Absorbing and Shattered Fragmentation Transitions in Multilayer Coevolution

We introduce a coevolution voter model in a multilayer, by coupling a fraction of nodes across two network layers and allowing each layer to evolve according to its own topological temporal scale. When these time scales are the same the dynamics preserve the absorbing-fragmentation transition observed in a monolayer network at a critical value of the temporal scale that depends on interlayer connectivity. The time evolution equations obtained by pair approximation can be mapped to a coevolution voter model in a single layer with an effective average degree. When the two layers have different topological time scales we find an anomalous transition, named shattered fragmentation, in which the network in one layer splits into two large components in opposite states and a multiplicity of isolated nodes. We identify the growth of the number of components as a signature of this anomalous transition. We also find a critical level of interlayer coupling needed to prevent the fragmentation in a layer connected to a layer that does not fragment.Comment: 7 pages, 6 figures, last figure caption includes link to animation

Data-driven modeling of systemic delay propagation under severe meteorological conditions

The upsetting consequences of weather conditions are well known to any person involved in air transportation. Still the quantification of how these disturbances affect delay propagation and the effectiveness of managers and pilots interventions to prevent possible large-scale system failures needs further attention. In this work, we employ an agent-based data-driven model developed using real flight performance registers for the entire US airport network and focus on the events occurring on October 27 2010 in the United States. A major storm complex that was later called the 2010 Superstorm took place that day. Our model correctly reproduces the evolution of the delay-spreading dynamics. By considering different intervention measures, we can even improve the model predictions getting closer to the real delay data. Our model can thus be of help to managers as a tool to assess different intervention measures in order to diminish the impact of disruptive conditions in the air transport system.Comment: 9 pages, 5 figures. Tenth USA/Europe Air Traffic Management Research and Development Seminar (ATM2013

Noise in Coevolving Networks

Coupling dynamics of the states of the nodes of a network to the dynamics of the network topology leads to generic absorbing and fragmentation transitions. The coevolving voter model is a typical system that exhibits such transitions at some critical rewiring. We study the robustness of these transitions under two distinct ways of introducing noise. Noise affecting all the nodes destroys the absorbing-fragmentation transition, giving rise in finite-size systems to two regimes: bimodal magnetisation and dynamic fragmentation. Noise Targeting a fraction of nodes preserves the transitions but introduces shattered fragmentation with its characteristic fraction of isolated nodes and one or two giant components. Both the lack of absorbing state for homogenous noise and the shift in the absorbing transition to higher rewiring for targeted noise are supported by analytical approximations.Comment: 20 page

Microscopic Abrams-Strogatz model of language competition

The differential equations of Abrams and Strogatz for the competition between two languages are compared with agent-based Monte Carlo simulations for fully connected networks as well as for lattices in one, two and three dimensions, with up to 10^9 agents.Comment: 10 pages, 7 figure

Dynamical origins of the community structure of multi-layer societies

Social structures emerge as a result of individuals managing a variety of different of 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 network layers in the multiplex. Community size distributions are either similar to a power-law 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. Depending on link- and node fluctuation rates, 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. We show that the empirical pairwise similarities of network layers, in terms of link overlap and degree correlations, practically coincide with the model. This suggests that several detailed features of the fragmentation in societies can be traced back to the triadic closure processes.Comment: 8 pages, 6 figure

Anticipated synchronization: a metaphorical linear view

We study the regime of anticipated synchronization recently described on a number of dynamical systems including chaotic and noisy ones. We use simple linear caricatures to show the minimal setups able to reproduce the basic facts described.Comment: 7 pages,5 figure

Homophily, Cultural Drift and the Co-Evolution of Cultural Groups

In studies of cultural differentiation, the joint mechanisms of homophily and influence have been able to explain how distinct cultural groups can form. While these mechanisms normally lead to cultural convergence, increased levels of heterogeneity can allow them to produce global diversity. However, this emergent cultural diversity has proven to be unstable in the face of "cultural drift"- small errors or innovations that allow cultures to change from within. We develop a model of cultural differentiation that combines the traditional mechanisms of homophily and influence with a third mechanism of 2network homophily", in which network structure co-evolves with cultural interaction. We show that if social ties are allowed to change with cultural influence, a complex relationship between heterogeneity and cultural diversity is revealed, in which increased heterogeneity can reduce cultural group formation while simultaneously increasing social connectedness. Our results show that in certain regions of the parameter space these co-evolutionary dynamics can lead to patterns of cultural diversity that are stable in the presence of cultural drift.Comment: (8 pages, 8 figures