The correlated variability control problem: a dominant approach

TL;DR

This paper investigates how the structure of linear networks influences the control of correlated variability in systems with independent random inputs, highlighting the role of dominant slow dynamics.

Contribution

It introduces the correlated variability control problem in linear networks and links network structure and slow dynamics to correlated variability emergence.

Findings

Dominant slow dynamics are crucial for correlated variability control.

Network structure determines the ability to regulate correlations.

Linear models reveal fundamental connections between dynamics and variability.

Abstract

Given a population of interconnected input-output agents repeatedly exposed to independent random inputs, we talk of correlated variability when agents' outputs are variable (i.e., they change randomly at each input repetition) but correlated (i.e., they do not vary independently across input repetitions). Correlated variability appears at multiple levels in neuronal systems, from the molecular level of protein expression to the electrical level of neuronal excitability, but its functions and origins are still debated. Motivated by advancing our understanding of correlated variability, we introduce the (linear) "correlated variability control problem" as the problem of controlling steady-state correlations in a linear dynamical network in which agents receive independent random inputs. Although simple, the chosen setting reveals important connections between network structure, in particular, the existence and the dimension of dominant (i.e., slow) dynamics in the network, and the emergence of correlated variability.