[projects] fixed noiseficurves

projects/project_lif/lif.tex

@@ -2,43 +2,47 @@
 
 \newcommand{\ptitle}{Integrate-and-fire neuron}
 \input{../header.tex}
-\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}%
+\firstpagefooter{Supervisor: Jan Benda}{}%
 {email: jan.benda@uni-tuebingen.de}
 
 \begin{document}
 
 \input{../instructions.tex}
 
+The leaky integrate-and-fire model is a simple but powerful model of
+spiking neurons. It adds to the dynamics of a passive membrane a
+voltage threshold to simulate the generation of action potentials. In
+this project you learn how to simulate such a model and explore some
+of its stimulus encoding properties.
 
-%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
+The temporal evolution of the membrane voltage $V(t)$ of a passive
+neuron is described by the membrane equation
+\begin{equation}
+  \label{passivemembrane}
+  \tau \frac{dV}{dt} = -V + E
+\end{equation}
+where $\tau=10$\,ms is the membrane time constant and $E(t)$ is the
+reversal potential that also depends on time $t$.
 
-\begin{questions}
-  \question The temporal evolution of the membrane voltage $V(t)$ of a
-  passive neuron is described by the membrane equation
-  \begin{equation}
-    \label{passivemembrane}
-    \tau \frac{dV}{dt} = -V + E
-  \end{equation}
-  where $\tau=10$\,ms is the membrane time constant and $E(t)$ is the
-  reversal potential that also depends on time $t$.
-
-  Such a differential equation can be numerically solved with the Euler method.
-  For this the time is discretized by a time step $\Delta t=0.1$\,ms.
-  The $i$-th time point is then at time $t_i = i \cdot \Delta t$.
-  In matlab we get the time points $t_i$ simply by
-  \begin{lstlisting}
+Such a differential equation can be numerically solved with the Euler
+method.  For this the time is discretized by a time step $\Delta
+t=0.1$\,ms.  The $i$-th time point is then at time $t_i = i \cdot
+\Delta t$.  In matlab we get the time points $t_i$ simply by
+\begin{lstlisting}
 dt = 0.1;
 tmax = 100.0;
 time = [0.0:dt:tmax]; % t_i
-  \end{lstlisting}
-  When the membrane potential at time $t_0 = 0$ is $V_0$, the so
-  called ``initial condition'', then we can iteratively compute the 
-  membrane potentials $V_i$ for successive time points $t_i$ according to
-  \begin{equation}
-    \label{euler}
-    V_{i+1} = V_i + (-V_i + E_i) \frac{\Delta t}{\tau}
-  \end{equation}
+\end{lstlisting}
+When the membrane potential at time $t_0 = 0$ is $V_0$, the so called
+``initial condition'', then we can iteratively compute the membrane
+potentials $V_i$ for successive time points $t_i$ according to
+\begin{equation}
+  \label{euler}
+  V_{i+1} = V_i + (-V_i + E_i) \frac{\Delta t}{\tau}
+\end{equation}
 
+\begin{questions}
+  \question Passive membrane
   \begin{parts}
     \part Write a function that computes the time course of the
     membrane potential of the passive membrane. The function gets as
@@ -80,19 +84,22 @@ time = [0.0:dt:tmax]; % t_i
     neuron.
 
     How does the filter function depend on the membrane time constant?
+  \end{parts}
 
-    \part Leaky integrate-and-fire neuron.
+  \question Leaky integrate-and-fire neuron
 
-    The passive neuron can be turned into a spiking neuron by
-    introducing a fixed voltage threshold. Whenever the computed
-    membrane potential of the passive neuron crosses the voltage
-    threshold a spike is generated and the membrane voltage is set to
-    the reset potential $V_R$ that we here set to zero. ``Generating a
-    spike'' only means that we note down the time of the threshold
-    crossing as a time where an action potential occurred. The
-    waveform of the action potential is not modeled. Here we use a
-    voltage threshold of 1\,mV.
+  The passive neuron can be turned into a spiking neuron by
+  introducing a fixed voltage threshold. Whenever the computed
+  membrane potential of the passive neuron crosses the voltage
+  threshold a spike is generated and the membrane voltage is set to
+  the reset potential $V_R$ that we here set to zero. ``Generating a
+  spike'' only means that we note down the time of the threshold
+  crossing as a time where an action potential occurred. The waveform
+  of the action potential is not modeled. Here we use a voltage
+  threshold of 1\,mV.
 
+  \begin{parts}
+    \part 
     Write a function that implements this leaky integrate-and-fire
     neuron by expanding the function for the passive neuron
     appropriately. The function returns a vector of spike times.