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

projects/disclaimer.tex

@@ -8,30 +8,34 @@
       \vspace{.5cm}
 
       The {\bf code} and the {\bf presentation} should be uploaded to
-      ILIAS before the presentations start on Thursday. Everything
-      should be bundeled into a {\em single} zip-file. The
-      presentation should be handed in as pdf.
+      ILIAS at latest on Thursday, November 6th, 12:00h.
+      The presentations start on Thursday 13:00h. Please hand in
+      your presentation as a pdf file. Bundle everything into a
+      {\em single} zip-file.
 
       \vspace{.5cm}
 
       The {\bf code} should be exectuable without any further
-      adjustments from us. This means that you should include all
+      adjustments from us. This means that you need to include all
       additional functions you wrote and the data into the
-      zip-file. The {\em main script} should produce the same {\em
-      figures} that you use in your slides. The figures should follow
-      the guidelines for proper plotting as discussed in the first
-      statistics lecture. The code should be properly commented and
-      comprehensible by third persons (use proper and consistent
+      zip-file. A single {\em main script} should produce the same
+      {\em figures} that you use in your slides. The figures should
+      follow the guidelines for proper plotting as discussed in the
+      first statistics lecture. The code should be properly commented
+      and comprehensible by third persons (use proper and consistent
       variable names).
 
+      \vspace{.5cm} \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}
       
-      The {\bf slides} should be handed in along with the code and in
-      pdf format. We will store them all on one computer to allow fast
-      transitions between talks. The {\bf presentation} itself should
-      be {\em at most} 10min long and be held in English. In the
-      presentation you should (i) briefly describe the problem, (ii)
-      explain how you solved it algorithmically (don't show your
-      entire code), and (iii) present figures showing your results. 
+      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) explain how you solved it
+      algorithmically (don't show your entire code), and (iii) present
+      figures showing your results. We will store all presentations on
+      one computer to allow fast transitions between talks.
 
     }}

projects/pca_natural_img/Makefile

@@ -1,11 +0,0 @@
-latex:
-	pdflatex *.tex > /dev/null
-	pdflatex *.tex > /dev/null
-	pdflatex *.tex > /dev/null
-
-clean:
-	rm -rf *.log *.aux *.zip *.out auto *.bbl *.blg
-	rm -f `basename *.tex .tex`.pdf
-
-zip: latex
-	zip `basename *.tex .tex`.zip *.pdf *.jpg

projects/pca_natural_img/pca_natural_images.tex

@@ -1,61 +0,0 @@
-\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
-
-
-\begin{document}
-%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
-\sffamily
-% \begin{flushright}
-% \gradetable[h][questions]
-% \end{flushright}
-
-\begin{center}
-  \input{../disclaimer.tex}
-\end{center}
-
-%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
-
-In you zip file you find a natural image called {\tt natimg.jpg}. 
-\begin{questions}
-
-  \question Load the image and extract all pixels as three dimensional
-  vectors (red, green, and blue channel). 
-  
-  \question Perform a principal component analysis on these
-  three-dimensional vectors.
-
-  \question Try to find a interpretation of the principal components
-  you find in terms of colors. Find a good way to visualize this. 
-
-  \question What could be the biological significance of that (\cite{BG} can
-  give you a clue)?
-
-\end{questions}
-
-\begin{thebibliography}{1}
-\bibitem{BG} Buchsbaum, G., \& Gottschalk, A. (1983). Trichromacy,
-  opponent colours coding and optimum colour information transmission
-  in the retina. Proceedings of the Royal Society of London. Series B,
-  Containing Papers of a Biological Character. Royal Society (Great
-  Britain), 220(1218), 89–113.
-\end{thebibliography}
-
-
-
-\end{document}

projects/project_eod/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

projects/project_eod/eod.tex

@@ -0,0 +1,61 @@
+\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
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+% \begin{flushright}
+% \gradetable[h][questions]
+% \end{flushright}
+
+\begin{center}
+  \input{../disclaimer.tex}
+\end{center}
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{questions}
+  \question In the data file {\tt EOD\_data.mat} you find a time trace
+  and the {\em electric organ discharge (EOD)} of a weakly electric
+  fish {\em Apteronotus leptorhynchus}. 
+  \begin{parts}
+    \part Load and plot the data in an appropriate way. Time is in
+    seconds and the voltage is in mV/cm.
+    \part Fit the following curve to the eod (select a smaller time
+    window for fitting, not the entire trace) using least squares:
+    $$f_{\omega_0,b_0,\varphi_1, ...,\varphi_n}(t) = b_0 +
+    \sum_{j=1}^n \sin(2\pi j\omega_0\cdot t + \varphi_j ).$$
+    $\omega_0$ is called {\em fundamental frequency}. The single terms
+    $\sin(2\pi j\omega_0\cdot t + \varphi_j )$ are called {\em
+      harmonic components}. The variables $\varphi_j$ are called {\em
+      phases}. For the beginning choose $n=3$. 
+    \part Play around with $n$ and see how the fit changes. Plot the
+    fits and the original curve for different choices of $n$. If you
+    want you can also play the different fits and the original as
+    sound.
+    
+  \end{parts}
+\end{questions}
+
+
+
+
+
+\end{document}

