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 6: Contrast enhancement through inhibition

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

In this exercise you will investigate how inhibition can be useful for enhancing contrast in the input. For this exercise too, you will use the CSIM tool.

Description

In this exercise you have the following setup:

You have $ N$ excitatory neurons $ (n^E_1, n^E_2, \cdots, n^E_N)$, topologically arranged into a circle, and $ N$ inhibitory neurons $ (n^I_1, n^I_2, \cdots, n^I_N)$, which are also arranged in a cirle on a plane parallel to the plane which has excitatory neurons. Each excitatory neuron $ n^E_i$, is connected to the corresponding inhibitory neuron $ n^I_i$, through an excitatory synapse. Each inhibitory neuron, inhibits the neighbours of its corresponding excitatory neuron, in a certain inhibition radius, $ r$. For example if the inhibition radius $ r = 2$, then the inhibitory neuron $ n^I_i$ will make inhibitory synapses to excitatory neurons $ n^E_{i-2}, n^E_{i-1}, n^E_{i+1},$ and $ n^E_{i+2}$ (in wrap-around configuration). The external input is applied to the excitatory neurons. The external input to any neuron $ n^E_i$ is a current of constant magnitude.

Given this setup, the firing rate of neuron $ n^E_i$ will show a definite peak, if the neurons $ n^E_1, n^E_2, \cdots, n^E_i$, recieve a constant input current $ I_{hi}$ and neurons $ n^E_{i+1}, n^E_{i+2}, \cdots, n^E_N$ recive a constant input current of magnitude $ I_{lo}$, where $ I_{hi} > I_{lo}$.

Figure 1 shows the experimental setup for a linear arrangement of neurons.

Figure: Conceptual Figure to explain the experimental setup
\includegraphics[width=11cm]{nw}

Setting up the system

  1. Just use CSIM and create a circuit with desired connectivity structure.

Experiments

In your code define the following variables:

For each of the experiments given below, you are required to submit a plot with four panels. The first panel of the plot will show the input stimulus (x axis - neuron index, Y axis - the magnitude of stimulus). The second panel will show the firing rate of the excitatory neurons (X axis - neuron index, Y axis - firing rate). Panel 3 and 4 will show the spike rasters over time for the excitatory and inhibitory neurons respectively (X axis - time, Y axis - spike rasters for neurons 1 to $ N$).

  1. Initially set the values of the variables to the following: $ N=50$, $ radius = 5$, $ I_{lo} = 5\times10^{-7} A$, $ I_{hi} = 9\times10^{-7} A$, $ bufferTime = 50 \times 10^{-3} sec$, $ enhIdx = 25$. Set the time of simulation, $ TSTIM$ to $ 3$ seconds, and choose the time-step of simulation to be $ 1 msec$. Set up the stimulus, so that neurons $ n^E_1$ to $ n^E_{enhIdx}$ recieve $ I_{hi}$, and neurons $ n^E_{enhIdx+1}$ to $ n^E_N$ receive $ I_{lo}$. Now choose appropriate weight values for $ WIP2E$, $ WE2I$, and $ WI2E$, so that you can observe contrast enhancement. Submit the plot, and the weight settings that worked for you.

  2. Keep all the values as in previous experiment, only change the stimulus, so that neurons $ n^E_1$ to $ n^E_{enhIdx}$ recieve $ I_{lo}$, and neurons $ n^E_{enhIdx+1}$ to $ n^E_N$ receive $ I_{hi}$. Does the setup still shows contrast enhancement. Explain your reason for the answer. Also submit a plot for this.

  3. Now find another setting of parameters (at least $ I_hi$, $ I_{lo}$, and all three weight values should be different) that give correct results. Show a plot for this and submit the values for chosen parameters.

  4. Submit a printout of all the MATLAB code that you have written.

About this document ...

Neural Networks B, SS06 1

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Footnotes

... SS061
Class Website: http://www.igi.tugraz.at/lehre/NNB/SS06/


Joshi Prashant 2006-05-16