Effective Brain–Computer Interfaces (BCIs) require that the time-varying activation patterns of 2-D neural ensembles be modelled. The cluster variation method (CVM) offers a means for the characterization of 2-D local pattern distributions. This paper provides neuroscientists and BCI researchers with a CVM tutorial that will help them to understand how the CVM statistical thermodynamics formulation can model 2-D pattern distributions expressing structural and functional dynamics in the brain. The premise is that local-in-time free energy minimization works alongside neural connectivity adaptation, supporting the development and stabilization of consistent stimulus-specific responsive activation patterns. The equilibrium distribution of local patterns, or configuration variables, is defined in terms of a single interaction enthalpy parameter (h) for the case of an equiprobable distribution of bistate (neural/neural ensemble) units. Thus, either one enthalpy parameter (or two, for the case of non-equiprobable distribution) yields equilibrium configuration variable values. Modeling 2-D neural activation distribution patterns with the representational layer of a computational engine, we can thus correlate variational free energy minimization with specific configuration variable distributions. The CVM triplet configuration variables also map well to the notion of a M = 3 functional motif. This paper addresses the special case of an equiprobable unit distribution, for which an analytic solution can be found.
Abstract. We consider a model of a neuron coupled with a surrounding dendritic network subject to Langevin noise and a weak periodic modulation. Through an adiabatic elimination procedure, the single-neuron dynamics are extracted from the coupled stochastic differential equations describing the network of dendrodendritic interactions. Our approach yields a "reduced neuron" model whose dynamics may correspond to neurophysiologically realistic behavior for certain ranges of soma and bath parameters. Cooperative effects (e.g., stochastic resonance) arising from the interplay between the noise and modulation are discussed in detail.
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