papers available

[Nicolas Brunel]

Dear connectionists,

The following two papers on the analysis of the dynamics of sparsely
connected networks of excitatory and inhibitory spiking neurons are 
now available on my web page:

http://mumitroll.ccs.brandeis.edu/~brunel/journal.html

"Fast global oscillations in networks of integrate-and-fire neurons 
with low firing rates"

N Brunel and V Hakim 

to appear in Neural Computation, 11, 1621-1671 (1999)

Abstract:
We study analytically the dynamics of a network of sparsely connected
inhibitory integrate-and-fire neurons in a regime where individual
neurons emit spikes irregularly and at a low rate. In the limit when
the number of neurons $N\rightarrow\infty$, the network exhibits a
sharp transition between a stationary and an oscillatory global
activity regime where neurons are weakly synchronized. The activity
becomes oscillatory when the inhibitory feedback is strong enough.
The period of the global oscillation is found to be mainly controlled
by synaptic times, but depends also on the characteristics of the
external input.  In large but finite networks, the analysis shows that
global oscillations of finite coherence time generically exist both
above and below the critical inhibition threshold.  Their
characteristics are determined as functions of systems parameters, in
these two different regimes.  The results are found to be in good
agreement with numerical simulations.


"Dynamics of sparsely connected networks of excitatory and 
inhibitory spiking neurons"

N Brunel

to appear in Journal of Computational Neuroscience

Abstract: 
The dynamics of networks of sparsely connected excitatory and
inhibitory integrate-and-fire neurons is studied analytically.  The
analysis reveals a very rich repertoire of states, including:
Synchronous states in which neurons fire regularly; Asynchronous
states with stationary global activity and very irregular individual
cell activity; States in which the global activity oscillates but
individual cells fire irregularly, typically at rates lower than the
global oscillation frequency.  The network can switch between these
states, provided the external frequency, or the balance between
excitation and inhibition, is varied.  Two types of network
oscillations are observed: In the `fast' oscillatory state, the
network frequency is almost fully controlled by the synaptic time
scale. In the `slow' oscillatory state, the network frequency depends
mostly on the membrane time constant. Finite size effects in the
asynchronous state are also discussed.




Nicolas Brunel
Volen Center for Complex Systems, MS 013, Brandeis University
415 South Street, Waltham, MA 02254-9110, USA
Tel (781) 736 2890 -- Fax (781) 736 4877
Email brunel at asterix.ccs.brandeis.edu       
http://mumitroll.ccs.brandeis.edu/~brunel