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[pointprocesses] fixed spike count exercise

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Jan Benda 2021-01-25 18:42:05 +01:00
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pointprocesses/exercises/pointprocesses-1.tex
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@ -158,20 +158,25 @@
\question \qt{Statistics of spike counts} \question \qt{Statistics of spike counts}
Now let's have a look at the statistics of the spike counts. Now let's have a look at the statistics of the spike counts.
\begin{parts} \begin{parts}
\part Write a function that counts and returns a vector with the \part \label{counts} Write a function that counts with the number
number of spikes in windows of a given width $W$. of spikes in windows of a given width $W$. The spikes are passed
to the function as a cell array containing vectors of spike times.
The function returns a single vector with all the spike counts.
\begin{solution}
\lstinputlisting{counts.m}
\end{solution}
Use this function to generate a properly normalized histogram of \part Generate a properly normalized histogram of spike counts for
spike counts for the data of the three types of neurons. Use the data of the three types of neurons. Use 100\,ms for the window
100\,ms for the window width. width and the function from (\ref{counts}) for computing the spike
counts.
Compare the distributions with the Poisson distribution expected In addition, compare the distributions with the Poisson
for a Poisson spike train: distribution expected for a Poisson spike train:
\[ P(k) = \frac{(\lambda W)^ke^{\lambda W}}{k!} \; , \] where \[ P(k) = \frac{(\lambda W)^ke^{\lambda W}}{k!} \; , \] where
$\lambda$ is the rate of the spike train that you should estimate $\lambda$ is the rate of the spike train that you should estimate
from the data. from the data.
\begin{solution} \begin{solution}
\lstinputlisting{counts.m}
\newsolutionpage \newsolutionpage
\lstinputlisting{spikecountshists.m} \lstinputlisting{spikecountshists.m}
\colorbox{white}{\includegraphics[width=1\textwidth]{spikecountshists}} \colorbox{white}{\includegraphics[width=1\textwidth]{spikecountshists}}