Proposal for a nonlinear top-down toy model of the brain

Abstract

Solutions to Newton's equations for particles in one-body potentials of form V 1(x i)=∑ p A (i) 2px i 2p , where p>0 and an integer, can be regarded as generators of infinite sequences of correlated frequencies {Ω m} . Simple nonlinear potentials can hence provide efficient ways of generating correlated information. Two-body potentials V 2( x i − x j ) can provide ways to communicate aspects of that information between the correlated frequency sequences. Temperature and noise can play a role in introducing a time scale across which the frequencies retain their identity. Introduction of explicit time dependence in the energy terms might be appropriate for constructing top down versions of toy models for the brain, something that is lacking at the present time. The richness of the nonlinear system along with the effects of heat baths, external noise and time dependence allows for the possibility of describing aging effects, processing of information “templates” in the brain and of the development of correlations between such “templates”. In short, nonlinearity, interactions, noise effects and introduction of time-dependent energies might allow for the construction of “top-down” models of the brain with the eventual goal of possibly unifying the neurological, molecular biological, biochemical and psychiatric approaches toward studying the brain.