REPORT
on the activity at NORDITA
by Andrius Bernotas
a NORDITA Baltic / NW Russia fellow 1998
My presence at NORDITA was split into two periods, one
month in May-June, and a month in October-November. All this time I have
been guided by Professor John Hertz, and worked in his laboratory.
I collaborated with Thomas Z. Lauritzen, a Professor's M.Sc. student from
Copenhagen University during the first period of my stay, and with Andrea
Fazzini and Sergio Solinas, the M.Sc. students from the Bologna University,
during the last visit.
The problem that we have investigated is the emergence
of spontaneous asynchronous chaotic activity in neural networks comprising
populations of excitatory and inhibitory neurons. And we have tried to
model this activity via the computer simulations of networks consisting
of "simple neurons" (with the key parameters chosen to be biologically
plausible). Specifically, I am working with the synfiren code simulating
the network of "integrate & fire" leaky neurons. (The code was originally
developed by a former NORDITA fellow Adam Pruegel-Bennett for simulating
the synchronous firing chain, hence its name synfire). In the course
of work I modified the code to perform the proper network connections,
and to display the spikes emitted by neurons as its output. Also, the afferent
excitatory and inhibitory potentials are displayed now. A number of new
input parameters were introduced, too.
The theoretical background for this work are the
publications by W. Gerstner, D. Amit, C. van Vreeswijk and H. Sompolinsky,
and their co-workers. Although in the mean-field theory framework that
they are considering, their models are predictive, we have found that the
computer simulations we make often are not exactly in the thermodynamic
limit, i. e. our networks are not big enough. The open questions that may
arise are: 1) should we attempt to stretch these limits (anyway, even the
biological networks aren't infinite); 2) if yes, how far can we do that
in simulations; 3) what corrections are expected in the "not-clean-limit"
case? These are just few of the problems that need further consideration.
Still, the asynchronous spontaneous chaotic activity of neurons in our
simulated networks demonstrates itself.
I would like to thank NORDITA for the support, Professor
John Hertz for his guidance, and NORDITA's staff for the courses, seminars,
discussions and other activities that I had a pleasure to participate in
here.
Andrius Bernotas
Institute of Theoretical Physics and Astronomy
A. Gostauto 12, 2600 Vilnius, Lithuania