Theory and simulation of integrate-and-fire neurons driven by shot noise (Droste & Lindner 2017)

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Accession:228604
This archive contains source code for the paper "Exact analytical results for integrate-and-fire neurons driven by excitatory shot noise" by Droste and Lindner, 2017. Specifically, it contains a Python implementation of the analytical formulas derived in that paper (allowing to calculate firing rate, CV and stationary voltage distribution of general integrate-and-fire neurons driven by excitatory shot noise, as well as power spectrum and rate-response of leaky integrate-and-fire neurons with such input) and C++ code implementing a Monte-Carlo simulation to estimate these quantities. A sample Jupyter notebook to play around with the analytics is included, as are scripts to reproduce the figures from the paper.
Reference:
1 . Droste F, Lindner B (2017) Exact analytical results for integrate-and-fire neurons driven by excitatory shot noise J. Comp. Neurosci.
Model Information (Click on a link to find other models with that property)
Model Type:
Brain Region(s)/Organism:
Cell Type(s): Abstract integrate-and-fire leaky neuron; Abstract theta neuron;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: C or C++ program; Python;
Model Concept(s):
Implementer(s): Droste, Felix [fedro at posteo.de];
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analytics for IF neurons driven by ecitatory shot noise - Examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import analytics.shot_noise_driven.lif_neuron as snlif  # analytics for LIF neurons driven by SN\n",
    "import analytics.shot_noise_driven.if_neuron as snif # analytics for general IF neurons driven by SN\n",
    "import analytics.gaussian_white_noise_driven.lif_neuron as dalif\n",
    "import analytics.gaussian_white_noise_driven.if_neuron as daif\n",
    "import numpy as np\n",
    "import pylab as pl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Firing rate\n",
    "\n",
    "Functions in the analytics module enforce the use of named parameters. This makes it easier to understand what is going on, avoids bugs due to a wrong order of parameters, and allows to give feedback about missing parameters. \n",
    "E.g. the following call to calculate the firing rate of a leaky integrate-and-fire neuron (LIF) is missing parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r0 is missing arguments: 'rin_e','vt','tr'\n"
     ]
    }
   ],
   "source": [
    "try:\n",
    "    snlif.r0(mu=0.1, vr=0, a_e=0.15)\n",
    "except TypeError as e:\n",
    "    print e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If instead we supply all of them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.660220667961072"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "snlif.r0(mu=0.1, rin_e=17.6, a_e=0.15, vr=0, vt=1, tr=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that for all of the supplied functions, time is measured in units of the membrane time constant. For a membrane time constant of 20ms, the above corresponds to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "r0 = 83.011 Hz\n"
     ]
    }
   ],
   "source": [
    "tau = 0.02 # s\n",
    "rin_si = 880 # Hz\n",
    "tr_si = 0.002 # s\n",
    "print \"r0 = %g Hz\" % (snlif.r0(mu=0.1, rin_e=rin_si*tau, a_e=0.15, vr=0, vt=1, tr=tr_si/tau) / tau)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The provided functions also accept one non-keyword argument, which is interpreted as a dictionary with default parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.660220667961072"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prms = {\"mu\": 0.1, \"rin_e\": 17.6, \"a_e\": 0.15, \"vr\": 0, \"vt\": 1, \"tr\": 0.1}\n",
