Related papers: Poissonian bursts in e-mail correspondence
We show that any sequence $(x_n)_{n \in \mathbb{N}} \subseteq [0,1]$ that has Poissonian correlations of $k$-th order is uniformly distributed, also providing a quantitative description of this phenomenon. Additionally, we extend…
Using empirical data from a social media site (Twitter) and on trading volumes of financial securities, we analyze the correlated human activity in massive social organizations. The activity, typically excited by real-world events and…
Temporal hypergraphs capture time-resolved group interactions among nodes. Empirical data support that time-stamped group interactions show bursty event sequences and non-trivial temporal correlations. In the present study, we introduce…
Cascades of Poisson processes are probabilistic models for spatio-temporal phenomena in which (i) previous events may trigger subsequent events, and (ii) both the background and triggering processes are conditionally Poisson. Such phenomena…
We consider the propagation of a single particle in a random chain, assisted by the coupling to dispersive bosons. Time evolution treated with rate equations for hopping between localized states reveals a qualitative difference between…
Temporal inhomogeneities in event sequences of natural and social phenomena have been characterized in terms of interevent times and correlations between interevent times. The inhomogeneities of interevent times have been extensively…
In this paper, we are analyzing the interactivity time, defined as the duration between two consecutive tasks such as sending emails, collecting friends and followers and writing comments in online social networks (OSNs). The distributions…
Quantum-classical correspondence in conservative chaotic Hamiltonian systems is examined using a uniform structure measure for quantal and classical phase space distribution functions. The similarities and differences between quantum and…
Recent analysis of social communications among humans has revealed that the interval between interactions for a pair of individuals and for an individual often follows a long-tail distribution. We investigate the effect of such a…
We study the asymptotic behavior of empirical processes generated by measurable bounded functions of an infinite source Poisson transmission process when the session length have infinite variance. In spite of the boundedness of the…
Social networks are made out of strong and weak ties having very different structural and dynamical properties. But, what features of human interaction build a strong tie? Here we approach this question from an practical way by finding what…
Walking droplets -- millimetric oil droplets that self-propel across the surface of a vibrating fluid bath -- exhibit striking emergent statistics that remain only partially understood. In particular, in a variety of experiments, a robust…
Patterns in complex systems store hidden information of the system which is needed to be explored. We present a simple model of cytokine and T-cells interaction and studied the model within stochastic framework by constructing Master…
The problem to accurately and parsimoniously characterize random series of events (RSEs) present in the Web, such as e-mail conversations or Twitter hashtags, is not trivial. Reports found in the literature reveal two apparent conflicting…
We investigate the communication sequences of millions of people through two different channels and analyze the fine grained temporal structure of correlated event trains induced by single individuals. By focusing on correlations between…
We consider a weighted sum of a series of independent Poisson random variables and show that it results in a new compound Poisson distribution which includes the Poisson distribution and Poisson distribution of order k. An explicit…
Non-Gaussianity indicates complex dynamics related to extreme events or significant outliers. However, the correlation between non-Gaussianity and the dynamics of heterogeneous environments in anomalous diffusion remains uncertain. Inspired…
The Poisson process of order $i$ is a weighted sum of independent Poisson processes and is used to model the flow of clients in different services. In the paper below we study some extensions of this process, for different forms of the…
We construct the temporal network using the two-dimensional active particle systems which are described by the Vicsek model. The bursts of the interevent times for a specific pair of particles are investigated numerically. We find that for…
Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic…