arXiv subjects

Raúl Toral

Publications and source records attributed to Raúl Toral.

At least 19 recordsLinked to original sources

arXiv2026

Partisan voter model on complex networks: Dynamics of local ordering

We investigate the processes of local ordering for the partisan voter model on complex networks. In this model, agents hold a binary opinion and a fixed preference that biases updates toward alignment with their preferred opinion. We first study the dynamics on uncorrelated random networks and derive a pair approximation that resolves the densities of links connecting different classes of agents. The analytical predictions are in excellent agreement with Monte Carlo simulations. In this setting, partisan bias leaves the total stationary density of links connecting nodes in different sates unchanged and at the same value as in the standard voter model, but redistributes it among different categories of links. We then consider preference-dependent networks with homophilic and heterophilic attachment to analyze the competition between the global bias mechanism and the local effect of preference-based connectivity. In this case, structural correlations qualitatively modify the stationary state. We identify different regimes of local ordering in the space of parameters measuring the strength of the preference and the strength of the homophilic attachment. Our work clarifies the distinct roles of dynamical partisan bias and structural assortativity, and provides an analytical framework to study partisan opinion dynamics beyond mean-field theory.

physics.soc-ph↗

arXiv2026

Stochastic Thermodynamics of Social Imitation beyond Energetics

The development of stochastic thermodynamics during the last decades prompted the discovery of novel nonequilibrium relations refining our understanding of the second law in small fluctuating systems and its connection with information theory. A fundamental open question is whether these powerful tools can illuminate other areas of complex systems, such as social phenomena, where energy plays no fundamental role. Here we develop a framework that derives a ``second law" for social systems. Similarly to Landauer's principle, it constrains spontaneous changes in agent attributes (opinions, cultural traits, etc.) and their informational entropy. We illustrate this framework to toy agent-based models of social imitation with non-trivial phase diagrams. We demonstrate how cornerstone results -- fluctuation theorems, kinetic and thermodynamic uncertainty relations, and second-law-like inequalities -- emerge naturally in this context, even across symmetry-breaking transitions. These results reveal fundamental trade-offs in opinion currents arising from the competition between herding and anti-conformity. Moreover, they provide inference tools to extract model parameters from observations of stochastic changes in agents.

physics.soc-ph↗

arXiv2026

Reducibility of higher-order to pairwise interactions: Social impact models on hypergraphs

We show that a general class of social impact models with higher-order interactions on hypergraphs can be exactly reduced to an equivalent model with pairwise interactions on a weighted projected network. This reduction is made by a mapping that preserves the microscopic probabilities of changing the state of the nodes. As a particular case, we introduce hypergraph-voter models, for which we compute the weights of the projected network both analytically and numerically across several hypergraph ensembles, and we characterize their ordering dynamics through simulations of both higher-order and reduced dynamics. For a linear social impact function (hypergraph-linear voter model) the weights of the projected network are static, allowing us to develop a pair approximation that describes with accuracy the time evolution of macroscopic observables, which turn out to be independent of those weights. The macroscopic dynamics is thus equivalent to that of the standard voter model on the unweighted projected network. For a power-law social impact function (hypergraph-nonlinear voter model) the weights of the projected network depend on the instantaneous system configuration. Nevertheless, the nonlinear voter model on the unweighted projected network still reproduces the main macroscopic trends for well connected hypergraphs.

physics.soc-ph↗

arXiv2026

Barrier crossing in a two-state system: Effect of bias and stochastic fields

We study barrier crossing in a two-state system, namely the kinetic Ising model, in the presence of a weak bias field and spatially homogeneous, but time-dependent, Gaussian random fields. We find that the bias field determines the location of the dominant maxima of the probability distribution function of the magnetization, whereas the noise intensity controls their sharpness and stability of the distribution. A moderate stochastic field lowers the effective energy barrier and facilitates transitions between ordered states, while strong noise induces broad distributions and significant backflow, which reduces directional selectivity. Our results suggest that efficient barrier crossing requires a balanced combination of moderate stochastic driving and controlled bias.

