arXiv subjects

Raul Toral

Publications and source records attributed to Raul Toral.

At least 19 recordsLinked to original sources

arXiv2026

Phonological distances for linguistic typology and the origin of Indo-European languages

We show that short-range phoneme dependencies encode large-scale patterns of linguistic relatedness, with direct implications for quantitative typology and evolutionary linguistics. Specifically, using an information-theoretic framework, we argue that phoneme sequences modeled as second-order Markov chains essentially capture the statistical correlations of a phonological system. This finding enables us to quantify distances among 67 modern languages from a multilingual parallel corpus employing a distance metric that incorporates articulatory features of phonemes. The resulting phonological distance matrix recovers major language families and reveals signatures of contact-induced convergence. Remarkably, we obtain a clear correlation with geographic distance, allowing us to constrain a plausible homeland region for the Indo-European family, consistent with the Steppe hypothesis.

cs.CL↗

arXiv2026

Stochastic field effects in a two-state system: symmetry breaking and symmetry restoring

We study the Ising model under a time-varying, but spatially homogeneous, Gaussian random magnetic field. In the Monte Carlo simulations, we go beyond the standard analysis of the order parameter by measuring the magnetization probability distribution as a function of temperature and field strength, and by computing the time required for the system to escape from a completely ordered state of the magnetization. We identify three distinct phases: a soft-paramagnetic phase, a soft-ferromagnetic phase and a bona-fide ferromagnetic phase. These soft phases display broad magnetization distributions that tend to limiting forms that remain finite in both height and width in the thermodynamic limit. The transition between the soft-paramagnetic and soft-ferromagnetic phases is a noise-induced transition and, for small field amplitudes, occurs at the critical temperature of the field-free Ising model. The transition from the soft-ferromagnetic to the ferromagnetic phase occurs at lower temperatures and is discontinuous, yet it does not fall into the conventional first-order class. Instead, it is characterized by a diverging escape time from an ordered magnetization state.

cond-mat.stat-mech↗

arXiv2024

Entropy estimators for Markovian sequences: A comparative analysis

Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data and the lack of unbiased estimators. Most existing entropy estimators are designed for sequences of independent events and their performance vary depending on the system being studied and the available data size. In this work we compare different entropy estimators and their performance when applied to Markovian sequences. Specifically, we analyze both binary Markovian sequences and Markovian systems in the undersampled regime. We calculate the bias, standard deviation and mean squared error for some of the most widely employed estimators. We discuss the limitations of entropy estimation as a function of the transition probabilities of the Markov processes and the sample size. Overall, this paper provides a comprehensive comparison of entropy estimators and their performance in estimating entropy for systems with memory, which can be useful for researchers and practitioners in various fields.

cond-mat.stat-mech↗

arXiv2024

Language dynamics within adaptive networks: An agent-based approach of nodes and links coevolution

Motivated by the dramatic disappearance of endangered languages observed in recent years, a great deal of attention has been given to the modeling of language competition in order to understand the factors that promote the disappearance of a language and its unfolding dynamics. With this in mind, we build on existing network models of language competition in bilingual societies. These models deal with the interplay between the usage of a language (link state) and the preference or attitude of the speakers towards the language (node state). In this work, we allow for the case where agents have the freedom to adapt their local interactions in accordance with their language preference. This is modeled by introducing a local rewiring mechanism triggered by the dissatisfaction of an agent with its usage of a given language. Our numerical simulations show that permitting this freedom to agents likely results in linguistically segregated communities for small network sizes. However, for networks of sufficiently large size, the extinction of one of the languages is the most probable scenario. Furthermore, we analyze how the fraction of minority speakers changes with the system size and we find that this fraction grows as the total population increases, which is consistent with existing data. Overall, the results of this work help us understand the impact of speakers' preferences and choices in the complex language landscape of bilingual societies.

