117 lines
4.6 KiB
TeX
117 lines
4.6 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
|
|
|
|
\newcommand{\ptitle}{Stimulus discrimination: time}
|
|
\input{../header.tex}
|
|
\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
|
|
{email: jan.benda@uni-tuebingen.de}
|
|
|
|
\begin{document}
|
|
|
|
\input{../instructions.tex}
|
|
|
|
|
|
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
|
\begin{questions}
|
|
\question An important property of sensory systems is their ability
|
|
to discriminate similar stimuli. For example, discrimination of two
|
|
colors, light intensities, pitch of two tones, sound intensities, etc.
|
|
Here we look at the level of a single neuron. What does it mean that
|
|
two similar stimuli can be discriminated given the spike train
|
|
responses that have been evoked by the two stimuli?
|
|
|
|
You are recording the activity of a neuron in response to two
|
|
different stimuli $I_1$ and $I_2$ (think of them, for example, of
|
|
two different light intensities, $I_1$ and $I_2$, and the spiking
|
|
activity of a ganglion cell in the retina). The neuron responds to a
|
|
stimulus with a number of spikes. You (an upstream neuron) can count
|
|
the number of spikes of this response within an observation time of
|
|
duration $T$. For perfect discrimination, the number of spikes
|
|
evoked by the stronger stimulus within $T$ is always larger than for
|
|
the smaller stimulus. The situation is more complicated, because the
|
|
number of spikes evoked by one stimulus is not fixed but varies,
|
|
such that the number of spikes evoked by the stronger stimulus could
|
|
happen to be lower than the number of spikes evoked by the smaller
|
|
stimulus.
|
|
|
|
The central questions of this project are:
|
|
\begin{itemize}
|
|
\item How can an upstream neuron discriminate two stimuli based
|
|
on the spike counts $n$?
|
|
\item How does this depend on the duration $T$ of the observation
|
|
time?
|
|
\end{itemize}
|
|
|
|
The neuron is implemented in the file \texttt{lifspikes.m}.
|
|
Call it like this:
|
|
\begin{lstlisting}
|
|
trials = 10;
|
|
tmax = 50.0;
|
|
input = 15.0;
|
|
spikes = lifspikes(trials, input, tmax);
|
|
\end{lstlisting}
|
|
The returned \texttt{spikes} is a cell array with \texttt{trials}
|
|
elements, each being a vector of spike times (in seconds) computed
|
|
for a duration of \texttt{tmax} seconds. The intensity of the
|
|
stimulus is given by \texttt{input}.
|
|
|
|
Think of calling the \texttt{lifspikes()} function as a simple way
|
|
of doing an electrophysiological experiment. You are presenting a
|
|
stimulus with an intensity $I$ that you set. The neuron responds to
|
|
this stimulus, and you record this response. After detecting the
|
|
time points of the spikes in your recordings you get what the
|
|
\texttt{lifspikes()} function returns.
|
|
|
|
For the two inputs $I_1$ and $I_2$ to be discriminated use
|
|
\begin{lstlisting}
|
|
input = 14.0; % I_1
|
|
input = 15.0; % I_2
|
|
\end{lstlisting}
|
|
|
|
\begin{parts}
|
|
\part
|
|
Show two raster plots for the responses to the two different
|
|
stimuli. Use an appropriate time window and an appropriate
|
|
number of trials for the spike raster.
|
|
|
|
Just by looking at the raster plots, can you discriminate the two
|
|
stimuli? That is, do you see differences between the two
|
|
responses?
|
|
|
|
\part Generate properly normalized histograms of the spike counts
|
|
within $T$ (use $T=100$\,ms) of the spike responses to the two
|
|
different stimuli. Do the two histograms overlap? What does this
|
|
mean for the discriminability of the two stimuli?
|
|
|
|
How do the histograms of the spike counts depend on the
|
|
observation time $T$? Plot them for four different values of $T$
|
|
(use values of 10\,ms, 100\,ms, 300\,ms and 1\,s).
|
|
|
|
\part \label{discrmeasure} Think about a measure based on the
|
|
spike-count histograms that quantifies how well the two stimuli
|
|
can be distinguished based on the spike counts. Plot the
|
|
dependence of this measure as a function of the observation time
|
|
$T$.
|
|
|
|
For which observation times can the two stimuli perfectly
|
|
discriminated?
|
|
|
|
\underline{Hint:} A possible readout is to set a threshold
|
|
$n_{thresh}$ for the observed spike count. Any response smaller
|
|
than the threshold assumes that the stimulus was $I_1$, any
|
|
response larger than the threshold assumes that the stimulus was
|
|
$I_2$. For a given $T$ find the threshold $n_{thresh}$ that
|
|
results in the best discrimination performance. How can you
|
|
quantify ``best discrimination'' performance?
|
|
|
|
\part Another way to quantify the discriminability of the spike
|
|
counts in response to the two stimuli is to apply an appropriate
|
|
statistical test and check for significant differences. How does
|
|
this compare to your findings from (\ref{discrmeasure})?
|
|
|
|
\end{parts}
|
|
|
|
\end{questions}
|
|
|
|
\end{document}
|