[plotting] scatterplot

plotting/code/scatterplot.m

@@ -0,0 +1,28 @@
+x = 1:2:100;
+y = (0.5 .* x - 0.56) + randn(size(x)) .* 5.;
+
+f = figure();
+set(f, 'paperunits', 'centimeter', 'papersize', [15, 5], ...
+    'paperposition', [0, 0, 15, 5], 'color', 'white');
+
+subplot(1, 3, 1);
+scatter(x, y, 15, 'r', 'filled');
+xlabel('x');
+ylabel('y');
+text(-35, max(ylim) * 1.075,'A', 'FontSize', 12);
+
+subplot(1, 3, 2)
+scatter(x, y, 1:length(x), 'r');
+xlabel('x');
+ylabel('y');
+text(-35, max(ylim) * 1.075,'B', 'FontSize', 12);
+
+subplot(1, 3, 3)
+colors = zeros(length(x),3);
+colors(:,1) = round(1:255/length(x):255)/255';
+scatter(x, y, 15, colors, 'filled')
+xlabel('x');
+ylabel('y');
+text(-35, max(ylim) * 1.075,'C', 'FontSize', 12);
+
+saveas(f, '../lecture/images/scatterplot.png')

plotting/lecture/plotting-chapter.tex

@@ -16,10 +16,6 @@
 
 \input{plotting}
 
-\subsection{Scatter plot}
-
-\subsection{Histograms}
-
 \subsection{Heatmaps}
 
 \subsection{3-D plot}

plotting/lecture/plotting.tex

@@ -444,7 +444,51 @@ various examples and the respective code on their website
 
 For some types of plots we present examples in the following sections.
 
-\subsection{Line plot, subplots}
+\subsection{Scatter}
+
+For displaying events or pairs of x-y coordinates the standard line
+plot is not optimal. Rather, we use \code[scatter()]{scatter} for this
+purpose. For example, we have a number of measurements of a system's
+response to a certain stimulus intensity. There is no dependency
+between the data points, drawing them with a line-plot would be
+nonsensical (figure\,\ref{scatterplotfig}\,A).  In contrast to
+\codeterm{}{plot} we need to provide x- and y-coordinates in order to
+draw the data. In the example we also provide further arguments to set
+the size, color of the dots and specify that they are filled
+(listing\,\ref{scatterlisting1}).
+
+\lstinputlisting[caption={Creating a scatter plot with red filled dots.},
+  label=scatterlisting1, firstline=9, lastline=9]{scatterplot.m}
+
+We could have used plot for this purpose and set the marker to
+something and the line-style to ``none'' to draw an equivalent
+plot. Scatter, however offers some more advanced features that allows
+to add two more dimensions to the plot
+(figure\,\ref{scatterplotfig}\,B,\,C). For each dot one can define an
+individual size and color. In this example the size argument is simply
+a vector of the same size as the data that contains number from 1 to
+the length of 'x' (line 1 in listing\,\ref{scatterlisting2}). To
+manipulate the color we need to specify a length(x)-by-3 matrix. For
+each dot we provide an individual color (i.e. the RGB triplet in each
+row of the color matrix, lines 2-4 in listing\,\ref{scatterlisting2})
+
+
+\lstinputlisting[caption={Creating a scatter plot with size and color
+    variations. The RGB triplets define the respective color intensity
+    in a range 0:1. Here, we modify only the red color channel.},
+  label=scatterlisting2, linerange={15-15, 21-23}]{scatterplot.m}
+
+\begin{figure}[t]
+  \includegraphics{scatterplot}
+  \titlecaption{Scatterplots.}{Scatterplots are used to draw
+    datapoints where there is no direct dependency between the
+    individual measurements (like time). Scatter offers several
+    advantages over the standard plot command. One can vary the size
+    and/or the color of each dot.}\label{scatterplotfig}
+\end{figure}
+
+
+\subsection{Subplots}
 A very common scenario is to combine several plots in the same
 figure. To do this we create so-called subplots
 figures\,\ref{regularsubplotsfig},\,\ref{irregularsubplotsfig}. The

projects/project_eod/solution/fit_eod.py

@@ -44,8 +44,9 @@ def gradient(p, t, y, scale=None):
 def gradient_descent(t, y):
     count = 80
     b_0 = np.mean(y)
-    omega_0 = 650
-    params = [b_0, omega_0, np.min(y) +  np.max(y), np.pi/2, (np.min(y) +  np.max(y))/2,  np.pi/3, (np.min(y) +  np.max(y))/4,  np.pi/4, (np.min(y) +  np.max(y))/5,  np.pi]
+    omega_0 = 870
+    amplitude = np.max(y) - np.min(y)
+    params = [b_0, omega_0, amplitude, np.pi/2, amplitude/2,  np.pi/3, amplitude/4,  np.pi/4, amplitude/5,  np.pi]
     scale = np.ones(len(params))
     scale[1] = 1000
     eps = 0.01

spike_trains/exercises/xcorr.tex

@@ -13,8 +13,8 @@
 
 %%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry}
-\pagestyle{headandfoot} \header{{\bfseries\large \"Ubung
-    }}{{\bfseries\large Korrelation Stimulus und Antwort}}{{\bfseries\large 20. Dezember, 2016}}
+\pagestyle{headandfoot} \header{{\bfseries\large Exercise
+    }}{{\bfseries\large Correlation of stimulus and response}}{{\bfseries\large December 19, 2017}}
 \firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email:
   jan.grewe@uni-tuebingen.de} \runningfooter{}{\thepage}{}
 
