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AreTwoPSTHsIdentical.html
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<!DOCTYPE html>
<html>
<head><meta charset="utf-8" />
<title>Are two PSTHs identical?</title>
<script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.1.10/require.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.0.3/jquery.min.js"></script>
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<h1 id="Setting-up-Python">Setting up <code>Python</code><a class="anchor-link" href="#Setting-up-Python">¶</a></h1><p>The analysis presented in the manuscript and detailed next is carried
out with <code>Python 3</code> (the following code runs and gives identical results
with <code>Python 2</code>). We are going to use the 3 classical modules of
Python's scientific ecosystem: <code>numpy</code>, <code>scipy</code> and <code>matplotlib</code>. We are
also going to use two additional modules: <code>sympy</code> as well as <code>h5py</code>. We
start by importing these modules:</p>
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<div class=" highlight hl-ipython3"><pre><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="o">%</span><span class="k">matplotlib</span> inline
<span class="n">plt</span><span class="o">.</span><span class="n">style</span><span class="o">.</span><span class="n">use</span><span class="p">(</span><span class="s">'ggplot'</span><span class="p">)</span>
<span class="kn">import</span> <span class="nn">scipy</span>
<span class="kn">import</span> <span class="nn">h5py</span>
</pre></div>
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<p>Python 2 users <strong>must</strong> also type:
<code>from __future__ import print_function, division, unicode_literals, absolute_import</code></p>
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<h1 id="Getting-the-data">Getting the data<a class="anchor-link" href="#Getting-the-data">¶</a></h1><p>Our data (<a href="https://zenodo.org/record/14281">Pouzat and Chaffiol,2015</a>) are stored in
<a href="http://www.hdfgroup.org/HDF5/">HDF5</a> format on the
<a href="https://zenodo.org/">zenodo</a> server (<code>DOI:10.5281/zenodo.1428145</code>).
They are all contained in a file named
<code>CockroachDataJNM_2009_181_119.h5</code>. The data within this file have an
hierarchical organization similar to the one of a file system (one of
the main ideas of the HDF5 format). The first organization level is the
experiment; there are 4 experiments in the file: <code>e060517</code>, <code>e060817</code>,
<code>e060824</code> and <code>e070528</code>. Each experiment is organized by neurons,
<code>Neuron1</code>, <code>Neuron2</code>, etc, (with a number of recorded neurons depending
on the experiment). Each neuron contains a <code>dataset</code> (in the HDF5
terminology) named <code>spont</code> containing the spike train of that neuron
recorded during a period of spontaneous activity. Each neuron also
contains one or several further sub-levels named after the odor used for
stimulation <code>citronellal</code>, <code>terpineol</code>, <code>mixture</code>, etc. Each a these
sub-levels contains as many <code>datasets</code>: <code>stim1</code>, <code>stim2</code>, etc, as
stimulations were applied; and each of these data sets contains the
spike train of that neuron for the corresponding stimulation. Another
<code>dataset</code>, named <code>stimOnset</code> containing the onset time of the stimulus
(for each of the stimulations). All these times are measured in seconds.</p>
<p>The data can be downloaded with <code>Python</code> as follows:</p>
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<div class=" highlight hl-ipython3"><pre><span class="k">try</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">urllib.request</span> <span class="k">import</span> <span class="n">urlretrieve</span> <span class="c"># Python 3</span>
<span class="k">except</span> <span class="ne">ImportError</span><span class="p">:</span>
<span class="kn">from</span> <span class="nn">urllib</span> <span class="k">import</span> <span class="n">urlretrieve</span> <span class="c"># Python 2</span>
<span class="n">name_on_disk</span> <span class="o">=</span> <span class="s">'CockroachDataJNM_2009_181_119.h5'</span>
<span class="n">urlretrieve</span><span class="p">(</span><span class="s">'https://zenodo.org/record/14281/files/'</span><span class="o">+</span>
<span class="n">name_on_disk</span><span class="p">,</span>
<span class="n">name_on_disk</span><span class="p">)</span>
</pre></div>
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<p>The file is opened with:</p>
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<div class=" highlight hl-ipython3"><pre><span class="n">f</span> <span class="o">=</span> <span class="n">h5py</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="s">"CockroachDataJNM_2009_181_119.h5"</span><span class="p">,</span><span class="s">"r"</span><span class="p">)</span>
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<h1 id="Making-the-raster-plots">Making the raster plots<a class="anchor-link" href="#Making-the-raster-plots">¶</a></h1><p>We make our raster plots with a short function <code>raster_plot</code> that we define with:</p>
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<div class=" highlight hl-ipython3"><pre><span class="k">def</span> <span class="nf">raster_plot</span><span class="p">(</span><span class="n">train_list</span><span class="p">,</span>
<span class="n">stim_onset</span><span class="o">=</span><span class="k">None</span><span class="p">,</span>
<span class="n">color</span> <span class="o">=</span> <span class="s">'black'</span><span class="p">):</span>
<span class="sd">"""Create a raster plot.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> train_list: a list of spike trains (1d vector with strictly</span>
<span class="sd"> increasing elements).</span>
<span class="sd"> stim_onst: a number giving the time of stimulus onset. If</span>
<span class="sd"> specificied, the time are realigned such that the stimulus</span>
<span class="sd"> comes at 0.</span>
<span class="sd"> color: the color of the ticks representing the spikes.</span>
<span class="sd"> Side effect:</span>
<span class="sd"> A raster plot is created.</span>
<span class="sd"> """</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="k">if</span> <span class="n">stim_onset</span> <span class="ow">is</span> <span class="k">None</span><span class="p">:</span>
<span class="n">stim_onset</span> <span class="o">=</span> <span class="mi">0</span>
<span class="k">for</span> <span class="n">idx</span><span class="p">,</span><span class="n">trial</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">train_list</span><span class="p">):</span>
<span class="n">plt</span><span class="o">.</span><span class="n">vlines</span><span class="p">(</span><span class="n">trial</span><span class="o">-</span><span class="n">stim_onset</span><span class="p">,</span>
<span class="n">idx</span><span class="o">+</span><span class="mf">0.6</span><span class="p">,</span><span class="n">idx</span><span class="o">+</span><span class="mf">1.4</span><span class="p">,</span>
