Bessel Functions in Mass Action. Modeling of Memories and Remembrances

TL;DR

This paper models neurological processes exhibiting Bessel function behavior using coupled oscillators, linking cellular dynamics to brain activity and memory lifetime through complex mathematical analysis.

Contribution

It introduces a novel oscillator-based model for neural processes that captures Bessel function behavior and relates thermodynamic features to memory duration.

Findings

Oscillatory models reproduce Bessel function distributions in neural data.

Root loci analysis links cellular dynamics to brain functional activity.

Thermodynamic features relate to the breaking of time-reversal symmetry and memory lifetime.

Abstract

Data from experimental observations of a class of neurological processes (Freeman K-sets) present functional distribution reproducing Bessel function behavior. We model such processes with couples of damped/amplified oscillators which provide time dependent representation of Bessel equation. The root loci of poles and zeros conform to solutions of K-sets. Some light is shed on the problem of filling the gap between the cellular level dynamics and the brain functional activity. Breakdown of time-reversal symmetry is related with the cortex thermodynamic features. This provides a possible mechanism to deduce lifetime of recorded memory.