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## A thermodynamic counterpart of the Axelrod model of social influence: The one-dimensional case

Gandica, Y.; Medina, E.; Bonalde, I.
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
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We propose a thermodynamic version of the Axelrod model of social influence. In one-dimensional (1D) lattices, the thermodynamic model becomes a coupled Potts model with a bonding interaction that increases with the site matching traits. We analytically calculate thermodynamic and critical properties for a 1D system and show that an order–disorder phase transition only occurs at T=0 independent of the number of cultural traits q and features F. The 1D thermodynamic Axelrod model belongs to the same universality class of the Ising and Potts models, notwithstanding the increase of the internal dimension of the local degree of freedom and the state-dependent bonding interaction. We suggest a unifying proposal to compare exponents across different discrete 1D models. The comparison with our Hamiltonian description reveals that in the thermodynamic limit the original out-of-equilibrium 1D Axelrod model with noise behaves like an ordinary thermodynamic 1D interacting particle system.

## Coexistence of interacting opinions in a generalized Sznajd model

Timpanaro, André Martin; Prado, Carmen Pimentel Cintra do
Fonte: AMER PHYSICAL SOC Publicador: AMER PHYSICAL SOC
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
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The Sznajd model is a sociophysics model that mimics the propagation of opinions in a closed society, where the interactions favor groups of agreeing people. It is based in the Ising and Potts ferromagnetic models and, although the original model used only linear chains, it has since been adapted to general networks. This model has a very rich transient, which has been used to model several aspects of elections, but its stationary states are always consensus states. In order to model more complex behaviors, we have, in a recent work, introduced the idea of biases and prejudices to the Sznajd model by generalizing the bounded confidence rule, which is common to many continuous opinion models, to what we called confidence rules. In that work we have found that the mean field version of this model (corresponding to a complete network) allows for stationary states where noninteracting opinions survive, but never for the coexistence of interacting opinions. In the present work, we provide networks that allow for the coexistence of interacting opinions for certain confidence rules. Moreover, we show that the model does not become inactive; that is, the opinions keep changing, even in the stationary regime. This is an important result in the context of understanding how a rule that breeds local conformity is still able to sustain global diversity while avoiding a frozen stationary state. We also provide results that give some insights on how this behavior approaches the mean field behavior as the networks are changed.; FAPESP

## An opinion dynamics model for the diffusion of innovations

MARTINS, Andre C. R.; PEREIRA, Carlos de B.; VICENTE, Renato
Fonte: ELSEVIER SCIENCE BV Publicador: ELSEVIER SCIENCE BV
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
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## SZNAJD MODEL AND PROPORTIONAL ELECTIONS: THE ROLE OF THE TOPOLOGY OF THE NETWORK

Vannucchi, Fabio Stucchi; Prado, Carmen Pimentel Cintra do
Fonte: WORLD SCIENTIFIC PUBL CO PTE LTD Publicador: WORLD SCIENTIFIC PUBL CO PTE LTD
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
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The Sznajd model (SM) has been employed with success in the last years to describe opinion propagation in a community. In particular, it has been claimed that its transient is able to reproduce some scale properties observed in data of proportional elections, in different countries, if the community structure (the network) is scale-free. In this work, we investigate the properties of the transient of a particular version of the SM, introduced by Bernardes and co-authors in 2002. We studied the behavior of the model in networks of different topologies through the time evolution of an order parameter known as interface density, and concluded that regular lattices with high dimensionality also leads to a power-law distribution of the number of candidates with v votes. Also, we show that the particular absorbing state achieved in the stationary state (or else, the winner candidate), is related to a particular feature of the model, that may not be realistic in all situations.; CNPq; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

## Connections between the Sznajd model with general confidence rules and graph theory

Timpanaro, André Martin; Prado, Carmen Pimentel Cintra do
Fonte: AMER PHYSICAL SOC; COLLEGE PK Publicador: AMER PHYSICAL SOC; COLLEGE PK
Tipo: Relatório
ENG
Relevância na Pesquisa
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The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabasi-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q > 2...

## Dilema do prisioneiro evolucionário Darwiniano e Pavloviano no autômato celular unidimensional: uma nova representação e exploração exaustiva do espaço de parâmetros; Darwinian and Pavlovian Evolutionary Prisoner Dilemma in the One-Dimensional Cellular Automata: a new representation and exhaustive exploration of parameter space

Pereira, Marcelo Alves
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
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## O modelo de Axelrod com tensão superficial; Axelrod's model with surface tension

Pace, Bruno
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
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Nesta dissertação foram estudados alguns modelos vetoriais que pretendem modelar e descrever alguns aspectos de sistemas sociais e de sua organização cultural. Partimos do modelo de Axelrod, um processo estocástico definido em uma rede, e introduzimos uma pequena alteração no modelo que desencadeou mudanças qualitativas interessantes, especialmente o surgimento de uma tensão superficial, que leva ao aparecimento de estados metaestáveis e de regiões culturais mais fixamente localizadas no espaço. Através da ótica da mecânica estatística e de extensas simulações computacionais, exploramos alguns dos aspectos que julgamos mais importantes na caracterização desse rico modelo.; Axelrod's model for cultural dissemination is a discrete vector representation for modeling social and cultural systems. In this work we have studied it and other related models, and a subtle change in the model's rule was proposed. Our slight alterations to the model yielded significant qualitative changes, specifically the emergence of surface tension, driving the system to metastable states. Using concepts from statistical mechanics and extensive numerical simulations, we explored some of the aspects that better describe the rich model devised...

