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Use of Cellular Automata-Like Models to Understand Cortical Very Fast Oscillations
Prof.Roger D. Traub
(IBM T.J. Watson Research Center and Columbia University, New York)
Cellular automata (CA) were introduced in the 1940s in order to model the statistical behavior of
gases; they have since been studied as objects of mathematical interest in themselves, and for
modeling a variety of processes in physics, computing and biology. Networks of electrically
coupled axons lend themselves to CA models because - to first approximation, when electrical
coupling is strong - the axon exists in an "on" or "off" state, with brief refractoriness, and with
changes of state induced by recent states of nearby other axons. CA models are suitable for large,
fast simulations, and for illuminating physical principles. For example, they have been used to
show that very fast oscillations (VFO, >100 Hz) can be generated in two distinctive ways in an
axonal plexus: the first is by a series of propagating, non-intersecting, randomly initiated waves; the
second, by re-entry around particular "minimal" cycles, whose length is just longer than that needed
to overcome axonal refractoriness. Prof. Traub propose that the first mechanism may account for
ripples, at up to ~250 Hz; and the second may account for so-called fast ripples, >250 Hz, and likely
is of epilepsy-related significance.