**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 |

The questions 1 to 5 are for 10 points in total. Question 6 is a bonus question for 3 points.

The action potentials of two coupled I&F neurons may synchronize. In this exercise, you will examine the circumstances under which two coupled I&F neurons synchronise.

The Matlab program
http://www.igi.tugraz.at/lehre/NNB/SS06/aufgaben/sync.m
simulates two I&F neuons which are mutually coupled by two synapses.
It plots the temporal evolution of the membrane potential, the spikes
and the PSCs. You need to unzip the file
http://www.igi.tugraz.at/lehre/NNB/SS05/aufgaben/csim.zip
into the same directory as `sync.m` to make `sync.m` work.
(it contains ` csim.dll` for Windows and `csim.mexglx` for Linux).

- 1)
- Do a simulation with the standard parameters. Describe /
explain the result. At which rates
^{2}do the neurons fire? - 2)
- Do a simultaion with
`I1=I2=18`.`I1`resp.`I2`are external currents , which are injected into the neurons. Describe the results. Why do the neurons not synchronize? - 3)
- Do a simultaion with
`I1=I2=18`,`w = 30`resp.`w=10`. Describe the results. Describe the mechanism that leads to synchronization. - 4)
- Do a simultaion with
`w=30`,`Tsim=5.0`,`I1=18`and`I2=18.5`respectively`I2=22`.`Tsim`defines the duration of the simulation. Describe / explain the results. - 5)
- Make some diagrams (think about well suited diagrams) which
show quantitatively how the quality and speed of synchrony depends on which
parameters. Describe / explain your approach and the results.
- 6*)
- Examine how the results change if you add noise to the
model (set the parameter
`Inoise`). Describe / explain the results.

- A well suited measure for the quality of synchronization is the
*cross-correlation*^{3}and , where and are the averages of and over and are the considered time interval. - You can use the time until
is above a
certain value (for a well suited choice of ) as a measure
for the speed of synchronization.
- Present your results clearly arranged and document them in a way that one can reproduce then anytime.
- Submit the Matlab-Code per email that is important to reproduce your results.

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The translation was initiated by Joshi Prashant on 2006-05-02

- ... SS06
^{1} - Class Website: http://www.igi.tugraz.at/lehre/NNB/SS06/
- ... rates
^{2} - The vectors
`st1`and`st2`contain all firing times of neuons 1 and 2. - ... PSCs
^{3} - The PSCs are available in the vectors
`psc1`and`psc2`.

Joshi Prashant 2006-05-02