{ "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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"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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\nn0jkRH5CPJFyc/dHzWySmU0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"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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"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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hQmPwunFkfJ1tJdn2NExugqlzhz42RzLlRCOGTWiEpddCRzgb5kysg0WT4a2D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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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ZSY5KRMR7ShhdVB2Zzzs3w8/qHauZO3ouuem5SY5KRMR7ShhdVFXXQHa6n43lG9hbvZcL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\nnyziwdPnMMzsIjPbbGZbzWx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"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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"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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kpVoGTQzubPP/rC/47lfbm5GOM6ZrFCH+tYwy9vGDgbfB/i/h1OFGh9GxTRDxEUHaAa1U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\nraGt5Wdg7KPWiq3evq6OzG0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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 }