added lif project

projects/project_lif/solution/lif.m

@@ -0,0 +1,116 @@
+%% general settings:
+tau = 10.0;
+dt = 0.1;
+
+%% test passive membrane:
+tmax = 50.0;
+time = [0:dt:tmax];
+E = zeros(length(time), 1);
+V = passivemembrane(1.0, E, tau, dt);
+expfun = exp(-time/tau);
+figure()
+plot(time, V, 'b', 'linewidth', 2);
+hold on;
+plot(time, expfun, 'r');
+hold off;
+
+%% step input:
+tmax = 120.0;
+time = [0:dt:tmax];
+E = zeros(length(time), 1);
+E(20/dt:70/dt) = 10;
+V = passivemembrane(0.0, E, tau, dt);
+figure()
+plot(time, E, 'r');
+hold on;
+plot(time, V, 'b', 'linewidth', 2);
+hold off;
+
+%% sine waves:
+tmax = 1000.0;
+time = [0:dt:tmax];
+freqs = [1.0 10.0 30.0 100.0];
+figure();
+for k = 1:length(freqs)
+    f = freqs(k);
+    E = sin(2*pi*0.001*f*time);
+    V = passivemembrane(0.0, E, tau, dt);
+    subplot(4, 1, k);
+    plot(time, E, 'r');
+    hold on;
+    plot(time, V, 'b', 'linewidth', 2);
+    hold off;
+end
+
+
+%% transfer function:
+tmax = 1000.0;
+time = [0:dt:tmax];
+taus = [3.0 10.0 30.0];
+figure();
+for tau = taus
+    freqs = [1.0:1.0:100.0];
+    rates = zeros(length(freqs), 1);
+    for k = 1:length(freqs)
+        f = freqs(k);
+        E = sin(2*pi*0.001*f*time);
+        V = passivemembrane(0.0, E, tau, dt);
+        rates(k) = max(V(100/dt:end));
+    end
+    plot(freqs, rates);
+    hold on;
+end
+hold off;
+
+
+%% leaky IaF:
+tau = 10.0;
+tmax = 50.0;
+time = [0:dt:tmax];
+E = zeros(length(time), 1) + 1.5;
+[spikes, V] = lifspikes(0.0, E, tau, dt);
+figure()
+plot(time, V, 'b', 'linewidth', 2);
+hold on;
+plot(spikes, ones(length(spikes), 1), 'or');
+hold off;
+
+
+%% leaky IaF and sine input:
+tau = 10.0;
+tmax = 500.0;
+time = [0:dt:tmax];
+f = 10.0;
+E = 2.0*sin(2*pi*0.001*f*time);
+[spikes, V] = lifspikes(0.0, E, tau, dt);
+figure()
+subplot(2, 1, 1);
+plot(time, V, 'b', 'linewidth', 2);
+hold on;
+plot(spikes, ones(length(spikes), 1), 'or');
+hold off;
+
+
+%% transfer function of LIF spikes:
+tmax = 1000.0;
+time = [0:dt:tmax];
+taus = [3.0 10.0];
+figure();
+for tau = taus
+    freqs = [5.0:0.1:30.0];
+    rates = zeros(length(freqs), 1);
+    for k = 1:length(freqs)
+        f = freqs(k);
+        E = 2.0*sin(2*pi*0.001*f*time);
+        [spikes, V] = lifspikes(0.0, E, tau, dt);
+        spikes = spikes(spikes>100.0);
+        if length(spikes) > 2
+            rates(k) = 1000.0*(length(spikes)-1)/(spikes(end)-spikes(1));
+        else
+            rates(k) = 0.0;
+        end
+    end
+    plot(freqs, rates);
+    hold on;
+end
+hold off;

projects/project_lif/solution/lifspikes.m

@@ -0,0 +1,14 @@
+function [spikes, voltage] = lifspikes(V0, E, tau, dt)
+voltage = zeros(length(E), 1);
+V = V0;
+thresh = 1.0;
+spikes = [];
+for k = 1:length(E)
+    voltage(k) = V;
+    if V > thresh
+        spikes = [spikes; k*dt];
+        V = 0.0;
+    end
+    V = V + (-V+E(k))*dt/tau;
+end
+end

projects/project_lif/solution/passivemembrane.m

@@ -0,0 +1,8 @@
+function voltage = passivemembrane(V0, E, tau, dt)
+voltage = zeros(length(E), 1);
+V = V0;
+for k = 1:length(E)
+    voltage(k) = V;
+    V = V + (-V+E(k))*dt/tau;
+end
+end