System size stochastic resonance in a model for opinion formation

We study a model for opinion formation which incorporates three basic ingredients for the evolution of the opinion held by an individual: imitation, influence of fashion and randomness. We show that in the absence of fashion, the model behaves as a bistable system with random jumps between the two stable states with a distribution of times following Kramer's law. We also demonstrate the existence of system size stochastic resonance, by which there is an optimal value for the number of individuals N for which the average opinion follows better the fashion.Comment: 10 pages, to appear in Physica

Synchronised firing induced by network dynamics in excitable systems

We study the collective dynamics of an ensemble of coupled identical FitzHugh--Nagumo elements in their excitable regime. We show that collective firing, where all the elements perform their individual firing cycle synchronously, can be induced by random changes in the interaction pattern. Specifically, on a sparse evolving network where, at any time, each element is connected with at most one partner, collective firing occurs for intermediate values of the rewiring frequency. Thus, network dynamics can replace noise and connectivity in inducing this kind of self-organised behaviour in highly disconnected systems which, otherwise, wouldn't allow for the spreading of coherent evolution.Comment: 5 pages, 5 figure

Quantifying the effects of social influence

How do humans respond to indirect social influence when making decisions? We analysed an experiment where subjects had to repeatedly guess the correct answer to factual questions, while having only aggregated information about the answers of others. While the response of humans to aggregated information is a widely observed phenomenon, it has not been investigated quantitatively, in a controlled setting. We found that the adjustment of individual guesses depends linearly on the distance to the mean of all guesses. This is a remarkable, and yet surprisingly simple, statistical regularity. It holds across all questions analysed, even though the correct answers differ in several orders of magnitude. Our finding supports the assumption that individual diversity does not affect the response to indirect social influence. It also complements previous results on the nonlinear response in information-rich scenarios. We argue that the nature of the response to social influence crucially changes with the level of information aggregation. This insight contributes to the empirical foundation of models for collective decisions under social influence.Comment: 3 figure

Analysing the sensitivity of nestedness detection methods

Many bipartite and unipartite real-world networks display a nested structure. Examples pervade different disciplines: biological ecosystems (e.g. mutualistic networks), economic networks (e.g. manufactures and contractors networks) to financial networks (e.g. bank lending networks), etc. A nested network has a topology such that a vertex’s neighbourhood contains the neighbourhood of vertices of lower degree; thus – upon vertex reordering – the adjacency matrix is step-wise. Despite its strictmathematical definition and the interest triggered by their common occurrence, it is not easy to measure the extent of nested graphs unequivocally. Among others, there exist three methods for detection and quantification of nestedness that are widely used: BINMATNEST, NODF, and fitness-complexity metric (FCM). However, thesemethods fail in assessing the existence of nestedness for graphs of low (NODF) and high (NODF, BINMATNEST) network density. Another common shortcoming of these approaches is the underlying assumption that all vertices belong to a nested component. However, many real-world networks have solely a sub-component (i.e. a subset of its vertices) that is nested. Thus, unveiling which vertices pertain to the nested component is an important research question, unaddressed by the methods available so far. In this contribution, we study in detail the algorithm Nestedness detection based on Local Neighbourhood (NESTLON). This algorithm resorts solely on local information and detects nestedness on a broad range of nested graphs independently of their nature and density. Further, we introduce a benchmark model that allows us to tune the degree of nestedness in a controlled manner and study the performance of different algorithms. Our results show that NESTLON outperforms both BINMATNEST and NODF

Hierarchical Consensus Formation Reduces the Influence of Opinion Bias

We study the role of hierarchical structures in a simple model of collective consensus formation based on the bounded confidence model with continuous individual opinions. For the particular variation of this model considered in this paper, we assume that a bias towards an extreme opinion is introduced whenever two individuals interact and form a common decision. As a simple proxy for hierarchical social structures, we introduce a two-step decision making process in which in the second step groups of like-minded individuals are replaced by representatives once they have reached local consensus, and the representatives in turn form a collective decision in a downstream process. We find that the introduction of such a hierarchical decision making structure can improve consensus formation, in the sense that the eventual collective opinion is closer to the true average of individual opinions than without it. In particular, we numerically study how the size of groups of like-minded individuals being represented by delegate individuals affects the impact of the bias on the final population-wide consensus. These results are of interest for the design of organisational policies and the optimisation of hierarchical structures in the context of group decision making.Comment: 12 pages, 5 figure

Diversity-induced resonance

We present conclusive evidence showing that different sources of diversity, such as those represented by quenched disorder or noise, can induce a resonant collective behavior in an ensemble of coupled bistable or excitable systems. Our analytical and numerical results show that when such systems are subjected to an external subthreshold signal, their response is optimized for an intermediate value of the diversity. These findings show that intrinsic diversity might have a constructive role and suggest that natural systems might profit from their diversity in order to optimize the response to an external stimulus.Comment: 4 pages, 3 figure

Antagonistic Structural Patterns in Complex Networks

Identifying and explaining the structure of complex networks at different scales has become an important problem across disciplines. At the mesoscale, modular architecture has attracted most of the attention. At the macroscale, other arrangements --e.g. nestedness or core-periphery-- have been studied in parallel, but to a much lesser extent. However, empirical evidence increasingly suggests that characterizing a network with a unique pattern typology may be too simplistic, since a system can integrate properties from distinct organizations at different scales. Here, we explore the relationship between some of those organizational patterns: two at the mesoscale (modularity and in-block nestedness); and one at the macroscale (nestedness). We analytically show that nestedness can be used to provide approximate bounds for modularity, with exact results in an idealized scenario. Specifically, we show that nestedness and modularity are antagonistic. Furthermore, we evince that in-block nestedness provides a parsimonious transition between nested and modular networks, taking properties of both. Far from a mere theoretical exercise, understanding the boundaries that discriminate each architecture is fundamental, to the extent modularity and nestedness are known to place heavy constraints on the stability of several dynamical processes, specially in ecology.Comment: 7 pages, 4 figures and 1 supplemental information fil