Merge branch 'master' of whale.am28.uni-tuebingen.de:scientificComputing

plotting/lecture/plotting-chapter.tex

@@ -28,6 +28,8 @@
 
 \subsection{Polar plot}
 
+\subsection{print instead of saveas????}
+
 \subsection{Movies and animations}
 
 \section{TODO}

projects/header.tex

@@ -7,7 +7,7 @@
 %%%%% layout %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry}
 \pagestyle{headandfoot}
-\header{{\bfseries\large Scientific Computing}}{{\bfseries\large Project: \ptitle}}{{\bfseries\large Januar 18th, 2018}}
+\header{\textbf{\large Scientific Computing Project: \ptitle}}{}{\textbf{\large January 18th, 2018}}
 \runningfooter{}{\thepage}{}
 
 \setlength{\baselineskip}{15pt}
@@ -15,6 +15,8 @@
 \setlength{\parskip}{0.3cm}
 \renewcommand{\baselinestretch}{1.15}
 
+\setcounter{secnumdepth}{-1}
+
 %%%%% listings %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \usepackage{listings}
 \lstset{

projects/instructions.tex

@@ -1,31 +1,31 @@
 \setlength{\fboxsep}{2ex}
-\fbox{\parbox{1\linewidth}{\small 
+\fbox{\parbox{0.95\linewidth}{\small 
 
-      {\bf Evaluation criteria:}
+      \textbf{Evaluation criteria:}
 
       Each project has three elements that are graded: (i) the code,
-      (ii) the slides/figures, and (iii) the presentation.
+      (ii) the quality of the figures, and (iii) the presentation (see below).
 
       \vspace{1ex}
-      {\bf Dates:}
+      \textbf{Dates:}
 
-      The {\bf code} and the {\bf presentation} should be uploaded to
+      The code and the presentation should be uploaded to
       ILIAS at latest on Sunday, February 4th, 23:59h. We will
       store all presentations on one computer to allow fast
       transitions between talks. The presentations start on Monday,
       February 5th at 9:15h. 
 
       \vspace{1ex}
-      {\bf Files:}
+      \textbf{Files:}
 
       Please hand in your presentation as a pdf file. Bundle
       everything (the pdf, the code, and the data) into a {\em single}
       zip-file.
 
       \vspace{1ex}
-      {\bf Code:}
+      \textbf{Code:}
 
-      The {\bf code} should be executable without any further
+      The code should be executable without any further
       adjustments from our side.  A single \texttt{main.m} script
       should coordinate the analysis by calling functions and
       sub-scripts and should produce the {\em same} figures
@@ -43,17 +43,15 @@
 
 
       \vspace{1ex}
-      {\bf Presentation:}
-      
-      The {\bf presentation} should be {\em at most} 10min long and be
-      held in English. In the presentation you should (i) briefly
-      describe the problem, (ii) present figures introducing, showing,
-      and discussing your results, and (iii) explain how you solved
-      the problem algorithmically (don't show your entire code). All
-      data-related figures you show in the presentation should be
-      produced by your program --- no editing or labeling by
-      PowerPoint or other software. It is always a good idea to
-      illustrate the problem with basic plots of the raw-data. Make
-      sure the axis labels are large enough!
+      \textbf{Presentation:}
+      
+      The presentation should be {\em at most} 10min long and be held
+      in English. In the presentation you should present figures
+      introducing, explaining, showing, and discussing your data,
+      methods, and results. All data-related figures you show in the
+      presentation should be produced by your program --- no editing
+      or labeling by PowerPoint or other software. It is always a good
+      idea to illustrate the problem with basic plots of the
+      raw-data. Make sure the axis labels are large enough!
 
