ACRI 2004: Cellular Automata pp 435-443 | Cite as

Neuropercolation: A Random Cellular Automata Approach to Spatio-temporal Neurodynamics

  • Robert Kozma
  • Marko Puljic
  • Paul Balister
  • Bela Bollobas
  • Walter J. Freeman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3305)

Abstract

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 \(\mathbb Z^{2}\). 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.

Keywords

Cellular Automaton Critical Exponent Adaptive Resonance Theory Solid Theoretical Foundation Bootstrap Percolation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Robert Kozma
    • 1
  • Marko Puljic
    • 1
  • Paul Balister
    • 1
  • Bela Bollobas
    • 1
  • Walter J. Freeman
    • 2
  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA
  2. 2.Division of NeurobiologyUniversity of California at BerkeleyBerkeleyUSA

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