0E98sgjpNNpurq6Zh4bGxtjw4YNrFy5ki9/+ctMTEzcxBbe\nGAYGBrjrrrvo7Oxk9erVPP3000B5alEoFLjjjjvo6emho6OD7373u0B5ahHieR69vb3cf2VClnLV\noqWlhTVr1tDb28u6deuA+WtxQw2+3C+C+uY3v8muXbtmPbZ9+3Y2bNjAiRMnWL9+Pdu3b79Jrbtx\nGIbBD37wA44ePcrbb7/Nj370I44dO1aWWkSjUfbs2cPBgwc5dOgQe/bsYd++fWWpRciOHTvo6OiY\nOSOvXLVQFIW9e/dy4MAB+vr6gA+hxUc+bWYe7N+/f9YZNk888YR44oknbmQTbjr9/f1i9erVM8vt\n7e1iaGhICCHE4OCgaG9vv1lNu2k8+OCD4tVXXy17LbLZrFi7dq04cuRI2WoxMDAg1q9fL3bv3i3u\nu+8+IUT57iMtLS1idHR01mPz1eKGjuDlRVDXMjw8TDqdBiCdTjM8PHyTW3RjOXv2LAcOHOCOO+4o\nWy1836enp4d0Oj1z6KpctXjsscd46qmnUEvunVquWiiKwj333MPatWv58Y9/DMxfi+t+Fs0fQ14E\n9cdRFKWsNJqenmbz5s3s2LGDioqKWc+VkxaqqnLw4EEmJyfZuHEje/bsmfV8uWjx0ksvkUql6O3t\nfd/pCcpFC4A333yThoYGRkZG2LBhA6tWrZr1/AfR4oaO4BsbGxkYGJhZHhgYoOkj3qX8ViedTjM0\nNATA4OAgqVTqJrfoxuA4Dps3b2br1q089NBDQPlqEVJVVcWmTZt45513ylKL/fv38+KLL7J8+XIe\nfvhhdu/ezdatW8tSC4CGhgYA6urq+OpXv0pfX9+8tbihBr927VpOnjzJ2bNnsW2b5557jgceeOBG\nNuETxwMPPMAzzzwDwDPPPDNjdgsZIQSPPvooHR0dfOc735l5vBy1GB0dnTkTIp/P8+qrr9Lb21uW\nWmzbto2BgQH6+/v55S9/yd13382zzz5bllrkcjkymQwA2WyWV155ha6urvlr8XH9QfB+/PrXvxYr\nV64Ura2tYtu2bTd69TeVLVu2iIaGBmEYhmhqahI/+clPxOXLl8X69etFW1ub2LBhgxgfH7/ZzfzY\neeONN4SiKKK7u1v09PSInp4e8fLLL5elFocOHRK9vb2iu7tbdHV1ie9///tCCFGWWpSyd+9ecf/9\n9wshylOLM2fOiO7ubtHd3S06OztnvHK+WsgLnSQSiWSBIm/ZJ5FIJAsUafASiUSyQJEGL5FIJAsU\nafASiUSyQJEGL5FIJAsUafASiUSyQJEGL5FIJAsUafASiUSyQPl/3r57X+fKDFkAAAAASUVORK5C\nYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "for i,s in enumerate(km.cluster_centers_):\n", " plot(s,label=str(i))\n", "legend()" ] }, { "cell_type": "markdown", "id": "6b9b0ca4", "metadata": {}, "source": [ "Let's look at the corresponding dynamic behaviors.\n", "\n" ] }, { "cell_type": "code", "execution_count": 83, "id": "a0bb2a61", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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/9Uae/2AeU9as5W9FKifaspO6d339Xuz20RgMp2CzXcHy5bdRWPhawp9f5w5g\n14zs3BnpXTMv5Y3j8j3LwLWdB7bsw1NxPO6dwJTpFJ09joYXP8J7xnlR7+/x7AUGsHu3maysF9m4\n8Qy83jMwGsvi2iaEoDYQxF1lYmenOqVwp3UYdzk3MmnRSl4uHos1xkpm86KdZBWWUb0TMJST/ov7\nsE+5ieq3vsLp3Et9fSlm81n4/W+zcuWjZGf/Jq59O5sCCEzsjNCvnEAB9+conL1sJf8pGUdFN9Z0\nNDbuxVhroolSsrMfZ+V593DcFfOpPe8GAmMjn9u7qTGA2R/td+2bBAIBpk+fzrp161BVlREjRvDe\ne+9RUVER9TOp/n49mje0cMdSzj96Chdc0Pk9vz8klO3/NTWB0xmab9m1C5qbwe2GsekbOONoC4+9\nAoHAUMYffT9ceR+LL3uKf+X8El0/IG5ChP7tuFVj9WyVZ1YeeK39+0LkoZwQ5NxLV1D4QCVqrTXu\n9zGbobwcnn46iKbVMaCkgDGB8zj//17nr399mNdf/32bkAsR6gBa//0zUMVXpjG88WTIIx8TfILX\nf3MO619+h0tvMmDcE96xHPj/MlyXBak8aiXZ949D9RkjXBP+/wUFVfz+94VcdZWComRTWfk0V155\nM7/73Uo0LfGJ4/opOqadKgs/rueJ+kwmndT6zkW8UvM0C056DeXYH3HlbWvIe3gs5m2Je1V33FHF\nxx8XsnIlmEx/5E9/Gs306f9j1apJCX3eU6njmqhy0qPRrjChZYzjqbuWotvK2XNvEfMfBDAzwfMo\n9974M84onERAiVwexxxTxUknFfHkkwDjuPji2ygr+zlPPvnfuLYJVRD8B0z4XrQBsoJQhlF381rG\n2leT+9hoFD3ytWd46rjKlcf1LWVvEDfxSfUzPHr0u1zwwj5+/OMimpsN5Oc/z733Hsu1115Obe3A\nmPbV3Kmx7AMD96yOdkU+wVOCnHnJCvIfqMSYQNuIxOTJ+7ikUeGeD9KYZz2Pn//8dVb+QOW4S37C\nhfnzI3pSzefoaNkqX/27S4/sFfLy8li4cGFSnznppPjXJEWXo/MJ0v4R5j8UiOff3NPte+77/A9i\n1VP5bX9rWkAs/PoIUXVeuhBRJvFOWbJEzK6vj3vvh7dvF6O+/VY0BQIJ2+P17hJz5xaKLa/vF1/y\npVh07Sfiq69yRH39TuHzCREMCtFuTi/EWWcJ8dFH4a/dcIMYOHOm2Op2x3yeruvix+vWibOXLxfB\nTjfuTEM9h5SLAAAgAElEQVTDPLFo0fFhr61YcZ7Yvv3BRL5eG1PWrhX/3LNHiHnzhDg+/H5i+XIh\nCguFaGwUb1dXiwHffCN2e70J33vhwjGiqWlp2981NR+IBQuOEJqW2ITx61VV4oerVsW9bpvHI0re\neUd8+N134W+cc07YJHZHdu2aIdavv6Xt72DQI+bPHyJqa/8X95kNgYBwfPVV3Ov8mibOWrZM/GzD\nhugXvf66ED/8Yfhrn3witCOGitmzTULXtbaXt269V6xaNTnuc09avFjMTWDy++Ht28VR330nnMlO\n9rawdu00sfu2ciEWLBBCCOF2bxFff50rPBNGCvHuuxE/88C2beJ3mzdHfK8H5KtHiPY9uvP9emx1\niSfgIWBo5Ojhha0dSpfvFfBXYfbb2/42GIwMG/0cm2/SCf7tLxE/49I00hJIK/v1wIGcmJnJtPXr\nE7bR79+HxVKMtqCe8v8rxz8ngzymsmfPbzGbQx56J2fE6YSMjPDX7roLj9+PLU6sX1EU/jZsGF5d\n555t2+LaFwjUYDbnh71WUfE4O3Y8hM+XeD61R9OwGQyhYZPdHv7m2LEwaRLMmMHF+fncXFLCpatX\n40swVNfRxry887DZKti164mEPu/VdawJ/L7lVitv/vWvXO92s97tPvDG/feHJiKjTE4HAvsxmQ7Y\np6pWKioeY9Omn6Lr/pTYZjIYeG3kSGbW1fFCtAndSGV/1lkEhhdiDNpQ2u1hVFb2G5qbF1NXF3v+\nyaProd81Dr8qK2NsWhrXr1vXpfYbCFRjqtWgJTXWZhtMaentbP59VijlN0JdaatzkqTosRLb1bQb\nmksYPMhAfSBAxbffctzixezrQpaHFmxGFeFL2rOyTiEj71R2b/tLSDQ74NK0hPPAn6qoYIvHw+O7\ndiV0fTDYgNGYjXuDG8cxDsp+XUbgyck0NMyhsXF+5A9FaqDl5XhtNmx//3vcZxoNBl4fOZIX9+3j\ngzgTlprmRFXDJ6ZttqGUlNzI1q13x31WK20C5Xa3Nc4w7rgDnnoKvF5+X15OidnMLzZtSujeIRvD\nQzehzudBAoH42TbJCMBJK1bw/woKuHjVqgMLccaPh1Gj4KWXYtgXXoa5uedjsZSzZ8+zKbMt22Ti\n/dGjuWPLFlZEykaJVG8A7bYbUOu8YeKoqjaGDv0Lmzf/GiGid7CeBDseRVH4+/DhbPN6eSLBthFm\no+ZEbfCH2V9WdgdN6btoHOIOZfpEsE0Ke/L0WIltq6rD4M0lIwNeq67maIeDSdnZXLx6Nf4kJmAB\ntKATg9I5zjd47OPsujBI4LXnOr3n0vWEhd2qqvx39Gj+tGNH5MbV0Z6WRu/b4cM60Erx1GKavgww\nwHEn27ZFEc4oDdRjNmN75pnQpEMcCs1m/jNyJDdu2EB1jOs1zYXB0FmIy8p+w/797+J2Jya+bY3M\n5YpoO6NHw9FHw8svY1AUnj/ySD6qreXj2tgZLkIINM2NqobbaLdXkJ9/CTt3PpK4bYngcnHDgAGM\nS0/nd1u2HHj9zjtDWSYRvFFNc6Gq4d9ZURSGDPkjO3b8CU2LvhoyWXE6Mi2NR4YO5aq1a/F2XAEa\nTdhPPArVb4CPPw57PS/vIgwGEzU1b0d9njcJ+6yqymsjR/LHHTtYlWQapKa5UBt9YU6BqtooL7+L\nrTeaYMaMiLYl0ulIwumxEtu9vxGzCJ0i9HVjI+fl5nLf4MHkmUwJhRPao2kuVEPnym23DyfXciq7\ntj7U6b1kPHYIDdn/PGQIU9atIxCn42kVdu8OL5aBFlS7SuGPCtH+eyZu9/rIXnuEBhrUdXTAeOSR\n8M47Cdl5UmYm1xYWcuuGDVGHxyFR6izsJlM2paU/Zfv2+xJ6lkfXsalqVHEB4Kc/hWdDHmym0ciL\nRx7JDevXx9x6QNe9KIoJRen8+5SX38WePX/H76+JaVvCAiBEm/1/HTaM/+7fz+ete0Kcemrov998\n0+lj0TpHh2M8Dsex7NkTfZTVFXG6trCQI2w27tq6NfyNKGWv627U3AGh1ajtUBSFQYPuY9u2u6Om\nPyYb7hhqs/HnIUO4eu3auG2jPZrmQq33dhrtFRVNwZvppsG3MLQopL1trXVOkhQ9JuxVjY1YCAn7\nSqeTsWlpGBSF54YP57m9e5Pq/XXdjRqhkQGUn/A3dp9UTfC7r8JeTzTG3p7ri4ooNJv5S5xcJE1z\nYhBp6D4dY1YoS6VoahFVz9cxsOx3kYUzQgNt9ZyUm26CBMIxrdw7aBBr3G7ejRKS0fXIwg5QWvpz\namtn4vFsjfh+R/us0WLsrZxxRihPfNUqACZmZ3NxXl5ngWpHtI4HwGodSEHBZXFj7QkLgMcTygFX\nVXJMJp4ZPpxbN2wIjRoVBW64oa1jStTGQYPuYefOh6LG2rsiToqi8Mzw4bxUVcXK9m0jmseuuVDz\nB8KcOVAdfgZvTs7ZqKqD/fvfi2pfsh3P1KIiisxmZiSx542uuVCbfJ3sNxhMlA+azvafZME//xn2\nnvTYu0aPlVh1UyM2JRNNCDZ6PIxo+XGLLBbuHzSIWzZuTHhCRhMeDGpkYbGlVZDlGU7VggNiGtR1\ngkJgSbKCKIrCkxUVPLxzJ1UxQx1OlKAdY6axbeWj4ygHplwT1o0X0dy8BLd7ffiHIjTQNgG46KLQ\nqqd9+xKy06qqPFlRwW82b444WRlLlIzGDIqKprBnz9/iPqctpBBL2FU1tKLwX/9qe+n+wYN5u6Ym\n6grGWB0PhDqfvXufQ9OiL8xKONzhcoV5jOfm5jLMZjswn3LNNfDee6EOIEEbHY6jsNuPpKYmcupj\nV+PEeWYzdw8axO3t20YMYTeYM+DCC0N7ybRDURTKyn7Brl1PRnyOt4sdzxPDhvH/duyI2TY62Sis\nEKEsCguvwlnQjOvrV8JCYbHKLjs7G0VRDvl/2dnJrflIhB4T9v3NjaSpmewPBMgwGrG2q0g/Limh\nPhDgozix2FY04UU1Rs+RLh38a3blzUHooaFnmyfcha1Ih9ntXFdUxP/F8TiVgA1jRviygLxL86h7\nt5ni4mns2dNuqwFdB68XrOHzBG2ek8UCP/hBwuEYgDNycjjSbuevETyoaGGEVgYM+Al7974Qd6uB\nhDx2CG3u9PbbbQ0022Ti3kGD+FWUidRYHQ+A3X4EDsfRVFe/Ht+2eHQQdoDHKip4cMeOULiooAAq\nK+HTT5OyccCAn7J7d3Th7KrXeVNxMXXBIO+3to0oE9e63jJHcdllEetNXt4leDybcDqXh72uCUFA\nCMxdaBtH2O1MKSpKOJQaLYQKYDBYKCm7hd1nOg9sm0rssqurq0MIEfXf53V1DJk/n4Cmxbyu9d/G\njb9k+/aHor7vuexUvv7CQSDQjBCCJ3bu5LaWEKgQAvHss4jLL0/oWQ2BAIVz57KiuZm6bmzFEY0e\nE/Z6dyPp5oxOe6EAqIrC/YMHM33btoS2qNXxopqiC3vm0ddjCBpoXPQ80P3h3PTyct6qqYm6lF/T\nnOCzoWaGez35F+ez/939FBffyL59L6FpLel1raLewaYw7+TSS+G/8Re/tOfBoUN5aMeOTluuxhMl\nm20wmZknUV39Zsz7t8ViI4hjGGPHQiAA69a1vTStuJjNXi/zIuwNEq/jARgw4LbwzjGabfGIYPsw\nu51L8vMPeO0XX9xJHOPZmJd3Pj7fnk7CmZRtETAaDNwzaBD3b9sW8tpjhWLUtNCOlcuXQwcnyWAw\nUVJyU6e5gNa20dX91+8oK+ON6mp2xdnmQgiBLjyoxujbhpQMuIWq73nR3v1P22vdKbvTsrMZaLXy\n7w6hqWjEayfWfYIsZRzV1aEV0Z1GE+edB7Nmhep+HDKNRn5ZVsYft29PyLZk6TFhb/A2kmHOZK/f\n30nYAS7KywPgkwR6L83gw2COLuyKwUBh47FUbQ1NJHl1PekwTHuyTSamFhfzWJRYu6Y5UXz2Th67\nfaQdg8VAcG0uDsd4amtb0rmiNM6w7IRJk2DBgtC1CTIqLY3jMzJ4sUMIJ16oA6Cw8Bqqq2Mv70so\nFAOhWPV558EHH7S9ZDIYuHPgQB6IUJHjNSiA7OxJeL1b8Hg2R3y/Ox47wO8GDuTp3btpCATgggtg\n5sywkEA8GxVFpbDwKqqqOpdhd1P2LsrLwydEqG1EyUhqs89qhYkTQ/Z3oLDwampq3kTXDwhPMhkx\nkcg3m5laXMxDceahdN2DATOKPbqwWywlZJjGUlt1oFPtbtlNLy/nge3b0RJxGOO1E7ebQsv5be2k\nU50rLoaKCvj664Rsu6WkhC8aGsLXU6SIHhP2Rl8jWbZM9vn9FEUQdkVR+NmAAQlNxmiKH9WcGfOa\ngoFTqHEsQ9d9KZmA+XlpKS9VVYUafkd7NCe4rRgzw4VdURRyzsqh/ot6Cgoup6bmjdAbbjdEOFrO\no2kH7ExPD3m+86PkwUfhtwMH8pedO8NGPokIZ27ueTQ3f4fPFz2un3AoBuDss+Hzz8NemlJUxJLm\nZjZ0qMiJdDwGg4n8/MuihmO6GmNvZYjNxhnZ2bxcVQWDB4d+n3YjjkRsLCi4kurq1zvljHe3/hkU\nhd+UlfHU7t2xY+ytI4pJk0KbMHXAZhuMzTaM+voDYaawOtdFflFayitVVThjbGKmaS4MWGOP9IDC\nipuoGrYjtMMe3S+7iVlZZKhqQjuPxh05ut3kOM7A6VyOz7c78mjirLPgiy8Sss1hNHJzSUnE8Gl3\n6TFhdwYayU2L7rEDXF5QwKLmZjbF6cF0NYBqjS3s1lMuJW2rRn3NLHxCdLvyDrBYOD07m//UdE67\n0zQXwt05FAOQeWomDV82kJd3MXV1/yMYdEbPYe8oThMnRmygsTgxIwO7qvJVQ0OYffFCHapqIzf3\nPPbvj5zvLIQ4MAeQiLCfdFJoxNEuLGQxGLi2qIjnO6yqTKTjASgouILq6jcivpdw5kmMMNJNJSU8\nt3dvKOQxYUIowyQJG9PTx6CqDpqavu2abTH4YX4+3zY1sd1sjpLu2M6+k0+GuXMj3qdjGaZiAVCJ\nxcKpWVm8HiPkoWkuVGGJK+x5RT+k4ShBcPbMA/Z1o+wUReHGkhKeTWBr5ri/sduNmpZNXt6F1NS8\nFbnsTj45YrpsNKYVF/PvqqqUn1jVY8Lu1prITQ8JeySPHcCmqlxZUMBrcWJimjGAwRrnzMjsbHK2\nFlC34dVuh2JamVJUxL8iZKpomhPhtHQKxQBkfT+LxrmNqEoWDscxNDR8GVvY21fiU09NeFjXiqIo\nTCkqCgvHJCqcOTnnUlcXedvlgBCoioIxUWHPywsNTVvSHluZVlzMi/v2EWyXvZNIxwOQkXECPt9O\nfL49nd5L2LOLYfuErCw8us53zc2hsv/qQMpsojbm5nYuw1SIp01V+VFhIS+OGRM7FAOhFbTV1Z3S\nHlvtq6+f1ZZl05WMmEjcWFzMP2KIp667UHVzXGE3GjPIcJfTsO2dNvu665RdWVDAlw0NcbN34raT\nljBYqJ3MimzbiSeGJn8TPDKy3Grl2IwM3u7idtfR6Lm9YkQjBRmZ1Pj9MY+iu6yggDcieMXt0Ywa\nqi0n7jNzOJ469+yU5cKelZ3NZo+n05mLmuZENHcOxQCYC8xYSiy4VrrIzj6T+vrPEouxQ2gV57Jl\nEffQiMVVhYW8s39/W+pjImEEgJycM2lomB0xHztMnKJtKdCR730P5s0Le+kIu51Si4W57SZRI63q\njITBYCQ7+wzq6mbFti8WHk/EMBiEOsXL8/N5u6YGjjkGliwBQNeDCBHEYIh/TFxOzqRO9qWq/l1R\nUMB/ExF2VQ3tJ71gQafrbLahqGo6LtcKoGs57JE4MzubjR4PO6MmGLgw6KaE6k22fQJ14ts2+7rb\nKTqMRs7Kzo679UYiMXbsdrKzT6excS5+zdO5U8zMhEGDYMWKhO27sqAgVOdSSI8Ju19ppCg7M+JB\nEu05MSOD+kCAda7oqXe6WUO1xxf29EGnERTN+LzbUlJ5jQYDP8jN7ZSWqWlO9EYzakZkzyd9fDrO\nZU6ys8+IKeydGlleXmijsBiplpEoNJsZlZbGnJZwTKIeu8mUi91+JI2N8zq9FxZPjLalQEfGjQud\ntNSBC/PyeK9dGSba8QDk5JxFff3/YtsXixjCDqGJynf374cjj4QdO8DlarMvkcyRzMyTcbvXEAgc\nOOE8VRtZnZCRQZXDweYI7afTiCJK2QNkZ59FXV2oDFO1F4vRYOC83FzeiyKemuZCDZoSqjc5R1xN\n3YC9IETKyu6ivDzeibunkjv6qKxdRpLJlE1a2miyfIsj2zZuXFLCfm5uLp/V16c0HNNjwh4wNFKU\nnRHxJJkwgxSFs3Ny+LS+PuL7uu5HAIo9I+L77VGOOprMTVYCzoUpCcUAnJuTw8wOEzGa5kI0RvbY\nARyVDpxLnTgclfh8u/F79kYW9kiVuLIytFgpSc5r1wGFGn0CQkxImJqaOk/YhnmdiYRiILR3TIdQ\nDMAFeXm8366RxWxQEeyLtEVDwl5xHGEf73Dg1DQ2BAIwYgSsWhVxH5toGAwWHI5jaG4+sB93qsRT\nVRTO/+47PogwzA91Pu1+kzFjogp7+9+4u1kx7bkwL+9Avn0n+9yoQWNCHnta+akEHQL/lsUpG+2c\nk5vLV42NuGOIZ0wHyOejbatWIDPzFHL9yyLbNmZMxHofjVyTicr0dL5oNy/WXXpM2IPGRkrzMuMK\nO4TONPw8irBrmhvVp6AkEgoYOxbHIifCtShly5LPzMnh64aGsBWeuu5GqzdF99gr03EudaIoKg7H\neJqDaxKbPIVQJVkd9QSEqJydk8P/WsqwbfFKAmRkHB8mShFtS1TYWyt4h1SzsWlpNGkaO1qG7cnY\nZ7MNQ9Ma8furotsXC4+n08Kw9iiKwsTs7NBoZ+xYWLECXU+84wFwOI6jqelAGaYqjg1w2qJFfBUh\n3NGp8xk9OqqwZ2Qc32ZfKrJiWpmQlcWCpqaw+ZMw+/yGhIRdUQw49mVRvyU0gWpKgX2ZRiOj7HYW\nxtgSO2Y97FDnMzKOoyCwInKdi1H20Tittc6liB4Rdl/QB4pGUa4tIWGfmJXFnMbGiLmnuu5C9ZGY\nsGRkkLHNjqF5Ycoqb6bRSIXNxrJ2y+M1zY1eZ47qsaeNTcO1KhRacjiOoZn1UWPsneysqIDNkXO3\nYzE2LY1dPh+1fj+a5sFgiO6ltickSt922t6hSx57fj4YjZ22RlAUhZMzM/mmJc4e8tgTs09RDDgc\nx4YJZ6t9Ce8VE8NjBzglM5OvGxvbyj4kmonZB6FG39FjT0n90zROWbqUr53OTr+Prnf4jUeMgE2b\nQmcxdsBqHYQQvlDKXgr3YskxmSi3WlkaYesIXXdj8CuJzc0ADu9gGhoWpHSfmO9nZfFVjMOzY9bD\nDnXe4TiOYm01lkjhuVGjknbG2upciugRYa9zN4IvE2NaqCe3x2mARRYL2UYjmzydt0LVNDcGD4kJ\nC+BgGMbAOix0/WCPjpyYmcmCdj2/rrvRak0Rs2IATLkmhBAE6gIhj924JXIeeyRxGjo01ECTxGgw\ncIzDwcLGWhRFCTt/NRZW6yB03RfZI261LdHJU4AhQyLOEZycmdk2gRrylBL7PSHUOTqdSzrZl4pQ\nDLRrZEOHwubNLR57MvaNp7l5cdvfKdvIyuOhzOUizWDotKglJErtbLRYQtsjRMiRVhSF9PTxNDcv\nSWkoBqILlKa5MfhIXNitY2nW16d0Z8dY4imEhhB+DIYoo7kOwm6xlAI6Vq2q87WlpVBTE/XQlkgc\nn5HBSqczZXH2HhH2PbWNKP5M6vX43norlenpEU9G1zU3qkfEHE63x1h6BJpuJ0dE+AG6yAkZGW3C\nrusBhNAJ1hMxjx1CDclWYcOzyUNa2hjc5igx9kiNrIseO4Qmohc3VSclSoqiYLePwOMJ37QsTAAS\nnTyFUIZAhL1EjnM4WNLi2XUSpTjY7SM6baqWSmE/wm5nfyBA/ZAh7Tz2xO2zWMoIBpsIBkN1JGXi\n2VLu4x2OsBEjROkco5Q9QFpaqAxTvXtiJNva7POSsLDbi47Da6k+KLZF2mywdVQbdYK8Q51XFIV9\nyiCM/ghOl9EYEvcdOxK2za6qVNhsrI6RNJIMPSPsdU0Yg4nF11upTE+POKTTPA0YAkrEHeIiMnQo\nXm8+efq2JCyOzdi0tLYfoMnfhKra0Rv1qB47gG1oSNhttiF4zfXoaZ1T5yJOnhYXh07xjtDJxWNM\nWhobXfVJiRKA3X4kbve6sNfahDMQCMXME/wdKS+HCNsIjGopQyEEuu5JysaO9gV1HS3RjawSEHaD\nojDKbmdVcXGXPHZFMWC3D2/rfFIW7mjxGsemp7OygwBE7BxjCHtrGaYy/g+hOtfRtpB9HgwePWFh\nt5UeRzDdjUOJvpo1WYrNZnQhIuazx62DEcKPu5WBGCIJO4TKPsl9YMZE+F27So8I+9660CEbyQj7\nUenpEU8v0j11qIEkKmJpKS5nHtnalvjXJsgRdjsbPR6Cus7QBbPxYyXYFIwaYwfaPHaDwYLFl443\ns/MEWETvSVGgpCS0x3mSjExLY5u7LuH4dSuRhL3N62yt4IluGhVFXHJMJhyqyg6fL6kYe8i+I3C7\n17ct3fcJkfjunQkIO8DotDRWKgpoGpqrK2V4RFsZpswrbin7SOIZEqYONiYo7Kn0ikelpbHe7e40\ngarrbtQkhN1QOghDrYlSJXXL7RVFidrxhDrvGL9xBGHfxUCEd2Pk62OUfTSi2dYVekTYqxsbsRA/\n1bE9FTYbmyPN/nsbMQSTEPaiIpqdmTi0xIdF8bCrKkVmM1u9Xqx48WFDc