 }}

projects/project_adaptation_fit/adaptation_fit.tex

@@ -11,10 +11,10 @@
 
 
 %%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
-\section*{Estimating the adaptation time-constant.}
+\section{Estimating the adaptation time-constant}
 Stimulating a neuron with a constant stimulus for an extended period of time
 often leads to a strong initial response that relaxes over time. This
-process is called adaptation and is ubiquitous. Your task here is to
+process is called adaptation. Your task here is to
 estimate the time-constant of the firing-rate adaptation in P-unit
 electroreceptors of the weakly electric fish \textit{Apteronotus
   leptorhynchus}.
@@ -26,27 +26,41 @@ electroreceptors of the weakly electric fish \textit{Apteronotus
   in the file. The contrast of the stimulus is a measure relative to
   the amplitude of fish's field, it has no unit. The data is sampled
   with 20\,kHz sampling frequency and spike times are given in
-  milliseconds relative to the stimulus onset.
+  milliseconds (not seconds!) relative to the stimulus onset.
   \begin{parts}
-    \part Estimate for each stimulus intensity the PSTH and plot
-    it. You will see that there are three parts.  (i) The first
-    200\,ms is the baseline (no stimulus) activity. (ii) During the
-    next 1000\,ms the stimulus was switched on. (iii) After stimulus
-    offset the neuronal activity was recorded for further 825\,ms.
+    \part Estimate for each stimulus intensity the PSTH. You will see
+    that there are three parts: (i) The first 200\,ms is the baseline
+    (no stimulus) activity. (ii) During the next 1000\,ms the stimulus
+    was switched on. (iii) After stimulus offset the neuronal activity
+    was recorded for further 825\,ms. Find an appropriate bin-width
+    for the PSTH.
+
     \part Estimate the adaptation time-constant for both the stimulus
-    on- and offset. To do this fit an exponential function to the
-    data. For the decay use:
-    \begin{equation}
-       f_{A,\tau,y_0}(t) = y_0 + A \cdot e^{-\frac{t}{\tau}},
-    \end{equation}
-    where $y_0$ the offset, $A$ the amplitude, $t$ the time, $\tau$
-    the time-constant.
-    For the increasing phases use an exponential of the form:
+    on- and offset. To do this fit an exponential function
+    $f_{A,\tau,y_0}(t)$ to appropriate regions of the data:
     \begin{equation}
-       f_{A,\tau, y_0}(t) = y_0 + A \cdot \left(1 - e^{-\frac{t}{\tau}}\right ),
+       f_{A,\tau,y_0}(t) = A \cdot e^{-\frac{t}{\tau}} + y_0,
     \end{equation}
-    \part Plot the best fits into the data.
-    \part Plot the estimated time-constants as a function of stimulus intensity.
+    where $t$ is time, $A$ the (positive or negative) amplitude of the
+    exponential decay, $\tau$ the adaptation time-constant, and $y_0$
+    an offset.
+
+    Before you do the fitting, familiarize yourself with the three
+    parameter of the exponential function. What is the value of
+    $f_{A,\tau,y_0}(t)$ at $t=0$? What is the value for large times? How does
+    $f_{A,\tau,y_0}(t)$ change if you change either of the parameter?
+
+    Which of the parameter could you directly estimate from the data
+    (without fitting)?
+
+    How could you get good estimates for the other parameter?
+
+    Do the fit and show the resulting exponential function together
+    with the data.
+
+    \part Do the estimated time-constants depend on stimulus intensity?
+
+    Use an appropriate statistical test to support your observation.
   \end{parts}
 \end{questions}
 

projects/project_ficurves/ficurves.tex

@@ -0,0 +1,73 @@
+\documentclass[a4paper,12pt,pdftex]{exam}
+
+\newcommand{\ptitle}{F-I curves}
+\input{../header.tex}
+\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
+{email: jan.grewe@uni-tuebingen.de}
+
+\begin{document}
+
+\input{../instructions.tex}
+
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+\section{Quantifying the responsiveness of a neuron by its F-I curves}
+The responsiveness of a neuron is often quantified using an F-I
+curve. The F-I curve plots the \textbf{F}iring rate of the neuron as a
+function of the stimulus \textbf{I}ntensity.
+
+\begin{questions}
+  \question In the accompanying datasets you find the
+  \textit{spike\_times} of an P-unit electroreceptor of the weakly
+  electric fish \textit{Apteronotus leptorhynchus} to a stimulus of a
+  certain intensity, i.e. the \textit{contrast}. The spike times are
+  given in milliseconds relative to the stimulus onset.
+  \begin{parts}
+    \part For each stimulus intensity estimate the average response
+    (PSTH) and plot it. You will see that there are three parts.  (i)
+    The first 200\,ms is the baseline (no stimulus) activity. (ii)
+    During the next 1000\,ms the stimulus was switched on. (iii) After
+    stimulus offset the neuronal activity was recorded for further
+    825\,ms.
+
+    \part Extract the neuron's activity for every 50\,ms after
+    stimulus onset and for one 50\,ms slice before stimulus onset.
+
+    For each time slice plot the resulting F-I curve by plotting the
+    computed firing rates against the corresponding stimulus
+    intensity, respectively the contrast.
+
+    \part Fit a Boltzmann function to each of the F-I-curves. The
+    Boltzmann function is a sigmoidal function and is defined as
+    \begin{equation}
+       f(x) = \frac{\alpha-\beta}{1+e^{-k(x-x_0)}}+\beta \; .
+    \end{equation}
+    $x$ is the stimulus intensity, $\alpha$ is the starting
+    firing rate, $\beta$ the saturation firing rate, $x_0$ defines the
+    position of the sigmoid, and $k$ (together with $\alpha-\beta$)
+    sets the slope.
+
+    Before you do the fitting, familiarize yourself with the four
+    parameter of the Boltzmann function. What is its value for very
+    large or very small stimulus intensities? How does the Boltzmann
+    function change if you change either of the parameter?
+
+    How could you get good initial estimates for the parameter?
+
+    Do the fits and show the resulting Boltzmann functions together
+    with the corresponding data.
+
+    \part Illustrate how the F-I curves change in time also by means
+    of the parameter you obtained from the fits with the Boltzmann
+    function. 
+
+    Which parameter stay the same, which ones change with time?
+
+    Support your conclusion with appropriate statistical tests.
+
+    \part Discuss you results with respect to encoding of different
+    stimulus intensities.
+  \end{parts}
+\end{questions}
+
+\end{document}

