Diagrammatic expansion of pulse-coupled network dynamics.

We introduce a framework wherein various long-time measurements of a pulse-coupled network's stationary dynamics can be expanded in terms of the network's connectivity. Such measurements include the occurrence rate of pulses as well as higher-order correlations in activity between various nodes in the network. The various terms in this expansion can be interpreted as diagrams corresponding to subnetworks of the original network which span both space (in terms of the network's graph) as well as time (in the sense of causality).