  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.
