Aging and percolation dynamics in a Non-Poissonian temporal network model

Moinet, Antoine; Starnini, Michele; Pastor-Satorras, Romualdo

doi:10.1103/physreve.94.022316

Cited by 9 publications

(15 citation statements)

References 56 publications

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“…, N an activity a i drawn from a distribution ρ(a i ). The activation rate of node i is defined by its inter-event time distribution Ψ a i (τ ) [8][9][10][11][12]: this sets the statistic of time intervals between consecutive activations of node i, so that the average inter-event time equals the inverse of the activity of node i, i.e. τ i = a −1 i .…”

Section: Activity-driven Temporal Networkmentioning

confidence: 99%

“…Besides, a large amount of work has been devoted to clarify the effects of intermittent patterns on the temporal structures of interactions, as described by temporal networks [7]. Bursty dynamics can indeed influence the structure of links on the local and on the global scale [8][9][10][11][12]. More importantly, heterogenous temporal patterns in the evolution of time-varying networks can affect in a non-trivial way dynamical processes.…”

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confidence: 99%

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Burstiness in activity-driven networks and the epidemic threshold

Mancastroppa¹,

Vezzani²,

Muñoz³

et al. 2019

J. Stat. Mech.

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We study the effect of heterogeneous temporal activations on epidemic spreading in temporal networks. We focus on the susceptible-infected-susceptible (SIS) model on activity-driven networks with burstiness. By using an activity-based mean-field approach, we derive a closed analytical form for the epidemic threshold for arbitrary activity and inter-event time distributions. We show that, as expected, burstiness lowers the epidemic threshold while its effect on prevalence is twofold. In low-infective systems burstiness raises the average infection probability, while it weakens epidemic spreading for high infectivity. Our results can help clarify the conflicting effects of burstiness reported in the literature. We also discuss the scaling properties at the transition, showing that they are not affected by burstiness.as in Poisson processes but, typically, it features a fat tail, easily measured from large datasets [1,2].Recent studies have addressed the problem of the origin of this highly heterogeneous behavior, arising from the decision-based queuing process that humans apply in performing tasks and allocating their priority [5,6]. Besides, a large amount of work has been devoted to clarify the effects of intermittent patterns on the temporal structures of interactions, as described by temporal networks [7]. Bursty dynamics can indeed influence the structure of links on the local and on the global scale [8][9][10][11][12]. More importantly, heterogenous temporal patterns in the evolution of time-varying networks can affect in a non-trivial way dynamical processes. Analytical arguments [13][14][15] and numerical approaches [16,17] have indeed shown that burstiness can significantly modify processes mediated by interactions, such as random walks, epidemics, information diffusion, consensus formation, percolation. Among these, epidemic spreading is one of the most representative and widely applicable example [18]. Analytical results on epidemics in temporal network have focused on the epidemic threshold [19,20], in general pushed to lower values by bursty effects. In other works, burstiness is introduced on a static network as a non-Markovian effect in infection (or recovery) processes [21][22][23][24][25].Interestingly, when comparing bursty with Poisson dynamics in epidemics, conflicting observations have been reported. On the one hand, numerical results [14,16,17] and modeling techniques [15,24,26,27] provided strong evidence of a slowing down for the late time spreading in the presence of burstiness, while opposite effects are reported in the early-time dynamics [28]. In [14] and [16], burstiness is found to slow down spreading in early times, while other works observe the opposite effect [17,26].To understand such conflicting observations and keep track at the same time of the temporal evolution of interactions, in this paper we focus on the Susceptible-Infected-Susceptible (SIS) process in the presence of burstiness on activity-driven networks [29][30][31]. In activity-driven networks, the propensity to engage...

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Section: Activity-driven Temporal Networkmentioning

confidence: 99%

mentioning

confidence: 99%

Burstiness in activity-driven networks and the epidemic threshold

Mancastroppa¹,

Vezzani²,

Muñoz³

et al. 2019

J. Stat. Mech.

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“…In this paper, we contribute to this endeavor with the study of passive random walks on temporal networks characterized by non-Markovian dynamics, by considering the case of networks generated by the NoPAD model. In the NoPAD model, nodes establish connections to randomly chosen neighbors following a heavytailed inter-event time distribution y~a --( ) t t c 1 , with 0<α<2, depending on an activity parameter c assigned to each node [24,37]. We show that the dynamics of passive random walks on NoPAD networks fundamentally departs from the one observed on classical Poissonian activity-driven networks.…”

mentioning

confidence: 85%

“…In the NoPAD model [24,37], nodes establish instantaneous connections with randomly chosen peers by following a renewal process. Each node is activated independently from the others, with the same functional form of the inter-event time distribution y~a --( ) t t c 1 , with α>0, between consecutive activation events, which depends on an activity parameter c, heterogeneously distributed among the population with a probability distribution η(c).…”

