The correlated variability control problem: a dominant approach

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.