20 de junio de 2017

Characterizing segregation in the Schelling–Voter model

I. Caridi,  J.P. Pinasco, N. Saintier, P. Schiaffino, Physica A 487, 125 (2017)

In this work we analyze several aspects related with segregation patterns appearing in the Schelling–Voter model in which an unhappy agent can change her location or her state in order to live in a neighborhood where she is happy. Briefly, agents may be in two possible states, each one represents an individually-chosen feature, such as the language she speaks or the opinion she supports; and an individual is happy in a neighborhood if she has, at least, some proportion of agents of her own type, defined in terms of a fixed parameter T . We study the model in a regular two dimensional lattice. The parameters of the model are ρ, the density of empty sites, and p, the probability of changing locations. The stationary states reached in a system of N agents as a function of the model parameters entail the extinction of one of the states, the coexistence of both, segregated patterns with conglomerated clusters of agents of the same state, and a diluted region. Using indicators as the energy and perimeter of the populations of agents in the same state, the inner radius of their locations (i.e., the side of the maximum square which could fit with empty spaces or agents of only one type), and the Shannon Information of the empty sites, we measure the segregation phenomena. We have found that there is a region within the coexistence phase where both populations take advantage of space in an equitable way, which is sustained by the role of the empty sites.

1 de junio de 2017

Adoption of innovations with contrarian agents and repentance

M. B. Gordon, M. F. Laguna, S. Gonçalves, J. R. Iglesias, Physica A 486, 192 (2017)

The dynamics of adoption of innovations is an important subject in many fields and areas, like technological development, industrial processes, social behavior, fashion or marketing. The number of adopters of a new technology generally increases following a kind of logistic function. However, empirical data provide evidences that this behavior may be more complex, as many factors influence the decision to adopt an innovation. On the one hand, although some individuals are inclined to adopt an innovation if many people do the same, there are others who act in the opposite direction, trying to differentiate from the "herd". People who prefer to behave like the others are called mimetic, whereas individuals who resist adopting new products, the stronger the greater the number of adopters, are named contrarians. Besides, in the real world new adopters may have second thoughts and change their decisions accordingly. In this contribution we include this possibility by means of repentance, a feature which was absent in previous models. The model of adoption of an innovation has all the ingredients of a previous version, in which the agents decision to adopt depends on the appeal of the novelty, the inertia or resistance to adopt it, and the social interactions with other agents, but now agents can repent and turn back to the old technology. We present analytic calculations and numerical simulations to determine the conditions for the establishment of the new technology. The inclusion of repentance can modify the balance between the global incentive to adopt and the number of contrarians who prevent full adoption, generating a rich landscape of temporal evolution that includes cycles of adoption.

22 de mayo de 2017

Interacting opinion and disease dynamics in multiplex networks: Discontinuous phase transition and nonmonotonic consensus times

F.  Velásquez-Rojas, F. Vazquez, Phys. Rev. E 95, 052315 (2017)

Opinion formation and disease spreading are among the most studied dynamical processes on complex networks. In real societies, it is expected that these two processes depend on and affect each other. However, little is known about the effects of opinion dynamics over disease dynamics and vice versa, since most studies treat them separately. In thisworkwe study the dynamics of the voter model for opinion formation intertwined with that of the contact process for disease spreading, in a population of agents that interact via two types of connections, social and contact. These two interacting dynamics take place on two layers of networks, coupled through a fraction q of links present in both networks. The probability that an agent updates its state depends on both the opinion and disease states of the interacting partner. We find that the opinion dynamics has striking consequences on the statistical properties of disease spreading. The most important is that the smooth (continuous) transition from a healthy to an endemic phase observed in the contact process, as the infection probability increases beyond a threshold, becomes abrupt (discontinuous) in the two-layer system. Therefore, disregarding the effects of social dynamics on epidemics propagation may lead to a misestimation of the real magnitude of the spreading. Also, an endemic-healthy discontinuous transition is found when the coupling q overcomes a threshold value. Furthermore, we show that the disease dynamics delays the opinion consensus, leading to a consensus time that varies nonmonotonically with q in a large range of the model’s parameters. A mean-field approach reveals that the coupled dynamics of opinions and disease can be approximately described by the dynamics of the voter model decoupled from that of the contact process, with effective probabilities of opinion and disease transmission.

