diff --git a/projects/disclaimer.tex b/projects/disclaimer.tex
index 9ef1771..5f15c3e 100644
--- a/projects/disclaimer.tex
+++ b/projects/disclaimer.tex
@@ -5,7 +5,7 @@
Each project has three elements that are graded: (i) the code,
(ii) the slides/figures, and (iii) the presentation.
- \vspace{.5cm}
+ \vspace{1ex}
The {\bf code} and the {\bf presentation} should be uploaded to
ILIAS at latest on Thursday, November 6th, 12:00h.
@@ -13,7 +13,7 @@
your presentation as a pdf file. Bundle everything into a
{\em single} zip-file.
- \vspace{.5cm}
+ \vspace{1ex}
The {\bf code} should be exectuable without any further
adjustments from us. This means that you need to include all
@@ -25,11 +25,11 @@
and comprehensible by third persons (use proper and consistent
variable names).
- \vspace{.5cm} \textbf{Please write your name and matriculation
+ \vspace{1ex} \textbf{Please write your name and matriculation
number as a comment at the top of a script called \texttt{main.m}!}
The \texttt{main.m} script then should call all your scripts.
- \vspace{.5cm}
+ \vspace{1ex}
The {\bf presentation} should be {\em at most} 10min long and be
held in English. In the presentation you should (i) briefly
@@ -38,4 +38,4 @@
figures showing your results. We will store all presentations on
one computer to allow fast transitions between talks.
- }}
\ No newline at end of file
+ }}
diff --git a/projects/project_adaptation_fit/adaptation_fit.tex b/projects/project_adaptation_fit/adaptation_fit.tex
old mode 100755
new mode 100644
diff --git a/projects/project_eod/eod.tex b/projects/project_eod/eod.tex
old mode 100755
new mode 100644
diff --git a/projects/project_eyetracker/eyetracker.tex b/projects/project_eyetracker/eyetracker.tex
old mode 100755
new mode 100644
diff --git a/projects/project_vector_strength/Makefile b/projects/project_fano_slope/Makefile
similarity index 74%
rename from projects/project_vector_strength/Makefile
rename to projects/project_fano_slope/Makefile
index dad25ce..6422eb4 100644
--- a/projects/project_vector_strength/Makefile
+++ b/projects/project_fano_slope/Makefile
@@ -7,4 +7,4 @@ clean:
rm -f `basename *.tex .tex`.pdf
zip: latex
- zip `basename *.tex .tex`.zip *.pdf *.dat *.mat
+ zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m
diff --git a/projects/project_fano_slope/fano_slope.tex b/projects/project_fano_slope/fano_slope.tex
new file mode 100644
index 0000000..1ffe91e
--- /dev/null
+++ b/projects/project_fano_slope/fano_slope.tex
@@ -0,0 +1,133 @@
+\documentclass[addpoints,10pt]{exam}
+\usepackage{url}
+\usepackage{color}
+\usepackage{hyperref}
+
+\pagestyle{headandfoot}
+\runningheadrule
+\firstpageheadrule
+\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
+ -- 11/06/2014}
+%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
+\firstpagefooter{}{}{}
+\runningfooter{}{}{}
+\pointsinmargin
+\bracketedpoints
+
+%\printanswers
+%\shadedsolutions
+
+%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{listings}
+\lstset{
+ basicstyle=\ttfamily,
+ numbers=left,
+ showstringspaces=false,
+ language=Matlab,
+ breaklines=true,
+ breakautoindent=true,
+ columns=flexible,
+ frame=single,
+% captionpos=t,
+ xleftmargin=2em,
+ xrightmargin=1em,
+% aboveskip=10pt,
+ %title=\lstname,
+% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
+ }
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+% \begin{flushright}
+% \gradetable[h][questions]
+% \end{flushright}
+
+\begin{center}
+ \input{../disclaimer.tex}
+\end{center}
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+\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.
+
+ 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
+ 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)?