    "snlif.r0(prms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When a parameter dict is passed, individual parameters can still be overwritten:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1583099022343237"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "snlif.r0(prms, tr=0.2, mu=-0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The firing rate can also be calculated using the functions for general IF neurons:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6602206679610714"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "snif.r0(prms, model=snif.LIF())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Obviously, the result is different if we use a different neuron model, e.q. the quadratic integrate-and-fire (QIF) neuron:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.129546663431224"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "snif.r0(prms, model=snif.QIF())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model can also be an EIF, for which we need to supply an \"effective\" threshold vtb and the spike onset parameter d. Compared to PIF, LIF, and QIF, evaluating the anayltics for an EIF entails one more numerical integration. To speed this up, we rely on a small C library that implements the integrand. Let's see if this is present.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ":) library present, r0 = 0.969802\n"
     ]
    }
   ],
   "source": [
    "if snif.eiflib is not None:\n",
    "    print \":) library present, r0 = %g\" %snif.r0(prms, model=snif.EIF(vtb=1.0, d=0.5), vt=10)\n",
    "else:\n",
    "    import os\n",
    "    print \":( library not present. You probably need to go to %s and compile it, using e.g. %s)\" % (os.path.dirname(snif.eiflibpath), \"cc -fPIC -O2 --shared -o libeif_phi.so eif_phi.c\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's compare the firing rate of a shot-noise-driven perfect integrator (PIF) to the diffusion approximation (DA) for different mean spike weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Yjpv6t6CabsaSSnAk+K21e4A9h/9+0BizHmgMKPhFivbDrFtg8xfQ6TK45GWo\n8cfe+968Yh6ZvZov12fRvWkd/jFSvXw5OY6P8RtjmgPdgR+dblsk4KQvh4/GQmEWXPxPSL7xD/Pz\n3W7L1OXpPD1/PWVuN49c3J7rz9BYvpw8R4PfGBMNfAzcZa3N/93PbgZuBmjatKmTZYk4z+32PCnr\nq8ehdmO48QtI7P6HzbbtK+Shman8kLafvi3r88xlnbWwmpwyx4LfGBOBJ/QnWWtn/v7n1tqJwESA\n5ORk61RdIo4ryPYM7WxdBO0vhUtf+cNUzTKXm4lL0nhp0WZqVAvj6RGduaqX5uWLdzg1q8cA7wDr\nrbUvONGmSEDa+hXMGgeHDsDFL0DyDX8Y2lmxI5e/zlrNhr0HGdy5IY9e0lF334pXOdXjPwMYA6w2\nxqw8/NrD1tr5DrUv4l/lJbDo7/D9qxDfDq6ZCQ07/WaTvENlPLdgA5P/t5OGtSOZOKYngzo29FPB\nUpU5NatnGaB/o0poylrveR7u3tXQ608w6AmIqPnrj3+5EevxuevZX1jC9f1acM+gNkTX0P2V4hs6\ns0R8xe2GH1+HLx+DGjGetXbaXvSbTbZmF/C32Wv4bmsOXZrE8p+xvejcJNZPBUuoUPCL+MKBnTD7\nNti+FNoO9szNj47/9cdFpeW8+tUW3lqaRmREOI8P7cjoPs00RVMcoeAX8SZrIeV9+Pyvnu8vfRW6\nX/PrBVxrLZ+t2csTc9exO6+YET0a8+BF7UiI0cVbcY6CX8RbDqTDnDs90zRbnAVDX/M8E/ewTZkH\neWzOWr7dkkO7hjG8NKo7vfQYRPEDBb/IqXK7YcW7sHACWLfnkYjJN/66omZeURn/WrSJ/36/g+ga\n1fj70I6M7t1U6+uI3yj4RU7Fvi0wZzzs+BZanu0Zy6/bDIByl5sp/9vJCws3ceBQGaN7N+XeQW2p\nV6u6X0sWUfCLnIzyUvj2JVjyD6gW6bn7tvuYX8fyF2/K5sl569iUWcDpLevxf0M60iGxtp+LFvFQ\n8ItU1o7vYe5dkL0BOg6HC5+BGM+NVhv3HuTJ+etZsimbpvWieOOaHlzQsaGWWpCAouAXqajCfZ5x\n/JUfQmwSjJ4ObS4AIDO/mBcXbmL6T+lE16jGIxe3Z0zfZtSoFu7nokX+SMEvciJuF6x4z7PkQmkB\nnHEXDPgLVK/FweIyJi5J462labjclrH9WnDHua2oq3F8CWAKfpHj2fkDzL8f9qZCszPh4uchoT3F\nZS4+XJp