  In this article, a correlation metric $\kappa_C$ is proposed for the
inference of the dynamical state of neuronal networks. $\kappa_C$ is computed
from the scaling of the correlation length with the size of the observation
region, which shows qualitatively different behavior near and away from the
critical point of a continuous phase transition. The implementation is first
studied on a neuronal network model, where the results of this new metric
coincide with those obtained from neuronal avalanche analysis, thus well
characterizing the critical state of the network. The approach is further
tested with brain optogenetic recordings in behaving mice from a publicly
available database. Potential applications and limitations for its use with
currently available optical imaging techniques are discussed.