physics.soc-ph↗

arXiv2023

Aging in some opinion formation models: a comparative study

Changes of mind can become less likely the longer an agent has adopted a given opinion state. This resilience or inertia to change has been called ``aging''. We perform a comparative study of the effects of aging on the critical behavior of two standard opinion models with pairwise interactions. One of them is the voter model, which is a two-state model with a dynamic that proceeds by simple social contagion, another is the so-called kinetic exchange model, which allows a third (neutral) state and the formed opinion depends on the previous opinions of both interacting agents. Furthermore, in the noisy version of both models, random opinion changes are also allowed, regardless of the interactions. Due to aging, the probability of change diminishes with the age, and to take this into account we consider algebraic and exponential kernels. We investigate the situation where aging acts only on pairwise interactions. Analytical predictions for the critical curves of the order parameters are obtained for the opinion dynamics on a complete graph, in good agreement with agent-based simulations. For both models considered, consensus is optimized by an intermediate value of the parameter that rules the rate of decrease of the aging factor.

physics.soc-ph↗

arXiv2023

Partisan Voter Model: Stochastic description and noise-induced transitions

We give a comprehensive mean-field analysis of the Partisan Voter Model (PVM) and report analytical results for exit probabilities, fixation times, and the quasi-stationary distribution. In addition, and similarly to the noisy voter model, we introduce a noisy version of the PVM, named as the Noisy Partisan Voter Model (NPVM) which accounts for the preferences of each agent for the two possible states, as well as for idiosyncratic spontaneous changes of state. We find that the finite-size noise-induced transition of the noisy voter model is modified in the NPVM leading to the emergence of new intermediate phases and both continuous and discontinuous transitions.

cond-mat.stat-mech↗

arXiv2023

Ordinal analysis of lexical patterns

Words are fundamental linguistic units that connect thoughts and things through meaning. However, words do not appear independently in a text sequence. The existence of syntactic rules induces correlations among neighboring words. Using an ordinal pattern approach, we present an analysis of lexical statistical connections for 11 major languages. We find that the diverse manners that languages utilize to express word relations give rise to unique pattern structural distributions. Furthermore, fluctuations of these pattern distributions for a given language can allow us to determine both the historical period when the text was written and its author. Taken together, our results emphasize the relevance of ordinal time series analysis in linguistic typology, historical linguistics and stylometry.

cs.CL↗

arXiv2022

An improved estimator of Shannon entropy with applications to systems with memory

We investigate the memory properties of discrete sequences built upon a finite number of states. We find that the block entropy can reliably determine the memory for systems modeled as Markov chains of arbitrary finite order. Further, we provide an entropy estimator that remarkably gives accurate results when correlations are present. To illustrate our findings, we calculate the memory of daily precipitation series at different locations. Our results are in agreement with existing methods being at the same time valid in the undersampled regime and independent of model selection.

cond-mat.stat-mech↗

arXiv2022

Analytical and numerical treatment of continuous ageing in the voter model

The conventional voter model is modified so that an agent's switching rate depends on the `age' of the agent, that is, the time since the agent last switched opinion. In contrast to previous work, age is continuous in the present model. We show how the resulting individual-based system with non-Markovian dynamics and concentration-dependent rates can be handled both computationally and analytically. Lewis' thinning algorithm can be modified in order to provide an efficient simulation method. Analytically, we demonstrate how the asymptotic approach to an absorbing state (consensus) can be deduced. We discuss three special cases of the age dependent switching rate: one in which the concentration of voters can be approximated by a fractional differential equation, another for which the approach to consensus is exponential in time, and a third case in which the system reaches a frozen state instead of consensus. Finally, we include the effects of spontaneous change of opinion, i.e., we study a noisy voter model with continuous ageing. We demonstrate that this can give rise to a continuous transition between coexistence and consensus phases. We also show how the stationary probability distribution can be approximated, despite the fact that the system cannot be described by a conventional master equation.