projects/project_mutualinfo/mutualinfo.tex

@@ -20,25 +20,33 @@
   
   \begin{parts}
     \part Plot the data appropriately.
+
     \part Compute a 2-d histogram that shows how often different
     combinations of reported and presented came up.
+
     \part Normalize the histogram such that it sums to one (i.e. make
     it a probability distribution $P(x,y)$ where $x$ is the presented
     object and $y$ is the reported object). Compute the probability
     distributions $P(x)$ and $P(y)$ in the same way.
+
     \part Use that probability distribution to compute the mutual
-    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. 
+    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)?
-    \part Use bootstrapping to compute the $95\%$ confidence interval
-    for the mutual information estimate in that dataset. 
+
+    \part Use bootstrapping (permutation test) to compute the $95\%$
+    confidence interval for the mutual information estimate in the
+    dataset from {\tt decisions.mat}.
+
   \end{parts}
 
 \end{questions}

projects/project_onset_fi/onset_fi.tex

@@ -1,47 +0,0 @@
-\documentclass[a4paper,12pt,pdftex]{exam}
-
-\newcommand{\ptitle}{Onset f-I curve}
-\input{../header.tex}
-\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
-{email: jan.grewe@uni-tuebingen.de}
-
-\begin{document}
-
-\input{../instructions.tex}
-
-
-%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
-\section*{Quantifying the responsiveness of a neuron using the F-I curve.}
-The responsiveness of a neuron is often quantified using an F-I
-curve. The F-I curve plots the \textbf{F}iring rate of the neuron as a
-function of the stimulus \textbf{I}ntensity.
-
-\begin{questions}
-  \question In the accompanying datasets you find the
-  \textit{spike\_times} of an P-unit electroreceptor of the weakly
-  electric fish \textit{Apteronotus leptorhynchus} to a stimulus of a
-  certain intensity, i.e. the \textit{contrast}. The spike times are
-  given in milliseconds relative to the stimulus onset.
-  \begin{parts}
-    \part For each stimulus intensity estimate the average response
-    (PSTH) and plot it. You will see that there are three parts.  (i)
-    The first 200\,ms is the baseline (no stimulus) activity. (ii)
-    During the next 1000\,ms the stimulus was switched on. (iii) After
-    stimulus offset the neuronal activity was recorded for further
-    825\,ms.
-    \part Extract the neuron's activity in the first 50\,ms after
-    stimulus onset and plot it against the stimulus intensity,
-    respectively the contrast, in an appropriate way.
-    \part Fit a Boltzmann function to the FI-curve. The Boltzmann function
-    is defined as:
-    \begin{equation}
-       y=\frac{\alpha-\beta}{1+e^{(x-x_0)/\Delta x}}+\beta,
-    \end{equation}
-    where $\alpha$ is the starting firing rate, $\beta$ the saturation
-    firing rate, $x$ the current stimulus intensity, $x_0$ starting
-    stimulus intensity, and $\Delta x$ a measure of the slope.
-    \part Plot the fit into the data.
-  \end{parts}
-\end{questions}
-
-\end{document}

projects/project_serialcorrelation/serialcorrelation.tex

@@ -16,10 +16,9 @@
   \question P-unit electroreceptor afferents of the gymnotiform weakly
   electric fish \textit{Apteronotus leptorhynchus} are spontaneously
   active when the fish is not electrically stimulated. 
-  \begin{itemize}
-  \item How do the firing rates and the serial correlations of the
+
+  How do the firing rates and the serial correlations of the
   interspike intervals vary between different cells?
-  \end{itemize}
 
   In the file \texttt{baselinespikes.mat} you find two variables:
   \texttt{cells} is a cell-array with the names of the recorded cells
@@ -34,7 +33,7 @@
     this project.
 