cond-mat.stat-mech↗

arXiv2026

An Analytics Framework for Modeling Residential Photovoltaic Adoption and Decision Dynamics

Photovoltaic generation plays a central role in the energy transition, yet understanding its adoption dynamics requires robust analytical frameworks that capture both temporal and spatial patterns of decision behavior. This study applies a data-driven decision analytics approach to examine residential self-consumption photovoltaic installations in Catalonia within an innovation diffusion framework. The temporal evolution of adoption is modeled using a logistic growth function, providing evidence that imitation effects are a primary driver of adoption decisions. To extend the analysis, a quantitative methodology is developed to estimate the influence of external factors on adoption behavior, revealing that social perception exerts a stronger impact than regulatory and socioeconomic variables when considered independently. In addition, a spatial analytics component is incorporated to assess territorial heterogeneity, identifying correlations between adoption patterns and demographic and socioeconomic characteristics. The findings contribute to predictive and diagnostic analytics by offering a structured framework to model technology diffusion and inform policy and investment decisions aimed at accelerating sustainable energy adoption.

physics.soc-ph↗

arXiv2026

Numerical methods for quasi-stationary distributions

In stochastic processes with absorbing states, the quasi-stationary distribution provides valuable insights into the long-term behaviour prior to absorption. In this work, we revisit two well-established numerical methods for its computation. The first is an iterative algorithm for solving the non-linear equation that defines the quasi-stationary distribution. We generalise this technique to accommodate general Markov stochastic processes, either with discrete or continuous state space, and with multiple absorbing states. The second is a Monte Carlo method with resetting, for which we propose a novel single-trajectory approach that uses the trajectory's own history to perform resets after absorption. In addition to these methodological contributions, we provide a detailed analysis of implementation aspects for both methods. We also compare their accuracy and efficiency across a range of examples. The results indicate that the iterative algorithm is generally the preferred choice for problems with simple boundaries, while the Monte Carlo approach is more suitable for problems with complex boundaries, where the implementation of the iterative algorithm is a challenging task.

cond-mat.stat-mech↗

arXiv2026

Information-theoretic analysis of temporal dependence in discrete stochastic processes: Application to precipitation predictability

Understanding the temporal dependence of precipitation is key to improving weather predictability and developing efficient stochastic rainfall models. We introduce an information-theoretic approach to quantify memory effects in discrete stochastic processes and apply it to daily precipitation records across the contiguous United States. The method is based on the predictability gain, a quantity derived from block entropy that measures the additional information provided by higher-order temporal dependencies. This statistic, combined with a bootstrap-based hypothesis testing and Fisher's method, enables a robust memory estimator from finite data. Tests with generated sequences show that this estimator outperforms other model-selection criteria such as Akaike Information Criterion and Bayesian Information Criterion. Applied to precipitation data, the analysis reveals that daily rainfall occurrence is well described by low-order Markov chains, exhibiting regional and seasonal variations, with stronger correlations in winter along the West Coast and in summer in the Southeast, consistent with known climatological patterns. Overall, our findings establish a framework for building parsimonious stochastic descriptions, useful when addressing spatial heterogeneity in the memory structure of precipitation dynamics, and support further advances in real-time, data-driven forecasting schemes.

physics.data-an↗

arXiv2026

Anticipated synchronization in systems with distributed delay

Anticipated synchronisation occurs when a driven dynamical system synchronises with the future state of the driver system to which it is unidirectionally coupled. Previous theoretical and experimental studies have focused on setups with a single delay time in the coupling term, for which exact anticipation can arise as a solution. Here we extend this framework to configurations with distributed delay times. Our main result is that, for a given delay distribution, approximate anticipated synchronisation can emerge over a range of coupling strengths. We analyse this phenomenon analytically for systems of linear oscillators, where we identify simple cases exhibiting exact synchronisation--up to a constant amplitude factor. Numerical simulations of nonlinear chaotic systems reveal stable forms of approximate anticipated synchronisation.

