From cc2515f22b9684594b895f35f5fbf117dee738cf Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Tue, 27 Oct 2015 09:39:02 +0100 Subject: [PATCH 1/5] move regression code from statistics to regression folder --- {statistics => regression}/code/boltzmann.m | 0 .../code/create_linear_data.m | 0 .../code/estimate_regression.m | 0 {statistics => regression}/code/exponential.m | 0 statistics/code/lsq_gradient_sigmoid.m | 9 ---- statistics/code/lsq_sigmoid_error.m | 8 ---- statistics/code/sigmoidal_gradient_descent.m | 44 ------------------- 7 files changed, 61 deletions(-) rename {statistics => regression}/code/boltzmann.m (100%) rename {statistics => regression}/code/create_linear_data.m (100%) rename {statistics => regression}/code/estimate_regression.m (100%) rename {statistics => regression}/code/exponential.m (100%) delete mode 100644 statistics/code/lsq_gradient_sigmoid.m delete mode 100644 statistics/code/lsq_sigmoid_error.m delete mode 100644 statistics/code/sigmoidal_gradient_descent.m diff --git a/statistics/code/boltzmann.m b/regression/code/boltzmann.m similarity index 100% rename from statistics/code/boltzmann.m rename to regression/code/boltzmann.m diff --git a/statistics/code/create_linear_data.m b/regression/code/create_linear_data.m similarity index 100% rename from statistics/code/create_linear_data.m rename to regression/code/create_linear_data.m diff --git a/statistics/code/estimate_regression.m b/regression/code/estimate_regression.m similarity index 100% rename from statistics/code/estimate_regression.m rename to regression/code/estimate_regression.m diff --git a/statistics/code/exponential.m b/regression/code/exponential.m similarity index 100% rename from statistics/code/exponential.m rename to regression/code/exponential.m diff --git a/statistics/code/lsq_gradient_sigmoid.m b/statistics/code/lsq_gradient_sigmoid.m deleted file mode 100644 index 05e9721..0000000 --- a/statistics/code/lsq_gradient_sigmoid.m +++ /dev/null @@ -1,9 +0,0 @@ -function gradient = lsq_gradient_sigmoid(parameter, x, y) -h = 1e-6; - -gradient = zeros(size(parameter)); -for i = 1:length(parameter) - parameter_h = parameter; - parameter_h(i) = parameter_h(i) + h; - gradient(i) = (lsq_sigmoid_error(parameter_h, x, y) - lsq_sigmoid_error(parameter, x, y)) / h; -end \ No newline at end of file diff --git a/statistics/code/lsq_sigmoid_error.m b/statistics/code/lsq_sigmoid_error.m deleted file mode 100644 index 5f05f21..0000000 --- a/statistics/code/lsq_sigmoid_error.m +++ /dev/null @@ -1,8 +0,0 @@ -function error = lsq_sigmoid_error(parameter, x, y) -% p(1) the amplitude -% p(2) the slope -% p(3) the x-shift -% p(4) the y-shift - -y_est = parameter(1)./(1+ exp(-parameter(2) .* (x - parameter(3)))) + parameter(4); -error = mean((y_est - y).^2); \ No newline at end of file diff --git a/statistics/code/sigmoidal_gradient_descent.m b/statistics/code/sigmoidal_gradient_descent.m deleted file mode 100644 index 9763f5a..0000000 --- a/statistics/code/sigmoidal_gradient_descent.m +++ /dev/null @@ -1,44 +0,0 @@ - - -%% fit the sigmoid - -clear -close all - -load('iv_curve.mat') - -figure() -plot(voltage, current, 'o') -xlabel('voltate [mV]') -ylabel('current [pA]') - -% amplitude, slope, x-shift, y-shift -%parameter = [10 0.25 -50, 2.5]; -parameter = [20 0.5 -50, 2.5]; - -eps = 0.1; -% do the descent -gradient = []; -steps = 0; -error = []; - -while isempty(gradient) || norm(gradient) > 0.01 - steps = steps + 1; - gradient = lsq_gradient_sigmoid(parameter, voltage, current); - error(steps) = lsq_sigmoid_error(parameter, voltage, current); - parameter = parameter - eps .