+
+ \begin{parts}
+ \part The neuron is implemented in the file \texttt{lifboltzmanspikes.m}.
+ Call it with the following parameters:
+ \begin{lstlisting}
+ trials = 10;
+ tmax = 50.0;
+ Dnoise = 1.0;
+ imax = 25.0;
+ ithresh = 10.0;
+ slope=0.2;
+ input = 10.0;
+
+ spikes = lifboltzmanspikes( trials, input, tmax, Dnoise, imax, ithresh, slope );
+ \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.
+
+ For the two inputs use $I_1=10$ and $I_2=I_1 + 1$.
+
+ 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 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 $W$.
+
+ For which slopes can the two stimuli perfectly discriminated?
+
+ 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 $I_2$. What is the
+ probability that the stimulus was indeed $I_1$ or $I_2$,
+ respectively? 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?
+
+ \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 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?
+
+ \end{parts}
+
+\end{questions}
+
+\end{document}
diff --git a/projects/project_fano_slope/lifboltzmanspikes.m b/projects/project_fano_slope/lifboltzmanspikes.m
new file mode 100644
index 0000000..14640e4
--- /dev/null
+++ b/projects/project_fano_slope/lifboltzmanspikes.m
@@ -0,0 +1,51 @@
+function spikes = lifboltzmanspikes( trials, input, tmaxdt, D, imax, ithresh, slope )
+% Generate spike times of a leaky integrate-and-fire neuron
+% trials: the number of trials to be generated
+% input: the stimulus either as a single value or as a vector
+% tmaxdt: in case of a single value stimulus the duration of a trial
+% in case of a vector as a stimulus the time step
+% D: the strength of additive white noise
+% imax: maximum output of boltzman
+% ithresh: threshold of boltzman input
+% slope: slope factor of boltzman input
+
+ tau = 0.01;
+ if nargin < 4
+ D = 1e0;
+ end
+ if nargin < 5
+ imax = 20;
+ end
+ if nargin < 6
+ ithresh = 10;
+ end
+ if nargin < 7
+ slope = 1;
+ end
+ vreset = 0.0;
+ vthresh = 10.0;
+ dt = 1e-4;
+
+ if length( input ) == 1
+ input = input * ones( ceil( tmaxdt/dt ), 1 );
+ else
+ dt = tmaxdt;
+ end
+ inb = imax./(1.0+exp(-slope.*(input - ithresh)));
+ spikes = cell( trials, 1 );
+ for k=1:trials
+ times = [];
+ j = 1;
+ v = vreset;
+ noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
+ for i=1:length( noise )
+ v = v + ( - v + noise(i) + inb(i))*dt/tau;
+ if v >= vthresh
+ v = vreset;
+ times(j) = i*dt;
+ j = j + 1;
+ end
+ end
+ spikes{k} = times;
+ end
+end
diff --git a/projects/project_fano_time/Makefile b/projects/project_fano_time/Makefile
new file mode 100644
index 0000000..6422eb4
--- /dev/null
+++ b/projects/project_fano_time/Makefile
@@ -0,0 +1,10 @@
+latex:
+ pdflatex *.tex > /dev/null
+ pdflatex *.tex > /dev/null
+
+clean:
+ rm -rf *.log *.aux *.zip *.out auto
+ rm -f `basename *.tex .tex`.pdf
+
+zip: latex
+ zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m
diff --git a/projects/project_fano_time/fano_time.tex b/projects/project_fano_time/fano_time.tex
new file mode 100644
index 0000000..48eb889
--- /dev/null
+++ b/projects/project_fano_time/fano_time.tex
@@ -0,0 +1,119 @@
+\documentclass[addpoints,10pt]{exam}
+\usepackage{url}
+\usepackage{color}
+\usepackage{hyperref}
+
+\pagestyle{headandfoot}
+\runningheadrule
+\firstpageheadrule
+\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
+ -- 11/06/2014}
+%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
+\firstpagefooter{}{}{}
+\runningfooter{}{}{}
+\pointsinmargin
+\bracketedpoints
+
+%\printanswers
+%\shadedsolutions
+
+%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{listings}
+\lstset{
+ basicstyle=\ttfamily,
+ numbers=left,
+ showstringspaces=false,
+ language=Matlab,
+ breaklines=true,
+ breakautoindent=true,
+ columns=flexible,
+ frame=single,
+% captionpos=t,
+ xleftmargin=2em,
+ xrightmargin=1em,
+% aboveskip=10pt,
+ %title=\lstname,
+% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
+ }
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+% \begin{flushright}
+% \gradetable[h][questions]
+% \end{flushright}
+
+\begin{center}
+ \input{../disclaimer.tex}
+\end{center}
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+\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.
