arXiv subjects

Maxi San Miguel

Publications and source records attributed to Maxi San Miguel.

At least 37 records · Page 2Linked to original sources

arXiv2022

Echo chambers and information transmission biases in homophilic and heterophilic networks

We study how information transmission biases arise by the interplay between the structural properties of the network and the dynamics of the information in synthetic scale-free homophilic/heterophilic networks. We provide simple mathematical tools to quantify these biases. Both Simple and Complex Contagion models are insufficient to predict significant biases. In contrast, a Hybrid Contagion model -- in which both Simple and Complex Contagion occur -- gives rise to three different homophily-dependent biases: emissivity and receptivity biases,and echo chambers. Simulations in an empirical network with high homophily confirm the existence of these biases. Our results shed light into the mechanisms that cause inequalities in the visibility of information sources, reduced access to information, and lack of communication among distinct groups.

physics.soc-ph↗

arXiv2022

Biased-voter model: how persuasive a small group can be?

We study the voter model dynamics in the presence of confidence and bias. We assume two types of voters. Unbiased voters whose confidence is indifferent to the state of the voter and biased voters whose confidence is biased towards a common fixed preferred state. We study the problem analytically on the complete graph using mean field theory and on an Erdős-Rényi random network topology using the pair approximation, where we assume that the network of interactions topology is independent of the type of voters. We find that for the case of a random initial setup, and for sufficiently large number of voters $N$, the time to consensus increases proportionally to $\log(N)/γv$, with $γ$ the fraction of biased voters and $v$ the parameter quantifying the bias of the voters ($v=0$ no bias). We verify our analytical results through numerical simulations. We study this model on a biased-dependent topology of the network of interactions and examine two distinct, global average-degree preserving strategies (model I and model II) to obtain such biased-dependent random topologies starting from the biased-independent random topology case as the initial setup. Keeping all other parameters constant, in model I, $μ_{BU}$, the average number of links among biased (B) and unbiased (U) voters is varied at the expense of $μ_{UU}$ and $μ_{BB}$, i.e. the average number of links among only unbiased and biased voters respectively. In model II, $μ_{BU}$ is kept constant, while $μ_{BB}$ is varied at the expense of $μ_{UU}$. We find that if the agents follow the strategy described by model II, they can achieve a significant reduction in the time to reach consensus as well as an increment in the probability to reach consensus to the preferred state.

physics.soc-ph↗

arXiv2021

Coordination and equilibrium selection in games: the role of local effects

We study the role of local effects and finite size effects in reaching coordination and in equilibrium selection in different types of two-player coordination games. We investigate three update rules -- the replicator dynamics (RD), the best response (BR), and the unconditional imitation (UI) -- for coordination games on random graphs. Local effects turn out to me significantly more important for the UI update rule. For the pure coordination game with two equivalent strategies we find a transition from a disordered state to a state of full coordination for a critical value of the network connectivity. The transition is system-size-independent for the BR and RD update rules. For the IU update rule it is system size dependent, but coordination can always be reached below the connectivity of a complete graph. We also consider the general coordination game which covers a range of games, such as the stag hunt. For these games there is a payoff-dominant strategy and a risk-dominant strategy with associated states of equilibrium coordination. We analyse equilibrium selection analytically and numerically. For the RD and BR update rules mean-field predictions agree with simulations and the risk-dominant strategy is evolutionary favoured independently of local effects. When players use the unconditional imitation, however, we observe coordination in the payoff-dominant strategy. Surprisingly, the selection of pay-off dominant equilibrium only occurs below a critical value of the network connectivity and it disappears in complete graphs. As we show, it is a combination of local effects and update rule that allows for coordination on the payoff-dominant strategy.

physics.soc-ph↗

arXiv2020

On the importance of trip destination for modeling individual human mobility patterns

Getting insights on human mobility patterns and being able to reproduce them accurately is of the utmost importance in a wide range of applications from public health, to transport and urban planning. Still the relationship between the effort individuals will invest in a trip and its purpose importance is not taken into account in the individual mobility models that can be found in the recent literature. Here, we address this issue by introducing a model hypothesizing a relation between the importance of a trip and the distance traveled. In most practical cases, quantifying such importance is undoable. We overcome this difficulty by focusing on shopping trips (for which we have empirical data) and by taking the price of items as a proxy. Our model is able to reproduce the long-tailed distribution in travel distances empirically observed and to explain the scaling relationship between distance traveled and item value found in the data.

physics.soc-ph↗

arXiv2020

Absorbing transition in a coevolution model with node and link states in an adaptive network: Network fragmentation transition at criticality