* gradient; -end -plot(1:steps, error) - -disp('gradient descent done!') -disp(strcat('final position: ', num2str(parameter))) -disp(strcat('final error: ', num2str(error(end)))) - -%% use fminsearch -parameter = [10 0.5 -50, 2.5]; - -objective_function = @(p)lsq_sigmoid_error(p, voltage, current); -param = fminunc(objective_function, parameter); -disp(param) -param1 = fminsearch(objective_function, parameter); -disp(param1) From c8427269507f677eae528687d2ddfd7fbe6ba4ea Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Tue, 27 Oct 2015 12:24:33 +0100 Subject: [PATCH 2/5] python script to create firing rates in different ways --- programming/code/firing_rates.py | 198 +++++++++++++++++++++++++++++++ 1 file changed, 198 insertions(+) create mode 100644 programming/code/firing_rates.py diff --git a/programming/code/firing_rates.py b/programming/code/firing_rates.py new file mode 100644 index 0000000..5d5d8f9 --- /dev/null +++ b/programming/code/firing_rates.py @@ -0,0 +1,198 @@ +import numpy as np +import matplotlib.pyplot as plt +import scipy.io as spio +import scipy as sp +import seaborn as sb +from IPython import embed +sb.set_context("paper") + + +def set_axis_fontsize(axis, label_size, tick_label_size=None, legend_size=None): + """ + Sets axis, tick label and legend font sizes to the desired size. + + :param axis: the axes object + :param label_size: the size of the axis label + :param tick_label_size: the size of the tick labels. If None, lable_size is used + :param legend_size: the size of the font used in the legend.If None, the label_size is used. + + """ + if not tick_label_size: + tick_label_size = label_size + if not legend_size: + legend_size = label_size + axis.xaxis.get_label().set_fontsize(label_size) + axis.yaxis.get_label().set_fontsize(label_size) + for tick in axis.xaxis.get_major_ticks() + axis.yaxis.get_major_ticks(): + tick.label.set_fontsize(tick_label_size) + + l = axis.get_legend() + if l: + for t in l.get_texts(): + t.set_fontsize(legend_size) + + +def get_instantaneous_rate(times, max_t=30., dt=1e-4): + time = np.arange(0., max_t, dt) + indices = np.asarray(times / dt, dtype=int) + intervals = np.diff(np.hstack(([0], times))) + inst_rate = np.zeros(time.shape) + + for i, index in enumerate(indices[1:]): + inst_rate[indices[i-1]:indices[i]] = 1/intervals[i] + return time, inst_rate + + +def plot_isi_rate(spike_times, max_t=30, dt=1e-4): + times = np.squeeze(spike_times[0][0])[:100000] + time, rate = get_instantaneous_rate(times, max_t=100000*dt) + + rates = np.zeros((len(rate), len(spike_times))) + for i in range(len(spike_times)): + _, rates[:, i] = get_instantaneous_rate(np.squeeze(spike_times[i][0])[:100000], + max_t=100000*dt) + avg_rate = np.mean(rates, axis=1) + rate_std = np.std(rates, axis=1) + + fig = plt.figure() + ax1 = fig.add_subplot(311) + ax2 = fig.add_subplot(312) + ax3 = fig.add_subplot(313) + + ax1.vlines(times[times < (100000*dt)], ymin=0, ymax=1, color="dodgerblue", lw=1.5) + ax1.set_ylabel("skpikes", fontsize=12) + set_axis_fontsize(ax1, 12) + + ax2.plot(time, rate, label="instantaneous rate, trial 1") + ax2.set_ylabel("firing rate [Hz]", fontsize=12) + ax2.legend(fontsize=12) + set_axis_fontsize(ax2, 12) + + ax3.fill_between(time, avg_rate+rate_std, avg_rate-rate_std, color="dodgerblue", + alpha=0.5, label="standard deviation") + ax3.plot(time, avg_rate, label="average rate") + ax3.set_xlabel("times [s]", fontsize=12) + ax3.set_ylabel("firing rate [Hz]", fontsize=12) + ax3.legend(fontsize=12) + ax3.set_ylim([0, 450]) + set_axis_fontsize(ax3, 12) + + fig.set_size_inches(15, 10) + fig.subplots_adjust(left=0.1, bottom=0.125, top=0.95, right=0.95) + fig.set_facecolor("white") + fig.savefig("../lectures/images/instantaneous_rate.png") + plt.close() + + +def