Anomalous lifetime distributions and topological traps in ordering dynamics

Castelló, Xavier; Toivonen, Riitta; Eguı́luz, Vı́ctor M.; Saramäki, Jari; Kaski, Kimmo; Miguel, M. San

doi:10.1209/0295-5075/79/66006

Cited by 48 publications

(59 citation statements)

References 29 publications

(57 reference statements)

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“…Detailed analytical results give the probabilities, as a function of the initial conditions, of ending up with full consensus in one of the three states or with a mixture of the extremists, with little change between d = 1 (Vazquez et al, 2003) and mean field (Vazquez and Redner, 2004). A similar model with three states is the AB-model (Castelló et al, 2006). Here the state of an agent evolves according to the following rules.…”

Section: Modifications and Applicationsmentioning

confidence: 99%

Statistical physics of social dynamics

2009

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Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. Here we review the state of the art by focusing on a wide list of topics ranging from opinion, cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, social spreading. We highlight the connections between these problems and other, more traditional, topics of statistical physics. We also emphasize the comparison of model results with empirical data from social systems.

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Section: Modifications and Applicationsmentioning

confidence: 99%

Statistical physics of social dynamics

2009

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“…Studies of the CP, as well as other processes [8,9], have shown that quenched disorder in networks is relevant in the dynamical systems defined on top of them. Very recently it has been shown [16][17][18] that generic slow (power-law or logarithmic) dynamics is observable by simulating CP on networks with finite d. This observation is relevant for recent developments in dynamical processes on complex networks such as the simple model of "working memory" [19], brain dynamics [20], social networks with heterogeneous communities [21], or slow relaxation in glassy systems [22].…”

Section: Introductionmentioning

confidence: 99%

Rare regions of the susceptible-infected-susceptible model on Barabási-Albert networks

Ódor

2013

Phys. Rev. E

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I extend a previous work to susceptible-infected-susceptible (SIS) models on weighted Barabási-Albert scale-free networks. Numerical evidence is provided that phases with slow, power-law dynamics emerge as the consequence of quenched disorder and tree topologies studied previously with the contact process. I compare simulation results with spectral analysis of the networks and show that the quenched mean-field (QMF) approximation provides a reliable, relatively fast method to explore activity clustering. This suggests that QMF can be used for describing rare-region effects due to network inhomogeneities. Finite-size study of the QMF shows the expected disappearance of the epidemic threshold λ c in the thermodynamic limit and an inverse participation ratio ∼0.25, meaning localization in case of disassortative weight scheme. Contrarily, for the multiplicative weights and the unweighted trees, this value vanishes in the thermodynamic limit, suggesting only weak rare-region effects in agreement with the dynamical simulations. Strong corrections to the mean-field behavior in case of disassortative weights explains the concave shape of the order parameter ρ(λ) at the transition point. Application of this method to other models may reveal interesting rare-region effects, Griffiths phases as the consequence of quenched topological heterogeneities.

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“…al. in the study of the dynamics of competing opinions [19]. In the voter model, the state of the agents can be either A or B [42], whereas in the AB model a third, intermediate AB state is included as well [18].…”

Section: Further Resultsmentioning

confidence: 99%

k-Clique Percolation and Clustering

Palla

Ábel

Farkas

et al. 2008

Bolyai Society Mathematical Studies

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We summarise recent results connected to the concept of k-clique percolation. This approach can be considered as a generalisation of edge percolation with a great potential as a community finding method in real-world graphs. We present a detailed study of the critical point for the appearance of a giant kclique percolation cluster in the Erdős-Rényi-graph. The observed transition is continuous and at the transition point the scaling of the giant component with the number of vertices is highly non-trivial. The concept is extended to weighted and directed graphs as well. Finally, we demonstrate the effectiveness of k-clique percolation as a community finding method via a series of real-world applications.

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Anomalous lifetime distributions and topological traps in ordering dynamics

Cited by 48 publications

References 29 publications

Statistical physics of social dynamics

Statistical physics of social dynamics

Rare regions of the susceptible-infected-susceptible model on Barabási-Albert networks

k-Clique Percolation and Clustering

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