[pointprocesses] updated some figures

pointprocesses/lecture/isihexamples.py

@@ -55,11 +55,11 @@ def plotisih( ax, isis, binwidth=None ) :
             binwidth = 5e-4
     h, b = np.histogram(isis, np.arange(0.0, np.max(isis)+binwidth, binwidth), density=True)
     ax.text(0.9, 0.85, 'rate={:.0f}Hz'.format(1.0/np.mean(isis)), ha='right', transform=ax.transAxes)
-    ax.text(0.9, 0.75, 'mean={:.0f}ms'.format(1000.0*np.mean(isis)), ha='right', transform=ax.transAxes)
+    ax.text(0.9, 0.7, 'mean={:.0f}ms'.format(1000.0*np.mean(isis)), ha='right', transform=ax.transAxes)
-    ax.text(0.9, 0.65, 'CV={:.2f}'.format(np.std(isis)/np.mean(isis)), ha='right', transform=ax.transAxes)
+    ax.text(0.9, 0.55, 'CV={:.2f}'.format(np.std(isis)/np.mean(isis)), ha='right', transform=ax.transAxes)
     ax.set_xlabel('ISI', 'ms')
     ax.set_ylabel('p(ISI)', '1/s')
-    ax.bar( 1000.0*b[:-1], h, bar_fac*1000.0*np.diff(b), facecolor=colors['blue'])
+    ax.bar( 1000.0*b[:-1], h, bar_fac*1000.0*np.diff(b), **fsA)
 
 # parameter:
 rate = 20.0
@@ -85,16 +85,18 @@ x[x<0.0] = 0.0
 inhspikes = pifspikes(x, trials, dt, D=0.3)
 
 fig, (ax1, ax2) = plt.subplots(1, 2)
-fig.subplots_adjust(**adjust_fs(fig, top=1.5))
+fig.subplots_adjust(**adjust_fs(fig, top=0.5, right=1.5))
-ax1.set_title('stationary')
+ax1.set_xlim(0.0, 150.0)
-ax1.set_xlim(0.0, 200.0)
+ax1.set_ylim(0.0, 31.0)
-ax1.set_ylim(0.0, 40.0)
+ax1.set_xticks(np.arange(0.0, 151.0, 50.0))
-plotisih(ax1, isis(homspikes))
+ax1.set_yticks(np.arange(0.0, 31.0, 10.0))
+plotisih(ax1, isis(homspikes), 0.005)
 
-ax2.set_title('non-stationary')
+ax2.set_xlim(0.0, 150.0)
-ax2.set_xlim(0.0, 200.0)
+ax2.set_ylim(0.0, 31.0)
-ax2.set_ylim(0.0, 40.0)
+ax2.set_xticks(np.arange(0.0, 151.0, 50.0))
-plotisih(ax2, isis(inhspikes))
+ax2.set_yticks(np.arange(0.0, 31.0, 10.0))
+plotisih(ax2, isis(inhspikes), 0.005)
 
 plt.savefig('isihexamples.pdf')
 plt.close()

pointprocesses/lecture/pointprocesses.tex

@@ -1,36 +1,41 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\chapter{Spiketrain analysis}
+\chapter{Spike-train analysis}
 \label{pointprocesseschapter}
-\exercisechapter{Spiketrain analysis}
+\exercisechapter{Spike-train analysis}
 
 \entermde[action potential]{Aktionspotential}{Action potentials}
-(\enterm[spike|seealso{action potential}]{spikes}) are the carriers of
+(\enterm[spike|seealso{action potential}]{spikes}) carry information
-information in the nervous system. Thereby it is the time at which the
+within neural systems. More precisely, the times at which action
-spikes are generated that is of importance for information
+potentials are generated contain the information.  The waveform of the
-transmission. The waveform of the action potential is largely
+action potential is largely stereotyped and therefore conveys no
-stereotyped and therefore does not carry information.
+information. Analyzing the statistics of spike times and their
-
+relation to sensory stimuli or motor actions is central to
-The result of the pre-processing of electrophysiological recordings are
+neuroscientific research. With multi-electrode arrays it is nowadays
-series of spike times, which are termed \enterm{spiketrains}. If
+possible to record from hundreds or even thousands of neurons
-measurements are repeated we get several \enterm{trials} of
+simultaneously. The open challenge is how to analyze such data sets in
-spiketrains (\figref{rasterexamplesfig}).
+order to understand how neural systems work. Let's start with the
-
+basics in this chapter.
-Spiketrains are times of events, the action potentials. Analyzing
+
-spike trains leads into the realm of the so called \entermde[point
+The result of the pre-processing of electrophysiological recordings
+are series of spike times, which are termed \enterm[spike train]{spike
+  trains}. If measurements are repeated we get several \enterm{trials}
+of spike trains (\figref{rasterexamplesfig}).  Spike trains are lists
+of times of events, the action potentials. Analyzing spike trains
+leads into the realm of the statistics of so called \entermde[point
 process]{Punktprozess}{point processes}.
 
