Emergence of event cascades in inhomogeneous networks

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.Comment: 16 pages, 5 figure

Bursting activity spreading through asymmetric interactions

People communicate with those who have the same background or share a common interest by using a social networking service (SNS). News or messages propagate through inhomogeneous connections in an SNS by sharing or facilitating additional comments. Such human activity is known to lead to endogenous bursting in the rate of message occurrences. We analyze a multi-dimensional self-exciting process to reveal dependence of the bursting activity on the topology of connections and the distribution of interaction strength on the connections. We determine the critical conditions for the cases where interaction strength is regulated at either the point of input or output for each person. In the input regulation condition, the network may exhibit bursting with infinitesimal interaction strength, if the dispersion of the degrees diverges as in the scale-free networks. In contrast, in the output regulation condition, the critical value of interaction strength, represented by the average number of events added by a single event, is a constant $1-1/\sqrt{2} \approx 0.3$, independent of the degree dispersion. Thus, the stability in human activity crucially depends on not only the topology of connections but also the manner in which interactions are distributed among the connections.Comment: 8 pages, 8 figure

テンポラルネットワーク上の感染症ダイナミクスにおけるコンカレンシーがもたらす転移

京都大学0048新制・課程博士博士(理学)甲第20893号理博第4345号新制||理||1624(附属図書館)京都大学大学院理学研究科物理学・宇宙物理学専攻(主査)准教授 篠本 滋, 教授 佐々 真一, 教授 川上 則雄学位規則第4条第1項該当Doctor of ScienceKyoto UniversityDFA

Financial fire sales as continuous-state complex contagion

Trading activities in financial systems create various channels through which systemic risk can propagate. An important contagion channel is financial fire sales, where a bank failure causes asset prices to fall due to asset liquidation, which in turn drives further bank defaults, triggering the next rounds of liquidation. This process can be considered as complex contagion, yet it cannot be modeled using the conventional binary-state contagion models because there is a continuum of states representing asset prices. Here, we develop a threshold model of continuous-state cascades in which the states of each node are represented by real values. We show that the solution of a multi-state contagion model, for which the continuous states are discretized, accurately replicates the simulated continuous state distribution as long as the number of states is moderately large. This discretization approach allows us to exploit the power of approximate master equations (AME) to trace the trajectory of the fraction of defaulted banks and obtain the distribution of asset prices that characterize the dynamics of fire sales on asset-bank bipartite networks. We examine the accuracy of the proposed method using real data on asset-holding relationships in exchange-traded funds (ETFs).Comment: 13 pages, 9 figures + S

Concurrency-induced transitions in epidemic dynamics on temporal networks

Social contact networks underlying epidemic processes in humans and animals are highly dynamic. The spreading of infections on such temporal networks can differ dramatically from spreading on static networks. We theoretically investigate the effects of concurrency, the number of neighbors that a node has at a given time point, on the epidemic threshold in the stochastic susceptible-infected-susceptible dynamics on temporal network models. We show that network dynamics can suppress epidemics (i.e., yield a higher epidemic threshold) when the node's concurrency is low, but can also enhance epidemics when the concurrency is high. We analytically determine different phases of this concurrency-induced transition, and confirm our results with numerical simulations

Branching process descriptions of information cascades on twitter

A detailed analysis of Twitter-based information cascades is performed, and it is demonstrated that branching process hypotheses are approximately satisfied. Using a branching process framework, models of agent-to-agent transmission are compared to conclude that a limited attention model better reproduces the relevant characteristics of the data than the more common independent cascade model. Existing and new analytical results for branching processes are shown to match well to the important statistical characteristics of the empirical information cascades, thus demonstrating the power of branching process descriptions for understanding social information spreading.</p

Similarity in neuronal firing regimes across mammalian species

The architectonic subdivisions of the brain are believed to be functional modules, each processing parts of global functions. Previously, we showed that neurons in different regions operate in different firing regimes in monkeys. It is possible that firing regimes reflect differences in underlying information processing, and consequently the firing regimes in homologous regions across animal species might be similar. We analyzed neuronal spike trains recorded from behaving mice, rats, cats, and monkeys. The firing regularity differed systematically, with differences across regions in one species being greater than the differences in similar areas across species. Neuronal firing was consistently most regular in motor areas, nearly random in visual and prefrontal/medial prefrontal cortical areas, and bursting in the hippocampus in all animals examined. This suggests that firing regularity (or irregularity) plays a key role in neural computation in each functional subdivision, depending on the types of information being carried. © 2016 the authors9911Nsciescopu