nlin.CD↗

arXiv2026

Forecasting emergency department visits in the reference hospital of the Balearic Islands: the role of tourist and weather data

Accurate forecasting of patient arrivals at emergency departments (EDs) is vital for efficient resource allocation and high-quality patient care. In this study we investigate the relevance of exogenous variables, namely tourism, weather, calendar and demographic variables, in forecasting ED visits in the reference hospital in Palma de Mallorca, a city with significant seasonal population fluctuations due to tourism. Using a machine learning approach, we develop a model that predicts ED visits based solely on these exogenous variables. We test different machine learning algorithms (random forests, support vector machines, and feedforward neural networks) with different combinations of input variables and compare their symmetric mean average percentage errors (SMAPEs). Our findings reveal that calendar information, resident, and tourist population data are statistically significant for the accuracy of the predictions, while the addition of weather data does not provide any further improvement. Comparison of non-time-series with time-series prediction models reveals that the latter provide better accuracy for short prediction horizons (e.g. shorter than a week). Furthermore, time-series models become less or equally accurate to models relying only on exogenous variables for long prediction horizons (e.g. fortnight or month). Our study highlights the importance of carefully selecting predictive variables to ensure short- and long-term, robust and reliable forecasts. This demonstrates that, despite their lower complexity, non-time-series models with well-chosen input variables can be as effective as time-series models when predicting for long time horizons.

physics.soc-ph↗

arXiv2026

Universality of noise-induced transitions in nonlinear voter models

We analyze the universality classes of phase transitions in a variety of nonlinear voter models. By mapping several models with symmetric absorbing states onto a canonical model introduced in previous studies, we confirm that they exhibit a Generalized Voter (GV) transition. We then propose a canonical mean-field model that extends the original formulation by incorporating a noise term that eliminates the absorbing states. This generalization gives rise to a phase diagram featuring two distinct types of phase transitions: a continuous Ising transition and a discontinuous transition we call Modified Generalized Voter (MGV). These two transition lines converge at a tricritical point. We map diverse noisy nonlinear voter models onto this extended canonical form. Using finite-size scaling techniques above and below the upper critical dimension, we show that the continuous transition of these models belongs to the Ising universality class in their respective dimensionality. We also find universal behavior at the tricitical point. Our results provide a unifying framework for classifying phase transitions in stochastic models of opinion dynamics with both nonlinearity and noise.

physics.soc-ph↗

arXiv2024

Complete aging in the noisy voter model enhances consensus formation

We investigate the effects of aging in the noisy voter model considering that the probability to change states decays algebraically with age $τ$, defined as the time elapsed since adopting the current state. We study the complete aging scenario, which incorporates aging to both mechanisms of interaction: herding and idiosyncratic behavior, and compare it with the partial aging case, where aging affects only the herding mechanism. Analytical mean-field equations are derived, finding excellent agreement with agent-based simulations on a complete graph. We observe that complete aging enhances consensus formation, shifting the critical point to higher values compared to the partial aging case. However, when the aging probability decays asymptotically to zero for large $τ$, a steady state is not always attained for complete aging.

physics.soc-ph↗

arXiv2024

Exploring language relations through syntactic distances and geographic proximity

Languages are grouped into families that share common linguistic traits. While this approach has been successful in understanding genetic relations between diverse languages, more analyses are needed to accurately quantify their relatedness, especially in less studied linguistic levels such as syntax. Here, we explore linguistic distances using series of parts of speech (POS) extracted from the Universal Dependencies dataset. Within an information-theoretic framework, we show that employing POS trigrams maximizes the possibility of capturing syntactic variations while being at the same time compatible with the amount of available data. Linguistic connections are then established by assessing pairwise distances based on the POS distributions. Intriguingly, our analysis reveals definite clusters that correspond to well known language families and groups, with exceptions explained by distinct morphological typologies. Furthermore, we obtain a significant correlation between language similarity and geographic distance, which underscores the influence of spatial proximity on language kinships.