-\begin{figure}[ht]
+\begin{figure}[bt]
   \includegraphics[width=1\textwidth]{rasterexamples}
-  \titlecaption{\label{rasterexamplesfig}Raster-plot.}{Raster-plots of
+  \titlecaption{\label{rasterexamplesfig}Raster plot.}{Raster plots of
-    ten trials of data illustrating the times of the action
+    ten trials of data illustrating the times of action
-    potentials. Each vertical dash illustrates the time at which an
+    potentials. Each vertical stroke illustrates the time at which an
-    action potential was observed. Each line displays the events of
+    action potential was observed. Each row displays the events of one
-    one trial. Shown is a stationary point process (homogeneous point
+    trial. Shown is a stationary point process (homogeneous point
     process with a rate $\lambda=20$\;Hz, left) and an non-stationary
-    point process (perfect integrate-and-fire neuron driven by
+    point process with a rate that varies in time (noisy perfect
-    Ohrnstein-Uhlenbeck noise with a time-constant $\tau=100$\,ms,
+    integrate-and-fire neuron driven by Ohrnstein-Uhlenbeck noise with
-    right).}
+    a time-constant $\tau=100$\,ms, right).}
 \end{figure}
 
 
@@ -43,7 +48,7 @@ spike trains leads into the realm of the so called \entermde[point
   crosses some threshold. For example:\vspace{-1ex}
   \begin{itemize}
   \item Action potentials/heart beat: created by the dynamics of the
-    neuron/sinoatrial node
+    neuron/sinoatrial node.
   \item Earthquake: defined by the dynamics of the pressure between
     tectonical plates.
   \item Communication calls in crickets/frogs/birds: shaped by
@@ -59,21 +64,21 @@ spike trains leads into the realm of the so called \entermde[point
     $T_i=t_{i+1}-t_i$ and the number of events $n_i$. }
 \end{figure}
 
+\noindent
 A temporal \entermde{Punktprozess}{point process} is a stochastic
-process that generates a sequence of events at times $\{t_i\}$, $t_i
+process that generates a sequence of events at times $\{t_i\}$.  In
-\in \reZ$.  In the neurosciences, the statistics of point processes is
+the neurosciences, the statistics of point processes is of importance
-of importance since the timing of neuronal events (action potentials,
+since the timing of neuronal events (action potentials, post-synaptic
-post-synaptic potentials, events in EEG or local-field recordings,
+potentials, events in EEG or local-field recordings, etc.) is crucial
-etc.) is crucial for information transmission and can be treated as
+for information transmission and can be treated as such a process.
-such a process.
 
 The events of a point process can be illustrated by means of a raster
 plot in which each vertical line indicates the time of an event. The
 event from two different point processes are shown in
-\figref{rasterexamplesfig}.  Point processes can be described using
+\figref{rasterexamplesfig}.  In addition to the event times, point
-the intervals between successive events $T_i=t_{i+1}-t_i$ and the
+processes can be described using the intervals $T_i=t_{i+1}-t_i$
-number of observed events within a certain time window $n_i$
+between successive events or the number of observed events within a
-(\figref{pointprocessscetchfig}).
+certain time window $n_i$ (\figref{pointprocessscetchfig}).
 
 \begin{exercise}{rasterplot.m}{}
   Implement a function \varcode{rasterplot()} that displays the times of
@@ -94,7 +99,7 @@ real-valued variables:
 
 \begin{figure}[t]
   \includegraphics[width=0.96\textwidth]{isihexamples}\vspace{-2ex}
-  \titlecaption{\label{isihexamplesfig}Interspike interval
+  \titlecaption{\label{isihexamplesfig}Interspike-interval
     histograms}{of the spike trains shown in \figref{rasterexamplesfig}.}
 \end{figure}
 
@@ -144,7 +149,7 @@ the interval $T_i$. The parameter $k$ is called the \enterm{lag}
 (\determ{Verz\"ogerung}) $k$. Stationary and non-stationary return
 maps are distinctly different \figref{returnmapfig}.
 
-\begin{figure}[t]
+\begin{figure}[tp]
   \includegraphics[width=1\textwidth]{returnmapexamples}
   \includegraphics[width=1\textwidth]{serialcorrexamples}
   \titlecaption{\label{returnmapfig}Interspike interval

pointprocesses/lecture/rasterexamples.py

@@ -1,5 +1,6 @@
 import numpy as np
 import matplotlib.pyplot as plt
+from plotstyle import *
 
 def hompoisson(rate, trials, duration) :
     spikes = []
@@ -64,23 +65,22 @@ x[x<0.0] = 0.0
 # pif spike trains:
 inhspikes = pifspikes(x, trials, dt, D=0.3)
 