We consider a general model in which there is a coupled dynamics of node states and links states in a network. This coupled dynamics coevolves with dynamical changes of the topology of the network caused by a link rewiring mechanism. Such coevolution model features the interaction of the local dynamics of node and link states with the nonlocal dynamics of link-rewiring in a random network. The coupled dynamics of the states of the nodes and the links produces by itself an absorbing phase transition which is shown to be robust against the link rewiring mechanism. However, the dynamics of the network gives rise to significant physical changes, specially in the limit in which some links do not change state but are always rewired: First a network fragmentation occurs at the critical line of the absorbing transition, and only at this line, so that fragmentation is a manifestation of criticality. Secondly, in the active phase of the absorbing transition, finite-size fluctuations take the system to a single network component consensus phase, while other configurations are possible in the absence of rewiring. In addition, this phase is reached after a survival time that scales linearly with system size, while the survival time scales exponentially with system size when there is no rewiring. A social interpretation of our results contribute to the description of processes of emergence of social fragmentation and polarization.

physics.soc-ph↗

arXiv2020

Emergence of complex structures from nonlinear interactions and noise in coevolving networks

We study the joint effect of the non-linearity of interactions and noise on coevolutionary dynamics. We choose the coevolving voter model as a prototype framework for this problem. By numerical simulations and analytical approximations we find three main phases that differ in the absolute magnetization and the size of the largest component: a consensus phase, a coexistence phase, and a dynamical fragmentation phase. More detailed analysis reveals inner differences in these phases, allowing us to divide two of them further. In the consensus phase we can distinguish between a weak or alternating consensus (switching between two opposite consensus states), and a strong consensus, in which the system remains in the same state for the whole realization of the stochastic dynamics. Additionally, weak and strong consensus phases scale differently with the system size. The strong consensus phase exists for superlinear interactions and it is the only consensus phase that survives in the thermodynamic limit. In the coexistence phase we distinguish a fully-mixing phase (both states well mixed in the network) and a structured coexistence phase, where the number of links connecting nodes in different states (active links) drops significantly due to the formation of two homogeneous communities of opposite states connected by a few links. The structured coexistence phase is an example of emergence of community structure from not exclusively topological dynamics, but coevolution. Our numerical observations are supported by an analytical description using a pair approximation approach and an ad-hoc calculation for the transition between the coexistence and dynamical fragmentation phases. Our work shows how simple interaction rules including the joint effect of non-linearity, noise, and coevolution lead to complex structures relevant in the description of social systems.

physics.soc-ph↗

arXiv2020

Pair approximation for the noisy threshold $q$-voter model

In the standard $q$-voter model, a given agent can change its opinion only if there is a full consensus of the opposite opinion within a group of influence of size $q$. A more realistic extension is the threshold $q$-voter, where a minimal agreement (at least $0<q_0\le q$ opposite opinions) is sufficient to flip the central agent's opinion, including also the possibility of independent (non conformist) choices. Variants of this model including non-conformist behavior have been previously studied in fully connected networks (mean-field limit). Here we investigate its dynamics in random networks. Particularly, while in the mean-field case it is irrelevant whether repetitions in the influence group are allowed, we show that this is not the case in networks, and we study the impact of both cases, with or without repetition. Furthermore, the results of computer simulations are compared with the predictions of the pair approximation derived for uncorrelated networks of arbitrary degree distributions.

physics.soc-ph↗

arXiv2018

Chimera and anticoordination states in learning dynamics

In many real-life situations, individuals are dared to simultaneously achieve social objectives of acceptance or approval and strategic objectives of coordination. Since these two objectives may take place in dfferent environments, a two-layer network is the simple and natural framework for the study of such kind of dynamical situations. In this paper we present a model in which the state of the agents corresponds to one of two possible strategies. They change their states by interaction with their neighbors in the network. Inside each layer the agents interact by a social pressure mechanism, while between the layers the agents interact via a coordination game. From an evolutionary approach, we focus on the asymptotic solutions for all-to-all interactions across and inside the layers and for any initial distribution of strategies. We find new asymptotic configurations which do not exist in a single isolated social network analysis. We report the emergence and existence of chimera states in which two different collective states coexist in the network. Namely, one layer reaches a state of full coordination while the other remains in a dynamical state of coexistence of strategies. In addition, the system may also reach a state of global anticoordination where a full coordination is reached inside each layer but with opposite strategies in each of the two network layers. We trace back the emergence of chimera states and global anticoordination states to the agents inertia against social pressure, referred here to as the level of skepticism, along with the degree of risk taken into account in a general coordination game.

physics.soc-ph↗

arXiv2018

Herding and idiosyncratic choices: Nonlinearity and aging-induced transitions in the noisy voter model

We consider the herding to non-herding transition caused by idiosyncratic choices or imperfect imitation in the context of the Kirman Model for financial markets, or equivalently the Noisy Voter Model for opinion formation. In these original models this is a finite size transition that disappears for a large number of agents. We show how the introduction of two different mechanisms make this transition robust and well defined. A first mechanism is nonlinear interactions among agents taking into account the nonlinear effect of local majorities. The second one is aging, so that the longer an agent has been in a given state the more reluctant she becomes to change state.

