Merge branch 'translation' of https://whale.am28.uni-tuebingen.de/git/teaching/scientificComputing into translation

bootstrap/lecture/bootstrapsem.py

@@ -15,13 +15,13 @@ x = rng.randn(nsamples)
 
 # bootstrap the mean:
 mus = []
-for i in xrange(nresamples) :
+for i in range(nresamples) :
     mus.append(np.mean(x[rng.randint(0, nsamples, nsamples)]))
 hmus, _ = np.histogram(mus, bins, density=True)
 
 # many SRS:
 musrs = []
-for i in xrange(nresamples) :
+for i in range(nresamples) :
     musrs.append(np.mean(rng.randn(nsamples)))
 hmusrs, _ = np.histogram(musrs, bins, density=True)
 

bootstrap/lecture/permutecorrelation.py

@@ -19,7 +19,7 @@ rd = np.corrcoef(x, y)[0, 1]
 # permutation:
 nperm = 1000
 rs = []
-for i in xrange(nperm) :
+for i in np.arange(nperm) :
     xr=rng.permutation(x)
     yr=rng.permutation(y)
     rs.append( np.corrcoef(xr, yr)[0, 1] )

chapter.mk

@@ -8,7 +8,8 @@ PYPDFFILES=$(PYFILES:.py=.pdf)
 pythonplots : $(PYPDFFILES)
 
 $(PYPDFFILES) : %.pdf: %.py
-	python $<
+	echo $$(which python)
+	python3 $<
 
 cleanpythonplots :
 	rm -f $(PYPDFFILES)

likelihood/lecture/mlemean.py

@@ -41,7 +41,7 @@ for mu in mus :
         ax.text(mu-0.1, 0.04, '?', zorder=1, ha='right')
     else :
         ax.text(mu+0.1, 0.04, '?', zorder=1)
-for k in xrange(len(mus)) :
+for k in np.arange(len(mus)) :
     ax.plot(x, g[:,k], zorder=5)
 ax.scatter(xd, 0.05*rng.rand(len(xd))+0.2, s=30, zorder=10)
 

plotting/code/simple_plot.m

@@ -0,0 +1,8 @@
+frequency = 5;          % frequency of the sine wave in Hz
+time = 0.01:0.01:1.0;   % the time axis
+signal = sin(2 * pi * time * frequency);
+
+plot(time, signal);
+xlabel('time [s]');
+ylabel('signal');
+title('5Hz sine wave')

plotting/lecture/plotting.tex

@@ -146,7 +146,7 @@ additional options consult the help.
 The following listing shows a simple line plot with axis labeling and a title
 
 \lstinputlisting[caption={A simple plot showing a sinewave.},
-  label=niceplotlisting]{simple_plot.m}
+  label=simpleplotlisting]{simple_plot.m}
 
 
 \subsection{Changing properties of a line plot}

pointprocesses/lecture/firingrates.py

@@ -86,7 +86,7 @@ def plot_isi_rate(spike_times, max_t=30, dt=1e-4):
 def get_binned_rate(times, bin_width=0.05, max_t=30., dt=1e-4):
     time = np.arange(0., max_t, dt)
     bins = np.arange(0., max_t, bin_width)
-    bin_indices = bins / dt
+    bin_indices = np.asarray(bins / dt, np.int)
     hist, _ = sp.histogram(times, bins)
     rate = np.zeros(time.shape)
     

pointprocesses/lecture/isihexamples.py

@@ -31,7 +31,7 @@ def pifspikes(input, trials, dt, D=0.1) :
         times = []
         v = vreset
         noise = np.sqrt(2.0*D)*np.random.randn(len(input))/np.sqrt(dt)
-        for k in xrange(len(noise)) :
+        for k in np.arange(len(noise)) :
             v += (input[k]+noise[k])*dt/tau
             if v >= vthresh :
                 v = vreset
@@ -41,7 +41,7 @@ def pifspikes(input, trials, dt, D=0.1) :
 
 def isis( spikes ) :
     isi = []
-    for k in xrange(len(spikes)) :
+    for k in np.arange(len(spikes)) :
         isi.extend(np.diff(spikes[k]))
     return isi
 
@@ -76,7 +76,7 @@ rng = np.random.RandomState(54637281)
 time = np.arange(0.0, duration, dt)
 x = np.zeros(time.shape)+rate
 n = rng.randn(len(time))*drate*tau/np.sqrt(dt)+rate
-for k in xrange(1,len(x)) :
+for k in np.arange(1,len(x)) :
     x[k] = x[k-1] + (n[k]-x[k-1])*dt/tau
 x[x<0.0] = 0.0
 

pointprocesses/lecture/pointprocesses.tex

@@ -1,186 +1,186 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\chapter{Analyse von Spiketrains}
+\chapter{Spiketrain analysis}
 
-\selectlanguage{ngerman}
+\selectlanguage{english}
 
-\determ[Aktionspotential]{Aktionspotentiale} (\enterm{spikes}) sind die Tr\"ager der
+\enterm[Actionspotentials]{Actionspotentials} (\enterm{spikes}) are
-Information in Nervensystemen.  Dabei ist in erster Linie nur der
+the carriers of information in the nervous system. Thereby it is
-Zeitpunkt des Auftretens eines Aktionspotentials von Bedeutung. Die
+mainly the time at which the spikes are generated that is of
-genaue Form des Aktionspotentials spielt keine oder nur eine
+importance. The waveform of the action potential is largely
-untergeordnete Rolle.
+stereotyped and does not carry information.
 