+
+ How well can an upstream neuron discriminate the two
+ stimuli based on the spike counts $n_i$? 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)?
+
+ \begin{parts}
+ \part The neuron is implemented in the file \texttt{lifadaptspikes.m}.
+ Call it with the following parameters:
+ \begin{lstlisting}
+ trials = 10;
+ tmax = 50.0;
+ input = 65.0;
+ Dnoise = 0.1;
+ adapttau = 0.2;
+ 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.
+
+ For the two inputs $I_1$ and $I_2$ use
+ \begin{lstlisting}
+ input = 65.0; % I_1
+ input = 75.0; % I_2
+ \end{lstlisting}
+
+ Show two raster plots for the responses to the two differrent stimuli.
+
+ \part Generate histograms of the spike counts within $W$ of the
+ responses to the two differrent 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 $W$.
+
+ For which observation times can the two stimuli perfectly discriminated?
+
+ 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 $I_2$. What is the
+ probability that the stimulus was indeed $I_1$ or $I_2$,
+ respectively? 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?
+
+ \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.
+
+ \end{parts}
+
+\end{questions}
+
+\end{document}
diff --git a/projects/project_fano_time/lifadaptspikes.m b/projects/project_fano_time/lifadaptspikes.m
new file mode 100644
index 0000000..2ef1874
--- /dev/null
+++ b/projects/project_fano_time/lifadaptspikes.m
@@ -0,0 +1,53 @@
+function spikes = lifadaptspikes( trials, input, tmaxdt, D, tauadapt, adaptincr )
+% Generate spike times of a leaky integrate-and-fire neuron
+% with an adaptation current
+% trials: the number of trials to be generated
+% input: the stimulus either as a single value or as a vector
+% tmaxdt: in case of a single value stimulus the duration of a trial
+% in case of a vector as a stimulus the time step
+% D: the strength of additive white noise
+% tauadapt: adaptation time constant
+% adaptincr: adaptation strength
+
+ tau = 0.01;
+ if nargin < 4
+ D = 1e0;
+ end
+ if nargin < 5
+ tauadapt = 0.1;
+ end
+ if nargin < 6
+ adaptincr = 1.0;
+ end
+ vreset = 0.0;
+ vthresh = 10.0;
+ dt = 1e-4;
+
+ if max( size( input ) ) == 1
+ input = input * ones( ceil( tmaxdt/dt ), 1 );
+ else
+ dt = tmaxdt;
+ end
+ spikes = cell( trials, 1 );
+ for k=1:trials
+ times = [];
+ j = 1;
+ v = vreset;
+ a = 0.0;
+ noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
+ for i=1:length( noise )
+ v = v + ( - v - a + noise(i) + input(i))*dt/tau;
+ a = a + ( - a )*dt/tauadapt;
+ if v >= vthresh
+ v = vreset;
+ a = a + adaptincr/tauadapt;
+ spiketime = i*dt;
+ if spiketime > 4.0*tauadapt
+ times(j) = spiketime - 4.0*tauadapt;
+ j = j + 1;
+ end
+ end
+ end
+ spikes{k} = times;
+ end
+end
diff --git a/projects/project_isicorrelations/Makefile b/projects/project_isicorrelations/Makefile
new file mode 100644
index 0000000..6422eb4
--- /dev/null
+++ b/projects/project_isicorrelations/Makefile
@@ -0,0 +1,10 @@
+latex:
+ pdflatex *.tex > /dev/null
+ pdflatex *.tex > /dev/null
+
+clean:
+ rm -rf *.log *.aux *.zip *.out auto
+ rm -f `basename *.tex .tex`.pdf
+
+zip: latex
+ zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m
diff --git a/projects/project_isicorrelations/isicorrelations.tex b/projects/project_isicorrelations/isicorrelations.tex
