diff --git a/projects/disclaimer.tex b/projects/disclaimer.tex index 261c2a4..9ef1771 100644 --- a/projects/disclaimer.tex +++ b/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. }} \ No newline at end of file diff --git a/projects/pca_natural_img/Makefile b/projects/pca_natural_img/Makefile deleted file mode 100644 index 3da8318..0000000 --- a/projects/pca_natural_img/Makefile +++ /dev/null @@ -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 diff --git a/projects/pca_natural_img/natimg.jpg b/projects/pca_natural_img/natimg.jpg deleted file mode 100644 index 4788b73..0000000 Binary files a/projects/pca_natural_img/natimg.jpg and /dev/null differ diff --git a/projects/pca_natural_img/pca_natural_images.tex b/projects/pca_natural_img/pca_natural_images.tex deleted file mode 100755 index 6ca956f..0000000 --- a/projects/pca_natural_img/pca_natural_images.tex +++ /dev/null @@ -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} diff --git a/projects/project_eod/EOD_data.mat b/projects/project_eod/EOD_data.mat new file mode 100644 index 0000000..406ee21 Binary files /dev/null and b/projects/project_eod/EOD_data.mat differ diff --git a/projects/project_eod/Makefile b/projects/project_eod/Makefile new file mode 100644 index 0000000..dad25ce --- /dev/null +++ b/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 diff --git a/projects/project_eod/eod.tex b/projects/project_eod/eod.tex new file mode 100755 index 0000000..dcd2598 --- /dev/null +++ b/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} diff --git a/projects/project_fano_test/Makefile b/projects/project_fano_test/Makefile new file mode 100644 index 0000000..dad25ce --- /dev/null +++ b/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 diff --git a/projects/project_fano_test/fano.tex b/projects/project_fano_test/fano.tex new file mode 100755 index 0000000..556e9c0 --- /dev/null +++ b/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} diff --git a/projects/project_mutualinfo/Makefile b/projects/project_mutualinfo/Makefile new file mode 100644 index 0000000..dad25ce --- /dev/null +++ b/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 diff --git a/projects/project_mutualinfo/decisions.mat b/projects/project_mutualinfo/decisions.mat new file mode 100644 index 0000000..918c0de Binary files /dev/null and b/projects/project_mutualinfo/decisions.mat differ diff --git a/projects/project_mutualinfo/mutualinfo.tex b/projects/project_mutualinfo/mutualinfo.tex new file mode 100755 index 0000000..312deed --- /dev/null +++ b/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} diff --git a/projects/project_q-values/Makefile b/projects/project_q-values/Makefile new file mode 100644 index 0000000..dad25ce --- /dev/null +++ b/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 diff --git a/projects/project_q-values/p_values.dat b/projects/project_q-values/p_values.dat new file mode 100644 index 0000000..caa3d0e --- /dev/null +++ b/projects/project_q-values/p_values.dat @@ -0,0 +1,1352 @@ +6.986624685324906991e-01 +8.333615995295426404e-02 +4.328020871196971431e-01 +4.066720408416106824e-01 +8.557530459986344429e-01 +7.401945999729832304e-02 +1.437858625210597097e-01 +7.038569852646472391e-01 +4.359208624695755097e-01 +7.081548443984664321e-01 +9.544557809531003523e-01 +8.434229656109852868e-01 +9.258124448925199035e-01 +2.580826797629524605e-01 +6.148788266928260221e-02 +8.102785030898772556e-01 +3.866850086925593954e-01 +7.165593698650062349e-01 +5.944075446397871776e-01 +9.582417299981267345e-01 +9.101902386681537394e-01 +3.577577623337484525e-01 +5.737590011358219000e-01 +2.641257840394647394e-01 +3.522171071109388152e-02 +8.954496958011308738e-01 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index 0000000..c3f0441 --- /dev/null +++ b/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} diff --git a/projects/project_template/Makefile b/projects/project_template/Makefile index 585d602..dad25ce 100644 --- a/projects/project_template/Makefile +++ b/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