-Nach etwas Vorverarbeitung haben elektrophysiologische Messungen
+The result of the processing of electrophysiological recordings are
-deshalb Listen von Spikezeitpunkten als Ergebniss --- sogenannte
+series of spike times, which are then termed \enterm{spiketrains}. If
-\enterm{spiketrains}. Diese Messungen k\"onnen wiederholt werden und
+measurements are repeated we yield several \enterm{trials} of
-es ergeben sich mehrere \enterm{trials} von Spiketrains
+spiketrains (\figref{rasterexamplesfig}).
-(\figref{rasterexamplesfig}).
 
-Spiketrains sind Zeitpunkte von Ereignissen --- den Aktionspotentialen
+Spiketrains are times of events, the action potentials. The analysis
---- und deren Analyse f\"allt daher in das Gebiet der Statistik von
+of these leads into the realm of the so called \enterm[point
-sogenannten \determ[Punktprozess]{Punktprozessen}.
+  process]{point processes}.
 
 \begin{figure}[ht]
   \includegraphics[width=1\textwidth]{rasterexamples}
-  \titlecaption{\label{rasterexamplesfig}Raster-Plot.}{Raster-Plot von
+  \titlecaption{\label{rasterexamplesfig}Raster-plot.}{Raster-plot of
-    jeweils 10 Realisierungen eines station\"arenen Punktprozesses
+    ten realizations of a stationary point process (homogeneous point
-    (homogener Poisson Prozess mit Rate $\lambda=20$\;Hz, links) und
+    process with a rate $\lambda=20$\;Hz, left) and an inhomogeneous
-    eines nicht-station\"aren Punktprozesses (perfect
+    point process (perfect integrate-and-fire neuron dirven by
-    integrate-and-fire Neuron getrieben mit Ohrnstein-Uhlenbeck
+    Ohrnstein-Uhlenbeck noise with a time-constant $\tau=100$\,ms,
-    Rauschen mit Zeitkonstante $\tau=100$\,ms, rechts).  Jeder
+    right). Each vertical dash illustrates the time at which the
-    vertikale Strich markiert den Zeitpunkt eines Ereignisses.
+    action potential was observed. Each line represents the event of
-    Jede Zeile zeigt die Ereignisse eines trials.}
+    each trial.}
 \end{figure}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Punktprozesse}
+\section{Point processes}
 
-Ein zeitlicher Punktprozess (\enterm{point process}) ist ein
+A temporal \enterm{point process} is a stochastic process that
-stochastischer Prozess, der eine Abfolge von Ereignissen zu den Zeiten
+generates a sequence of events at times $\{t_i\}$, $t_i \in
-$\{t_i\}$, $t_i \in \reZ$, generiert.
+\reZ$.
 
-\begin{ibox}{Beispiele von Punktprozessen}
+\begin{ibox}{Examples of point processes}
-Jeder Punktprozess wird durch einen sich in der Zeit kontinuierlich
+  Every point process is generated by a temporally continuously
-entwickelnden Prozess generiert. Wann immer dieser Prozess eine
+  developing process. An event is generated whenever this process
-Schwelle \"uberschreitet wird ein Ereigniss des Punktprozesses
+  reaches a certain threshold. For example:
-erzeugt. Zum Beispiel:
   \begin{itemize}
-\item Aktionspotentiale/Herzschlag: wird durch die Dynamik des
+  \item Action potentials/heart beat: created by the dynamics of the
-  Membranpotentials eines Neurons/Herzzelle erzeugt.
+    neuron/sinoatrial node
-\item Erdbeben: wird durch die Dynamik des Druckes zwischen
+  \item Earthquake: defined by the dynamics of the pressure between
-  tektonischen Platten auf beiden Seiten einer geologischen Verwerfung
+    tectonical plates.
-  erzeugt.
+  \item Evoked communication calls in crickets/frogs/birds: shaped by
-\item Zeitpunkt eines Grillen/Frosch/Vogelgesangs: wird durch die
+    the dynamics of nervous system and the muscle appartus.
-  Dynamik des Nervensystems und des Muskelapparates erzeugt.
   \end{itemize}
 \end{ibox}
 
 \begin{figure}[t]
   \texpicture{pointprocessscetch}
-  \titlecaption{\label{pointprocessscetchfig} Statistik von
+  \titlecaption{\label{pointprocessscetchfig} Statistics of point
-    Punktprozessen.}{Ein Punktprozess ist eine Abfolge von
+    processes.}{A point process is a sequence of instances in time
-    Zeitpunkten $t_i$ die auch durch die Intervalle $T_i=t_{i+1}-t_i$
+    $t_i$ that can be characterized through the inter-event-intervals
-    oder die Anzahl der Ereignisse $n_i$ beschrieben werden kann. }
+    $T_i=t_{i+1}-t_i$ and the number of events $n_i$. }
 \end{figure}
 