get_binned_rate(times, bin_width=0.05, max_t=30., dt=1e-4): + time = np.arange(0., max_t, dt) + bins = np.arange(0., max_t, bin_width) + bin_indices = bins / dt + hist, _ = sp.histogram(times, bins) + rate = np.zeros(time.shape) + + for i, b in enumerate(bin_indices[1:]): + rate[bin_indices[i-1]:b] = hist[i-1]/bin_width + return time, rate + + +def plot_bin_rate(spike_times, bin_width, max_t=30, dt=1e-4): + times = np.squeeze(spike_times[0][0]) + time, rate = get_binned_rate(times) + rates = np.zeros((len(rate), len(spike_times))) + for i in range(len(spike_times)): + _, rates[:, i] = get_binned_rate(np.squeeze(spike_times[i][0])) + avg_rate = np.mean(rates, axis=1) + rate_std = np.std(rates, axis=1) + + fig = plt.figure() + ax1 = fig.add_subplot(311) + ax2 = fig.add_subplot(312) + ax3 = fig.add_subplot(313) + + ax1.vlines(times[times < (100000*dt)], ymin=0, ymax=1, color="dodgerblue", lw=1.5) + ax1.set_ylabel("skpikes", fontsize=12) + ax1.set_xlim([0, 10]) + set_axis_fontsize(ax1, 12) + + ax2.plot(time, rate, label="binned rate, trial 1") + ax2.set_ylabel("firing rate [Hz]", fontsize=12) + ax2.legend(fontsize=12) + ax2.set_xlim([0, 10]) + set_axis_fontsize(ax2, 12) + + ax3.fill_between(time, avg_rate+rate_std, avg_rate-rate_std, color="dodgerblue", + alpha=0.5, label="standard deviation") + ax3.plot(time, avg_rate, label="average rate") + ax3.set_xlabel("times [s]", fontsize=12) + ax3.set_ylabel("firing rate [Hz]", fontsize=12) + ax3.legend(fontsize=12) + ax3.set_xlim([0, 10]) + ax3.set_ylim([0, 450]) + set_axis_fontsize(ax3, 12) + + fig.set_size_inches(15, 10) + fig.subplots_adjust(left=0.1, bottom=0.125, top=0.95, right=0.95) + fig.set_facecolor("white") + fig.savefig("../lectures/images/binned_rate.png") + plt.close() + + +def get_convolved_rate(times, sigma, max_t=30., dt=1.e-4): + time = np.arange(0., max_t, dt) + kernel = sp.stats.norm.pdf(np.arange(-8*sigma, 8*sigma, dt),loc=0,scale=sigma) + indices = np.asarray(times/dt, dtype=int) + rate = np.zeros(time.shape) + rate[indices] = 1.; + conv_rate = np.convolve(rate, kernel, mode="same") + return time, conv_rate + + +def plot_conv_rate(spike_times, sigma=0.05, max_t=30, dt=1e-4): + times = np.squeeze(spike_times[0][0]) + time, rate = get_convolved_rate(times, sigma) + + rates = np.zeros((len(rate), len(spike_times))) + for i in range(len(spike_times)): + _, rates[:, i] = get_convolved_rate(np.squeeze(spike_times[i][0]), sigma) + avg_rate = np.mean(rates, axis=1) + rate_std = np.std(rates, axis=1) + + fig = plt.figure() + ax1 = fig.add_subplot(311) + ax2 = fig.add_subplot(312) + ax3 = fig.add_subplot(313) + + ax1.vlines(times[times < (100000*dt)], ymin=0, ymax=1, color="dodgerblue", lw=1.5) + ax1.set_ylabel("skpikes", fontsize=12) + ax1.set_xlim([0, 10]) + set_axis_fontsize(ax1, 12) + + ax2.plot(time, rate, label="convolved rate, trial 1") + ax2.set_ylabel("firing rate [Hz]", fontsize=12) + ax2.legend(fontsize=12) + ax2.set_xlim([0, 10]) + set_axis_fontsize(ax2, 12) + + ax3.fill_between(time, avg_rate+rate_std, avg_rate-rate_std, color="dodgerblue", + alpha=0.5, label="standard deviation") + ax3.plot(time, avg_rate, label="average rate") + ax3.set_xlabel("times [s]", fontsize=12) + ax3.set_ylabel("firing rate [Hz]", fontsize=12) + ax3.legend(fontsize=12) + ax3.set_xlim([0, 10]) + ax3.set_ylim([0, 450]) + set_axis_fontsize(ax3, 12) + + fig.set_size_inches(15, 10) + fig.subplots_adjust(left=0.1, bottom=0.125, top=0.95, right=0.95) + fig.set_facecolor("white") + fig.savefig("../lectures/images/concolved_rate.png") + plt.close() + + +if __name__ == "__main__": + spike_times = spio.loadmat('lifoustim.mat')["spikes"] + # plot_isi_rate(spike_times) + # plot_bin_rate(spike_times, 