projects/project_fano_test/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

projects/project_fano_test/fano.tex

@@ -0,0 +1,66 @@
+\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
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+% \begin{flushright}
+% \gradetable[h][questions]
+% \end{flushright}
+
+\begin{center}
+  \input{../disclaimer.tex}
+\end{center}
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+\begin{questions}
+  \question The Fano factor $\frac{\sigma^2}{\mu}$ is a common measure
+  in neural coding because a Poisson process---for which each spike is
+  independent of every other---has a Fano factor of one.
+
+  The table contains spike counts from a neuron measured in twelve
+  trials.
+
+  \begin{center}
+    \begin{tabular}{cccc}
+      \multicolumn{4}{c}{\bf number of spikes} \\ \hline\\
+      36.00 & 28.00 & 38.00 & 35.00\\
+      32.00 & 30.00 & 35.00 & 29.00\\
+      29.00 & 24.00 & 26.00 & 34.00
+    \end{tabular}
+  \end{center}
+
+  \begin{parts}
+    \part Use {\em Eden, U. T., \& Kramer, M. (2010). Drawing
+      inferences from Fano factor calculations. Journal of
+      neuroscience methods, 190(1), 149--152} to construct a test that
+    uses the Fano factor as test statistic and tests against the Null
+    hypothesis that the spike counts come from a Poisson process.
+    \part Plot the spike counts appropriately. 
+    \part Implement the test and use that it on the data above.
+  \end{parts}
+
+\end{questions}
+
+
+
+\end{document}

projects/project_mutualinfo/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

projects/project_mutualinfo/mutualinfo.tex

@@ -0,0 +1,66 @@
+\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
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+% \begin{flushright}
+% \gradetable[h][questions]
+% \end{flushright}
+
+\begin{center}
+  \input{../disclaimer.tex}
+\end{center}
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+\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
+  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. 
+  
+  \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. 
+    \part What is the maximally achievable mutual information (try to
+    find out by generating your own dataset; the situation in which
+    the information is maximal is pretty straightforward)?
+    \part Use bootstrapping to compute the $95\%$ confidence interval
+    for the mutual information estimate in that dataset. 
+  \end{parts}
+
+\end{questions}
+
+
+
+
+
+\end{document}

projects/project_q-values/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

projects/project_q-values/qvalues.tex

@@ -0,0 +1,81 @@
+\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
+
+
+\begin{document}
+%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
+\sffamily
+% \begin{flushright}
+% \gradetable[h][questions]
+% \end{flushright}
+
+\begin{center}
+  \input{../disclaimer.tex}
+\end{center}
+
+%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{questions}
+  \question The p-value corresponds to the probability
+  $$P(\mbox{result seems significant}| H_0 \mbox{is true}).$$
+  This means that if your significance threshold is $\alpha=0.05$ and
+  you accept all test with $p \le \alpha$ as significant, then $5\%$
+  of all cases in which $H_0$ was true (there was no effect) your test
+  will appear significant (false positive). 
+
+  The problem with that is that you do not know for how many of the
+  tests $H_0$ is actually true. What you really would like to know is:
+  From all those tests that came out significant ($p\le\alpha$) how
+  many of them are false positives? This probability corresponds to
+  $$P(H_0 \mbox{is true}|\mbox{result seems significant})$$ and is
+  called {\em false discovery rate}. In general you cannot compute
+  it. However, if you have many p-values, then you can actually
+  estimate it. The corresponding ``p-value'' for the false discovery
+  rate is called ``q-value''. 
+
+  In the paper 
+
+  {\em Storey, J. D., \& Tibshirani, R. (2003). Statistical
+    significance for genomewide studies. Proceedings of the National
+    Academy of Sciences of the United States of America, 100,
+    9440–9445. doi:10.1073/pnas.1530509100}
+
+  you can find an algorithm how to compute q-values from p-values. 
+
+  The attached data file {\tt p\_values.dat} contains p-values from
+  test of several neurons whether they respond to a certain stimulus
+  condition or not. 
+
+  \begin{parts}
+    \part Plot a histogram of the p-values.
+    \part Read and understand the paper by Storey and
+    Tibshirani. Visualize their method at your histogram. 
+    \part Implement their method and convert each p-value to a
+    q-value. 
+    \part From running the script, estimate the proportion of neurons
+    that show a true effect (i.e. $P(H_A)$).
+  \end{parts}
+  
+\end{questions}
+
+
+
+
+
+\end{document}

projects/project_template/Makefile

@@ -3,7 +3,7 @@ latex:
 	pdflatex *.tex > /dev/null
 
 clean:
-	rm -f *.log *.aux *.zip *.out auto
+	rm -rf *.log *.aux *.zip *.out auto
 	rm -f `basename *.tex .tex`.pdf
 
 zip: latex