4P0YfAAAM6klEQVTGa19vIbeojEu7JnLfoLZ6yLkEBQW/yNHk7YJFj0HqNM96+SPfhY4j\nKHdbZi5P56VFm9l14BD9W8dx/wVt6dKkzomPKRIgFPwiRyotgu9egW//5Rni6X8vnHkP7ohazFm1\nm399uZlt+wrp2iSW50Z24YxWcf6uWKTSFPwi4LkJK3Wq52Hn+bugwzA4/zHcsc34bM1eXlq0gk2Z\nBbRrGMPEMT05v0MDzdSRoKXgF9n6FSz8P8+yyYk9YMRbuJv2Y8Havbz8/lI27D3IafG1eHlUd4Z0\nbkSYFlKTIKfgl9C1KwW+fBS2LfasqXPZO7g6DGfemkxefWkJmzILaBlXi5eu6saQLolaOVOqDAW/\nhJ6sDfDNU7DuE4iqDxc+Q1n3scxevY/X/7WUtOxCWiVEK/ClylLwS+jI2QqLn4XU6VC9Fgx4gKLk\ncUxPzeOtF79n14FDdGhUm9dG9+CiTg01pCNVloJfqr6crbDkec/UzPDqcMZ4crvdyvurDvL+iz+R\nW1RGcrO6PDG8E2e3iddFW6nyFPxSdWVvgmUveHr44RHQZxw729/ExJ8LmPHySorL3Axs34BxA1qS\nrHXxJYQo+KXq2ZMKS5+HdZ9CtUhsn1tISbqON1cUsHDxOiLCwhjWPZGb+rekdYMYf1cr4jgFv1QN\n1sK2JZ4br7Z+BTVqU97vbubVGsabP+Wz7put1I2K4M9nt+Lafs30qEMJaQp+CW6uMs/snO9egT0r\noVYCeWf8lf+UnMP7P+SSW5RBmwbRPDOiM8O6NyYyQqtliij4JTgdyoWUD+DHNyE/A1u/FZt6PcGL\nWT354qtcIIvzOzTgur7N6XtafV2wFTmCI8FvjHkXGAJkWWs7OdGmVFFZG+B/b8KqqVBWRGnSGSxs\nei/PbW3GjqXFxEUXMm7AaYzu05QmdbVSpsjRONXjfw94FfivQ+1JVeIqg43zYfnbsG0JNrwGe5pd\nwrulg3hvawzlbkufFlHce2F7LuzYkOrV9BBzkeNxJPittUuMMc2daEuqkAM7PcM5P38AB/dQFtOE\n75veypN7+rBxXXXq16rODWc24cpeSZwWH+3vakWCRsCM8RtjbgZuBmjatKmfqxG/KS+FTZ95An/L\nl1hgT/wZ/CfsZt7JbA37whjQJp67eyVxbrsG6t2LnISACX5r7URgIkBycrL1cznitMy18PMkz9LI\nRTkU12zAl3XH8HxWL7an16d1QjR/uagJw7s3pkFtTcUUORUBE/wSggqyYPUMWDUZ9q7GHRbBmuh+\nvEE/FuR2pF50JJecnsjw7o3p3DhWM3NEvETBL84qOQjr58Lq6di0bzDWTUbNdkwJu4HJRb0pLa/L\nBZ0a8m7XRM5sFUe1cA3liHibU9M5pwBnA3HGmAxggrX2HSfalgBQWgSbP4c1H2M3L8SUF7M/ohGz\nGcaUktNJdzXlvHYNeLJLI85tl6CbrER8zKlZPaOcaEcCSEkBbP4C1s32hH1ZEfnh9ZjrOpuPS/qw\n3t2ec9o14M5ODTm3XQJR1fWPTxGn6P828Z7CHM98+w1zsVu/xrhKyAury9zyM5lb3ouNNTpzTodE\nbu7YgAFt4tWzF/ETBb+cPGsheyNs+gz3xs8wGcsx1k2mSWBe2TkscPUiu243zu2QyB3tE+jdvJ7G\n7EUCgIJfKqe0CLYvg81fUL5xAdXy0wHYYFvwhWsYX9lkopp255x2DXiyXQKtEqI1G0ckwCj45fjc\nbshaC1u/pmzTl4Slf0+4u5RD1GCZqyPfuM9nba3Tad+uPQPaxHNDqzhqR0b4u2oROQ4Fv/xR7nbY\ntoTSLd9gt35DjZIcALa5G7PYPZD/hXUjrPmZnN42ketbx3FavHr1IsFEwR/qrIUDO2D7txRvWYJ7\n21KiinYBkGdjWebuxA90Jr/RGbRv254zWtVnbJM6RGisXiRoKfhDjdsFmWtx7/yBgs1LqZb+A1El\nWQAU2hj+527HcjOIgw37ktiqG31bxfFYUh3NwBGpQhT8VV3RfshYTsHW7ynZ9iMx+1ZS3V1EGFBo\n67Hc3ZZ11S6huHFfGrfuTs8W9XkwMVaLn4lUYQr+qqSkAPamUrBtOYVpP1IjaxV1ijMAqGkNO2xT\nPrNnsCe2K2FJvWnRqgM9m9fjknpRGqMXCSEK/mBVtB/3nlQOpK3g0M6fidy3mrqHdhCGJRrIs/VZ\n4T6N9JrnUtKwJ7Gn9aZjs4aMbByrYRuREKfgD3SuMti3mfydq8jfsQq7dw0xeRupU5ZFGFAP2G3r\n8bO7Obui+lEa34Wo5j05reVp9E+sTYymVorI7yj4A0V5KXb/Vg7sWEN++hrcmeuJyttE/eJ0qlFO\nbaCmDSfNNiI1rC25MZdgG3QipnkPWjRrzpkNY9STF5EKUfA7yVooyKRg90Zyd66jOHMjYTlbiCnY\nRv2y3YTjpi5QF9jpjmdDWBI5UcmU1mtL9cZdSGjRkTaJcQyOqaExeRE5aQp+b3OV4TqQQe6uzeTv\n3kRp9lbCcrcTVbiD+iW7qEkx0UA0UGIj2GYbsjYiifzaZ1FerzWRjdpTv1lHWiYmcJYCXkR8QMFf\nWWXFlOxPZ/+eNAoyt1GaswMO7KRGwS5iS3ZT15VNNdzEAXFAqQ0nwyaQXi2RNdFdKI1tTrW41kQ3\nbkvDpFY0j4uhnYZoRMRBCv4j2OJ8CvZlkJe5k8J9OynJ3QX5u6lWuIeoQ5nElmVR1x6gBtDo8D5u\na8ikLplhCeyq3p7i2PNx12lGRFxLYhu1pkGTliTVq0VL3ekqIgGiyge/LS/hUO5e8vbtoWD/bkpy\n91Cen4ktyKJaUSY1ivcRXbaPOq79RFFMDBBzxP55NoosU5/savFsr9WKsuhEqN2YGvWbUatBc+IS\nW9CwXiyNqqnXLiLBoUoFf+bOTWRNv5vI0v1ElR+gtvsAMRQRBUT9btsCG0mOqUteeF1yqrdmU2Q8\n7ugGhMU0IqJeE6LjmlAnoRkN4uvTWkMxIlKFVKngd1moWZhOYXgdciLbUFajLq6oeEx0POExCdSs\n04ha9RoRG59Ivbp1aaZeuoiEoCoV/InN2sCEVH+XISIS0HTFUUQkxCj4RURCjIJfRCTEOBb8xpgL\njTEbjTFbjDEPOtWuiIj8liPBb4wJB14DLgI6AKOMMR2caFtERH7LqR5/b2CLtTbNWlsKTAWGOtS2\niIgcwangbwykH/F9xuHXRETEYQFzcdcYc7Mx5idjzE/Z2dn+LkdEpMpy6gauXUDSEd83Ofzar6y1\nE4GJAMaYbGPMASDvOMeMPc7P44B9J12tfxzv9wnktk7lWJXdt6LbV2S7E21T1c4vcO4c0/nlv/Or\nWYW2stb6/AvPB0wa0AKoDqwCOp5gn4kn+3PgJyd+Ly+/R8f9fQO1rVM5VmX3rej2Fdku1M4vb/93\nd6odnV+++XKkx2+tLTfG3A58DoQD71pr155gtzmn+PNg4+Tv4822TuVYld23ottXZLtQO7/Aud9J\n51eAn1/m8CdMlWKM+clam+zvOqRq0vklvuTE+RUwF3e9bKK/C5AqTeeX+JLPz68q2eMXEZFjq6o9\nfhEROQYFv4hIiFHwi4iEmJAKfmPMMGPMW8aYacaYQf6uR6oeY0xLY8w7xpgZ/q5FqgZjTC1jzPuH\ns+tqbxwzaILfGPOuMSbLGLPmd69XeLlna+1sa+1NwDjgSl/WK8HHS+dYmrX2Rt9WKsGukufaCGDG\n4ey61BvtB03wA+8BFx75wrGWezbGdDbGzP3dV8IRuz5yeD+RI72H984xkeN5jwqea3iWuPllkUuX\nNxoPmoetW2uXGGOa/+7lX5d7BjDGTAWGWmufBob8/hjGGAM8A3xmrU3xbcUSbLxxjolURGXONTyr\nGTcBVuKlznow9fiPprLLPd8BDARGGmPG+bIwqTIqdY4ZY+obY94AuhtjHvJ1cVKlHOtcmwlcZox5\nHS8t9RA0PX5vsNa+DLzs7zqk6rLW5uC5hiTiFdbaQuB6bx4z2Hv8J1zuWeQU6RwTpzh2rgV78C8H\nWhtjWhhjqgNXAZ/6uSapWnSOiVMcO9eCJviNMVOA74G2xpgMY8yN1tpy4JflntcD0yuw3LPIUekc\nE6f4+1zTIm0iIiEmaHr8IiLiHQp+EZEQo+AXEQkxCn4RkRCj4BcRCTEKfhGREKPgFxEJMQp+EZEQ\no+AXqSBjzGxjzApjzFpjzM3+rkfkZOnOXZEKMsbUs9buN8bUxLOuyoDDq3GKBJWQWpZZ5BSNN8YM\nP/z3JKA1oOCXoKPgF6kAY8zZeB7i09daW2SM+QaI9GtRIidJY/wiFRML5B4O/XbA6f4uSORkKfhF\nKmYBUM0Ysx7Pc5t/8HM9IidNF3dFREKMevwiIiFGwS8iEmIU/CIiIUbBLyISYhT8IiIhRsEvIhJi\nFPwiIiFGwS8iEmL+H4TZ0mCR1NNwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc610709690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def mueff(mu, rin_e, a_e):\n",
    "    return mu  + rin_e*a_e\n",
    "\n",
    "def Deff(rin_e, a_e):\n",
    "    return a_e**2 * rin_e\n",
    "\n",
    "a_es = np.logspace(-2,0,100)\n",
    "\n",
    "pl.plot(a_es, [snif.r0(prms, model=snif.PIF(), a_e=a_e) for a_e in a_es], label=\"shotnoise\")\n",
    "pl.plot(a_es, [daif.r0(prms, model=daif.PIF(), mu=mueff(prms[\"mu\"], prms[\"rin_e\"], a_e), D=Deff(prms[\"rin_e\"], a_e)) for a_e in a_es], label=\"DA\")\n",
    "pl.xlabel(\"a\")\n",
    "pl.ylabel(\"$r_0$\")\n",
    "pl.xscale(\"log\")\n",
    "pl.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stationary voltage distribution\n",
    "\n",
    "We first define the voltage axis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "vs = np.linspace(-0.2, 1, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot the stationary probability density $P_0(v)$ for $\\mu > v_T$ and $\\mu < v_T$. One can see that the density at the threshold is only non-vanishing if trajectories can cross the threshold even between input spikes (by drifting)... "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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f8LrO9fz9teM716vqi1LAuzsH29McCAvig+1p9rWmgoK9vbOgDo6H57Xn7wuW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\nIpKjpCAiIjlKCiIikqOkICIiOf8fbpDZgbDPNukAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc6106dfc10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.plot(vs, [snif.P0(prms, model=snif.LIF(), v=v, mu=1.5) for v in vs], label=\"mu = 1.5\")\n",
    "pl.plot(vs, [snif.P0(prms, model=snif.LIF(), v=v, mu=0.5) for v in vs], label=\"mu = 0.5\")\n",
    "pl.xlabel(\"v\")\n",
    "pl.ylabel(\"P(v)\")\n",
    "pl.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This can be quantified by looking at $\\alpha$, the fraction of trajectories that cross the threshold due to input spikes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xu9GDWb91N9cm0Q2LUd9Hci5QBLQH8oGHzKxF0Haqu+dTcWjsBjM7rfLGXnHx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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc60d934190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mus = np.linspace(0.5, 1.5, 100)\n",
    "pl.plot(mus, [snif.alpha(prms, model=snif.LIF(), mu=mu) for mu in mus])\n",
    "pl.xlabel(r\"$\\mu$\")\n",
