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@mundya
Last active August 29, 2015 14:07
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{
"metadata": {
"name": "",
"signature": "sha256:2a752b543b88fd7b9bfa575b1ec997c0187d6a94b9a07c4a4ca0cc48d9b6ae53"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import numpy as np\n",
"import scipy.optimize\n",
"from matplotlib import pyplot as plt\n",
"import seaborn as sns\n",
"import fwm_utils as neurons\n",
"\n",
"np.random.seed(2909)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stderr",
"text": [
"/usr/lib/python2.7/site-packages/pandas/io/excel.py:626: UserWarning: Installed openpyxl is not supported at this time. Use >=1.6.1 and <2.0.0.\n",
" .format(openpyxl_compat.start_ver, openpyxl_compat.stop_ver))\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Effect of factoring weight matrices on interspike intervals (ISI)\n",
"## Illustration of experiment\n",
"\n",
"Generate a random population of neurons and a weight matrix. Connect the pre-synapses to a selection of random sources and determine the characteristics of the post-synaptic neuron spiking."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pop = neurons.generate_population(100, 0.02, 0.002, 75)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"wm_full = np.zeros((100, 100))\n",
"wm_full[np.random.uniform(size=(100, 100)) < 0.75] = 0.05"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Generate a set of input spikes for 1 second of simulation at 1msec intervals:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"inputs = np.zeros((100, 1000))\n",
"inputs[np.random.uniform(size=(100, 1000)) < 0.05] = 1."
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Simulate the neurons for this period of time and get the interspike intervals."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"full_spikes = neurons.simulate_feedforward(pop, inputs, wm_full)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we factorise the weight matrix:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k = 5\n",
"\n",
"U, s, V = np.linalg.svd(wm_full, full_matrices=True)\n",
"e = s[:k] * U[:,:k]\n",
"d = V[:k,:]\n",
"\n",
"wm_factored = e.dot(d)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"factored_spikes = neurons.simulate_feedforward(pop, inputs, wm_factored)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, [ax1, ax2] = plt.subplots(1, 2, sharey=True, figsize=(10, 4))\n",
"ax1.eventplot(full_spikes, colors=[[0, 0, 1]]);\n",
"ax2.eventplot(factored_spikes, colors=[[0, 0, 1]]);\n",
"ax1.set_xlim(0, 1); ax2.set_xlim(0, 1);\n",
"ax1.set_ylim(0, 100); ax2.set_ylim(0, 100);\n",
"ax1.set_title('Full WM'); ax2.set_title('Factored WM');\n",
"ax1.set_xlabel('Neuron'); ax1.set_xlabel('Time / s'); ax2.set_xlabel('Time / s');\n",
"fig.tight_layout()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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"text": [
"<matplotlib.figure.Figure at 0x7f2c9e2c5ad0>"
]
}
],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, [ax0, ax1] = plt.subplots(1, 2)\n",
"ax0.matshow(wm_full);\n",
"ax1.matshow(wm_factored);\n",
"ax0.set_xticks([]); ax0.set_yticks([]); ax1.set_xticks([]); ax1.set_yticks([]);\n",
"ax0.set_title('Full WM'); ax1.set_title('Factored WM');\n",
"fig.tight_layout();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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m2C+zTrxGixYtSm1bb711skm/WNiO5SSYMeWyDBSlY4YShd6cocJx0SbN4n5J\n75H6sgAds3CYofb0008PGy/pA8rsc22cGUN6iPNxFg3LVXDNKdTn7BtmB22++ebJJvXl9eN9CVJB\nXidSfRyD50Dqk9k/FNzzWWD2FksbcO7eC5biIKXq+bCCPMfIauCeL0USma3EDDP3wf2nuB+fKWcv\nMnuLGXUW4GSWI2lB/s0wXUmajmUbOE9fxzN25plnBkUVCAQCgUBg8DFisc069WqIXnseirxhVhlD\nu36r6P5U9TItr/ILvQrAzruuzvPRq0D3dp93KlRa5foyYylz3zLfLfIsd7N/9MA44JF6Gj/4wQ+S\nTTl7F6qkZ4J9UTfEkvbUuaGXyG+0DFLlWyPfnu+8805J2XIH1GRh0KbXI09qfmi78cwzzyR7p512\nSra1eHg939pZuuD222+XlA1InjJlSrLZ7jGwxASDre3p2mOPPVIbPVr0ytgjRf0WriO1S/KCXqmT\nYk8HdWXoCZs8eXKy77//fklZ+X56A+g5sEeD60ivivuSWoGy9MrwHvZeUMOGGk4s4eD9o6YLvUwO\n8GV/DFim9pDnQ28ePWwco71LDGinl/CFF14YNl57R6Xs2XcxVaml8TNx4sTURo+kwWeD42XhTT/D\n9CYxKJ7By94LehzzEB6cQCAQCAQCA4f4gRMIBAKBQGDgMKIv+Y0cv3TdLv9eBFrWEWRc9bu97qtq\ndfTf14Dl5VXFvE7aqI4z2AndVgjv1G+vdXAWLFiQOvL11JihG58Bj3aXP/vss6mNrvc999wz2Q5Y\npNQ8AzhNo5C2Iu3AQElTEKQUGMBJN771URgsTJ0brqGDVxmUy6BOj4c0DwNTSevtvPPOkrJUFCk7\n0g6+B9tId82cOVNSVmeH83WZC6lFUXDcrDZOGsV0BUsFkJb42te+Jkk6+OCDUxsrhFMHx1QOg5+p\nv8P5eC9Is+2+++7J5l47mJe0EtfRNAtpSa4NdXtMETn4Vsrqu7DUhs8hzwqfLe8723ieueamdxhU\nz/NI+s7fIcXFM0Ra0LQSKTmWX3AQN4O5XeVeymoLec04B55tUrlem7vvvju1nXrqqRFkHAgEAoFA\nYPARP3ACgUAgEAgMHEbMouqWRml3fb9l7EcaQ52lGvpR6bkM5ZNHH9SpEVSk6neZ+3Y7xqp0Zaf7\n9ipLqs4Ms35kTBXtq8p5p3vfJQboCidtQf2WT37yk5KyGTDM4qA0vimGa665JrWR7rLmDSkBVhBn\nmQLTXceZQGGlAAAgAElEQVQee2zufB599NFk2yVvmkeSDjzwwGTnVSwnvcNMrVVXXVVSlrIjLcUs\nGdM31CVhBhmzzZxddeqpp6Y2Vh539hSpDK4jNVNMjZx44omp7dJLL002NWRMF957772pjRSWK6mf\nfPLJqY2lD0idmGLk/m222Wa5Y/R52WeffVLbDTfckOx58+Yl+6STThqxr0996lOSpFmzZqU2Z7BJ\n0rhx45JtGo1UIOkuUqqm50jJjRo1KtnO9GKW1kYbbZRs7o/ppqlTp6Y2PpvM1PrMZz4jqVWtXJLO\nP//8ZLMsg9ecWXKk90xBUa+ImXzM1HM2IMuF+LxLWRrT54K0Yx7CgxMIBAKBQGDgED9wAoFAIBAI\nDBwKC/0ZdWT/VOmvjJu/Tnd9kXv0uoJ0p7WrSluUWdNuaZoifZVZx6IUVNWzUIamyUM/qLFeYXlQ\nyMx8sfz6Sy+9lNos6Cdl6ShnozAbhtkuzARxdgiFAilG54rJFLOzOKAk/ehHP0q2qS1mbzEzhi57\nC8GROll99dWTzT5MJ+WVSZBasv8sO8AsHYqzeW7MYDGlJ2XF+SyYRrpjxx13TPbNN98sSTr88MNT\nG2Xyme1iSoZUE7OKODeXYGhXQuD444+XlBU7NIUpZTOf3vWud0nKZr7l7ZnUyioiNdquYr337eGH\nH84do6977LHHUhuzlUgxOdvMAnlS9rxxbUzJcG1YEsHiehS5bDabyeYz5b8lzKxiFhX7dSV10pGk\nFVlawrQSP6cgn0uHkLZi2RVSjAbXltQ0/x44i4qikHkID04gEAgEAoGBQ6dXtcKvsSuSPP+Khn4W\nsuw0hjo8BDVoo3SNKkUvVwQdo7ruP3QMVTxGfZpDoZt8+tOfThOwNgpl2KmNQc0VexE4F0q902ti\nbwy9MtTssKw/vUEsEcC3UI9n/fXXz/2cwbz2ONErwLdueqc8Z76ZMkDTb8d80+ebNr1X/i7vRa8L\nx+uAUvZrj4jU8hKxLAS/y7d298UyCSxESTvvDZ/j9V4xkJpeOZ4Re6Q4LhdQlbJeNXshuF6cG8+T\nPR3tyj7YY0RPGsfA0gQ+bzwLnM8qq6ySbK8TvUH0sDmAnv3Tu8lz4/Xl9fR08Vy4j3brwb3yPPg5\nx+Dv8jnj9dR7soeNOlb0AhJeX973vPPOCx2cQCAQCAQCg4/4gRMIBAKBQGDgMGKQcR6qBgsvr4DJ\nOlAnvdMLFBlLmQDcoporRYKUq2rxdPpulTXvleYR0e242iEvoLzbsh1Vy3p0+m4VkLYwFbDXXnul\ntgMOOCDZ1OewDgYDRFlqgdc5+JWBi2PGjEm2K4ST1qBLnzSJ+6V+y1lnnZVsan2YrqI+D4NmqUGy\n9dZbZ8YiZbVLrCdDfRBSEZSzdzAnKQzq3Gy33XbJPuKIIyRlK3VTy8fjZdXoK6+8Mtk///nPk+31\nY7Ao9Xm4vqbiWHqCtIXnw/lSe4hVv93Oz1n64Mwzzxx230022SS1MZiXe23KhXo11M9Zb731JGVp\nGFKMXP/77rtv2OcM0OaZnz9//rDPGQxsKodrx+DzL37xi8k2Fcdng5Qd537bbbdJytJ/DObed999\nh12XVwaD4DPHZ4pr6uuoEcUgcJZlcHAyNaLyEB6cQCAQCAQCA4f4gRMIBAKBQGDgUFsWVRlUkdTv\nRwXqOvRZlgd6RR/UQcN1m1FVB41S9Pp2ffWz0nqv+q36eQ1VygtN8qyzzko3cmYNsymYDUWqxxkZ\nzAKhu526Hx7fyiuvnNqY7WJaghQYNWjo0vd1zNhiJhH7dZYMx8LyCdQVcXXyvHFLrQwv0j/MKuN9\nrU3CjJ33ve99ySY9YDA7iFSSv0sKrF1mjPvgnjEji5TNr3/9a0nZTCJm4bhKNbPZmOW22mqrDRsP\n145rQ+rE3+Fes1I6z7D1jajZwn33GWFFbWYg8b5uZ2YUM6dIQXlNSP/lZW/xc1JBpLa85swg5HVc\npx/84AfD7kVaifdw5hgz33jefC54Pjh3rpOpSY6F32UfPpt8Jk8++eTIogoEAoFAIDD4iB84gUAg\nEAgEBg6FSzXU6dJfXmUOuqU1yvRb9bt13jfvurrLWNTZRyc6pNNeVaVWqvTVqd+qZTA69dsr1FGl\nvBuwUvMzzzwjKVv6gO5yuvTtZmeJArrmSQVZCI6ueVNCUov2GT9+fGpjFgel7++66y5J2WrIplv4\nudSiMz72sY+lNlY55xhNmZDucsVtSXr66aclZWkaVgWn7fnQtb/GGmskmxk1pnceeOCB1Ma5uQzB\njBkzUtuSJUuSzQrTLkNBWol7ycwm7yVpCWYwOQONWTqs8O4K8FKrGvjaa6+d2ky3SNlSDaZBKchI\nusTrLLVoOY6RJSC8v9x/rgfHY2qMezJ27Fjlwc+es5qk7P6a0iHlx3HzHrZJ7xJcJ1NM7Sg3ztN7\nxYwrClc6w49UIM8Cs9hMc5FiZLYZaUzTgqSm8xAenEAgEAgEAgOHwkHGvdKCKSr7X6QsQJ0aJVU8\nP/0OQq7ilVnRCjv2E/0IIq/i7anaf9Vnpsr9uvBoFRrErFmzUqd5MuwMbqVmjoMc6RGhvDs9NH6r\nZqCtvUWSNGnSJEnZQoh86+e8XdSQejYMyn3iiSeSbQ0SlgWgXsmaa66ZbAeOsiwA38qt25MXyCll\n337dzsBVF82Ustom9m7Rm5Qnqc9CiQw85du13+rpaaOHjevkPaZXjevsvaIu0CGHHJLsPK8L5+Bi\nnlK2IKQ9C3lBu0Pn4zWl94uB4dZC4uf0LDBY3nPnuOkNYrkH7zHPAmHvBj9n8dhHHnkk2d5LBkdz\nf6mlZA8cvT30IlGXyfOgV45B1T7zDBzn2nHN7JW56aabUhv1j/hde964tieccEIEGQcCgUAgEBh8\nxA+cQCAQCAQCA4ee6OBUobPqpJX6Ubm6zmDfbgOWi6xdFUqtV1XQ+6lpVDftVFS3qUxfdYyL6AUN\n1sW4C3159uzZ6QZ2zdP9fMcddySbbniPi1QSyzZcc801yTalQspm4403Tva55547rI2g9oxd/d/9\n7ndT27x584bdS2oFtFKjhmUSSPvst99+krIufwbYHnfccZKy+iAMYiX9Yz0gBmoeddRRyZ41a1ay\nvabUxnFpC0maPXu2JOnkk09ObS4lIGWDah1MTXrItIckvfDCC8l2cDMDw0nvOOj5nHPOSW0uZyFJ\nO++8c7Id6Mr7fupTn0o21zmP4pg2bVqyGWBrypM0KPWRXOaCNA732vsvSa+//rqkLA162GGHJZu6\nPtbd4VlgkLGpIPY1Z86cZB9++OHJNh1FDSjTklL2mTBFRFrphBNOSDbPgMGSJ9TasWYOzyDpSmop\n+TpSkPfcc0+yn3322WQ7EYB02LHHHhsUVSAQCAQCgcFH/MAJBAKBQCAwcBjRffwG/NK9zqypqnHS\na7qryPVl9FuWN81SR8mFFSHLquj+VC31sCLQTr3WhurTWSh0k+OPPz51anqAGVB0p5OOsiYHs0+Y\nEcKMKmdi0a3NbCTfj1owzNxgFtTDDz8sSdpzzz1TG13zrHzsNaIWCG1SYnbZm8qQsvSB9XHo2mdp\nCmaduBo4x83MGWYbuazCa6+9lvu5KTfuN+X5SR9Yl4W6Qdw/3uMjH/mIpGwGEykd02+uwi1lSyr4\neklasGCBpKxeDSk7ngVquRiU/Sc942wiri0/f+mllyRltWBIfTHrz/fgnpKS4z08xueffz61US/K\nmXikwzh3rqn3nRl7XANSSN43UrKcD0tWeD7MCmO2Wt555drx+bJNTR7OnectL9vwlFNOCYoqEAgE\nAoHA4GNEJeMyWiHdvnn227NQ5i22aL9F1GDLrGOnz/vpVaujQGZeX1XvUdQDU4d6cbfK3FX7qhNl\nFLurqnt3gy222CLZfrtl8CSDGDfaaKNkL1y4UJL08ssvpzbqiuy2227J9hs89T34tui3TAbt0jNE\nhVYH+fJNnMq91LnxmynfkhnESo+UA1nppaDHw/osDG7m2zO/6/vSI/Lggw8me5dddkn2rbfeKikb\n7OuAZ6kVeEpvEQOH884tvSfU5+EYrUNDzwU9bFYt5plk4c7NN9882faqMQj58ssvTzYVoe1BY0Ay\nA8PpZfD60VtENWV7aKipxD1hX15fnivO/cUXX0z2pptuKim71zxv9rTQc0ibWkw+2zx39CLymbHn\njl43BlhTB8dzYwFOzt3eKa4BA9np9fI68tnhWWCAtedOz2EewoMTCAQCgUBg4BA/cAKBQCAQCAwc\nSuvg9DMIspf3KIMVKdi3zvv2ap17pZ9T5V51XNfr87iinfeaUWhCRx99dFoE