From e22e81fa2a001fee9b558158fa7261413277b0aa Mon Sep 17 00:00:00 2001 From: Jan Benda Date: Tue, 24 Jan 2017 00:15:50 +0100 Subject: [PATCH] added opulation vector project --- projects/project_populationvector/Makefile | 10 ++ .../code/generatedata.py | 105 ++++++++++++++++++ .../project_populationvector/population01.mat | Bin 0 -> 32824 bytes .../project_populationvector/population02.mat | Bin 0 -> 33272 bytes .../project_populationvector/population03.mat | Bin 0 -> 34896 bytes .../project_populationvector/population04.mat | Bin 0 -> 33672 bytes .../project_populationvector/population05.mat | Bin 0 -> 33288 bytes .../project_populationvector/population06.mat | Bin 0 -> 33488 bytes .../project_populationvector/population07.mat | Bin 0 -> 32984 bytes .../project_populationvector/population08.mat | Bin 0 -> 34864 bytes .../project_populationvector/population09.mat | Bin 0 -> 33344 bytes .../project_populationvector/population10.mat | Bin 0 -> 34888 bytes .../project_populationvector/population11.mat | Bin 0 -> 32960 bytes .../project_populationvector/population12.mat | Bin 0 -> 34640 bytes .../project_populationvector/population13.mat | Bin 0 -> 32752 bytes .../project_populationvector/population14.mat | Bin 0 -> 34792 bytes .../project_populationvector/population15.mat | Bin 0 -> 34784 bytes .../project_populationvector/population16.mat | Bin 0 -> 32952 bytes .../project_populationvector/population17.mat | Bin 0 -> 34944 bytes .../project_populationvector/population18.mat | Bin 0 -> 33104 bytes .../project_populationvector/population19.mat | Bin 0 -> 32896 bytes .../project_populationvector/population20.mat | Bin 0 -> 34120 bytes .../project_populationvector/population21.mat | Bin 0 -> 34256 bytes .../project_populationvector/population22.mat | Bin 0 -> 33976 bytes .../project_populationvector/population23.mat | Bin 0 -> 33048 bytes .../project_populationvector/population24.mat | Bin 0 -> 33912 bytes .../project_populationvector/population25.mat | Bin 0 -> 34120 bytes .../project_populationvector/population26.mat | Bin 0 -> 33128 bytes .../project_populationvector/population27.mat | Bin 0 -> 34312 bytes .../project_populationvector/population28.mat | Bin 0 -> 33344 bytes .../project_populationvector/population29.mat | Bin 0 -> 33312 bytes .../project_populationvector/population30.mat | Bin 0 -> 33448 bytes .../project_populationvector/population31.mat | Bin 0 -> 35128 bytes .../project_populationvector/population32.mat | Bin 0 -> 33728 bytes .../project_populationvector/population33.mat | Bin 0 -> 34032 bytes .../project_populationvector/population34.mat | Bin 0 -> 34776 bytes .../project_populationvector/population35.mat | Bin 0 -> 33672 bytes .../project_populationvector/population36.mat | Bin 0 -> 33304 bytes .../project_populationvector/population37.mat | Bin 0 -> 35216 bytes .../project_populationvector/population38.mat | Bin 0 -> 32888 bytes .../project_populationvector/population39.mat | Bin 0 -> 34896 bytes .../project_populationvector/population40.mat | Bin 0 -> 32864 bytes .../project_populationvector/population41.mat | Bin 0 -> 32824 bytes .../project_populationvector/population42.mat | Bin 0 -> 34120 bytes .../project_populationvector/population43.mat | Bin 0 -> 32832 bytes .../project_populationvector/population44.mat | Bin 0 -> 34368 bytes .../project_populationvector/population45.mat | Bin 0 -> 34464 bytes .../project_populationvector/population46.mat | Bin 0 -> 33288 bytes .../project_populationvector/population47.mat | Bin 0 -> 35064 bytes .../project_populationvector/population48.mat | Bin 0 -> 32792 bytes .../project_populationvector/population49.mat | Bin 0 -> 34760 bytes .../project_populationvector/population50.mat | Bin 0 -> 34328 bytes .../populationvector.tex | 99 +++++++++++++++++ .../solution/firingrate.m | 9 ++ .../solution/populationvector.m | 43 +++++++ .../solution/spikeraster.m | 30 +++++ projects/project_populationvector/unit1.mat | Bin 0 -> 67728 bytes projects/project_populationvector/unit2.mat | Bin 0 -> 70288 bytes projects/project_populationvector/unit3.mat | Bin 0 -> 70600 bytes projects/project_populationvector/unit4.mat | Bin 0 -> 67304 bytes projects/project_populationvector/unit5.mat | Bin 0 -> 63376 bytes projects/project_populationvector/unit6.mat | Bin 0 -> 64352 bytes 62 files changed, 296 insertions(+) create mode 100644 projects/project_populationvector/Makefile create mode 100644 projects/project_populationvector/code/generatedata.py create mode 100644 projects/project_populationvector/population01.mat create mode 100644 projects/project_populationvector/population02.mat create mode 100644 projects/project_populationvector/population03.mat create mode 100644 projects/project_populationvector/population04.mat create mode 100644 projects/project_populationvector/population05.mat create mode 100644 projects/project_populationvector/population06.mat create mode 100644 projects/project_populationvector/population07.mat create mode 100644 projects/project_populationvector/population08.mat create mode 100644 projects/project_populationvector/population09.mat create mode 100644 projects/project_populationvector/population10.mat create mode 100644 projects/project_populationvector/population11.mat create mode 100644 projects/project_populationvector/population12.mat create mode 100644 projects/project_populationvector/population13.mat create mode 100644 projects/project_populationvector/population14.mat create mode 100644 projects/project_populationvector/population15.mat create mode 100644 projects/project_populationvector/population16.mat create mode 100644 projects/project_populationvector/population17.mat create mode 100644 projects/project_populationvector/population18.mat create mode 100644 projects/project_populationvector/population19.mat create mode 100644 projects/project_populationvector/population20.mat create mode 100644 projects/project_populationvector/population21.mat create mode 100644 projects/project_populationvector/population22.mat create mode 100644 projects/project_populationvector/population23.mat create mode 100644 projects/project_populationvector/population24.mat create mode 100644 projects/project_populationvector/population25.mat create mode 100644 projects/project_populationvector/population26.mat create mode 100644 projects/project_populationvector/population27.mat create mode 100644 projects/project_populationvector/population28.mat create mode 100644 projects/project_populationvector/population29.mat create mode 100644 projects/project_populationvector/population30.mat create mode 100644 projects/project_populationvector/population31.mat create mode 100644 projects/project_populationvector/population32.mat create mode 100644 projects/project_populationvector/population33.mat create mode 100644 projects/project_populationvector/population34.mat create mode 100644 projects/project_populationvector/population35.mat create mode 100644 projects/project_populationvector/population36.mat create mode 100644 projects/project_populationvector/population37.mat create mode 100644 projects/project_populationvector/population38.mat create mode 100644 projects/project_populationvector/population39.mat create mode 100644 projects/project_populationvector/population40.mat create mode 100644 projects/project_populationvector/population41.mat create mode 100644 projects/project_populationvector/population42.mat create mode 100644 projects/project_populationvector/population43.mat create mode 100644 projects/project_populationvector/population44.mat create mode 100644 projects/project_populationvector/population45.mat create mode 100644 projects/project_populationvector/population46.mat create mode 100644 projects/project_populationvector/population47.mat create mode 100644 projects/project_populationvector/population48.mat create mode 100644 projects/project_populationvector/population49.mat create mode 100644 projects/project_populationvector/population50.mat create mode 100644 projects/project_populationvector/populationvector.tex create mode 100644 projects/project_populationvector/solution/firingrate.m create mode 100644 projects/project_populationvector/solution/populationvector.m create mode 100644 projects/project_populationvector/solution/spikeraster.m create mode 100644 projects/project_populationvector/unit1.mat create mode 100644 projects/project_populationvector/unit2.mat create mode 100644 projects/project_populationvector/unit3.mat create mode 100644 projects/project_populationvector/unit4.mat