new file mode 100644
index 0000000..2b50881
--- /dev/null
+++ b/projects/project_isicorrelations/isicorrelations.tex
@@ -0,0 +1,109 @@
+\documentclass[addpoints,10pt]{exam}
+\usepackage{url}
+\usepackage{color}
+\usepackage{hyperref}
+
+\pagestyle{headandfoot}
+\runningheadrule
+\firstpageheadrule
+\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
+ -- 11/06/2014}
+%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
+\firstpagefooter{}{}{}
+\runningfooter{}{}{}
+\pointsinmargin
+\bracketedpoints
+
+%\printanswers
+%\shadedsolutions
+
+%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{listings}
+\lstset{
+ basicstyle=\ttfamily,
+ numbers=left,
+ showstringspaces=false,
+ language=Matlab,
+ breaklines=true,
+ breakautoindent=true,
+ columns=flexible,
+ frame=single,
+% captionpos=t,
+ xleftmargin=2em,
+ xrightmargin=1em,
+% aboveskip=10pt,
+ %title=\lstname,
+% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
+ }
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+% \begin{flushright}
+% \gradetable[h][questions]
+% \end{flushright}
+
+\begin{center}
+ \input{../disclaimer.tex}
+\end{center}
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+\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 $I$). The neuron has an adaptatation
+ current that adapts the firing rate with a slow time constant down.
+
+ Explore the dependence of interspike interval correlations on the firing rate,
+ adaptation time constant and noise level.
+
+ \begin{parts}
+ \part The neuron is a neuron with an adaptation current.
+ It is implemented in the file \texttt{lifadaptspikes.m}. Call it
+ with the following parameters:
+ \begin{lstlisting}
+ trials = 10;
+ tmax = 50.0;
+ input = 10.0; % the input I
+ Dnoise = 1e-2; % noise strength
+ adapttau = 0.1; % adaptation time constant in seconds
+ adaptincr = 0.5; % adaptation strength
+
+ 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 input is set via the \texttt{input} variable, the noise strength via \texttt{Dnoise},
+ and the adaptation time constant via \texttt{adapttau}.
+
+ \part Measure the intensity-response curve of the neuron, that is the mean firing rate
+ as a function of the input for a range of inputs from 0 to 120.
+
+ \part Compute the correlations between each interspike interval $T_i$ and the next one $T_{i+1}$
+ (serial interspike interval correlation at lag 1). Plot this correlation as a function of the
+ firing rate by varying the input as in (a).
+
+ \part How does this dependence change for different values of the adaptation
+ time constant \texttt{adapttau}? Use values between 10\,ms and
+ 1\,s for \texttt{adapttau}.
+
+ \part Determine the firing rate at which the minimum interspike interval correlation
+ occurs. How does the minimum correlation and this firing rate
+ depend on the adaptation time constant \texttt{adapttau}?
+
+ \part How do the results change if the level of the intrinsic noise \texttt{Dnoise} is modified?
+ Use values of 1e-4, 1e-3, 1e-2, 1e-1, and 1 for \texttt{Dnoise}.
+
+
+ \uplevel{If you still have time you can continue with the following question:}
+
+ \part How do the interspike interval distributions look like for the different noise levels
+ at some example values for the input and the adaptation time constant?
