From db1133352e2c013557f6d7638323b84846792741 Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 6 Feb 2018 10:40:16 +0100 Subject: [PATCH] improved projects --- plotting/lecture/plotting-chapter.tex | 2 + projects/header.tex | 4 +- projects/instructions.tex | 36 ++++++------- .../project_adaptation_fit/adaptation_fit.tex | 52 ++++++++++++------- projects/project_onset_fi/onset_fi.tex | 2 +- .../serialcorrelation.tex | 20 +++---- regression/lecture/regression-chapter.tex | 21 +++++++- 7 files changed, 86 insertions(+), 51 deletions(-) diff --git a/plotting/lecture/plotting-chapter.tex b/plotting/lecture/plotting-chapter.tex index 022eaf1..4dd0a9d 100644 --- a/plotting/lecture/plotting-chapter.tex +++ b/plotting/lecture/plotting-chapter.tex @@ -28,6 +28,8 @@ \subsection{Polar plot} +\subsection{print instead of saveas????} + \subsection{Movies and animations} \section{TODO} diff --git a/projects/header.tex b/projects/header.tex index 4d4fe9b..690de17 100644 --- a/projects/header.tex +++ b/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{ diff --git a/projects/instructions.tex b/projects/instructions.tex index 63ddbec..d68dd46 100644 --- a/projects/instructions.tex +++ b/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:} + \textbf{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! + 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! }} diff --git a/projects/project_adaptation_fit/adaptation_fit.tex b/projects/project_adaptation_fit/adaptation_fit.tex index 13ea510..24d4355 100644 --- a/projects/project_adaptation_fit/adaptation_fit.tex +++ b/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} diff --git a/projects/project_onset_fi/onset_fi.tex b/projects/project_onset_fi/onset_fi.tex index f8df064..94be9b5 100644 --- a/projects/project_onset_fi/onset_fi.tex +++ b/projects/project_onset_fi/onset_fi.tex @@ -11,7 +11,7 @@ %%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%% -\section*{Quantifying the responsiveness of a neuron using the F-I curve.} +\section{Quantifying the responsiveness of a neuron by its 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. diff --git a/projects/project_serialcorrelation/serialcorrelation.tex b/projects/project_serialcorrelation/serialcorrelation.tex index fd96704..98dc07e 100644 --- a/projects/project_serialcorrelation/serialcorrelation.tex +++ b/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 - interspike intervals vary between different cells? - \end{itemize} + + How do the firing rates and the serial correlations of the + interspike intervals vary between different cells? 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} diff --git a/regression/lecture/regression-chapter.tex b/regression/lecture/regression-chapter.tex index fcb8f16..39b8a29 100644 --- a/regression/lecture/regression-chapter.tex +++ b/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}