[projects] added solution to isicorrelations

projects/README

@@ -29,8 +29,7 @@ Improve questions
 
 project_isicorrelations
 medium-difficult
-Add statistical test for dependence on adapttau!
+Need to finish solution
-Need to program a solution!
 
 project_isipdffit
 Too technical

projects/instructions.tex

@@ -4,7 +4,7 @@
       \textbf{Evaluation criteria:}
 
       You can view the evaluation criteria on the
-      emph{SciCompScoreSheet.pdf} on Ilias.
+      \emph{SciCompScoreSheet.pdf} on Ilias.
 
       \vspace{1ex}
       \textbf{Dates:}
@@ -23,7 +23,7 @@
       zip-file.
 
       Hint: make the zip file you want to upload, unpack it somewhere
-       else and check if your main script is running properly.
+       else and check if your main script is still running properly.
 
       \vspace{1ex}
       \textbf{Code:}

projects/project.mk

@@ -19,7 +19,8 @@ clean:
 
 latex:
 	pdflatex $(BASENAME).tex
+	pdflatex $(BASENAME).tex
 
-zip: pdf
+zip: latex
 	rm -f zip $(BASENAME).zip
 	zip $(BASENAME).zip *.pdf *.m data/* $(ZIPFILES)

projects/project_isicorrelations/isicorrelations.tex

@@ -1,6 +1,6 @@
 \documentclass[a4paper,12pt,pdftex]{exam}
 
-\newcommand{\ptitle}{Interspike-intervall correlations}
+\newcommand{\ptitle}{Adaptation and interspike-interval correlations}
 \input{../header.tex}
 \firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
 {email: jan.benda@uni-tuebingen.de}
@@ -20,10 +20,10 @@
   Explore the dependence of interspike interval correlations on the firing rate,
   adaptation time constant and noise level.
 
-The neuron is a neuron with an adaptation current. 
+  The neuron is a neuron with an adaptation current.  It is
-    It is implemented in the file \texttt{lifadaptspikes.m}.  Call it
+  implemented in the file \texttt{lifadaptspikes.m}.  Call it with the
-    with the following parameters:
+  following parameters:
-    \begin{lstlisting}
+  \begin{lstlisting}
 trials = 10;
 tmax = 50.0;
 input = 10.0;  % the input I
@@ -31,7 +31,7 @@ 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 );
+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.
@@ -39,29 +39,42 @@ spikes = lifadaptspikes( trials, input, tmax, Dnoise, adapttau, adaptincr );
     and the adaptation time constant via \texttt{adapttau}.
 
   \begin{parts}
-    \part Measure the intensity-response curve of the neuron, that is the mean firing rate 
+    \part Show a spike-raster plot and a time-resolved firing rate of
-    as a function of the input for a range of inputs from 0 to 120.
+    the neuron for an input current of 50 for three different
-
+    adaptation time constants \texttt{adapttau} (10\,m, 100\,ms,
-    \part Compute the correlations between each interspike interval $T_i$ and the next one $T_{i+1}$
+    1\,s). How do the neural responses look like and how do they
-    (serial interspike interval correlation at lag  1). Plot this correlation as a function of the 
+    depend on the adaptation time constant?
-    firing rate by varying the input as in (a).
+
-
+    \uplevel{For all the following analysis we only use the spike
-    \part How does this dependence change for different values of the adaptation 
+      times of the steady-state response, i.e. we skip all spikes
-    time constant \texttt{adapttau}?  Use values between 10\,ms and
+      occuring before at least three times the adaptation time
-    1\,s for \texttt{adapttau}.
+      constant.}
-
+
-    \part Determine the firing rate at which the minimum interspike interval correlation
+    \part \label{ficurve} Measure the intensity-response curve of the
-    occurs. How does the minimum correlation and this firing rate
+    neuron, that is the mean firing rate as a function of the input
-    depend on the adaptation time constant \texttt{adapttau}?
+    for a range of inputs from 0 to 120.
-
+
-    \part How do the results change if the level of the intrinsic noise \texttt{Dnoise} is modified?
+    \part Additionally compute the correlations between each
-    Use values of 1e-4, 1e-3, 1e-2, 1e-1, and 1 for \texttt{Dnoise}.
+    interspike interval $T_i$ and the next one $T_{i+1}$ (serial
-
+    interspike interval correlation at lag 1) for the same range of
-
+    inputs as in (\ref{ficurve}). Plot the correlation as a function
-    \uplevel{If you still have time you can continue with the following question:}
+    of the input.
-
+
-    \part How do the interspike interval distributions look like for the different noise levels
+    \part How does the intensity-response curve and the
-    at some example values for the input and the adaptation time constant?
+    interspike-interval correlations depend on the adaptation time
+    constant \texttt{adapttau}?  Use several values between 10\,ms and
+    1\,s for \texttt{adapttau} (logarithmically distributed).
+
+    \part Determine the firing rate at which the minimum interspike
+    interval correlation occurs. How does the minimum correlation and
+    this firing rate (or the inverse of it, the mean interspike
+    interval) depend on the adaptation time constant
+    \texttt{adapttau}? Is this dependence siginificant? If yes, can
+    you explain this dependence?
+
+    \part How do all 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}.
 