create mode 100644 projects/project_populationvector/unit5.mat create mode 100644 projects/project_populationvector/unit6.mat diff --git a/projects/project_populationvector/Makefile b/projects/project_populationvector/Makefile new file mode 100644 index 0000000..6422eb4 --- /dev/null +++ b/projects/project_populationvector/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 *.m diff --git a/projects/project_populationvector/code/generatedata.py b/projects/project_populationvector/code/generatedata.py new file mode 100644 index 0000000..dfe1829 --- /dev/null +++ b/projects/project_populationvector/code/generatedata.py @@ -0,0 +1,105 @@ +import numpy as np +from scipy.io import savemat +import matplotlib.pyplot as plt + +def lifadaptspikes(stimulus, gain=10.0, trials=50, duration=200.0, before=200.0, after=400.0): + dt = 0.1 + s0 = 9.5 + tau = 10.0 + D = 1.0 + taua = 60.0 + da = 100.0 + Vth = 10.0 + n = int((duration+before+after)/dt) + delay = 10.0 + sig = np.zeros(n) + s0 + n1 = int((before+delay)/dt) + n2 = int((before+duration+delay)/dt) + sig[n1:n2] += (gain * stimulus - 1.0) * np.exp(-np.arange(n2-n1)*dt/0.4/duration) + spikes = [] + for j in range(trials): + noise = np.sqrt(2.0*D/dt)*np.random.randn(n) + V = np.random.rand()*Vth + A = 0.0 + s = s0 + As = np.zeros(n) + times = [] + for k in range(n): + As[k] = A + V += (-V-A+sig[k]+noise[k])*dt/tau + A += (-A)*dt/taua + if V >= Vth: + V = 0.0 + A += da/taua + times.append(k*dt-before) + spikes.append(np.array(times)) + #plt.plot(np.arange(n)*dt-before, As) + #plt.plot(np.arange(n)*dt-before, sig) + #return spikes + return spikes + +def firingrate(spikes, tmin, tmax): + rates = [] + for st in spikes: + times = st[(st>=tmin)&(st<=tmax)] + r = len(times)/(tmax-tmin) + rates.append(1000.0*r) + return np.mean(rates), np.std(rates) + +""" +nangles = 12 +angles = 180.0*np.arange(nangles)/nangles +rates = np.zeros(nangles) +ratessd = np.zeros(nangles) +allspikes = [] +for k, angle in enumerate(angles): + spikes = lifadaptspikes(0.5*(1.0-np.cos(2.0*np.pi*angle/180.0))) + rm, rsd = firingrate(spikes, 0.0, 200.0) + rates[k] = rm + ratessd[k] = rsd + allspikes.append(spikes) + #plt.subplot(2, 5, k+1) + #plt.title('%g' % (angle/2.0/np.pi)) + #plt.eventplot(spikes, colors=['r']) +plt.plot(angles, rates, 'r', lw=2) +plt.plot(angles, rates+ratessd, 'b') +plt.plot(angles, rates-ratessd, 'b') +plt.show() +""" + +# tuning curves: +nunits = 6 +unitphases = np.linspace(0.0, 1.0, nunits) + 0.05*np.random.randn(nunits)/float(nunits) +unitgains = 15.0 + 5.0*(2.0*np.random.rand(nunits)-1.0) +nangles = 12 +angles = 180.0*np.arange(nangles)/nangles +for unit, (phase, gain) in enumerate(zip(unitphases, unitgains)): + print '%.1f %.0f' % (gain, phase*180.0) + allspikes = [] + for k, angle in enumerate(angles): + spikes = lifadaptspikes(0.5*(1.0-np.cos(2.0*np.pi*(angle/180.0-phase))), gain) + allspikes.append(spikes) + spikesobj = np.zeros((len(allspikes), len(allspikes[0])), dtype=np.object) + for k in range(len(allspikes)): + for j in range(len(allspikes[k])): + spikesobj[k, j] = 0.001*allspikes[k][j] + savemat('unit%d.mat'%(unit+1), mdict={'angles': angles, 'spikes': spikesobj}) + +# population activity: +nangles = 50 +angles = 180.0*np.random.rand(nangles) +for k, angle in enumerate(angles): + print '%.0f' % angle + allspikes = [] + for unit, (phase, gain) in enumerate(zip(unitphases, unitgains)): + spikes = lifadaptspikes(0.5*(1.0-np.cos(2.0*np.pi*(angle/180.0-phase))), gain) + allspikes.append(spikes) + spikesobj = np.zeros((len(allspikes), len(allspikes[0])), dtype=np.object) + for i in range(len(allspikes)): + for j in range(len(allspikes[i])): + spikesobj[i, j] = 0.001*allspikes[i][j] + savemat('population%02d.mat'%(k+1), mdict={'spikes': spikesobj, + 'angle': angle, + 'phases': unitphases, + 'gains': unitgains}) + diff --git a/projects/project_populationvector/population01.mat b/projects/project_populationvector/population01.mat new file mode 100644 index 0000000000000000000000000000000000000000..9a0f13d778db64456c738054b3a342544f60b014 GIT binary patch literal 32824 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+\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 visual cortex V1 orientation sensitive neurons + respond to bars in