2qo6dHtspRa8O0Oxdxs\nTZl4MjvPzkfN7Cgu7pKwD7fZqPY1JuVtAi3e5oZw21qzJxKdOG1l4ECIskHUqLQ0VrlcScfYjcYM\njMaMthWoSYmT15uwsK92u6GoCL1+b9KjHpvtCDyeDcnbF4uWsh/dbsTYSsRRRVlZ1LK32Ybj8WxI\nubCnqSrFZnOntqtpbgzuxIWdnByoNlOqp67dAhHLrs2+WO0kwrzSdlGK5o3iscco+2iMimJbV+gZ\nYW9qxG7IpDYQINcY3attz2CbjR1eb+ee39uAqiUYBgAoLsbptGPXEju0IlFG2O2sc7ux4kXHimpX\nUdToHqO52Ix/b2gIaGu040mPIuyRhsVFRQkfutEem6pSYtIJRDgfNhYWSxk+X7inFOaxJ9o4ITSB\nF2WLiAqbjS0eT0tGR3LCabGU4feHbEwqZS9Bj32IzcY2rxeKitAakpunALBay/D5QtsApyzG3iLs\n5VYru3y+tqwxIXR03dd54q+gIDSJFwGzuZBgsBGf5kn5CUVtZdcOXfeguoKJ1x1FQQ9kkxdM3qFJ\n1rY2+5IMxewS+Wj+KCOKGPU+qm1Wa0TbukKPCHutq5E0YygUE2vVaXssBgOFZjM7Oswsa94mDMkI\ne1ERTc1WrCkW9nKrlTVuNxZ8BDRL1InTVsxFB4Td0mTGb+3cM0eNxXbRYwcoMwn8xF8K3x6LpbRN\nlDrZlqzHHqOCl1utbPd6kw7FdLQxKeFMUNgHtTayoiL05pqk0h0j2Zcyjz0tDYvBQL7JxJ6WthHq\nGK2dQ1Exyl5RDJjNxRDYl3JhL7dYIgi7G4MzkJRTEBB5ZKe43Q6KIp5x62CHei+EYLfIw9+hnbTR\nBWEvt1rZ4fMldCZFPHpE2OvdjThMoS17o+3sGImhLR5de/RAE6pI/B4UFtLgsmMOpraClFksLGpu\nDoVigpE3AGuPpdiCb2+oIZrrDfjMnSdDoy6f7oawDzAF8SQp7CZTHprmRNMOlH2bOLlcCQljG/n5\nIa8xQmUtt1jY7vMlHYqBbghngsLe2umIwkJ0Z20XRhQHQdjblX15O4EKZXREsC+OuFgspajBvSkX\n9kjiqWlu1GZ/UsLuVwvJjpROmGLbIIGU2w713i8EPhwIESAYjJDYEGO0FA27qpKhqgkfNRiLHhH2\nBm8jmZZM9vj9lFgSF5kBZjN7OnxJzd+MIRlhN5loMuajag3oeuJ5pfEos1j4rqkJCz68fkvUVaet\nmIvMBKoDCF1gqTPgN3bOp/XoOvZIjawLvX8rhUYdl0hO2BVFwWIZEBaOaQsTxTs9qSN2e2gZdoSJ\n8HCPvevCmVTWSYLCnmk0YjIYqB0wAM2dfGZRyL5Q+aXaY4dwgYoqSgkIuymwN6V57B1ta0XX3Ria\n/EmN9rxqERmia/U+GdsggRh7h3rv0TSsqhr2O4fRxTZbnqJwTI8Ie7M/dMjGngjH4sWiyGxmXwdh\n1wNO1CQ9UE+aA13Jwe9Pndde1uJtjraC12eO67EbLAbUNJVgfRDzfvCpnbdMiBpjz86GLi43zjcG\ncepJhK5asFhK2mLY0MFjT0bYIar3UmaxsNPnSzrdEcBsLumacCYo7AClFgu7CgrQg86kOx5VzUAI\njWCwOXXL9tuVfanFwu6WUEzUMILDEUpPjXK+gcVSgllLfSimvW2taJoHQ5MvqbrjNpWQTmq3s802\nGvEJgavDQqCEYuztbG+tcx3bSRtdFPZSi4VdSSxsikaPCHujv5aijNykPfYis5m9HT32oAtDkpOB\nXrsdgYNAILHDshNhQMv3GGYFvy/6zo7tMWYbCdQHsFRr+Ol8okvUrJisLIiyd048sg0BGpMZ4bRg\nMuURCBxoVJ6uTp5CaJfKCMKebzZT6/eh697oK/5i2hf6PZPKxU5C2AtMJmoyM1s2UUsuxq4oSlsZ\npjQU01L2BWYzNS2bgUX12BUFcnPbTiPqiMmUh1GrT7mw57ezrRVdd6M2eJOqOy5bIVYl+fUbsVAU\nJfS7dnQY46U7dnBoWud1OraTNrKzobEx7KCZRCgwmTqVXVfoGY9dr6Y0P5/aQIDCRBe2AMUWS2eP\nXXOhKsk1Mq/NhqKlp1TYC1pGHgOMGrrPgpKgsAfrgxjr/ARxIUT4jx41xt4Nj92h+GnWkxd2ozGX\nQJx33Z4AACAASURBVOCAIHTLY8/KClXyDlgMBjINQRSDBUVJriqaTLltv+fBCMUA5JtM1DgcXRpR\ntNro9dcgAGMXD4sOo90EXr7JRHWbsMfIKsrMhCgbX5lMuZj0hpQLe4HJRHUkh8xHaIfEBHHbCzAa\nvOh66hYpQXin2GZfsqGYljoXaicRdMVgCB1vmeTCwki2dYUeEXa3oZqswlzyTabQCTwJEikUo8Xr\nWSPgs1pRgvaUCntG6/adhgAmn41gevzvZcwyEmwIorg8GJU0gsFwsYvqsWdnd9ljtyl+mvTEUkzb\n0144oV3mSVeEPSMjqrgMMAtQuiaaweABj/1gCHuB2Uy13Y4mvEmHYlptdPtrE188FY/2Hns78YyZ\n0ZGREbFThVDnbT4Iwp5jMtGkaWGpynqS2zIAeO3pBINWgsGu1f1otO8UW0lo8rTd/EBrnQu1kyjn\nqWZmRi37mLYdKpOnAVMNap6D4cmkydHiMXUaMnlQk2xkbqsVo8/SJgSpoLWhOhQfJq8Nf1r8htvq\nsePxYDRmdaqwHl2PvEFaVlaXPXYbXhq64LGbTDlh5dUWJ06xsBcbg4gkwzAh+3LDQzGJiJOmgd+f\n8D5D+SYTNVYrOr6k0x0hJJwe//7UCWe7MFh+IqEYiOuxW0XqhV1VFLKNRva3E09dc2Ewpid1H4/d\nTjBgTalDBlFGFPF2QI0QY7epaqd2EkaMeh/VtkPJYxdGF550A8OTSZMDsoxGGjpsO6oJDwZjcsLi\nMpsxecwpryA7TziBUrOOxW3Fkx2/KE3ZpnbCntOpp4/qsWdkhLJKurDzm1G4aBQ2/Eker9dxiHmw\nPPYi1Y9mSK7BQ2hyUtc96Lo/8VBMq9eVoJAVmM1UG41oRj+q6kjaRpMpF28ghcIexWMPBptR1SgH\nz8TwGk2mXGx6Y8qzYtrsaydQQd2Jaop/OE57vGYzeoodMmj5XTuFYppj/8bJhmIg5mgpGoeUx25w\nDWCT35O0x54dSdgVD8ZolTgKbrMZa7MSeZKjG5RarWiaC0uzDXecs7Wh1WMPgMuFyZxLMHhA2AO6\njhAi8qECBkMow6EL+zVrWjOKmk5tkl5Ax1CMp32MPcnfMZawF6peAkqSHQWhEVNr55hwKKa5OVSO\nCZJrNFJrMBA0B6MLZwxMplx8gdrUCntL2eeYTNS1tA1Na8JojPK9YoiLyZSLXTSm3GNvta++xT4h\nNHThQzUl1zl6TSZ0tynlDlmO0Uh9J2FvwmiM8RtHmDw9EIqJYl+M0VI0ck0maiPsoZ8s3f5FP/nk\nE4488kiGDRvGgw8+GPGa9OAQvm1q4tgkGhVAuqri1XUC7bzNoOJBtcQ/77Q9LlXF6hRt26imEl13\nY2my0JSZQCgmy0hgvxeMRozm8Nhc1FTHVtLTQ5UrSYLBJoxqRtiwOBGMxmyCwQPhn25NnsbwGrMM\nHvxdEPaQjVkEgw2Jh2KczqSEPcNopBnQbAJjF+YBjMZs/IEUZp20CwfYDQb8LW0jGGyK7bFHERej\nMRsbzQdF2DNUlcYWgQoGm1GFDSU9ufbvMRrBYwirhymxzWikscPoN2YZQsQYu81gaGknUeYAuhCK\nyVBVmntb2DVN47bbbuOTTz5hzZo1vPbaa6xdu7bTdbmWYaxyuTgmSWFXFIVMo7GtggBoqgejLS+p\n+7hUFVuzhqalNnUKQuckmhqsNGbGv1ZNV9HrvZCR0Uk44x7tZrd3Sdg1rQnVmEFTkmEcVU1H0w4s\nKvJ0R9hjVHCH4sHbRWFXVQea5sSdaJ54c3Oog0yQDFWlUdMIpoHqT34tgKqmE9CaSU/Vtrjtyl5R\nFDKMRpo0Lba3GcNjNxhsGAmQbkjdITStZBqNNLUfUQhbUmUP4FFVDC4RVg9TQYaqttnWSlyPvUOM\nvbXOdWwnYXRh8jRSp9MVuiXsCxcupKKigkGDBmEymbjiiit47733Ol2XU3ESp2Rmxj05KRId4+xB\nox81LT/hzwshcCkK9qZAyisIhDISzLUWmhMR9jQVrdEHGRmdhTPeaexpaVEXmsQiGGzCoGYk7QUY\njY6wjtClaSGBSrGwp+PBS1eFPR1Na8apaTgSqVtJhmIyjUaaAgE0Oxi9yTcVVXUQDDpTK+ztz91s\nEahQfDiKKDkcMVPuvNiwkpqNp9rT2ulAizesWZMW9mbA1KyhpXik3dFZhAQ99nb1vrXOhdpJFF1x\nOLrksTcFgxEPA0mGbgn77t27KSsra/u7tLSU3RGO4qquGMyPS0q69Iwso7EtVgegmQIYHUUJf94v\nBCpgaQwcNI/duN+ckMduSDOgNfnB4UBV09C0Ax541IyYVtLSuuyxG9UMmrvpsTdrGg6jMWRDkg0U\nuz1qp5SmuHF3UdhbG1WbbfHoQijGo3lAKBg8yQ+PWzuelAl7h44ps0U8g8EY3qbdHkrxjIBP1/Fg\nQ9FTs1Vse9qHYjStCWPQnFTZAziFwOQWaP7UnQUK4Z1OK3E99g6jvVZhj+mxxyj7aJgMBiwGA+4k\nkx060i1hTzQ399QCO5fkJRc+aaW9x67rfoRBYHAkfi+XppEGqAfLYw+4EJqVJnP8HlZNU9GagxE9\ndpemRd4nppUuCnsw2ITZ2FVhP9ARNrd6xQ0NofTLZLDZogq7Vbhwknz8ur2NztbRRDy6EIoJBptC\n3noXRkutHU9CnU4iNDSE1jS02tfieWpaDG/TZosqLk5Nw4f9oLSLzI4eu9+UvMeuaVj8BoLe1Oax\nZ0YIxcT02DUt5BRkHvDemlvqXCgcGMVhjFH2sYgUKkqWbtW4AQMGsLPdZvI7d+6ktLS003Xp91zK\nvaOvB2DChAlMmDAh4Wekq2rbvg7BYBOqR0EZkIB73IJL00hTlP/f3nnHyVWVffx77/TZ3pPsppFe\nNw0CSFO6IkWKoCAoiPqKVFHhVcFCFxQUUHgBUWmiNIFAsIQk1JBskk12k2zatuxutu9On3vvef+4\nM7MzO312N5j9zO/zyYdl5t47zzn3nN95znOegqHPOyYau+J1oObnReWeiAVDjgHNocC0ILEP1TId\nUFUKEhHACGzsFlNhhsTuDFQpkobIMxNiT6C5WIWDAZG+j7gu45DGnhKxp6mx5xoMyMKBwWfMiNgN\nhlzQRtEUM6zvgwSQrwzEd9VLsFtyqCo+yT4m8yLfYAjLZTOA0WtIm9gdqorVZ0T1jv3haUKNfWBA\nHzdhipdDVZlksSDLNjTNh6YpyPKw+Wu3Q0fq2SnXrFnDmjVr8Le0cMcbb6R8XyyMiNhXrFhBQ0MD\n+/fvZ9KkSbzwwgs899xzUdddcnkXR55yBTbbtLR/I8dgwBnYlqjqAEaXpNtsU4RTVcmRZQx9vtjp\nNUcI1e9CFOXiSJHYVZcWMsVoYVvgQVUNRbPGRAY2diFUVNWNzZibto1dkgzIshVNc+PHigyYZTlz\njT0OsZuFgwFRmd7zAsjIxp4GuUiSRLnsRvJbMlpUdWJ3jg6xe72gKBFRswUBgpqg9McnpSQauyKN\njcaeH2bHVpR+DG4pQuNNBYOKgs1vRPWPsilmmEYshBaIBYizOMYY80FlQpKk0FyW5WHtS1NjDyq9\nb2zcyNdmzeLhu+5K+d7hGJEpxmg08rvf/Y7TTz+d+fPn8+Uvf5l58+ZF/8j6pXS3/DWj37DLckgb\n9vt7MA6I9Ig9YLs29LjHZABrmhNKc1PS2GW7jOoWMU0xA4pCfiKNPQNTjN/fjdFYSJ7RnLbGDsHD\nv8EhM4wQo26KMao9dGnpB/8E5VNVR+qmmJ4eveRaGqgwDCKU+PInk08