0.05) + plot_conv_rate(spike_times, 0.05) From 72d29dc4065564fb7207a30194f770d9f4633286 Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Tue, 27 Oct 2015 17:53:31 +0100 Subject: [PATCH 3/5] psth exercises --- programming/exercises/plotting_psth.tex | 78 +++++++++++++++++++++++++ 1 file changed, 78 insertions(+) create mode 100644 programming/exercises/plotting_psth.tex diff --git a/programming/exercises/plotting_psth.tex b/programming/exercises/plotting_psth.tex new file mode 100644 index 0000000..8dcee53 --- /dev/null +++ b/programming/exercises/plotting_psth.tex @@ -0,0 +1,78 @@ +\documentclass[12pt,a4paper,pdftex]{exam} + +\usepackage[german]{babel} +\usepackage{natbib} +\usepackage{graphicx} +\usepackage[small]{caption} +\usepackage{sidecap} +\usepackage{pslatex} +\usepackage{amsmath} +\usepackage{amssymb} +\setlength{\marginparwidth}{2cm} +\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue]{hyperref} + +%%%%% text size %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage[left=20mm,right=20mm,top=25mm,bottom=25mm]{geometry} +\pagestyle{headandfoot} \header{{\bfseries\large \"Ubung + }}{{\bfseries\large Peri Stimulus Time Histogram}}{{\bfseries\large 28. Oktober, 2015}} +\firstpagefooter{Dr. Jan Grewe}{Phone: 29 74588}{Email: + jan.grewe@uni-tuebingen.de} \runningfooter{}{\thepage}{} + +\setlength{\baselineskip}{15pt} +\setlength{\parindent}{0.0cm} +\setlength{\parskip}{0.3cm} +\renewcommand{\baselinestretch}{1.15} + +\newcommand{\code}[1]{\texttt{#1}} +\renewcommand{\solutiontitle}{\noindent\textbf{L\"osung:}\par\noindent} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{document} + +\vspace*{-6.5ex} +\begin{center} + \textbf{\Large Einf\"uhrung in die wissenschaftliche Datenverarbeitung}\\[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 Graphische Darstellung der zeitabh\"angigen Antwort eines + Neurons. PSTH auf Basis der instantanen Feuerrate. Verwendet den Datensatz \code{} + \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\"uckgiebt. + \part Benutzt diese Funktion in einem Skript und stellt das PSTH + eines einzelnen Trials sowie den Mittelwert \"uber alle Trials + dar. + \part Erweitert das Programm so, dass die Abbildung den Standards + z.B. vom \textit{Journal of Neuroscience} entspricht + (Schriftgr\"o{\ss}e, Abbildungsgr\"o{\ss}e). + \part Die Abbildung sollte als pdf gespeichert werden. + \end{parts} + + \question Wie zuvor nur unter Verwendung der Binning Methode. + + \question Wie zuvor nur unter Verwendung der Faltungsmethode. + + \question Entscheidet euch f\"ur eine Varainte und erweitert das + entsprechende Skript, sodass auch die Interspikeintervallverteilung + und die Verteilung der Spikecounts dargestellt werden. Die + Abbildungen sollten nat\"urlich ``publikationsreif'' sein und + gespeichert werden. + + \question Einige trials sind anders als die \"Ubrigen. Benutzt den + Rasterplot um sie zu finden. Speichert alle Abbildungen in + ``publikationsreifer'' Form. + \begin{parts} + \part Benutzt den Rasterplot um sie zu finden. + \part Plottet die Verteilung der Spike counts. + \part Filtert all die trials heraus, deren spike count mehr als + $2\sigma$ vom Mittelwert abweicht. + \part Plottet das PSTH vor und nach dem Filtern. + \end{parts} + +\end{questions} + +\end{document} \ No newline at end of file From 938efd9ae1de28967615fc6fa2ec18362b715c31 Mon Sep 17 00:00:00 2001 From: Jan Grewe Date: Tue, 27 Oct 2015 17:53:56 +0100 Subject: [PATCH 4/5] plotting, psth, sta lecture --- programming/code/firing_rates.py | 30 +- .../lectures/plotting_spike_trains.tex | 271 ++++++++++++++---- 2 files changed, 235 insertions(+), 66 