added opulation vector project
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projects/project_populationvector
Makefile
code
population01.matpopulation02.matpopulation03.matpopulation04.matpopulation05.matpopulation06.matpopulation07.matpopulation08.matpopulation09.matpopulation10.matpopulation11.matpopulation12.matpopulation13.matpopulation14.matpopulation15.matpopulation16.matpopulation17.matpopulation18.matpopulation19.matpopulation20.matpopulation21.matpopulation22.matpopulation23.matpopulation24.matpopulation25.matpopulation26.matpopulation27.matpopulation28.matpopulation29.matpopulation30.matpopulation31.matpopulation32.matpopulation33.matpopulation34.matpopulation35.matpopulation36.matpopulation37.matpopulation38.matpopulation39.matpopulation40.matpopulation41.matpopulation42.matpopulation43.matpopulation44.matpopulation45.matpopulation46.matpopulation47.matpopulation48.matpopulation49.matpopulation50.matpopulationvector.texsolution
unit1.matunit2.matunit3.matunit4.matunit5.matunit6.mat
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projects/project_populationvector/Makefile
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latex:
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pdflatex *.tex > /dev/null
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pdflatex *.tex > /dev/null
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clean:
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rm -rf *.log *.aux *.zip *.out auto
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rm -f `basename *.tex .tex`.pdf
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zip: latex
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zip `basename *.tex .tex`.zip *.pdf *.dat *.mat *.m
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projects/project_populationvector/code/generatedata.py
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projects/project_populationvector/code/generatedata.py
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import numpy as np
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from scipy.io import savemat
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import matplotlib.pyplot as plt
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def lifadaptspikes(stimulus, gain=10.0, trials=50, duration=200.0, before=200.0, after=400.0):
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dt = 0.1
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s0 = 9.5
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tau = 10.0
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D = 1.0
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taua = 60.0
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da = 100.0
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Vth = 10.0
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n = int((duration+before+after)/dt)
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delay = 10.0
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sig = np.zeros(n) + s0
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n1 = int((before+delay)/dt)
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n2 = int((before+duration+delay)/dt)
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sig[n1:n2] += (gain * stimulus - 1.0) * np.exp(-np.arange(n2-n1)*dt/0.4/duration)
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spikes = []
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for j in range(trials):
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noise = np.sqrt(2.0*D/dt)*np.random.randn(n)
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V = np.random.rand()*Vth
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A = 0.0
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s = s0
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As = np.zeros(n)
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times = []
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for k in range(n):
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As[k] = A
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V += (-V-A+sig[k]+noise[k])*dt/tau
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A += (-A)*dt/taua
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if V >= Vth:
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V = 0.0
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A += da/taua
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times.append(k*dt-before)
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spikes.append(np.array(times))
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#plt.plot(np.arange(n)*dt-before, As)
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#plt.plot(np.arange(n)*dt-before, sig)
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#return spikes
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return spikes
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def firingrate(spikes, tmin, tmax):
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rates = []
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for st in spikes:
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times = st[(st>=tmin)&(st<=tmax)]
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r = len(times)/(tmax-tmin)
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rates.append(1000.0*r)
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return np.mean(rates), np.std(rates)
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"""
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nangles = 12
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angles = 180.0*np.arange(nangles)/nangles
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rates = np.zeros(nangles)
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ratessd = np.zeros(nangles)
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allspikes = []
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for k, angle in enumerate(angles):
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spikes = lifadaptspikes(0.5*(1.0-np.cos(2.0*np.pi*angle/180.0)))
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rm, rsd = firingrate(spikes, 0.0, 200.0)
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rates[k] = rm
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ratessd[k] = rsd
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allspikes.append(spikes)
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#plt.subplot(2, 5, k+1)
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#plt.title('%g' % (angle/2.0/np.pi))
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#plt.eventplot(spikes, colors=['r'])
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plt.plot(angles, rates, 'r', lw=2)
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plt.plot(angles, rates+ratessd, 'b')
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plt.plot(angles, rates-ratessd, 'b')
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plt.show()
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"""
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# tuning curves:
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nunits = 6
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unitphases = np.linspace(0.0, 1.0, nunits) + 0.05*np.random.randn(nunits)/float(nunits)
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unitgains = 15.0 + 5.0*(2.0*np.random.rand(nunits)-1.0)
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nangles = 12
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angles = 180.0*np.arange(nangles)/nangles
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for unit, (phase, gain) in enumerate(zip(unitphases, unitgains)):
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print '%.1f %.0f' % (gain, phase*180.0)
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allspikes = []
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for k, angle in enumerate(angles):
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spikes = lifadaptspikes(0.5*(1.0-np.cos(2.0*np.pi*(angle/180.0-phase))), gain)
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allspikes.append(spikes)
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spikesobj = np.zeros((len(allspikes), len(allspikes[0])), dtype=np.object)
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for k in range(len(allspikes)):
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for j in range(len(allspikes[k])):
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spikesobj[k, j] = 0.001*allspikes[k][j]
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savemat('unit%d.mat'%(unit+1), mdict={'angles': angles, 'spikes': spikesobj})
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# population activity:
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nangles = 50
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angles = 180.0*np.random.rand(nangles)
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for k, angle in enumerate(angles):
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print '%.0f' % angle
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allspikes = []
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for unit, (phase, gain) in enumerate(zip(unitphases, unitgains)):
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spikes = lifadaptspikes(0.5*(1.0-np.cos(2.0*np.pi*(angle/180.0-phase))), gain)
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allspikes.append(spikes)
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spikesobj = np.zeros((len(allspikes), len(allspikes[0])), dtype=np.object)
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for i in range(len(allspikes)):
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for j in range(len(allspikes[i])):
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spikesobj[i, j] = 0.001*allspikes[i][j]
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savemat('population%02d.mat'%(k+1), mdict={'spikes': spikesobj,
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'angle': angle,
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'phases': unitphases,
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'gains': unitgains})
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projects/project_populationvector/populationvector.tex
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\documentclass[addpoints,11pt]{exam}
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\usepackage{url}
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\usepackage{color}
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\usepackage{hyperref}
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\pagestyle{headandfoot}
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\runningheadrule
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\firstpageheadrule
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\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
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-- 11/06/2014}
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%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
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\firstpagefooter{}{}{}
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\runningfooter{}{}{}
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\pointsinmargin
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\bracketedpoints
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%\printanswers
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%\shadedsolutions
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
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\sffamily
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% \begin{flushright}
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% \gradetable[h][questions]
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% \end{flushright}
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\begin{center}
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\input{../disclaimer.tex}
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\end{center}
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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{questions}
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\question In the visual cortex V1 orientation sensitive neurons
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respond to bars in dependence on their orientation.
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How is the orientation of a bar encoded by the activity of a
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population of orientation sensisitive neurons?
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In an electrophysiological experiment, 6 neurons have been recorded
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simultaneously. First, the tuning of these neurons was characteried
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by presenting them bars in a range of 12 orientation angles. Each
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orientation was presented 50 times. Each of the \texttt{unit*.mat}
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files contains the responses of one of the neurons. In there,
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\texttt{angles} is a vector with the orientation angles of the bars
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in degrees. \texttt{spikes} is a cell array that contains the
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vectors of spike times for each angle and presentation. The spike
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times are given in seconds. The stimulation with the bar starts a
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time $t_0=0$ and ends at time $t_1=200$\,ms.
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Then the population activity of the 6 neurons was measured in
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response to arbitrarily oriented bars. The responses of the 6
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neurons to 50 presentation of a bar are stored in the
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\texttt{spikes} variables of the \texttt{population*.mat} files.
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The \texttt{angle} variable holds the angle of the presented bar.
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\begin{parts}
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\part Illustrate the spiking activity of the V1 cells in response
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to different orientation angles of the bars by means of spike
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raster plots (of one unit).
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\part Plot the firing rate of each of the 6 neurons as a function
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of the orientation angle of the bar. As the firing rate compute
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the number of spikes in the time interval $0<t<200$\,ms divided by
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200\,ms. The resulting curves are the tuning curves $r(\varphi)$
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of the neurons.
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\part Fit the function \[ r(\varphi) =
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g(1-\cos(\varphi-\varphi_0))/2 \] to the measured tuning curves in
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order to estimated the orientation angle at which the neurons
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respond strongest. In this function $\varphi_0$ is the position of
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the peak (really? How exactly is $\varphi_0$ related to the
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position of the peak? Do you find a better function where
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$\varphi_0$ is identical with the peak position?) and $g$ is a
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gain factor that sets the maximum firing rate.
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\part How can the orientation angle of the presented bar be read
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out from the population activity of the 6 neurons? One is the so
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called ``population vector''. Think of another (simpler) method.
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Load one of the \texttt{population*.mat} files, illustrate the data,
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and estimate the orientation angle of the bar by two different methods.
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\part Compare, illustrate and discuss the performance of your two
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decoding methods.
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\end{parts}
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\end{questions}
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\end{document}
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gains and angles of the 6 neurons:
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14.6 0
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17.1 36
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17.6 72
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14.1 107
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10.7 144
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11.4 181
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9
projects/project_populationvector/solution/firingrate.m
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function rate = firingrate(spikes, tmin, tmax)
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% mean firing rate between tmin and tmax.
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rates = zeros(length(spikes), 1);
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for i = 1:length(spikes)
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times= spikes{i};
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rates(i) = length(times((times>=tmin)&(times<=tmax)))/(tmax-tmin);
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end
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rate = mean(rates);
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end
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close all
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files = dir('../unit*.mat');
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for file = files'
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a = load(strcat('../', file.name));
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spikes = a.spikes;
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angles = a.angles;
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figure()
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for k = 1:size(spikes, 1)
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subplot(3, 4, k)
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spikeraster(spikes(k,:), -0.2, 0.6);
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end
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end
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|
%% 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
|
30
projects/project_populationvector/solution/spikeraster.m
Normal file
30
projects/project_populationvector/solution/spikeraster.m
Normal file
@ -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
|
||||||
|
|
BIN
projects/project_populationvector/unit1.mat
Normal file
BIN
projects/project_populationvector/unit1.mat
Normal file
Binary file not shown.
BIN
projects/project_populationvector/unit2.mat
Normal file
BIN
projects/project_populationvector/unit2.mat
Normal file
Binary file not shown.
BIN
projects/project_populationvector/unit3.mat
Normal file
BIN
projects/project_populationvector/unit3.mat
Normal file
Binary file not shown.
BIN
projects/project_populationvector/unit4.mat
Normal file
BIN
projects/project_populationvector/unit4.mat
Normal file
Binary file not shown.
BIN
projects/project_populationvector/unit5.mat
Normal file
BIN
projects/project_populationvector/unit5.mat
Normal file
Binary file not shown.
BIN
projects/project_populationvector/unit6.mat
Normal file
BIN
projects/project_populationvector/unit6.mat
Normal file
Binary file not shown.
Reference in New Issue
Block a user