Broad lifetime distributions for ordering dynamics in complex networks

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

doi:10.1103/physreve.79.016109

Cited by 28 publications

(35 citation statements)

References 42 publications

(51 reference statements)

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“…For static networks, it is known that spatial structure has an effect on epidemics (see, e.g., [6,7]), and community structure slows down information diffusion due to trapping in dense regions [8][9][10]. There is an intimate relation between inhomogeneous link weights and network topology in social and communication networks [11,12]: Links within communities are strong, while links between them are weak.…”

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confidence: 99%

Small but slow world: How network topology and burstiness slow down spreading

et al. 2011

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While communication networks show the small-world property of short paths, the spreading dynamics in them turns out slow. Here, the time evolution of information propagation is followed through communication networks by using empirical data on contact sequences and the SI model. Introducing null models where event sequences are appropriately shuffled, we are able to distinguish between the contributions of different impeding effects. The slowing down of spreading is found to be caused mainly by weight-topology correlations and the bursty activity patterns of individuals.PACS numbers: 05.45.Tp Most complex physical, biological and social networks show the small-world property, where the average shortest path length is strikingly short when compared to the network size [1]. This means that there is at least one short path between any two nodes, which should give rise to rapid transmission of influence. However, dynamic phenomena on networks [2], such as spreading of pandemics, electronic viruses, and information, follow their own pathways, which are not necessarily topologically efficient [3]. Spreading on real small-world networks turns out to be surprisingly slow, e.g., new infections by a computer virus are reported years after its emergence or the introduction of an anti-virus [4]. Here we aim at resolving this puzzle. For issues such as strategies and timing of vaccinations, improvement of information diffusion, and the slow decay of prevalence of computer viruses, it is crucial to understand the role of the underlying network and temporal activity patterns in the dynamics of spreading.The dynamics of spreading is commonly studied with SI, SIR, or SIS models [5] on static lattices or in mean field, where the dynamics is defined by state changes of individuals between (S)usceptible, (I)nfectious, and (R)ecovered. These models lead to a rapid, exponential growth of prevalence at early stages of spreading, while the dynamics at later stages depend on the model and lattice. For the SI process, the prevalence grows until the whole system reachable from initial conditions is infected, with exponential slowing down towards the end. For the SIR process, competing effects set in and the spreading may remain local or percolate through the system while the SIS process has more complex dynamics.While these results capture some of the qualitative features of real-world processes, the heterogeneity of the systems limits their applicability. First, the interactions of real-world systems span networks by broad distributions of node connections and mesoscopic features in the form of communities with dense internal and sparse external connectivity. Second, interaction intensities vary and are closely coupled to network topology. Third, the daily cycle and bursty character of interaction events give rise to important temporal inhomogeneities.Some aspects of these features have already been studied. For static networks, it is known that spatial structure has an effect on epidemics (see, e.g., [6,7]), and community structure s...

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confidence: 99%

Small but slow world: How network topology and burstiness slow down spreading

et al. 2011

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“…The results from experiments presented earlier, together with the observations narrated by other authors [Epstein 2000;Toivonen et al 2009;Villatoro et al 2009], convinced us that subconventions are problematic obstacles to the emergence of global conventions. These subconventions thrive (amongst other reasons) because of the topological structure of the network where they emerge.…”

Section: Understanding Subconventionsmentioning

confidence: 60%

“…Therefore, agents can develop subconventions depending on their position on the topology of interaction. As identified by several authors [Salazar-Ramirez et al 2008;Toivonen et al 2009;Villatoro et al 2009], metastable subconventions interfere with the speed of the emergence of more general conventions. The problem of subconventions is a critical bottleneck that can derail emergence of conventions in agent societies, and mechanisms need to be developed that can alleviate this problem.…”

Section: Introductionmentioning

confidence: 99%

Robust convention emergence in social networks through self-reinforcing structures dissolution

Villatoro

Sabater-Mir

Sen

2013

ACM Trans. Auton. Adapt. Syst.

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Convention emergence solves the problem of choosing, in a decentralized way and among all equally beneficial conventions, the same convention for the entire population in the system for their own benefit. Our previous work has shown that reaching 100% agreement is not as straighforward as assumed by previous researchers, that, in order to save computational resources fixed the convergence rate to 90% (measuring the time it takes for 90% of the population to coordinate on the same action). In this article we present the notion of social instruments as a set of mechanisms that facilitate and accelerate the emergence of norms from repeated interactions between members of a society, only accessing local and public information and thus ensuring agents' privacy and anonymity. Specifically, we focus on two social instruments: rewiring and observation. Our main goal is to provide agents with tools that allow them to leverage their social network of interactions while effectively addressing coordination and learning problems, paying special attention to dissolving metastable subconventions.The first experimental results show that even with the usage of the proposed instruments, convergence is not accelerated or even obtained in irregular networks. This result leads us to perform an exhaustive analysis of irregular networks discovering what we have defined as Self-Reinforcing Structures (SRS). The SRS are topological configurations of nodes that promote the establishment and persistence of subconventions by producing a continuous reinforcing effect on the frontier agents. Finally, we propose a more sophisticated composed social instrument (observation + rewiring) for robust resolution of subconventions, which works by the dissolution of the stable frontiers caused by the Self-Reinforcing Substructures (SRS) within the social network.

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“…An example is the possibility that fat-tailed IET distributions appear as a consequence of topological traps in the network of interaction under majority rule dynamics. These traps can lead to anomalous scaling of consensus times for a majority rule dynamics [31,32]. A consensus time is a global property of the system, but it remains unclear if this is also reflected in the microscopic dynamics, giving rise to broad IET distributions.…”

Section: Discussionmentioning

confidence: 99%

Timing Interactions in Social Simulations: The Voter Model

Fernández-Gracia

Eguı́luz

Miguel

2013

Understanding Complex Systems

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The recent availability of huge high resolution datasets on human activities has revealed the heavy-tailed nature of the interevent time distributions. In social simulations of interacting agents the standard approach has been to use Poisson processes to update the state of the agents, which gives rise to very homogeneous activity patterns with a well defined characteristic interevent time. As a paradigmatic opinion model we investigate the voter model and review the standard update rules and propose two new update rules which are able to account for heterogeneous activity patterns. For the new update rules each node gets updated with a probability that depends on the time since the last event of the node, where an event can be an update attempt (exogenous update) or a change of state (endogenous update). We find that both update rules can give rise to power law interevent time distributions, although the endogenous one more robustly. Apart from that for the exogenous update rule and the standard update rules the voter model does not reach consensus in the infinite size limit, while for the endogenous update there exist a coarsening process that drives the system toward consensus configurations.

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Broad lifetime distributions for ordering dynamics in complex networks

Cited by 28 publications

References 42 publications

Small but slow world: How network topology and burstiness slow down spreading

Small but slow world: How network topology and burstiness slow down spreading

Robust convention emergence in social networks through self-reinforcing structures dissolution

Timing Interactions in Social Simulations: The Voter Model

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