Finite-size correlation behavior near a critical point: a simple metric for monitoring the state of a neural network

In this note, a correlation metric $\kappa_c$ is proposed which is based on the universal behavior of the linear/logarithmic growth of the correlation length near/far the critical point of a continuous phase transition. The problem is studied on a previously described neuronal network model for which is known the scaling of the correlation length with the size of the observation region. It is verified that the $\kappa_c$ metric is maximized for the conditions at which a power law distribution of neuronal avalanches sizes is observed, thus characterizing well the critical state of the network. Potential applications and limitations for its use with currently available optical imaging techniques are discussed.Comment: 5 pages, 5 figure