aLY29v1/v9zDzZ16AoPz+\nLkymOA4FSTR2RcoZM419IDRvuzD1oyckSwMOVSVHMaP6R/fwdLiNXVH6MBhykOU4nk8xxny4MhGc\nJ1HIwMYOQ+91JBixA+uZZ57Jzp072b17N7fcckvMa9SNJ9DbGO0tkwpyDAZcwQHiacfUm0bdRHTC\nLDAakftcCKGgaSMP1w2HhhtjeWHqGrtbQGFhNLEn0zozIvZOzOYy8gyGDIk9N/Jw0unUkzilkcgJ\nSKi5SGo3B0X6wT8R8ilKahp7d3fa5FJKPyiZxRAYDLkYNNfoEHsMcrEbDLg1Db+/Mz6xJ1hUB1UV\nTR4bjT0oG+jj0NSjprWoCiEYVFVy/EbUUT7cNUkSmhCh+JiECyMk1Ngh2tEghAR9nwg5BsOne3ia\nKsxtUxj07czo3nBTjL93L2aXJUJrSYY+RaHQbEZyuaM8UUYKIQRCdmMuzkuZ2DWvBGVlIRt2EGOj\nsXdhMpWSZzSOgNjDTB2ZaOuQUHMRShedIyB2RUnj8LSrK21iL5YG0LS8jG3sBuEiVx6FBGCxiF2W\n8fgdCKFiMMRRdhL0vUNV0eSx0djtsow7TGM3d/rTInaPpmGSJMyaZdSJXZKkqIXHbE6P2Idr7DH7\nMMPDU5ssh2TLFIeE2O1MwG8ciMpmmApywg5Pff2NmJT0XON6FYUiqxWczoDNePR8djXNC8KArcCW\nmikmR0b1GQLEnhOlsSe0sWcwSHw+XZPLkeXQricd6AdDniHtJFNiT6C5qP4uDmrp2V5jyTdWGnsh\nfSgUZqSxS5KMiok8eeQBJ/T2RtmobbKMqnRjNpfF91BL0Pf9ihLqw9GGLUzr9Ps7MbW70+r7Ia8T\nO5oYffnsYeQZnCdxEUtjV5QwjT1OHyYwgyWTLZP5Go5DQuzWqXmYOopwu/ckv3gYwhvpd7ZgEumR\nQJ+iUGgygSwHBnH6K2g8aJoTyWfDWmBKTWO3G9BUI6KkFFnOSc/GbrHoB2hpILhFt4VpJ+lAH7Bu\nvQ+NRr1YRlnqwWEhBBelYUEXmqagKv10avaMAjIMBhuq5sKpqon7Lojubr3oRxrIpx+/KIAMy5Up\nkpkSwygQ+8GDUFER8ZHdYEBVkpgREmjsPYqC2WCPqG07Wgiftz5fJ6ZWZ1oae4/fT7HJhGywoTHy\npFjDYQvnlUSmLND7vrw8Uj5FoThQWyLoZBD9Ixlq7BnO13AcGmKfU4jclo/H05j2veGmGJ+nHbOc\nnsYVIiWLBYNkGVViV1UX+KzYCvRyW8kgyRKSpCAKSwOkOUTU/YqSWGMfCbFnuLUL7nC6/H5KTSa9\noPaE1IPDQjAYwGjUU+aGQVG6MZmKEJIRfwbELstWPIqbQqMRORXzXAYae77oxSMVpd33QfgwU2QY\nhUIR7e1RfW+TZUhmH06gsXf7/ZjjaZsjRPiY8/s7MbU4Inzwk6FbUSgJEfvo1SoOwj58R2FKsODH\n6Ptuv5+SgDIR1xIw3jV2y9xipNbizIk9uPIrHZhNFUnuiESvolAUIHYZy6gOYlV1gteKtcCEJ0Xi\nlPGj5ZdGDYbOIHnGg9WaNrl4vc1YLFVYZTll+SJkDWzTu/1+SkwmfYBPnJj2c4CYg9zj0eWzZ7zw\n2PCpLl22ZNA03caepsZeIDpwS+UZa+xeYaFQHhtitxsMGJUDWCzRsSNDFyXW2K1G+5gQe5A4hVDx\n+dqxqEWQRvW0IHHKxhw0RtfhAQILT4BX9HkyOf7Fw/rer2m4NC0UdxLXEpChxm4/XDR20+Q86CjH\nO7g77XvDVy+PoROrZWpa94c0dqsVGfMom2Jc4LFgL0yR2DUNWfjQ8kpiEntZooFvsaRNLh5PI1br\n1IhBnA6CW8yQdpKpxg4xB7nX24jFMjL5fKo7NWLv7NTdZFMsshFEnnoApzwhY43dg4n8MdTYrWor\nVmuCOWG16uMmxvjs8fuxGe2jOieCCB6eer0HMFGAPCHB4hMDQWVCNuagSqNvignX2IPzJC6GKTQ9\nAWUxeK4RV2MfweHpYeEVYyozo/VU4R3cl/a9QVOMEBpecz/WsoVp3d8V1DYtFmRhGn2N3WXFVmjC\nG8innhCdnciyH81gQZL03UPwnk6/n7JEboQZmGIiiH0EGnvIFDMSjT3GIA/Jl6F7lyxbUbQUib2l\nBSYn0MpiQFWdmIQbh6E0I2L3aRoeLNhHQ+OMpbHLMjYlCbFLUtyx0+33YzfmjOnhqcezH6u/GCrT\nC0ILEbs5ByGPPClWlHxhcyIpsQ9TaEKcEkDcA+hMNfbDxRRjKjOh9U3E72lL+96gKcbn68DgkTFM\nmZ3W/e0+HxPN5gCxm0f1oEjTXAinBXOBCZMk4Us2+BobkUygeTRk2YgkyQjhRwhBp8+XXGNPg1yE\nEHi9TSHizNTGrqruIVNMSwtkmMwNmy1qx+Hx6PKNxBSjqZ6QrTMhmpshRrqLRPB4mnAbJ+EymTMi\n9l5FQZMsiNHw6mhujiJHm8FArnoAi2VK4nvjEEyPopAzRhq7QZIwSRIO934szty0+74nYGOXLFYk\nzTjqi0+QPIUQiYldiKhxH25fh6F5EoXgbilNHDaHp+YyM0rPBHwZVDAKrqwez16sHRJMTc8U0+b1\nMiFE7KZRHcSKZxA8VmSLnJodu6kJ2SyhefXrgls4h6piCPjWxkWag8TnO4DBkI/BkDNijT1k/9+z\nB2bMSPs5gC7/MHJxu3djtR4R4aGQnny6qSjhTieIDDR2t3s3XuMUXCZTRsTe7vOFdmYjgqpCUxNM\nnx7xsV2WKdKasdmOSHx/jEUVoM3no9A0Nho76HN30NWArductsZ+MKjoWK3IqmHUZQySp8/XgSxb\nMBrjeNt1dOhjN8zVdPjuOqHG7vFEeYMlw2Gjsct2GfqK8JN+Mp9gI50DW8hp8Kc1OVUh6FYUykMD\nZHRXfr/TgaTpuTtSIvbGRmSbjOaJJPaDyezrkLbG7nRuJydnYUi2kdjYW7xeKkF3+0qTHEOIsTA5\nndvIyVk4gh2FPqGqLJbkF+/ZA9OmpfV8p3MbXssc3BkSe4vXi2E03Ambm3U302HnAxatD7NwJ9fY\nYyyqfk2j2++n2JI3Jho76HZsp6uOnN0KzJqV1r2tPp/+Xq1WDKpx1GUM8orLNTRPYmLPHpg5M+Kj\nFq83YszFdXeUZf3AOM0apodNgJIkSZgUG4rsRIj0CCZ4yOHo+ICc7gKd4FLEQZ+PYqMRoyzr7o7a\n6A4Qv2sQWdNTzqZE7Dt2IOdaEF59BQ8Se7PHw+Rkh3ppE/u20IC1ZegVE/Rjb/V6qWprgylTdLfF\nTDDMHKAoA/j9ndhs00dgirEiiRSJvb4eYuQxSgSncxuKZS4uozGjLXWr14vJMApBcbt3x9wpmbw7\naZWmJ0+fHcMU0x7QiE2GsfGKgUBkrHM7ORt7Yc6ctO4NkafFgqzKo2+KCSgT4fMkJmLsUmMTexz5\nYiyqqch2WByeApjtEgafNe3CtMHTdWffJnJM6dnX24L2dQgMkNHd0iluBxJpaOzbtiEX2sM0dl3j\nbPR6mZqMnNIm9lpychYAhApk+9McLLJsxeF3kWMwYG9oiNJc0sIwjd3p3I7dPhdJMmRsijEYbBiE\nl8ljRuy1YA0Qe4Yau2U0iHPXrpgar+Spo0maHuOGYYixW2r1eqkMpZ0dG2LPk1UU737sHzTD7PTm\nbog8rVZkZQxMMQHPE53YF8S/cNeupBp73MhTiGsGS4TDxhQDYMwHg8OOz3cwrftsBgMe1YeDPeSV\nHJ3WvXvdbqYH05yGiH00bexODFKKxC4E1NUhF+dG2dgbPR6mJtPY07Sx9/d/QH7+ytD/Z2LukGUb\ng4pDJ86aGliyJK37IzBsgA8MfEh+/lEZy6bLZ8WIl8pkNnanU3d3TMMUoygDuN17ka3zcRsMGRO7\n1TAKh5M1NbB0abSMzg3UMzf5/TE09iA5xT34GwXMFDuQDEcgF1WklbjPoSh4NU2PP7Fakf3SqJti\ngi62w+dJFGL0fcqmGMhIY7cZDBntsMNxyIjdVGTAMGDD7+9M6z6bLDNZ7MLab8U096i07t3tdjMz\nnNgVw6gOYsXrQA4UYk5K7I2NkJODnGeNsrE3ejxMGUVTjM93EJ+vPWKLmYndLqixT7ZaYdMmWL48\nrfsjMGyA9/evo6Dg+JBsmWgobg1UDJSbkpgiNm2ChQv1CNgUMTDwAXl5y7GZ7LhlOSNi3+t2kzca\nh5ObNsUkdtfAe9SIRcnvj6E17vV4mGa1jqnGPkfbgjY4DVasSOu+/QFFR5KkALGPjSnG7+/G620i\nJ6c6/oWbNsGyZVHyTYkg9iQae5rEbpGkw4jYS83IvTb8aXrGyJLEMqmWnM0arEywssbAHo+HGUHC\nDK38o+jH7ndiMKZoY3//fTj2WGSLHKWx7/N4mD6KxN7fv56CgmOQpCEiyyQISJZtDPodzLHZYOPG\nqAGeFsJ2HEJoARl1Ys/Uxt7gdqNgRkrmTvjBB3DMMWk9u69PX3jsspwxse90uyky545M2/R6dTPS\n4sURH3s8zQjNyR5RhZbM6yKG1rjT5WKO3Z5Y2xwhpms1+JoK0563O91ufcyBrpD5GPVdhU2WyfF8\nQn7+yujKR0EcOKAffIY5DDgUhW6/P0IRS6qxp2mKyTRSPByHzhRTbkXqTV9jB1gpPsS6IydtV7so\njd0vj26uGMWJwZiixr5+PRx3HLI12itmu9PJgmRb1TQGSHf36xQXnxl5e4Yau1NxMc/p1E1JaXqV\nRCBMcxkc3IDJVIrVqk+YTE0xO1wuhJTC4WQGxN7T8wbFxafpuwlJSnty9isKg4pCwUg19g8/hAUL\nokwZ3d1vUFR0GhY5hW17DI19p8vF3BCxj77GrqpOJis1OLfIaRP7joBsQEAhY0xs7GXuf1NcfEb8\ni959F44/PiJN+C63m1k2G4awzxL2YQYa+2FF7KYJOdCdkzax+3xdzBQ7MBSemlYediEE25xO5gUn\nhMUy6rY6VXViMKVI7O++C8cdh2SJ9GPv9Q3g1TQmJbMTp6ixa5pCd/c/KC09J+LzzEwxNjyKi3mb\nN8Mpp6TV/1EIW5g6O1+mtPS80FeZauw7XC6kZDZiRdH7/oQTUn6u270Pr7eVgoLP6ItOBhr7TpeL\n2Xa7nnZ2JGPuX/+Ck0+O+rir6yVKS89L7b3G0Nh3uFzMsdlCnk+jjZ6et+g0LMTZ0j9yYvcyBu6O\nUOn5N6Wl58a/KEbf14fLFoAs2+KPwQw1du/hQuzGyjzozkvbFNPV9Qo7/IvxnHBqWvcd8PmQYIgw\nLRYMvtEldk11Yfj3enj//cTEvnu3XpZt2bIojb3Z1c/CnJzkLmspEntf3xoslilRkXT2DA5kJNmC\nX3Ux9+23Y5JLWghojUIIurr+HkHsmdrYtzmdGJMR0/vv64E9aUTMdnb+jZKSs5Ekg77oQNrEXhvY\nhY34cHL16qi+9/m6GBj4iOLiM1IzsQ3TGtu8XgRQYTaPmSmms/NvtLqW4V64MO38PBEKmdWKwTP6\nxJ7n+QinXILNFscKIAS8805U3293OpkXRewJ+nDca+xVeWjdhfi8qVftBmhr/QOf9ByF66ST0rqv\nZnCQpbm5Q4RptSJ7xeimFBAujO2d8PrriV/Gq6/C2WfrOeGtcoQfe6O7n0WpFFg2mfQIxCSTuK3t\nMSZO/EbU55mQZ7NPwi75KH7jDfjCF9K6NwoBrbGv7z/Iso28vKGD2ExNMR8PDGBPFhL/j3/AWWel\n/EwhNNraHg/1oU2WcUHaxL5hYICj8vJGVgOgqQkaGuDEEyM+bm//I6Wl52I05qbm8zzMFPPx4CBH\n5ecjSVLo4G80c7H4fJ10d6+iY89U3MPOBpLBparsdLmoDiN22aONOrHn9P6ZzeZz4l+wYYPeb8Nc\nZD8eGOCoYTWXE77j8W5jN5WaEY4J+F2p54sZHNyIb6CRRv8yXGkUsAbY5HCwJJwwLZZR39JpuDG6\n/eBwJH4Zzz8PX/oSgH54GubHvs/dz7GptC1BMqcgfL4OenvfoaLi0qjvMjHF1LpUClUXfOYzaae7\njUJggB848HsmTfp2xA4lE1NMu9fLoKpiNeTEf6eqCs89BxdemPJz9YXHSn6+bpO3GQy4hUib2D8e\nHOTIkRL7X/+qj5swM52+8PyBSZO+o8uXgSlmw8AAR+bpBcQlSUaSzKNqw25v/yNlBWdhqmvBlSax\n1zgcLMjJwRr0YLJakT2jq5D5fJ0YBv/FBlMCZeW55+DiiyPMj5oQfBJ4r+FIaM7KxCtGllkoNqR1\nz3AcOlNMsRG1fyL+NPzYm5t/ReW7BdjKKtL26Hi3r48TwstZWSzIntE9hNFkFyavH/r64hP7pk16\nKP4ppwDoppiQjd1Ck7ufYwtSrAqVZPVvafkN5eWXxMx7kUk0W41LIcfTD1/9alr3xYTNhsvQTm/v\nv6MWnkx2E0HiNBgS2DffflvPUbIw9YygTU33Uln5vdDCY5fltIndparscLlYkpubuQ1bCHjqKfjK\nVyI+7up6BYOhIOR7nbIpJmzcfBjYTQQxmpXFVNVDa+tDTNp6BLbKStxB54UU8dEw2bBakd3qqCpk\nLS0PYig6j14RZ6fs9erEfsklER/vdOm5/4fnJhptG7vHs4+f8ou07hmOQ6exl5hQ+ibgV1KLPHU4\nttHb9Q6TnurDNnFiWqTkUVU+Ghjg+HDCtFoxjPKWThgGMXq8sH9/fGJ/9FG46qqQD3W4xj6omTAK\nD0ekaoNMUGzD5+viwIHHmDLlRzG/z8TdcX23A6vfCRdckNZ9MWG10jhvA1VV38NojNyhZGKK+Vdv\nLycVFib2IX7kEb3vU0R///u4XDuZMOHyIdmCubHTmJzv9vVxZF4eVoMh8aRPhH/+Ux8zYSZIITT2\n77+dadNuH1p4UlmwwzR2t6ry0eAgx4cpPaN5gNrW9n/k5FST/6vXsC1blvZ7/WfgvYbLbnCNHrH7\n/d0cOPAo+ZNujq9MPPecHow3LA3Cv4criwEkXBgz0NgbG3/JKum85BcmwKHT2IuMqL0V+EV/Sva8\n/ft/yuQNR2C84tvYjca0NLoPBgZYkJMTWQdzlFf+np7VCFUip8cMe/fGTrTV3AwvvQTf/nboo/DD\n091emGeTkx+chrUh3iBparqT8vKLsFpjJ4RKV2Pf63bT4/BjsBvTys8TD87cbnoqW6mquj5aguGK\ndQAAIABJREFUtgxMMW/39HBGcXH8SVVTo++WLrsspecJIdi378dMnfq/yPKQRmaRZfxCoMqy7mGT\nAlb39nJaoL5nxgFA998P110XYQo4ePCvyLKFkpIhE0JKppgwjX1tfz/VOTmh6j8jknEYFMVBU9Nd\nTDtwKmga9vnz01ImPKrKuv5+TgkvoWe1IruUUZu3TU33UFb2JXLtR8TuN02DX/8aro8ep2/19HBm\njLqto2ljd7l20tX1GqsNX075nljIMKNT+pCNMgYhg2ZEUfoxmeJXu+/peRtH7wbm3e+C7Tdi7+hI\ni5T+0d0d/QJsNmSXiqq6EUKgDqr4O/34On0o3QqqU0V1qmguDdWl/y18AqHq/9AI/S2Ej4Onfwvp\n0e9gnLsRauuwaxo9wwW580745jcjCkDLNhnNrbdlu1tjpT0NF8I4g8Th2EZHx5858sjtcW9N18a+\nqq6OEz6pRTtxaBEWmsDf7cfX7sPf7Ud1qKiDqv5fh953QhFR/zRFo+vIp7G99QX2vNwOtEPY2m7z\neDnFMciOkh0Rn8f7e1BRuLjbg7W8hf7jffgO7KF7T31kA/7zAVT+Fr6dWnEXz7RVOBcfwPzg0fSL\nyGfd2gF18i0YL68HU/IpU97VxfEFBdSb6vGVd+Bc3kP9b+qT3hdCewe8dxyUHQ3r9Ps0o5Pu826g\n4N372PHbHaFLv9jrxGBrot6awMS5axp05cAV9XQMDHKNLFGfOySP/xyZ3c9vx9g3skpFg8t/hWxf\nTuuPFFrn382Umw5i9fmoL0it7W1eH7c7ZNpLdtMe/FDTcDlPRFl9AN9HafRhDCgFe+g58/8oefUV\nnI69XN7to7582DP37oPWy+D5qfD80HeagCUHe5hTZqBejrQ6CNmHeqmb+itiyFezTF+c65LLLhD0\nnXYV1par+MXHpYzEAHrIiB3AZPcjvDn4/V1xiV1VPTQ0XMOsl6dg+J8zoagIe2dnyqQkhOBvnZ2s\nWrwYf7efwU2DOGuduFeV42g/HvfxH7L2xLVIRglzmRlTuQlTiQlDrgHZLmPIMWCwD/2NASSDhCRL\nob97K57AKs1m8ryF2A9uhf4p2Hp7cYWbfrZsgb//HerqIuSTbTKqW2VQUdjpEVxYmIY3QoxAEyEE\nDQ3XMG3a7ZjN5XFuTN0UI4TAvdtN/R/3cn7LErTjvWw8ZiPeJi/+g34M+QbME8x6n+UZ9H+5gX92\nA5JJQjJLyHYZySghGSUcpa8g5bmo+PAIpGvD7KeBNa3LbWJfp5P8qbqJJmIHE77uBf7+oLsHsz+P\nwomFeErysRbIFE4OG0919eB8H666AyzJc7Wr0iDdlb9iYuej2E+MPiTesasTyyf7yDvaAsMOzoaj\n1eOltkXi8hllSBJ4zGW4Cv0UnhRfkYmAJuCXv4WvngZHDyknB4seIlecQPn8k2H+0OWdB9yU59go\nTHROY/ZDbQvixELe3tPNdVVVFFqHdmF99hxyjjJh86UoYwx4TbvomvAK0167D2PuBrj8EtTBQZod\ngsLK1J77als7ZaYCCkvDrhfA3w7gqSxJvQ9jQCBoqbiHMucNFK2chUtV2byni6tnhz3Tr8Drz+rm\nu7mRv1Uz6GCgx0r51OiC3ALBQUmj4KRcpOGU6nDqu+wUZB+wvwaFfUzyfZfKs4zw94yaChxqYs8V\nqE57IEgpdqbA/ftvI2ewnJJ/HITa7wMBM0ISUhJC4NrhYvOb7Vz/hp+BvVv5sEchd2kuudW52KdK\n5It6XGUKx/Qch8Geet6QcDgctTRueZJlyzZga34TtGKorsbe3Iwr6IWjqvCd78Add0R5kxhsBjS3\nxt87OznCXoRRpFHgO4Yp5sCBR9A0F5MmfTvOTTrsYUXBw6H5NPrf76fvX30MfDTA4IZBMPmYPKOI\nmcdOpk2YmX7vJOzTijBXmJHN6VnvvN42mj65g4XKbRQUPQtXR/uTdzscvFvfze+OTM3X/KFPWnlg\nxgwmFhXhaCjBajUzcXKgZJ/fD0uvhcd+Dl9KrSjLjh0/oUz6AjNOie3+9tEH+7G+sZWJ59og+Dtx\n8Lu9e6kSE5k0Q7/O6eylc7vCxNNTLCn46KNQUQOP/E7P542e0M2x7WWOPHJr1OLdsnOAirw8Jk5K\n8PxcAT21rD/PxpZdZo48cmrE4tlek0/xyhwKCzMre6hpfmpqzuWIglupfOk2eOEFOHYSUmcnW9p9\nTFyU/Lk+TeNX7+9h44oVTBx25iS/uIvuafOZeHaGZRmBAwf+gHzAydxltyDLRryaxhvr9jDxxLBn\n/vjHcIIL7j4p6v7rtm/n5KLJcft591ob5ZcWYjQOW/h7B/U8UVcklt3n62DfJz9jwYIXKSgIpDD4\nejotjMQhJXZjAdBvjRt92tv7Lzra/8KK6yR45KlQYEO84q6aV6PnnR66Xuqi560eJJPEzhUy9i8W\nU33WEdhm2HRNG+CtPSgP76VB8mRM6qrqob7+qxxxxL3YbNOgrw8KC2HGDOwNDbiDhy133aW7qF15\nZdQzgqaYp9rbubloAqo3je1lVOrbevbvv52lS9+LyAsTCzZZpsuv1970tnvpeqmL7je76V/bj32u\nnaJTi6i8tpL8mSoP3f9jGr76VWafNIeD623krbRgMqUXZAL6Yd+OHVcwadLVFHQuB8+TcWVL1Ra7\n3enkoM8XOsSKsm/edpue+uC81A6fOjtfoq9vDStW1MS9xi7LuPPykh6CaULw7MGDvLRgKA1sWoen\njY3wk5/AunUhUleUAerrL2X27N/H3JGl5FEUUAieOXiQr1ZURJ3pjNQrprHx55hMxUz6xRY93uHY\nY3XZ0jjXeaunh/k5OTGznMrCjKY4M5bP5drJ3r3/y9Kl60J5YcyShCIEiqbp9RpqauCxx/Sd9jD0\nKwpv9/Tw+wSph4cOoIcRewqHp0IIduz4BhMmfJ2Cgs+k3b5YOLQae7ERrTc2sft8XdTXX87cF6dj\nPnkZnDoUaWqXZXoDB1eaotH7di8dz3TQs6qHnEU5lJ1fxtT/nYpvipHPf/QRdUfOwj78wM9qRXb4\nRuQPu3fvj7DZZjNhwhX6B319UFICn/0strvvxnXmmfD66/Dww3rSLDlau5VtMk6HnzqXl+WVZXR1\npCFPmClGVd3U13+F6dPvxG5Pnus6r08w6aUBNq/ZjGOzg5KzSpjwtQnMe3oeppJA9SYh0C64gD98\n/es8FUjRO5JJ39LyIIrSz9SpPwHHjrgDPB0CeLS1lSsmTAjl6ojw6Hj3Xd1FcPPmlNIfeDwt7Nr1\nPyxa9Gq0phUunyzrcRRJDsHe7O6m2GiMiJ9Iuf98Pt2t9OabQ0ExQTNbUdHJlJXFDn23p+JRZLPR\nLwQvHDxI7ZFHRn2dsecO0Ne3lra2/2P5gZ8jvX+v3vfBn03jXOeR1la+MaxYd0g+zKiKKyP5VNVD\nXd1XmT795+TkDAUbSZIUOrTPczp1t9L7749ZrP2P7e2cXlxMcYIqZ3HfcwqHp62tD+P3H2TatNtT\nblcyHFpiL7Xg647O8KhpfurqLqKieQ7F6/rg/fsivrcbDPTvcrH3ib20P92OdYqVissrmPnrmZgr\nhmyoT7S08LnCQibG8uKw2ZBcXkCgaX5kOYXK9mFob/8L3d3/YPnyDUMaT1+fnphs2TLsFguujRvh\nBz/Qox3jhLDLNpn2AS/fmjgRi9GJpqUxYAOalxCCXbuuxm6fy8SJ8d35hBD0remj7bE2ZrzZxb7j\nzVRdP5Oi04swWGNo+Pfcw+t5eRRWVPCZgM0200nf27uGpqa7WbbsA72vEwzwVL1iev1+nj14kG1h\n5CTLgcRyTU365HzySaioSPosVXWzfft5TJ58Y+J83ATIMycnqeb1YGsr11dVRWjEKbsSfv/7UFSk\nE3sAra2/w+GoYdmyD+PelqpXzJMLFnBGcTGVMeZGpou3x9NMXd3FzLH8FMt3boU334xIVmZPcSdW\n53Sy2eHg1UWxUxDLwoympk/s+sL4HWy26aGArnDYDAbcqkre17+uJ/uK4UGlCsFDLS38JUmRlrjz\nJInG3te3jsbGX7B06Xtpc1IiHFpTTGUe0gE7Hk9zxOd79tyI3NnPETe1wbr3Qu51QhP0vN3DzLsO\nMHu7B+2KSVSvriZnQXQmRJ+mcV9zMy/Mnx/1HQBWK5LbExrE6XTiwMAG9uy5gerq/2AyhXnbBE0x\nkoT99ttx79gBH30UVXQ4HH1GDafDz7VVVciu1vRIM0COLS2/xuncztKl62O6SioDCm3/18aB3x9A\ntshMvHoi239WxFv+Hq5cECeC9NVX4cEHeeDll7lxypTQczOZ9G73furqLmb+/GeHCi0nqCSTqinm\nsbY2Pl9czKRhubBVzwCcfzbccAOceWaCJ+gQQrBz5zex2WYxefLNSa+3yXJSYt/icLDd6eSi8khz\nSUr994c/wKpVehh7YJfX2/tvGht/ybJlH2AwxM/8aZNl+pPU1PRZLDx4zDG8UFUV8/tM/NhV1cW2\nbedSVfRNSr5wHzz4IAzbDaQan/Drlha+PWkSlhg7XACDZM2I2Ftbf8vg4CaWLXs/5jyxyzKuBx7Q\nlYJnnon5jFe7uig1mTgmSRBhJhq7x9NIXd1FzJv3J+z2EVQni4FDq7HPKEV+pgSnY8iO1dr6CD2t\nr7H8KgfSK2/D9OmobpWOP3fQ8psWJLOE58oCXnooh78sid/4P7a3M