27 de abril de 2017

Vaccination and public trust: A model for the dissemination of vaccination behaviour with external intervention

C. O. Dorso, A. Medus, P. Balenzuela, Physica A 482, 433 (2017)

Vaccination is widely recognized as the most effective way of immunization against many infectious diseases. However, unfounded claims about supposed side effects of some vaccines have contributed to spread concern and fear among people, thus inducing vaccination refusal. MMR (Measles, Mumps and Rubella) vaccine coverage has undergone an important decrease in a large part of Europe and US as a consequence of erroneously alleged side effects, leading to recent measles outbreaks. There is evidence that clusterization of unvaccinated individuals may lead to epidemics way larger that the ones that might appear in the case that unvaccinated agents are distributed at random in the population. In this work we explore the emergence of those clusters as a consequence of the social interaction driven mainly by homophily, where vaccination behaviour is part of a process of cultural dissemination in the spirit of Axelrod’s model. The ingredients of this calculation encompass: (i) interacting agents which are to decide if they vaccinate or not their children, (ii) their interaction with a small subset of stubborn agents who believe that the MMR vaccine is not safe and (iii) government sponsored propaganda trying to convince people of the benefits of vaccination. We find that these clusters, which emerge as a dynamical outcome of the model, are the responsible of the increasing probability of the occurrence of measles outbreaks, even in scenarios where the WHO (World Health Organization) recommendation of 95% vaccine coverage is fulfilled. However, we also illustrate that the mitigating effect of a public health campaign, could effectively reduce the impact and size of outbreaks.

14 de marzo de 2017

Modeling opinion dynamics: Theoretical analysis and continuous approximation

J. P.  Pinasco, V. Semeshenko, P. Balenzuela, Chaos Solit. Fract. 98, 210 (2017) 

Frequently we revise our first opinions after talking over with other individuals because we get convinced. Argumentation is a verbal and social process aimed at convincing. It includes conversation and persuasion and the agreement is reached because the new arguments are incorporated. Given the wide range of opinion formation mathematical approaches, there are however no models of opinion dynamics with nonlocal pair interactions analytically solvable. In this paper we present a novel analytical framework developed to solve the master equations with non-local kernels. For this we used a simple model of opinion formation where individuals tend to get more similar after each interactions, no matter their opinion differences, giving rise to nonlinear differential master equation with non-local terms. Simulation results show an excellent agreement with results obtained by the theoretical estimation.

8 de febrero de 2017

Unification of theoretical approaches for epidemic spreading on complex networks

W. Wang, M. Tang, H. E. Stanley, L. A. Braunstein, Rep. Prog. Phys. 80, 036603 (2017)

Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world scenarios. To understand the interplay between epidemic spreading and the topology of a contact network, several outstanding theoretical approaches have been developed. An accurate theoretical approach describing the spreading dynamics must take both the network topology and dynamical correlations into consideration at the expense of increasing the complexity of the equations. In this short survey we unify the most widely used theoretical approaches for epidemic spreading on complex networks in terms of increasing complexity, including the mean-field, the heterogeneous mean-field, the quench mean-field, dynamical message-passing, link percolation, and pairwise approximation. We build connections among these approaches to provide new insights into developing an accurate theoretical approach to spreading dynamics on complex networks.