-F\"ur die Neurowissenschaften ist die Statistik der Punktprozesse
+In the neurosciences, the statistics of point processes is of
-besonders wichtig, da die Zeitpunkte der Aktionspotentiale als
+importance since the timing of the neuronal events (the action
-zeitlicher Punktprozess betrachtet werden k\"onnen und entscheidend
+potentials) is crucial for information transmission and can be treated
-f\"ur die Informations\"ubertragung sind.
+as such a process.
-
-Bei Punktprozessen k\"onnen wir die Zeitpunkte $t_i$ ihres Auftretens,
-die Intervalle zwischen diesen Zeitpunkten $T_i=t_{i+1}-t_i$, sowie
-die Anzahl der Ereignisse $n_i$ bis zu einer bestimmten Zeit betrachten
-(\figref{pointprocessscetchfig}).
 
-Zwei Punktprozesse mit verschiedenen Eigenschaften sind in
+Point processes can be described using the intervals between
-\figref{rasterexamplesfig} als Rasterplot dargestellt, bei dem die
+successive events $T_i=t_{i+1}-t_i$ and the number of observed events
-Zeitpunkte der Ereignisse durch senkrechte Striche markiert werden.
+within a certain time window $n_i$ (\figref{pointprocessscetchfig}).
 
+The events originating from a point process can be illustrated in form
+of a scatter- or 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}.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-\section{Intervallstatistik}
+\section{Intervalstatistics}
 
-Die Intervalle $T_i=t_{i+1}-t_i$ zwischen aufeinanderfolgenden
+The intervals $T_i=t_{i+1}-t_i$ between successive events are real
-Ereignissen sind reelle, positive Zahlen. Bei Aktionspotentialen
+positive numbers. In the context of action potentials they are
-heisen die Intervalle auch \determ{Interspikeintervalle}
+referred to as \enterm{interspike intervals}. The statistics of these
-(\enterm{interspike intervals}). Deren Statistik kann mit den
+are described using the common measures.
-\"ublichen Gr\"o{\ss}en beschrieben werden.
 
 \begin{figure}[t]
   \includegraphics[width=0.96\textwidth]{isihexamples}\vspace{-2ex}
-  \titlecaption{\label{isihexamplesfig}Interspikeintervall Histogramme}{der in
+  \titlecaption{\label{isihexamplesfig}Interspike interval
-    \figref{rasterexamplesfig} gezeigten Spikes.}
+    histogram}{of the spikes depicted in \figref{rasterexamplesfig}.}
 \end{figure}
 
 \begin{exercise}{isis.m}{}
-  Schreibe eine Funktion \code{isis()}, die aus mehreren trials von Spiketrains die
+  Implement a function \code{isis()} that calculates the interspike
-  Interspikeintervalle bestimmt und diese in einem Vektor
+  intervals from several spike trains. The function should return a
-  zur\"uckgibt. Jeder trial der Spiketrains ist ein Vektor mit den
+  single vector of intervals. The action potentials recorded in the
-  Spikezeiten gegeben in Sekunden als Element in einem \codeterm{cell-array}.
+  individual trials are stored as vectors of spike times within a
+  \codeterm{cell-array}. Spike times are given in seconds.
 \end{exercise}
 
-\subsection{Intervallstatistik erster Ordnung}
+\subsection{First order interval statistics}
 \begin{itemize}
-\item Wahrscheinlichkeitsdichte $p(T)$ der Intervalle $T$
+\item Probability density $p(T)$ of the intervals $T$
-  (\figref{isihexamplesfig}). Normiert auf $\int_0^{\infty} p(T) \; dT
+  (\figref{isihexamplesfig}). Normalized to $\int_0^{\infty} p(T) \; dT
   = 1$.
-\item Mittleres Intervall: $\mu_{ISI} = \langle T \rangle =
+\item Average interval: $\mu_{ISI} = \langle T \rangle =
   \frac{1}{n}\sum\limits_{i=1}^n T_i$.
-\item Standardabweichung der Intervalle: $\sigma_{ISI} = \sqrt{\langle (T - \langle T
+\item Standard deviation of the interspike intervals: $\sigma_{ISI} = \sqrt{\langle (T - \langle T
     \rangle)^2 \rangle}$\vspace{1ex}
-\item \determ{Variationskoeffizient} (\enterm{coefficient of variation}): $CV_{ISI} =
+\item \enterm{Coefficient of variation}: $CV_{ISI} =
   \frac{\sigma_{ISI}}{\mu_{ISI}}$.
-\item \determ{Diffusionskoeffizient} (\enterm{diffusion coefficient}): $D_{ISI} =
+\item \enterm{Diffusion coefficient}): $D_{ISI} =
   \frac{\sigma_{ISI}^2}{2\mu_{ISI}^3}$.
 \end{itemize}
 