deletions(-) diff --git a/programming/code/firing_rates.py b/programming/code/firing_rates.py index 5d5d8f9..b38dac8 100644 --- a/programming/code/firing_rates.py +++ b/programming/code/firing_rates.py @@ -44,13 +44,13 @@ def get_instantaneous_rate(times, max_t=30., dt=1e-4): def plot_isi_rate(spike_times, max_t=30, dt=1e-4): - times = np.squeeze(spike_times[0][0])[:100000] - time, rate = get_instantaneous_rate(times, max_t=100000*dt) + times = np.squeeze(spike_times[0][0])[:50000] + time, rate = get_instantaneous_rate(times, max_t=50000*dt) rates = np.zeros((len(rate), len(spike_times))) for i in range(len(spike_times)): - _, rates[:, i] = get_instantaneous_rate(np.squeeze(spike_times[i][0])[:100000], - max_t=100000*dt) + _, rates[:, i] = get_instantaneous_rate(np.squeeze(spike_times[i][0])[:50000], + max_t=50000*dt) avg_rate = np.mean(rates, axis=1) rate_std = np.std(rates, axis=1) @@ -59,7 +59,7 @@ def plot_isi_rate(spike_times, max_t=30, dt=1e-4): ax2 = fig.add_subplot(312) ax3 = fig.add_subplot(313) - ax1.vlines(times[times < (100000*dt)], ymin=0, ymax=1, color="dodgerblue", lw=1.5) + ax1.vlines(times[times < (50000*dt)], ymin=0, ymax=1, color="dodgerblue", lw=1.5) ax1.set_ylabel("skpikes", fontsize=12) set_axis_fontsize(ax1, 12) @@ -112,13 +112,13 @@ def plot_bin_rate(spike_times, bin_width, max_t=30, dt=1e-4): ax1.vlines(times[times < (100000*dt)], ymin=0, ymax=1, color="dodgerblue", lw=1.5) ax1.set_ylabel("skpikes", fontsize=12) - ax1.set_xlim([0, 10]) + ax1.set_xlim([0, 5]) set_axis_fontsize(ax1, 12) ax2.plot(time, rate, label="binned rate, trial 1") ax2.set_ylabel("firing rate [Hz]", fontsize=12) ax2.legend(fontsize=12) - ax2.set_xlim([0, 10]) + ax2.set_xlim([0, 5]) set_axis_fontsize(ax2, 12) ax3.fill_between(time, avg_rate+rate_std, avg_rate-rate_std, color="dodgerblue", @@ -127,7 +127,7 @@ def plot_bin_rate(spike_times, bin_width, max_t=30, dt=1e-4): ax3.set_xlabel("times [s]", fontsize=12) ax3.set_ylabel("firing rate [Hz]", fontsize=12) ax3.legend(fontsize=12) - ax3.set_xlim([0, 10]) + ax3.set_xlim([0, 5]) ax3.set_ylim([0, 450]) set_axis_fontsize(ax3, 12) @@ -165,13 +165,13 @@ def plot_conv_rate(spike_times, sigma=0.05, max_t=30, dt=1e-4): ax1.vlines(times[times < (100000*dt)], ymin=0, ymax=1, color="dodgerblue", lw=1.5) ax1.set_ylabel("skpikes", fontsize=12) - ax1.set_xlim([0, 10]) + ax1.set_xlim([0, 5]) set_axis_fontsize(ax1, 12) ax2.plot(time, rate, label="convolved rate, trial 1") ax2.set_ylabel("firing rate [Hz]", fontsize=12) ax2.legend(fontsize=12) - ax2.set_xlim([0, 10]) + ax2.set_xlim([0, 5]) set_axis_fontsize(ax2, 12) ax3.fill_between(time, avg_rate+rate_std, avg_rate-rate_std, color="dodgerblue", @@ -180,19 +180,19 @@ def plot_conv_rate(spike_times, sigma=0.05, max_t=30, dt=1e-4): ax3.set_xlabel("times [s]", fontsize=12) ax3.set_ylabel("firing rate [Hz]", fontsize=12) ax3.legend(fontsize=12) - ax3.set_xlim([0, 10]) + ax3.set_xlim([0, 5]) ax3.set_ylim([0, 450]) set_axis_fontsize(ax3, 12) fig.set_size_inches(15, 10) fig.subplots_adjust(left=0.1, bottom=0.125, top=0.95, right=0.95) fig.set_facecolor("white") - fig.savefig("../lectures/images/concolved_rate.png") + fig.savefig("../lectures/images/convolved_rate.png") plt.close() if __name__ == "__main__": spike_times = spio.loadmat('lifoustim.mat')["spikes"] - # plot_isi_rate(spike_times) - # plot_bin_rate(spike_times, 0.05) - plot_conv_rate(spike_times, 0.05) + plot_isi_rate(spike_times) + plot_bin_rate(spike_times, 0.05) + plot_conv_rate(spike_times, 0.025) diff --git a/programming/lectures/plotting_spike_trains.tex b/programming/lectures/plotting_spike_trains.tex index 13d9e06..0926fbd 100644 --- a/programming/lectures/plotting_spike_trains.tex +++ b/programming/lectures/plotting_spike_trains.tex @@ -176,14 +176,14 @@ } \only <4> { \begin{figure} - \includegraphics[width=0.4\columnwidth]{images/badbarright} + \includegraphics[width=0.3\columnwidth]{images/badbarright} \end{figure} \vspace{0.5cm} \url{https://en.wikipedia.org/wiki/Misleading_graph} } \only <5> { \begin{figure} - \includegraphics[width=0.4\columnwidth]{images/badbarleft} + \includegraphics[width=0.3\columnwidth]{images/badbarleft} \end{figure} \vspace{0.5cm} \url{https://en.wikipedia.org/wiki/Misleading_graph} @@ -352,19 +352,18 @@ saveas(fig, 'spike_detection.pdf', 'pdf') \item Deutliche Unterscheidbarkeit von Kurven. \item Keine suggestive Darstellung. \item Ausgewogenheit von Linienst\"arken Schrift- und Plotgr\"o{\ss}e. - \item Vermeidung von Suggestiven Darstellungen. \item Fehlerbalken, wenn sie angebracht sind. \end{enumerate} \end{frame} \begin{frame}[plain] -\huge{2. Spiketrain Analyse I} +\huge{2. Spiketrain Analyse} \end{frame} \begin{frame} - \frametitle{Spiketrain Analyse I} + \frametitle{Spiketrain Analyse} \framesubtitle{Rasterplot} \begin{figure} \centering @@ -374,92 +373,221 @@ saveas(fig, 'spike_detection.pdf', 'pdf') \begin{frame} - \frametitle{Spiketrain Analyse I} + \frametitle{Spiketrain Analyse} \framesubtitle{Rasterplot} \"Ubung: \begin{enumerate} - \item Ladet die Datei: electrorecptor\_spike\_times.mat aus dem + \item Ladet die Datei: \code{lifoustim.mat} aus dem Ilias Ordner. \item Der Datensatz enth\"alt die Zeiten von Aktionspotentialen. - \item Schaut euch den Inhalt und skizziert wie das Problem gel\"ost - werden k\"onnte. - \item Erzeugt einen Rasterplot. + \item Erzeugt einen sch\"onen Rasterplot der Zellantworten, speichert ihn. + \item Welche Information liefert er, welche Information ist schwer + abzulesen? + \end{enumerate} +\end{frame} + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH} + + Darstellung der Feurreate eines Neuron als Funktion der Zeit. Es + gibt verschiedene Methoden dieses \textbf{P}eri \textbf{S}timulus + \textbf{T}ime \textbf{H}istogram zu erstellen. + \begin{enumerate} + \item Auf Basis der \textit{instantanen} Feuerrate. + \item Auf Basis des Zeithistogramms. + \item Durch Faltung der Zellantwort mit einem Gauss Kern. \end{enumerate} \end{frame} \begin{frame} - \frametitle{Spiketrain Analyse I} - \framesubtitle{Feuerrate \"uber - die Zeit} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Instantane Feuerrate ---} + \Large{Berechnung des PSTHs durch die Instantane Feurerrate:} + \normalsize \begin{enumerate} \item Die Feuerrate kann aus dem Abstand zwischen zwei aufeinanderfolgenden Aktionspotentialen (\textbf{Interspikeinterval}) berechnet werden. \pause - \item Auch als \textbf{Instantane Feuerrate} bezeichnet. + \item Die \textbf{Instantane Feuerrate} wird aus dem Kehrwert des + Interspikeintervals berechnet. \end{enumerate} +\end{frame} + + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Instantane Feuerrate ---} \begin{figure} \centering - \includegraphics[width=0.5\columnwidth]{images/isi} + \includegraphics[width=0.9\columnwidth]{images/instantaneous_rate} \end{figure} \end{frame} \begin{frame} - \frametitle{Spiketrain Analyse I} - \framesubtitle{Feuerrate \"uber - die Zeit} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Instantane Feuerrate ---} + Berechnung des PSTHs durch die Instantane Feurerrate: + \textbf{Vorteile:} + \begin{enumerate} - \item Z.B. das \textbf{P}eri- \textbf{S}timulus - \textbf{T}ime - - \textbf{H}istogram, \textbf{PSTH} - \item Wird berechnet indem die Zeit in ``bins'' geteilt wird die - Anzahl Spikes pro bin gezaehlt werden. - \item Die Anzahl wird dann in eine Feuerrate