We study the collective motion of a large set of self-propelled particles subject to voter-like interactions... [

*texto omitido por presencia de símbolos incompatibles con el editor*].

G. Baglietto, F. Vazquez, J. Stat. Mech. 033403 (2018)

We study the collective motion of a large set of self-propelled particles subject to voter-like interactions... [*texto omitido por presencia de símbolos incompatibles con el editor*].

We study the collective motion of a large set of self-propelled particles subject to voter-like interactions... [

J. P. Pinasco, M. Rodríguez Cartabia, N. Saintier, Dyn. Games Appl. (2018)

In this work we consider an agent based model in order to studythe wealth distribution problem where the interchange is determined with a symmetric zero sum game. Simultaneously, the agents update their way of play trying to learn the optimal one. Here, the agents use mixed strategies. We study this model using both simulations and theoretical tools. We derive the equations for the learning mechanism, and we show that the mean strategy of the population satis es an equation close to the classical replicator equation. Concerning the wealth distribution, there are two interesting situations depending on the equilibrium of the game. If the equilibrium is a pure strategy, the wealth distribution is xed after some transient time, and those players which are close to optimal strategy are richer. When the game has an equilibrium in mixed strategies, the stationary wealth distribution is close to a Gamma distribution with variance depending on the coe cients of the game matrix. We compute theoretically their second moment in this case.

In this work we consider an agent based model in order to studythe wealth distribution problem where the interchange is determined with a symmetric zero sum game. Simultaneously, the agents update their way of play trying to learn the optimal one. Here, the agents use mixed strategies. We study this model using both simulations and theoretical tools. We derive the equations for the learning mechanism, and we show that the mean strategy of the population satis es an equation close to the classical replicator equation. Concerning the wealth distribution, there are two interesting situations depending on the equilibrium of the game. If the equilibrium is a pure strategy, the wealth distribution is xed after some transient time, and those players which are close to optimal strategy are richer. When the game has an equilibrium in mixed strategies, the stationary wealth distribution is close to a Gamma distribution with variance depending on the coe cients of the game matrix. We compute theoretically their second moment in this case.

W. Wang, H. E. Stanley, L. A. Braunstein, New J. Phys. **20**, 013034 (2018)

Time-delays are pervasive in such real-world complex networks as social contagions and biological systems, and they radically alter the evolution of the dynamic processes in networks.We use a non-Markovian spreading threshold model to study the effects of time-delays on social contagions. Using extensive numerical simulations and theoretical analyses we find that relatively long time-delays induce a microtransition in the evolution of a fraction of recovered individuals, i.e., the fraction of recovered individuals versus time exhibits multiple phase transitions. The microtransition is sharper and more obvious when high-degree individuals have a higher probability of experiencing time delays, and the microtransition is obscure when the time-delay distribution reaches heterogeneity.We use an edge-based compartmental theory to analyze our research and find that the theoretical results agree well with our numerical simulation results.

Time-delays are pervasive in such real-world complex networks as social contagions and biological systems, and they radically alter the evolution of the dynamic processes in networks.We use a non-Markovian spreading threshold model to study the effects of time-delays on social contagions. Using extensive numerical simulations and theoretical analyses we find that relatively long time-delays induce a microtransition in the evolution of a fraction of recovered individuals, i.e., the fraction of recovered individuals versus time exhibits multiple phase transitions. The microtransition is sharper and more obvious when high-degree individuals have a higher probability of experiencing time delays, and the microtransition is obscure when the time-delay distribution reaches heterogeneity.We use an edge-based compartmental theory to analyze our research and find that the theoretical results agree well with our numerical simulation results.

X. Chen, R. Wang, M. Tang, S. Cai, H. E. Stanley, L. A. Braunstein, New J. Phys. **20**, 013007 (2018)

Although suppressing the spread of a disease is usually achieved by investing in public resources, in the real world only a small percentage of the population have access to government assistance when there is an outbreak, and most must rely on resources from family or friends.Westudy the dynamics of disease spreading in social-contact multiplex networks when the recovery of infected nodes depends on resources from healthy neighbors in the social layer.Weinvestigate how degree heterogeneity affects the spreading dynamics. Using theoretical analysis and simulations we find that degree heterogeneity promotes disease spreading. The phase transition of the infected density is hybrid and increases smoothly from zero to a finite small value at the first invasion threshold and then suddenly jumps at the second invasion threshold.Wealso find a hysteresis loop in the transition of the infected density.We further investigate how an overlap in the edges between two layers affects the spreading dynamics.We find that when the amount of overlap is smaller than a critical value the phase transition is hybrid and there is a hysteresis loop, otherwise the phase transition is continuous and the hysteresis loop vanishes. In addition, the edge overlap allows an epidemic outbreak when the transmission rate is below the first invasion threshold, but suppresses any explosive transition when the transmission rate is above the first invasion threshold.