 \begin{exercise}{isihist.m}{}
-  Schreibe eine Funktion \code{isiHist()}, die einen Vektor mit Interspikeintervallen
+  Implement a function \code{isiHist()} that calculates the normalized
-  entgegennimmt und daraus ein normiertes Histogramm der Interspikeintervalle
+  interspike interval histogram. The function should take two input
-  berechnet.
+  arguments; (i) a vector of interspike intervals and (ii) the width
+  of the bins used for the histogram. It further returns the
+  probability density as well as the centers of the bins.
 \end{exercise}
 
 \begin{exercise}{plotisihist.m}{}
-  Schreibe eine Funktion, die die Histogrammdaten der Funktion
+  Implement a function that takes the return values of
-  \code{isiHist()} entgegennimmt, um das Histogramm zu plotten.  Im
+  \code{isiHist()} as input arguments and then plots the data. The
-  Plot sollen die Interspikeintervalle in Millisekunden aufgetragen
+  plot should show the histogram with the x-axis scaled to
-  werden.  Das Histogramm soll zus\"atzlich mit Mittelwert,
+  milliseconds and should be annotated with the average ISI, the
-  Standardabweichung und Variationskoeffizient der
+  standard deviation and the coefficient of variation.
-  Interspikeintervalle annotiert werden.
 \end{exercise}
 
-\subsection{Korrelationen der Intervalle}
+\subsection{Interval correlations}
-In \enterm{return maps} werden die um das \enterm{lag} $k$ verz\"ogerten
+So called \enterm{return maps} are used to illustrate
-Intervalle $T_{i+k}$ gegen die Intervalle $T_i$ geplottet. Dies macht
+interdependencies between successive interspike intervals. The return
-m\"ogliche Abh\"angigkeiten von aufeinanderfolgenden Intervallen
+map plots the delayed interval $T_{i+k}$ against the interval
-sichtbar.
+$T_i$. The parameter $k$ is called the \enterm{lag} $k$. Stationary
+and non-stationary return maps are distinctly different
+\figref{returnmapfig}.
 
 \begin{figure}[t]
   \includegraphics[width=1\textwidth]{returnmapexamples}
   \includegraphics[width=1\textwidth]{serialcorrexamples}
-  \titlecaption{\label{returnmapfig}Interspikeintervall return maps und
+  \titlecaption{\label{returnmapfig}Interspike interval analyses of a
-    serielle Korrelationen}{zwischen aufeinander folgenden Intervallen
+    stationary and a non-stationary pointprocess.}{Upper plots show the
-    im Abstand des Lags $k$.}
+    return maps and the lower panels depict the serial correlation of
+    successive intervals separated by the lag $k$.}
 \end{figure}
 
-Solche Ab\"angigkeiten werden durch die \determ{serielle
+Such dependencies can be further quantified using the \enterm{serial
-  Korrelationen} (\enterm{serial correlations}) der Intervalle
+  correlations} \figref{returnmapfig}. The serial correlation is the
-quantifiziert.  Das ist der \determ{Korrelationskoeffizient} zwischen
+correlation coefficient of the intervals $T_i$ and the intervals
-aufeinander folgenden Intervallen getrennt durch lag $k$:
+delayed by the lag $T_{i+k}$:
 \[ \rho_k = \frac{\langle (T_{i+k} - \langle T \rangle)(T_i - \langle T \rangle) \rangle}{\langle (T_i - \langle T \rangle)^2\rangle} = \frac{{\rm cov}(T_{i+k}, T_i)}{{\rm var}(T_i)} 
-= {\rm corr}(T_{i+k}, T_i) \]
+= {\rm corr}(T_{i+k}, T_i) \] The resulting correlation coefficient
-\"Ublicherweise wird die Korrelation $\rho_k$ gegen den Lag $k$
+$\rho_k$ is usually plotted against the lag $k$
-aufgetragen (\figref{returnmapfig}).  $\rho_0=1$ (Korrelation jedes
+\figref{returnmapfig}. $\rho_0=1$ is the correlation of each interval
-Intervalls mit sich selber).
+with itself and is always 1.
 
 \begin{exercise}{isiserialcorr.m}{}
-  Schreibe eine Funktion \code{isiserialcorr()}, die einen Vektor mit Interspikeintervallen
+  Implement a function \code{isiserialcorr()} that takes a vector of
-  entgegennimmt und daraus die seriellen Korrelationen berechnet und plottet.
+  interspike intervals as input argument and calculates the serial
-  \pagebreak[4]
+  correlation. The function should further plot the serial
+  correlation. \pagebreak[4]
 \end{exercise}
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Z\"ahlstatistik}
+\section{Count statistics}
 
