Nonequilibrium phase transition in a model for social influence

Information synergy maximizes the growth rate of heterogeneous groups

Collective action and group formation are fundamental behaviors among both organisms cooperating to maximize their fitness and people forming socioeconomic organizations. Researchers have extensively explored social interaction structures via game theory and homophilic linkages, such as kin selection and scalar stress, to understand emergent cooperation in complex systems. However, we still lack a general theory capable of predicting how agents benefit from heterogeneous preferences, joint information, or skill complementarities in statistical environments. Here, we derive general statistical dynamics for the origin of cooperation based on the management of resources and pooled information. Specifically, we show how groups that optimally combine complementary agent knowledge about resources in statistical environments maximize their growth rate. We show that these advantages are quantified by the information synergy embedded in the conditional probability of environmental states given agents' signals, such that groups with a greater diversity of signals maximize their collective information. It follows that, when constraints are placed on group formation, agents must intelligently select with whom they cooperate to maximize the synergy available to their own signal. Our results show how the general properties of information underlie the optimal collective formation and dynamics of groups of heterogeneous agents across social and biological phenomena.

Metamagnetic fluctuation characteristics near dynamic phase transitions

We experimentally explore the magnetization dynamics of thin ferromagnetic Co films with uniaxial in-plane anisotropy near the dynamic phase transition (DPT) and, in particular, we study the temporal characteristics of anomalous metamagnetic fluctuations that occur in its vicinity, and for which no thermodynamic equivalent exists. For this purpose, we measure the real-time evolution of magnetization trajectories in the relevant dynamic phase space, conduct a Fourier analysis of these experimental results and compare it to a model, in which the fluctuating metamagnetic behavior occurs in a purely random manner, following individual state probability distributions. We find excellent quantitative agreement in between our experimental results and the random state model, clearly indicating that multiperiod time-correlations of magnetic states are not relevant in our DPT system, not even for the occurrence of the anomalous metamagnetic fluctuations that are nonetheless associated with nonperiodic magnetic state evolutions.

A hypernetwork-based urn model for explaining collective dynamics

The topological characterization of complex systems has significantly contributed to our understanding of the principles of collective dynamics. However, the representation of general complex networks is not enough for explaining certain problems, such as collective actions. Considering the effectiveness of hypernetworks on modeling real-world complex networks, in this paper, we proposed a hypernetwork-based Pólya urn model that considers the effect of group identity. The mathematical deduction and simulation experiments show that social influence provides a strong imitation environment for individuals, which can prevent the dynamics from being self-correcting. Additionally, the unpredictability of the social system increases with growing social influence, and the effect of group identity can moderate market inequality caused by individual preference and social influence. The present work provides a modeling basis for a better understanding of the logic of collective dynamics.

Emergence of Power-Law Particle Size Distribution in Microfluidic Calcium Carbonate Precipitation: An Extended Yule Process with a Ripening Effect

Precipitation of calcium carbonate in bulk solutions is well known to result in a bell-shaped or bimodal particle size distribution. However, it is unclear how the distribution behaves if precipitation occurs in a small, confined volume. In this Letter, we conduct microfluidic experiments where sodium carbonate and calcium chloride solutions are continuously injected into a microchannel to precipitate calcium carbonate particles. Results show that, regardless of the variations in reagent concentrations, mixing schemes, flow rates, and precipitation time, sizes of precipitated particles in the channel are power law distributed, with an exponent of 1.4. The data are described by an extended Yule process with the introduction of a ripening term. Since the Yule process is a general mechanism for power law generation, the extended Yule process proposed here provides a general model for systems where growth and ripening simultaneously present.

Second- to first-order phase transition: Coevolutionary versus structural balance

In social networks, the balance theory has been studied by considering either the triple interactions between the links (structural balance) or the triple interaction of nodes and links (coevolutionary balance). In the structural balance theory, the links are not independent from each other, implying a global effect of this term and it leads to a discontinuous phase transition in the system's balanced states as a function of temperature. However, in the coevolutionary balance the links only connect two local nodes and a continuous phase transition emerges. In this paper, we consider a combination of both to understand which of these types of interactions will identify the stability of the network. We are interested to see how adjusting the robustness of each term versus the other might affect the system to reach a balanced state. We use statistical mechanics methods and the mean-field theory and also the Monte Carlo numerical simulations to investigate the behavior of the order parameters and the total energy of the system. We find the phase diagram of the system which demonstrates the competition of these two terms at different ratios against each other and different temperatures. The system shows a tricritical point above which the phase transition switches from continuous to discrete. Also the superiority of the local perspective is observed at low temperatures and the global view will be the dominant term in determining the stability of the system at higher temperatures.