Although suppressing the spread of a disease is usually achieved by investing in public resources, in the real world only a small percentage of the population have access to government assistance when there is an outbreak, and most must rely on resources from family or friends.Westudy the dynamics of disease spreading in social-contact multiplex networks when the recovery of infected nodes depends on resources from healthy neighbors in the social layer.Weinvestigate how degree heterogeneity affects the spreading dynamics. Using theoretical analysis and simulations we find that degree heterogeneity promotes disease spreading. The phase transition of the infected density is hybrid and increases smoothly from zero to a finite small value at the first invasion threshold and then suddenly jumps at the second invasion threshold.Wealso find a hysteresis loop in the transition of the infected density.We further investigate how an overlap in the edges between two layers affects the spreading dynamics.We find that when the amount of overlap is smaller than a critical value the phase transition is hybrid and there is a hysteresis loop, otherwise the phase transition is continuous and the hysteresis loop vanishes. In addition, the edge overlap allows an epidemic outbreak when the transmission rate is below the first invasion threshold, but suppresses any explosive transition when the transmission rate is above the first invasion threshold.

L. G. Alvarez-Zuzek, C. E. La Rocca, J. R. Iglesias, L. A. Braunstein, PLoS ONE **12**, e0186492 (2017)

Through years, the use of vaccines has always been a controversial issue. People in a

society may have different opinions about how beneficial the vaccines are and as a consequence

some of those individuals decide to vaccinate or not themselves and their relatives.

This attitude in face of vaccines has clear consequences in the spread of diseases and their

transformation in epidemics. Motivated by this scenario, we study, in a simultaneous way,

the changes of opinions about vaccination together with the evolution of a disease. In our

model we consider a multiplex network consisting of two layers... [*texto omitido por presencia de símbolos incompatibles con el editor*].

Through years, the use of vaccines has always been a controversial issue. People in a

society may have different opinions about how beneficial the vaccines are and as a consequence

some of those individuals decide to vaccinate or not themselves and their relatives.

This attitude in face of vaccines has clear consequences in the spread of diseases and their

transformation in epidemics. Motivated by this scenario, we study, in a simultaneous way,

the changes of opinions about vaccination together with the evolution of a disease. In our

model we consider a multiplex network consisting of two layers... [

A. Woolcock, C. Connaughton, Y. Merali, F. Vazquez, Phys. Rev. E **96**, 032313 (2017)

We study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter... [*texto omitido por presencia de símbolos incompatibles con el editor*].

We study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter... [

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.

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

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.

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.

L. Gao, W. Wang, P. Shu, H. Gao, L. A. Braunstein, EPL** 118**, 18001 (2017)

Promoting information spreading is a booming research topic in network science community. However, the existing studies about promoting information spreading seldom took into account the human memory, which plays an important role in the spreading dynamics. In this letter we propose a non-Markovian information spreading model on complex networks, in which every informed node contacts a neighbor by using the memory of neighbor’s accumulated contact numbers in the past. We systematically study the information spreading dynamics on uncorrelated configuration networks and a group of 22 real-world networks, and find an effective contact strategy of promoting information spreading, i.e., the informed nodes preferentially contact neighbors with a small number of accumulated contacts. According to the effective contact strategy, the high degree nodes are more likely to be chosen as the contacted neighbors in the early stage of the spreading, while in the late stage of the dynamics, the nodes with small degrees are preferentially contacted. We also propose a mean-field theory to describe our model, which qualitatively agrees well with the stochastic simulations on both artificial and real-world networks.

Promoting information spreading is a booming research topic in network science community. However, the existing studies about promoting information spreading seldom took into account the human memory, which plays an important role in the spreading dynamics. In this letter we propose a non-Markovian information spreading model on complex networks, in which every informed node contacts a neighbor by using the memory of neighbor’s accumulated contact numbers in the past. We systematically study the information spreading dynamics on uncorrelated configuration networks and a group of 22 real-world networks, and find an effective contact strategy of promoting information spreading, i.e., the informed nodes preferentially contact neighbors with a small number of accumulated contacts. According to the effective contact strategy, the high degree nodes are more likely to be chosen as the contacted neighbors in the early stage of the spreading, while in the late stage of the dynamics, the nodes with small degrees are preferentially contacted. We also propose a mean-field theory to describe our model, which qualitatively agrees well with the stochastic simulations on both artificial and real-world networks.

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.

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

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