+
+ \end{parts}
+
+\end{questions}
+
+\end{document}
diff --git a/projects/project_isicorrelations/lifadaptspikes.m b/projects/project_isicorrelations/lifadaptspikes.m
new file mode 100644
index 0000000..2ef1874
--- /dev/null
+++ b/projects/project_isicorrelations/lifadaptspikes.m
@@ -0,0 +1,53 @@
+function spikes = lifadaptspikes( trials, input, tmaxdt, D, tauadapt, adaptincr )
+% Generate spike times of a leaky integrate-and-fire neuron
+% with an adaptation current
+% trials: the number of trials to be generated
+% input: the stimulus either as a single value or as a vector
+% tmaxdt: in case of a single value stimulus the duration of a trial
+% in case of a vector as a stimulus the time step
+% D: the strength of additive white noise
+% tauadapt: adaptation time constant
+% adaptincr: adaptation strength
+
+ tau = 0.01;
+ if nargin < 4
+ D = 1e0;
+ end
+ if nargin < 5
+ tauadapt = 0.1;
+ end
+ if nargin < 6
+ adaptincr = 1.0;
+ end
+ vreset = 0.0;
+ vthresh = 10.0;
+ dt = 1e-4;
+
+ if max( size( input ) ) == 1
+ input = input * ones( ceil( tmaxdt/dt ), 1 );
+ else
+ dt = tmaxdt;
+ end
+ spikes = cell( trials, 1 );
+ for k=1:trials
+ times = [];
+ j = 1;
+ v = vreset;
+ a = 0.0;
+ noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
+ for i=1:length( noise )
+ v = v + ( - v - a + noise(i) + input(i))*dt/tau;
+ a = a + ( - a )*dt/tauadapt;
+ if v >= vthresh
+ v = vreset;
+ a = a + adaptincr/tauadapt;
+ spiketime = i*dt;
+ if spiketime > 4.0*tauadapt
+ times(j) = spiketime - 4.0*tauadapt;
+ j = j + 1;
+ end
+ end
+ end
+ spikes{k} = times;
+ end
+end
diff --git a/projects/project_isipdffit/Makefile b/projects/project_isipdffit/Makefile
new file mode 100644
index 0000000..6422eb4
--- /dev/null
+++ b/projects/project_isipdffit/Makefile
@@ -0,0 +1,10 @@
+latex:
+ pdflatex *.tex > /dev/null
+ pdflatex *.tex > /dev/null
+
+clean:
+ rm -rf *.log *.aux *.zip *.out auto
+ rm -f `basename *.tex .tex`.pdf
+
+zip: latex
+ zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m
diff --git a/projects/project_isipdffit/isipdffit.tex b/projects/project_isipdffit/isipdffit.tex
new file mode 100644
index 0000000..7f3a117
--- /dev/null
+++ b/projects/project_isipdffit/isipdffit.tex
@@ -0,0 +1,140 @@
+\documentclass[addpoints,10pt]{exam}
+\usepackage{url}
+\usepackage{color}
+\usepackage{hyperref}
+
+\pagestyle{headandfoot}
+\runningheadrule
+\firstpageheadrule
+\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
+ -- 11/06/2014}
+%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
+\firstpagefooter{}{}{}
+\runningfooter{}{}{}
+\pointsinmargin
+\bracketedpoints
+
+%\printanswers
+%\shadedsolutions
+
+%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{listings}
+\lstset{
+ basicstyle=\ttfamily,
+ numbers=left,
+ showstringspaces=false,
+ language=Matlab,
+ breaklines=true,
+ breakautoindent=true,
+ columns=flexible,
+ frame=single,
+% captionpos=t,
+ xleftmargin=2em,
+ xrightmargin=1em,
+% aboveskip=10pt,
+ %title=\lstname,
+% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
+ }
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+% \begin{flushright}
+% \gradetable[h][questions]
+% \end{flushright}
+
+\begin{center}
+ \input{../disclaimer.tex}
+\end{center}
+
+%%%%%%%%%%%%%% 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 $I$).
+
+ For different inputs $I$ the interspike interval ($T$) distribution looks
+ quite different. You want to compare these distributions to
+ the following three standard distributions.
