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4
pointprocesses/lecture/pointprocessscetchA.eps
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%!PS-Adobe-2.0 EPSF-2.0
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%%CreationDate: Mon Oct 26 09:31:15 2015
%%CreationDate: Wed Oct 28 18:47:55 2015
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/Author (benda)
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% /Keywords ()
/CreationDate (Mon Oct 26 09:31:15 2015)
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pointprocesses/lecture/pointprocessscetchB.eps
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%!PS-Adobe-2.0 EPSF-2.0
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%%CreationDate: Mon Oct 26 09:31:16 2015
%%CreationDate: Wed Oct 28 18:47:56 2015
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@ -433,7 +433,7 @@ SDict begin [
/Author (benda)
% /Producer (gnuplot)
% /Keywords ()
/CreationDate (Mon Oct 26 09:31:16 2015)
/CreationDate (Wed Oct 28 18:47:56 2015)
/DOCINFO pdfmark
end
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projects/project_fano_slope/fano_slope.tex
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\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{}{}{}
@ -53,18 +53,19 @@
\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 sound waves with different intensities $I_1$ and $I_2$ and
you measure the activity af an auditory neuron). 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 slope of the
on the spike counts $n$? How does this depend on the slope of the
tuning curve of the neural responses? 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{lifboltzmanspikes.m}.
Call it with the following parameters:
The neuron is implemented in the file \texttt{lifboltzmanspikes.m}.
Call it with the following parameters:
\begin{lstlisting}
trials = 10;
tmax = 50.0;
@ -85,21 +86,24 @@ spikes = lifboltzmanspikes( trials, input, tmax, Dnoise, imax, ithresh, slope );
\begin{parts}
\part
First, show two raster plots for the responses to the two differrent stimuli.
First, show two raster plots for the responses to the two
differrent stimuli.
\part Measure the tuning curve of the neuron with respect to the input. That is,
compute the mean firing rate as a function of the input
strength. Find an appropriate range of input values. Do this for
different values of the \texttt{slope} parameter (values between
0.1 and 2.0).
\part Measure the tuning curve of the neuron with respect to the
input. That is, compute the mean firing rate as a function of the
input strength. Find an appropriate range of input values. Do
this for different values of the \texttt{slope} parameter (values
between 0.1 and 2.0).
\part Generate histograms of the spike counts within $W=200$\,ms of the
responses to the two differrent stimuli $I_1$ and $I_2$. How do they depend on the slope
of the tuning curve of the neuron?
\part Generate histograms of the spike counts within $W=200$\,ms
of the responses to the two differrent stimuli $I_1$ and
$I_2$. How do they depend on the slope of the tuning curve of the
neuron?
\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 slopes can the two stimuli be well discriminated?
@ -110,22 +114,26 @@ spikes = lifboltzmanspikes( trials, input, tmax, Dnoise, imax, ithresh, slope );
$I_2$. Find the threshold $n_{thresh}$ that results in the best
discrimination performance.
\part Also plot the Fano factor as a function of the slope. How is it related to the discriminability?
\part Also plot the Fano factor as a function of the slope. How is
it related to the discriminability?
\uplevel{If you still have time you can continue with the following questions:}
\uplevel{If you still have time you can continue with the
following questions:}
\part You may change the difference between the two stimuli $I_1$ and $I_2$
as well as 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 difference between the two stimuli $I_1$
and $I_2$ as well as 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 For $I_1=10$ the mean firing is about $80$\,Hz. When changing the slope of the tuning curve
this firing rate may also change. Improve your analysis by finding for each slope the input
that results exactly in a firing rate of $80$\,Hz. Set $I_2$ on unit above $I_1$.
\part For $I_1=10$ the mean firing is about $80$\,Hz. When
changing the slope of the tuning curve this firing rate may also
change. Improve your analysis by finding for each slope the input
that results exactly in a firing rate of $80$\,Hz. Set $I_2$ on
unit above $I_1$.
\part How does the dependence of the stimulus discrimination performance on the slope change
when you set both $I_1$ and $I_2$ such that they evoke $80$ and
$100$\,Hz firing rate, respectively?
\part How does the dependence of the stimulus discrimination
performance on the slope change when you set both $I_1$ and $I_2$
such that they evoke $80$ and $100$\,Hz firing rate, respectively?
\end{parts}