umgerechnet. - \end{enumerate}\pause + \item Sehr einfach zu Berechnen. + \item Macht keine Annahmen \"uber ein Zeitraster, oder die Zeitskala + der neuronalen Verarbeitung. + \end{enumerate} + + \textbf{Nachteile:} + \begin{enumerate} + \item Die Feuerrate ist nie null, auch wenn f\"ur lange Zeit kein + Aktionspotential auftritt. + \item Verh\"alt sich im Fourrier Raum nicht sehr sch\"on. + \end{enumerate} +\end{frame} + + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Binning Methode ---} + \Large{Binning Methode:} + \normalsize + \begin{enumerate} + \item Die Zeitachse wird in gleich gro{\ss}e Abschnitte ``bins'' + unterteilt. + \item F\"ur jedes ``bin'' wird die Anzahl vorkommender + Aktionspotentiale gez\"ahlt. + \item Der Spike-count pro bin muss nun noch in die Rate umgerechnet + werden. + \end{enumerate} +\end{frame} + + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Binning Methode ---} \begin{figure} - \centering - \includegraphics[width=0.5\columnwidth]{images/binning} + \includegraphics[width=0.9\columnwidth]{images/binned_rate} \end{figure} \end{frame} +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Binning Methode ---} + + Berechnung des PSTHs durch die Binning Methode: + + \textbf{Vorteile:} + \begin{enumerate} + \item Sehr einfach zu Berechnen. + \item Zeigt nur da Aktivit\"at an, wo auch Aktionspotentiale + generiert wurden. + \end{enumerate} + + \textbf{Nachteile:} + \begin{enumerate} + \item Mach Annahmen \"uber die relevante Zeitskala neuronaler + Verarbeitung. + \item Die Zeitachse wird diskretisiert. + \item Verh\"alt sich im Fourrier Raum nicht sehr sch\"on. + \end{enumerate} +\end{frame} + + +\begin{frame}[fragile] + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Faltungsmethode ---} + \Large{Faltung mit einem Gauss Kern:} + \normalsize + \[r_{est}(t) = \int_{-\infty}^{\infty}d\tau \omega(\tau)\rho(t-\tau) \] + + wobei $\omega(\tau)$ der Gauss Kern und $\rho(t)$ die Antwortfunktion ist. + + Gl\"ucklicherweise m\"ussen wir das nicht selbst implementieren... +\end{frame} + + \begin{frame}[fragile] - \frametitle{Spiketrain Analyse I} - \framesubtitle{Feuerrate \"uber die Zeit} + \frametitle{Spiketrain Analyse} + \framesubtitle{Zeitabh\"angige Feuerrate, PSTH --- Faltungsmethode ---} + \large Algortihmus: + \normalsize \begin{enumerate} - \item Z.B. das \textbf{P}eri- \textbf{S}timulus - \textbf{T}ime - - \textbf{H}istogram, \textbf{PSTH} - \item Wird berechnet indem man die Aktivit\"at bin\"ar ausdr\"uckt. - \item Jede 1 wird dann duch einen ``Kern'' ersetzt. - \item Der Vorgang heisst Faltung (\verb+conv+). - \end{enumerate}\pause + \item Die neuronalen Antworten werden ``bin\"ar'' ausgedr\"uckt. + \item Ein Filterkern wird berechnet, der das Integral 1 hat. + \item Mithilfe der Faltung (\code{conv} Funktion) wird jede 1 durch + den ``Kern'' ersetzt.\\ + \code{conv(x, kern, 'mode', 'same')} + \end{enumerate} +\end{frame} + + +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Feurerrate als Funktion der Zeit --- Faltungsmethode ---} \begin{figure} - \centering - \includegraphics[width=0.5\columnwidth]{images/conv} + \includegraphics[width=0.9\columnwidth]{images/convolved_rate} \end{figure} \end{frame} -\begin{frame} [fragile] - \frametitle{Spiketrain Analyse I} - \framesubtitle{\"Ubung} - \begin{enumerate} - \item Berechnet die Feuerrate eines Neurons mit einer der drei Methoden. - \item Die Abbildung soll f\"ur eine einspaltige Abbildung im - \textit{Journal of Neuroscience} geeignet sein - (\url{http://www.jneurosci.org/site/misc/ifa_illustrations.xhtml}). - \item Erzeugt/ver\"andert/erweitert das Programm zum plotten so, dass - die Abbildung automatisch erstellt und