+
+ The first is the exponential distribution of a Poisson spike train:
+ \begin{equation}
+ \label{exppdf}
+ p_{exp}(T) = \lambda e^{-\lambda T}
+ \end{equation}
+ where $\lambda$ is the mean firing rate of the response.
+
+ The second distribution is the inverse Gaussian:
+ \begin{equation}
+ \label{invgauss}
+ 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
+ $D=\textrm{var}(T)/(2\mu^3)$ is the so called diffusion coefficient.
+
+ The third one was derived for neurons driven with colored noise:
+ \begin{equation}\label{pcn}
+ p_\mathrm{cn}(T)=\frac{1}{2\tau\sqrt{4\pi\epsilon\gamma_1^3}}\exp\left[-\frac{(T-\mu)^2}{4\epsilon\tau^2\gamma_1}\right]\left\{\frac{[(\mu-T)\gamma_2+2\gamma_1\tau]^2}{2\gamma_1\tau^2}-\epsilon(\gamma_2^2-2\gamma_1e^{-T/\tau})\right\}
+ \end{equation}
+ with $\gamma_1(T)=T/\tau+e^{-T/\tau}-1$, $\gamma_2(T)=1-e^{-T/\tau}$
+ and correlation time of the colored noise $\tau$.
+ Eq.~(\ref{pcn}) thus has the three parameter $\mu$, $\epsilon>0$, and $\tau$.
+
+ The squared coefficient of variation (standard deviation of the
+ interspike intervals divided by their mean) of the density
+ eq.~(\ref{pcn}) is given by
+ \begin{equation}
+ \label{cvpcn}
+ C_V^2=\frac{2}{\delta}\left[\epsilon\left(1-\frac{1-e^{-\delta}}{\delta}\right)+\epsilon^2\left(e^{-\delta}+\frac{(1-e^{-\delta})(1-2e^{-\delta})}{\delta}\right)\right]
+ \end{equation}
+ with $\delta=\mu/\tau$.
+
+ \begin{parts}
+ \part 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;
+ 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 );
+ \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.
+
+ \part Find for both model neurons the inputs $I_i$ required to make the 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 Compare the interspike interval distributions with the exponential
+ distribution eq.~(\ref{exppdf}) and the inverse Gaussian
+ eq.~(\ref{invgauss}) by measuring their parameters from the
+ interspike intervals. How well do theu describe the real
+ distributions for the different conditions?
+
+ \part Also fit eq.~(\ref{pcn}) to the data. Here you need to apply a non-linear fit algorithm.
+
+ How well does this function describe the data?
+
+ 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.
+
+ \end{parts}
+
+\end{questions}
+
+\end{document}
diff --git a/projects/project_isipdffit/lifouspikes.m b/projects/project_isipdffit/lifouspikes.m
new file mode 100644
index 0000000..fc1f5d5
--- /dev/null
+++ b/projects/project_isipdffit/lifouspikes.m
@@ -0,0 +1,44 @@
+function spikes = lifouspikes( trials, input, tmaxdt, D, outau )
+% Generate spike times of a leaky integrate-and-fire neuron
+% trials: the number of trials to be generated
+% input: the stimulus either as a single value or as a vector
+% tmaxdt: in case of a single value stimulus the duration of a trial
+% in case of a vector as a stimulus the time step
+% D: the strength of additive white noise
+% outau: time constant of the colored noise
+
+ tau = 0.01;
+ if nargin < 4
+ D = 1e0;
+ end
+ if nargin < 5
+ outau = 1.0;
+ end
+ vreset = 0.0;
+ vthresh = 10.0;
+ dt = 1e-4;
+
+ if length( input ) == 1
+ input = input * ones( ceil( tmaxdt/dt ), 1 );
+ else
+ dt = tmaxdt;
+ end
+ spikes = cell( trials, 1 );
+ for k=1:trials
+ times = [];
+ j = 1;
+ n = 0.0;
+ v = vreset;
+ noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
