  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.
