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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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projects/project_isipdffit/isipdffit.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{}{}{}
@@ -51,9 +51,9 @@
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\begin{questions}
\question You are recording the activity of two neurons in response to
a constant stimulus $I$ (think of it, for example,
of a sound wave with intensity $I$).
\question You are recording the activity of two neurons in response
to a constant stimulus $I$ (think of it, for example, of a sound
wave with intensity $I$ and the activity of an auditory neuron).
For different inputs $I$ the interspike interval ($T$) distribution looks
quite different. You want to compare these distributions to
@@ -72,8 +72,8 @@
p_\mathrm{ig}(T) = \frac{1}{\sqrt{4 \pi D T^{3}}} \exp \left[ - \frac{(T - \mu)^{2} }{4 D T \mu^{2}} \right]
\end{equation}
where $\mu$ is the mean interspike interval and
% $D=\textrm{var}(T)/(2\mu^3)$
$D$ is the so called diffusion coefficient.
$D=\textrm{var}(T)/(2\mu^3)$
is the so called diffusion coefficient.
The third one was derived for neurons driven with colored noise:
\begin{equation}\label{pcn}
@@ -92,9 +92,9 @@
\end{equation}
with $\delta=\mu/\tau$.
The two neurons are implemented in the files \texttt{pifouspikes.m}
and \texttt{lifouspikes.m}.
Call them with the following parameters:
The two neurons are implemented in the files \texttt{pifouspikes.m}
and \texttt{lifouspikes.m}. Call them with the following
parameters:
\begin{lstlisting}
trials = 10;
tmax = 50.0;
@@ -102,16 +102,19 @@ input = 10.0; % the input I
Dnoise = 1.0; % noise strength
outau = 1.0; % correlation time of the noise in seconds
spikes = pifouspikes( trials, input, tmax, Dnoise, outau );
spikespif = pifouspikes( trials, input, tmax, Dnoise, outau );
spikeslif = lifouspikes( trials, input, tmax, Dnoise, outau );
\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 input is set via the \texttt{input} variable.
The returned \texttt{spikespif} and \texttt{spikeslif} are cell
arrays with \texttt{trials} elements, each being a vector of spike
times (in seconds) computed for a duration of \texttt{tmax}
seconds. The input is set via the \texttt{input} variable.
\begin{parts}
\part For both model neurons find the inputs $I_i$ required to
make them fire with a mean rate of 10, 20, 50, and 100\,Hz.
\part Compute interspike interval distributions of the two model neurons for these inputs $I_i$.
\part Compute interspike interval distributions of the two model
neurons for these inputs $I_i$.
\part Compare the interspike interval distributions with the exponential
distribution eq.~(\ref{exppdf}) and the inverse Gaussian
@@ -123,15 +126,17 @@ spikes = pifouspikes( trials, input, tmax, Dnoise, outau );
How well does this function describe the data?
Compare the fitted value for $\tau$ with the one used for the model (\texttt{outau}).
Compare the fitted value for $\tau$ with the one used for the
model (\texttt{outau}).
\uplevel{If you still have time you can continue with the following question:}
\part Compare the measured coefficient of variation with eq.~(\ref{cvpcn}).
\part Repeat your analysis for different values of the intrinsic noise strengh of the neurons
\texttt{Dnoise}. Increase or decrease it in factors of ten.
\part Repeat your analysis for different values of the intrinsic
noise strengh of the neurons \texttt{Dnoise}. Increase or decrease
it in factors of ten.
\end{parts}