Hierarchical burst model for complex bursty dynamics

Abstract

Temporal inhomogeneities observed in various natural and social phenomena have often been characterized in terms of scaling behaviors in the autocorrelation function with a decaying exponent $\gamma$, the interevent time distribution with a power-law exponent $\alpha$, and the burst size distributions. Here the interevent time is defined as a time interval between two consecutive events in the event sequence, and the burst size denotes the number of events in a bursty train detected for a given time window. In order to understand such temporal scaling behaviors implying a hierarchical temporal structure, we devise a hierarchical burst model by assuming that each observed event might be a consequence of the multi-level causal or decision-making process. By studying our model analytically and numerically, we confirm the scaling relation $\alpha +\gamma =2$, established for the uncorrelated interevent times, despite of the existence of correlations between interevent times. Such correlations between interevent times are supported by the stretched exponential burst size distributions, for which we provide an analytic argument. In addition, by imposing conditions for the ordering of events, we observe an additional feature of log-periodic behavior in the autocorrelation function. Our modeling approach for the hierarchical temporal structure can help us better understand the underlying mechanisms behind complex bursty dynamics showing temporal scaling behaviors.

arXiv comment8 pages, 5 figures

References in corpus (24)

• Statistical mechanics of complex networks
• Temporal Networks
• The origin of bursts and heavy tails in human dynamics
• Modeling bursts and heavy tails in human dynamics
• Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
• Long-Term Clustering, Scaling, and Universality in the Temporal Occurrence of Earthquakes
• A Poissonian explanation for heavy-tails in e-mail communication
• Impact of non-Poisson activity patterns on spreading processes
• The dynamical strength of social ties in information spreading
• On Universality in Human Correspondence Activity
• Diffusion on networked systems is a question of time or structure
• Bursty Human Dynamics
• Universality in solar flare and earthquake occurrence
• Communication activity in a social network: relation between long-term correlations and inter-event clustering
• Correlated dynamics in egocentric communication networks
• Multiscale Analysis of Spreading in a Large Communication Network
• Measuring burstiness for finite event sequences
• Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes
• Correlated bursts and the role of memory range
• Modelling bursty time series
• Two-state Markov-chain Poisson nature of individual cellphone call statistics
• Contextual analysis framework for bursty dynamics
• Modeling correlated bursts by the bursty-get-burstier mechanism
• Limits of memory coefficient in measuring correlated bursts

Cited by in corpus (6)

• Bursty Switching Dynamics Promotes the Collapse of Network Topologies
• Burst-tree decomposition of time series reveals the structure of temporal correlations
• Analytically solvable autocorrelation function for weakly correlated interevent times
• Temporal scaling theory for bursty time series with clusters of arbitrarily many events
• Towards a generalization of information theory for hierarchical partitions
• Hierarchical organization of bursty trains in event sequences