## Mudanças de opinião em redes complexas; Opinion propagation in scale free networks

Timpanaro, André Martin
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Relevância na Pesquisa
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Nos últimos anos, uma míriade de modelos de propagação de opinião foram propostos, motivados pelo interesse crescente dos físicos por problemas interdisciplinares tanto em sociologia, quanto em economia e biologia. Um dos objetivos desse trabalho é unificar alguns desses modelos em uma mesma formulação. Para isso, generalizamos a noção de confiança limitada para o que chamamos de regras de confiança, que podem ser interpretadas como a introdução de viéses ou preconceitos nas interações de agentes com opiniões distintas. Munidos dessa formulação, nos propusemos a estudar como modelos que promovem localmente conformidade (o que está de acordo com experimentos para grupos pequenos conduzidos por psicólogos), poderiam gerar diversidade globalmente (explicando a persistência de pontos de vista distintos em sociedades, por exemplo). Nós estudamos o campo médio do modelo do votante e de variantes do modelo Sznajd. Aplicando ferramentas de sistemas dinâmicos, conseguimos resolver analiticamente o comportamento qualitativo dos modelos na ausência de ruído e desenvolvemos uma teoria de perturbação para o modelo Sznajd com ruído infinitesimal, que nos forneceu um retrato parcial do comportamento na presença de ruído. Na ausência de ruído...

## Estudo de estratégias para mudanças coletivas em modelos de opinião; Study of strategies for collective changes in opinion models

Maizel, André Schraider
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Relevância na Pesquisa
16.63%
O estudo de sistemas sociais sempre foi visto como fora do escopo da física. No entanto, nos últimos anos, com o desenvolvimento da mecânica estatística e da aprendizagem de máquinas, em conjunto com recentes avanços na neurociência, tornou-se possível a criação de diversos modelos no intuito de estudar quantitativamente grandezas antes consideradas majoritariamente qualitativas. Dentre os problemas considerados está a moralidade, bem como suas consequências para as dinâmicas de opinião. Mais especificamente, considera-se relevante estudar como se dá a mudança de opiniões dentro de uma sociedade, bem como estratégias para convencer uma população a alterar sua direção moral. Utilizando um modelo baseado em agentes, na qual cada agente é representado por um vetor moral e utiliza uma estratégia de aprendizagem ótima para o cenário professor/aluno, estudamos a influência de duas estratégias de convencimento no comportamento macroscópico de nossa sociedade modelo. Tomando como base a aprendizagem sequencial sem a presença de ruído, e o fato de que seleção de exemplos na borda da dúvida gera um decaimento exponencial do erro de generalização em redes neurais artificiais, estudamos o efeito desta técnica como estratégia de convencimento populacional...

## Fenómenos complejos en sistemas extendidos en el espacio; Complex phenomena in spatially extended systems

Sánchez de la Lama, Marta
ENG
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RESUMEN: Uno de los aspectos más fascinantes del mundo que nos rodea es la gran variedad de escalas a las que tienen lugar los diversos fenómenos. En muchos casos esta diversidad pone de manifiesto la estructura fractal de la naturaleza y podemos hablar entonces de fenómenos complejos, en los que eventos de diferentes magnitudes no pueden analizarse de manera independiente. Dicha complejidad emerge como un fenómeno cooperativo a escalas microscópicas, que produce un complejo comportamiento macroscópico caracterizado por correlaciones de largo alcance e invarianza de escala. Aparecen así conceptos como leyes de escalado, universalidad y renormalización, pilares fundamentales dentro de la Física Estadística. El abanico de fenómenos complejos es muy amplio, y abarca sistemas de muy diversas disciplinas que van desde la Física más ortodoxa hasta la Biología, Sociología, Geología e, incluso, Economía. Esta Tesis se centra en fenómenos complejos extendidos en el espacio. En concreto hemos focalizado nuestra labor en tres grandes temas que constituyen importantes focos de interés dentro de la Mecánica Estadística: Crecimiento de Interfases, Sociofísica y Redes Complejas.; ABSTRACT: The ubiquity of complexity in Nature provides examples of a huge variety of systems to be analyzed by means of Statistical Mechanics and leads to the interconnection among various scientific disciplines. This Thesis focuses on three highlight topics of spatially extended complex systems: Interface Growth...