Phase diagram in a one-dimensional civil disorder model

Epstein's model for a civil disorder is an agent-based model that simulates a social protest process where the central authority uses the police force to dissuade it. The interactions of police officers and citizens produce dynamics that do not yet have any analysis from the sociophysics approach. We present numerical simulations to characterize the properties of the one-dimensional civil disorder model on stationary state. To do this, we consider interactions on a Moore neighborhood and a random neighborhood with two different visions. We introduce a Potts-like energy function and construct the phase diagram using the agent state concentration. We find order-disorder phases and reveal the principle of minimum grievance as the underlying principle of the model's dynamics. Besides, we identify when the system can reach stable or an instability conditions based on the agents' interactions. Finally, we identified the most relevant role of the police based on their capacity to dissuade a protest and their effect on facilitating a stable scenario.

How does homophily shape the topology of a dynamic network?

We consider a dynamic network of individuals that may hold one of two different opinions in a two-party society. As a dynamical model, agents can endlessly create and delete links to satisfy a preferred degree, and the network is shaped by homophily, a form of social interaction. Characterized by the parameter J∈[-1,1], the latter plays a role similar to Ising spins: agents create links to others of the same opinion with probability (1+J)/2 and delete them with probability (1-J)/2. Using Monte Carlo simulations and mean-field theory, we focus on the network structure in the steady state. We study the effects of J on degree distributions and the fraction of cross-party links. While the extreme cases of homophily or heterophily (J=±1) are easily understood to result in complete polarization or anti-polarization, intermediate values of J lead to interesting features of the network. Our model exhibits the intriguing feature of an "overwhelming transition" occurring when communities of different sizes are subject to sufficient heterophily: agents of the minority group are oversubscribed and their average degree greatly exceeds that of the majority group. In addition, we introduce an original measure of polarization which displays distinct advantages over the commonly used average edge homogeneity.

Dimension-reduction of dynamics on real-world networks with symmetry

We derive explicit formulae to quantify the Markov chain state-space compression, or lumping, that can be achieved in a broad range of dynamical processes on real-world networks, including models of epidemics and voting behaviour, by exploiting redundancies due to symmetries. These formulae are applied in a large-scale study of such symmetry-induced lumping in real-world networks, from which we identify specific networks for which lumping enables exact analysis that could not have been done on the full state-space. For most networks, lumping gives a state-space compression ratio of up to 10 7 , but the largest compression ratio identified is nearly 10 12 . Many of the highest compression ratios occur in animal social networks. We also present examples of types of symmetry found in real-world networks that have not been previously reported.

Heider and coevolutionary balance: From discrete to continuous phase transition

Structural balance in social complex networks has been modeled with two types of triplet interactions. First is the interaction that only considers the dynamic role for links or relationships (Heider balance), and second is the interaction that considers both individual opinions (nodes) and relationships in network dynamics (coevolutionary balance). The question is, as the temperature varies, which is a measure of the average irrationality of individuals in a society, how structural balance can be created or destroyed by each of these triplet interactions. We use statistical mechanics methods and observe through analytical calculation and numerical simulation that unlike the Heider balance triplet interaction which has a discrete phase transition, the coevolutionary balance has a continuous phase transition. The critical temperature of the presented model changes with the root square of the network size, which is a linear dependence in the thermal Heider balance.

Divergence and consensus in majority rule

We investigate majority rule dynamics in a population with two classes of people, each with two opinion states ±1, and with tunable interactions between people in different classes. In an update, a randomly selected group adopts the majority opinion if all group members belong to the same class; if not, majority rule is applied with rate ε. Consensus is achieved in a time that scales logarithmically with population size if ε≥ε_{c}=1/9. For ε<ε_{c}, the population can get trapped in a polarized state, with one class preferring the +1 state and the other preferring -1. The time to escape this polarized state and reach consensus scales exponentially with population size.

Polarization inhibits the phase transition of Axelrod's model

We study the effect of polarization in Axelrod's model of cultural dissemination. This is done through the introduction of a cultural feature that takes only two values, while the other features can present a larger number of possible traits. Our numerical results and mean-field approximations show that polarization reduces the characteristic phase transition of the original model to a finite-size effect, since at the thermodynamic limit only the ordered phase is present. Furthermore, for finite system sizes, the stationary state depends on the percolation threshold of the network where the model is implemented: a polarized phase is obtained for percolation thresholds below 1/2, and a fragmented multicultural one otherwise.

Generalized mean-field approximation for the Deffuant opinion dynamics model on networks

When the interactions of agents on a network are assumed to follow the Deffuant opinion dynamics model, the outcomes are known to depend on the structure of the underlying network. This behavior cannot be captured by existing mean-field approximations for the Deffuant model. In this paper, a generalized mean-field approximation is derived that accounts for the effects of network topology on Deffuant dynamics through the degree distribution or community structure of the network. The accuracy of the approximation is examined by comparison with large-scale Monte Carlo simulations on both synthetic and real-world networks.