 % \begin{figure}[t]
 %   \includegraphics[width=0.48\textwidth]{poissoncounthist100hz10ms}\hfill
 %   \includegraphics[width=0.48\textwidth]{poissoncounthist100hz100ms}
 %   \titlecaption{\label{countstatsfig}Count Statistik.}{}
 % \end{figure}
-
+The number of events $n_i$ (counts) in a time window $i$ of the duration $W$
-Die Anzahl der Ereignisse $n_i$ in Zeifenstern $i$ der
+yields positive integer random numbers that are commonly quantified
-L\"ange $W$ ergeben ganzzahlige, positive Zufallsvariablen, die meist
+using the following measures:
-durch folgende Sch\"atzer charakterisiert werden:
 \begin{itemize}
-\item Histogramm der counts $n_i$.
+\item Histogram of the counts $n_i$.
-\item Mittlere Anzahl von Ereignissen: $\mu_N = \langle n \rangle$.
+\item Average number of events: $\mu_N = \langle n \rangle$.
-\item Varianz der Anzahl: $\sigma_n^2 = \langle (n - \langle n \rangle)^2 \rangle$.
+\item Variance of the counts: $\sigma_n^2 = \langle (n - \langle n \rangle)^2 \rangle$.
-\item \determ{Fano Faktor} (Varianz geteilt durch Mittelwert): $F = \frac{\sigma_n^2}{\mu_n}$.
+\item \determ{Fano Faktor} (The variance divided by the average): $F = \frac{\sigma_n^2}{\mu_n}$.
 \end{itemize}
-Insbesondere ist die mittlere Rate der Ereignisse $r$ (Spikes pro
+And in particular the average firing rate $r$ (spike count per time interval
-Zeit, \determ{Feuerrate}) gemessen in Hertz \sindex[term]{Feuerrate!mittlere Rate}
+, \determ{Feuerrate}) that is given in Hertz \sindex[term]{Feuerrate!mittlere Rate}
 \begin{equation}
   \label{firingrate}
   r = \frac{\langle n \rangle}{W} \; .
@@ -200,110 +200,114 @@ Zeit, \determ{Feuerrate}) gemessen in Hertz \sindex[term]{Feuerrate!mittlere Rat
 % \end{figure}
 
 \begin{exercise}{counthist.m}{}
-  Schreibe eine Funktion \code{counthist()}, die aus mehreren trials
+  Implement a function \code{counthist()} that calculates and plots
-  von Spiketrains die Verteilung der Anzahl der Spikes in Fenstern
+  the distribution of spike counts observed in a certain time
-  einer der Funktion \"ubergegebenen Breite bestimmt, das Histogramm
+  window. The function should take two input arguments: (i) a
-  plottet und zur\"uckgibt. Jeder trial der Spiketrains ist ein Vektor
+  \codeterm{cell-array} of vectors containing the spike times in
-  mit den Spikezeiten gegeben in Sekunden als Element in einem
+  seconds observed in a number of trials and (ii) the duration of the
-  \codeterm{cell-array}.
+  time window that is used to evaluate the counts.
 \end{exercise}
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Homogener Poisson Prozess}
+\section{Homogeneous Poisson process}
-F\"ur kontinuierliche Me{\ss}gr\"o{\ss}en ist die Normalverteilung
+
-u.a. wegen dem Zentralen Grenzwertsatz die Standardverteilung. Eine
+The Gaussian distribution is, due to the central limit theorem, the
-\"ahnliche Rolle spielt bei Punktprozessen der \determ{Poisson
+standard for continuous measures. The equivalent in the realm of point
-  Prozess}.
+processes is the \enterm{Poisson distribution}.
-
+
-Beim \determ[Poisson Prozess!homogener]{homogenen Poisson Prozess}
+In a \enterm[Poisson process!homogeneous]{homogeneous Poisson process}
-treten Ereignisse mit einer festen Rate $\lambda=\text{const.}$ auf
+the events occur at a fixed rate $\lambda=\text{const.}$ and are
-und sind unabh\"angig von der Zeit $t$ und unabh\"angig von den
+independent of both the time $t$ and occurrence of previous events
-Zeitpunkten fr\"uherer Ereignisse (\figref{hompoissonfig}). Die
+(\figref{hompoissonfig}). The probability of observing an even within a
-Wahrscheinlichkeit zu irgendeiner Zeit ein Ereigniss in einem kleinen
+small time window of width $\Delta t$ is given by
-Zeitfenster der Breite $\Delta t$ zu bekommen ist
 \begin{equation}
   \label{hompoissonprob}
   P = \lambda \cdot \Delta t \; .
 \end{equation}
-Beim \determ[Poisson Prozess!inhomogener]{inhomogenen Poisson Prozess}
+
-h\"angt die Rate $\lambda$ von der Zeit ab: $\lambda = \lambda(t)$.
+In an \enterm[Poisson process!inhomogeneous]{inhomogeneous Poisson
+  process}, however, the rate $\lambda$ depends on the time: $\lambda =
+\lambda(t)$.
 
