Spiek response demo

demo.ipynb

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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline --no-import-all\n",
      "import numpy as np\n",
      "import pylab as plt\n",
      "from matplotlib.colors import LogNorm\n",
      "plt.rc('font', family='serif', size=20)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "WARNING: pylab import has clobbered these variables: ['plt']\n",
        "`%matplotlib` prevents importing * from pylab and numpy\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.io\n",
      "import urllib\n",
      "from IPython.display import HTML"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Get the data"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Kara, Prakash, Pamela Reinagel, and R. Clay Reid. \"Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons.\" Neuron 27.3 (2000): 635-646.\n",
      "\n",
      "Anesthetized cats have their heads placed in a vise and are made to watch sequence of images in small screen in front of them over and over again. Frame rate is 30Hz. Neural responses are recorded from different parts of the brain. We will be looking at the response of a LGN neuron (part of brain between retina and cortex)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "HTML('<iframe src=http://i.chzbgr.com/maxW500/408125184/hE96F7C11/ width=354 height=271></iframe>')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<iframe src=http://i.chzbgr.com/maxW500/408125184/hE96F7C11/ width=354 height=271></iframe>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<IPython.core.display.HTML at 0x1069ebf90>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f = urllib.URLopener()\n",
      "f.retrieve(\"http://neurotheory.columbia.edu/~larry/book/exercises/c2/data/c2p3.mat\", \"data.mat\")\n",
      "f.close()\n",
      "!ls -l"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "total 16696\r\n",
        "-rw-r--r--  1 gajomi  staff   122906 Sep 21 19:44 Spike Reponse Demo.ipynb\r\n",
        "-rw-r--r--  1 gajomi  staff  8421376 Sep 21 19:45 data.mat\r\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The data consists of a time series of spike counts and stimuli. Some destructuring and assignment: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "datadict = scipy.io.loadmat('data.mat')\n",
      "spikes,stim = datadict['counts'][:,0],datadict['stim']\n",
      "delta = 1000*(1/30.)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Look at the data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "spikes.shape,stim.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "((32767,), (16, 16, 32767))"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = len(spikes)\n",
      "T_minutes = (N/30)/60\n",
      "T_minutes"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "18"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "steps = range(64)\n",
      "plt.plot(delta*np.array(steps),spikes[steps],'_',color = 'k',ms = 4,mew=3)\n",
      "plt.axis([0,2000,-.5,5])\n",
      "plt.ylabel('counts')\n",
      "plt.xlabel('time (ms)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "<matplotlib.text.Text at 0x107b00710>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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JyeFHJ0kjpNFoQEnf/VXo4RwLbAfc2KPuXuDHwIHAQSmDkiQVqwoJ5xnZdl2f+nb54UOP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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107ae6290>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(4,4)\n",
      "fig.set_size_inches(10,8)\n",
      "timesteps = range(3)\n",
      "someframes = [np.array(stim[:,:,t]) for t in timesteps]\n",
      "axs = [plt.subplot2grid((1,3),(0,i),colspan=1,rowspan=3) for i in range(0,3)]\n",
      "for ax,frame in zip(axs,someframes):\n",
      "    ax.imshow(frame,cmap = 'gray',interpolation='nearest',aspect=\"equal\")\n",
      "    ax.axis('off')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAlYAAADNCAYAAAB6mz62AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1055f4b50>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Look at the spikes a little closer (summary statistics)"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Spike count histogram"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "counts = np.array(range(10))\n",
      "counthist,_ =np.histogram(spikes, bins=counts)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.bar(counts[:-1],counthist,align='center',color = 'k')\n",
      "plt.ylabel('total instances')\n",
      "plt.xlabel('spikes per step')\n",
