Memory of neuronal networks: the white noise approach

A novel technique was developed to measure the system memory of a neuronal network, from the duration of the first-order Wiener kernel which was estimated using Gaussian white noise inputs. The proposed technique estimates the system memory using the decay characteristics of the coefficients associated with the Laguerre expansion of the Wiener kernel using a small number of Laguerre basis functions. This technique was validated using a second-order linear model. The neuronal network was modelled using two bidirectionally coupled neurons described by Hodgkin-Huxley dynamics. This model demonstrated that the duration of the first-order Wiener kernel is sensitive to changes in the synaptic weights, suggesting its possible role as a measure of neuronal system memory