    "pl.ylabel(r\"$\\alpha$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a perfect integrate-and-fire (PIF), there is no leak term, so the two regimes are above or below $\\mu = 0$, respectively:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PSaHSde4OrusPT/T2SCw9T+FwUphWX0PKoeNQ72hHKCJjiJJCpTuYTgoNuUmh5ogZzQDT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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc60d8a4c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.plot(vs, [snif.P0(prms, model=snif.PIF(), v=v, mu=0.5) for v in vs], label=\"mu=0.5\")\n",
    "pl.plot(vs, [snif.P0(prms, model=snif.PIF(), v=v, mu=-0.5) for v in vs], label=\"mu=-0.5\")\n",
    "pl.xlabel(\"v\")\n",
    "pl.ylabel(\"P(v)\")\n",
    "pl.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Power spectrum and susceptibility"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The spectral quantities are expressed in terms of (confluent) hypergeometric functions. The only library I found (in either C/C++ or Python) that supports these with complex-valued arguments is mpmath, which is excellent but not too fast. We thus provide a small C library and its Python interface in analytics.specfunc. To make it available to the analytics implementations, it needs to be compiled. Let's see whether this has already happened..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Library has been loaded :)\n"
     ]
    }
   ],
   "source": [
    "import analytics.specfunc as sf\n",
    "if sf.lib is None:\n",
    "    msg = \"\"\"Library not loaded, you probably need to go to %s \n",
    "and compile it (e.g: cc -fPIC -O2 --shared -o libspecfunc.so specfunc.c).\n",
    "Until then, I fall back to the mpmath implementation\"\"\"\n",
    "    print msg % sf.libdir\n",
    "else:\n",
    "    print \"Library has been loaded :)\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The frequency range to be considered (including 0 would give division-by-zero issues):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "fs = np.linspace(1e-4, 10, 500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at power spectra for different input rate/avg. spike weight combinations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/+0wJoy37N8HQyRyuDQBoaHPpc0pLS+nfvz/jx4/XKAYpwDlHWVkZpaWlTJgw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\nnRN4ilhw0WIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc60dc78790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.plot(fs, snlif.powspec(prms, fs=fs, rin_e=18.0, a_e=0.05), label=\"rin = 18, a = 0.05\")\n",
    "pl.plot(fs, snlif.powspec(prms, fs=fs, mu=-0.1, rin_e=9, a_e=0.1), label=\"rin = 9, a = 0.1\")\n",
    "pl.plot(fs, snlif.powspec(prms, fs=fs, mu=-0.1, rin_e=4.5, a_e=0.2), label=\"rin = 4.5, a = 0.2\")\n",
    "pl.xlabel(\"f\")\n",
    "pl.ylabel(\"power\")\n",
    "pl.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The power spectrum of a shot-noise-driven IF neuron vs the diffusion approximation (the implementation of the DA-spectral quantities is quite small, due to the lack of efficient implementations for the parabolic cylinder functions):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/EYFmoN73fF+7D33/h3m7D/aufDioCHaSZs+TNot2odn0ROcwRpOCOorXC4e2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\nAGh84yadE/noAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc60d6f7e90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.plot(fs, dalif.powspec(prms, fs=fs, mu=mueff(0.5, 25.0, 0.1), D=Deff(25.0, 0.1)), label=\"DA\")\n",
    "pl.plot(fs, snlif.powspec(prms, fs=fs, mu=0.5, rin_e=25.0, a_e=0.1), label=\"shotnoise\")\n",
    "pl.xlabel(\"f\")\n",
    "pl.ylabel(\"power\")\n",