Analytical approach to the Axelrod model based on similarity vectors

Complex problems of social interaction are usually studied within the framework of agent-based models. Some of these problems, such as issue alignment and opinion polarization, are better suited in the framework of n-dimensional opinion space. Although this kind of complex problem may be explored by numerical simulations, these simulations can hinder our ability to obtain general results. In this work, we show how, under certain conditions, a classical multidimensional opinion model such as the Axelrod model can give rise to a closed set of master equations in terms of vector similarities between agents. The analytical results fully agree with the simulations on complete networks, accurately predict the similarity distribution of the whole system in sparse topologies, and provide a good approximation of the similarity of physical links that improves when the mean degree of the system increases.

A bird's-eye view of naming game dynamics: From trait competition to Bayesian inference

The present contribution reviews a set of different versions of the basic naming game model, differing in the underlying topology or in the mechanisms regulating the interactions between agents. We include also a Bayesian naming game model recently introduced, which merges the social dynamics of the basic naming game model with the Bayesian learning framework introduced by Tenenbaum and co-workers. The latter model goes beyond the fixed nature of names and concepts of standard semiotic dynamics models and the corresponding one-shot learning process by describing dynamically how agents can generalize a concept from a few examples, according to principles of Bayesian inference.

Erdós-Rényi phase transition in the Axelrod model on complete graphs

The Axelrod model has been widely studied since its proposal for social influence and cultural dissemination. In particular, the community of statistical physics focused on the presence of a phase transition as a function of its two main parameters, F and Q. In this work, we show that the Axelrod model undergoes a second-order phase transition in the limit of F→∞ on a complete graph. This transition is equivalent to the Erdős-Rényi phase transition in random networks when it is described in terms of the probability of interaction at the initial state, which depends on a scaling relation between F and Q. We also found that this probability plays a key role in sparse topologies by collapsing the transition curves for different values of the parameter F.

Against mass media trends: Minority growth in cultural globalization

We investigate the collective behavior of a globalized society under the influence of endogenous mass media trends. The mass media trend is a global field corresponding to the statistical mode of the states of the agents in the system. The interaction dynamics is based on Axelrod's rules for the dissemination of culture. We find situations where the largest minority group, possessing a cultural state different from that of the predominant trend transmitted by the mass media, can grow to almost half of the size of the population. We show that this phenomenon occurs when a critical number of long-range connections are present in the underlying network of interactions. We have numerically characterized four phases on the space of parameters of the system: an ordered phase; a semi-ordered phase where almost half of the population consists of the largest minority in a state different from that of the mass media; a disordered phase; and a chimera-like phase where one large domain coexists with many very small domains.

Discontinuous transitions can survive to quenched disorder in a two-dimensional nonequilibrium system

We explore the effects that quenched disorder has on discontinuous nonequilibrium phase transitions into absorbing states. We focus our analysis on the naming game model, a nonequilibrium low-dimensional system with different absorbing states. The results obtained by means of the finite-size scaling analysis and from the study of the temporal dynamics of the density of active sites near the transition point evidence that the spatial quenched disorder does not destroy the discontinuous transition.

Statistical Evolutionary Laws in Music Styles

If a cultural feature is transmitted over generations and exposed to stochastic selection when spreading in a population, its evolution may be governed by statistical laws and be partly predictable, as in the case of genetic evolution. Music exhibits steady changes of styles over time, with new characteristics developing from traditions. Recent studies have found trends in the evolution of music styles, but little is known about their relations to the evolution theory. Here we analyze Western classical music data and find statistical evolutionary laws. For example, distributions of the frequencies of some rare musical events (e.g. dissonant intervals) exhibit steady increase in the mean and standard deviation as well as constancy of their ratio. We then study an evolutionary model where creators learn their data-generation models from past data and generate new data that will be socially selected by evaluators according to the content dissimilarity (novelty) and style conformity (typicality) with respect to the past data. The model reproduces the observed statistical laws and can make non-trivial predictions for the evolution of independent musical features. In addition, the same model with different parameterization can predict the evolution of Japanese enka music, which is developed in a different society and has a qualitatively different tendency of evolution. Our results suggest that the evolution of musical styles can partly be explained and predicted by the evolutionary model incorporating statistical learning, which can be important for other cultures and future music technologies.

