Papers by André Timpanaro
Physical Review E, 2015
This paper studies the Sznajd model for opinion formation in a population connected through a gen... more This paper studies the Sznajd model for opinion formation in a population connected through a general network. A master equation describing the time evolution of opinions is presented and solved in a mean-field approximation. Although quite simple, this approximation allows us to capture the most important features regarding the steady states of the model. When spontaneous opinion changes are included, a discontinuous transition from consensus to polarization can be found as the rate of spontaneous change is increased. In this case we show that a hybrid mean-field approach including interactions between second nearest neighbors is necessary to estimate correctly the critical point of the transition. The analytical prediction of the critical point is also compared with numerical simulations in a wide variety of networks, in particular Barabási-Albert networks, finding reasonable agreement despite the strong approximations involved. The same hybrid approach that made it possible to deal with second-order neighbors could just as well be adapted to treat other problems such as epidemic spreading or predator-prey systems.
The Sznajd model is a Potts-like model that has been studied in the context of sociophysics [1,2]... more The Sznajd model is a Potts-like model that has been studied in the context of sociophysics [1,2](where spins are interpreted as opinions). In a recent work [3], we generalized the Sznajd model to include assymetric interactions between the spins (interpreted as biases towards opinions) and used dynamical systems techniques to tackle its mean-field version, given by the flow: {sub } = {sub }'{sup M} = 1{sub }'({sub }'-'').Where hs is the proportion of agents with opinion (spin)', M is the number of opinions and '' is the probability weight for an agent with opinion being convinced by another agent with opinion '. We made Monte Carlo simulations of the model in a complex network (using Barabasi-Albert networks [4]) and they displayed the same attractors than the mean-field. Using linear stability analysis, we were able to determine the mean-field attractor structure analytically and to show that it has connections with well known graph theory problems (maximal independent sets and positive fluxes in directed graphs). Our dynamical systems approach is quite simple and can be used also in other models, like the voter model.
Physical Review E, 2009
In the last decade the Sznajd Model has been successfully employed in modeling some properties an... more In the last decade the Sznajd Model has been successfully employed in modeling some properties and scale features of both proportional and majority elections. We propose a new version of the Sznajd model with a generalized bounded confidence rule -a rule that limits the convincing capability of agents and that is essential to allow coexistence of opinions in the stationary state. With an appropriate choice of parameters it can be reduced to previous models. We solved this new model both in a mean-field approach (for an arbitrary number of opinions) and numerically in a Barabási-Albert network (for three and four opinions), studying the transient and the possible stationary states. We built the phase portrait for the special cases of three and four opinions, defining the attractors and their basins of attraction. Through this analysis, we were able to understand and explain discrepancies between mean-field and simulation results obtained in previous works for the usual Sznajd Model with bounded confidence and three opinions. Both the dynamical system approach and our generalized bounded confidence rule are quite general and we think it can be useful to the understanding of other similar models.
Physical Review E, 2011
The Sznajd model is a sociophysics model that mimics the propagation of opinions in a closed soci... more The Sznajd model is a sociophysics model that mimics the propagation of opinions in a closed society, where the interactions favour 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, that has been used to model several aspects of elections, but its stationary states are always consensus states. In order to model more complex behaviours we have, in a recent work, introduced the idea of biases and prejudices to the Sznajd model, by generalizing the bounded confidence rule that is common to many continuous opinion models. In that work we have found that the mean-field version of this model (corresponding to a complete network) allows for stationary states where non-interacting 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. Moreover, we show that the model does not become inactive, that is, the opinions keep changing, even in the stationary regime. We also provide results that give some insights on how this behaviour approaches the mean-field behaviour, as the networks are changed.
Physical Review E, 2012
The Sznajd model is a sociophysics model, that is used to model opinion propagation and consensus... more 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 favour 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 modelled), 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 present some graph theory concepts, together with examples, and comparisons between the mean-field and simulations in Barabási-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q > 2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean-field, this would coincide with the q-voter model).
Journal of Physics: Conference Series, 2011
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
We discuss the exit probability of the one-dimensional q-voter model and present tools to obtain ... more We discuss the exit probability of the one-dimensional q-voter model and present tools to obtain estimates about this probability, both through simulations in large networks (around 10(7) sites) and analytically in the limit where the network is infinitely large. We argue that the result E(ρ) = ρ(q)/ρ(q) + (1-ρ)(q), that was found in three previous works [F. Slanina, K. Sznajd-Weron, and P. Przybyła, Europhys. Lett. 82, 18006 (2008); R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008), for the case q = 2; and P. Przybyła, K. Sznajd-Weron, and M. Tabiszewski, Phys. Rev. E 84, 031117 (2011), for q > 2] using small networks (around 10(3) sites), is a good approximation, but there are noticeable deviations that appear even for small systems and that do not disappear when the system size is increased (with the notable exception of the case q = 2). We also show that, under some simple and intuitive hypotheses, the exit probability must obey the inequality ρ(q)/ρ(q) + (1-ρ) ≤ E...
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Papers by André Timpanaro