BISC: BISC Seminar-Robert Kozma: Feb 21, 2002

From: masoud nikravesh (nikraves@eecs.berkeley.edu)
Date: Wed Feb 20 2002 - 20:45:54 MET

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    Berkeley Initiative in Soft Computing (BISC)
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    Neuropercolations: Dynamical Percolation Models of
    Phase Transitions in Physical and Biological Systems

                                                             Robert Kozma
                                                       Dept. Mathematical
    Sicences,
                                                      Institute for
    Intelligent Systems,
                                                          University of
    Memphis

                                                             Feb 21, 2002
                                                            320 Soda Hall
                                                             4:00-5:00pm

    Abstract:

    Contrary to the presently used digital computer memories where
    information is encoded in the form of a given string of symbols we
    propose a novel approach, in
    which encoding is embodied in oscillatory activity patterns of memory
    nodes. The approach is strongly biologically motivated and based on the
    observation that
    humans/ animals can solve difficult identification tasks fast and with
    high accuracy. Information encoding in such dynamical memories is
    closely related to percolation
    phenomena in random media.

    For about four decades, percolation theory has been an active area of
    research at the interface of probability theory, combinatorics, graph
    theory, and physics. In
    particular, computer experiments have been conducted, which indicated
    interesting non-trivial large-scale phenomena. We apply the solid
    mathematical theory of
    percolations to lay down the foundations of dynamical memories and
    related phase transitions. When an input pattern is presented to the
    model, the large-scale,
    aperiodic spatio-temporal oscillations undergo phase transitions and the
    dynamics is constrained to a lower-dimensional subspace. After removing
    the input stimulus,
    the system returns to a high-dimensional state. Mathematically such a
    property has been described in random graphs, where the connectivity
    density is an order
    parameter that can induce state transitions. Accordingly, the memory and
    recognition/identification process can be described as percolation
    phenomenon though the
    neurophil medium. The problem is related to 'small-world' phenomena, and
    recently rigorous proof of the scaling properties of large graphs have
    been given based
    on graph-theoretical arguments.

    In our work, we extend percolation theory to interpret the behavior of
    dynamical memories. We introduce a family of infection and recovery
    functions of bootstrap
    percolations, and thereby model evolutions and phase transitions in a
    class of generalized percolations. We aim to construct models that
    exhibit the complex behavior
    of biological systems while at the same time they are mathematically
    tractable.

    *This is a joint work with Paul Balister, Bela Bollobas (UoM and
    University of Cambridge, UK) and Walter Freeman (UCB)

    cs-seminars@CS.Berkeley.EDU

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