9du5+h4LyDQwUODOLUUBV5v\nK9u3f4nZsx8jN3dYBGN/f6h6ua28HFdfX0JSB3iit4MjFQPlZjODXnt6GrvNRre8gebmv7Js2UcY\nDJHJiLytXloebKHtiTaKTytm7tNzyT9azwli6+rCdSAOea5ZA9/8Jv987TVaJYkLwtwz0530ijLA\ntm3nMHXqLRQVhSVQSuCDb5FlfEKgChGRDjUc/YrC/c3NrBlWxUlWZbR3XocVZ8JNN6UkY3Pzvbhc\n9Sxdui6lGAKbLOsH4wm21D/et48fTpkSRU6SZEIIDU1TYuf9fvFF+PnPdTNS4NzA5dpNXd1XIhfG\nOEjFFPMEMKe9nZVxUleku3jrZyffwG6cweSvvAqXXhoVIQvxz8bC0eBy8XJnJzsTZICUpfQTlfX0\nrKax8c6EC6Otvx/3qlX6DjvGTkYVgp/u28fdRyR+B5BgnsTR2BVlkG3bzmXy5O9TXHx68galiUMW\noARgKrchtc7BMbgFTfPR0fEcjQ23s/h7Dox/eAZ13lKa7mviw+kf0v2PbmY9PIsVNSuQLi7GYYg/\nQFyqyi8bG7ktUb7wQAenY1rw+3vYsuV0KiuvoawsxmFcUGMntQCgRo+Hv/QfpEDRuz3dCTUwqY8d\n5U+yYMFLEYFIrp0u6i+vZ8OiDWg+jeUblzP/ufkUHFMQIq642tP69XDRRWgvvMCPjEbumD49VCM1\nXRlV1cO2bedSUHAslZXXRn6ZQHORJClpwe37m5v5fHEx88Pzkns8yA89hpZjhN//PiW7env707S2\nPsLCha9GLYzxYDcY9ND4OAvT+/39bHU4+HYM89tQoq0Y9776KlxzjW7CCNTV9Hrb2Lr1NKZP/3nk\nwhgHyUwxLlXlly4Xd77wQtxr0pkTQgh2774Rn6uJOd/dh/TZz8HPfhbz2lRMMbft38/1VVWUJLRf\nW1HTCKAaGNhAff2lLFjwN2y2OIrW449ja2/H/fjjcU13z3R0UGg08oWSkqS/mY7Grmletm07j7y8\nFVRV3Zj02Zng0GrsFSb83jnk+aZSW/tFnD2fsPgmDfOdL9JUO5vmKz6k8IRCqv9ZTe7CoQOoZKR5\nd1MTx+bnJ865EuhgWS5OiahU1UVt7VkUF5/O5Mk/iL7A6YSWliFiT2EQ/+/evXx9+iRwHwBAlu2o\nKW4xnc56ao9dxdy9X6bgFD1BlWu3i8ZfNNLzZg+V11WycvdKTMWxJ0jMArlvvgmXXw7PPMNz8+cj\nmpsjtHVdxtQmvRAq9fWXYjKVMGvW76I14aDGLkRMAg6aY3JilK9r9Hh4pLWVT8JL8w0MwPnnY1iR\ni7ZyOhiTD+WurtfZs+eHLFmyBqs1tlkiFmyyjNtuj7kwqUJw4+7d3D5tWnxTQiy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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from random import choice\n", "for i in range(amax(pred)+1):\n", " a,b = params[choice(find(pred==i))]\n", " plot(*fhm(a=a,b=b,tau=1.0/0.08,t=300,dt=1e-2,ie=lambda t:1.0 if t>50 and t<51 else 0)[:2],label=str(i))\n", "legend()" ] }, { "cell_type": "markdown", "id": "da3e5d36", "metadata": {}, "source": [ "It's also useful to see how these parameter values are distributed in parameter space.\n", "\n" ] }, { "cell_type": "code", "execution_count": 84, "id": "ab19b6ee", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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IziFr6mERSmVExSytbHpqQIv6ycz8Ak8/fUDQLsS1sxx7985KyO0jFx6PH6tW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\njUMrLUZPAamn1peO3uILeu049FJkuBX81ImfD+D/EBKiJiD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, "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "params = array(params)\n", "colors = [[\"cyan\",\"green\",\"blue\",\"red\",\"yellow\",\"black\"][i] for i in pred]\n", "for i,c in enumerate(pred):\n", " plot([params[i,0]],[params[i,1]],'o',c=colors[i])" ] }, { "cell_type": "markdown", "id": "68e87deb", "metadata": {}, "source": [ "# Integrate-and-Fire Models" ] }, { "cell_type": "markdown", "id": "64b25a7a", "metadata": {}, "source": [ "(Integrate and Fire Model)\n", "\n", "- earliest neuron model, developed by Lapique in 1907\n", "- predates understanding of the action potential\n", "\n", "Incoming signals charge a capacitor over time:\n", "\n", "$$ C \\dot{V} = I_e(t) $$\n", "\n", "If the voltage rises above the threshold, output a spike and reset to zero." ] }, { "cell_type": "markdown", "id": "783da169", "metadata": {}, "source": [ "(Leaky Integrate and Fire Model)\n", "\n", "Problem with integrate-and-fire: infinite time memory.\n", "\n", "Solution: add a small reset current.\n", "\n", "$$ C\\dot{V} = I_e(t) - \\sigma V(t) $$\n" ] }, { "cell_type": "code", "execution_count": 85, "id": "d59abe52", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ll1/m0ksvrf9CGgcvQeqf/zQja+6/H2691e5qzk5RkZml+/nncM45dlcj9WlO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\n+AAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.ndimage import filters\n", "ie = filters.gaussian_filter(rand(10000),10.0)\n", "ie = (ie-amin(ie))/(amax(ie)-amin(ie))\n", "plot(ie[:100])" ] }, { "cell_type": "code", "execution_count": 86, "id": "f771a6f0", "metadata": { "collapsed": false }, "outputs": [], "source": [ "def iaf(ie,cap=1.0,sigma=0.0,threshold=1.0):\n", " v = 0.0\n", " vs = []; outs = []\n", " for i,c in enumerate(ie):\n", " vs.append(v)\n", " dv = c/cap - sigma*v\n", " v = clip(v+dv,-10,10)\n", " if v>threshold:\n", " v = 0.0\n", " outs.append(1.0)\n", " else:\n", " outs.append(0.0)\n", " return vs,outs" ] }, { "cell_type": "code", "execution_count": 87, "id": "77dd2a97", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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blmmTt1XeGsBZNskieVOfIpEtw1Cq9KgYOmreJtQxkxIZR7lOpE0U5Z6kSEre\nXPbetqUB48ibI67KhQ+DyjlvE8hb5nF70TZSbFhyrkxkbb2wNW+13FS+/jgqAswqb03gVt4U7+EA\n0FvzllHKVPFEbxIq5a26YanjnHchkHcWHtJRvYdlJ27V9lryzkDZBMC8F1NxKHSZzc0k4F6ZqObg\nWAUmialCQqbUvNM8KghgNyy1gXPDkmKJD8A/GFw/0QFBfc47DeWt2j/Utl4fjg3LpO82kbUXycVZ\nNgGge0hHZ81bNoeteTOoHTcuFXnLxuFWlmkrb/uQjlxMnS+moprUTSibAOg7bcJdmqGEceTNobwB\naGresnU31QlJlpRF4slsWFKWbERiqPhxn/POcs0bgHbDUtekE9cGVT9OsWXLJsDbCWkpbze3irJM\nq+YNIN7mNE+b6FDelEgSk0tBitglKQtQkjeAnhWUCas0URhF3iY/pKMSJ8mFpSxdyLRDtuadBEnJ\nWxSm1LyTPqRDnUvUTle74+KY/JBOGjCKvLmPCupW3tzKUsZOZjKgnhCikGRlkqWyCUCy8gPHuBMt\nm6Rd805K3lz23rYVvPLm3rDUHUcHecuUOETyytS8qSZEFXA+pMNB3jpJMF/J2/1vrvwmTfQiMI68\n8015J3lIh9rONOXNPbmp5qBa7ge1QxUqJCRiZx/SUbd3fSx5My0/VGdtijhJyCmNmrcKeSeB6eRt\nkvLmICFR5Z1kw5KiH5OWTazyZgY3eRd6zdvUh3SSnPOmtvXCxHPesvYUkz/FpJMUSchbx9Feu2FJ\noOTC4lKQtwuTyBuA5zy4zpq3yUcFTVLetuatNt50KO+C37AE4K95646jqjxkbz7RdnCUTSjIW8Uv\na6dNTCRvAH7lXQgP6RQ8eXOXTdz/1h2H+yGdtGveWVDeWd+wVCEhmYe8KGKFgXLFq6PmbcIqTRSx\nw+mWW26Bjh07wjnnnMPaEK5OoCqbyMZxbZLUdClJmavmnQSqE7ZMbpV2cilvnTVvyg3LpMo7KVTv\nJZ3knQZi0958880wa9Ys9oZwdUISEvXHKRTypjzpQtGuJH6mqCnd5QfKmnfSSYeqbKKDWPPqIZ2+\nffvCcccdx94QHcpbdxzVvLLKSTSeKERtqchbxU8mtynkrYsEqSf1LNe87VFBDeDshLTKJknyytQs\nqVSyrPJO+6ig6HVQvSEpkSSmbD+Jkp2InSpxur5pK2/7kI4GcC0/vIOPgmhE4yTJS03KAGbWvAF4\nN3RdW1P0ZIGDAAAgAElEQVROECRR3irnlanKJroeLoqLY/JDOmmgiCLI4MGDD/13eXk5lJeXS8fg\nmMGamwGefRbg1FMBdu7MjvKmXvbKTgamnzYBkFfeutoVFbN9e/WYWT7nnRRJyZvL3usj0q6Kigqo\nqKiQSxABcvJWQVMTQH097QzW3Axw220Aa9cCTJ0K0KULHXnL2ptC3iJ5ZR/SaW6Otw1CUxPAX/4C\ncO65/GUT2WvQ3EyrvGtqADZuBPjBD5KRYJbIu7ERYN8+gE6dkvfj/v048ZmovGXGil/YDhkyRDxR\nAGJv6euuuw4uuOACWLduHZx++unw3HPPJUoYhFdfBejZE+Cb36S5YZqaAG65BW+YuXMxLuWGpUgb\n9+wB+PrX5fPW1uK/HTqIt0nULq7dtbUAX/uaHuU9cSLAyScDfOc78r4yhKzSzkWLAMrK5NsVhlGj\nAPr3B+jcWc1//Xo5Eqyrkxs/UXEPHMAxIYsnnwTo0QOguDj5Pf388wCXXy7vJztx79+P/SZqv3Il\nwPHHAxx7LH2JTQSx5D1+/HjYsmULHDx4EKqqquDmm28mbUBTE8CQIfhDVR/72c8AqqoApk8HOPLI\n1n9Txbp1AKefLh7nhRcA/vEf5fPOnw/wve/hDSPiJ/KEXE0NwOGHx8dbuBCgTx+x63DwIEBRkVqf\nNjUBPPAAwP33q13zLVsAvvENMT+XyERzfPwxwLZtAAMG0NyQBw8CPPIIwH33qX3W5maAl14CuP56\ncd/FiwG++12aFdk77wCcd55cu7duBfjDHwCeeir5PV1bC/DnPwPcc49crOZmgDVrxFfcBw9iv/Xt\nK57jqacAbr89WTksCVLfsJwwAWevgQPx/5N2wkMP4YCbPBngiCNafp90EM2ZA3DxxeKqdNQogJ/+\nVD7v9OkAl17aEicM1dVITHGz/iefABx9tJhymzUL4B/+IT43AMCSJTjJqMB7zWX7Z+tWgPffB7jo\nIjH7hQsBvv998fgvvABw4410N+TzzwOUlqKSVxmDixZhX4k+I+c4eB1/+EPxPY4wu927ATZtwrbL\ntPs3vwG49VaAbt3EfcIwZgyWm846S67/3nkH4Ljj0E8E8+djH598sliOHTsApkzBz0n9NK4oUiXv\nxkZUYK7qTtoJr78O8Kc/AUybBnDUUa3/RkHeomSzdCmq0u9+V14tTJmCS8Q4v0WLMP7Xvx5tt2AB\nqsi4eDU1uAzs3z/+Ohw4ALBsGRKoSi3Ue80B5GJMnIj9I7KSAGiZDEVsm5pQ5d50E80qsL4eYPhw\ngP/935bfycYcN06uPR9+iCuNbt2i7XfswNXdEUeE2y1fDnD++XIrl9Wrsc/dz5ykHxsbAR57DOB/\n/kc+1ptvAlx5pbjPG28AXHWVOAe9+CLAFVfgxGrsQzqcGD8eoGNHJBeAZJ1QWYlKd9IkPF3iR5KJ\n4YsvcDndt69YnNGjW2ZkmbzvvIODwVUZUZg/H8lTxM4l7ygsXIg36lFHiU0cpaXipQsvgq65DCZM\nALjuOrGxsnEjqsdvf1usnUuWAJxwAu6/UKipZ59FEnWVv2zM/ftxPF9/vfi9MW0awI9+FG+/dCm2\nK2qFsXSpeBkNAG3++78BBg/GFSFAsnt60iSAU05pWeHJHBbwknFc/qYmFE2i9gA4qf74x61z6kZq\n5B2kwFQvdEMDDvBf/Qpv1CAkGURz5gCUl6PKBYiOs3cvzvo33SSf9803cTYX8Zs3L15RNzYi0V54\nYXy7vSWTuNwy5RV/e5Jc88pKgA0bWog/zm/GDCwfiG5Yjh+PE4Nsu4Kwfz/Agw9i7deFbMzJk3FC\n7dRJ3Hf69BbyjsKSJShGorB0qbhgAQCYPRv3C37yk5bfJTnbPmJEi+r2/j4Oa9di//fqJeazbBlO\nEmecIdbeDz9EQeceHCk45f3ii6iQ+/dv/XuVThg6FOCYY3BTIwqqHTxzJpIAQPyFeuUVJMuTTpLP\nO3kyLvXi/LZuxR/3RESY3apV2McdO0a323HwM7qEHNdmtz9klWTQNZcZ+BMmAFx9NS7jRXK7JROR\nHPX1WHa79tqW3yW5IZ96CuCCC1qLCdmbfMwYAJnzAbt2AXz0EUC/fvj/caunfv3C21RXhyWQ3r3j\nY7l///3vAX73OywZJsWSJXhiy3vKRLT/Jk1qUdEiPpMmtRwuAIi3HzcO4IYbWjZ706p5k5zzlkVD\nA17oMWNa/16lE9atA3jiCRxoUTvnqrNjczMqzQceEIszdiyuAGTzfvopDlZXLUT5zZ+PBBh39tUt\nmcTF++wz3G0/++x4240bcbO0pAR380X7NOyaA4jHGD8ej6DFtREATyksXYqELzKu5s4F6NoV4O/+\nTix+FHbtQtW4aFHbv8msMtasaZnMRdozcyZeb/eIapj9nj14zXv1Crd77z0s+Rx9tFjuigp8EO6f\n/qn171X7ccQILMF472mZ+vUjj7T4RMFxkLynThWzd/dF5s6Vbxc1UlHeL7yAZ15dheBC5RD+f/4n\nHsNyj/GFQXV2fO89rIO6Z3Sj4lRV4YMnF18sn3fyZFQZ3tk8KSn77cLglkG8pYwwzJ4NMGgQtlPm\neo0di8vSoGsugo8/xvp1nz4tfnEbtb16Ye1VpJ1uLd3bLtUb8ne/QwXfvXvr38vEfO45LAUedpi4\nr/ekUpT9kiWoqN0VTJCdW+8Wzf2HP+AmZfv2rX+v0o9r1+Lmubem7MaKw1//CvC3v4m3fc0aXCmI\nCBcAnKROPhnPsHvbVRDkXV+PFzro4SLZTpg4EWD7doA774y3Ve1gb8kkLs7EiaiUvA81iOb1l0zC\nBqrjtGxWRtnV1QG8/XYLWUa1w1vDjrP194fIZ3Ovubt68UK0f156CQnRq8Si/LxEFof9+3Gjz6sa\nVSf7Dz7A8kvQQ8eiMZua8Ijhrbe29o36vA0NOLFeckl8rkWL4uu1fvKOwjvv4F7EDTe0/ZvKfffo\noyjKDj+87d9ESiCXX95SuonL7z9lEmf/5ptYupNtFwe0k/fYsQBnntkyMLyQudAHD2J54vHHxZ4m\nA1Dr4OnTW26IuDivvALwL/8in3f7dlSWIvX/9evx9+751bA+W74cT024u/5h8erqUIn5z00H2R48\niDe+eyZflIxGj0YVesEFbf8mcs2bm9vu7sfV8GfMaK1C3d8HYfp0fNKzY0e5dgXlvfNOfPjo+OPb\n/l005ty52JZzz20bPwzLluF91alTvH1FRdsVkBfNzRjPez4+KvfTT+PDKkH3oWw/btmCk9/tt6vF\ncuvdXkT5yNg7Doos91CBTLs4oLXmXV+PO/AvvxxuI9oJf/4zEoLoO7BUOvhvf0NF8YMfxMfZuBEf\naPATsEjeN9/EUoR7miXKL+joX5Cde747Lt7ixfhwgveV7WG2y5Zhn3/zm+Kfra4ON5TfeCPcRqSe\nesIJrR9UiZo4Pvig5axznC0ATrrejUrRdvnxzDOo4v/938NtRGI++2zrExsA8Z/BPWXitQ/KVV2N\n+yvuawmC7NauxcnHnQiirvPu3Xht162Lbp8o/vhHPKl1wglt/xY33nbsaPsAV1S/rV+Pp0a++10x\n+/ffx1W1t2QS58MJreQ9Zgx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7XU55802AX/xC3H7y5NbfISrSLgB8huKKK/C++fBD+TKi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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "vs,outs = iaf(0.1*ie)\n", "plot(5*array(outs[:500])+array(vs[:500]))" ] }, { "cell_type": "code", "execution_count": 88, "id": "7a56f8df", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "vs,outs = iaf(0.1*ie,sigma=0.05)\n", "plot(5*array(outs[:500])+array(vs[:500]))" ] }, { "cell_type": "markdown", "id": "6e607e79", "metadata": {}, "source": [ "(Limitations of Integrate and Fire)\n", "\n", "There is no oscillatory or bursting behavior in integrate-and-fire neurons.\n", "\n", "This makes them a poor match to real-world neurons, and probably precludes many kind of signalling or spiking." ] }, { "cell_type": "markdown", "id": "c5e2de22", "metadata": {}, "source": [ "# Izhikevich Model" ] }, { "cell_type": "markdown", "id": "3d17acd8", "metadata": {}, "source": [ "(The Model)\n", "\n", "Nonlinear quadratic equation, similar to FitzHugh-Nagumo:\n", "\n", "$$ C\\dot{v} = k(v-v_\\hbox{rest})(v-v_\\hbox{thresh})-w+I $$\n", "$$ \\dot{w} = a(b(v-v_\\hbox{rest})-w) $$\n", "\n", "But additionally add reset from integrate-and-fire:\n", "\n", "$$ u\\leftarrow c, w\\leftarrow u+d \\hbox{ if } v\\geq v_\\hbox{peak} $$\n", "\n", "This model has four independent parameters, $a$, $b$, $c$, and $d$.\n" ] }, { "cell_type": "code", "execution_count": 89, "id": "f58619cd", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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UsrIyRo8ejd1O/PVJ5XA4mG9ujte+vtUNkTGEmYV58fw5HDx6TGj2AUBXUwsW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\nq0yHQanhJCQkID4unifkFApAl1lExrD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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Izhikevich Justification\n", "figs(\"izhikevich-justification\")" ] }, { "cell_type": "markdown", "id": "7d7813e8", "metadata": {}, "source": [ "(Justification)\n", "\n", "The reasoning behind Izhikevich is...