Emergence of event cascades in inhomogeneous networks.

Tomokatsu Onaga,Shigeru Shinomoto

doi:10.1038/srep33321

Abstract

There is a commonality among contagious diseases, tweets, 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 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, 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, 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.

Highlights

There is a commonality among contagious diseases, tweets, and neuronal firings that past events facilitate the future occurrence of events
The proliferation process has been studied using both macroscopic models, such as the epidemic model[1], and microscopic models, such as the self-exciting point process proposed by Hawkes[2,3]
A key quantity representing the interaction in these various phenomena is the basic reproduction ratio, which is defined as the average number of additional events induced by a single event[19]

Summary

Introduction

There is a commonality among contagious diseases, tweets, and neuronal firings that past events facilitate the future occurrence of events. The event-occurrence does not cease if individuals are stimulated in external communities or exhibit spontaneous activity In such situations, the system may still exhibit cascades of event-occurrences intermittently, even if the reproduction ratio is smaller than the epidemic threshold, as in tweets[11,23,24] and neuronal firings in vivo[25]. It is important to comprehend the mechanism by which such cascades appear We show that such a transition between stationary and nonstationary states generally occurs in every proliferation system, obtain the condition on which cascades may emerge in a given network, and suggest a systematic method for controlling systems to oppress or promote the event-occurrence bursts

Methods

Results

Conclusion