cs.CL↗

arXiv2024

Biased versus unbiased numerical methods for stochastic simulations

Approximate numerical methods are one of the most used strategies to extract information from many-interacting-agents systems. In particular, numerical approximations are of extended use to deal with epidemic, ecological and biological models, since unbiased methods like the Gillespie algorithm can become unpractical due to high CPU time usage required. However, the use of approximations has been debated and there is no clear consensus about whether unbiased methods or biased approach is the best option. In this work, we derive scaling relations for the errors in approximations based on binomial extractions. This finding allows us to build rules to compute the optimal values of both the discretization time and number of realizations needed to compute averages with the biased method with a target precision and minimum CPU-time usage. Furthermore, we also present another rule to discern whether the unbiased method or biased approach is more efficient. Ultimately, we will show that the choice of the method should depend on the desired precision for the estimation of averages.

physics.soc-ph↗

arXiv2023

Noisy kinetic-exchange opinion model with aging

We study the critical behavior of a noisy kinetic opinion model subject to resilience to change depending on aging, defined as the time spent on the current opinion state. In this model, the opinion of each agent can take the three discrete values, the extreme ones $\pm 1$, and also the intermediate value 0, and it can evolve through kinetic exchange when interacting with another agent, or independently, by stochastic choice (noise). The probability of change by pairwise interactions depends on the age that the agent has remained in the same state, according to a given kernel. We particularly develop the cases where the probability decays either algebraically or exponentially with the age, and we also consider the anti-aging scenario where the probability increases with the age, meaning that it is more likely to change mind the longer the persistence in the current state. For the opinion dynamics in a complete graph, we obtain analytical predictions for the critical curves of the order parameters, in perfect agreement with agent-based simulations. We observe that sufficiently weak aging (slow change of the kernel with the age) favors partial consensus with respect to the aging-insensitive scenario, while for sufficiently strong aging, as well as for anti-aging, the opposite trend is observed.

physics.soc-ph↗

arXiv2023

Endemic infectious states below the epidemic threshold and beyond herd immunity

In the recent COVID-19 pandemic we assisted at a sequence of epidemic waves intertwined by anomalous fade-outs with periods of low but persistent epidemic prevalence. These long-living epidemic states complicate epidemic control and challenge current modeling approaches as classical epidemic models fail to explain their emergence. Inspired by this phenomenon, we propose a simple mechanism able to reproduce several features observed in real data. Specifically, here we introduce a modification of the Susceptible-Infected-Recovered (SIR) model in a meta-population framework where a small inflow of infected individuals accounts for undetected internal or imported cases. Focusing on a regime where this external seeding is so small that cannot be detected from the analysis of epidemic curves, we find that outbreaks of finite duration percolate in time resulting in overall low but long-living epidemic states below and above the epidemic threshold. Using a two-state description of the local dynamics, we can extract analytical predictions for the phase space. The comparison with epidemic data demonstrates that our model is able to reproduce some critical signatures observed in COVID-19 spreading in England. Finally, our findings defy our understanding of the concept of epidemic threshold and its relationship with outbreaks survival for disease control.

physics.soc-ph↗

arXiv2021

Quantum Consensus Dynamics by Entangling Maxwell Demon

We introduce a Maxwell demon which generates many-body entanglement robustly against bit-flip noises, which allows us to obtain quantum advantage. Adopting the protocol of the voter model used for opinion dynamics approaching consensus, the demon randomly selects a qubit pair and performs a quantum feedback control, in continuous repetitions. We derive upper bounds of the entropy reduction and the work extraction rates by demon's operation, which are determined by a competition between the quantum-classical mutual information acquired by the demon and the absolute irreversibility of the feedback control. Our finding of the upper bounds corresponds to a reformulation of the second law of thermodynamics under a class of Maxwell demon which generates many-body entanglement in a working substance.

cond-mat.stat-mech↗

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

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↗