scholarly journals Stochastic resonance in ion channels characterized by information theory

2000 ◽  
Vol 61 (4) ◽  
pp. 4272-4280 ◽  
Author(s):  
Igor Goychuk ◽  
Peter Hänggi
Keyword(s):  
Information Theory ◽  
Ion Channels ◽  
Stochastic Resonance

Noise Induced Order: Stochastic Resonance

1998 ◽  
Vol 08 (05) ◽  
pp. 869-879 ◽  
Author(s):  
Lutz Schimansky-Geier ◽  
Jan A. Freund ◽  
Alexander B. Neiman ◽  
Boris Shulgin
Keyword(s):  
Information Theory ◽  
Stochastic Resonance ◽  
Noise Intensity ◽  
Electronic Circuit ◽  
Schmitt Trigger ◽  
Periodic Component ◽  
Large Signal ◽  
Input Signals

We investigate stochastic resonance in the framework of information theory. Input signals are taken from an electronic circuit and output signals are produced by a Schmitt trigger. These electronic signals are analyzed with respect to their informational contents. Conditional entropies and Kullback measures exhibit extrema for values of noise intensity in the range of stochastic resonance. However, it has to be noted that these extrema are related to synchronization effects, observed in stochastic resonance for large signal amplitudes, rather than to a peak in the related spectrum indicating some periodic component.

LANGUAGE AND COHERENT NEURAL AMPLIFICATION IN HIERARCHICAL SYSTEMS: RENORMALIZATION AND THE DUAL INFORMATION SOURCE OF A GENERALIZED SPATIOTEMPORAL STOCHASTIC RESONANCE

2000 ◽  
Vol 10 (02) ◽  
pp. 493-502 ◽  
Author(s):  
RODRICK WALLACE
Keyword(s):  
Information Theory ◽  
Statistical Mechanics ◽  
Stochastic Resonance ◽  
Applied Mathematics ◽  
Information Source ◽  
Free Energy Density ◽  
Real Space ◽  
Neural Systems ◽  
Hierarchical Systems ◽  
System Approaches

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.

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