  \end{parts}
 

projects/project_isicorrelations/lifadaptspikes.m

@@ -41,11 +41,8 @@ function spikes = lifadaptspikes( trials, input, tmaxdt, D, tauadapt, adaptincr
             if v >= vthresh
                 v = vreset;
                 a = a + adaptincr/tauadapt;
-                spiketime = i*dt;
+                times(j) = i*dt;
-                if spiketime > 4.0*tauadapt
+                j = j + 1;
-                    times(j) = spiketime - 4.0*tauadapt;
-                    j = j + 1;
-                end
             end
         end
         spikes{k} = times;

projects/project_isicorrelations/solution/firingrate.m

@@ -0,0 +1,11 @@
+function [ rate ] = firingrate(spikes, t0, t1)
+% compute the firing rate from spikes between t0 and t1
+
+rates = zeros(length(spikes), 1);
+for k = 1:length(spikes)
+    spiketimes = spikes{k};
+    rates(k) = length(spiketimes((spiketimes>=t0)&(spiketimes<=t1)))/(t1-t0);
+end
+rate = mean(rates);
+end
+

projects/project_isicorrelations/solution/isicorrelations.m

@@ -0,0 +1,36 @@
+trials = 5;
+tmax = 10.0;
+Dnoise = 1e-2; % noise strength
+adapttau = 0.1; % adaptation time constant in seconds
+adaptincr = 0.5; % adaptation strength
+t0=2.0;
+t1=tmax;
+maxlag = 5;
+
+taus = [0.01, 0.1, 1.0];
+colors = ['r', 'b', 'g'];
+for j = 1:length(taus)
+    adapttau = taus(j);
+    % f-I curves:
+    Is = [0:10:80];
+    rate = zeros(length(Is),1);
+    corr = zeros(length(Is),maxlag);
+    for k = 1:length(Is)
+        input = Is(k);
+        spikes = lifadaptspikes(trials, input, tmax, Dnoise, adapttau, adaptincr);
+        rate(k) = firingrate(spikes, t0, t1);
+        corr(k,:) = serialcorr(spikes, t0, t1, maxlag);
+    end
+
+    figure(1);
+    hold on
+    plot(Is, rate, colors(j));
+    hold off
+
+    figure(2);
+    hold on
+    plot(Is, corr(:,2), colors(j));
+    hold off
+end
+
+pause

projects/project_isicorrelations/solution/lifadaptspikes.m

@@ -0,0 +1,50 @@
+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 + (vthresh-vreset)*rand();
+        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;
+                times(j) = i*dt;
+                j = j + 1;
+            end
+        end
+        spikes{k} = times;
+    end
+end

projects/project_isicorrelations/solution/serialcorr.m

@@ -0,0 +1,15 @@
+function [ isicorrs ] = serialcorr(spikes, t0, t1, maxlag)
+% compute the serial correlations from spikes between t0 and t1
+
+ics = zeros(length(spikes), maxlag);
+for k = 1:length(spikes)
+    spiketimes = spikes{k};
+    isis = diff(spiketimes((spiketimes>=t0)&(spiketimes<=t1)));
+    if length(isis) > 2*maxlag
+        for j=1:maxlag
+            ics(k, j) = corr(isis(j:end)', isis(1:end+1-j)');
+        end
+    end
+end
+isicorrs = mean(ics, 1);
+end

projects/project_photoreceptor/photoreceptor.tex

@@ -36,22 +36,29 @@ resting potential before stimulus onset.
   project, however, you can treat it as if it was the intensity.)
 
   \begin{parts}
-    \part{} Create a plot of the raw data. For each light intensity plot the average response 
+    \part Create a plot of the raw data. For each light intensity plot
-    as a function of time. This plot should also depict the across-trial
+    the average response as a function of time. This plot should also
-    variability in an appropriate way.\\[0.5ex]
+    depict the across-trial variability in an appropriate way.
-    \part{} You will notice that the responses have three main parts, a
+
+    \part You will notice that the responses have three main parts, a
     pre-stimulus phase, the phase in which the light was on, and
     finally a post-stimulus phase. Create an characteristic curve that
     plots the response strength as a function of the stimulus
     intensity for the ``onset'' and the ``steady state''
-    phases of the light response.\\[0.5ex]
+    phases of the light response.
-    \part{} The light switches on at time zero. Estimate the delay between stimulus and response.\\[0.5ex]
+
-    \part{} Analyze the across trial variability in the ``onset'' and ``steady state''. Check for statistically significant differences.
+    \part The light switches on at time zero. Estimate the delay
-    \pate{} The membrane potential shows some fluctuations (noise)
+    between stimulus and response.
+
+    \part Analyze the across trial variability in the ``onset'' and
+    ``steady state''. Check for statistically significant differences.
+
+    \part The membrane potential shows some fluctuations (noise)
     compare the noise before stimulus onset and in the steady state
     phase of the response.
-    \part{} (optional) You may also analyze the post-stimulus response in some
+
-    more detail.
+    \part (optional) You may also analyze the post-stimulus response
+    in some more detail.
   \end{parts}
 \end{questions}