-fig = plt.figure( figsize=(9,4) )
+fig, (ax1, ax2) = plt.subplots(1, 2, figsize=cm_size(figure_width, 0.5*figure_width))
-ax = fig.add_subplot(1, 2, 1)
+fig.subplots_adjust(**adjust_fs(fig, left=4.0, right=1.0, top=1.2))
-ax.set_title('stationary')
-ax.set_xlim(0.0, duration)
-ax.set_ylim(-0.5, trials-0.5)
-ax.set_xlabel('Time [s]')
-ax.set_ylabel('Trials')
-ax.eventplot(homspikes, colors=[[0, 0, 0]], linelength=0.8)
 
-ax = fig.add_subplot(1, 2, 2)
+ax1.set_title('stationary')
-ax.set_title('non-stationary')
+ax1.set_xlim(0.0, duration)
-ax.set_xlim(0.0, duration)
+ax1.set_ylim(-0.5, trials-0.5)
-ax.set_ylim(-0.5, trials-0.5)
+ax1.set_xlabel('Time [s]')
-ax.set_xlabel('Time [s]')
+ax1.set_ylabel('Trial')
-ax.set_ylabel('Trials')
+ax1.eventplot(homspikes, colors=[lsA['color']], linelength=0.8, lw=1)
-ax.eventplot(inhspikes, colors=[[0, 0, 0]], linelength=0.8)
+
+ax2.set_title('non-stationary')
+ax2.set_xlim(0.0, duration)
+ax2.set_ylim(-0.5, trials-0.5)
+ax2.set_xlabel('Time [s]')
+ax2.set_ylabel('Trial')
+ax2.eventplot(inhspikes, colors=[lsA['color']], linelength=0.8, lw=1)
 
-plt.tight_layout()
 plt.savefig('rasterexamples.pdf')
 plt.close()

pointprocesses/lecture/returnmapexamples.py

@@ -40,19 +40,21 @@ def pifspikes(input, trials, dt, D=0.1) :
         spikes.append( times )
     return spikes
 
+
 def isis( spikes ) :
     isi = []
     for k in range(len(spikes)) :
         isi.extend(np.diff(spikes[k]))
     return np.array( isi )
 
-def plotreturnmap(ax, isis, lag=1, max=None) :
+
+def plotreturnmap(ax, isis, lag=1, max=1.0) :
     ax.set_xlabel(r'ISI$_i$', 'ms')
     ax.set_ylabel(r'ISI$_{i+1}$', 'ms')
-    if max != None :
     ax.set_xlim(0.0, 1000.0*max)
     ax.set_ylim(0.0, 1000.0*max)
-    ax.scatter(1000.0*isis[:-lag], 1000.0*isis[lag:], c=colors['blue'])
+    isiss = isis[isis<max]
+    ax.plot(1000.0*isiss[:-lag], 1000.0*isiss[lag:], clip_on=False, **psAm)
 
 # parameter:
 rate = 20.0
@@ -79,11 +81,14 @@ inhspikes = pifspikes(x, trials, dt, D=0.3)
 
 fig, (ax1, ax2) = plt.subplots(1, 2)
 fig.subplots_adjust(**adjust_fs(fig, left=6.5, top=1.5))
-ax1.set_title('stationary')
 plotreturnmap(ax1, isis(homspikes), 1, 0.3)
+ax1.set_xticks(np.arange(0.0, 301.0, 100.0))
+ax1.set_yticks(np.arange(0.0, 301.0, 100.0))
 
-ax2.set_title('non-stationary')
 plotreturnmap(ax2, isis(inhspikes), 1, 0.3)
+ax2.set_ylabel('')
+ax2.set_xticks(np.arange(0.0, 301.0, 100.0))
+ax2.set_yticks(np.arange(0.0, 301.0, 100.0))
 
 plt.savefig('returnmapexamples.pdf')
 plt.close()

pointprocesses/lecture/serialcorrexamples.py

@@ -13,6 +13,7 @@ def hompoisson(rate, trials, duration) :
         spikes.append( times )
     return spikes
 
+
 def inhompoisson(rate, trials, dt) :
     spikes = []
     p = rate*dt
@@ -55,7 +56,9 @@ def plotserialcorr(ax, isis, maxlag=10) :
     ax.set_ylabel(r'ISI correlation $\rho_k$')
     ax.set_xlim(0.0, maxlag)
     ax.set_ylim(-1.0, 1.0)
-    ax.plot(lags, corr, '.-', markersize=15, c=colors['blue'])
+    ax.plot([0, 10], [0.0, 0.0], **lsGrid)
+    ax.plot(lags, corr, clip_on=False, zorder=100, **lpsAm)
+
     
 # parameter:
 rate = 20.0
@@ -87,6 +90,7 @@ plotserialcorr(ax1, isis(homspikes))
 ax1.set_ylim(-0.2, 1.0)
 
 plotserialcorr(ax2, isis(inhspikes))
+ax2.set_ylabel('')
 ax2.set_ylim(-0.2, 1.0)
 
 plt.savefig('serialcorrexamples.pdf')