Abstract

We consider a network whose nodes elaborate incoming input according to the Integrate and Fire paradigm. In these networks the input to each node is a suitable superposition of point processes generated by previous nodes. The output from each node is again a point process. Assuming that the inter-arrival times involved in the input are distributed as regularly varying vectors, together with some other technical hypotheses, we prove that the inter-arrival times of the output from the nodes are again regularly varying.This closure property of the regularly varying intervals with respect to elaboration in the node according to the Integrate and Fire model  may explain the often observed heavy tails of such inter-times  in real networks. For example, heavy tails are observed in neural networks and the phenomenon regards both input signals and output signals.