+ for i=1:length( noise )
+ n = n + ( - n + noise(i))*dt/outau;
+ v = v + ( - v + n + input(i))*dt/tau;
+ if v >= vthresh
+ v = vreset;
+ times(j) = i*dt;
+ j = j + 1;
+ end
+ end
+ spikes{k} = times;
+ end
+end
diff --git a/projects/project_isipdffit/pifouspikes.m b/projects/project_isipdffit/pifouspikes.m
new file mode 100644
index 0000000..b6516cc
--- /dev/null
+++ b/projects/project_isipdffit/pifouspikes.m
@@ -0,0 +1,44 @@
+function spikes = pifouspikes( trials, input, tmaxdt, D, outau )
+% Generate spike times of a perfect integrate-and-fire neuron
+% trials: the number of trials to be generated
+% input: the stimulus either as a single value or as a vector
+% tmaxdt: in case of a single value stimulus the duration of a trial
+% in case of a vector as a stimulus the time step
+% D: the strength of additive white noise
+% outau: time constant of the colored noise
+
+ tau = 0.01;
+ if nargin < 4
+ D = 1e0;
+ end
+ if nargin < 5
+ outau = 1.0;
+ end
+ vreset = 0.0;
+ vthresh = 10.0;
+ dt = 1e-4;
+
+ if length( input ) == 1
+ input = input * ones( ceil( tmaxdt/dt ), 1 );
+ else
+ dt = tmaxdt;
+ end
+ spikes = cell( trials, 1 );
+ for k=1:trials
+ times = [];
+ j = 1;
+ n = 0.0;
+ v = vreset;
+ noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
+ for i=1:length( noise )
+ n = n + ( - n + noise(i))*dt/outau;
+ v = v + ( n + input(i))*dt/tau;
+ if v >= vthresh
+ v = vreset;
+ times(j) = i*dt;
+ j = j + 1;
+ end
+ end
+ spikes{k} = times;
+ end
+end
diff --git a/projects/project_mutualinfo/mutualinfo.tex b/projects/project_mutualinfo/mutualinfo.tex
old mode 100755
new mode 100644
diff --git a/projects/project_noiseficurves/Makefile b/projects/project_noiseficurves/Makefile
new file mode 100644
index 0000000..6422eb4
--- /dev/null
+++ b/projects/project_noiseficurves/Makefile
@@ -0,0 +1,10 @@
+latex:
+ pdflatex *.tex > /dev/null
+ pdflatex *.tex > /dev/null
+
+clean:
+ rm -rf *.log *.aux *.zip *.out auto
+ rm -f `basename *.tex .tex`.pdf
+
+zip: latex
+ zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m
diff --git a/projects/project_noiseficurves/lifspikes.m b/projects/project_noiseficurves/lifspikes.m
new file mode 100644
index 0000000..cfa0f55
--- /dev/null
+++ b/projects/project_noiseficurves/lifspikes.m
@@ -0,0 +1,38 @@
+function spikes = lifspikes( trials, input, tmaxdt, D )
+% Generate spike times of a leaky integrate-and-fire neuron
+% trials: the number of trials to be generated
+% input: the stimulus either as a single value or as a vector
+% tmaxdt: in case of a single value stimulus the duration of a trial
+% in case of a vector as a stimulus the time step
+% D: the strength of additive white noise
+
+ tau = 0.01;
+ if nargin < 4
+ D = 1e0;
+ end
+ vreset = 0.0;
+ vthresh = 10.0;
+ dt = 1e-4;
+
+ if length( input ) == 1
+ input = input * ones( ceil( tmaxdt/dt ), 1 );
+ else
+ dt = tmaxdt;
+ end
+ spikes = cell( trials, 1 );
+ for k=1:trials
+ times = [];
+ j = 1;
+ v = vreset;
+ noise = sqrt(2.0*D)*randn( length( input ), 1 )/sqrt(dt);
+ for i=1:length( noise )
+ v = v + ( - v + noise(i) + input(i))*dt/tau;
+ if v >= vthresh
+ v = vreset;
+ times(j) = i*dt;
+ j = j + 1;
+ end
+ end
+ spikes{k} = times;
+ end
+end
diff --git a/projects/project_noiseficurves/noiseficurves.tex b/projects/project_noiseficurves/noiseficurves.tex