dependence on their orientation. + + How is the orientation of a bar encoded by the activity of a + population of orientation sensisitive neurons? + + In an electrophysiological experiment, 6 neurons have been recorded + simultaneously. First, the tuning of these neurons was characteried + by presenting them bars in a range of 12 orientation angles. Each + orientation was presented 50 times. Each of the \texttt{unit*.mat} + files contains the responses of one of the neurons. In there, + \texttt{angles} is a vector with the orientation angles of the bars + in degrees. \texttt{spikes} is a cell array that contains the + vectors of spike times for each angle and presentation. The spike + times are given in seconds. The stimulation with the bar starts a + time $t_0=0$ and ends at time $t_1=200$\,ms. + + Then the population activity of the 6 neurons was measured in + response to arbitrarily oriented bars. The responses of the 6 + neurons to 50 presentation of a bar are stored in the + \texttt{spikes} variables of the \texttt{population*.mat} files. + The \texttt{angle} variable holds the angle of the presented bar. + + \begin{parts} + \part Illustrate the spiking activity of the V1 cells in response + to different orientation angles of the bars by means of spike + raster plots (of one unit). + + \part Plot the firing rate of each of the 6 neurons as a function + of the orientation angle of the bar. As the firing rate compute + the number of spikes in the time interval $0=tmin)&(times<=tmax)))/(tmax-tmin); +end +rate = mean(rates); +end diff --git a/projects/project_populationvector/solution/populationvector.m b/projects/project_populationvector/solution/populationvector.m new file mode 100644 index 0000000..829e07d --- /dev/null +++ b/projects/project_populationvector/solution/populationvector.m @@ -0,0 +1,43 @@ +close all +files = dir('../unit*.mat'); +for file = files' + a = load(strcat('../', file.name)); + spikes = a.spikes; + angles = a.angles; + figure() + for k = 1:size(spikes, 1) + subplot(3, 4, k) + spikeraster(spikes(k,:), -0.2, 0.6); + end +end + + +%% tuning curves: +close all +cosine = @(p,xdata)0.5*p(1).*(1.0-cos(2.0*pi*(xdata/180.0-p(2)))); +files = dir('../unit*.mat'); +figure() +for j = 1:length(files) + file = files(j); + a = load(strcat('../', file.name)); + spikes = a.spikes; + angles = a.angles; + rates = zeros(size(spikes, 1), 1); + for k = 1:size(spikes, 1) + r = firingrate(spikes(k,:), 0.0, 0.2); + rates(k) = r; + end + [mr, maxi] = max(rates); + p0 = [mr, angles(maxi)/180.0-0.5]; + %p = p0; + p = lsqcurvefit(cosine, p0, angles, rates'); + phase = p(2)*180.0 + subplot(2, 3, j); + plot(angles, rates, 'b'); + hold on; + plot(angles, cosine(p, angles), 'r'); + hold off; + xlim([0.0 180.0]) + ylim([0.0 50.0]) + title(sprintf('unit %d', j)) +end diff --git a/projects/project_populationvector/solution/spikeraster.m b/projects/project_populationvector/solution/spikeraster.m new file mode 100644 index 0000000..4eb1b8b --- /dev/null +++ b/projects/project_populationvector/solution/spikeraster.m @@ -0,0 +1,30 @@ +function spikeraster(spikes, tmin, tmax) +% Display a spike raster of the spike times given in spikes. +% +% spikeraster(spikes, tmax) +% spikes: a cell array of vectors of spike times in seconds +% tmin: plot spike raster starting at tmin seconds +% tmax: plot spike raster upto tmax seconds + +ntrials = length(spikes); +for k = 1:ntrials + times = spikes{k}; + times = times((times>=tmin) & (times<=tmax)); + if tmax < 1.5 + times = 1000.0*times; % conversion to ms + end + for i = 1:length( times ) + line([times(i) times(i)],[k-0.4 k+0.4], 'Color', 'k'); + end +end +if (tmax-tmin) < 1.5 + xlabel('Time [ms]'); + xlim([1000.0*tmin 1000.0*tmax]); +else + xlabel('Time [s]'); + xlim([tmin tmax]); +end +ylabel('Trials'); +ylim([0.3 ntrials+0.7 ]); +end + diff --git a/projects/project_populationvector/unit1.mat b/projects/project_populationvector/unit1.mat new file mode 100644 index 0000000000000000000000000000000000000000..4964818b13aa079e49b976d91833f8d0aa572966 GIT binary patch literal 67728 zcmbt-2bh)B)it6)>@A8VM2xY;5G6`1F>XXch=o`PAw~@rECEGDVhf5QO+-gPdKqS5 zIxxM@oO|!wX&`0#3`H~=d(;p^)EM)hv)A6|0?zL|&-r*BKE4TZ-}k=nIs5Fr_F8LS 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