Finite-size scaling for discontinuous nonequilibrium phase transitions

A finite-size scaling theory, originally developed only for transitions to absorbing states [Phys. Rev. E 92, 062126 (2015)PLEEE81539-375510.1103/PhysRevE.92.062126], is extended to distinct sorts of discontinuous nonequilibrium phase transitions. Expressions for quantities such as response functions, reduced cumulants, and equal area probability distributions are derived from phenomenological arguments. Irrespective of system details, all these quantities scale with the volume, establishing the dependence on size. The approach generality is illustrated through the analysis of different models. The present results are a relevant step in trying to unify the scaling behavior description of nonequilibrium transition processes.

The emergence of consensus: a primer

The origin of population-scale coordination has puzzled philosophers and scientists for centuries. Recently, game theory, evolutionary approaches and complex systems science have provided quantitative insights on the mechanisms of social consensus. However, the literature is vast and widely scattered across fields, making it hard for the single researcher to navigate it. This short review aims to provide a compact overview of the main dimensions over which the debate has unfolded and to discuss some representative examples. It focuses on those situations in which consensus emerges 'spontaneously' in the absence of centralized institutions and covers topics that include the macroscopic consequences of the different microscopic rules of behavioural contagion, the role of social networks and the mechanisms that prevent the formation of a consensus or alter it after it has emerged. Special attention is devoted to the recent wave of experiments on the emergence of consensus in social systems.

Partial inertia induces additional phase transition in the majority vote model

Explosive (i.e., discontinuous) transitions have aroused great interest by manifesting in distinct systems, such as synchronization in coupled oscillators, percolation regime, absorbing phase transitions, and more recently, the majority-vote model with inertia. In the latter, the model rules are slightly modified by the inclusion of a term depending on the local spin (an inertial term). In such a case, Chen et al. [Phys Rev. E 95, 042304 (2017)2470-004510.1103/PhysRevE.95.042304] have found that relevant inertia changes the nature of the phase transition in complex networks, from continuous to discontinuous. Here we give a further step by embedding inertia only in vertices with degree larger than a threshold value 〈k〉k^{*}, 〈k〉 being the mean system degree and k^{*} the fraction restriction. Our results, from mean-field analysis and extensive numerical simulations, reveal that an explosive transition is presented in both homogeneous and heterogeneous structures for small and intermediate k^{*}'s. Otherwise, a large restriction can sustain a discontinuous transition only in the heterogeneous case. This shares some similarities with recent results for the Kuramoto model [Phys. Rev. E 91, 022818 (2015)PLEEE81539-375510.1103/PhysRevE.91.022818]. Surprisingly, intermediate restriction and large inertia are responsible for the emergence of an extra phase, in which the system is partially synchronized and the classification of phase transition depends on the inertia and the lattice topology. In this case, the system exhibits two phase transitions.

Large deviation induced phase switch in an inertial majority-vote model

We theoretically study noise-induced phase switch phenomena in an inertial majority-vote (IMV) model introduced in a recent paper [Chen et al., Phys. Rev. E 95, 042304 (2017)]. The IMV model generates a strong hysteresis behavior as the noise intensity f goes forward and backward, a main characteristic of a first-order phase transition, in contrast to a second-order phase transition in the original MV model. Using the Wentzel-Kramers-Brillouin approximation for the master equation, we reduce the problem to finding the zero-energy trajectories in an effective Hamiltonian system, and the mean switching time depends exponentially on the associated action and the number of particles N. Within the hysteresis region, we find that the actions, along the optimal forward switching path from the ordered phase (OP) to disordered phase (DP) and its backward path show distinct variation trends with f, and intersect at f = f_c that determines the coexisting line of the OP and DP. This results in a nonmonotonic dependence of the mean switching time between two symmetric OPs on f, with a minimum at f_c for sufficiently large N. Finally, the theoretical results are validated by Monte Carlo simulations.

Dynamics of organizational culture: Individual beliefs vs. social conformity

The complex nature of organizational culture challenges our ability to infer its underlying dynamics from observational studies. Recent computational studies have adopted a distinctly different view, where plausible mechanisms are proposed to describe a wide range of social phenomena, including the onset and evolution of organizational culture. In this spirit, this work introduces an empirically-grounded, agent-based model which relaxes a set of assumptions that describes past work–(a) omittance of an individual’s strive for achieving cognitive coherence; (b) limited integration of important contextual factors—by utilizing networks of beliefs and incorporating social rank into the dynamics. As a result, we illustrate that: (i) an organization may appear to be increasingly coherent in terms of its organizational culture, yet be composed of individuals with reduced levels of coherence; (ii) the components of social conformity—peer-pressure and social rank—are influential at different aggregation levels.

