Article of the Month, April 2018 (Burak's lab)

April 30, 2018

Theory of nonstationary Hawkes processes

Authors: Neta Ravid Tannenbaum and Yoram Burak

Published in Physical Review E on December 2017


We expand the theory of Hawkes processes to the non-stationary case, in which the mutually exciting point processes receive time-dependent inputs. We derive an analytical expression for the time- dependent correlations, which can be applied to networks with arbitrary connectivity, and inputs with arbitrary statistics. The expression shows how the network correlations are determined by the interplay between the network topology, the transfer functions relating units within the network, and

the pattern and statistics of the external inputs.  We illustrate the correlation structure using several examples, in which neural network dynamics are modeled as a Hawkes process.  In particular, we focus on the interplay between internally and externally generated oscillations, and their signatures in the spike and rate correlation functions.