Freezing and Slow Evolution in a Constrained Opinion Dynamics Model

We study opinion formation in a population that consists of leftists, centrists, and rightist. In an interaction between neighboring agents, a centrist and a leftist can become both centrists or leftists (and similarly for a centrist and a rightist). In contrast, leftists and rightists do not affect each other. The initial density of centrists rho_0 controls the evolution. With probability rho_0 the system reaches a centrist consensus, while with probability 1-rho_0 a frozen population of leftists and rightists results. In one dimension, we determine this frozen state and the opinion dynamics by mapping the system onto a spin-1 Ising model with zero-temperature Glauber kinetics. In the frozen state, the length distribution of single-opinion domains has an algebraic small-size tail x^{-2(1-psi)} and the average domain size grows as L^{2*psi}, where L is the system length. The approach to this frozen state is governed by a t^{-psi} long-time tail with psi-->2*rho_0/pi as rho_0-->0.Comment: 4 pages, 6 figures, 2-column revtex4 format, for submission to J. Phys. A. Revision contains lots of stylistic changes and 1 new result; the main conclusions are the sam

Memory-Based Snowdrift Game on Networks

We present a memory-based snowdrift game (MBSG) taking place on networks. We found that, when a lattice is taken to be the underlying structure, the transition of spatial patterns at some critical values of the payoff parameter is observable for both 4 and 8-neighbor lattices. The transition points as well as the styles of spatial patterns can be explained by local stability analysis. In sharp contrast to previously reported results, cooperation is promoted by the spatial structure in the MBSG. Interestingly, we found that the frequency of cooperation of the MBSG on a scale-free network peaks at a specific value of the payoff parameter. This phenomenon indicates that properly encouraging selfish behaviors can optimally enhance the cooperation. The memory effects of individuals are discussed in detail and some non-monotonous phenomena are observed on both lattices and scale-free networks. Our work may shed some new light on the study of evolutionary games over networks.Comment: 6 pages, 6 figures, to be published in Phys. Rev.

From simplicial Chern-Simons theory to the shadow invariant II

This is the second of a series of papers in which we introduce and study a rigorous "simplicial" realization of the non-Abelian Chern-Simons path integral for manifolds M of the form M = Sigma x S1 and arbitrary simply-connected compact structure groups G. More precisely, we introduce, for general links L in M, a rigorous simplicial version WLO_{rig}(L) of the corresponding Wilson loop observable WLO(L) in the so-called "torus gauge" by Blau and Thompson (Nucl. Phys. B408(2):345-390, 1993). For a simple class of links L we then evaluate WLO_{rig}(L) explicitly in a non-perturbative way, finding agreement with Turaev's shadow invariant |L|.Comment: 53 pages, 1 figure. Some minor changes and corrections have been mad

Statistical Dynamics of Religions and Adherents

Religiosity is one of the most important sociological aspects of populations. All religions may evolve in their beliefs and adapt to the society developments. A religion is a social variable, like a language or wealth, to be studied like any other organizational parameter. Several questions can be raised, as considered in this study: e.g. (i) from a ``macroscopic'' point of view : How many religions exist at a given time? (ii) from a ``microscopic'' view point: How many adherents belong to one religion? Does the number of adherents increase or not, and how? No need to say that if quantitative answers and mathematical laws are found, agent based models can be imagined to describe such non-equilibrium processes. It is found that empirical laws can be deduced and related to preferential attachment processes, like on evolving network; we propose two different algorithmic models reproducing as well the data. Moreover, a population growth-death equation is shown to be a plausible modeling of evolution dynamics in a continuous time framework. Differences with language dynamic competition is emphasized.Comment: submitted to EP

Link Invariants and Combinatorial Quantization of Hamiltonian Chern-Simons Theory

We define and study the properties of observables associated to any link in $\Sigma\times {\bf R}$ (where $\Sigma$ is a compact surface) using the combinatorial quantization of hamiltonian Chern-Simons theory. These observables are traces of holonomies in a non commutative Yang-Mills theory where the gauge symmetry is ensured by a quantum group. We show that these observables are link invariants taking values in a non commutative algebra, the so called Moduli Algebra. When $\Sigma=S^2$ these link invariants are pure numbers and are equal to Reshetikhin-Turaev link invariants.Comment: 39, latex, 7 figure

