The influence of persuasion in opinion formation and polarization

We present a model that explores the influence of persuasion in a population of agents with positive and negative opinion orientations. The opinion of each agent is represented by an integer number $k$ that expresses its level of agreement on a given issue, from totally against $k=-M$ to totally in favor $k=M$. Same-orientation agents persuade each other with probability $p$, becoming more extreme, while opposite-orientation agents become more moderate as they reach a compromise with probability $q$. The population initially evolves to (a) a polarized state for $r=p/q>1$, where opinions' distribution is peaked at the extreme values $k=\pm M$, or (b) a centralized state for $r<1$, with most opinions around $k=\pm 1$. When $r \gg 1$, polarization lasts for a time that diverges as $r^M \ln N$, where $N$ is the population's size. Finally, an extremist consensus ($k=M$ or $-M$) is reached in a time that scales as $r^{-1}$ for $r \ll 1$

Competition between surface relaxation and ballistic deposition models in scale free networks

In this paper we study the scaling behavior of the fluctuations in the steady state $W_S$ with the system size $N$ for a surface growth process given by the competition between the surface relaxation (SRM) and the Ballistic Deposition (BD) models on degree uncorrelated Scale Free networks (SF), characterized by a degree distribution $P(k)\sim k^{-\lambda}$, where $k$ is the degree of a node. It is known that the fluctuations of the SRM model above the critical dimension ($d_c=2$) scales logarithmically with $N$ on euclidean lattices. However, Pastore y Piontti {\it et. al.} [A. L. Pastore y Piontti {\it et. al.}, Phys. Rev. E {\bf 76}, 046117 (2007)] found that the fluctuations of the SRM model in SF networks scale logarithmically with $N$ for $\lambda <3$ and as a constant for $\lambda \geq 3$. In this letter we found that for a pure ballistic deposition model on SF networks $W_S$ scales as a power law with an exponent that depends on $\lambda$. On the other hand when both processes are in competition, we find that there is a continuous crossover between a SRM behavior and a power law behavior due to the BD model that depends on the occurrence probability of each process and the system size. Interestingly, we find that a relaxation process contaminated by any small contribution of ballistic deposition will behave, for increasing system sizes, as a pure ballistic one. Our findings could be relevant when surface relaxation mechanisms are used to synchronize processes that evolve on top of complex networks.Comment: 8 pages, 6 figure

Fluctuations of a surface relaxation model in interacting scale free networks

Isolated complex networks have been studied deeply in the last decades due to the fact that many real systems can be modeled using these types of structures. However, it is well known that the behavior of a system not only depends on itself, but usually also depends on the dynamics of other structures. For this reason, interacting complex networks and the processes developed on them have been the focus of study of many researches in the last years. One of the most studied subjects in this type of structures is the Synchronization problem, which is important in a wide variety of processes in real systems. In this manuscript we study the synchronization of two interacting scale-free networks, in which each node has $ke$ dependency links with different nodes in the other network. We map the synchronization problem with an interface growth, by studying the fluctuations in the steady state of a scalar field defined in both networks. We find that as $ke$ slightly increases from $ke=0$, there is a really significant decreasing in the fluctuations of the system. However, this considerable improvement takes place mainly for small values of $ke$, when the interaction between networks becomes stronger there is only a slight change in the fluctuations. We characterize how the dispersion of the scalar field depends on the internal degree, and we show that a combination between the decreasing of this dispersion and the integer nature of our growth model are the responsible for the behavior of the fluctuations with $ke$.Comment: 11 pages, 4 figures and 1 tabl

Epidemic Model with Isolation in Multilayer Networks

The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the propagation of such airborne diseases as influenza A (H1N1). Although the SIR model has recently been studied in a multilayer networks configuration, in almost all the research the isolation of infected individuals is disregarded. Hence we focus our study in an epidemic model in a two-layer network, and we use an isolation parameter to measure the effect of isolating infected individuals from both layers during an isolation period. We call this process the Susceptible-Infected-Isolated-Recovered ($SI_IR$) model. The isolation reduces the transmission of the disease because the time in which infection can spread is reduced. In this scenario we find that the epidemic threshold increases with the isolation period and the isolation parameter. When the isolation period is maximum there is a threshold for the isolation parameter above which the disease never becomes an epidemic. We also find that epidemic models, like $SIR$ overestimate the theoretical risk of infection. Finally, our model may provide a foundation for future research to study the temporal evolution of the disease calibrating our model with real data.Comment: 18 pages, 5 figures.Accepted in Scientific Report

Gene-network inference by message passing

The inference of gene-regulatory processes from gene-expression data belongs to the major challenges of computational systems biology. Here we address the problem from a statistical-physics perspective and develop a message-passing algorithm which is able to infer sparse, directed and combinatorial regulatory mechanisms. Using the replica technique, the algorithmic performance can be characterized analytically for artificially generated data. The algorithm is applied to genome-wide expression data of baker's yeast under various environmental conditions. We find clear cases of combinatorial control, and enrichment in common functional annotations of regulated genes and their regulators.Comment: Proc. of International Workshop on Statistical-Mechanical Informatics 2007, Kyot

Gene-network inference by message passing

The inference of gene-regulatory processes from gene-expression data belongs to the major challenges of computational systems biology. Here we address the problem from a statistical-physics perspective and develop a message-passing algorithm which is able to infer sparse, directed and combinatorial regulatory mechanisms. Using the replica technique, the algorithmic performance can be characterized analytically for artificially generated data. The algorithm is applied to genome-wide expression data of baker's yeast under various environmental conditions. We find clear cases of combinatorial control, and enrichment in common functional annotations of regulated genes and their regulators.Comment: Proc. of International Workshop on Statistical-Mechanical Informatics 2007, Kyot

Gene-network inference by message passing

The inference of gene-regulatory processes from gene-expression data belongs to the major challenges of computational systems biology. Here we address the problem from a statistical-physics perspective and develop a message-passing algorithm which is able to infer sparse, directed and combinatorial regulatory mechanisms. Using the replica technique, the algorithmic performance can be characterized analytically for artificially generated data. The algorithm is applied to genome-wide expression data of baker's yeast under various environmental conditions. We find clear cases of combinatorial control, and enrichment in common functional annotations of regulated genes and their regulators.Comment: Proc. of International Workshop on Statistical-Mechanical Informatics 2007, Kyot