\n", "\n", "- what matters for the dynamic behavior is the nullclines\n", "- neuron dynamics are primarily described by the behavior around the stationary point\n", "- around the stationary point, you have a line and a parabola as nullclines\n", "- once you're off to the right of the parabola, you have runaway signaling anyway\n", "- we can \"reset\" the neuron more effectively with a threshold" ] }, { "cell_type": "markdown", "id": "b89d79bc", "metadata": {}, "source": [ "Let's first write down the derivatives (the parameters come from the paper, more information here: http://www.izhikevich.org/publications/spikes.htm)." ] }, { "cell_type": "code", "execution_count": 90, "id": "6f872983", "metadata": { "collapsed": false }, "outputs": [], "source": [ "def izh_derivs(v=0,w=0,a=0.0,b=0.0,c=nan,d=nan,ie=0.0,dflt=nan):\n", " vdot = 0.04*v**2+5*v+140-w+ie\n", " wdot = a*(b*v-w)\n", " vdot = where(v>30,dflt,vdot)\n", " wdot = where(v>30,dflt,wdot)\n", " return (vdot,wdot)" ] }, { "cell_type": "markdown", "id": "848dfb64", "metadata": {}, "source": [ "In this model, the parameters have the following meanings:\n", "\n", "- 30mV is the peak of the spike\n", "- $c$ is the value that a spike is reset to\n", "- $d$ is the the additional inhibition that results from a spike\n", "- $b$ is the \"sensitivity\" of the inhibitory variable to the voltage\n", "- $a$ is the decay rate for the inhibitory variable\n", "\n", "http://www.izhikevich.org/publications/spikes.htm\n", "\n" ] }, { "cell_type": "code", "execution_count": 91, "id": "b22b52fb", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig(\"izh-parameters\")" ] }, { "cell_type": "markdown", "id": "3fde884e", "metadata": {}, "source": [ "Now that we have the derivatives, we can plot the regions in which the equations behave qualitatively different, by choosing different colors depending on the signs of the derivatives." ] }, { "cell_type": "code", "execution_count": 92, "id": "c36fa557", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "vs,ws = meshgrid(linspace(-100.0,100.0,200),linspace(-100.0,100.0,100))\n", "vdots,wdots = izh_derivs(v=vs,w=ws,a=0.02,b=0.2,c=-65,d=2,dflt=0)\n", "def rgbshow(r,g,b=None,**kw):\n", " if b is None: b = g\n", " imshow(transpose(array([r,g,b]),[1,2,0]),**kw)\n", "rgbshow(0.5+sign(vdots)/2.0,0.5+sign(wdots)/2.0,sign(wdots),extent=(-100,100,-100,100))" ] }, { "cell_type": "markdown", "id": "2164e897", "metadata": {}, "source": [ "(Question)\n", "\n", "Can you enumerate the topologically distinct arrangements of these kinds of patterns?\n", "\n", "Does enumerating them cover \"all\" possible behaviors (in some sense)?" ] }, { "cell_type": "markdown", "id": "301b4337", "metadata": {}, "source": [ "Once we have the derivatives, we can use them inside a loop that drives forward the differential equation." ] }, { "cell_type": "code", "execution_count": 93, "id": "3417d4e7", "metadata": { "collapsed": false }, "outputs": [], "source": [ "def izh(v=-65.0,w=0.0,n=500,dt=0.5,a=0.02,b=0.2,c=-65,d=2,ie=lambda t:0.0):\n", " t = 0\n", " result = []\n", " for i in range(n):\n", " t += dt\n", " v += (0.04*v**2+5*v+140-w+ie(t)) * dt\n", " w += (a*(b*v-w))*dt\n", " result.append((t,clip(v,-100,30),w))\n", " if v>30:\n", " v = c\n", " w = w+d\n", " return array(result)\n", " " ] }, { "cell_type": "markdown", "id": "5dd48fea", "metadata": {}, "source": [ "With steady stimulation, we get a spike train." ] }, { "cell_type": "code", "execution_count": 94, "id": "3b3c5dc0", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Vy99dCThYCshqq4m8WVpaGpyFqpruaN2stbomaiv2lK9E1rdrcfnqZUzoNQET4ifg7pvu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\nRABdXw/U/+Glf9Weay53BkFB9FESJSX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58zF06FD8+c9/hsPhwN69ewEAeXl5ToY/IiIC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\ngHAGAoFAIIBwBgKBQCAA8P+8ngGJYHCBCQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# steady state pulse in response to input\n", "result = izh(ie=lambda t: 20.0 if t>50 else 0.0)\n", "plot(result[:,0],result[:,1])\n", "plot(result[:,0],result[:,2])" ] }, { "cell_type": "markdown", "id": "e053fed2", "metadata": {}, "source": [ "(Response to Different Input Stimuli)\n", "\n", "Note that a higher input stimulus results in a higher output frequency.\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 95, "id": "3bf8f75d", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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V/r5279x666344R/+YQDAysoK3vSmN+Hy5cv40pe+hAcffBAA8OCDD+KLX/yi8XcqlT6r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\ne6HZa9UlEFnUqaMyGgFojtB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K9Ct4R8L0hWWaBRNZPN6hSp+fyJUyfUMkwOMd+tLIJnKT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0VvZyf1oW/eTMnghReMnXHor167nUYEPfccTeiXkcHObHg59H77LXVhzphBieFy9CO1Xkmifenx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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "result = izh(ie=lambda t:20,n=200)\n", "plot(result[:,0],result[:,1])\n", "result = izh(ie=lambda t:40,n=200)\n", "plot(result[:,0],result[:,1])" ] }, { "cell_type": "markdown", "id": "b707b127", "metadata": {}, "source": [ "(Frequency Modulation)\n", "\n", "We can think of the spike train as a frequency code or frequency modulation.\n", "\n", "Once that spiketrain stimulates a target via a synapse and is temporally integrated, it turns back into an amplitude.\n", "\n", "This way, we can think of neurons as passing around analog values:\n", "\n", "- in the dendritic tree, values are coded as currents and voltages\n", "- in the axon, values are coded as frequencies" ] }, { "cell_type": "markdown", "id": "a7f3053d", "metadata": {}, "source": [ "We can also get many other kinds of behaviors out of these neurons.\n", "\n" ] }, { "cell_type": "code", "execution_count": 96, "id": "19a9e975", "metadata": { "collapsed": false }, "outputs": [ { "ename": "NameError", "evalue": "name 'stimulus' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m# bursting behavior\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mizh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m50\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mie\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mstimulus\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3\u001b[0m \u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNameError\u001b[0m: name 'stimulus' is not defined" ] } ], "source": [ "# bursting behavior\n", "result = izh(b=0.1,c=-50,ie=stimulus)\n", "plot(result[:,0],result[:,1])\n", "plot(result[:,0],result[:,2])" ] }, { "cell_type": "code", "execution_count": null, "id": "87b4161e", "metadata": { "collapsed": false }, "outputs": [], "source": [ "\n" ] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }