added solution for fano time project

projects/project_fano_time/solution/counthist.m

@@ -0,0 +1,11 @@
+function [counts, cbins] = counthist(spikes, tmin, tmax, T, cmax)
+tbins = tmin+T/2:T:tmax;
+cbins = 0.5:cmax;
+counts = zeros(1, length(cbins));
+for k = 1:length(spikes)
+    times = spikes{k};
+    n = hist(times((times>=tmin)&(times<=tmax)), tbins);
+    counts = counts + hist(n, cbins);
+end
+counts = counts / sum(counts);
+end

projects/project_fano_time/solution/discriminability.m

@@ -0,0 +1,23 @@
+function [d, thresholds, true1s, false1s, true2s, false2s, pratio] = discriminability(spikes1, spikes2, tmax, T, cmax)
+[c1, b1] = counthist(spikes1, 0.0, tmax, T, cmax);
+[c2, b2] = counthist(spikes2, 0.0, tmax, T, cmax);
+thresholds = 0:cmax;
+true1s = zeros(length(thresholds), 1);
+true2s = zeros(length(thresholds), 1);
+false1s = zeros(length(thresholds), 1);
+false2s = zeros(length(thresholds), 1);
+for k = 1:length(thresholds)
+    th = thresholds(k);
+    t1 = sum(c1(b1<=th));
+    f1 = sum(c1(b1>th));
+    t2 = sum(c2(b2>=th));
+    f2 = sum(c2(b2<th));
+    true1s(k) = t1;
+    true2s(k) = t2;
+    false1s(k) = f1;
+    false2s(k) = f2;
+end
+%pratio = (true1s + true2s)./(false1s+false2s);
+pratio = (true1s + true2s)/2;
+d = max(pratio);
+end

projects/project_fano_time/solution/fanotime.m

@@ -0,0 +1,71 @@
+%% general settings for the model neuron:
+trials = 10;
+tmax = 50.0;
+D = 0.01;
+
+%% generate and plot spiketrains for two inputs:
+I1 = 14.0;
+I2 = 15.0;
+spikes1 = lifspikes(trials, I1, tmax, D);
+spikes2 = lifspikes(trials, I2, tmax, D);
+subplot(1, 2, 1);
+tmin = 10.0;
+spikeraster(spikes1, tmin, tmin+2.0);
+title(sprintf('I_1=%g', I1))
+subplot(1, 2, 2);
+spikeraster(spikes2, tmin, tmin+2.0);
+title(sprintf('I_2=%g', I2))
+%savefigpdf(gcf(), 'spikeraster.pdf')
+
+%% spike count histograms:
+Ts = [0.01 0.1 0.5 1.0];
+cmax = 100;
+figure()
+for k = 1:length(Ts)
+    T = Ts(k);
+    [c1, b1] = counthist(spikes1, 0.0, tmax, T, cmax);
+    [c2, b2] = counthist(spikes2, 0.0, tmax, T, cmax);
+    subplot(2, 2, k)
+    bar(b1, c1, 'r');
+    hold on;
+    bar(b2, c2, 'b');
+    xlim([0 cmax])
+    title(sprintf('T=%gms', 1000.0*T))
+    hold off;
+end
+
+%% discrimination measure:
+T = 0.1;
+cmax = 20;
+[d, thresholds, true1s, false1s, true2s, false2s, pratio] = discriminability(spikes1, spikes2, tmax, T, cmax);
+figure()
+subplot(1, 3, 1);
+plot(thresholds, true1s, 'b');
+hold on;
+plot(thresholds, true2s, 'b');
+plot(thresholds, false1s, 'r');
+plot(thresholds, false2s, 'r');
+hold off;
+% Ratio:
+subplot(1, 3, 2);
+fprintf('discriminability = %g\n', d);
+plot(thresholds, pratio);
+% ROC:
+subplot(1, 3, 3);
+plot(false2s, true1s);
+
+%% discriminability:
+Ts = 0.01:0.01:1.0;
+cmax = 100;
+ds = zeros(length(Ts), 1)
+for k = 1:length(Ts)
+    T = Ts(k);
+    [c1, b1] = counthist(spikes1, 0.0, tmax, T, cmax);
+    [c2, b2] = counthist(spikes2, 0.0, tmax, T, cmax);
+    [d, thresholds, true1s, false1s, true2s, false2s, pratio] = discriminability(spikes1, spikes2, tmax, T, cmax);
+    ds(k) = d;
+end
+figure()
+plot(Ts, ds)
+
+

projects/project_fano_time/solution/lifspikes.m

@@ -0,0 +1,39 @@
+function spikes = lifspikes(trials, input, tmaxdt, D)
+% Generate spike times of a leaky integrate-and-fire neuron.
+% trials: the number of trials to be generated
+% input: the stimulus either as a single value or as a vector
+% tmaxdt: in case of a single value stimulus the duration of a trial
+%         in case of a vector as a stimulus the time step
+% D: the strength of additive white noise
+    
+    tau = 0.01;
+    if nargin < 4
+        D = 1e0;
+    end
+    vreset = 0.0;
+    vthresh = 10.0;
+    dt = 5e-5;
+    
+    if max(size(input)) == 1
+        input = input * ones(ceil(tmaxdt/dt), 1);
+    else
+        dt = tmaxdt;
+    end
+    spikes = cell(trials, 1);
+    for k=1:trials
+        times = [];
+        j = 1;
+        v = vreset + (vthresh-vreset)*rand(1);
+        noise = sqrt(2.0*D)*randn(length(input), 1)/sqrt(dt);
+        for i=1:length(noise)
+            v = v + (- v + noise(i) + input(i))*dt/tau;
+            if v >= vthresh
+                v = vreset;
+                spiketime = i*dt;
+                times(j) = spiketime;
+                j = j + 1;
+            end
+        end
+        spikes{k} = times;
+    end
+end

projects/project_fano_time/solution/savefigpdf.m

@@ -0,0 +1,28 @@
+function savefigpdf(fig, name, width, height)
+% Saves figure fig in pdf file name.pdf with appropriately set page size
+% and fonts
+
+% default width:
+if nargin < 3
+    width = 11.7;
+end
+% default height:
+if nargin < 4
+    height = 9.0;
+end
+
+% paper:
+set(fig, 'PaperUnits', 'centimeters');
+set(fig, 'PaperSize', [width height]);
+set(fig, 'PaperPosition', [0.0 0.0 width height]);
+set(fig, 'Color', 'white')
+
+% font:
+set(findall(fig, 'type', 'axes'), 'FontSize', 12)
+set(findall(fig, 'type', 'text'), 'FontSize', 12)
+
+% save:
+saveas(fig, name, 'pdf')
+
+end
+

projects/project_fano_time/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
+