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

Sampling rare trajectories using stochastic bridges

The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have fixed start and end points (so-called stochastic bridges). We then show that by carefully choosing a set of such bridges and assigning an appropriate statistical weight to each bridge, one can focus more processing power on the rare events of a target stochastic process while faithfully preserving the statistics of these rate trajectories. Further, we also compare the stochastic bridges produced using our method to the Wentzel-Kramers-Brillouin (WKB) optimal paths of the target process, derived in the limit of low noise. We see that the paths produced using our method, encoding the full statistics of the process, collapse onto the WKB optimal path as the level of noise is reduced. We propose that our method can be used to judge the accuracy of the WKB approximation at finite levels of noise.

cond-mat.stat-mech↗

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

Binary-state dynamics on complex networks: Stochastic pair approximation and beyond

Theoretical approaches to binary-state models on complex networks are generally restricted to infinite size systems, where a set of non-linear deterministic equations is assumed to characterize its dynamics and stationary properties. We develop in this work the stochastic formalism of the different compartmental approaches, these are: approximate master equation (AME), pair approximation (PA) and heterogeneous mean field (HMF), in descending order of accuracy. Using different system-size expansions of a general master equation, we are able to obtain approximate solutions of the fluctuations and finite-size corrections of the global state. On the one hand, far from criticality, the deviations from the deterministic solution are well captured by a Gaussian distribution whose properties we derive, including its correlation matrix and corrections to the average values. On the other hand, close to a critical point there are non-Gaussian statistical features that can be described by the finite-size scaling functions of the models. We show how to obtain the scaling functions departing only from the theory of the different approximations. We apply the techniques for a wide variety of binary-state models in different contexts, such as epidemic, opinion and ferromagnetic models.

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↗

arXiv2019

Reduction from non-Markovian to Markovian dynamics: The case of aging in the noisy-voter model

We study memory dependent binary-state dynamics, focusing on the noisy-voter model. This is a non-Markovian process if we consider the set of binary states of the population as the description variables, or Markovian if we incorporate "age", related to the time one has spent holding the same state, as a part of the description. We show that, in some cases, the model can be reduced to an effective Markovian process, where the age distribution of the population rapidly equilibrates to a quasi-steady state, while the global state of the system is out of equilibrium. This effective Markovian process shares the same phenomenology of the non-linear noisy-voter model and we establish a clear parallelism between these two extensions of the noisy-voter model.

physics.soc-ph↗

arXiv2019

Ordering dynamics in the voter model with aging

The voter model with memory-dependent dynamics is theoretically and numerically studied at the mean-field level. The `internal age', or time an individual spends holding the same state, is added to the set of binary states of the population, such that the probability of changing state (or activation probability $p_i$) depends on this age. A closed set of integro-differential equations describing the time evolution of the fraction of individuals with a given state and age is derived, and from it analytical results are obtained characterizing the behavior of the system close to the absorbing states. In general, different age-dependent activation probabilities have different effects on the dynamics. When the activation probability $p_i$ is an increasing function of the age $i$, the system reaches a steady state with coexistence of opinions. In the case of aging, with $p_i$ being a decreasing function, either the system reaches consensus or it gets trapped in a frozen state, depending on the value of $p_\infty$ (zero or not) and the velocity of $p_i$ approaching $p_\infty$. Moreover, when the system reaches consensus, the time ordering of the system can be exponential ($p_\infty>0$) or power-law like ($p_\infty=0$). Exact conditions for having one or another behavior, together with the equations and explicit expressions for the exponents, are provided.

physics.soc-ph↗

arXiv2019

Phase transitions in persistent and run-and-tumble walks

We calculate the large deviation function of the end-to-end distance and the corresponding extension-versus-force relation for (isotropic) random walks, on and off-lattice, with and without persistence, and in any spatial dimension. For off-lattice random walks with persistence, the large deviation function undergoes a first order phase transition in dimension $d> 5$. In the corresponding force-versus-extension relation, the extension becomes independent of the force beyond a critical value. The transition is anticipated in dimensions $d=4$ and $d=5$, where full extension is reached at a finite value of the applied stretching force. Full analytic details are revealed in the run-and-tumble limit. Finally, on-lattice random walks with persistence display a softening phase in dimension $d=3$ and above, preceding the usual stiffening appearing beyond a critical value of the force.

cond-mat.stat-mech↗

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↗