 \begin{exercise}{poissonspikes.m}{}
-  Schreibe eine Funktion \code{poissonspikes()}, die die Spikezeiten
+  Implement a function \code{poissonspikes()} that uses a homogeneous
-  eines homogenen Poisson-Prozesses mit gegebener Rate in Hertz f\"ur
+  Poisson process to generate events at a given rate for a certain
-  eine Anzahl von trials gegebener maximaler L\"ange in Sekunden in
+  duration and a number of trials. The rate should be given in Hertz
-  einem \codeterm{cell-array} zur\"uckgibt. Benutze \eqnref{hompoissonprob}
+  and the duration of the trials is given in seconds. The function
-  um die Spikezeiten zu bestimmen.
+  should return the event times in a cell-array. Each entry in this
+  array represents the events observed in one trial. Apply
+  \eqnref{hompoissonprob} to generate the event times.
 \end{exercise}
 
 \begin{figure}[t]
   \includegraphics[width=1\textwidth]{poissonraster100hz}
-  \titlecaption{\label{hompoissonfig}Rasterplot von Spikes eines homogenen
+  \titlecaption{\label{hompoissonfig}Rasterplot of spikes of a
-    Poisson Prozesses mit $\lambda=100$\,Hz.}{}
+    homogeneous Poisson process with a rate $\lambda=100$\,Hz.}{}
 \end{figure}
 
 \begin{figure}[t]
   \includegraphics[width=0.45\textwidth]{poissonisihexp20hz}\hfill
   \includegraphics[width=0.45\textwidth]{poissonisihexp100hz}
-  \titlecaption{\label{hompoissonisihfig}Interspikeintervallverteilungen
+  \titlecaption{\label{hompoissonisihfig}Distribution of interspike intervals of two Poisson processes.}{}
-    zweier Poissonprozesse.}{}
 \end{figure}
 
-Der homogene Poissonprozess hat folgende Eigenschaften:
+The homogeneous Poisson process has the following properties:
 \begin{itemize}
-\item Die Intervalle $T$ sind exponentiell verteilt (\figref{hompoissonisihfig}):
+\item Intervals $T$ are exponentially distributed (\figref{hompoissonisihfig}):
   \begin{equation}
     \label{poissonintervals}
     p(T) = \lambda e^{-\lambda T} \; .
   \end{equation}
-\item Das mittlere Intervall ist $\mu_{ISI} = \frac{1}{\lambda}$ .
+\item The average interval is $\mu_{ISI} = \frac{1}{\lambda}$ .
-\item Die Varianz der Intervalle ist $\sigma_{ISI}^2 = \frac{1}{\lambda^2}$ .
+\item The variance of the intervals is $\sigma_{ISI}^2 = \frac{1}{\lambda^2}$ .
-\item Der Variationskoeffizient ist also immer $CV_{ISI} = 1$ .
+\item Thus, the coefficient of variation is always $CV_{ISI} = 1$ .
-\item Die \determ[serielle Korrelationen]{seriellen Korrelationen}
+\item The serial correlation is $\rho_k =0$ for $k>0$, since the
-  $\rho_k =0$ f\"ur $k>0$, da das Auftreten der Ereignisse
+  occurrence of an event is independent of all previous events. Such a
-  unabh\"angig von der Vorgeschichte ist. Ein solcher Prozess wird
+  process is also called a \enterm{renewal process}.
-  auch \determ{Erneuerungsprozess} genannt (\enterm{renewal process}).
+\item The number of events $k$ within a temporal window of duration
-\item Die Anzahl der Ereignisse $k$ innerhalb eines Fensters der
+  $W$ is Poisson distributed:
-  L\"ange W ist \determ[Poisson-Verteilung]{Poissonverteilt}:
 \[ P(k) = \frac{(\lambda W)^ke^{\lambda W}}{k!} \]
 (\figref{hompoissoncountfig})
-\item Der \determ{Fano Faktor} ist immer $F=1$ .
+\item The Fano Faktor is always $F=1$ .
 \end{itemize}
 
 \begin{exercise}{hompoissonspikes.m}{}
-  Schreibe eine Funktion \code{hompoissonspikes()}, die die Spikezeiten
+  Implement a function \code{hompoissonspikes()} that uses a
-  eines homogenen Poisson-Prozesses mit gegebener Rate in Hertz f\"ur
+  homogeneous Poisson process to generate spike events at a given rate
-  eine Anzahl von trials gegebener maximaler L\"ange in Sekunden in
+  for a certain duration and a number of trials. The rate should be
-  einem \codeterm{cell-array} zur\"uckgibt. Benutze die exponentiell-verteilten
+  given in Hertz and the duration of the trials is given in
-  Interspikeintervalle \eqnref{poissonintervals}, um die Spikezeiten zu erzeugen.
+  seconds. The function should return the event times in a
+  cell-array. Each entry in this array represents the events observed
+  in one trial. Apply \eqnref{poissonintervals} to generate the event
+  times.
 \end{exercise}
 