First-order phase transition in a majority-vote model with inertia

We generalize the original majority-vote model by incorporating inertia into the microscopic dynamics of the spin flipping, where the spin-flip probability of any individual depends not only on the states of its neighbors, but also on its own state. Surprisingly, the order-disorder phase transition is changed from a usual continuous or second-order type to a discontinuous or first-order one when the inertia is above an appropriate level. A central feature of such an explosive transition is a strong hysteresis behavior as noise intensity goes forward and backward. Within the hysteresis region, a disordered phase and two symmetric ordered phases are coexisting and transition rates between these phases are numerically calculated by a rare-event sampling method. A mean-field theory is developed to analytically reveal the property of this phase transition.

Layered social influence promotes multiculturality in the Axelrod model

Despite the presence of increasing pressure towards globalisation, the coexistence of different cultures is a distinctive feature of human societies. However, how multiculturality can emerge in a population of individuals inclined to imitation, and how it remains stable under cultural drift, i.e. the spontaneous mutation of traits in the population, still needs to be understood. To solve such a problem, we propose here a microscopic model of culture dissemination which takes into account that, in real social systems, the interactions are organised in various layers corresponding to different interests or topics. We show that the addition of multiplexity in the modeling of our society generates qualitatively novel dynamical behavior, producing a new stable regime of cultural diversity. This finding suggests that the layered organisation of social influence typical of modern societies is the key ingredient to explain why and how multiculturality emerges and thrives in our world.

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

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 this work we 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.

Effect of long-range interactions on the phase transition of Axelrod's model

Axelrod's model with F=2 cultural features, where each feature can assume k states drawn from a Poisson distribution of parameter q, exhibits a continuous nonequilibrium phase transition in the square lattice. Here we use extensive Monte Carlo simulations and finite-size scaling to study the critical behavior of the order parameter ρ, which is the fraction of sites that belong to the largest domain of an absorbing configuration averaged over many runs. We find that it vanishes as ρ∼(q_{c}^{0}-q)^{β} with β≈0.25 at the critical point q_{c}^{0}≈3.10 and that the exponent that measures the width of the critical region is ν^{0}≈2.1. In addition, we find that introduction of long-range links by rewiring the nearest-neighbors links of the square lattice with probability p turns the transition discontinuous, with the critical point q_{c}^{p} increasing from 3.1 to 27.17, approximately, as p increases from 0 to 1. The sharpness of the threshold, as measured by the exponent ν^{p}≈1 for p>0, increases with the square root of the number of nodes of the resulting small-world network.

Finite-size scaling analysis of a nonequilibrium phase transition in the naming game model

We realize an extensive numerical study of the naming game model with a noise term which accounts for perturbations. This model displays a nonequilibrium phase transition between an absorbing ordered consensus state, which occurs for small noise, and a disordered phase with fragmented clusters characterized by heterogeneous memories, which emerges at strong noise levels. The nature of the phase transition is studied by means of a finite-size scaling analysis of the moments. We observe a scaling behavior typical of a discontinuous transition and we are able to estimate the thermodynamic limit. The scaling behavior of the clusters size seems also compatible with this kind of transition.

Culture and cooperation in a spatial public goods game

We study the coevolution of culture and cooperation by combining the Axelrod model of cultural dissemination with a spatial public goods game, incorporating both noise and social influence. Both participation and cooperation in public goods games are conditional on cultural similarity. We find that a larger "scope of cultural possibilities" in the model leads to the survival of cooperation, when noise is not present, and a higher probability of a multicultural state evolving, for low noise rates. High noise rates, however, lead to both rapid extinction of cooperation and collapse into cultural "anomie," in which stable cultural regions fail to form. These results suggest that cultural diversity can actually be beneficial for the evolution of cooperation, but that cultural information needs to be transmitted accurately in order to maintain both coherent cultural groups and cooperation.

Emergence of metapopulations and echo chambers in mobile agents

Multi-agent models often describe populations segregated either in the physical space, i.e. subdivided in metapopulations, or in the ecology of opinions, i.e. partitioned in echo chambers. Here we show how both kinds of segregation can emerge from the interplay between homophily and social influence in a simple model of mobile agents endowed with a continuous opinion variable. In the model, physical proximity determines a progressive convergence of opinions but differing opinions result in agents moving away from each others. This feedback between mobility and social dynamics determines the onset of a stable dynamical metapopulation scenario where physically separated groups of like-minded individuals interact with each other through the exchange of agents. The further introduction of confirmation bias in social interactions, defined as the tendency of an individual to favor opinions that match his own, leads to the emergence of echo chambers where different opinions coexist also within the same group. We believe that the model may be of interest to researchers investigating the origin of segregation in the offline and online world.