physics.soc-ph↗

arXiv2018

Competition and dual users in complex contagion processes

We study the competition of two spreading entities, for example innovations, in complex contagion processes in complex networks. We develop an analytical framework and examine the role of dual users, i.e. agents using both technologies. Searching for the spreading transition of the new innovation and the extinction transition of a preexisting one, we identify different phases depending on network mean degree, prevalence of preexisting technology, and thresholds of the contagion process. Competition with the preexisting technology effectively suppresses the spread of the new innovation, but it also allows for phases of coexistence. The existence of dual users largely modifies the transient dynamics creating new phases that promote the spread of a new innovation and extinction of a preexisting one. It enables the global spread of the new innovation even if the old one has the first-mover advantage.

physics.soc-ph↗

arXiv2018

Multilayer coevolution dynamics of the nonlinear voter model

We study a coevolving nonlinear voter model on a two-layer network. Coevolution stands for coupled dynamics of the state of the nodes and of the topology of the network in each layer. The plasticity parameter p measures the relative time scale of the evolution of the states of the nodes and the evolution of the network by link rewiring. Nonlinearity of the interactions is taken into account through a parameter q that describes the nonlinear effect of local majorities, being q = 1 the marginal situation of the ordinary voter model. Finally the connection between the two layers is measured by a degree of multiplexing `. In terms of these three parameters, p, q and ` we find a rich phase diagram with different phases and transitions. When the two layers have the same plasticity p, the fragmentation transition observed in a single layer is shifted to larger values of p plasticity, so that multiplexing avoids fragmentation. Different plasticities for the two layers lead to new phases that do not exist in a coevolving nonlinear voter model in a single layer, namely an asymmetric fragmented phase for q > 1 and an active shattered phase for q < 1. Coupling layers with dfferent types of nonlinearity, q1 < 1 and q2 > 1, we can find two different transitions by increasing the plasticity parameter, a first absorbing transition with no fragmentation and a subsequent fragmentation transition.

nlin.AO↗

arXiv2018

Absorbing phase transition in the coupled dynamics of node and link states in random networks

We present a stochastic dynamics model of coupled evolution for the binary states of nodes and links in a complex network. In the context of opinion formation node states represent two possible opinions and link states a positive or negative relation. Dynamics proceeds via node and link state update towards pairwise satisfactory relations in which nodes in the same state are connected by positive links or nodes in different states are connected by negative links. By a mean-field rate equations analysis and Monte Carlo simulations in random networks we find an absorbing phase transition from a dynamically active phase to an absorbing phase. The transition occurs for a critical value of the relative time scale for node and link state updates. In the absorbing phase the order parameter, measuring global order, approaches exponentially the final frozen configuration. Finite size effects are such that in the absorbing phase the final configuration is reached in a characteristic time that scales logarithmically with system size, while in the active phase, finite-size fluctuation take the system to a frozen configuration in a characteristic time that grows exponentially with system size. There is also a finite-size topological transition associated with group splitting in the network of these final frozen configurations.

physics.soc-ph↗

arXiv2018

First-passage distributions for the one-dimensional Fokker-Planck equation

We present an analytical framework to study the first-passage (FP) and first-return (FR) distributions for the broad family of models described by the one-dimensional Fokker-Planck equation in finite domains, identifying general properties of these distributions for different classes of models. When in the Fokker-Planck equation the diffusion coefficient is positive (nonzero) and the drift term is bounded, as in the case of a Brownian walker, both distributions may exhibit a power-law decay with exponent -3/2 for intermediate times. We discuss how the influence of an absorbing state changes this exponent. The absorbing state is characterized by a vanishing diffusion coefficient and/or a diverging drift term. Remarkably, the exponent of the Brownian walker class of models is still found, as long as the departure and arrival regions are far enough from the absorbing state, but the range of times where the power law is observed narrows. Close enough to the absorbing point, though, a new exponent may appear. The particular value of the exponent depends on the behavior of the diffusion and the drift terms of the Fokker-Planck equation. We focus on the case of a diffusion term vanishing linearly at the absorbing point. In this case, the FP and FR distributions are similar to those of the voter model, characterized by a power law with exponent -2. As an illustration of the general theory, we compare it with exact analytical solutions and extensive numerical simulations of a two-parameter voter-like family models. We study the behavior of the FP and FR distributions by tuning the importance of the absorbing points throughout changes of the parameters. Finally, the possibility of inferring relevant information about the steady-sate probability distribution of a model from the FP and FR distributions is addressed.