22 de noviembre de 2016

Coherent oscillations in word-use data from 1700 to 2008

M. A. Montemurro, D. H. Zanette, Palgrave Comm. 2, 16084 (2016)

In written language, the choice of specific words is constrained by both grammatical requirements and the specific semantic context of the message to be transmitted. To a significant degree, the semantic context is in turn affected by a broad cultural and historical environment, which also influences matters of style and manners. Over time, those environmental factors leave an imprint in the statistics of language use, with some words becoming more common and other words being preferred less. Here we characterize the patterns of language use over time based on word statistics extracted from more than 4.5 million books written over a period of 308 years. We find evidence of novel systematic oscillatory patterns in word use with a consistent period narrowly distributed around 14 years. The specific phase relationships between different words show structure at two independent levels: first, there is a weak global phase modulation that is primarily linked to overall shifts in the vocabulary across time; and second, a stronger component dependent on well defined semantic relationships between words. In particular, complex network analysis reveals that semantically related words show strong phase coherence. Ultimately, these previously unknown patterns in the statistics of language may be a consequence of changes in the cultural framework that influences the thematic focus of writers.

24 de octubre de 2016

Payoff nonmonotonic dynamics in an evolutionary game

A. Chacoma, M. N. Kuperman, D. H. Zanette, Adv. Compl. Sys. 19, 1650007 (2016)

We propose an evolutionary game with dynamics rules derived from the consideration of field observations on human social behavior driven by self-confidence and social imitation. This dynamics turns out to be payoff nonmonotonic. The effects on the dynamics induced by this property are studied both numerically and analytically.

30 de septiembre de 2016

Interacting social processes on interconnected networks

L. G. Alvarez Zuzek, C. E. La Rocca, F. Vazquez, L. A. Braunstein, PLoS ONE 11, e0163593 (2016)

We propose and study a model for the interplay between two different dynamical processes -one for opinion formation and the other for decision making- on two interconnected networks A and B. The opinion dynamics on network A corresponds to that of the M-model, where the state of each agent can take one of four possible values (S = −2,−1, 1, 2), describing its level of agreement on a given issue. The likelihood to become an extremist (S = ±2) or a moderate (S = ±1) is controlled by a reinforcement parameter r  ≥ 0. The decision making dynamics on network B is akin to that of the Abrams-Strogatz model, where agents can be either in favor (S = +1) or against (S = −1) the issue. The probability that an agent changes its state is proportional to the fraction of neighbors that hold the opposite state raised to a power β. Starting from a polarized case scenario in which all agents of network A hold positive orientations while all agents of network B have a negative orientation, we explore the conditions under which one of the dynamics prevails over the other, imposing its initial orientation. We find that, for a given value of β, the two-network system reaches a consensus in the positive state (initial state of network A) when the reinforcement overcomes a crossover value r*(β), while a negative consensus happens for r < r*(β). In the r − β phase space, the system displays a transition at a critical threshold βc, from a coexistence of both orientations for β < βc to a dominance of one orientation for β > βc. We develop an analytical mean-field approach that gives an insight into these regimes and shows that both dynamics are equivalent along the crossover line (r*, β*).

23 de agosto de 2016

Statistical fluctuations in pedestrian evacuation times and the effect of social contagion

A. Nicolas, S. Bouzat, M. N. Kuperman, Phys. Rev.  E 94, 022313 (2016)

Mathematical models of pedestrian evacuation and the associated simulation software have become essential tools for the assessment of the safety of public facilities and buildings.While a variety of models is now available, their calibration and test against empirical data are generally restricted to global averaged quantities; the statistics compiled from the time series of individual escapes (“microscopic” statistics) measured in recent experiments are thus overlooked. In the same spirit, much research has primarily focused on the average global evacuation time, whereas the whole distribution of evacuation times over some set of realizations should matter. In the present paper we propose and discuss the validity of a simple relation between this distribution and the microscopic statistics, which is theoretically valid in the absence of correlations. To this purpose, we develop a minimal cellular automaton, with features that afford a semiquantitative reproduction of the experimental microscopic statistics. We then introduce a process of social contagion of impatient behavior in the model and show that the simple relation under test may dramatically fail at high contagion strengths, the latter being responsible for the emergence of strong correlations in the system.We conclude with comments on the potential practical relevance for safety science of calculations based on microscopic statistics.