Discrete scaling and criticality in a chain of adaptive excitable integrators

TL;DR

This paper models a chain of adaptive excitable elements to explore how criticality and discrete scaling emerge in hierarchical systems, revealing insights into brain electrophysiology and inference under uncertainty.

Contribution

It introduces a minimal model of adaptive excitable elements with hierarchical coupling, demonstrating emergent criticality and scaling behaviors relevant to neural dynamics.

Findings

Avalanche activity exhibits discrete scaling distribution largely independent of input.

Subthreshold activities show Lorentzian spectra with power-law ranges.

Model reproduces empirical features of intracellular membrane potentials.

Abstract

We describe a chain of unidirectionally coupled adaptive excitable elements slowly driven by a stochastic process from one end and open at the other end, as a minimal toy model of unresolved irreducible uncertainty in a system performing inference through a hierarchical model. Threshold potentials adapt slowly to ensure sensitivity without being wasteful. Activity and energy are released as intermittent avalanches of pulses with a discrete scaling distribution largely independent of the exogenous input form. Subthreshold activities and threshold potentials exhibit Lorentzian temporal spectra, with a power-law range determined by position in the chain. Subthreshold bistability closely resembles empirical measurements of intracellular membrane potential. We suggest that critical cortical cascades emerge from a trade-off between metabolic power consumption and performance requirements in a critical world, and that the temporal scaling patterns of brain electrophysiological recordings ensue from weighted linear combinations of subthreshold activities and pulses from different hierarchy levels.