Nature of phase transitions in Axelrod-like coupled Potts models in two dimensions

We study F coupled q-state Potts models in a two-dimensional square lattice. The interaction between the different layers is attractive to favor a simultaneous alignment in all of them, and its strength is fixed. The nature of the phase transition for zero field is numerically determined for F = 2,3. Using the Lee-Kosterlitz method, we find that it is continuous for F = 2 and q = 2, whereas it is abrupt for higher values of q and/or F. When a continuous or a weakly first-order phase transition takes place, we also analyze the properties of the geometrical clusters. This allows us to determine the fractal dimension D of the incipient infinite cluster and to examine the finite-size scaling of the cluster number density via data collapse. A mean-field approximation of the model, from which some general trends can be determined, is presented too. Finally, since this lattice model has been recently considered as a thermodynamic counterpart of the Axelrod model of social dynamics, we discuss our results in connection with this one.

Three is much more than two in coarsening dynamics of cyclic competitions

The classical game of rock-paper-scissors has inspired experiments and spatial model systems that address the robustness of biological diversity. In particular, the game nicely illustrates that cyclic interactions allow multiple strategies to coexist for long-time intervals. When formulated in terms of a one-dimensional cellular automata, the spatial distribution of strategies exhibits coarsening with algebraically growing domain size over time, while the two-dimensional version allows domains to break and thereby opens the possibility for long-time coexistence. We consider a quasi-one-dimensional implementation of the cyclic competition, and study the long-term dynamics as a function of rare invasions between parallel linear ecosystems. We find that increasing the complexity from two to three parallel subsystems allows a transition from complete coarsening to an active steady state where the domain size stays finite. We further find that this transition happens irrespective of whether the update is done in parallel for all sites simultaneously or done randomly in sequential order. In both cases, the active state is characterized by localized bursts of dislocations, followed by longer periods of coarsening. In the case of the parallel dynamics, we find that there is another phase transition between the active steady state and the coarsening state within the three-line system when the invasion rate between the subsystems is varied. We identify the critical parameter for this transition and show that the density of active boundaries has critical exponents that are consistent with the directed percolation universality class. On the other hand, numerical simulations with the random sequential dynamics suggest that the system may exhibit an active steady state as long as the invasion rate is finite.

Diversity and Community Can Coexist

We examine the (in)compatibility of diversity and sense of community by means of agent-based models based on the well-known Schelling model of residential segregation and Axelrod model of cultural dissemination. We find that diversity and highly clustered social networks, on the assumptions of social tie formation based on spatial proximity and homophily, are incompatible when agent features are immutable, and this holds even for multiple independent features. We include both mutable and immutable features into a model that integrates Schelling and Axelrod models, and we find that even for multiple independent features, diversity and highly clustered social networks can be incompatible on the assumptions of social tie formation based on spatial proximity and homophily. However, this incompatibility breaks down when cultural diversity can be sufficiently large, at which point diversity and clustering need not be negatively correlated. This implies that segregation based on immutable characteristics such as race can possibly be overcome by sufficient similarity on mutable characteristics based on culture, which are subject to a process of social influence, provided a sufficiently large "scope of cultural possibilities" exists.

Generic finite size scaling for discontinuous nonequilibrium phase transitions into absorbing states

Based on quasistationary distribution ideas, a general finite size scaling theory is proposed for discontinuous nonequilibrium phase transitions into absorbing states. Analogously to the equilibrium case, we show that quantities such as response functions, cumulants, and equal area probability distributions all scale with the volume, thus allowing proper estimates for the thermodynamic limit. To illustrate these results, five very distinct lattice models displaying nonequilibrium transitions-to single and infinitely many absorbing states-are investigated. The innate difficulties in analyzing absorbing phase transitions are circumvented through quasistationary simulation methods. Our findings (allied to numerical studies in the literature) strongly point to a unifying discontinuous phase transition scaling behavior for equilibrium and this important class of nonequilibrium systems.

Adoption of a High-Impact Innovation in a Homogeneous Population

Adoption of innovations, whether new ideas, technologies, or products, is crucially important to knowledge societies. The landmark studies of adoption dealt with innovations having great societal impact (such as antibiotics or hybrid crops) but where determining the utility of the innovation was straightforward (such as fewer side effects or greater yield). Recent large-scale studies of adoption were conducted within heterogeneous populations and focused on products with little societal impact. Here, we focus on a case with great practical significance: adoption by small groups of highly trained individuals of innovations with large societal impact but for which it is impractical to determine the true utility of the innovation. Specifically, we study experimentally the adoption by critical care physicians of a diagnostic assay that complements current protocols for the diagnosis of life-threatening bacterial infections and for which a physician cannot estimate the true accuracy of the assay based on personal experience. We show through computational modeling of the experiment that infection-spreading models-which have been formalized as generalized contagion processes-are not consistent with the experimental data, while a model inspired by opinion models is able to reproduce the empirical data. Our modeling approach enables us to investigate the efficacy of different intervention schemes on the rate and robustness of innovation adoption in the real world. While our study is focused on critical care physicians, our findings have implications for other settings in education, research, and business, where small groups of highly qualified peers make decisions about the adoption of innovations whose utility is difficult if not impossible to gauge.