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}

41
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}

12
projects/project_mutualinfo/mutualinfo.tex
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@ -6,10 +6,10 @@
\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:} Fabian Sinz}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Benda}
\runningfooter{}{}{}
\pointsinmargin
\bracketedpoints
@ -33,7 +33,7 @@
\begin{questions}
\question A subject was presented two possible objects for a very
brief time ($50$ms). The task of the subject was to report which of
brief time ($50$\,ms). The task of the subject was to report which of
the two objects was shown. In {\tt decisions.mat} you find an array
that stores which object was presented in each trial and which
object was reported by the subject.
@ -50,6 +50,10 @@
information $$I[x:y] = \sum_{x\in\{1,2\}}\sum_{y\in\{1,2\}} P(x,y)
\log_2\frac{P(x,y)}{P(x)P(y)}$$ that the answers provide about the
actually presented object.
The mutual information is a measure from information theory that is
used in neuroscience to quantify, for example, how much information
a spike train carries about a sensory stimulus.
\part What is the maximally achievable mutual information (try to
find out by generating your own dataset which naturally should
yield maximal information)?

19
projects/project_noiseficurves/noiseficurves.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{}{}{}
@ -53,15 +53,15 @@
\begin{questions}
\question You are recording the activity of a neuron in response to
constant stimuli of intensity $I$ (think of that, for example,
of sound waves with intensities $I$).
as a current $I$ injected via a patch-electrode into the neuron).
Measure the tuning curve (also called the intensity-response curve) of the
neuron. That is, what is the firing rate of the neuron's response
as a function of the input $I$. How does this depend on the level of
the intrinsic noise of the neuron?
The neuron is implemented in the file \texttt{lifspikes.m}.
Call it with the following parameters:
The neuron is implemented in the file \texttt{lifspikes.m}. Call it
with the following parameters:
\begin{lstlisting}
trials = 10;
tmax = 50.0;
@ -81,8 +81,13 @@ spikes = lifspikes( trials, input, tmax, Dnoise );
\part Do the same for various noise strength \texttt{Dnoise}. Use $D_{noise} = 1e-3$,
1e-2, and 1e-1. How does the intrinsic noise influence the response curve?
\part Show some interspike interval histograms for some interesting values of the input
and the noise strength.
\part Show some interspike interval histograms for some
interesting values of the input and the noise strength.
\part How does the coefficient of variation $CV_{isi}$ (standard
deviation divided by mean) of the interspike intervalls depend on
the input and the noise level?
\end{parts}

5
scientificcomputing-script.tex
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@ -4,7 +4,7 @@
\setcounter{maxexercise}{10000} % show listings up to exercise maxexercise
\graphicspath{{statistics/lecture/}{statistics/lecture/figures/}{bootstrap/lecture/}{bootstrap/lecture/figures/}{likelihood/lecture/}{likelihood/lecture/figures/}{pointprocesses/lecture/}{pointprocesses/lecture/figures/}{programming/lectures/images/}}
\graphicspath{{statistics/lecture/}{statistics/lecture/figures/}{bootstrap/lecture/}{bootstrap/lecture/figures/}{likelihood/lecture/}{likelihood/lecture/figures/}{pointprocesses/lecture/}{pointprocesses/lecture/figures/}{programming/lectures/images/}{spike_trains/lecture/images/}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -34,8 +34,7 @@
\renewcommand{\texinputpath}{pointprocesses/lecture/}
\include{pointprocesses/lecture/pointprocesses}
lstset{inputpath=spike_trains/code/}
\renewcommand{\texinputpath}{spike_trains/lecture/}
\lstset{inputpath=spike_trains/code/}
\include{spike_trains/lecture/psth_sta}
\lstset{inputpath=designpattern/code/}