# Neural Networks B, SS06 1

UA Dr. Robert Legenstein, WiMAus Prashant Joshi, M.S.

Institute for Theoretical Computer Science
Technische Universität Graz
A-8010 Graz, Austria
{legi, joshi}@igi.tugraz.at

 NACHNAME Vorname Matrikelnmr Teammitglieder

# Exercise 3: The Integrate and Fire Neuron Model

NOTE: You can download this exercise in pdf or postscript(ps) format here.

In this exercise also, you are going to use the CSIM circuit simulator to further investigate the properties of an integrate-and-fire neuron.

# The Gain Function of Integrate and Fire Neuron (10 marks)

• Select the Integrate-and-fire'' model. Apply a step-current with a step-size of (you can assume the value before the step to be 0 A). What happens as you vary the size of the step?

• For a given series of values of , measure the mean spike frequency () and draw the gain function(membrane potential vs. input current).

• How does the gain function change if you vary the membrane time constant ?

• How does the gain function change if you vary the threshold ?

# Phase Locking ( 8 bonus points!!)

Use a periodic current. Choose a signal frequency and time interval such that you can observe about ten cycles of the sinusoid in the display window.

• Modify the neuron parameters in such a way as to obtain one spike per cycle with a constant phase delay relative to the signal.

• Modify the threshold so that the ratio between the signal period and the spiking period is . That is, every 4 signal periods, there should be 3 spikes.

• Add noise to the neuron model. You can do this, by setting , and drawing from a non-zero distribution (e.g. setting to nA, means the value is drawn at each time-step from a distribution with mean 0 and SD chosen randomly from a gaussian distribution over the interval nA). What happens to the phase-locking phenomenon you observed previously?

Neural Networks B, SS06 1

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