A model for cross-cultural reciprocal interactions through mass media

We investigate the problem of cross-cultural interactions through mass media in a model where two populations of social agents, each with its own internal dynamics, get information about each other through reciprocal global interactions. As the agent dynamics, we employ Axelrod's model for social influence. The global interaction fields correspond to the statistical mode of the states of the agents and represent mass media messages on the cultural trend originating in each population. Several phases are found in the collective behavior of either population depending on parameter values: two homogeneous phases, one having the state of the global field acting on that population, and the other consisting of a state different from that reached by the applied global field; and a disordered phase. In addition, the system displays nontrivial effects: (i) the emergence of a largest minority group of appreciable size sharing a state different from that of the applied global field; (ii) the appearance of localized ordered states for some values of parameters when the entire system is observed, consisting of one population in a homogeneous state and the other in a disordered state. This last situation can be considered as a social analogue to a chimera state arising in globally coupled populations of oscillators.

Effect of external fields in Axelrod's model of social dynamics

The study of the effects of spatially uniform fields on the steady-state properties of Axelrod's model has yielded plenty of counterintuitive results. Here, we reexamine the impact of this type of field for a selection of parameters such that the field-free steady state of the model is heterogeneous or multicultural. Analyses of both one- and two-dimensional versions of Axelrod's model indicate that the steady state remains heterogeneous regardless of the value of the field strength. Turning on the field leads to a discontinuous decrease on the number of cultural domains, which we argue is due to the instability of zero-field heterogeneous absorbing configurations. We find, however, that spatially nonuniform fields that implement a consensus rule among the neighborhood of the agents enforce homogenization. Although the overall effects of the fields are essentially the same irrespective of the dimensionality of the model, we argue that the dimensionality has a significant impact on the stability of the field-free homogeneous steady state.

Evolution of cooperation in multiplex networks

We study evolutionary game dynamics on structured populations in which individuals take part in several layers of networks of interactions simultaneously. This multiplex of interdependent networks accounts for the different kind of social ties each individual has. By coupling the evolutionary dynamics of a Prisoner's Dilemma game in each of the networks, we show that the resilience of cooperative behaviors for extremely large values of the temptation to defect is enhanced by the multiplex structure. Furthermore, this resilience is intrinsically related to a non-trivial organization of cooperation across the network layers, thus providing a new way out for cooperation to survive in structured populations.

Coevolutionary network approach to cultural dynamics controlled by intolerance

Starting from Axelrod's model of cultural dissemination, we introduce a rewiring probability, enabling agents to cut the links with their unfriendly neighbors if their cultural similarity is below a tolerance parameter. For low values of tolerance, rewiring promotes the convergence to a frozen monocultural state. However, intermediate tolerance values prevent rewiring once the network is fragmented, resulting in a multicultural society even for values of initial cultural diversity in which the original Axelrod model reaches globalization.

Cluster-size entropy in the Axelrod model of social influence: small-world networks and mass media

We study the Axelrod's cultural adaptation model using the concept of cluster-size entropy S(c), which gives information on the variability of the cultural cluster size present in the system. Using networks of different topologies, from regular to random, we find that the critical point of the well-known nonequilibrium monocultural-multicultural (order-disorder) transition of the Axelrod model is given by the maximum of the S(c)(q) distributions. The width of the cluster entropy distributions can be used to qualitatively determine whether the transition is first or second order. By scaling the cluster entropy distributions we were able to obtain a relationship between the critical cultural trait q(c) and the number F of cultural features in two-dimensional regular networks. We also analyze the effect of the mass media (external field) on social systems within the Axelrod model in a square network. We find a partially ordered phase whose largest cultural cluster is not aligned with the external field, in contrast with a recent suggestion that this type of phase cannot be formed in regular networks. We draw a q-B phase diagram for the Axelrod model in regular networks.

Reinforced communication and social navigation: remember your friends and remember yourself

In social systems, people communicate with each other and form groups based on their interests. The pattern of interactions, the network, and the ideas that flow on the network naturally evolve together. Researchers use simple models to capture the feedback between changing network patterns and ideas on the network, but little is understood about the role of past events in the feedback process. Here, we introduce a simple agent-based model to study the coupling between peoples' ideas and social networks, and better understand the role of history in dynamic social networks. We measure how information about ideas can be recovered from information about network structure and, the other way around, how information about network structure can be recovered from information about ideas. We find that it is, in general, easier to recover ideas from the network structure than vice versa.

Self-organization in social tagging systems

Individuals often imitate each other to fall into the typical group, leading to a self-organized state of typical behaviors in a community. In this paper, we model self-organization in social tagging systems and illustrate the underlying interaction and dynamics. Specifically, we introduce a model in which individuals adjust their own tagging tendency to imitate the average tagging tendency. We found that when users are of low confidence, they tend to imitate others and lead to a self-organized state with active tagging. On the other hand, when users are of high confidence and are stubborn to change, tagging becomes inactive. We observe a phase transition at a critical level of user confidence when the system changes from one regime to the other. The distributions of post length obtained from the model are compared to real data, which show good agreement.

Selective advantage of tolerant cultural traits in the Axelrod-Schelling model

The Axelrod-Schelling model incorporates into the original Axelrod's model of cultural dissemination the possibility that cultural agents placed in culturally dissimilar environments move to other places, the strength of this mobility being controlled by an intolerance parameter. By allowing heterogeneity in the intolerance of cultural agents, and considering it as a cultural feature, i.e., susceptible of cultural transmission (thus breaking the original symmetry of Axelrod-Schelling dynamics), we address here the question of whether tolerant or intolerant traits are more likely to become dominant in the long-term cultural dynamics. Our results show that tolerant traits possess a clear selective advantage in the framework of the Axelrod-Schelling model. We show that the reason for this selective advantage is the development, as time evolves, of a positive correlation between the number of neighbors that an agent has in its environment and its tolerant character.

Dual-phase evolution in complex adaptive systems

Understanding the origins of complexity is a key challenge in many sciences. Although networks are known to underlie most systems, showing how they contribute to well-known phenomena remains an issue. Here, we show that recurrent phase transitions in network connectivity underlie emergent phenomena in many systems. We identify properties that are typical of systems in different connectivity phases, as well as characteristics commonly associated with the phase transitions. We synthesize these common features into a common framework, which we term dual-phase evolution (DPE). Using this framework, we review the literature from several disciplines to show that recurrent connectivity phase transitions underlie the complex properties of many biological, physical and human systems. We argue that the DPE framework helps to explain many complex phenomena, including perpetual novelty, modularity, scale-free networks and criticality. Our review concludes with a discussion of the way DPE relates to other frameworks, in particular, self-organized criticality and the adaptive cycle.

Statistics of opinion domains of the majority-vote model on a square lattice

The existence of juxtaposed regions of distinct cultures in spite of the fact that people's beliefs have a tendency to become more similar to each other's as the individuals interact repeatedly is a puzzling phenomenon in the social sciences. Here we study an extreme version of the frequency-dependent bias model of social influence in which an individual adopts the opinion shared by the majority of the members of its extended neighborhood, which includes the individual itself. This is a variant of the majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors' opinions. We assume that the individuals are fixed in the sites of a square lattice of linear size L and that they interact with their nearest neighbors only. Within a mean-field framework, we derive the equations of motion for the density of individuals adopting a particular opinion in the single-site and pair approximations. Although the single-site approximation predicts a single opinion domain that takes over the entire lattice, the pair approximation yields a qualitatively correct picture with the coexistence of different opinion domains and a strong dependence on the initial conditions. Extensive Monte Carlo simulations indicate the existence of a rich distribution of opinion domains or clusters, the number of which grows with L2 whereas the size of the largest cluster grows with ln L2. The analysis of the sizes of the opinion domains shows that they obey a power-law distribution for not too large sizes but that they are exponentially distributed in the limit of very large clusters. In addition, similarly to other well-known social influence model--Axelrod's model--we found that these opinion domains are unstable to the effect of a thermal-like noise.

Phase transitions in a two-parameter model of opinion dynamics with random kinetic exchanges

Recently, a model of opinion formation with kinetic exchanges has been proposed in which a spontaneous symmetry-breaking transition was reported [M. Lallouache, A. S. Chakrabarti, A. Chakraborti, and B. K. Chakrabarti, Phys. Rev. E 82, 056112 (2010)]. We generalize the model to incorporate two parameters: λ, to represent conviction, and μ, to represent the influencing ability of individuals. A phase boundary given by λ=1-μ/2 is obtained separating the symmetric and symmetry broken phases: The effect of the influencing term enhances the possibility of reaching a consensus in the society. The time scale diverges near the phase boundary in a power-law manner. The order parameter and the condensate also show power-law growth close to the phase boundary albeit with different exponents. The exponents in general change along the phase boundary, indicating a nonuniversality. The relaxation times, however, become constant with increasing system size near the phase boundary, indicating the absence of any diverging length scale. Consistently, the fluctuations remain finite but show strong dependence on the trajectory along which it is estimated.