@@ -24,54 +24,61 @@
 \renewcommand{\baselinestretch}{1.15}
 
 \newcommand{\code}[1]{\texttt{#1}}
-\renewcommand{\solutiontitle}{\noindent\textbf{L\"osung:}\par\noindent}
+\renewcommand{\solutiontitle}{\noindent\textbf{Solution:}\par\noindent}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
 \begin{document}
 
 \vspace*{-6.5ex}
 \begin{center}
-  \textbf{\Large Einf\"uhrung in die wissenschaftliche Datenverarbeitung}\\[1ex]
+  \textbf{\Large Introduction to scientific computing}\\[1ex]
   {\large Jan Grewe, Jan Benda}\\[-3ex]
   Abteilung Neuroethologie \hfill --- \hfill Institut f\"ur Neurobiologie \hfill --- \hfill \includegraphics[width=0.28\textwidth]{UT_WBMW_Black_RGB} \\
 \end{center}
 
 \begin{questions}
-  \question Stellt die zeitabh\"angige Feuerrate eines Neurons
-  dar. Diese soll mit der Faltungsmethode bestimmt werden. Verwendet
-  den Datensatz \code{lifoustim.mat}. Dieser enth\"at drei Variablen:
-  1. die Spikezeiten, 2. den Stimulus und 3. die zeitliche
-  Aufl\"osung. Die Dauer eines Trials betr\"agt 30 Sekunden.
+  \question Estimate the time-dependent firing rate of a neuron. Use
+  the ``convoluion'' method to do it. The dataset \code{lifoustim.mat}
+  contains three variables. 1st the spike times in different trials,
+  2nd the stimulus, and 3rd the temporal resolution. The total
+  duration of each trial amounts to 30 seconds.
+  
   \begin{parts}
-    \part Schreibt eine Funktion, die einen Vektor mit Spikezeiten,
-    die Dauer des Trials, und die zeitliche Aufl\"osung entgegennimmt
-    und die Zeitachse sowie die Feuerrate zur\"uckgibt.
-    \part Benutzt diese Funktion in einem Skript und stellt die Feuerrate
-    eines einzelnen Trials sowie den Mittelwert \"uber alle Trials
-    dar.
-    \part Erweitert das Programm so, dass die Abbildung den Richtlinien
-    des \textit{Journal of Neuroscience} entspricht
-    (Schriftgr\"o{\ss}e, Abbildungsgr\"o{\ss}e).
-    \part Die Abbildung sollte als pdf gespeichert werden.
+    \part{} Write a function that estimates the firing rate with the
+    ``convolution'' method. This function should take four input
+    arguments: (i) a vector of spike times, (ii) the temporal
+    resolution of the recording, (iii) the duration of the
+    trial, and (iv) the standard deviation of the applied Gaussian
+    kernel. The function should return two variables: (i) the firing
+    rate, and (ii) a vector representing time.
+    \part{} Write a script that uses this function to estimate the
+    firing rate of all trial. Plot the mean (across trials) firing
+    rate as a function of time. Use two different kernel standard
+    deviations (e.g. 20\,ms and 100\,ms).
+    \part{} Save the figure according the style defined by the
+    \emph{J. Neuroscience} (figure width 1, 1.5, or two columns, 8.5,
+    11.6, or 17.6\,cm, respectively; fontsize 10 pt). Save the figure
+    as pdf.
   \end{parts}
 
-  \question In einer vorherigen \"Ubung wurde die Korrelation zwischen
-  einer Reihe von Messungen und einer entsprechenden Anzahl
-  unabh\"angiger Variablen bestimmt (Kapitel 4.4 im Skript). Wir
-  k\"onnen diese Korrelation benutzen um den Zusammenhang zwischen
-  Stimulus und Antwort zu bestimmen.
+  \question In a previous exercise you were asked to estimate the
+  correlation between a set of independent variables and the
+  respective measurements (Chapter 6.4 in the script).  We can use
+  this function to learn a few things about the relation between
+  stimulus and response.
+
   \begin{parts}
-    \part Ermittelt die zeitabh\"angige Feuerrate mit einer der drei
-    Methoden und korrelliert sie mit dem Stimulus.
-    \part Verschiebt nun den Stimulus relativ zur Antwort um $\pm$
-    50\,ms in 1\,ms Schritten und berechnet f\"ur jede Verschiebung
-    die Korrelation.
-    \part Stellt die so berechnete Kreuzkorrelation graphisch dar
-    (x-Achse die Verschiebung, y-Achse der Korrelationskoeffizient).
-    \part Was ist die maximale Korrelation und bei welcher
-    Verschiebung kommt sie vor?
-    \part Was k\"onnte uns die Breite des Korrelationspeaks sagen?
+    \part{} Estimate the firing rate of the neuronal response using one
+    of the three methods. Use the same dataset as before.
+    \part{} Calculate the correlation of stimulus and response.
+    \part{} Calculate the correlation of stimulus and response
+    while shifting the response relative to the stimulus in a range
+    $\pm$ 50\,ms (1\,ms steps).
+    \part{} Plot these correlations as a function of the temporal shift
+    (often called lag).
+    \part{} What is the maximum correlation and at which lag does it occur?
+    \part{} What could this tell us about the neuronal response properties?
   \end{parts}
 \end{questions}
 
-\end{document}
+\end{document}