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Banisch S.,Bielefeld University | Banisch S.,Institute for Complexity Science ICC | Banisch S.,Max Planck Institute for Mathematics in the Sciences
Advances in Complex Systems | Year: 2014

An analytical treatment of a simple opinion model with contrarian behavior is presented. The focus is on the stationary dynamics of the model and in particular on the effect of inhomogeneities in the interaction topology on the stationary behavior. We start from a micro-level Markov chain description of the model. Markov chain aggregation is then used to derive a macro chain for the complete graph as well as a meso-level description for the two-community graph composed of two (weakly) coupled sub-communities. In both cases, a detailed understanding of the model behavior is possible using Markov chain tools. More importantly, however, this setting provides an analytical scenario to study the discrepancy between the homogeneous mixing case and the model on a slightly more complex topology. We show that memory effects are introduced at the macro-level when we aggregate over agent attributes without sensitivity to the microscopic details and quantify these effects using concepts from information theory. In this way, the method facilitates the analysis of the relation between microscopic processes and their aggregation to a macroscopic level of description and informs about the complexity of a system introduced by heterogeneous interaction relations. © 2014 World Scientific Publishing Company. Source


Banisch S.,Bielefeld University | Banisch S.,Institute for Complexity Science ICC | Araujo T.,Research Unit on Complexity in Economics UECE | Araujo T.,Institute for Complexity Science ICC
Physics Letters, Section A: General, Atomic and Solid State Physics | Year: 2010

While the number and variety of models to explain opinion exchange dynamics is huge, attempts to justify the model results using empirical data are relatively rare. As linking to real data is essential for establishing model credibility, this Letter develops an empirical confirmation experiment by which an opinion model is related to real election data. The model is based on a representation of opinions as a vector of k bits. Individuals interact according to the principle that similarity leads to interaction and interaction leads to still more similarity. In the comparison to real data we concentrate on the transient opinion profiles that form during the dynamic process. An artificial election procedure is introduced which allows to relate transient opinion configurations to the electoral performance of candidates for which data are available. The election procedure based on the well-established principle of proximity voting is repeatedly performed during the transient period and remarkable statistical agreement with the empirical data is observed. © 2010 Elsevier B.V. All rights reserved. Source


Banisch S.,Institute for Complexity Science ICC | Banisch S.,BauhausUniversity Weimar | Banisch S.,Research Unit on Complexity in Economics UECE | AraUjo T.,Institute for Complexity Science ICC | And 3 more authors.
Advances in Complex Systems | Year: 2010

This paper examines the interplay of opinion exchange dynamics and communication network formation. An opinion formation procedure is introduced which is based on an abstract representation of opinions as k-dimensional bit-strings. Individuals interact if the difference in the opinion strings is below a defined similarity threshold dI. Depending on dI, different behavior of the population is observed: low values result in a state of highly fragmented opinions and higher values yield consensus. The first contribution of this research is to identify the values of parameters d I and k, such that the transition between fragmented opinions and homogeneity takes place. Then, we look at this transition from two perspectives: first by studying the group size distribution and second by analyzing the communication network that is formed by the interactions that take place during the simulation. The emerging networks are classified by statistical means and we find that nontrivial social structures emerge from simple rules for individual communication. Generating networks allows to compare model outcomes with real-world communication patterns. © 2010 World Scientific Publishing Company. Source


Floriani E.,Aix - Marseille University | Floriani E.,University of Toulon | Ciraolo G.,Ecole Centrale Marseille | Ciraolo G.,Aix - Marseille University | And 5 more authors.
Plasma Physics and Controlled Fusion | Year: 2013

The interplay between turbulent bursts and transport barriers is analyzed with a simplified model of interchange turbulence in magnetically confined plasmas. The turbulent bursts spread into the transport barriers and, depending on the competing magnitude of the burst and stopping capability of the barrier, can burn through. Simulations of two models of transport barriers are presented: a hard barrier where interchange turbulence modes are stable in a prescribed region and a soft barrier with external plasma biasing. The response of the transport barriers to the non-linear perturbations of the turbulent bursts, addressed in a predator-prey approach, indicates that the barriers monitor an amplification factor of the turbulent bursts, with amplification smaller than one for most bursts and, in some cases, amplification factors that can significantly exceed unity. The weak barriers in corrugated profiles and magnetic structures, as well as the standard barriers, are characterized by these transmission properties, which then regulate the turbulent burst transport properties. The interplays of barriers and turbulent bursts are modeled as competing stochastic processes. For different classes of the probability density function (PDF) of these processes, one can predict the heavy tail properties of the bursts downstream from the barrier, either exponential for a leaky barrier, or with power laws for a tight barrier. The intrinsic probing of the transport barriers by the turbulent bursts thus gives access to the properties of the barriers. The main stochastic variables are the barrier width and the spreading distance of the turbulent bursts within the barrier, together with their level of correlation. One finds that in the case of a barrier with volumetric losses, such as radiation or particle losses as addressed in our present simulations, the stochastic model predicts a leaky behavior with an exponential PDF of escaping turbulent bursts in agreement with the simulation data. © 2013 IOP Publishing Ltd. Source

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