Emergence of event cascades in inhomogeneous networks

TL;DR

This paper explores how nonstationary event cascades occur in inhomogeneous networks even below the critical threshold, highlighting the influence of network structure and proposing methods to predict and control such cascades.

Contribution

It reveals the presence of subthreshold cascades in inhomogeneous networks and introduces a predictive framework and connection-reallocation method to control cascade emergence.

Findings

Cascades occur in the subthreshold regime depending on network structure.

Network reallocation can either impede or facilitate cascades.

Prediction of cascade emergence based on interaction data.

Abstract

There is a commonality among contagious diseases, tweets, urban crimes, nuclear reactions, and neuronal firings that past events facilitate the future occurrence of events. The spread of events has been extensively studied such that the systems exhibit catastrophic chain reactions if the interaction represented by the ratio of reproduction exceeds unity; however, their subthreshold states for the case of the weaker interaction are not fully understood. Here, we report that these systems are possessed by nonstationary cascades of event-occurrences already in the subthreshold regime. Event cascades can be harmful in some contexts, when the peak-demand causes vaccine shortages, heavy traffic on communication lines, frequent crimes, or large fluctuations in nuclear reactions, but may be beneficial in other contexts, such that spontaneous activity in neural networks may be used to generate motion or store memory. Thus it is important to comprehend the mechanism by which such cascades appear, and consider controlling a system to tame or facilitate fluctuations in the event-occurrences. The critical interaction for the emergence of cascades depends greatly on the network structure in which individuals are connected. We demonstrate that we can predict whether cascades may emerge in a network, given information about the interactions between individuals. Furthermore, we develop a method of reallocating connections among individuals so that event cascades may be either impeded or impelled in a network.