Birth, death and diffusion of interacting particles

Individual-based models of chemical or biological dynamics usually consider individual entities diffusing in space and performing a birth-death type dynamics. In this work we study the properties of a model in this class where the birth dynamics is mediated by the local, within a given distance, density of particles. Groups of individuals are formed in the system and in this paper we concentrate on the study of the properties of these clusters (lifetime, size, and collective diffusion). In particular, in the limit of the interaction distance approaching the system size, a unique cluster appears which helps to understand and characterize the clustering dynamics of the model.Comment: 15 pages, 6 figures, Iop style. To appear in Journal of Physics A: Condensed matte

Networking Effects on Cooperation in Evolutionary Snowdrift Game

The effects of networking on the extent of cooperation emerging in a competitive setting are studied. The evolutionary snowdrift game, which represents a realistic alternative to the well-known Prisoner's Dilemma, is studied in the Watts-Strogatz network that spans the regular, small-world, and random networks through random re-wiring. Over a wide range of payoffs, a re-wired network is found to suppress cooperation when compared with a well-mixed or fully connected system. Two extinction payoffs, that characterize the emergence of a homogeneous steady state, are identified. It is found that, unlike in the Prisoner's Dilemma, the standard deviation of the degree distribution is the dominant network property that governs the extinction payoffs.Comment: Changed conten

Critical behavior in an evolutionary Ultimatum Game

Experimental studies have shown the ubiquity of altruistic behavior in human societies. The social structure is a fundamental ingredient to understand the degree of altruism displayed by the members of a society, in contrast to individual-based features, like for example age or gender, which have been shown not to be relevant to determine the level of altruistic behavior. We explore an evolutionary model aiming to delve how altruistic behavior is affected by social structure. We investigate the dynamics of interacting individuals playing the Ultimatum Game with their neighbors given by a social network of interaction. We show that a population self-organizes in a critical state where the degree of altruism depends on the topology characterizing the social structure. In general, individuals offering large shares but in turn accepting large shares, are removed from the population. In heterogeneous social networks, individuals offering intermediate shares are strongly selected in contrast to random homogeneous networks where a broad range of offers, below a critical one, is similarly present in the population.Comment: 13 pages, 7 figure

Nonequilibrium phase transition in a model for social influence

We present extensive numerical simulations of the Axelrod's model for social influence, aimed at understanding the formation of cultural domains. This is a nonequilibrium model with short range interactions and a remarkably rich dynamical behavior. We study the phase diagram of the model and uncover a nonequilibrium phase transition separating an ordered (culturally polarized) phase from a disordered (culturally fragmented) one. The nature of the phase transition can be continuous or discontinuous depending on the model parameters. At the transition, the size of cultural regions is power-law distributed.Comment: 5 pages, 4 figure

D₂ Dopamine Receptors Colocalize Regulator of G-Protein Signaling 9-2 (RGS9-2) via the RGS9 DEP Domain, and RGS9 Knock-Out Mice Develop Dyskinesias Associated with Dopamine Pathways

Regulator of G-protein signaling 9-2 (RGS9-2), a member of the RGS family of Gα GTPase accelerating proteins, is expressed specifically in the striatum, which participates in antipsychotic-induced tardive dyskinesia and in levodopa-induced dyskinesia. We report that RGS9 knock-out mice develop abnormal involuntary movements when inhibition of dopaminergic transmission is followed by activation of D₂-like dopamine receptors (DRs). These abnormal movements resemble drug-induced dyskinesia more closely than other rodent models. Recordings from striatal neurons of these mice establish that activation of D₂-like DRs abnormally inhibits glutamate-elicited currents. We show that RGS9-2, via its DEP domain (for Disheveled, EGL-10, Pleckstrin homology), colocalizes with D₂DRs when coexpressed in mammalian cells. Recordings from oocytes coexpressing D₂DR or the m2 muscarinic receptor and G-protein-gated inward rectifier potassium channels show that RGS9-2, via its DEP domain, preferentially accelerates the termination of D₂DR signals. Thus, alterations in RGS9-2 may be a key factor in the pathway leading from D₂DRs to the side effects associated with the treatment both of psychoses and Parkinson's disease