 \begin{figure}[t]
   \includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz10ms}\hfill
   \includegraphics[width=0.48\textwidth]{poissoncounthistdist100hz100ms}
-  \titlecaption{\label{hompoissoncountfig}Z\"ahlstatistik von Poisson Spikes.}{}
+  \titlecaption{\label{hompoissoncountfig}Count statistics of Poisson
+    spiketrains.}{}
 \end{figure}
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Zeitabh\"angige Feuerraten}
+\section{Time-dependent firing rate}
-
+
-Bisher haben wir station\"are Spiketrains betrachtet, deren Statistik
+So far we discussed stationary spiketrains. The statistical properties
-sich innerhalb der Analysezeit nicht ver\"andert (station\"are
+of these did not change within the observation time (stationary point
-Punktprozesse).  Meistens jedoch \"andert sich die Statistik der
+processes. Most commonly, however, this is not the case. A sensory
-Spiketrains eines Neurons mit der Zeit. Z.B. kann ein sensorisches
+neuron, for example, might respond to a stimulus by modulating its
-Neuron auf einen Reiz hin mit einer erh\"ohten Feuerrate antworten
+firing rate (non-stationary point process).
-(nichtstation\"arer Punktprozess).
+
-
+How the firing rate $r(t)$ changes over time is the most important
-Wie die mittlere Anzahl der Spikes sich mit der Zeit ver\"andert, die
+measure, when analyzing non-stationary spike trains. The unit of the
-\determ{Feuerrate} $r(t)$, ist die wichtigste Gr\"o{\ss}e bei
+firing rate is Hertz, i.e. the number of action potentials per
-nicht-station\"aren Spiketrains.  Die Einheit der Feuerrate ist Hertz,
+second. There are different ways to estimate the firing rate and three
-also Anzahl Aktionspotentiale pro Sekunde. Es gibt verschiedene
+of these methods will are illustrated in \figref{psthfig}. All of
-Methoden diese zu bestimmen. Drei solcher Methoden sind in Abbildung
+these have their own justifications and pros- and cons. In the
-\ref{psthfig} dargestellt. Alle Methoden haben ihre Berechtigung und
+following we will discuss the methods shown in \figref{psthfig} more
-ihre Vor- und Nachteile. Im folgenden werden die drei Methoden aus
+closely.
-Abbildung \ref{psthfig} n\"aher erl\"autert.
 
 \begin{figure}[tp]
   \includegraphics[width=\columnwidth]{firingrates}

pointprocesses/lecture/rasterexamples.py

@@ -31,7 +31,7 @@ def pifspikes(input, trials, dt, D=0.1) :
         times = []
         v = vreset
         noise = np.sqrt(2.0*D)*np.random.randn(len(input))/np.sqrt(dt)
-        for k in xrange(len(noise)) :
+        for k in range(len(noise)) :
             v += (input[k]+noise[k])*dt/tau
             if v >= vthresh :
                 v = vreset
@@ -55,7 +55,7 @@ rng = np.random.RandomState(54637281)
 time = np.arange(0.0, duration, dt)
 x = np.zeros(time.shape)+rate
 n = rng.randn(len(time))*drate*tau/np.sqrt(dt)+rate
-for k in xrange(1,len(x)) :
+for k in range(1,len(x)) :
     x[k] = x[k-1] + (n[k]-x[k-1])*dt/tau
 x[x<0.0] = 0.0
 

pointprocesses/lecture/returnmapexamples.py

@@ -31,7 +31,7 @@ def pifspikes(input, trials, dt, D=0.1) :
         times = []
         v = vreset
         noise = np.sqrt(2.0*D)*np.random.randn(len(input))/np.sqrt(dt)
-        for k in xrange(len(noise)) :
+        for k in range(len(noise)) :
             v += (input[k]+noise[k])*dt/tau
             if v >= vthresh :
                 v = vreset
@@ -41,7 +41,7 @@ def pifspikes(input, trials, dt, D=0.1) :
 
 def isis( spikes ) :
     isi = []
-    for k in xrange(len(spikes)) :
+    for k in range(len(spikes)) :
         isi.extend(np.diff(spikes[k]))
     return np.array( isi )
 
@@ -84,7 +84,7 @@ rng = np.random.RandomState(54637281)
 time = np.arange(0.0, duration, dt)
 x = np.zeros(time.shape)+rate
 n = rng.randn(len(time))*drate*tau/np.sqrt(dt)+rate
-for k in xrange(1,len(x)) :
+for k in range(1,len(x)) :
     x[k] = x[k-1] + (n[k]-x[k-1])*dt/tau
 x[x<0.0] = 0.0
 

pointprocesses/lecture/serialcorrexamples.py

@@ -31,7 +31,7 @@ def pifspikes(input, trials, dt, D=0.1) :
         times = []
         v = vreset
         noise = np.sqrt(2.0*D)*np.random.randn(len(input))/np.sqrt(dt)
-        for k in xrange(len(noise)) :
+        for k in range(len(noise)) :
             v += (input[k]+noise[k])*dt/tau
             if v >= vthresh :
                 v = vreset
@@ -41,7 +41,7 @@ def pifspikes(input, trials, dt, D=0.1) :
 
 def isis( spikes ) :
     isi = []
-    for k in xrange(len(spikes)) :
+    for k in range(len(spikes)) :
         isi.extend(np.diff(spikes[k]))
     return np.array( isi )
 
