Raúl Toral

Institute for Cross-Disciplinary Physics and Complex Systems, Palma, Balearic Islands, Spain

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Publications (216)372.97 Total impact

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    ABSTRACT: In recent years the statistical mechanics of non-spherical molecules, such as polypeptide chains and protein molecules, has garnered considerable attention as their phase behavior has important scientific and health implications. One example is provided by immunoglobulin, which has a "Y"-shape. In this work, we determine the phase diagram of Y-shaped molecules on a hexagonal lattice through Monte Carlo Grand Canonical ensemble simulation, using histogram reweighting, multicanonical sampling, and finite-size scaling. We show that (as expected) this model is a member of the Ising universality class. For low temperatures, we implemented multicanonical sampling to induce faster phase transitions in the simulation. By studying several system sizes, we use finite-size scaling to determine the two phase coexistence curve, including the bulk critical temperature, critical chemical potential, and critical density.
    12/2014;
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    ABSTRACT: We study anticipated synchronization in two complex Ginzburg-Landau systems coupled in a master-slave configuration. Master and slave systems are ruled by the same autonomous function, but the slave system receives the injection from the master and is subject to a negative delayed self-feedback loop. We give evidence that the magnitude of the largest anticipation time depends on the dynamical regime where the system operates (defect turbulence, phase turbulence or bichaos) and scales with the linear autocorrelation time of the system. Moreover, we find that the largest anticipation times are obtained for complex-valued coupling constants. We provide analytical conditions for the stability of the anticipated synchronization manifold that are in qualitative agreement with those obtained numerically. Finally, we report on the existence of anticipated synchronization in coupled two-dimensional complex Ginzburg-Landau systems.
    04/2014;
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    ABSTRACT: We study a network model that couples the dynamics of link states with the evolution of the network topology. The state of each link, either A or B, is updated according to the majority rule or zero-temperature Glauber dynamics, in which links adopt the state of the majority of their neighboring links in the network. Additionally, a link that is in a local minority is rewired to a randomly chosen node. While large systems evolving under the majority rule alone always fall into disordered topological traps composed by frustrated links, any amount of rewiring is able to drive the network to complete order, by relinking frustrated links and so releasing the system from traps. However, depending on the relative rate of the majority rule and the rewiring processes, the system evolves towards different ordered absorbing configurations: either a one-component network with all links in the same state or a network fragmented in two components with opposite states. For low rewiring rates and finite size networks there is a domain of bistability between fragmented and non-fragmented final states. Finite size scaling indicates that fragmentation is the only possible scenario for large systems and any nonzero rate of rewiring.
    Physical review. E, Statistical, nonlinear, and soft matter physics. 03/2014; 89(6-1).
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    ABSTRACT: We numerically show that extreme events induced by parameter mismatches or noise in coupled oscillatory systems can be anticipated and suppressed before they actually occur. We show this in a main system unidirectionally coupled to an auxiliary system subject to a negative delayed feedback. Each system consists of two electronic oscillators coupled in a master-slave configuration. Extreme events are observed in this coupled system as large and sporadic desynchronization events. Under certain conditions, the auxiliary system can predict the dynamics of the main system. We use this to efficiently suppress the extreme events by applying a direct corrective reset to the main system.
    Physical Review E 01/2014; 89(1-1):012921. · 2.31 Impact Factor
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    ABSTRACT: In the model for continuous opinion dynamics introduced by Hegselmann and Krause, each individual moves to the average opinion of all individuals within an area of confidence. In this work we study the effects of noise in this system. With certain probability, individuals are given the opportunity to change spontaneously their opinion to another one selected randomly inside the opinion space with different rules. If the random jump does not occur, individuals interact through the Hegselmann-Krause's rule. We analyze two cases, one where individuals can carry out opinion random jumps inside the whole opinion space, and other where they are allowed to perform jumps just inside a small interval centered around the current opinion. We found that these opinion random jumps change the model behavior inducing interesting phenomena. Using pattern formation techniques, we obtain approximate analytical results for critical conditions of opinion cluster formation. Finally, we compare the results of this work with the noisy version of the Deffuant et al. model for continuous-opinion dynamics.
    Physics of Condensed Matter 09/2013; 86(12). · 1.28 Impact Factor
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    ABSTRACT: We provide an algorithm based on weighted-ensemble (WE) methods, to accurately sample systems at steady state. Applying our method to different one- and two-dimensional models, we succeed in calculating steady-state probabilities of order 10^{-300} and reproduce the Arrhenius law for rates of order 10^{-280}. Special attention is payed to the simulation of nonpotential systems where no detailed balance assumption exists. For this large class of stochastic systems, the stationary probability distribution density is often unknown and cannot be used as preknowledge during the simulation. We compare the algorithm's efficiency with standard Brownian dynamics simulations and the original WE method.
    Physical Review E 06/2013; 87(6-1):063311. · 2.31 Impact Factor