     By just looking on the spike rasters, what are the differences
-    betwen the cells?
+    between the cells?
 
     \part Compute the firing rate of each cell, i.e. number of spikes per time.
 
@@ -46,15 +45,18 @@
     correlations similar betwen the cells? How do they differ?
 
     \part Implement a permutation test for computing the significance
-    at a 1\,\% level of the serial correlations. Illustrate for a few
-    cells the computed serial correlations and the 1\,\% and 99\,\%
-    percentile from the permutation test. At which lag are the serial
-    correlations clearly significant?
+    at an appropriate significance level of the serial
+    correlations. Keep in mind that you test the correlations at 10
+    different lags. At which lags are the serial correlations
+    statistically significant?
 
     \part Are the serial correlations somehow dependent on the firing rate?
 
     Plot the significant correlations against the firing rate. Do you
     observe any dependence?
+
+    Use an appropriate statistical test to support your observation.
+
   \end{parts}
 
 \end{questions}

projects/project_steady_state_fi/Makefile

@@ -1,3 +0,0 @@
-ZIPFILES=
-
-include ../project.mk

projects/project_steady_state_fi/steady_state_fi.tex

@@ -1,45 +0,0 @@
-\documentclass[a4paper,12pt,pdftex]{exam}
-
-\newcommand{\ptitle}{Steady-state f-I curve}
-\input{../header.tex}
-\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
-{email: jan.grewe@uni-tuebingen.de}
-
-\begin{document}
-
-\input{../instructions.tex}
-
-
-%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
-\section*{Quantifying the responsiveness of a neuron using the F-I curve.}
-The responsiveness of a neuron is often quantified using an F-I
-curve. The F-I curve plots the \textbf{F}iring rate of the neuron as a function
-of the stimulus \textbf{I}ntensity.
-
-\begin{questions}
-  \question In the accompanying datasets you find the
-  \textit{spike\_times} of an P-unit electrorecptor of the weakly
-  electric fish \textit{Apteronotus leptorhynchus} to a stimulus of a
-  certain intensity, i.e. the \textit{contrast}. The contrast is also
-  part of the file name itself.
-  \begin{parts}
-    \part Estimate for each stimulus intensity the average response 
-    (PSTH) and plot it. You will see that there are three parts.  (i)
-    The first 200 ms is the baseline (no stimulus) activity. (ii) During
-    the next 1000 ms the stimulus was switched on. (iii) After stimulus
-    offset the neuronal activity was recorded for further 825 ms.
-    \part Extract the neuron's activity in the last 200 ms before
-    stimulus offset and plot it against the stimulus intensity or the
-    contrast, respectively.
-    \part Fit a Boltzmann function to the FI-curve. The Boltzmann function
-    is defined as:
-    \begin{equation}
-       y=\frac{\alpha-\beta}{1+e^{(x-x_0)/\Delta x}}+\beta,
-    \end{equation}
-    where $\alpha$ is the starting firing rate, $\beta$ the saturation
-    firing rate, $x$ the current stimulus intensity, $x_0$ starting
-    stimulus intensity, and $\Delta x$ a measure of the slope.
-  \end{parts}
-\end{questions}
-
-\end{document}

regression/lecture/regression-chapter.tex

@@ -16,8 +16,25 @@
 
 \input{regression}
 
-Example for fit with matlab functions lsqcurvefit, polyfit
+\section{Fitting in practice}
+
+Fit with matlab functions lsqcurvefit, polyfit
+
+
+\subsection{Non-linear fits}
+\begin{itemize}
+\item Example that illustrates the Nebenminima Problem (with error surface)
+\item You need got initial values for the parameter!
+\item Example that fitting gets harder the more parameter yuo have.
+\item Try to fix as many parameter before doing the fit.
+\item How to test the quality of a fit? Residuals. $\Chi^2$ test. Run-test.
+\end{itemize}
+
+\subsection{Linear fits}
+\begin{itemize}
+\item Polyfit is easy: unique solution!
+\item Example for overfitting with polyfit of a high order (=number of data points)
+\end{itemize}
 
-Example for overfitting with polyfit of a high order (=number of data points)
 
 \end{document}