new file mode 100644
index 0000000..dc68952
--- /dev/null
+++ b/projects/project_noiseficurves/noiseficurves.tex
@@ -0,0 +1,91 @@
+\documentclass[addpoints,10pt]{exam}
+\usepackage{url}
+\usepackage{color}
+\usepackage{hyperref}
+
+\pagestyle{headandfoot}
+\runningheadrule
+\firstpageheadrule
+\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
+ -- 11/06/2014}
+%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
+\firstpagefooter{}{}{}
+\runningfooter{}{}{}
+\pointsinmargin
+\bracketedpoints
+
+%\printanswers
+%\shadedsolutions
+
+%%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\usepackage{listings}
+\lstset{
+ basicstyle=\ttfamily,
+ numbers=left,
+ showstringspaces=false,
+ language=Matlab,
+ breaklines=true,
+ breakautoindent=true,
+ columns=flexible,
+ frame=single,
+% captionpos=t,
+ xleftmargin=2em,
+ xrightmargin=1em,
+% aboveskip=10pt,
+ %title=\lstname,
+% title={\protect\filename@parse{\lstname}\protect\filename@base.\protect\filename@ext}
+ }
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+% \begin{flushright}
+% \gradetable[h][questions]
+% \end{flushright}
+
+\begin{center}
+ \input{../disclaimer.tex}
+\end{center}
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+\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 $I$).
+
+ 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?
+
+ \begin{parts}
+ \part The neuron is implemented in the file \texttt{lifspikes.m}.
+ Call it with the following parameters:
+ \begin{lstlisting}
+ trials = 10;
+ tmax = 50.0;
+ input = 10.0; % the input I
+ Dnoise = 1.0; % noise strength
+
+ spikes = lifspikes( trials, input, tmax, Dnoise );
+ \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 noise strength via \texttt{Dnoise}.
+
+ \part First set the noise \texttt{Dnoise=0} (no noise). Compute and plot the firing rate
+ as a function of the input for inputs ranging from 0 to 20.
+
+ \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.
+
+ \end{parts}
+
+\end{questions}
+
+\end{document}
diff --git a/projects/project_numbers/numbers.tex b/projects/project_numbers/numbers.tex
old mode 100755
new mode 100644
diff --git a/projects/project_onset_fi/onset_fi.tex b/projects/project_onset_fi/onset_fi.tex
old mode 100755
new mode 100644
diff --git a/projects/project_q-values/qvalues.tex b/projects/project_q-values/qvalues.tex
old mode 100755
new mode 100644
diff --git a/projects/project_spectra/spectra.tex b/projects/project_spectra/spectra.tex
old mode 100755
new mode 100644
diff --git a/projects/project_steady_fi/steady_state_fi.tex b/projects/project_steady_fi/steady_state_fi.tex
old mode 100755
new mode 100644
diff --git a/projects/project_stimulus_reconstruction/stimulus_reconstruction.tex b/projects/project_stimulus_reconstruction/stimulus_reconstruction.tex
old mode 100755
new mode 100644
diff --git a/projects/project_template/Makefile b/projects/project_template/Makefile
index dad25ce..6422eb4 100644
--- a/projects/project_template/Makefile
+++ b/projects/project_template/Makefile
@@ -7,4 +7,4 @@ clean:
rm -f `basename *.tex .tex`.pdf
zip: latex
- zip `basename *.tex .tex`.zip *.pdf *.dat *.mat
+ zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m
diff --git a/projects/project_template/template.tex b/projects/project_template/template.tex
old mode 100755
new mode 100644