demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": false,
    "level": 1
   },
   "source": [
    "<div class=\"clearfix\" style=\"padding: 10px; padding-left: 0px\">\n",
    "<a href=\"http://briansimulator.org/\"><img src=\"http://briansimulator.org/WordPress/wp-content/ata-images/brian1.png\" alt=\"The Brian spiking neural network simulator\" title=\"The Brian spiking neural network simulator\" width=\"200px\" style=\"display: inline-block; margin-top: 5px;\"></a>\n",
    "<a href=\"http://mybinder.org/\"><img src=\"https://mybinder.org/static/logo.svg\" alt=\"binder logo\" title=\"binder\" width=\"375px\" class=\"pull-right\" style=\"display: inline-block; margin: 0px;\"></a>\n",
    "</div>\n",
    "\n",
    "# Brian demo\n",
    "\n",
    "The code below shows a demonstration of Brian in action with a simple graphical interface. Run the cell below by clicking on it and hitting `CTRL+ENTER`. You can change the parameters of the model with the sliders, and immediately see the change in behaviour.\n",
    "\n",
    "The model is a group of $N$ source neurons that fire Poisson spikes with a rate $R_\\mathrm{max}(1+\\sin(2\\pi f t))/2$, connected via synapses to a target neuron. Each source neuron has a probability $p$ of being connected, and synapses have a certain fixed weight $w$. The target neuron has two variables, the membrane potential $V$ and the adaptation potential $V_t$ that evolve according to the differential equations:\n",
    "\n",
    "$$\\tau\\frac{\\mathrm{d}V}{\\mathrm{dt}}=-V$$\n",
    "\n",
    "$$\\tau_t\\frac{\\mathrm{d}V_t}{\\mathrm{dt}}=1-V_t$$\n",
    "\n",
    "Each time the event $V>V_t$ occurs, the neuron spikes and $V$ is reset to 0, while $V_t$ increases by $\\delta_t$.\n",
    "\n",
    "This model is implemented with the following code:\n",
    "\n",
    "```python\n",
    "G = PoissonGroup(N, rates='R_max*0.5*(1+sin(2*pi*f*t))')\n",
    "eqs = '''\n",
    "dV/dt = -V/tau : 1\n",
    "dVt/dt = (1-Vt)/tau_t : 1\n",
    "'''\n",
    "H = NeuronGroup(1, eqs, threshold='V>Vt', reset='V=0; Vt += delta_t', method='linear')\n",
    "H.Vt = 1\n",
    "S = Synapses(G, H, on_pre='V += w')\n",
    "S.connect(p=p)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from brian2 import *\n",
    "from brian2tools import *\n",
    "import ipywidgets as ipw\n",
    "prefs.codegen.target = 'numpy'\n",
    "\n",
    "def model(N=20, R_max=150, f=10, w=0.1, p=0.5, tau=5, tau_t=50, delta_t=0.1):\n",
    "    # Get parameters\n",
    "    R_max = R_max*Hz\n",
    "    f = f*Hz\n",
    "    tau = tau*ms\n",
    "    tau_t = tau_t*ms\n",
    "    duration = 200*ms\n",
    "    \n",
    "    # Simulation code\n",
    "    G = PoissonGroup(N, rates='R_max*0.5*(1+sin(2*pi*f*t))')\n",
    "    eqs = '''\n",
    "    dV/dt = -V/tau : 1\n",
    "    dVt/dt = (1-Vt)/tau_t : 1\n",
    "    '''\n",
    "    H = NeuronGroup(1, eqs, threshold='V>Vt', reset='V=0; Vt += delta_t', method='linear')\n",
    "    H.Vt = 1\n",
    "    S = Synapses(G, H, on_pre='V += w')\n",
    "    S.connect(p=p)\n",
    "    # Run it\n",
    "    MG = SpikeMonitor(G)\n",
    "    MH = StateMonitor(H, ('V', 'Vt'), record=True)\n",
    "    run(duration)\n",
    "    \n",
    "    # Plotting code\n",
    "    figure(figsize=(15, 4))\n",
    "    subplot(131)\n",
    "    brian_plot(MG)\n",
    "    title('Source neurons (Poisson)')\n",
    "    subplot(132)\n",
    "    plot(zeros(N), arange(N), 'ob')\n",
    "    plot([0, 1], [S.i, ones(len(S.i))*N/2.], '-k')\n",
    "    plot([1], [N/2.], 'og')\n",
    "    xlim(-0.1, 1.1)\n",
    "    ylim(-1, N)\n",
    "    axis('off')\n",
    "    title('Synapses')\n",
    "    subplot(133)\n",
    "    plot(MH.t, MH.V[0], label='V')\n",
    "    plot(MH.t, MH.Vt[0], label='Vt')\n",
    "    legend(loc='upper left')\n",
    "    title('Target neuron')\n",
    "    \n",
    "layout = ipw.Layout(width='100%')\n",
    "style = {'description_width': 'initial'}\n",
    "ipw.interact(model,\n",
    "             N=ipw.IntSlider(value=20, min=5, max=100, step=5, continuous_update=False,\n",
    "                             description=\"Number of source neurons\", style=style, layout=layout),\n",
    "             R_max=ipw.FloatSlider(value=300, min=0, max=500, step=10, continuous_update=False,\n",
    "                                   description=r\"Source neuron max firing rate (Hz)\", style=style, layout=layout),\n",
    "             f=ipw.FloatSlider(value=10, min=1, max=50, step=1, continuous_update=False,\n",
    "                               description=r\"Source neuron frequency (Hz)\", style=style, layout=layout),\n",
    "             p=ipw.FloatSlider(value=0.5, min=0, max=1, step=0.01, continuous_update=False,\n",
    "                               description=r\"Synapse probability\", style=style, layout=layout),\n",
    "             w=ipw.FloatSlider(value=0.3, min=0, max=1, step=0.01, continuous_update=False,\n",
    "                               description=r\"Synapse weight\", style=style, layout=layout),\n",
    "             tau=ipw.FloatSlider(value=5, min=1, max=50, step=1, continuous_update=False,\n",
    "                                 description=r\"Target neuron membrane time constant (ms)\", style=style, layout=layout),\n",
    "             tau_t=ipw.FloatSlider(value=30, min=5, max=500, step=5, continuous_update=False,\n",
    "                                   description=r\"Target neuron adaptation constant (ms)\", style=style, layout=layout),\n",
    "             delta_t=ipw.FloatSlider(value=1.0, min=0, max=20, step=0.1, continuous_update=False,\n",
    "                                     description=r\"Target neuron adaptation strength\", style=style, layout=layout),\n",
    "            );"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}