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Jan Benda
2015-11-02 09:36:45 +01:00
parent 0bdc7eab98
commit ce2345acdb
10 changed files with 115 additions and 88 deletions
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46
projects/project_fano_time/fano_time.tex
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@@ -6,8 +6,8 @@
\pagestyle{headandfoot}
\runningheadrule
\firstpageheadrule
\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
-- 11/06/2014}
\firstpageheader{Scientific Computing}{Project Assignment}{11/02/2014
-- 11/05/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Benda}
\runningfooter{}{}{}
@@ -53,17 +53,18 @@
\begin{questions}
\question 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 sound waves with different intensities $I_1$ and
$I_2$). Within an observation time of duration $W$ the neuron
responds stochastically with $n_i$ spikes.
of two light intensities with different intensities $I_1$ and $I_2$
and the activity of a ganglion cell in the retina). Within an
observation time of duration $W$ the neuron responds stochastically
with $n$ spikes.
How well can an upstream neuron discriminate the two
stimuli based on the spike counts $n_i$? How does this depend on the
stimuli based on the spike counts $n$? How does this depend on the
duration $W$ of the observation time? How is this related to the fano factor
(the ratio between the variance and the mean of the spike counts)?
The neuron is implemented in the file \texttt{lifadaptspikes.m}.
Call it with the following parameters:
The neuron is implemented in the file \texttt{lifadaptspikes.m}.
Call it with the following parameters:
\begin{lstlisting}
trials = 10;
tmax = 50.0;
@@ -74,8 +75,9 @@ adaptincr = 0.5;
spikes = lifadaptspikes( trials, input, tmax, Dnoise, adapttau, adaptincr );
\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 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.
For the two inputs $I_1$ and $I_2$ use
\begin{lstlisting}
@@ -88,12 +90,13 @@ input = 75.0; % I_2
Show two raster plots for the responses to the two different stimuli.
\part Generate histograms of the spike counts within $W$ of the
responses to the two different stimuli. How do they depend on the observation time $W$
(use values between 1\,ms and 1\,s)?
responses to the two different stimuli. How do they depend on the
observation time $W$ (use values between 1\,ms and 1\,s)?
\part 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 $W$.
\part 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 $W$.
For which observation times can the two stimuli perfectly discriminated?
@@ -104,13 +107,16 @@ input = 75.0; % I_2
$I_2$. For a given $W$ find the threshold $n_{thresh}$ that
results in the best discrimination performance.
\part Also plot the Fano factor as a function of $W$. How is it related to the discriminability?
\part Also plot the Fano factor as a function of $W$. How is it
related to the discriminability?
\uplevel{If you still have time you can continue with the following question:}
\uplevel{If you still have time you can continue with the
following question:}
\part You may change the two stimuli $I_1$ and $I_2$ and the intrinsic noise of the neuron via
\texttt{Dnoise} (change it in factors of ten, higher values will make the responses more variable)
and repeat your analysis.
\part You may change the two stimuli $I_1$ and $I_2$ and the
intrinsic noise of the neuron via \texttt{Dnoise} (change it in
factors of ten, higher values will make the responses more
variable) and repeat your analysis.
\end{parts}