PHYSICAL MATHEMATICS SEMINAR

TOPIC:	MINIMAL PATHS AND SIGNAL 
	PROPAGATION IN A MODEL CORTEX

SPEAKER:	RAVA DA SILVEIRA
 		Harvard University

ABSTRACT:

The cortex is the outer shell of the brain largely responsible for sensory
and higher faculties, each of which relies on collective processing by a
large number of neurons. Given the complexity of cortical function, a
natural first step in a theoretical approach consists in delineating the
constraints imposed upon 'macroscopic' processing, and in particular upon
'macroscopic' length and time scales, by 'microscopic' parameters such as
local wiring and single-neuron dynamics.

Experiments demonstrate the existence of cortex-spanning paths of
synaptically connected neurons with no more than about ten synapses.  At
the same time, only few long axons are available for the construction of
such paths. Is a fine-tuned 'design' of cortical wiring necessary to
resolve this paradox?  Based on experimental data, we introduce a simple
model of random ('non-designed') wiring, in which the probability of a
synapse between two neurons decreases algebraically with the distance
separating the two neurons. (This model can be viewed as a random graph
embedded in a metric space, and serves as a natural interpolation between
usual random graphs and locally connected lattices.)  We then show that
the number of synapses needed in a path spanning a distance $r$ grows very
slowly with $r$, as a power of $ln(r)$. Thus, according to this model,
paths that crisscross the cortex with a few synapses are present even in
the absence of any 'design.'

Beyond purely structural questions, we turn to dynamics and ask how neural
activity propagates in the (model) cortex, a question for which precise
experimental data are again available.  Here, the central conceptual
difficulty lies in the requirement that the dynamics be at the same time
sensitive to weak stimuli and stable with respect to stronger ones.  We
present preliminary results on the mechanisms of signal propagation and on
its dependence upon 'microscopic' parameters, based on a crude model of
single-neuron dynamics.  To conclude, we mention a number of interesting
questions suggested by our approach.


DATE:		TUESDAY, MARCH 9, 2004

TIME:		2:30 PM

LOCATION:	Building 2, Room 338

Refreshments at 3:30 PM in Building 2, Room 349.

Massachusetts Institute of Technology, Department of Mathematics
Cambridge, MA  02139