@@ -95,7 +95,7 @@ rng = np.random.RandomState(54637281)
 time = np.arange(0.0, duration, dt)
 x = np.zeros(time.shape)+rate
 n = rng.randn(len(time))*drate*tau/np.sqrt(dt)+rate
-for k in xrange(1,len(x)) :
+for k in range(1,len(x)) :
     x[k] = x[k-1] + (n[k]-x[k-1])*dt/tau
 x[x<0.0] = 0.0
 

pointprocesses/lecture/sta.py

@@ -6,7 +6,7 @@ from IPython import embed
 
 def plot_sta(times, stim, dt, t_min=-0.1, t_max=.1):
     count = 0
-    sta = np.zeros((abs(t_min) + abs(t_max))/dt)
+    sta = np.zeros(int((abs(t_min) + abs(t_max))/dt))
     time = np.arange(t_min, t_max, dt)
     if len(stim.shape) > 1 and stim.shape[1] > 1:
         stim = stim[:,1]

programming/lecture/programming.tex

@@ -40,14 +40,12 @@ variable.
 \begin{figure}
   \centering
   \begin{subfigure}{.5\textwidth}
-    \includegraphics[width=0.8\textwidth]{variable}
+    \includegraphics[width=0.8\textwidth]{variable}\label{variable:a}
-    \label{variable:a}
   \end{subfigure}%
   \begin{subfigure}{.5\textwidth}
-    \includegraphics[width=.8\textwidth]{variableB}
+    \includegraphics[width=.8\textwidth]{variableB}\label{variable:b}
-    \label{variable:b}
   \end{subfigure}
-  \titlecaption{Variables} point to a memory
+  \titlecaption{Variables}{ point to a memory
     address. They further are described by their name and
     data type. The variable's value is stored as a pattern of binary
     values (0 or 1). When reading the variable this pattern is
@@ -630,7 +628,7 @@ matrix). The function \code{cat()} allows to concatenate n-dimensional
 matrices.
 
 To request the length of a vector we used the function
-\code{length()}. This function is \tetbf{not} suited to request
+\code{length()}. This function is \textbf{not} suited to request
 information about the size of a matrix. As mentioned above,
 \code{length()} would return the length of the largest dimension. The
 function \code{size()} however, returns the length in each dimension

programmingstyle/lecture/programmingstyle.tex

@@ -345,7 +345,7 @@ access (read or write) variables of the calling function. Interaction
 with the local function requires to pass all required arguments and to
 take care of the return values of the function.
 
-\emp{Nested functions} are different in this respect. They are
+\emph{Nested functions} are different in this respect. They are
 defined within the body of the parent function (between the keywords
 \code{function} and \code{end}) and have full access to all variables
 defined in the parent function. Working (in particular changing) the

regression/lecture/regression.tex

@@ -86,7 +86,7 @@ large deviations.
 $f_{cost}(\{(x_i, y_i)\}|\{y^{est}_i\})$ is a so called
 \enterm{objective function} or \enterm{cost function}. We aim to adapt
 the model parameters to minimize the error (mean square error) and
-thus the \emph{objective function}. In Chapter~\ref{maximumlikelihood}
+thus the \emph{objective function}. In Chapter~\ref{maximumlikelihoodchapter}
 we will show that the minimization of the mean square error is
 equivalent to maximizing the likelihood that the observations
 originate from the model (assuming a normal distribution of the data
@@ -270,7 +270,7 @@ The gradient is given by partial derivatives
 (Box~\ref{partialderivativebox}) with respect to the parameters $m$
 and $b$ of the linear equation. There is no need to calculate it
 analytically but it can be estimated from the partial derivatives
-using the difference quotient (Box~\ref{differentialquotient}) for
+using the difference quotient (Box~\ref{differentialquotientbox}) for
 small steps $\Delta m$ und $\Delta b$. For example the partial
 derivative with respect to $m$:
 

scientificcomputing-script.tex

@@ -67,7 +67,7 @@
 \lstset{inputpath=regression/code}
 \include{regression/lecture/regression}
 
-\setboolean{showexercisesolutions}{true}
+\setboolean{showexercisesolutions}{false}
 \graphicspath{{likelihood/lecture/}{likelihood/lecture/figures/}}
 \lstset{inputpath=likelihood/code}
 \include{likelihood/lecture/likelihood}

statistics/lecture/displayunivariatedata.py

@@ -53,7 +53,7 @@ ax.annotate('mean plus\nstd. dev.',
             arrowprops=dict(arrowstyle="->", relpos=(0.5,0.0),
             connectionstyle="angle3,angleA=-60,angleB=80") )
 
-ax = fig.add_axes([xpos, ypos, width, height], axis_bgcolor='none')
+ax = fig.add_axes([xpos, ypos, width, height])
 ax.spines['right'].set_visible(False)
 ax.spines['top'].set_visible(False)
 ax.spines['left'].set_visible(False)
@@ -92,7 +92,7 @@ ax.annotate('median',
             arrowprops=dict(arrowstyle="->", relpos=(0.8,0.0),
             connectionstyle="angle3,angleA=-60,angleB=20") )
 
-ax = fig.add_axes([xpos+width+0.03, ypos, 0.98-(xpos+width+0.03), height], axis_bgcolor='none')
+ax = fig.add_axes([xpos+width+0.03, ypos, 0.98-(xpos+width+0.03), height])
 ax.spines['right'].set_visible(False)
 ax.spines['top'].set_visible(False)
 ax.xaxis.set_ticks_position('bottom')