gespeichert wird. - \item Speichert die Abbildung als pdf. - \item Ladet den Stimulus aus dem Ilias Ordner und benutzt die - \verb+subplot+ Funktion um den Stimulus zu der neuronalen - Aktivit\"at zu plotten. - \end{enumerate} +\begin{frame} + \frametitle{Spiketrain Analyse} + \framesubtitle{Feurerrate als Funktion der Zeit --- Faltungsmethode ---} + \textbf{Vorteile:} + \begin{enumerate} + \item Sehr ``nat\"urliche'' erscheinende Darstellung. + \item Sehr gutes Verhalten im Fourrier Raum. + \end{enumerate} + + \textbf{Nachteile:} + \begin{enumerate} + \item Relativ rechenintensiv. + \item Macht Annahmen \"uber die Zeitskalen neuronaler Verarbeitung. + \end{enumerate} +\end{frame} + +\begin{frame}[plain] + \huge{3. Analyse der Beziehung zwischen Stimulus und Antwort} +\end{frame} + + +\begin{frame}[fragile] + \frametitle{Spiketrain Analyse} + \framesubtitle{Spike-Triggered-Average} + \begin{itemize} + \item[] Die Antworten darzustellen ist gut und sch\"on, aber was sagt es uns?\pause + \item[] Idealerweise wollen wir die Antworten in Beziehung zum + hervorrufenden Stimulus setzen. + \item[] Eine Methode ist der sogenannte \textbf{Spike-Triggered-Average} (STA). + \end{itemize} \end{frame} + \begin{frame}[fragile] \frametitle{Spiketrain Analyse} \framesubtitle{Spike-Triggered-Average} + + Der STA stellt den (mittleren) Stimulus dar, der zu einem + Aktionspotential gef\"uhrt hat: + + \begin{equation} + STA(\tau) = \frac{1}{\langle n \rangle} \left\langle \displaystyle\sum_{i=1}^{n}{s(t_i - \tau)} \right\rangle + \end{equation} + Wobei: $\tau$ ist eine bestimmte Zeit relativ zur Zeit eines + Aktionspotentials, $t_i$ ist der Zeitpunkt eines APs, $s(t)$ ist der + Stimulus.\\ + + Leider m\"ussen wir das selbst implementieren... +\end{frame} + + +\begin{frame}[fragile] + \frametitle{Spiketrain Analyse} + \framesubtitle{Spike-Triggered-Average} + \large{Algorithmus:} + \normalsize \begin{enumerate} \item Der \textbf{STA} ist der mittlere Stimulus, der zu einem Aktionspotential f\"uhrt. \item F\"ur jeden Spike wird ein entsprechender Abschnitt um die Zeit des Spikes herausgeschnitten. @@ -471,4 +599,45 @@ saveas(fig, 'spike_detection.pdf', 'pdf') \end{figure} \end{frame} +\begin{frame}[fragile] + \frametitle{Spiketrain Analyse} + \framesubtitle{Spike-Triggered-Average} + \vspace{-1em} + \begin{figure} + \centering + \includegraphics[width=0.6\columnwidth]{images/sta} + \end{figure} + \pause + \vspace{-0.5em} + Welche Information liefert der \textbf{STA}? + \small + \begin{enumerate} + \item Gibt es eine Beziehung zwischen Stimulus und Antwort?\pause + \item Gibt es eine Verz\"ogerung zwischen Stimulus und Antwort? Wie + gro{\ss} ist diese?\pause + \item Wie weit h\"angt das Auftreten eines Aktionspotentials von der + Vergangenheit ab? \pause + \item Kann die Zelle in die Zukunft sehen? + \end{enumerate} +\end{frame} + \end{document} + + + +\begin{frame} [fragile] + \frametitle{Spiketrain Analyse} + \framesubtitle{\"Ubung} + \begin{enumerate} + \item Berechnet die Feuerrate eines Neurons mit einer der drei Methoden. + \item Die Abbildung soll f\"ur eine einspaltige Abbildung im + \textit{Journal of Neuroscience} geeignet sein + (\url{http://www.jneurosci.org/site/misc/ifa_illustrations.xhtml}). + \item Erzeugt/ver\"andert/erweitert das Programm zum plotten so, dass + die Abbildung automatisch erstellt und gespeichert wird. + \item Speichert die Abbildung als pdf. + \item Ladet den Stimulus aus dem Ilias Ordner und benutzt die + \verb+subplot+ Funktion um den Stimulus zu der neuronalen + Aktivit\"at zu plotten. + \end{enumerate} +\end{frame} \ No newline at end of file From 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