    "pl.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the same for the susceptibility (the firing rate response) to a current signal:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VeR5rP9dizd2YzkNzt3FpfAC3l75rtcEne3gLW1A4jH8SjqyBTW/W69Kfjkyk\n0mZ4fdUhZ0SmlHKQugxX/VREPgFCgRQRWSEiX2PNZnbzjQWcwxjD7G8P8Kt52xnZJZL/xC1DinNh\n4tP1ngDWLPW/FRJGw5e/g9N1n58QFxHE1X3b87+1aWQVaK1BKXflU4cyDVsox0OVVdj4zYIdfLgp\ngyt7x/CvMT74vPYKDLgV2vdzdXhNQwSu/j94eQQsehBumlvnhPjA+K4s2n6cl74+wJPXNNOlQpTy\ncLUmBmPMN00RSHOQfrKY+9/fwuYjedx3WRceuCwRr9cvtzevPOXq8JpWeII1t+GLR2Hre9D/5jpd\nlhAZzPUDO/LeuiP8bHQiHVoHOjlQpVR91aUpaZX9sUBE8qscBSKS7/wQXc8Yw0ebMpj0/Er2Zxby\nwoz+PHRFN7zWv2ItFTHpb1ZyaGmG3AmdLoHPfwW5B+p82b3jkgD4v6/2OysypVQj1GWC20j74/lr\nJrWItZL2nMjnpv+u45cfbiO5XRiL7x/F1X3bw4md1hIR3a60NrVpiby84drZ1uNHP4WKsjpd1qF1\nIDcPi2Pe5gz2ntB5DUq5m/rMY/jBWgg1nfMUh3KKePSj7Vz1f6vYfTyfP0zpyZw7hxEbHgTlZ+Cj\nn0Bga7jmhZbR4XwhrTpav4Njm+HrP9f5snsvSyI0wIfff7xT11BSys3UpfP5rGo9hSLiAwx0bDiu\nVV5p49t92Xy4MYMlu0/g6+3FLUPjeGB8V9oE+1mFjIHFD0P2HrhlPgQ3ww14HC15Cgy8DVY/Bx0H\nQ4/JtV4SHuzHIxO68ZsFO/lk2zGm9KtxO3CllAvUmhhE5DHgcSDQ3qdw9s/jMmC2E2NzuvJKG2m5\nxWxKO8l3B0+yYm8Wp4rLaRPky11jOnP7JQlEhfpXv2j9f2HLOzDqYegyzjWBu6OJf4Pj22HBzyFy\nOUR1q/WSGwfH8cGGdP78WQqXdY8mNMDDlhFRqpmqdaOecwVFnjbGPObkeOqkoRv1/P7jnRzKKaKw\ntIK84nLSTxZTYbM+f2SIH5d0ieSavu0ZlRSFn08NrWypy+Dd6yHpCrjxPfBqRns4N4XTR2H2GAho\nBT9bbj3WYmt6HtNeWs3MYZ14akqvJghSqZarrhv11Kcp6XERuRYYibWj20pjTP13bnGh7IJSCksr\nCPH3oX2rQCb1iiEhMph+sa3pEh2CXKyvIH0DfHALRPewd7hqUviBVh3g+rfgf9fA/DvtyfPiy4P0\ni23NbSOkiYPWAAAdNklEQVTieWP1YcYnt2VUUlQTBauUupD61BheAroAc+ynbgAOGGN+4aTYLqjJ\nt/Y8tgX+N9VaI+iOJRDazHdlc7YNr8Jnv4TBP4Urn621c76kvJLJL6yioKScJQ+MpnWQXxMFqlTL\n4rCtPauo9yJ6IjJRRPaKSKqIPHqBMmNFZKuI7BIR95tMd2glvHk1+IfBzIWaFOpi8E9hxH1Wglj9\nXK3FA3y9+deP+pFbWMZvF+ooJaVczWmL6ImIN/AiMAlIBmaISPJ5ZVoDLwHXGGN6Au61XvXmt+Gd\n66wmkp8sgTbxro6o+Rj/FPSaDl89Cdvn1lq8d8dWPHi5tVzGm2sOOz08pdSF1aeP4ewieuux+hiG\nABvtC+xhjLnmvPJDgFRjzEEAEXkfmALsrlLmJmC+MeaI/R5ZDfoUjlZaAEt+A5vfgsSxMP2Nljmz\nuTG8vGDqS1CYCQvvAv9Qaxe4i7hrTGe2pefxp89S6NY2lBFddCiwUq5Qnz6GMRd7/fw1lURkOjDR\nGPNT+/NbgaHGmHuqlHkO8MWaIxEKPG+M+d8F3v9O4E6AuLi4gWlpaXWKu16Mgf1Lrfbx0+lwyf1w\n2e/Auz75U1VTkg9vT7U29pkxB7qMv2jxwtIKpr24mpzCUj7+xUjiIoKaKFClPJ/D+xjsX/yHAV/7\nz+uBzcaYbxqx0N7ZSXJXAROA34lI1wu8/2xjzCBjzKCoKAePXLHZ4MByeHMyvHc9+PhbncyXP6VJ\nobECwuCWj6x5De/fDIe+vWjxEH8fZs8chM3ALa+t0019lHKB+iyJ8TNgHvAf+6mOwMWGqx7F6oc4\nq6P9XFUZwBJjTJExJgf4Fuhb15gapbQADq+22sD/PRDengY5+6xRNHetgbihTRJGixDYBm79GNok\nwHs3WEn4IhIig3nrjiHkFpZyy6vrOFlUtzWYlFKOUZ+mpK1Y/QbrjDH97ed2GGN6X6C8D7APGIeV\nEDYANxljdlUp0wP4N1ZtwQ+rFnKjMWbnxWJp8HDVuTMhaw+UnIbCE9Y5Lx+IGw4DZlpLO/j4X/we\nquEKs75PwNPfqHXpjLUHcrntjfUkRoXw1h2DiQ4NaKJAlfJMzpjgVmqMKTs7Ccz+xX/BrGKMqRCR\ne4AlgDfwujFml4jMsr/+ijEmRUS+ALYDNuDV2pJCowRFQHR3a+hpm3ho2xM6jajTDF3lACHRcNsi\neGe6laSnvgx9b7hg8eGdI/jvzEHMemcT1760hrfuGELnqJAmDFiplqk+NYZngDxgJnAvcDew2xjz\nG+eFV7Mmn+CmHKu0AObMgMOr4Mq/w5CfXbT4tvQ87nhzAzZjePGmATpaSakGcsYEt0eBbGAH8HNg\nMfDbhoWnWjT/ULh5njV8dfHD1tBgm+2CxfvGtmb+3SMID/bj5tfW8dxX+6i06SQ4pZylPjWGYKDE\nGFNpf+4N+Btjip0YX420xuAhbJXW1qDrZ0OPq2HabPC78PDUotIKfrtwJwu2HGVIQjhPX9tbm5aU\nqgdn1BiWAVU36A0EvqpvYEqd4+UNk56BCU9DyiJ462oozL5g8WB/H/75o778fXof9hzPZ9JzK/nX\n0n0Ul1U0YdBKeb76JIYAY0zh2Sf2n3X2kWocERh+N9zwNmTuglcvsybDXbC4cP2gWJb9ciyTesfw\n/LL9jH5mBW+sPkRJeWUTBq6U56pPYigSkQFnn4jIQOCM40NSLVKPq+H2z6CyHF69HHbMu2jxqFB/\nnr+xPx/dNZyk6BCe+nQ3l/x1Oc8u2cvx0/rPUqnGqE8fw2DgfeAY1i5uMcANxphNzguvZtrH4MEK\nMuHDH8ORtTDiXhj3ZJ1mn685kMMbqw/zVUomAEPiw7mqTzsm9owhOkznPygFde9jqHNisN/UFzi7\nZ+NeY0x5A+NrFE0MHq6iDJY8Dhv+CwljrMlwwRF1ujT9ZDEfbc5g8Y7j7Mu0Wj67tg1hWGIEQxMi\n6Nk+jLjwILy8Lr5HhFKeyOGJQUSuB74wxhSIyG+BAcCfjDGbGxdq/WliaCG2vAOLHoLgKJj+er2X\nKdmXWcBXKZmsPZDLxsOnOGPvgwj09aZbTCido0Lo0DqA9q0Dad86kJhWAbQO9CUs0JcA34vvPKdU\nc+SMxLDdGNNHREYCfwSeBX5vjGnyRYU0MbQgRzfDh7fB6QwY9zsYcX+DtlUtr7Sx+1g+e08UkHIi\nn5Tj+aTlFpOZX0JNUyICfL1oFehLq0BfQgN8CfH3OXcE+/sQEuBDaJWfQ/y9CfGvUi7Ah2B/b/x9\nNMEo9+GMxLDFGNNfRJ4Gdhhj3jt7rrHB1pcmhham5DR8ej/sWgCdx8G0/0CIY1bYLa+0kZlfwrG8\nEk7kl3D6TDmni8usR/tRUFJBUWkFBaXWY2FJBUVldRsB5eftdS5JWInDm/BgP9q1CqR964Bqj23D\nAvDWJi7lRM5IDIuwFsO7HKsZ6Qyw3hjTNKuhVqGJoQUyBja9AV88Zq1tde1/IfGiW4Q4lc1mKCqr\noNCeLKzkUUlh6feJpLC0gkL7uaLSSgpKKigsLSensIzjeWd+kFz8vL3oFBFEYlQwnaNCSIwKoXNU\nMN1iQgny0+XfVeM5IzEEAROxagv7RaQd0NsY82XjQq0/TQwtWOYuq2kpZz+MfADGPg4+fq6Oqt6M\nMRSUVnA8r4Rjp89wPK+EtJNFHMwu4mB2IWm5xVTY27hErKXIe7ZvRc/2YfajFeHBze9zK9dyRmKI\nq+n82W05m5ImhhaurMhaSmPz/6Btb7h2NrRNrv26ZqSi0kb6qTPszywg5XgBu46dZtexfI7mfT9H\no1NEEAM7tTl3dI0O1dFW6qKckRh2YC2zLUAAkIA1ZLVnYwJtCE0MCoC9n8Mn91p9EOOegGF3N6hj\nujnJKy5j97F8dhw9zZYjeWxMO0VOYSkAoQE+9I9rw6BObRjROYK+sa3x9fbs34eqH6fMYzjvDQYA\nd5/d07kpaWJQ5xTlWB3TexZB/CiY+hK0rrFy65GMMaSfPMPGtJNsSjvFprRT7M0swBgI8vNmSEI4\nl3SOZHjnCJLbhWmNooVzemKwv8kFd3BzJk0MqhpjYOu78PmjVoP8hD9D/1utn1ugvOIyvjuYy+rU\nXNYcyOFAdhEAbYJ8Gd45ghGdIxnTNYrYcF3qrKVxRlPSQ1WeegEDgXBjzISGhdhwmhhUjU4dhoW/\ngLRVkDgWrn7e2qmvhTtxuoS1B3OsRJGaw7HTJQB0jgpmTNdoxnaLYkhCuE7qawGckRieqPK0AjgM\nfGSMKWlQhI2giUFdkM0Gm16HpU9YNYnxT8Dgn3l830NdGWM4mFPEir3ZrNibxbpDJymrsBHg68Xw\nxAjGdrMSRaeIYFeHqpzAqU1JIuIFhBhj8mspNxF4HmvP51eNMX897/WxwMfAIfup+caYP9T2/poY\nVK3y0mHRA5D6FcQOgyn/hsgkV0flds6UVfLdwVxW7M3im33ZHM619t2KjwhibLdoxnSNYlhiBIF+\nWpvwBM6oMbwHzAIqgQ1AGPC8MebvFyjvDezDmhCXYb9mhjFmd5UyY4GHjTGT6xSEnSYGVSfGwLb3\nraGt5Wdg7KPWiq3evq6OzG0dzik6lyTWHsylpNyGv48XwxIjGNstirHdokmI1NpEc+WMxLDVGNNP\nRG7Gmvn8KLDJGNPnAuWHA0+e7YMQkccAjDFPVykzFk0MytkKMq29pVM+gehkmPwviBvm6qjcXkl5\nJesOnbQSxd5sDuZYndidIoIY29VKElqbaF7qmhjqM8/e177s9lTg38aYcrn4qI8OQHqV5xlATQvu\njRCR7VjLbTxsjNlVj5iUql1oW2uHuD2fweJfwesTYMBMGP8UBIW7Ojq3FeDrzZiuUYzpGgVXQ1ru\n930TH2xM5621aVqb8FD1qTHcB/wa2AZcBcQB7xhjRl2g/HRg4tl5DiJyKzDUGHNPlTJhgM0YUygi\nV2I1TdXYECwidwJ3AsTFxQ1MS0ur40dUqorSQvjmb7D2RQhsDVf8CfrOaLFDWxtKaxPNk8Oaks5b\nCkOwZj+DNWTVGzi7WU9e1c7oujQl1fBeh4FBxpici8WkTUmq0U7shM8egvR10GkkTP4nRHWr/TpV\noyO5xazYl8WKvdmsOZCjfRNuypGJ4Wu+XwrjbOGzf15VPf+mMeZ/Va7zwep8HofVTLQBuKlqU5GI\nxACZxhgjIkOAeUAnU0tQmhiUQ9hssOVtWPp7a/2l4XfD6EfAP9TVkTVrJeWVrD90kq8vUJsY3TWK\noYkRhPjrirFNrUlmPtchiCuB57BqFq8bY/4sIrMAjDGviMg9wF1Y8yLOAA8ZY9bUdl9NDMqhCrPh\nqyes2dMhba2+hz436NwHB6mpNuHtJfTt2IqRXSIZ0SWS/nGtdVOjJuAWicFZNDEop8jYCJ//Co5u\ngg6D4MpnoMNAV0flUUrKK9mcdorVB6yZ2Nsz8rAZa8e8wfHhXNIlkks6R5LcPkw3LXICTQxKNYTN\nBtvfh6+ehMJM6HcLjPu9NbJJOVx+STnrDp5kdWoOaw7ksC+zEIBWgb4MT4xgRJcIBseH062tLinu\nCJoYlGqMknxY+SysfQl8AmDMr2DorGa5KVBzkpVfwpoDufZEkXtu/4mwAB8Gx4czOCGcIQnh9Grf\nCj8fbeqrL00MSjlCTioseRz2L4E2CdbaS8lTdXhrEzDGkHHqDBsOn2T9Ies425Ed4OvFgLg2DI4P\nZ2hCOP3j2ujQ2DrQxKCUI+3/Cpb+DrJ2Q8fB1vwHnT3d5LILSqslipQT+RgD3l5Cj3ahDIhrQ/+4\n1vSPbUOniCBqmYTb4mhiUMrRbJWw9T34+s9QcBy6T7ZGMEV2cXVkLdbpM+VsTjvFhsMn2Zqex7b0\nPIrKKgFr/4n+cW3oH9ua/nFt6BPbirCAlr1OliYGpZylrMjqe1j9HFSUwMDbrQX6giNdHVmLV2kz\n7M8qYMuRPLYcOcWWI3nsz7I6tEUgKTqEfrGt6d2xNb07tKJ7TGiL2odCE4NSzlaYBSv+CpveBN8g\na+XWYXdBQJirI1NVnD5TzvaMvHPJYmt6HqeKrQUbfLyEpLah9O4QRu8OrejZoRXJ7cI8NlloYlCq\nqWTvg2VPWftOB4bDyAdhyM/AN9DVkakaGGM4mneGnUdPs+PoaXYczWfn0dOcLCoDrP6KpOgQenVo\nZSWL9mF0bxfmETO1NTEo1dSOboblf4IDyyAkBsY8Av1n6hDXZsAYw7HTJezIOH0uYew8eppce7IA\niAsPontMKD3ahdGjnfUY2yaoWc2v0MSglKscXg3L/whH1kLrOBj7mH2JDc9snvBUxhiOny4h5Xi+\ndZwoIOV4PodzirDZvzaD/bzpFhNK93ZhVsKw/+yutQtNDEq5kjGQusxKEMe3QmRXK0EkT9U1mJq5\nM2WV7MssYM+JfFKOF5xLHPklFefKxIYH0jU6lKS2oSRFh9C1bShdokNcPtdCE4NS7sAYSPnUGuKa\nvQeiulsruPacpjUID1K1drHHXrPYn1nIwZxCyiut71gRiG0TRFJ0CEltQ+naNoSk6KZNGJoYlHIn\ntkrYvRC+fdaaJBfRBUY9DL2vB2/3bHZQjVdRaeNwbjH7MwvYl1nI/qyCOieMztHBBPk59t+GJgal\n3JHNZo1e+uYZyNwBbeJh1C+hz43aSd2ClFfaSMstYn9mIfsyC9mXVUDqeQkDoH2rADpHh9AlOoTO\nUdbjgLg2DV4nShODUu7MGNj3hbXN6LEt0CoWRj5grebqG+Dq6JSLVE0YqVmFHMguJDW7kANZRZwp\nt2Z07/7DhAbXJDQxKNUcGAOpX1kJImODtVHQ0Fkw6A5rT2qlAJvNcOz0GY7kFjOiS8Nn2GtiUKo5\nMQYOfQOrn4cDy8EvFAbdBsPuhrD2ro5OeYi6JgYdN6eUOxCBxLFw6wL4+bfQdQKsfRGe6wMLfwHZ\ne10doWpBNDEo5W7a9YXpr8F9W2DQ7bDzI3hxCMyZAWlrrdqFUk7k1MQgIhNFZK+IpIrIoxcpN1hE\nKkRkujPjUapZaRMPV/4dHtwFYx6FI9/BGxPhv5fCtg+goqzWWyjVEE5LDCLiDbwITAKSgRkiknyB\ncn8DvnRWLEo1a8ERcOlj8OBOuOqf1rLfC+6E53pZw14Ls10dofIwzqwxDAFSjTEHjTFlwPvAlBrK\n3Qt8BGQ5MRalmj+/YBj8E7h7HdzyEcT0tmZU/6un1Q9xYoerI1QewplTLjsA6VWeZwBDqxYQkQ7A\nNOBSYLATY1HKc3h5QZfx1pG9D9a9AtvmwNZ3IH6UNdy160SdUa0azNWdz88BvzbG2GorKCJ3ishG\nEdmYna1VZ6UAiOoKk/8JD+2Gy/8AJw/BBzfD832sZqaCE66OUDVDTpvHICLDgSeNMRPszx8DMMY8\nXaXMIeDsYuaRQDFwpzFm4cXurfMYlLqAygrY9zlseA0Ofg1ePtD9Khj0E0gYbQ2LVS1WXecxOLOu\nuQFIEpEE4ChwI3BT1QLGmISzP4vIm8Ci2pKCUuoivH2gx9XWkXsANr4OW9+F3R9DRJI1o7rfDAhs\n4+pIlRtzWlOSMaYCuAdYAqQAc40xu0RklojMctb7KqXsIjrDhD/DQykw9RVriY0lj8E/elid1UfW\n6ZwIVSNdEkOpluT4dqsWsX0ulBdZGwj1vwX6zoCQaFdHp5xM10pSSl1YaSHsWgBb3oH076y+iKQJ\nMOBW6HK5jmjyUO7Qx6CUclf+IVYSGHCrNeR1y9uw7X3Y+5m1wmvfGdD/Vojs4upIlQtojUEpZaks\nh/1fwua3rUdTCbHDoO+N0HOqdlh7AG1KUko1XMEJ+6S59yBnH3j7WSu+9rkRki4HH39XR6gaQBOD\nUqrxjIHjW63O6h0fQlE2BLSGXtdCnxsgdqjOjWhGNDEopRyrsgIOroDt70PKIqg4A607WQmiz48g\nMsnVEapaaGJQSjlPaYGVHLZ/YO08Z2zQtjf0mgY9p0F4oqsjVDXQxKCUahr5x2H3Qtg5HzLWW+fa\n9bOam3pOg9Zxro1PnaOJQSnV9PLSrfkRuxbAsc3WuQ6DrCSRPBVadXBtfC2cJgallGudPGRPEvO/\n3ysidph9LafJ1g51qklpYlBKuY+cVCtJ7F4ImTutczG9obs9SUQn6+imJqCJQSnlnk4ehD2fQcqn\nkL4eMFZndffJVm2iwyBrMyLlcJoYlFLuryDTWoYjZZE1uslWASEx1h4SPSZDp5Hg4+fqKD2GJgal\nVPNyJs9aiiPlU0j9CsqLwS8EOl9qbVWadIWuANtIuoieUqp5CWxtTZTr8yMoP2NNptu3xDpSPrXK\ndBhoJYmuEyCmj/ZLOInWGJRS7s0Ya1TTviWwfwlkbAQMhLazahFdJ0LiGPALdnWkbk+bkpRSnqkw\nG1KXwr4vIHU5lBWAtz/Ej4Qu46DzZRDVXWsTNdDEoJTyfBVlcGSNVZtI/cpaCRYgrIPVN9F5HCSO\nhaBwV0bpNjQxKKVanrx0OLAcDiyz+ihKTgMCHQZYSaLzZdBxcIvdoc4tEoOITASeB7yBV40xfz3v\n9SnAHwEbUAE8YIxZVdt9NTEopWpVWQHHtlhJInUZHN1oLfbnHwYJo60aRcJYiOjcYpqdXJ4YRMQb\n2AdcDmQAG4AZxpjdVcqEAEXGGCMifYC5xpjutd1bE4NSqt7OnIJD31pJ4sByOJ1unQ9tbyWKhNGQ\nMMqjF/1zh+GqQ4BUY8xBe0DvA1OAc4nBGFNYpXww0PzatZRSzUNgG0ieYh3GWDOwD30Dh1Za/RPb\n37fKtYm3J4kxED8KQtu6NGxXcGZi6ACkV3meAQw9v5CITAOeBqKBq5wYj1JKWUSsJqSIzjDoDitR\nZKVYNYpD38Kuj2Hz/6yyUd2tRBE/CjqNgOBI18beBFzeA2OMWQAsEJHRWP0N42sqJyJ3AncCxMV5\nblVPKeUCItA22TqGzQJbJRzf9n2i2PIOrJ9tlY3saiWIuBHWY+tY18buBM7sYxgOPGmMmWB//hiA\nMebpi1xzEBhijMm52L21j0Ep1aQqyqz9JdLWwJG1cOQ7KM23XmsVa08Uw63HyK5u25ntDn0MG4Ak\nEUkAjgI3AjdVLSAiXYAD9s7nAYA/kOvEmJRSqv58/CBumHWAVaPI3GVPFGuszuztH1ivBUVa5Tpd\nYj3G9AZvX9fF3gBOSwzGmAoRuQdYgjVc9XVjzC4RmWV//RXgOmCmiJQDZ4AbTHOcWKGUalm8vKFd\nH+sYNsvqo8g9AGmrrRpF2mrYs8gq6xNozaPoOBhih0DHIRAS5dr4a6ET3JRSyhlOZ0D6OmvPifT1\ncGK7taw4QJsEK0mcTRTRyU0y6c4dmpKUUqrlatXROnpdZz0vPwPHtkKGPVEc+Pr75iffYKtWETvU\nShYdBrp09JMmBqWUagq+gdBpuHWA1fyUlwbpG+zJYh2s+heYSuv1NvFWgjh7tOtr3aMJaGJQSilX\nELG+/NvEQ5/rrXNlRdYyHkc3WUf6etj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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc60d84c7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.plot(fs, np.abs(dalif.suscep(prms, fs=fs, mu=mueff(0.5, 25.0, 0.1), D=Deff(25.0, 0.1))), label=\"DA\")\n",
    "pl.plot(fs, np.abs(snlif.suscep(prms, fs=fs, mu=0.5, rin_e=25.0, a_e=0.1)), label=\"shotnoise\")\n",
    "pl.xlabel(\"f\")\n",
    "pl.ylabel(\"|susceptibility|\")\n",
    "pl.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}

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