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    ABSTRACT: Parrondo’s games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the Fokker–Planck equation, that rigorously establish the connection between Parrondo’s games and a physical model known as the flashing Brownian ratchet. This gives rise to a new set of Parrondo’s games, of which the original games are a special case. For the first time, we perform a complete analysis of the new games via a discrete-time Markov chain analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs.
    Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences 03/2013; 460:2269–2284. · 2.38 Impact Factor
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    ABSTRACT: A growing part of the behavioral finance literature has addressed some of the stylized facts of financial time series as macroscopic patterns emerging from herding interactions among groups of agents with heterogeneous trading strategies and a limited rationality. We extend a stochastic herding formalism introduced for the modeling of decision making among financial agents, in order to take also into account an external influence. In particular, we study the amplification of an external signal imposed upon the agents by a mechanism of resonance. This signal can be interpreted as an advertising or a public perception in favor or against one of the two possible trading behaviors, thus periodically breaking the symmetry of the system and acting as a continuously varying exogenous shock. The conditions for the ensemble of agents to more accurately follow the periodicity of the signal are studied, finding a maximum in the response of the system for a given range of values of both the noise and the frequency of the input signal.
    02/2013;
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    Luis F Lafuerza, Raul Toral
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    ABSTRACT: We study stochastic particle systems made up of heterogeneous units. We introduce a general framework suitable to analytically study this kind of systems and apply it to two particular models of interest in economy and epidemiology. We show that particle heterogeneity can enhance or decrease the size of the collective fluctuations depending on the system, and that it is possible to infer the degree and the form of the heterogeneity distribution in the system by measuring only global variables and their fluctuations. Our work shows that, in some cases, heterogeneity among the units composing a system can be fully taken into account without losing analytical tractability.
    Scientific Reports 01/2013; 3:1189. · 5.08 Impact Factor
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    L F Lafuerza, R Toral
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    ABSTRACT: We study general stochastic birth and death processes including delay. We develop several approaches for the analytical treatment of these non-Markovian systems, valid, not only for constant delays, but also for stochastic delays with arbitrary probability distributions. The interplay between stochasticity and delay and, in particular, the effects of delay in the fluctuations and time correlations are discussed.
    Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 01/2013; 371(1999):20120458. · 2.89 Impact Factor
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    ABSTRACT: We study a model for continuous-opinion dynamics under bounded confidence. In particular, we analyze the importance of the initial distribution of opinions in determining the asymptotic configuration. Thus, we sketch the structure of attractors of the dynamical system, by means of the numerical computation of the time evolution of the agents density. We show that, for a given bound of confidence, a consensus can be encouraged or prevented by certain initial conditions. Furthermore, a noisy perturbation is added to the system with the purpose of modeling the free will of the agents. As a consequence, the importance of the initial condition is partially replaced by that of the statistical distribution of the noise. Nevertheless, we still find evidence of the influence of the initial state upon the final configuration for a short range of the bound of confidence parameter.
    Journal of Statistical Physics 08/2012; 151(1-2). · 1.40 Impact Factor
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    ABSTRACT: Recent advances in sleep neurobiology have allowed development of physiologically based mathematical models of sleep regulation that account for the neuronal dynamics responsible for the regulation of sleep-wake cycles and allow detailed examination of the underlying mechanisms. Neuronal systems in general, and those involved in sleep regulation in particular, are noisy and heterogeneous by their nature. It has been shown in various systems that certain levels of noise and diversity can significantly improve signal encoding. However, these phenomena, especially the effects of diversity, are rarely considered in the models of sleep regulation. The present paper is focused on a neuron-based physiologically motivated model of sleep-wake cycles that proposes a novel mechanism of the homeostatic regulation of sleep based on the dynamics of a wake-promoting neuropeptide orexin. Here this model is generalized by the introduction of intrinsic diversity and noise in the orexin-producing neurons, in order to study the effect of their presence on the sleep-wake cycle. A simple quantitative measure of the quality of a sleep-wake cycle is introduced and used to systematically study the generalized model for different levels of noise and diversity. The model is shown to exhibit a clear diversity-induced resonance: that is, the best wake-sleep cycle turns out to correspond to an intermediate level of diversity at the synapses of the orexin-producing neurons. On the other hand, only a mild evidence of stochastic resonance is found, when the level of noise is varied. These results show that disorder, especially in the form of quenched diversity, can be a key-element for an efficient or optimal functioning of the homeostatic regulation of the sleep-wake cycle. Furthermore, this study provides an example of a constructive role of diversity in a neuronal system that can be extended beyond the system studied here.
    PLoS Computational Biology 08/2012; 8(8):e1002650. · 4.87 Impact Factor
