Local interaction scale controls the existence of a non-trivial optimal critical mass in opinion spreading

We study a model of opinion formation where the collective decision of group is said to happen if the fraction of agents having the most common opinion exceeds a threshold value, a \textit{critical mass}. We find that there exists a unique, non-trivial critical mass giving the most efficient convergence to consensus. In addition, we observe that for small critical masses, the characteristic time scale for the relaxation to consensus splits into two. The shorter time scale corresponds to a direct relaxation and the longer can be explained by the existence of intermediate, metastable states similar to those found in [P.\ Chen and S.\ Redner, Phys.\ Rev.\ E \textbf{71}, 036101 (2005)]. This longer time-scale is dependent on the precise condition for consensus---with a modification of the condition it can go away.Comment: 4 pages, 6 figure

Enhanced Anandamide Plasma Levels in Patients with Complex Regional Pain Syndrome following Traumatic Injury: A Preliminary Report

The complex regional pain syndrome (CRPS) is a disabling neuropathic pain condition that may develop following injuries of the extremities. The pathogenesis of this syndrome is not clear; however, it includes complex interactions between the nervous and the immune system resulting in chronic inflammation, pain and trophic changes. This interaction may be mediated by chronic stress which is thought to activate the endogenous cannabinoid (endocannabinoid) system (ECS). We conducted an open, prospective, comparative clinical study to determine plasma level of the endocannabinoid anandamide by high-performance liquid chromatography and a tandem mass spectrometry system in 10 patients with CRPS type I versus 10 age- and sex-matched healthy controls. As compared to healthy controls, CRPS patients showed significantly higher plasma concentrations of anandamide. These results indicate that the peripheral ECS is activated in CRPS. Further studies are warranted to evaluate the role of the ECS in the limitation of inflammation and pain. Copyright (C) 2009 S. Karger AG, Base

On Spatial Consensus Formation: Is the Sznajd Model Different from a Voter Model?

In this paper, we investigate the so-called ``Sznajd Model'' (SM) in one dimension, which is a simple cellular automata approach to consensus formation among two opposite opinions (described by spin up or down). To elucidate the SM dynamics, we first provide results of computer simulations for the spatio-temporal evolution of the opinion distribution $L(t)$, the evolution of magnetization $m(t)$, the distribution of decision times $P(\tau)$ and relaxation times $P(\mu)$. In the main part of the paper, it is shown that the SM can be completely reformulated in terms of a linear VM, where the transition rates towards a given opinion are directly proportional to frequency of the respective opinion of the second-nearest neighbors (no matter what the nearest neighbors are). So, the SM dynamics can be reduced to one rule, ``Just follow your second-nearest neighbor''. The equivalence is demonstrated by extensive computer simulations that show the same behavior between SM and VM in terms of $L(t)$, $m(t)$, $P(\tau)$, $P(\mu)$, and the final attractor statistics. The reformulation of the SM in terms of a VM involves a new parameter $\sigma$, to bias between anti- and ferromagnetic decisions in the case of frustration. We show that $\sigma$ plays a crucial role in explaining the phase transition observed in SM. We further explore the role of synchronous versus asynchronous update rules on the intermediate dynamics and the final attractors. Compared to the original SM, we find three additional attractors, two of them related to an asymmetric coexistence between the opposite opinions.Comment: 22 pages, 20 figures. For related publications see http://www.ais.fraunhofer.de/~fran

Effective Free Energy for Individual Dynamics

Physics and economics are two disciplines that share the common challenge of linking microscopic and macroscopic behaviors. However, while physics is based on collective dynamics, economics is based on individual choices. This conceptual difference is one of the main obstacles one has to overcome in order to characterize analytically economic models. In this paper, we build both on statistical mechanics and the game theory notion of Potential Function to introduce a rigorous generalization of the physicist's free energy, which includes individual dynamics. Our approach paves the way to analytical treatments of a wide range of socio-economic models and might bring new insights into them. As first examples, we derive solutions for a congestion model and a residential segregation model.Comment: 8 pages, 2 figures, presented at the ECCS'10 conferenc

Role of social environment and social clustering in spread of opinions in co-evolving networks

Taking a pragmatic approach to the processes involved in the phenomena of collective opinion formation, we investigate two specific modifications to the co-evolving network voter model of opinion formation, studied by Holme and Newman [1]. First, we replace the rewiring probability parameter by a distribution of probability of accepting or rejecting opinions between individuals, accounting for the asymmetric influences in relationships among individuals in a social group. Second, we modify the rewiring step by a path-length-based preference for rewiring that reinforces local clustering. We have investigated the influences of these modifications on the outcomes of the simulations of this model. We found that varying the shape of the distribution of probability of accepting or rejecting opinions can lead to the emergence of two qualitatively distinct final states, one having several isolated connected components each in internal consensus leading to the existence of diverse set of opinions and the other having one single dominant connected component with each node within it having the same opinion. Furthermore, and more importantly, we found that the initial clustering in network can also induce similar transitions. Our investigation also brings forward that these transitions are governed by a weak and complex dependence on system size. We found that the networks in the final states of the model have rich structural properties including the small world property for some parameter regimes. [1] P. Holme and M. Newman, Phys. Rev. E 74, 056108 (2006)

Quantum Games

In these lecture notes we investigate the implications of the identification of strategies with quantum operations in game theory beyond the results presented in [J. Eisert, M. Wilkens, and M. Lewenstein, Phys. Rev. Lett. 83, 3077 (1999)]. After introducing a general framework, we study quantum games with a classical analogue in order to flesh out the peculiarities of game theoretical settings in the quantum domain. Special emphasis is given to a detailed investigation of different sets of quantum strategies.Comment: 13 pages (LaTeX), 3 figure

Statistical physics of the Schelling model of segregation

We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics methods shed light on the rich phenomenology of this simple model, exhibiting static phase transitions typical of kinetic constrained models, nontrivial coarsening like in driven-particle systems and percolation-related phenomena.Comment: 4 pages, 3 figure

Analysis of a threshold model of social contagion on degree-correlated networks

We analytically determine when a range of abstract social contagion models permit global spreading from a single seed on degree-correlated random networks. We deduce the expected size of the largest vulnerable component, a network's tinderbox-like critical mass, as well as the probability that infecting a randomly chosen individual seed will trigger global spreading. In the appropriate limits, our results naturally reduce to standard ones for models of disease spreading and to the condition for the existence of a giant component. Recent advances in the distributed, infinite seed case allow us to further determine the final size of global spreading events, when they occur. To provide support for our results, we derive exact expressions for key spreading quantities for a simple yet rich family of random networks with bimodal degree distributions.Comment: 7 Pages, 1 figure, submitted to Phys. Rev.