Conservation laws for the voter model in complex networks

We consider the voter model dynamics in random networks with an arbitrary distribution of the degree of the nodes. We find that for the usual node-update dynamics the average magnetization is not conserved, while an average magnetization weighted by the degree of the node is conserved. However, for a link-update dynamics the average magnetization is still conserved. For the particular case of a Barabasi-Albert scale-free network the voter model dynamics leads to a partially ordered metastable state with a finite size survival time. This characteristic time scales linearly with system size only when the updating rule respects the conservation law of the average magnetization. This scaling identifies a universal or generic property of the voter model dynamics associated with the conservation law of the magnetization.Comment: 5 pages, 4 figures; for related material please visit http://www.imedea.uib.e

Search strategies of Wikipedia readers

The quest for information is one of the most common activity of human beings. Despite the the impressive progress of search engines, not to miss the needed piece of information could be still very tough, as well as to acquire specific competences and knowledge by shaping and following the proper learning paths. Indeed, the need to find sensible paths in information networks is one of the biggest challenges of our societies and, to effectively address it, it is important to investigate the strategies adopted by human users to cope with the cognitive bottleneck of finding their way in a growing sea of information. Here we focus on the case of Wikipedia and investigate a recently released dataset about users’ click on the English Wikipedia, namely the English Wikipedia Clickstream. We perform a semantically charged analysis to uncover the general patterns followed by information seekers in the multi-dimensional space of Wikipedia topics/categories. We discover the existence of well defined strategies in which users tend to start from very general, i.e., semantically broad, pages and progressively narrow down the scope of their navigation, while keeping a growing semantic coherence. This is unlike strategies associated to tasks with predefined search goals, namely the case of the Wikispeedia game. In this case users first move from the ‘particular’ to the ‘universal’ before focusing down again to the required target. The clear picture offered here represents a very important stepping stone towards a better design of information networks and recommendation strategies, as well as the construction of radically new learning paths

Heterogeneous pair approximation for voter models on networks

For models whose evolution takes place on a network it is often necessary to augment the mean-field approach by considering explicitly the degree dependence of average quantities (heterogeneous mean-field). Here we introduce the degree dependence in the pair approximation (heterogeneous pair approximation) for analyzing voter models on uncorrelated networks. This approach gives an essentially exact description of the dynamics, correcting some inaccurate results of previous approaches. The heterogeneous pair approximation introduced here can be applied in full generality to many other processes on complex networks.Comment: 6 pages, 6 figures, published versio

The evolution of classification systems: Ontogeny of the UDC

To classify is to put things in meaningful groups, but the criteria for doing so can be problematic. Study of evolution of classification includes ontogenetic analysis of change in classification over time. We present an empirical analysis of the UDC over the entire period of its development. We demonstrate stability in main classes, with major change driven by 20th century scientific developments. But we also demonstrate a vast increase in the complexity of auxiliaries. This study illustrates an alternative to Tennis' "scheme-versioning" method.Comment: ISKO conference 201

Voter Model with Time dependent Flip-rates

We introduce time variation in the flip-rates of the Voter Model. This type of generalisation is relevant to models of ageing in language change, allowing the representation of changes in speakers' learning rates over their lifetime and may be applied to any other similar model in which interaction rates at the microscopic level change with time. The mean time taken to reach consensus varies in a nontrivial way with the rate of change of the flip-rates, varying between bounds given by the mean consensus times for static homogeneous (the original Voter Model) and static heterogeneous flip-rates. By considering the mean time between interactions for each agent, we derive excellent estimates of the mean consensus times and exit probabilities for any time scale of flip-rate variation. The scaling of consensus times with population size on complex networks is correctly predicted, and is as would be expected for the ordinary voter model. Heterogeneity in the initial distribution of opinions has a strong effect, considerably reducing the mean time to consensus, while increasing the probability of survival of the opinion which initially occupies the most slowly changing agents. The mean times to reach consensus for different states are very different. An opinion originally held by the fastest changing agents has a smaller chance to succeed, and takes much longer to do so than an evenly distributed opinion.Comment: 16 pages, 6 figure

Anomalous lifetime distributions and topological traps in ordering dynamics

We address the role of community structure of an interaction network in ordering dynamics, as well as associated forms of metastability. We consider the voter and AB model dynamics in a network model which mimics social interactions. The AB model includes an intermediate state between the two excluding options of the voter model. For the voter model we find dynamical metastable disordered states with a characteristic mean lifetime. However, for the AB dynamics we find a power law distribution of the lifetime of metastable states, so that the mean lifetime is not representative of the dynamics. These trapped metastable states, which can order at all time scales, originate in the mesoscopic network structure.Comment: 7 pages; 6 figure

Irreducibility of multilayer network dynamics: the case of the voter model

10 pages, 6 figuresThis work has been supported by the Spanish MINECO and FEDER under projects INTENSE@COSYP (FIS2012-30634), and by the EU Commission through the project LASAGNE (FP7-ICT-318132). VL also acknowledges support from EPSRC project GALE (EP/K020633/1

Lack of consensus in social systems

We propose an exactly solvable model for the dynamics of voters in a two-party system. The opinion formation process is modeled on a random network of agents. The dynamical nature of interpersonal relations is also reflected in the model, as the connections in the network evolve with the dynamics of the voters. In the infinite time limit, an exact solution predicts the emergence of consensus, for arbitrary initial conditions. However, before consensus is reached, two different metastable states can persist for exponentially long times. One state reflects a perfect balancing of opinions, the other reflects a completely static situation. An estimate of the associated lifetimes suggests that lack of consensus is typical for large systems.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let

Consensus formation on coevolving networks: groups' formation and structure

We study the effect of adaptivity on a social model of opinion dynamics and consensus formation. We analyze how the adaptivity of the network of contacts between agents to the underlying social dynamics affects the size and topological properties of groups and the convergence time to the stable final state. We find that, while on static networks these properties are determined by percolation phenomena, on adaptive networks the rewiring process leads to different behaviors: Adaptive rewiring fosters group formation by enhancing communication between agents of similar opinion, though it also makes possible the division of clusters. We show how the convergence time is determined by the characteristic time of link rearrangement. We finally investigate how the adaptivity yields nontrivial correlations between the internal topology and the size of the groups of agreeing agents.Comment: 10 pages, 3 figures,to appear in a special proceedings issue of J. Phys. A covering the "Complex Networks: from Biology to Information Technology" conference (Pula, Italy, 2007