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

Satellite Image Restoration using the VMCA Model

One of the most common patterns of the geographic landscape is the fractal or nearfractal form. Unfortunately, most traditional methods of spatial interpolation assume some type of continuous and regionalizeable variation of the underlying geographic form, an assumption at odds with the observed fractal properties of many landscapes. An extremely simple iterative algorithm, the voter model cellular automata (CA), produces discontinuous fractal patterns useful for interpolation while at the same preserving a realistic amount of spatial autocorrelation, extracted from neighboring existing data, also found in these landscapes. This adaptive algorithm is based on the principle of iteratively interpolating a missing data point using the value of a randomly selected neighbor cell. The model can also be extended to interpolate field-like variables by adding random deviations from the randomly chosen neighbor cell value. In this paper we explore the effect of satellite image restoration using a simple VMCA over obscured by clouds areas. This model is computationally advantageous, given its localty and restricted underlying computational model. Thus, an adequate computer implementation may perform significantly faster than other restoration methods, with roughly similar overall results. Also the local/scalable/parallelizable nature of CAs allows hardware FPGA implementation that might be embedded within the imager devices in satellites and remote sensors. On the other end, a GPU implementation might take advantage of highly specialized parallel processors capablde of restoring huge images in real time.Eje: Computación gráfica, visualización e imágenesRed de Universidades con Carreras en Informática (RedUNCI

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Universality classes in nonequilibrium lattice systems

This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.Comment: Updated comprehensive review, 62 pages (two column), 29 figs included. Scheduled for publication in Reviews of Modern Physics in April 200