Noise in coevolving networks

Diakonova, Marina; Eguı́luz, Vı́ctor M.; Miguel, M. San

doi:10.1103/physreve.92.032803

Cited by 25 publications

(59 citation statements)

References 37 publications

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“…This is the hallmark of a shattered fragmentation; topologies with at least one giant components and a multiplicity of components of smaller size. Shattered fragmentation was first observed in the CVM in multiplex networks where not all nodes are present in each layer (MCVM) [33] and for the CVM on a single-layer network with noise that targets a fixed subpopulation of nodes [34]. Here, we find the same phenomenology for re-wiring processes that are dominated by triadic closure processes.…”

Section: Normalized Mutual Informationsupporting

confidence: 68%

“…In the simulations the network is initialized as a random regular network with size N and degree m = 4 for each node, which results in a network that is initially connected. In [33,34] shattered fragmentation was demonstrated on networks with these parameters, and we use them here to facilitate comparisons to earlier works. These prior works suggest that changing the initial intra-layer connectivity does not lead to major qualitative differences in the phase diagram of the model and that an average degree of m = 4 is representative of a wide range of values for μ.…”

Section: Normalized Mutual Informationmentioning

confidence: 98%

“…Fragmentation is the phenomenon in which a network might undergo a transition from a state where almost all nodes belong to a single giant component to a fragmented state in which the network breaks into several components. The fragmentation transition is a phenomenon generically associated with co-evolution network dynamics [29][30][31][32][33][34]. Here we consider the voter model (VM) [35,36] as a paradigmatic example.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical origins of the community structure of an online multi-layer society

et al. 2016

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Social structures emerge as a result of individuals managing a variety of different social relationships. Societies can be represented as highly structured dynamic multiplex networks. Here we study the dynamical origins of the specific community structures of a large-scale social multiplex network of a human society that interacts in a virtual world of a massive multiplayer online game. There we find substantial differences in the community structures of different social actions, represented by the various layers in the multiplex network. Community sizes distributions are either fat-tailed or appear to be centered around a size of 50 individuals. To understand these observations we propose a voter model that is built around the principle of triadic closure. It explicitly models the co-evolution of node-and link-dynamics across different layers of the multiplex network. Depending on link and node fluctuation probabilities, the model exhibits an anomalous shattered fragmentation transition, where one layer fragments from one large component into many small components. The observed community size distributions are in good agreement with the predicted fragmentation in the model. This suggests that several detailed features of the fragmentation in societies can be traced back to the triadic closure processes.

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Section: Normalized Mutual Informationsupporting

confidence: 68%

Section: Normalized Mutual Informationmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Dynamical origins of the community structure of an online multi-layer society

et al. 2016

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“…for the correlations, where, for simplicity and brevity of the expressions, we have assumed that the deterministic contributions δ k (t), δ ρ (t) are well captured by the linear system of equations (85) and (86) and that δ k (0)=δ ρ (0)=0. An important difference with respect to the expansion around the deterministic solution, equations (63)- (64), is that the equations for the moments are not closed, as indicated by the presence of the last term in equation (98). Nevertheless, we will argue later on in this same section that this term can be neglected at this level of approximation.…”

Section: Expansion Around the Dynamical Attractormentioning

confidence: 99%

“…The finite-size character of the transition is due to the fact that the critical point tends to zero in the thermodynamic limit of large system sizes. Although most of the initial literature about the noisy voter model focused only on regular lattices [57,61] and a fully connected network [60,62], recent studies have addressed more complex topologies, both from an effective-field perspective [26,63,64] and using an annealed network approximation [42]. In particular, while the effective-field approach was only able to broadly capture the effect of the network size and mean degree on the results of the model for highly homogeneous and connected networks, the annealed approximation [42] was, in addition, able to reproduce the impact of the degree heterogeneity-variance of the underlying degree distribution-on the critical point of the transition and the temporal correlations with a high level of accuracy, as well as the main effects on the local order parameter, though with significantly less accuracy.…”

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confidence: 99%

Stochastic pair approximation treatment of the noisy voter model

et al. 2018

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We present a full stochastic description of the pair approximation scheme to study binary-state dynamics on heterogeneous networks. Within this general approach, we obtain a set of equations for the dynamical correlations, fluctuations and finite-size effects, as well as for the temporal evolution of all relevant variables. We test this scheme for a prototypical model of opinion dynamics known as the noisy voter model that has a finite-size critical point. Using a closure approach based on a system size expansion around a stochastic dynamical attractor we obtain very accurate results, as compared with numerical simulations, for stationary and time-dependent quantities whether below, within or above the critical region. We also show that finite-size effects in complex networks cannot be captured, as often suggested, by merely replacing the actual system size N by an effective network dependent size N eff . IntroductionFrom classical problems in statistical physics [1, 2] to questions in biology and ecology [3][4][5], and over to the spreading of opinions and diseases in social systems [6-10], stochastic binary-state models have been widely used to study the emergence of collective phenomena in systems of stochastically interacting components. In general, these components are modeled as binary-state variables -spin up or down-sitting at the nodes of a network whose links represent the possible interactions among them. While initial research focused on the limiting cases of a well-mixed population, where each of the components is allowed to interact with any other, and regular lattice structures, later works turned to more complex and heterogeneous topologies [11][12][13][14]. A most important insight derived from these more recent works is that the macroscopic dynamics of the system can be greatly affected by the particular topology of the underlying network. In the case of systems with critical behavior, different network characteristics have been shown to have a significant impact on the critical values of the model parameters [15][16][17], such as the critical temperature of the Ising model [18][19][20] and the epidemic threshold in models of infectious disease transmission [21][22][23][24][25]. Thus, the identification of the particular network characteristics that have an impact on the dynamics of these models, as well as the quantification of their effect, are of paramount importance.The first theoretical treatments introduced for the study of stochastic, binary-state dynamics on networks relied on a global-state approach [2, 26], i.e. they focused on a single variable-for example, the number of nodes in one of the two possible states-assumed to represent the whole state of the system. In order to write a master equation for this global-state variable, some approximation is required to move from the individual particle transition rates defining the model to some effective transition rates depending only on the chosen global variable. Within this global-state approach, the effective-field approximation assumes...

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Herding and idiosyncratic choices: Nonlinearity and aging-induced transitions in the noisy voter model

Artime

Carro

Peralta

et al. 2019

Comptes Rendus. Physique

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We consider the herding to non-herding transition caused by idiosyncratic choices or imperfect imitation in the context of the Kirman Model for financial markets, or equivalently the Noisy Voter Model for opinion formation. In these original models this is a finite size transition that disappears for a large number of agents. We show how the introduction of two different mechanisms make this transition robust and well defined. A first mechanism is nonlinear interactions among agents taking into account the nonlinear effect of local majorities. The second one is aging, so that the longer an agent has been in a given state the more reluctant she becomes to change state.

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Noise in coevolving networks

Cited by 25 publications

References 37 publications

Dynamical origins of the community structure of an online multi-layer society

Dynamical origins of the community structure of an online multi-layer society

Stochastic pair approximation treatment of the noisy voter model

Herding and idiosyncratic choices: Nonlinearity and aging-induced transitions in the noisy voter model

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