Section: Passive Random Walks On Nopad Networkmentioning

confidence: 99%

“…both mathematical modeling [24][25][26][27][28][29][30][31] and dynamical processes, especially regarding epidemic spreading [32][33][34][35][36]. Within the framework of non-Markovian networks modeling, the non-Poissoinan activity driven (NoPAD) model [24,37] offers a simple, mathematically tractable framework aimed at reproducing empirically observed inter-event time distributions, overcoming the limitations of the classical activity-driven paradigm. See [35] for a related model also relaying on a non-poissonian intervent time distribution.…”

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Random walks in non-Poissoinan activity driven temporal networks

2019

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The interest in non-Markovian dynamics within the complex systems community has recently blossomed, due to a new wealth of time-resolved data pointing out the bursty dynamics of many natural and human interactions, manifested in an inter-event time between consecutive interactions showing a heavy-tailed distribution. In particular, empirical data has shown that the bursty dynamics of temporal networks can have deep consequences on the behavior of the dynamical processes running on top of them. Here, we study the case of random walks, as a paradigm of diffusive processes, unfolding on temporal networks generated by a non-Poissonian activity driven dynamics. We derive analytic expressions for the steady state occupation probability and first passage time distribution in the infinite network size and strong aging limits, showing that the random walk dynamics on non-Markovian networks are fundamentally different from what is observed in Markovian networks. We found a particularly surprising behavior in the limit of diverging average inter-event time, in which the random walker feels the network as homogeneous, even though the activation probability of nodes is heterogeneously distributed. Our results are supported by extensive numerical simulations. We anticipate that our findings may be of interest among the researchers studying non-Markovian dynamics on time-evolving complex topologies. IntroductionTemporal networks [1, 2] constitute a recent new description of complex systems, that, moving apart from the classical static paradigm of network science [3], in which nodes and edges do not change in time, consider dynamic connections that can be created, destroyed or rewired at different time scales. Within this framework, a first round of studies proposed temporal network models ruled by homogeneous Markovian dynamics [4]. A prominent example is represented by the activity-driven model [5] (see also [6]), in which nodes are characterized by a different degree of activity, i.e. the constant rate at which an agent sends links to other peers, following a Poissonian process. The memoryless property implied by the Markovian dynamics greatly simplifies the mathematical treatment of these models, regarding both the topological properties of the time-integrated network representation [7], and the description of the dynamical processes unfolding on activity-driven networks [8][9][10][11][12][13].However, the Markovian assumption in temporal network modeling has been challenged by the increasing availability of time-resolved data on different kinds of interactions, ranging from phone communications [14] and face-to-face interactions [15], to natural phenomena [16,17], biological processes [18] and physiological systems [19][20][21]. These empirical observations have uncovered a rich variety of dynamical properties, in particular that the inter-event times t between two successive interactions (either the creation of the same edge or two consecutive creations of an edge by the same node), ψ(t), follows heavy-tailed distributions...

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Bursty Human Dynamics

Karsai¹,

Jo²,

Kaski³

2018

SpringerBriefs in Complexity

133

160

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Springer Complexity is an interdisciplinary program publishing the best research and academic-level teaching on both fundamental and applied aspects of complex systems-cutting across all traditional disciplines of the natural and life sciences, engineering, economics, medicine, neuroscience, social and computer science.Complex Systems are systems that comprise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous formation of distinctive temporal, spatial or functional structures. Models of such systems can be successfully mapped onto quite diverse "real-life" situations like the climate, the coherent emission of light from lasers, chemical reaction-diffusion systems, biological cellular networks, the dynamics of stock markets and of the internet, earthquake statistics and prediction, freeway traffic, the human brain, or the formation of opinions in social systems, to name just some of the popular applications.Although their scope and methodologies overlap somewhat, one can distinguish the following main concepts and tools: self-organization, nonlinear dynamics, synergetics, turbulence, dynamical systems, catastrophes, instabilities, stochastic processes, chaos, graphs and networks, cellular automata, adaptive systems, genetic algorithms and computational intelligence.The three major book publication platforms of the Springer Complexity program are the monograph series "Understanding Complex Systems" focusing on the various applications of complexity, the "Springer Series in Synergetics", which is devoted to the quantitative theoretical and methodological foundations, and the "SpringerBriefs in Complexity" which are concise and topical working reports, case-studies, surveys, essays and lecture notes of relevance to the field. In addition to the books in these two core series, the program also incorporates individual titles ranging from textbooks to major reference works. This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any erro...

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Aging and percolation dynamics in a Non-Poissonian temporal network model

Cited by 9 publications

References 56 publications

Burstiness in activity-driven networks and the epidemic threshold

Burstiness in activity-driven networks and the epidemic threshold

Random walks in non-Poissoinan activity driven temporal networks

Bursty Human Dynamics

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