<span class="n">color</span><span class="o">=</span><span class="n">color</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span><span class="nb">len</span><span class="p">(</span><span class="n">train_list</span><span class="p">))</span>
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<p>The raster plots of the responses of Neuron 1 to citronellal and terpineol are then obtained with:</p>
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<div class=" highlight hl-ipython3"><pre><span class="n">citron_onset</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="s">"e060817/Neuron1/citronellal/stimOnset"</span><span class="p">][</span><span class="o">...</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
<span class="n">e060817citron</span> <span class="o">=</span> <span class="p">[[</span><span class="n">f</span><span class="p">[</span><span class="n">y</span><span class="p">][</span><span class="o">...</span><span class="p">]</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span>
<span class="p">[</span><span class="s">"e060817/Neuron"</span><span class="o">+</span><span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">+</span><span class="s">"/citronellal/stim"</span><span class="o">+</span><span class="nb">str</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">21</span><span class="p">)]]</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">4</span><span class="p">)]</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">121</span><span class="p">)</span>
<span class="n">raster_plot</span><span class="p">(</span><span class="n">e060817citron</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">citron_onset</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">6</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">21</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="k">True</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">"Time (s)"</span><span class="p">,</span><span class="n">fontdict</span><span class="o">=</span><span class="p">{</span><span class="s">'fontsize'</span><span class="p">:</span><span class="mi">15</span><span class="p">})</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">"Trial"</span><span class="p">,</span><span class="n">fontdict</span><span class="o">=</span><span class="p">{</span><span class="s">'fontsize'</span><span class="p">:</span><span class="mi">15</span><span class="p">})</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">"Citronellal"</span><span class="p">,</span><span class="n">fontdict</span><span class="o">=</span><span class="p">{</span><span class="s">'fontsize'</span><span class="p">:</span><span class="mi">20</span><span class="p">})</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">122</span><span class="p">)</span>
<span class="n">terpi_onset</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="s">"e060817/Neuron1/terpineol/stimOnset"</span><span class="p">][</span><span class="o">...</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
<span class="n">e060817terpi</span> <span class="o">=</span> <span class="p">[[</span><span class="n">f</span><span class="p">[</span><span class="n">y</span><span class="p">][</span><span class="o">...</span><span class="p">]</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span>
<span class="p">[</span><span class="s">"e060817/Neuron"</span><span class="o">+</span><span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">+</span><span class="s">"/terpineol/stim"</span><span class="o">+</span><span class="nb">str</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">21</span><span class="p">)]]</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">4</span><span class="p">)]</span>
<span class="n">raster_plot</span><span class="p">(</span><span class="n">e060817terpi</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">terpi_onset</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span><span class="mi">6</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">21</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="k">True</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s">"Time (s)"</span><span class="p">,</span><span class="n">fontdict</span><span class="o">=</span><span class="p">{</span><span class="s">'fontsize'</span><span class="p">:</span><span class="mi">15</span><span class="p">})</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s">"Trial"</span><span class="p">,</span><span class="n">fontdict</span><span class="o">=</span><span class="p">{</span><span class="s">'fontsize'</span><span class="p">:</span><span class="mi">15</span><span class="p">})</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s">"Terpineol"</span><span class="p">,</span><span class="n">fontdict</span><span class="o">=</span><span class="p">{</span><span class="s">'fontsize'</span><span class="p">:</span><span class="mi">20</span><span class="p">})</span>
<span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span><span class="p">(</span><span class="n">wspace</span><span class="o">=</span><span class="mf">0.4</span><span class="p">,</span><span class="n">hspace</span><span class="o">=</span><span class="mf">0.4</span><span class="p">)</span>
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<pre>/home/xtof/anaconda3/lib/python3.4/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison
if self._edgecolors == str('face'):
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<h1 id="Choosing-the-initial-bin-size">Choosing the initial bin size<a class="anchor-link" href="#Choosing-the-initial-bin-size">¶</a></h1><p>The bin width should be chosen large enough to have a few events per bin most of the time. We set this width such that an expected number of 3 events per bin was obtained using the spontaneous frequency estimated from 60 seconds long recordings without stimulus presentation—more specifically, the width was set to the smallest millisecond larger or equal to the targeted count divided by the product of the spontaneous frequency and the number of trials.</p>
<p>For the neurons of the data set we get the following spontaneous discharge rates:</p>
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<div class=" highlight hl-ipython3"><pre><span class="n">e060817_spont_nu</span> <span class="o">=</span> <span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="s">"e060817/Neuron"</span><span class="o">+</span><span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">+</span><span class="s">"/spont"</span><span class="p">])</span><span class="o">/</span><span class="mi">60</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">4</span><span class="p">)]</span>
<span class="nb">print</span><span class="p">(</span><span class="s">"The spontaneous discharge rates are:"</span><span class="p">)</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">e060817_spont_nu</span><span class="p">)):</span>
<span class="nb">print</span><span class="p">(</span><span class="s">" Neuron {0}: {1:.2f} (Hz)"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">e060817_spont_nu</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span>
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