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Modeling phase transitions in the cortex using neuropercolation approach
Robert Kozma
University of Memphis, TN, USA


We outline the basic principles of neuropercolation, a generalized percolation model motivated by the dynamical properties of the neuropil, the densely interconnected neural tissue structure in the cortex. We apply the mathematical theory of percolation in lattices to analyze chaotic dynamical memories and their related phase transitions. This approach has several advantages, including the natural introduction of noise that is necessary for system stability, a greater degree of biological plausibility, a more uniform and simpler model description, and a more solid theoretical foundation for neural modeling. Critical phenomena and scaling properties of a class of random cellular automata (RCA) are studied on the lattice ZZ2. In addition to RCA, we study phase transitions in mean-field models, as well as in models with axonal, non-local interactions. Relationship to the Ising universality class and to Toom cellular automata is thoroughly analyzed. This si a joint work with Wa lter Freeman (Berkeley), Bela Bollobas (Cambridge), Marko Puljic and Paul Balister (Memphis).