      "plt.axis([-.5,8,0,22000])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "[-0.5, 8, 0, 22000]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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IxVOwExGRiqdgJyIiFU/BTkREKp6CnYiIVDwFOxERqXgKdiIiUvEU7EREpOIp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\niIhUuv8H9NIM7fdr7+0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108741ad0>"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Inter-spike intervals"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So most time steps have no spikes. What is happening during these periods?"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Lagged correlations between spike counts"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "acorr = np.correlate(spikes-np.mean(spikes),spikes-np.mean(spikes),\"full\")/(N*np.std(spikes)**2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(2,1)\n",
      "fig.set_size_inches(12,5)\n",
      "ax[0].plot(delta*np.linspace(-N,N,2*N-1),acorr,'.',color = 'k')\n",
      "ax[0].axis([-N,N,-.2,1.1])\n",
      "ax[1].plot(delta*np.linspace(0,256,256),acorr[N-1:N+255],'.',color = 'k')\n",
      "ax[1].axis([0,delta*256,-.2,1.1])\n",
      "ax[1].set_xlabel('delay (ms)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<matplotlib.text.Text at 0x1086b56d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3cBNwFDZLpdsSJ73OtSwG3ItNruOt21TsSveP6R50g40FflXOtRURERERiUg+Jp2JYdO8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\nZmZmZmZmZmZmZmZmZmZmZmZmZtY+/gegprEma0HrIgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107ae6190>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What is happening every four seconds or so?"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Relationship between spikes and stimulus"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will consider a very simplified version of the ``decoding problem'', wherein we try to associate spiking events with events in the stimulus space by looking at the spike triggered average..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def sta(frames,spikes,lag):\n",
      "    laggedspikes = spikes[lag:-1]\n",
      "    weighted_frames = [float(s)*frame for s,frame in zip(laggedspikes,frames)]\n",
      "    return sum(weighted_frames)/len(laggedspikes)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "allframes = [np.array(stim[:,:,t]) for t in range(N)]\n",
      "lags = range(16)\n",
      "lagged_stas = [sta(allframes,spikes,lag) for lag in lags]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.imshow(lagged_stas[0],cmap = 'gray',interpolation = 'nearest',aspect=\"equal\")\n",
      "plt.colorbar()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "<matplotlib.colorbar.Colorbar instance at 0x108565f38>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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m88uWLWP58uVJtwYuRHGRjqNcGRnpmLGdYOr/Usw9CzHluV2Ax+M6lhEVQmQm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\nQgghhBBCCCGEEEIIIYQQYrDx/wEOycxaI0RCwQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107addfd0>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So, we see a bright spot here. Looks cool. Lets look at this as a function of the lag."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(4,4)\n",
      "fig.set_size_inches(10,10)\n",
      "timesteps = range(3)\n",
      "axs = [[plt.subplot2grid((4,4),(j,i),colspan=1,rowspan=1) for i in range(0,4)] for j in range(0,4)]\n",
      "for lag,axframe in enumerate(zip(sum(axs,[]),lagged_stas)):\n",
      "    ax,frame = axframe\n",
      "    ax.imshow(frame,cmap = 'gray',vmin=-.2,vmax = .5,interpolation = 'nearest',aspect=\"equal\")\n",
      "    ax.set_title(lag)\n",
      "    ax.axis('off')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x107cf3710>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "There seems to be a charateristic hotspot in the center. Lets look at it as a function of time"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(delta*np.array(lags),[lagged_stas[lag][7,8] for lag in lags],color='k',lw=3)\n",
      "plt.xlabel('lag (ms)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "<matplotlib.text.Text at 0x1086b0350>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1086ad850>"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Is there a simple coordinate in space that you can find?"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Fun things to think about..."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "- Are there other patterns in the response?\n",
      "- How do we know how well we did? What exactly can we tell about the stimulus from the spike data?\n",
      "- Can we do better by using pairs of spike counts at different lags? Triplets?\n",
      "- Can we do better by not just looking at the average but other statistical weights?\n",
      "- Can we do better with a feed forward neural network architecture?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}