0xl0x7NAH0st5MnY\nU0uENJdd56QH2JcDIum6Z4BuXvAy3eZ08zNI2O55UlztigQ6CJS0BKkRlyNgoCf7zStayfkwyNTl\nJqQWbUeNElJnpiBYoJN6Niy14D0hXcLgZgasmv5hECqfB9MWpLsc1CtlNZF8bkiHMYiVlIuDY7m/\npOdIJ3o8pF645j5PLHrJAF2eN/fLAGBSogzM9hkjjcryFz5j7ItUEalYByLz2WhXHsPrx/ky4JwF\nSn0dn8O8/8dwz3lfBiT7WWSZDOorMSjaZ4vP5DnnnBNBxoFAIBAIBAYf8QMnEAgEAoHAwGHELKo6\nsSJkkuShyLh6Jalf5bqqYylDw/T6XitCFfOq1cSLah79PusNLY8x0B1uFzXpA1ICpG+cJdVOv4Xu\nfdvU0+A9nLGx1lprpbYlS5Ykm1k2zv5gRo8pLimbuWR6YKuttkpt999/f7JNJUmtLCXSKaSdTDu0\ny1AiHWIqgHQYs1JIqYwePVpSVrOFVZ89Bma93H777ckmnWW6gpQPNWiYMed7kIIk5eL15X2t2SNl\nqS9TeeyLNBkzwHzGmZHHyuKLFi1KtqkT0iGsbm/KhnQls6GYXecsJtIwpElJuTnbiGtLqsflQlgh\nnFQRNZ58Llhiol2VcmdMkc7ifV1Znjbpo29/+9vJNv1GrR7OnWfEVCrPM7MJ+Uz5+SDFlYfw4AQC\ngUAgEBg4xA+cQCAQCAQCA4fSFFWdgm/8TifhuzrogzwUoUu6FefrdXZPv8sKVClj0Suqo4496YXA\nYJHPq5T46Ad9VKbkRafrioIUk/thJegrrrgi2aRcTBtMmjQptZFKeuSRR5K94447SspW4mamloXg\nSL2MHTs22aR3SBsZpFHohvfcLEooZTOjWOHZLnnSIcycMVVAOoQZO6TyTPWQ/iMFwqwv02scN9fu\n7//+7yVl6aG8DCapRSGSCuR6kRY07cDMKFIy2267rSTpzjvvTG0bbrhhsimuZ2qR60Fa8MYbb0y2\nM9tIS1EskueCWWgG98TnYv3118+dAzOyTJPyemYlsRSDaSWK5PGsWBCPa891Jn3jdSa1xrlz3y08\nyL5ID3Ev/HeBVBPXzmMnReVq81KW2vL9eIYpMMgMP2cAMlMsD+HBCQQCgUAgMHAorYOT+XAFCIgs\ngzpLD3QbpNrv4qEjjaXdeFYErZ68z9t9px/6O532r0z/dQZ25/Xbq75KeqQKDeKkk05KF1sLhG+2\n1H3hfRykys+pqUKvirVP+AZJD4DfJhnkSg8AZf39JszAYgZiMtDZwZz0UrDMAQOhPTa+BX/jG99I\ntoNuGQDMt2sWJ9xhhx0kZT1e1BVh4K8Djlm+gd4ae2UY/MwgVK6zg1u5tvSq0bPwyiuvSMoGvDJw\n22vO67n/DKp2v5wjg6bpCfFe08tEjR/O57rrrpOU9eBxjPbWsAwCPSUMil9vvfUkZb0R3B8GTTsg\nmIHB9Gj40eK5Y2Axz5C/w4Ki1MxhYVuXP2AJCT7GeUVYueY8N34u6QXjGaIHx4Hz3FN6lgjPjV63\nr3zlK6GDEwgEAoFAYPARP3ACgUAgEAgMHLrSwanDTd9PVKUtqsyjXb95fVUNlK06hry2Xge0FqHZ\n8u7b7rtVaJgygdD9oLs6zTcPdZaYqHr2e6FjRFe03el041NLhJWcp0yZIkmaN29ebl9001977bWS\nskGZDDi2a5yBxe36tWuddAv1V6gx4zU65JBDUtsFF1yQbOqGmFJhIC6pjy233FJSNkiZbnrux5NP\nPpmZl9SihKQs7TNhwgRJWcomr6QCqZf58+cne9999022g5o32WST1Ma9ZLuDRBnwTArDwdacAyk5\nwpospCsXL16cbNNDUmudWWGc2kKkDR28TIqL6+R1ZgAw58CAcN+DFCPpLmrMPProo5KypRy4jqY5\nWY6Cuj+syu11ZOAw50Pba81+XW1eygZT+zyQOiOVO27cuEyfUvaZy9PaeeCBB1LbMccck2zSutaO\nYqB0HsKDEwgEAoFAYOAQP3ACgUAgEAgMHHpaTbzXWUtl+60TZXRWuqV/+j3fOrWJRrp+KFakEh0r\nWoZZP1Ez3Vzown322Sfd1Nkd06ZNS5+TDqGb3XRIO30PUkwbb7yxpCxFRTrDFMaVV16Z2rbeeutk\nk3YybeQ+pWz2FittO/uGtAR1Q+im99hJSzHDyBlepCJInZEm8Zrxu6S+8qpJM7OG67TTTjtJypaV\nIE3D7C33QWqFWTTMFDIlQ+qF+2vqjDpIlO9nFo7Xhplt22+/fbIXLFiQbO8lyyRwDFxzz5P0ETOM\nvNekUTlH0lXONmLZCFI2LGPhteb1rDbu7DruE7O/uD/OriK9xPPIs+usMD4bfP5Jc3odSbNx/7wX\n7TIbqXljKo+aOabppGx2oylNZpj94z/+Y2RRBQKBQCAQGHzED5xAIBAIBAIDhxHdx2/AV12FYqqz\nhECvaJp+ZwpVuW9VIcCiYymCFY1SW5Goojfb2pSk7woN4pJLLkmdOuODpQKYNcQyBs7+oIge7z9q\n1KhkO6OG1cIpo2/XOCkjuvE5b9Mw7Isia6QVnGlFWoKZT3Tfm7piphAF+Uw7tKtcTiG3NddcU0PB\nbCUKtnnuzCRi9o+zaHgNs6yYkWWajWPkOpMyM73CbDeuufeMVb9JSzELyoJ67aqCc688du4Zhf5I\n1bnfvHFLrfNGqonifbzO9A/3gdlKXFPTr+yLNKlpIWZA8XOeBbeTduI6k5LzdcwQpHgfy0l43yjK\nyXVwv6QolyxZkuy86uYURuSzyLNnapFU8IknnhgUVSAQCAQCgcFHV6UayqDMW18EgGbRb+9VlSDT\nfnsxip6bInPsVcmLXmN5zaFkkHihgU2dOjV16qDZyZMnp89vvvnmZNMz4NIGDNrlmzoDhvkGaPDt\n2m+Z9AZRO4Vv9Q7m5Rs3dUfoCfF4GVBJm2/H1oihpg6DW/3WTY8Jx8C3fffBN3wWyLzrrruG3Zdv\n9Y899liyd9ttN0lZj8eLL76Ye197pOiV4Xw5Bq8N38TpTbAXih4CBptSr8ZzuP/++1MbtYfuu+++\nZDvAevTo0amNZR0Y6Op9p6dt0003TbY9FvRGtAvWtueG/dPr4nWWWh5MBkJz/b0m7J+BxTwjPgNc\ne3paeF6tacOCoNzLBx98MNk+m/Qi0lvnZ5lry77Y7n1noDyfDXoyHYRPbZyZM2eGBycQCAQCgcDg\nI37gBAKBQCAQGDgUpqh6XYphRQjU7BX11e14qwYv5323n0GuVe+xIo+xnzRov8syFO2fKHCvQjc7\n8cQT00V2YdONT1c1NW/sqqYOB+9P298hlcBgT9+v2WymNuqokLryd1daaaXc+ZB28HcYXMmK5qQd\nrB3DtrwyBgwgZTAoKSZTdVwDrulrr72W7Ndff11SVmOGwbrWiOG4SA+Qlhjap5Sl2UjfWC+GFBbv\na90YrjOpItIZv/zlLyVlq36TDiGVY1qP32VQNfs1VcdAWWoP+TwxOJZaL2z3XnENODcG0FtXh3pF\nXCfr5JCyJeVD2tbngmeB68Ez5L10kLOUpXep8WPqi/1Sa8nnldeQYiR96nXkHElNMrjc54ln7MIL\nLwyKKhAIBAKBwOAjfuAEAoFAIBAYOJSuJl6k8nUvaKPlWRag2/IKndrLZPeUoc7qzFDq9HknLZ46\nMrZ6RX2VGUOvNY3a3avKXvcqW60T6nr+mcXBCtTUxrj88sslZTVmrrnmmmTvvffeyTb9w6wUau18\n7nOfkyR98pOfTG3HH398sun+d0VzV/eWsjL7zz77bLJNubDKMsfAchDOCiKNxr4mTZokKVuBnOtE\nl73nS/pu5syZyT7yyCOTffjhh0uSdtlll9RGOsvU1UEHHZTaDj300GSzVIPl9ZkNRSqC9Jr3jZQP\n99fZSnvuuWdqY8kF6rpcd911krK0IjPBmCnk+3LctKn14vVnmQTqHD333HOSstQM6S5m17kPau7c\neOONueM97rjjJGXPHc8NKVNjhx12GDYu9sHMKe4v4fPP73JcrBxvqo26TszUcuYTsxVJd/G5HTt2\nrCRp4cKFueMibWi6ijRbHsKDEwgEAoFAYODQk2KbZd7wexGEWscbdZW337q9WHUGtPYiSLwf69yt\n16wONe1eBfAuL8XhXl/XrZKxg2oZMMs3dQbw2mvCN0hq1zCQ1m+873znO1NbXqAsPTH33ntvsqkM\n7H7pWaIHwMGxvN8ee+yR2qjrwzdpB1Bbi2TofPxGTN0Rrg3fiK0tw/2gIjQ9A54zNWToSbFnaccd\nd0xtLIBJ74gDVq3ay7FI2YBjB9UyiJy2g1MZ/MxgbSpV+22e86I+D4NmHZjLgHUG2tKzZ28ag595\nhrzX9JTxPLLApc8Ng4zpLWKB0ocfflhSVueIXiLvKwOT2+nveB3oXeHz5QBt9pGnv8S+OB6uOb1b\nfr54xhk4nKe2Tb0b7g/Pts8FPUN77LFHBBkHAoFAIBAYfMQPnEAgEAgEAgOH2ko1VJXJzx1UxVIO\nVYJfq7ruy/Tx+yrlX3XtypyFbtGPcgW9or7qRLfB63VSyEO7KPKl008/PQ3AFBSDERmwSje7KSS6\n7hnUueGGGyZ71VVXlZTVHSElYwrp9NNPT22f/vSnk03aydfts88+qY1UxEMPPTRs7LfccktqYxDq\nNttsk2wHCVMLhHSJaR/r0kjZIGPCNAqpk2uvvTbZU6dOTfYll1wiKRv8SsrGejJz5sxJbQ5MlrJr\n7gBoXk9akSUeHDhK+oeBtP78jDPOSG2nnXbasHFxbpzDK6+8kmxSOab4rKMkZbV8Nt9882Rbx4ZB\nxgyUdkkMBkqTCuTaeP+oUcNgYfY7YcIESdKrr76a2lhc1MG4fHZJZzIQ3ZQc6SXSRtQ32m677SS1\ndHaGjsHBwFKLcuPakWZjYL1BepXB9NaGevLJJ1MbaV8+E9ZCYiD0RRddFBRVIBAIBAKBwUf8wAkE\nAoFAIDBwGNF9/EaO37of5Qp+36qJ97qUQx3ZMJ2wItBsdWbfValSX2aM7cZSVEOoyBjq3PdeV20f\nAYVufPbZZ6dOt9pqK0nSokWL0uekEijZbpc7M2To/ud3Tf9YS0bKZmzceuutkloS+VKWEnjggQeS\nvfvuu0uSrr766tTmrBdJOvDAA5Ntioh0CcfAPkz7kE5hRo7nwMwaZvSQGjvhhBMkZTNgmNl01lln\nJduVp0lbMQPNlBwzWUh3kJ5zRtVll12W2saNG5dsZmeZYqTGCSnEiy++WJJ00kknpTbTaVK2era1\ncu64447Uxiwc0mSmVJiFc8ABBySblOfZZ58tKUs18Yz4uttvvz13jjy7zvriWWFfLAfhPSHls3jx\n4mR7zVhRnXSXqSapNXdmMFEzidlxp556qqRsOZExY8bkzmeDDTaQlD2PPOfWP2KWFUuhmN6TWtTV\nxIkTUxtpPz6rPm9cjxNPPDEoqkAgEAgEAoOP+IETCAQCgUBg4DBiqYZuM0XqKG1QZly9yBRq12+Z\n8Za5rgpdVUd2VyfUXSqj6D26FZOsKkxZZozdot0Yq9KVnc5Ft/PtxRowm8LZH3TXk4oYPXp0su3i\nJq1BGoWVmO1yJ6VDKoES/8Z73/veZLMsg2mj8ePHpzbSWbyvXe+kQyjOt9NOOyXb2USklUj/mFph\n9ggrV++1117J9j6zTALXkdlbzt4hLbjxxhsn2xlRnCP7Im3h+XLcpLNI5eRVo2a1cGcusWI294TU\nifeEZ4kZWRSz8xkmTUO6g2fEWXC8FylEj5dnkNQo6S6vEylViiQSptc4LmcCSi0hP2ZDcU9I6Xju\nHCPvSyFG006cQ7tq4KYueQaZPWfRTlJYfK6ZmeasSYpvcu4ULvR54HzzEB6cQCAQCAQCA4fSxTbL\nvG32O9jX6LagYbvryuik1PlWXmYOVfutomNU1QNQR1B1lTXpR+mCqudtpLYi1/fz+etFkL8DfKVW\nICyDJFk4kMU07c3hGyTfABnoar0YytnTu+E3U2pv8E2eAZou0cCyAdSroafDb+1cF7/ZSlldGAdV\n8l5867Z3hN4XvtnS8+OgWHpPGLR52223JdveCc7XxR6lVoFFBjzTa0PvlOdDbRWOYeedd062A2Tb\nlXJwMDYDnqmHwnIR06ZNk5QN2v7iF7+YbM7XHjYX85SynhB6aOzJoNYLC6S6tAS1c9gXNYvsKaMW\nDIuH7rrrrsm2d4TlDLhO7pfaOVxnehHt6WDQNfeagc72SDG4mZ4wnnl7y+iRYpkRnwueD64TtaXc\nB3WbWIqDAck+29QbykN4cAKBQCAQCAwc4gdOIBAIBAKBgcOIFFWeK7ruytZ5/XYbiFu3a76KFkg/\ndWWqBjxXRa+pxzootzL9dlsxu+pedntGqgZN90pLKe+aovdyYKPUclFTsp1BuQxMtBue7mvSA5Ty\ndx8MgqTr3HQJA4/pemc5Acv3k8pgyYRf/epXyXZQLKssM/CU7n8HtLJMBe87f/58SVmqiPQc18kB\nqQwQpfuftITpOQaA7rfffsm25D4DvBngSWrM68s9IVgew9eRduL+3XjjjZKylBDLBpDCMN1BrR/q\nwnCvfd/HH388tbGKPMdgiorBz0888USyHXxObRtSgQzKNSXK4GaWV2AldbezjfSdaS7ei/QQz6aD\nfO0bk2cAACAASURBVFm+gZQbA4pNMVJfhwH2PE++H88wnxnTpwwyJs1GGtPPyXve857Uxv1jYL2f\nUa5NHsKDEwgEAoFAYOAQP3ACgUAgEAgMHArr4PS6HEGR64pe3yvKoE4UuVeVudexNkVpmKrVt+su\nn9BtX1Uq1letaN8P6rKoDlVVTZ2q+jsjgdW1neXETCPSIXRLu3I0M1UscS9lM0lM61APhVk0/u70\n6dNTGzVbSH14jnSn0/3PsgCmfVh5nFWWWbXZ2ULMrHJVaamVJUOtH643KTlTNhwLqUBSG9tuu62k\nbCYYqTzfg+t1/vnnJ5trbqqOdAoz1/hdU0WkKrgepkN4PljRnOtgKo/z5VllBpHXkdQKdXtMBUrS\nRz/6UUnZc0Pa0JQMKUrSc6T1TE2RHmLGHcdoKse0pZTda9+PcyC1xrk7E486OtQTYr9+1kgbkpbK\n0whiGzOjnNFIiopZXyyr4n0jNcZnjmtjCpfzzUN4cAKBQCAQCAwc4gdOIBAIBAKBgUMnH/gwX3O/\n3e397Lcq6qzeXOW+dVSurtJvmfuWKSfRD0G+31dULX1RtAp6WdRVTXzjjTdOA7Db+gtf+EL6nGJo\nzmCSWmJkpD0ofPf0008n25kXzDSiaNn+++8vSTr44INT28yZM5NNYTu75il3z4rJXE9Tbcw0okuf\nfTi7ipQAM6amTJmSmYuUpew494ULF0rKUhhcD2YVeT7s98QTT0y2M59OO+201EZKhvN1uQdSLxS2\nY7VoZ5vdd999qY17aVqPVc5PP/30ZF977bXJ9lngnlIs8sEHH0y2M4yYnXXXXXclm+J6pg1JuZka\nlVoVzy2GOBTMBnS2EumWiy66KNms6u19Z6YYs/O+8Y1vSMo+gxSAZKkGz5cUFSk3UkWmhUhRsko9\nMwC9JnwmSUf6vu1KrZBicnV0ilzyWaV90003ScpmoB1//PHD/taEBycQCAQCgcDAoXSphnaos/hk\np6DNfr+dV9EVqVoAc6T7D72+Tu8HUWY+Ra8v4y2os/REP8oVtBtDlb6KzL3ovcqMcXl5Yw2+0frN\nkUGwDMrkG611MtZZZ53URu8I3/ocIMvxU0PGgZjUgqEXgm+8DizluHhfwt9lUO65556bbAbKeh34\npk6PhgMwGVTtN9+hY3exTHpPuE70aDgoll4K6sLYi8EgZnoL6IHxeDhGFu6kp8Rv+Bw3A7ft/aJn\niWU7WGrDe0HdGXqvqGNjb9stt9yS2njdhhtuOGwMDHrn8+DSA9SgYVA0NW989hhUzYBlniefV3rl\n6LHwWaAuEIPXN9poo2Q7yJdrQO0bPiceLz2W7Gvu3LnJtreFHiCXMZFaXibOgWU36GWyZ4jPN8tu\nMPDe+8fA/jyEBycQCAQCgcDAIX7gBAKBQCAQGDgUpqiq6Ht0S2sU6bdq1e8qwa9lxtBP+qDqd6vO\nvVuKoh8UY6+pqTr7L9JX1fOUd31VirAoqtBZDFg1nUEtEVbU/tnPfpZs0y/PPvts7j3pOn/00Ucl\nZbVgqMlhdzvpCZZXoDvdminU7OC4rJ0itfREttpqq9RGGf3FixcPmyepF47B1AYDmqk7Qml7B9iS\nDmHwMrVJTOVwbTjGV155RVJ2bd0mZcs+eC9JlzCgmevrQFrSbJy7dYjYP9eD43FwLCX9eS5Ir1lz\nhWUFxo8fn+w11lgj2Q5a5llhYLdpTtIlPK9cR8+DdBfPCsdjypNBuaR3XLKEwcCkmhi87r2mLhQp\nV5bwcHA6NWhIs/GZ8l6zL37Xa066mdQXnynTZ1xbagDxDHi8XI88hAcnEAgEAoHAwCF+4AQCgUAg\nEBg4jOg/fgO+5jp1VDp9tx/y/d2OsY4x9KKvOui7Tp8vr6yxTt/Nu28RmrQKHVlV16fMd8vsT6/Q\n6fnMG8+QORQa5FlnnZUucrYEM0bYDakV01nUzqCbn65zZ8mQSmLmkzVRSDuR/iF9Y12Qgw46KHeM\nd999d7Kt9cGso6uuuirZH/vYx5Jtl327CtKmBJh5xTmyCrkzUOjmp0ufGjC+B/VOqF3ijCrSXdSb\nYbvXeeedd05tpgelbGaTaRD2xQwy03qzZ89ObdS2IfVhvRlSNqTkeC49XtIe1Kvhvm+22WaSWjo7\nQ2Edm8mTJ6c2VsxmhqAzrUgfMZuJdJT3guuR1xezzjgf7qVpMur3cM/4/DgrjNTaPffck+y11lor\n2ab6SN+RPvVetPszwPGYdmKWHc/+hz/84WSb1uV8p0yZEjo4gUAgEAgEBh/xAycQCAQCgcDAoXCp\nhio0TVUBM6JXAmRVKKoy4+oVljdVUff96qh4XbR/olu6sR/VwvuZ9dfpui4ECAvd7IQTTkgdWdiO\nkvDPP/98sumqdiYP21wpWsoKp33kIx+RlM3YImVj6orZPwceeGCyH3vssWTbnU5xOLrmSZ14HqSt\nKOtPETRTFKQPmHHjTB3OixlIlMm3SCEzazgulr/wOpiOkbJ76/uRHqT4Gykdg1lWpHeY5WR6jZQb\nxRedcUOajRQj201Ncr14X9Iwpn1YPoPZTLzutttuk5SdO6kTrzMztlxFW8qeJ1M27QQiaZsS5Rgp\nCmgqlVlLHCMF83xOWRqBY+B4XXaBzx+pM2Y3OouR54pj9HdJFVJskHNzGQlS048//niyWWXeVCyz\nsC688MKgqAKBQCAQCAw+CuvgVHnjLfKW2yYwccR+O3l96vA2VC09UfT6MkGbndr6gV7dt4zmTpV9\nraOgZJl79Pq7/fCelVnnusbDN89msykpK8/PQEy+PfvtOC/IVcoG4FqTg2UB2K8DXl1YUsoGWlLb\nxN4AFi+kJ4UeJ/dB/Q/qkbAPrz3nQ4+UvUS8noHFDLD1mvJ6ek+szyNJzzzzjKTW2g/t13Ogl+q9\n731vslnE0/el54helyeeeCLZ9tzwzNFzYE8ZvQb08HAMXnPq6NBb4IBYqbXvDChvVyzV54laPvSE\n2PvFs0avHD0lvgf3hEHEPG++B88Sy2fYc0MPDq+nd9KePQbg03vCfbdXjN7AdgVdva8MHKcnzNdx\n7emlYiC79XW4f/QMcgw+W3wO8hAenEAgEAgEAgOH+IETCAQCgUBg4FA4yLgK6g7wLHqPqtWolxe6\n1eqpY517FexbZ3B6Fa2eImtTJpC2n+emW9q2V5XJS3630IIdeuih6SLTLNSdufPOO5NtOkWS9t57\nb0ntAyKpn2K6grL0DG41XUE3PvsljWatENIHN954Y7InTJiQbLvxOR/2xUDKKVOmSMpSBpTGN8VB\nLRK68UmTUJvEYBDxJZdckuwZM2ZIytJ79957b7LHjRsnKau54uBbKVvawIGnPAdc54kTJybbFccZ\niEuKwjQa6TSXEpCy6+Q5sAL19OnTk00tHtNG22+/fWrjueCaujQEKZItt9wy2aaYuE8MfiVtZDqJ\nAbOkbHbbbbdk33rrrZKyOkmsqO3AXVJNDOZlML3pNerGcAwOwJdaFC01akjPuUK41KKjSNlxL11V\nnZ+TniPFZNqJCQOkIEmv5lHEe+21VwQZBwKBQCAQGHzED5xAIBAIBAIDh9p0cLqlMDKDqlhSoWj/\n7e7V7roqmV51oAwlk/d5r+5b5vrlUZl6RUAdejV519VBuVVBF+UmCg3itNNOSxeZFqIrm92QNjKl\nwmwZur0piW83ObODXM1aamVtUc+ElA6zVXxfUjPU/6AWizVC2MY5kPYxTcLPKfvv+TDzhpQaM1/s\n3mdfzz33XLJJqXhu1H/hmnovSAmZfpCyGVOkufLAzBnew+B4nU3GSt3U3yF1YiqJlBApO54nj5ff\nZV/M1DItRM0d9uU1Z1+k1JjN5H65XqSY2K/3j/1y7UxBMuOOVCD3wVlM7bK3OF5TjJwvzz733fQa\nP8+rXs+/CaRnWeHd1JRpy6HXUWvHVC3P+8knnxwUVSAQCAQCgcFHaR2cTno27dCPgOMy/eeNp5O3\noI459sITVrWvbveyiHZKL7wJ/UYVL2BV/Z2qOjllPI5VPHS90voxqBHjgEcrGkvZAE8GgFoTh4Gp\n9ADkBWDS08LARWt50NPC6xmU6TdxapzwOt7Db9J8a6fmCufuYor8nG/HXhMGhVJjhm/lftvnGzXn\nQ6+I38T5Rk09oLFjx0pqeUnYv5T1lHlN6C1gAO+GG26YbBeM5BztQZBa+8vgWnpa2O6AU86L86Fn\nz2tCbwTXnPvnfaM3iGfTHhrrKElZ7wfPGAOKDc6dWkoOeud68azw7BmcL59z7xWfE2rTUD/J82Rh\nT3pK2Ie9gNTG4XzsXeRZoJ4Unwl7WDluniuunXWR6N3KQ3hwAoFAIBAIDBziB04gEAgEAoGBQ2GK\nylgRSgzUQYd0Gwid19fyCjwu8nne2lTVPum2lEYZ1Knl0g6dzk23GjF1Bn4XGWPR81pmn3od7E2N\nGAdXkvJh8OT48eOTffPNN0vK0hoMhKW0vd33DAwmpWPah7QH6QGWeHBBwnXWWSe1URuFhSbtxqfu\nzKRJk5KdVyiU0vekEuzGf+ihh1Ib50OX/SabbCIpSymQpiE9c9VVV0lqFY6UpP322y/ZTz31lKT2\nmi2kTkxBsI200rXXXjtsvBwLg65feuklSdnzR62XbbfdNtkPPvigJGnddddNbdQpyqNv5s+fn9qo\nqcLxeP1JOzFY20Hr1H/hufFZkVrnmLowpKUY9O6CrCwnwTIIbmfQLqkgjtcULwOeea5IYzrgmMVl\nCVKTphg5hvXXXz/ZXhNSUTyDpKtM+7GNmle8r58Zlv3IQ3hwAoFAIBAIDBziB04gEAgEAoGBQ2mK\nqh26zZwpQ4dUzR7phG4pijLV08ugztIFZVBnRk8R9IJiLEKjdku51FnmoMw9us1MrOPZqIsqtKtb\narneSQkRzO5xtgtd73SHs1yB6QrLvEtZWsEucF7/wAMPJJt0ljNj2lXqJq3gbBfSFosXL042s7NM\nXZBOoRvesv2ktVgRnWOfN2+epCxVcd999yWbe2cajdlq3BOPh1TGXXfdlWxSUO6DNFs7HRX3xywd\n6rd4f7kGpOFIY7ov7jkzzAjvGylGZlGRpjQtxyr2XNNFixZJylJNzDZjRpbPEGlDzp3aRC6JwOs5\nH9tce46RFd59Rkjlch05dz+/zBQz/SdJa665ZrJ9b1KypCY9Tz4ntHlGfF+Om5pVPPN+3kld5yE8\nOIFAIBAIBAYO8QMnEAgEAoHAwKG2Ug3dootqxYW/S5QRvuu19H0/1rTX9yqDXu1ft6h6VjqhV3Ps\nVXmUqmjznBTq+MILL0yDcqbIww8/nD4n9UL6xhQF6SxmW1By39SJReukbIaLSzRQtt6ZSFKWVrKo\nG6koUg0U4rOIGukw9suMnG222UZStvwCSzW4SjUpObr5mYVzyCGHSMpmy5AeMLUitagTVzOXstL4\n1113naTs2pOSYdVn0wasAM8q1sSrr74qSVp99dVTG+fuavDOKBo6bpfXkFrZV6TDSN+RyrEwHekw\nV6aXshTUFVdcIam9YN8OO+wgSZo7d27uuChMOWrUKEnZPefakF5zSQpmFbFKucUT21GjLLvh+ZLS\no1CgxyW16CjuLzP1OHdTSFxHiv75XJEC855L2bPp/WM2WztxTNO9rGx+9tlnR6mGQCAQCAQCg4/C\nHpzcD3/PCiH2qoBmr4N9q6JbT0kvtILqRq/WtmqZiyrj6oeXqup4OwXQE23GW2gSRxxxxLBO6Umh\n1D89GhMmTJCU1TuhN4cehyVLlgxrY2G/cePGScrqdLST73c7i3HyLZbBui4o6bFK0mWXXZZsvqE7\n8JNrSW/N5MmTJWVl9Kn7w7dye6c4X+rnULfHHgcGnnq9JGnMmDGSsoVI6Q1Yb731km2PArWN6Fna\nfvvtk+01s86OlNW5WWuttSRJ99xzT2rbddddk02PhgNa6RVoF+xrUCeJZ4HBvN4LlmLgebzgggsk\nSVtvvXVqY+B43v4yyJheFwY9P/LII5Ky3hWO0evEwGLq5DAw2PdjEDO1a+g18zpxT6nhtOOOOybb\n/dGTYu0izodeVXrV6K2xx9DaVlLLoyllvXxeG57tAw88MDw4gUAgEAgEBh/xAycQCAQCgcDAoTRF\nVTelUzSAs8i9yrjTy/Q70r3YR5G16UWAZ78psDJB13VqIlXpt9/B3HXq/vSj307913BeC315xowZ\n6UZ2kbMkw8KFC3Ovs2udAZF0/zOY04G/dMczINXu8jlz5qS2qVOnJpsByXa5k35gpW7SZKZMSDUx\nsJRBm9b6YKAmaSdXSs+jW6QsveM+WF2dn3PuDj7mOpKOckkEtpEaYYC16R0GKbP8ArVLPB5STawg\nbc0VUlQMniVN5kBnVhM3tSZlaTBTjNRZYbVwtnvfuU/cP9NgDGhnQDPpOZ8LnlHSTqSYTOVw/9iv\nqVqeO+4JaTQH63JtSakyUN3PPPeMpSVI+3mP+Tn/ZjjImJ8zIJ26Sn7+GAhPLSaO12eXFNUpp5wS\nFFUgEAgEAoHBR/zACQQCgUAgMHAY0X38BnxNdZYY6PRdop8URD8zY3o1337SVUVKSCyvMdTZL1Gl\nbMebBd3o4MyZMyctuKXeWVKB2UykrkxB0QVOqoDtlqmnW5tUhDOx6MYnmAmyYMECSVlNHcKf8x7M\nziIVRCpglVVWkZSlj6ipc+WVV0rKUkWsAM5+TZ8xa4UUCDN9TJOQRjviiCOSfdZZZ0mSpk+fntpY\nuoLy+qYaSFtxDHfccUeyPV+Wb3DWmSQ9+uijkrKZU6SrjjrqqGTfeuutkrJrwL64f8704jputdVW\nySZFaHqHVBH30pl0zFAjzUJK1BQVtWtYlZ3j9TrecsstqW3ixInD5sCMPWYwMdPO9A4zE0ltkZ7z\ns0ZNHp5znk2fIWaY0TaFSHqJa0660eMlhUXNIz7Lm2++uaTs34hzzz03KKpAIBAIBAKDj/iBEwgE\nAoFAYOBQmqLqp3Q+71eH6Fy3mTxVSzn0mkbp99p06ndFohV7hRVN5LLb8XQrBDjCfUtnUZna2HTT\nTdPnpKhIMdHNbjCzhvSAqSvKv7Nq9P777y9JOvvss1Pbdtttl+w86uSAAw5IbXTNs0yB14guf1I2\nkyZNSrZl/ZmFxerMFr7jurNCNLO6XBqCWUusju7MKKm1Dsx8yhvjvffem9pYHf1b3/pWsp354srn\nUjZLiuto+q6dIJ/FEQ8//PDUdsYZZySbWTjz58/P9Cll95q0k7OYuHbMuCO943NNwT3CFNLGG2+c\n2khR8Tzm9c/7uqwHx0jRQe+/1CodQuqNe0LxS2er8b58pij6Z3E97pOF9SRp3XXXTbbXlGebNBhp\nSoPPL6lJiwJSoJD0G8+xq5czUywoqkAgEAgEAm8KvH2kDzu9CdatbVL0Hp36KuNJaddXmX47ebeq\nopMGSZVyE73yNnS7p0QZL1Mnb0KRPanicerH2W/XR6e+ehHoXMZrU2W+DHL0WzWDhZ955plkX3XV\nVck++eSTJWWDNiklT4+DA2EZrEg9EntlHPgqZYMcqRXiwF7el8GgfEt14O6MGTNy58CyDX7DZoFG\nFn702n784x9PbQzaZPCr23k9367t8eDY/GYstUoQSK3yCnzjvvjii5PN4qHWauEa0EPwqU99ath4\nKc9Pr4z7omQ/dYEYzO3v0Evl8htDx2Dv1J577pnaWDaAWjred3rV6Cl5/PHHJWUDgLkn1vKRWp4u\nnjuuEwt+nn766ZKyQfXcHwc904vBfukJc+A1vaL0aNFz5+Bxeqx4zvl8+znguPjM+H4cFz0xHKOD\nl6nVxLIe1ADyeKhzdO6552oowoMTCAQCgUBg4BA/cAKBQCAQCAwcCgcZpwv67Jovg15rkCyv4Ng6\nNHM6XbO8qoFXRdHA7jrOa5V9XxE0gjqhV9QZ8ZaCHX/9619PHVkG//rrr0+fU5uG7vIPfehDkrLB\nwnSBU1Lf+ivU9GAQpGmwKVOm5N6L9I+rb/N6Btqy8rF1PTxWKVv2gS59V/hmcDSDjE3fsWI2g0Ed\nWCxJu+yyi6RsoC2/y8Bfa+2sv/76qY2VxWfPni2pNW8pK6PPSukOlHUQLMc99B5PPPGEpCxNQ82U\nq6++WpJ0zDHHpDZWriatZGqRQb2vvvpqstdYY41key9J2e20007J5r7ef//9w9q4Ni6vwXsx8JfU\nigNpPW8pW3Wd+2MqlRXGeVZIFxqsTM4xOKA4r6TG0HvcdtttkrJB4gxIppaS6TdSVNRE8rki7cg5\nsPyF/5bwu6z2zufa9DXLb3zuc5+LIONAIBAIBAKDj/iBEwgEAoFAYOBQupp4GdRZjqAOSidvDFUr\nV4f+Shb9KLXRTz2hqppHRe/FPuqsnt7uXkSfz02hm1199dVpsC4bQBc6dUWoBeKMGtJHpDtIJdj9\nz4wRZqA4s4b0EDOu+N3HHntMUlYnh5ki1PKwa52f0+VP3RaPndQY6bknn3xSUpZeov4Ov+v58Bxw\nDnlZKeyXVN3cuXMlZbOSuOakRlx6grQU9UxIJ3q8LFfBtXEGGjPbqJmz8847DxsjSzUwOy+v1ALX\nmfQb52YahRQJ+7X2EEsY8NxwnU0XsswFqSCumffKZ02SRo8enWyvKfWKmGHG59yUJquNM6uM8/H5\nZ7+cO59FrxPnmFcOgn2xejozzPwcUNuKpUO4NqZ7Od+TTz45KKpAIBAIBAKDjxF1cIhOAatVPmd7\nGQ2aOt6uq6gPl9G5KRJkmodudWz6+dZe1aNSpyZSp3sUOTfdah6VOYNVz2u3elDdajT12tPGt7r1\n1ltPUtazQd0Yvu074JQFC6n74gBRfodvsXxbdICugywl6bzzzkv2nDlzkm3PAbVkqCvCN1N7AKjG\na0+MlA3WtYeEb9e0ra/CdW03H2uIMCCZ3q9TTz012Q6QpoYQg5vtTaC+CxWYqWTrsVHbZq+99ko2\ng4DtheCeUWPGZ4lBsPQW3X333cl2QCuDWLnmLsYptd78GRhOLxE9Q1/96lclZc/FRhttlOzjjjtO\nknTDDTekNgbHch0ccM5A6pdffjnZ9FJ4DPTa0FtnrwsVixnoPHPmzGTbG0pPDQOauZfWFmKQ8iGH\nHJJs6iNZx4Yqzg66llrPH88rg6rpzbPniPeitg2fZT8neSrRRHhwAoFAIBAIDBziB04gEAgEAoGB\nQ2GKqkqxzU60VLt++xEEWbWg4EjXt/u8yvW8rlc0ThnUQc/ltfVKWygP/SxdUEYHp+4A+irf7YRe\nn0HSMM1mU1KWimLQpj+XWvQMP2eQMN3wP/7xjyVl3fQcq/U3SJeQDiFMR5lyGDoH3sNjY3kF9stA\nVweqeqxSNjjWQdMsmsjgZY7npZdeytxfygaAMpjXejIM2iTl5nVmMCnLGVBfxePhGLk2H/jAB5Lt\nPaZWD9fDeiekdBgkzvIJeeednzM41utITReeBZ4xj5Hfpb6S94qUKqnCvMBvnlGC/TrAlgHPDBL3\nXlE3hsHADND1fXk+uP9cfwe6U6OG68/veq/5Oc+215xnlOeZlJvHzrPEZ5G6Px47z1IewoMTCAQC\ngUBg4BA/cAKBQCAQCAwcRqSoqlIr3X63TAZTnRRHkcyXovctQ3fVXYV8pDFU1VwpQ0FWzSoaadxl\nx1hn1hBRhUIqQ9l1uq6OZ6oXWj7dgtk7zqxh1gvd8NQQsXYJ5eFJbVGe39o0dNOzbINLCxx99NGp\njWNgdojHyPILzOhgNXCP58tf/nJqY6mG73znO8k2rfPCCy+ktq233jrZpm9IW5AOY8Vzu/r5uTPU\neC+ppcXCStzMfDrjjDMy/5aymW1cU1NxpLs4XtI3zhoijUM9GWcuXXrppamN1dcPOuigYffgHFmF\nnhSHs/ZI3zGTiNlxa6+99rBxE6ZySK0899xzyWbGVZ7eEKvM8+xa74dUIZ89Z2qx9AUzjTg3P6ek\nGFnJm9pCLrtAKpDZc3l/c7k23D+fR16zcOHCZPP5cTYZq4mTYmRmos8Yqdw8hAcnEAgEAoHAwCF+\n4AQCgUAgEBg49LRUQ69QRyZXt9/tNK4VqYxCEVTJBCpDrZT5vMwYy6DO8gtl5kj8PpT1qLmcRKEb\nH3rooekGzthpJ99PtzVF7Ay62ymCZ5Caefzxx5NtKuGee+5JbXvssUeyKQpnyowudrr8mVXiDBJe\nz2wmXud2Zo9YeE1qZfK0yx4iNeYMJJcSkKRHHnkk2cxAMa3AUgzMJDIVeN9996U2irsxS4YUhcGs\nIdJRXidmWXFtTKk89NBDqY0lJEgLOWOOZQGYRcczZDArietIOsSlErhPXFNnDbFECOfobDapRXPy\nXjwXzDByVlFeFpbUorl4Fkijcm3ynhNSlzzHpg1dFX7oHEgB+pxyDqSYPN52fzMobLj66qtLylK2\nPFd5pUX4nJ133nlRqiEQCAQCgcDgoycenF4XJOyEfmvB1Knf0smzUFXrpUpBySL9FkVVXZiqY6jz\nDJYZS7f3rRN1eBRrmE+hCxctWpQGa8+Bg36l7Bs+JfUdxEjPBYNFKV3v0gN8+2YA7+zZsyVJhx56\naGq78cYbk80yB35jZeAqyy/Qi+EA3C233DK18S2VHqfNNttMkrRkyZLUxrIBlq6nVgw9UnyD99sz\n33L32WefZLOIo9/KWY7i4IMPTvaJJ54oSTr//PNT25VXXplsBoFvvvnmkrKBpwyqpWfIb+X0FlC/\n5Y477pAkXX755alt+vTpyWY5Auvy8KzSQ8B9d3kMBqyz3Ae9eNa3oQeItgPV6WljmYtPfOITyXYg\neruSCvRaeo9djkTKepa8dtxfethcukJqaddY70jKBi+zsK0DiqkbtNVWWyWbgdv2kPHcMbjZXi3e\n69FHH002nx//rckrRyFlz5ifEz4H++yzT3hwAoFAIBAIDD7iB04gEAgEAoGBwwofZFyGWqnrXu36\nrbOKeTv0+r5V6a5uA1brporqDPyuQsnVEcBb5fqqY+hVgHYBFPryjBkz0g2mTZs27HNqZ5BWYkA2\n8AAAIABJREFUsGudrnsGOfK7Doik9o21caSWpgbbqL9y4YUXJts0CT+nts2BBx44bA68/oQTTkj2\nvffem+w999wzM1YpSxuZwmBgKfdj7ty5yf7iF7847Luk+i6++OJkm8I488wzU9v1118/7L533nln\naps8eXKyWabAtAKvnzp1arLXXXfdZHvu1FwhbeEK76RuuL/UP/KaX3fddaltk002STYDZR10y9IG\nPBesaP75z39eUpaaYb8TJ04c9jn7uummm5Jt+s5aM1KWzmJQratuM/CbQfGmh0jPcq9JK/k5IDVG\n2nDvvfdO9rXXXispuwZ5pSmkVtA7KS72a70olncg9UUa2kHxnC8pKpYGcXA42y666KKgqAKBQCAQ\nCAw+4gdOIBAIBAKBgUNhimp5Z4d0ocPRdb953yW61QrpB31QRrum6Fj6kdnW78y1op9X/W4vrm/X\nR506RkX2us19C03oiiuuSBc56+jFF19MnzMLwzL7UoseoJt/9OjRyWZGjt37zCShxoizO0inPPHE\nE8lmdeV11llnWP+kmiif/453vENSNmPL1IskPfzww8nedtttJWWzQ/LKL1CThWUQeF1epXVqmFBb\nxhlEzHwivefSEZwDSzW4bIDUyt4hdUJQP8fZaKQiSHc4m4wlGXhfro3pn0WLFqU2Un3cP68TK4Sz\npAKpHOvccG2pIeQxcNymZqRs1p/B0gebbrppsnk2Td+QsuN1zp5jdhEpG9J6PoPMJGMpDWZBOXOQ\n60ENGtKcLmNBzR2uv2k2nkE+1x6X1Dp7PNsuISJl6TvvJc/ojjvuGBRVIBAIBAKBwUf8wAkEAoFA\nIDBwGLGaONGt673bfot8r06huE7Xd6J02tEDdWYglcmMqrMi+kht3aBK5fGifY50fdHq6e1QZ0Zd\nVVqpzP50orCqVjzv9N2RQGrEVYVJL1CinpkvdlvT9U63N6kPZ2nwXizl4KwRZukQlLO3m91VjaVs\nBotpDY6drn1SGKa72Add/hQ+Mw1CWoIZSKQ7nHnGrBVmwDDzyfdlthrpH9u8F+k90oamzJh5Q2FD\nZs64hAPXg3vmtXn++edTG0sicG2cJcX58lyQzvB82wnQkQoy5UaqiWPw3ChWyPNKesaZdnxuuNek\nqCwmyHGRdiKNZrAkAymzt73tbZJalJGUpXxYvd5lOdqNkcKCvof7H3qdzxvXgOCamnYidWZhRClb\nxsL7xjOYh/DgBAKBQCAQGDiM6MGpueheYVQJmGx3v05jqCMgudv5VvVYdOtVKaOJ04/yGd3Op0yw\nbrfaNVX7yruuyLirPH/txlhnwkC3AdoGpe/tVeFbId/E+VaXty4ssMi31LwgRnpz/GbKYo8E32I9\nRrZxXPR02NvCsgF8G2VZB7+Rsjgl7+F+HYgttdcgcR/0aPBNmv16jAw2ZfCyx8t70ftBb401Suix\nYoAvNYs8BvZL75Q9LQxy5dr99Kc/TbY9LXlFUaXsWfTZogeP+05vj6/jfOjBsceQnkOeV55B34/j\n5p7QtheIXg564PL2l88Mz5vHwDWgx5FB014/njGOlx5UezX5OffSZ4H7wGedz6o9p/R+ce48AwbP\nVR7CgxMIBAKBQGDgED9wAoFAIBAIDBwKBxkbdQTS1hm8WvX6KvRKHQGeVcbVac3r0Gzplmqoc4x1\njKHTNWXWuei92F4k2LsKVVSV6ivbR1HUVTZl9913T7arch999NGpjRWkGSjp4FdXApeybvztttsu\n2bfffrukbGAqA0Nd1XvWrFmpbf/990/2HnvskewbbrhBknTMMcekNgbtWu5ealEyrCrtKtlSlgow\nZUM6hIGULgfAQF3TAFIrkFpq0QJ0+TOYd8qUKcPuwYDWL33pS8ned999JWWrkXMMK6+8crIdrE1K\nwWsvZStee+6siP7II48k+7LLLpOU3V/qDZ111lnJdsXx7bffPrWdcsopyT7kkEOS7XVgeQ1rEEnZ\noGiXDuD+shK715e6Qvz8yCOP1FCQHjzssMOSzX23nhO1mHgWHIBNuswB+lK2rENekC/LJ7Biuaki\nrg2D5j/5yU8m2+vEc0W6ys8aqaivf/3ryebz5bmzHMguu+ySbJa/sO4Sx5iH8OAEAoFAIBAYOMQP\nnEAgEAgEAgOHTj7l5V6qoc77dqv70it9nTJYXpXUlxeqrnmVcgR1oM4K753orF6tTc0odJNZs2al\nyTgjh9lFLInATJG8NmbDUNPG+iosV0DNDWePMBuGcvXUCrFeCcsR0I1PPRNnPjHLito37HfSpEmS\nsvQB5273P/VOmFVEPRq79NkX6Yz58+cn2zQXyygwk8iaK8wOY3YQ9VncFyt9MzuL3/Wak2bjfExX\nugyD1CrfMHQ+1m9h1XBmSXE+zhDjvcaPH59szvPWW2+VlD0rpIpGjRolKVuCgLQjKVNnHTHTixlM\nvK91oKhHZBqVYNYSy0msscYayc7LUOJ3WeHdVJuz0qRsNhN1ijwfUmvs15lapKj4XPM6nwvei2eX\nGY9eM5ZoOeecc4b9rQkPTiAQCAQCgYFD6SDjfqNO5d+qwZdF1Vrr9vB0q7BbZ7BvVXTrSelnQHJV\nraVOYymDqjo4ZVSRu00CaPfdotfkIU8JlV4Kvk2yUKUDQKl0yzdMvh3bG0B9EHpVrKlBxWKqxVI3\nxGDgKd+O6aWwp4MBuvfff3+yqQxrbw49CxyDlYqpRfK9730v2XzDtyYOtULoVckrHspgX6+X1AoW\nZQApvRCTJ09OtteJXiquDYNF7Z2gl4r77vFwT1nIlGvnMdJrR28BA7DtHWExRwacs18Xu6SWC72E\nXgcGWnMM9Eh4jNSu4bniGH0W1lprrdRG75W9SNwzfpceRT9f9BDR+8V2n+lNNtkktS1YsCDZW265\nZbIdQM9AaHoR7d2it49/M6j35PV97rnnUhuTD7g2Ptscdx7CgxMIBAKBQGDgED9wAoFAIBAIDBwK\nBxl3QtXik1UCHvsRDFymNEE/i0B26qsd6qSollcAb7t7jITlOcaiqKqZ04+g9xooqEJfPu+889KN\nTN9Qp4U0DYNBTW2QEmIphkWLFiXbdBaDQamJYypi7ty5qY20A6mAr371q5Kk4447LrWRNjrnnHOG\nzZHrRoqCbngHpJJyo36OdWoYcMlgUuuDSC0NGdJdDH5lILRpljlz5qQ26sKYtiPdQm2Va665Zlg7\n94+B1NQ5MbVFCopB3hMmTJAkXX/99anN+yRli4uef/75krLU2Nprr507Bge3Uo+Gwcmc28SJEyVl\nA7AZ/GptIlKbLJlB+tUUISlX0l3UeHJQ9MUXX5zaqLtkLSUG6jJYm+2mCLfaaqvcObDI6tSpUyVl\n6TBSQXmFUxmkzAK03/72t0ccI8+rzyODlLnvpAhNAXIdjz322AgyDgQCgUAgMPiIHziBQCAQCAQG\nDrXp4HSrMdMJ/dZ/qZJJUkeF6jL0XRX6oB+ZQr3O0uF1Vc9dryqEl0G3ejR1lOioE23mU+hmF1xw\nQRqgXefMpqHbmnomLgvQTtOj2Wwm25o1zB5hZoY1NaiTQ3c8XeumUUiH0aXPrBHTUaRTSIcw08dZ\nJ8zuIo3m7zL7hFQD197rRNc+s2xI1W222WaSstL3vIfXd8yYMamNVBOz1aw9QxqOFBTnYz0aVi4n\nneGsLdIeLCtACtH0G7N4mBnFzCZrx3Asq6++erK5Nl4/rjO1aQx+ToqKa+PsLH7O80ZKzdQXs904\nB68vNWb4HLBUhs8FabS8avFSa+5cm3bV7U3LktJjRpz3h5/zbJNa9hhJ6ZFS5Xky+N1p06YFRRUI\nBAKBQGDwET9wAoFAIBAIDBxGFPqrUnGb11UVqMsbQx3ZMHnf7Qc9UBV1itV1e68y19dJnXRbGbuq\n6CNRhQYrsgZlvluXoF4/UOUM0lVtFznd2r/5zW+SzWwWu9l5T7reKaJmCoKUDYX67KYnvUQKi3SH\nM7122mmn3M/vvvvuZJsSozAeYXqI3yU95xIEkvTKK69IylJvzIYixWEBQFInpC0omGeBQFIz06ZN\nS7ZpBdJ0pNyY9eV7kF6g0N/VV1+dbJdwsPCelKVhTL+Q0mFfrrgttSgz7innzjPic8GK6BRJZHkF\nC+qRliIV5D0jNUOhQN7XlBvnyKwx0j/OWCMVuPXWWyfbVBwz6ng97+HzRKqJVKDPldTaY1Ym5xnj\n3L3vpOH4zHgdSStznUjxms7iM2uabiic0cg55iE8OIFAIBAIBAYOhUs1VPEG1OHl6FWphjq/O9JY\n2vW7vPRZqhaB7NRXr4PMq/bRjzPYbYmJdqjTa1PH2e3UVzdzZuCo30JdeFKSnn322WTTQ+O3eXpP\n6Pnhm781Rvg2yTdXF9a88sorUxu1YH7yk58k214evgXTO0KPlL0Q9LrwjZdv8P4uvUjUAPI8OV/q\nqPCN2F6vdmUfeF97FviGf9NNNyXbxS5diFHKFrL8xS9+kWx7jqjPw0BYenZWWmklSVmPCeez3Xbb\nSZKuvfba1EYPHr1iDjjlnjsIXcp6A7w21C5iXxyj58b95dy9pgzg5fUMIrfHgefjwQcfTDY1fHyO\neZ65Tk899ZSk7BnkuaBnx/OlJ5Q252ZPJ72I7byAnkdeADD7oNeUXkauo+/LgHSWIaG3xuUc8oK9\nifDgBAKBQCAQGDjED5xAIBAIBAIDhxF9ym/AV92ti7uTBsn/b+9sQq6q/i++RjUPatSoQSBolAW9\nEBaFZmSZhZWaWJaKGWovRJKWGFQaIQRFZfkSWImphZSmmCVpFFEjixCaBA2kpk1//9Ha93P03ufe\nc++597H7X2viZt/zsvc++8hzvuv7XauOXcEoNHF6Gdu55w3L+boOmkzwbcISo87aTFYibZNjHKW2\nTbdrNEmTDUCp9jSIV155pVzINAtpDepdmNaQWtQKjyVdQirIoX7aDVC+3xQD++icbJ0cqUVzOUlW\nqibKMmHV8yFF1YlWMmVCaXzq65gSYBIrj6Xbt+dJ2onJwKRn7Dxtmk6q0gqmGqiTQ70h0iheGyYD\nk3LjPvEx1HrhfEyzkHaaNm1aaTPp2WvOe5HOZL8pF86R60FbDlNB3Hecg6kTrgEpKrp6+7qkh0gx\nMcHWSbfc+2z//ffflblI1T3I9fcz4fVJYZHqMd3Efcl9RerR9CcTh/l/QjstJt6Xz8+2C3x3ODdS\nrV5/0n+bN2+ODk4QBEEQBOOP/IETBEEQBMHYYcIqqn4pjmG4b/dy/qB0Vqfzeq24GoW7MzGo3lC3\ndep3nTvdY6Jr8dhO1+qHMutlPbpV/U2WDcmwNI2atKloam//8MMPpe3Q+IoVK0of9UpY+WQahtob\nrMIg3WQ9GYbb2bZzNZ2xqfXCcLnpClaUdNI2sV4JKQOC1zC9xjA9dUdstUAqiZRcO2qF1AuvRWrE\nNBbXbvv27aX9zjvvSGq5YUst6wupSrl4zWlBQGqFVVCmFu2SLlXXbuHChZKk1atXlz67XUvSoUOH\nStt0JKlAO8ifew/TMHRqP378+Hm/s02KinOz4/XcuXPbnk/qyvQMtXq+++670qYVhteRGjSkmPx8\niZtuuqm0TWFJrfeU7tukirhH/E6xj+8f52M6kf8PsPrK68BnSu0iwpQcrVS4R0lz+bnTWb4dEsEJ\ngiAIgmDskD9wgiAIgiAYO/Qs9GfUkZUfViVJE1TQMCpNmjh/UHpgFLRGN2G7OhRIHZG8QW0b+p1D\nk1VS7cYzDOG8iTBZVXsTgVSBQ9wUZmN4+p577into0ePSqpWUbHihtUsprFYucHrmkZh2JuOysTJ\nkyclSVdeeWXpY/vYsWOl7UqrL774ovRxvrRMcPiflA6rWVyR8+2335a+dlUtUqvaiFVUpMlIV9gO\ngOc/99xzpe1nQSpw1qxZpU2axdVVpCU4n23btpW2r0fhOx578OBBSVV6iHYSphUl6fPPPz9vXnSD\n5zX83D/99NPS105wUWpRgKzu4vO1lYPtO6SqyzkpVc+zk8M7aT/Taz/++GPps+Ci1KITSTWRYuRz\ndzXZmTNnSh/3QrsKQVJcrEAjhWQ6kM9sypQppe0KQK4n3cQpTHjxxRdLqlJc3Oe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"text": [
"<matplotlib.figure.Figure at 0x7f2c9dbbc610>"
]
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 9
}
],
"metadata": {}
}
]
}
import collections
import numpy as np
Population = collections.namedtuple('Population', 'n_neurons t_rc t_ref gains biases')
SimStep = collections.namedtuple('SimStep', 'voltage refs spikes')
def generate_population(n_neurons, t_rc, t_ref, max_rate):
"""Generate a population for simulation using the given parameters."""
# Generate the max_rates for the population, and the intercepts (in range
# +/- 1)
max_rates = np.random.uniform(0, max_rate, size=n_neurons)
intercepts = np.linspace(-1., 1., n_neurons, endpoint=False)
z = 1. / (1 - np.exp((t_ref - 1./max_rates)/t_rc))
gains = (1. - z)/(intercepts - 1.)
biases = 1. - gains*intercepts
# Generate and return the population
return Population(n_neurons, t_rc, t_ref, gains, biases)
def simulate_population_step(population, in_currents, pstep, dt):
"""Simulate a population of neurons given the input current and the
previous simulation step.
"""
# Add the biases to the input currents
in_currents += population.biases
# Calculate dV and the subsequent voltage
dv = (in_currents - pstep.voltage)*dt / population.t_rc
dv[pstep.refs < 0] = 0
voltage = pstep.voltage + dv
voltage[voltage < 0] = 0.
# Decrease refractory periods
refs = pstep.refs
refs[refs > 0.] -= 1
# Deal with spikes
spikes = voltage > 1.
voltage[spikes] = 0.
pets = np.random.rand(population.n_neurons) < (voltage - 1.)/dv
refs[spikes] = int((population.t_ref) / dt)
refs[np.all(np.vstack([spikes, pets]), axis=0)] -= 1
# Return the simulation step
return SimStep(voltage, refs, spikes)
def simulate_feedforward(population, inputs, weight_matrix, dt=0.001,
filter_tc=0.005):
"""Simulate a feedforward connection from the spiking inputs to the
population of neurons.
`inputs` is expected to be a m-by-t matrix of input values.
"""
assert weight_matrix.shape == (inputs.shape[0], population.n_neurons)
spike_times = [list([-1.]) for n in range(population.n_neurons)]
# Create a series of filter holder values
synaptic_filters = np.zeros(population.n_neurons)
f_m1 = np.exp(-dt/filter_tc)
f_m2 = 1. - f_m1
# For each simulation step (i.e., each column of the input) apply the input
# to the population.
pstep = SimStep(np.zeros(population.n_neurons),
np.zeros(population.n_neurons), [])
for t, inp in enumerate(inputs.T):
# Apply any spikes to the synapses to get the current contributions for
# this simulation step.
ins = inp.dot(weight_matrix)
synaptic_filters *= f_m2
synaptic_filters += f_m1 * ins
# Simulate the neurons for this step
pstep = simulate_population_step(
population, np.copy(synaptic_filters), pstep, dt)
# Save the spike times
for n in np.where(pstep.spikes)[0]:
spike_times[n].append(t * dt)
# Return the spike times
return spike_times
def get_interspike_times(spike_times):
"""Get a list of interspike times for each neuron."""
interspike_times = list()
for spikes in spike_times:
interspike_times.append(
[spikes[n] - spikes[n-1] for n in range(1, len(spikes))]
)
return interspike_times
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