cond-mat.stat-mech↗

arXiv2018

Aging-induced continuous phase transition

Aging is considered as the property of the elements of a system to be less prone to change states as they get older. We incorporate aging into the noisy voter model, a stochastic model in which the agents modify their binary state by means of noise and pair-wise interactions. Interestingly, due to aging the system passes from a finite-size discontinuous transition between ordered (ferromagnetic) and disordered (paramagnetic) phases to a second order phase transition, well defined in the thermodynamic limit, belonging to the Ising universality class. We characterize it analytically by finding the stationary solution of an infinite set of mean field equations. The theoretical predictions are tested with extensive numerical simulations in low dimensional lattices and complex networks. We finally employ the aging properties to understand the symmetries broken in the phase transition.

cond-mat.stat-mech↗

arXiv2018

Competing contagion processes: Complex contagion triggered by simple contagion

Empirical evidence reveals that contagion processes often occur with competition of simple and complex contagion, meaning that while some agents follow simple contagion, others follow complex contagion. Simple contagion refers to spreading processes induced by a single exposure to a contagious entity while complex contagion demands multiple exposures for transmission. Inspired by this observation, we propose a model of contagion dynamics with a transmission probability that initiates a process of complex contagion. With this probability nodes subject to simple contagion get adopted and trigger a process of complex contagion. We obtain a phase diagram in the parameter space of the transmission probability and the fraction of nodes subject to complex contagion. Our contagion model exhibits a rich variety of phase transitions such as continuous, discontinuous, and hybrid phase transitions, criticality, tricriticality, and double transitions. In particular, we find a double phase transition showing a continuous transition and a following discontinuous transition in the density of adopted nodes with respect to the transmission probability. We show that the double transition occurs with an intermediate phase in which nodes following simple contagion become adopted but nodes with complex contagion remain susceptible.

cond-mat.stat-mech↗

arXiv2018

Coevolving nonlinear voter model with triadic closure

We study a nonlinear coevolving voter model with triadic closure local rewiring. We find three phases with different topological properties and configuration in the steady state: absorbing consensus phase with a single component, absorbing fragmented phase with two components in opposite consensus states, and a dynamically active shattered phase with many isolated nodes. This shattered phase, which does not exist for a coevolving model with global rewiring, has a lifetime that scale exponentially with system size. We characterize the transitions between these phases in terms of the size of the largest cluster, the number of clusters, and the magnetization. Our analysis provides a possible solution to reproduce isolated parts in adaptive networks and high clustering widely observed in social systems.

physics.soc-ph↗

arXiv2018

Zealots in the mean-field noisy voter model

The influence of zealots on the noisy voter model is studied theoretically and numerically at the mean-field level. The noisy voter model is a modification of the voter model that includes a second mechanism for transitions between states: apart from the original herding processes, voters may change their states because of an intrinsic, noisy in origin source. By increasing the importance of the noise with respect to the herding, the system exhibits a finite-size phase transition from a quasi-consensus state, where most of the voters share the same opinion, to a one with coexistence. Upon introducing some zealots, or voters with fixed opinion, the latter scenario may change significantly. We unveil the new situations by carrying out a systematic numerical and analytical study of a fully connected network for voters, but allowing different voters to be directly influenced by different zealots. We show that this general system is equivalent to a system of voters without zealots, but with heterogeneous values of their parameters characterizing herding and noisy dynamics. We find excellent agreement between our analytical and numerical results. Noise and herding/zealotry acting together in the voter model yields not a trivial mixture of the scenarios with the two mechanisms acting alone: it represents a situation where the global-local (noise-herding) competitions is coupled to a symmetry breaking (zealots). In general, the zealotry enhances the effective noise of the system, which may destroy the original quasi--consensus state, and can introduce a bias towards the opinion of the majority of zealots, hence breaking the symmetry of the system and giving rise to new phases ...

physics.soc-ph↗

arXiv2017

Fragmentation transitions in a coevolving nonlinear voter model

We study a coevolving nonlinear voter model describing the coupled evolution of the states of the nodes and the network topology. Nonlinearity of the interaction is measured by a parameter q. The network topology changes by rewiring links at a rate p. By analytical and numerical analysis we obtain a phase diagram in p, q parameter space with three different phases: Dynamically active coexistence phase in a single component network, absorbing consensus phase in a single component network, and absorbing phase in a fragmented network. For finite systems the active phase has a lifetime that grows exponentially with system size, at variance with the similar phase for the linear voter model that has a lifetime proportional to system size. We find three transition lines that meet at the point of the fragmentation transition of the linear voter model. A first transition line corresponds to a continuous absorbing transition between the active and fragmented phases. The other two transition lines are discontinuous transitions fundamentally different from the transition of the linear voter model. One is a fragmentation transition between the consensus and fragmented phases, and the other is an absorbing transition in a single component network between the active and consensus phases.

physics.soc-ph↗