## Damage spreading, coarsening dynamics and distribution of political votes in Sznajd model on square lattice

Bernardes, Am?rico Trist?o; Costa, Uriel Medeiros de Souza; Ara?jo, Asc?nio Dias; Stauffer, Dietrich
EN_US
Relevância na Pesquisa
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In the Sznajd model of sociophysics on the square lattice, neighbors having the same opinion convince their neighbors of this opinion. We study scaling of the cluster growth. The spreading-of-damage technique is applied for the spread of opinions. We study the time evolution of the damage and compare it with the magnetization evolution. We also compare this model with the Ising model at low temperatures. It was recently shown that the distribution of votes in Brazilian elections follows a power law behavior with exponent '?1: 0. A model for elections based on the Sznajd model is proposed. The exponent obtained for the distribution of votes during the transient agrees with that obtained for elections.

## Uncovering the Internal Structure of the Indian Financial Market: Cross-correlation behavior in the NSE

Sinha, Sitabhra; Pan, Raj Kumar
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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The cross-correlations between price fluctuations of 201 frequently traded stocks in the National Stock Exchange (NSE) of India are analyzed in this paper. We use daily closing prices for the period 1996-2006, which coincides with the period of rapid transformation of the market following liberalization. The eigenvalue distribution of the cross-correlation matrix, $\mathbf{C}$, of NSE is found to be similar to that of developed markets, such as the New York Stock Exchange (NYSE): the majority of eigenvalues fall within the bounds expected for a random matrix constructed from mutually uncorrelated time series. Of the few largest eigenvalues that deviate from the bulk, the largest is identified with market-wide movements. The intermediate eigenvalues that occur between the largest and the bulk have been associated in NYSE with specific business sectors with strong intra-group interactions. However, in the Indian market, these deviating eigenvalues are comparatively very few and lie much closer to the bulk. We propose that this is because of the relative lack of distinct sector identity in the market, with the movement of stocks dominantly influenced by the overall market trend. This is shown by explicit construction of the interaction network in the market...

## A Biased Review of Sociophysics

Stauffer, Dietrich
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Various aspects of recent sociophysics research are shortly reviewed: Schelling model as an example for lack of interdisciplinary cooperation, opinion dynamics, combat, and citation statistics as an example for strong interdisciplinarity.; Comment: 16 pages for J. Stat. Phys. including 2 figures and numerous references

## Sociophysics: a personal testimony

Galam, Serge
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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The origins of Sociophysics are discussed from a personal testimony. I trace back its history to the late seventies. My twenty years of activities and research to establish and promote the field are reviewed. In particular the conflicting nature of Sociophysics with the physics community is revealed from my own experience. Recent presentations of a supposed natural growth from Social Sciences are criticized.; Comment: 7 pages, no figure, Proceedings of the XVIII Max Born Symposium on Statistical Physics outside Physics, Ladek, Poland, September 2003

## The time evaluation of resistance probability of a closed community against to occupation in a Sznajd like model with synchronous updating: A numerical study

Aydiner, Ekrem
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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In the present paper, we have briefly reviewed Sznajd's sociophysics model and its variants, and also we have proposed a simple Sznajd like sociophysics model based on Ising spin system in order to explain the time evaluation of resistance probability of a closed community against to occupation. Using a numerical method, we have shown that time evaluation of resistance probability of community has a non-exponential character which decays as stretched exponential independent the number of soldiers in one dimensional model. Furthermore, it has been astonishingly found that our simple sociophysics model is belong to the same universality class with random walk process on the trapping space.; Comment: 12 pages, 5 figures. Added a paragraph and 1 figure. To be published in International Journal of Modern Physics C

## Sociophysics Simulations I: Language Competition

Schulze, Christian; Stauffer, Dietrich
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Using a bit-string model similar to biological simulations, the competition between different languages is simulated both without and with spatial structure. We compare our agent-based work with differential equations and the competing bit-string model of Kosmidis et al.; Comment: 8th Granada Seminar (sociophysics); for AIP Conf. Proc. (8 pages incl. figs)

## Sznajd model and its applications

Sznajd-Weron, Katarzyna
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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In 2000 we proposed a sociophysics model of opinion formation, which was based on trade union maxim "United we Stand, Divided we Fall" (USDF) and latter due to Dietrich Stauffer became known as the Sznajd model (SM). The main difference between SM compared to voter or Ising-type models is that information flows outward. In this paper we review the modifications and applications of SM that have been proposed in the literature.; Comment: Paper presented at First Polish Symposium on Econo- and Sociophysics

## Sznajd sociophysics model on a triangular lattice: ferro and antiferromagnetic opinions

Chang, Iksoo
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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The Sznajd sociophysics model is generalized on the triangular lattice with pure antiferromagnetic opinion and also with both ferromagnetic and antiferromagnetic opinions. The slogan of the trade union "united we stand, divided we fall" can be realized via the propagation of ferromagnetic opinion of adjacent people in the union, but the propagation of antiferromagnetic opinion can be observed among the third countries between two big super powers or among the family members of conflicting parents. Fixed points are found in both models. The distributions of relaxation time of the mixed model are disperse and become loser to log-normal as the initial concentration of down spins approaches 0.5, whereas for pure antiferromagnetic spins they are collapsed into one master curve which is roughly lognormal. We do not see the phase transition in the model.; Comment: 3pages,2figures

## Sociophysics: A review of Galam models

Galam, Serge
Tipo: Artigo de Revista Científica