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    ABSTRACT: We analyze stochastic resonance in systems driven by non-Gaussian noises. For the bistable double well we compare the signal-to-noise ratio resulting from numerical simulations with some quasi-analytical results predicted by a consistent Markovian approximation in the case of a colored non-Gaussian noise. We also study the FitzHugh–Nagumo excitable system in the presence of the same noise. In both systems, we find that, as the noise departs from Gaussian behavior, there is a regime (different for the excitable and the bistable systems) in which there is a notable robustness against noise tuning since the signal-to-noise ratio curve broadens and becomes less sensitive to the actual value of the noise intensity. We also compare our results with some experiments in sensory systems.
    Fluctuation and Noise Letters 01/2012; 03(04). · 0.89 Impact Factor
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    C. Mayol, C.R. Mirasso, R. Toral
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    ABSTRACT: We study the synchronization region of two unidirectionally coupled, in a master-slave configuration, FitzHugh-Nagumo systems under the influence of external forcing terms. We observe that anticipated synchronization is robust to the different types of forcings. We then use the predict-prevent control method to suppress unwanted pulses in the master system by using the information of the slave output. We find that this method is more efficient than the direct control method based on the master. Finally, we observe that a perfect matching between the parameters of the master and the slave is not necessary for the control to be efficient. Moreover, this parameter mismatch can, in some cases, improve the control.
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 01/2012; 85(5).
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    L F Lafuerza, R Toral
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    ABSTRACT: We study a stochastic model of protein dynamics that explicitly includes delay in the degradation. We rigorously derive the master equation for the processes and solve it exactly. We show that the equations for the mean values obtained differ from others intuitively proposed and that oscillatory behavior is not possible in this system. We discuss the calculation of correlation functions in stochastic systems with delay, stressing the differences with Markovian processes. The exact results allow us to clarify the interplay between stochasticity and delay.
    Physical Review E 11/2011; 84(5 Pt 1):051121. · 2.31 Impact Factor
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    L F Lafuerza, R Toral
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    ABSTRACT: We develop an approximate theoretical method to study discrete stochastic birth and death models that include a delay time. We analyze the effect of the delay in the fluctuations of the system and obtain that it can qualitatively alter them. We also study the effect of distributed delay. We apply the method to a protein-dynamics model that explicitly includes transcription and translation delays. The theoretical model allows us to understand in a general way the interplay between stochasticity and delay.
    Physical Review E 08/2011; 84(2 Pt 1):021128. · 2.31 Impact Factor
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    ABSTRACT: Circadian rhythms in mammals are controlled by the neurons located in the suprachiasmatic nucleus of the hypothalamus. In physiological conditions, the system of neurons is very efficiently entrained by the 24 h light-dark cycle. Most of the studies carried out so far emphasize the crucial role of the periodicity imposed by the light-dark cycle in neuronal synchronization. Nevertheless, heterogeneity as a natural and permanent ingredient of these cellular interactions seemingly plays a major role in these biochemical processes. In this paper, we use a model that considers the neurons of the suprachiasmatic nucleus as chemically coupled modified Goodwin oscillators, and introduce non-negligible heterogeneity in the periods of all neurons in the form of quenched noise. The system response to the light-dark cycle periodicity is studied as a function of the interneuronal coupling strength, external forcing amplitude and neuronal heterogeneity. Our results indicate that the right amount of heterogeneity helps the extended system to respond globally in a more coherent way to the external forcing. Our proposed mechanism for neuronal synchronization under external periodic forcing is based on heterogeneity-induced oscillator death, damped oscillators being more entrainable by the external forcing than the self-oscillating neurons with different periods.
    Interface focus: a theme supplement of Journal of the Royal Society interface 02/2011; 1(1):167-76. · 2.21 Impact Factor
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    Luis F Lafuerza, Raul Toral
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    ABSTRACT: We consider a model for the evolution of surname distribution under a gender-equality measure currently being discussed by the Spanish Parliament (whereby children would adopt their mother's and father's surnames in alphabetical order). We quantify how this would bias the alphabetical distribution of surnames, and analyze its effect on the present distribution of surnames in Spain.
    PLoS ONE 01/2011; 6(4):e18105. · 3.53 Impact Factor
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    Teresa Vaz Martins, Raúl Toral
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    ABSTRACT: We consider a system of identical van der Pol oscillators, globally coupled through their velocities, and study how the presence of competitive interactions affects its synchronisation properties. We will address the question from two points of view. Firstly, we will investigate the role of competitive interactions on the synchronisation among identical oscillators. Then, we will show that the presence of an intermediate fraction of repulsive links results in the appearance of macroscopic oscillations at that signal's rhythm, in regions where the individual oscillator is unable to synchronise with a weak external signal.
    Progress of Theoretical Physics 11/2010; · 2.48 Impact Factor
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    L F Lafuerza, R Toral
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    ABSTRACT: We consider a model for the evolution of the surnames distribution under a gender-equality measurement presently discussed in the Spanish parliament (the children take the surname of the father or the mother according to alphabetical order). We quantify how this would bias the alphabetical distribution of surnames, and analyze its effect on the present distribution of the surnames in Spain.
    11/2010;

Publication Stats

3k Citations
372.97 Total Impact Points

Institutions

  • 2007–2014
    • Institute for Cross-Disciplinary Physics and Complex Systems
      Palma, Balearic Islands, Spain
    • University of Aveiro
      • Department of Physics
      Aveiro, Aveiro, Portugal
  • 2013
    • Humboldt-Universität zu Berlin
      • Department of Physics
      Berlin, Land Berlin, Germany
  • 2000–2013
    • Mediterranean Institute for Advanced Studies (IMEDEA)
      Esporles, Balearic Islands, Spain
  • 1989–2013
    • University of the Balearic Islands
      • • Institute for Cross-Disciplinary Physics and Complex Systems (IFISC)
      • • Departamento de Física
      Palma, Balearic Islands, Spain
    • Temple University
      • Department of Physics
      Philadelphia, Pennsylvania, United States
  • 2010
    • Université Libre de Bruxelles
      Bruxelles, Brussels Capital Region, Belgium
  • 1989–2010
    • Lehigh University
      • Department of Physics
      Bethlehem, PA, United States
  • 2009
    • Universität Stuttgart
      • Institute for Computational Physics
      Stuttgart, Baden-Wuerttemberg, Germany
  • 2004–2006
    • University of Porto
      • Faculdade de Ciências
      Porto, Distrito do Porto, Portugal
  • 2003
    • University of Leipzig
      • Institut für Informatik
      Leipzig, Saxony, Germany
    • University Carlos III de Madrid
      • High Technical College
      Getafe, Madrid, Spain
  • 1997–2000
    • University of Barcelona
      • Departament d'Estructura i Constituents de la Matèria
      Barcino, Catalonia, Spain
  • 1994–1999
    • Kansas State University
      • Department of Physics
      Kansas, United States
  • 1998
    • University of Granada
      Granata, Andalusia, Spain