Language and coherent neural amplification in hierarchical systems: Renormalization and the dual information source of a generalized spatiotemporal stochastic resonance

A growing body of work suggests an important unifying perspective in the study of stochastic resonance: Examining the "prehistory probability density" of the ensemble of pathways by which a system approaches the trigger of the nonlinear oscillator. This view, in the context of the Shannon-McMillan Theorem of information theory, leads to a draconian simplification of the complex of "signal," "noise" and oscillator in terms of a single object, an ergodic information source dual to a certain class of resonances. For "spatial" stochastic resonator arrays, in the most general sense, the Shannon-McMillan Theorem further provides an analogy between the Shannon uncertainty of the dual information source and the free energy density of a physical system which allows imposition of real-space renormalization to give essential results in a straightforward manner. We find in particular threshold behavior in the onset of an epileptiform spatiotemporal coherence, and a likely usefulness of tuned spatial arrays for the detection of very subtle pattern. These simplifications may provide, in addition, a natural context for discussing hierarchical structure in neural systems. In sum, we attempt to bring stochastic resonance into the contemporary framework of applied mathematics which has begun to unify the study of fluctuations, statistical mechanics and information theory. Our critical generalization lies in the transfer of renormalization methods from statistical mechanics to information theory, via a parametization of source uncertainty.