Raúl Toral

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

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Publications (233)469.18 Total impact

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    D.P. Ruth · R. Toral · D. Holz · J.M. Rickman · J.D. Gunton
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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 the phase behavior of these systems has important scientific and health implications. More recently, it has been realized that surface binding may have a considerable impact on this behavior. With this in mind, we examine here the role of surface interactions on the phase behavior of Y-shaped molecules (a simplified model of immunoglobulin) using grand-canonical Monte Carlo simulation. In particular, we investigate the critical behavior of a system of such molecules on a hexagonal lattice using histogram reweighting, multicanonical sampling, and finite-size scaling. After obtaining the critical properties of the three-dimensional bulk system, we investigate the impact of a patterned solid surface on these properties as a function of patterning geometry and surface interaction strength. Our results suggest avenues for tailoring phase behavior by selectively controlling surface characteristics.
    Full-text · Article · Nov 2015 · Thin Solid Films
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    ABSTRACT: As an instance of diversity-induced resonance and of the constructive role of heterogeneity in complex systems, here we study a generalized version of a physiologically-motivated sleep-wake cycle model taking into account the role of orexin [Patriarca etal. (2012) [16]; Postnova etal. (2009) [9]]. With respect to the versions of the model studied previously, here we consider systems containing both a set of orexin neurons - responsible for the production of orexin - and a set of glutaminergic neurons - representing mental activity or sleep depending on their firing or silent state, respectively - within some basic network topologies. The neurons of one or both types are diversified and it is shown how the interplay between the heterogeneous constituent units produces as an emergent effect the recovering or improving of the sleep-wake cycle. At a general level, the results obtained suggest that also systems with a dynamics driven by a homeostatic mechanism, with a time scale much longer than that of the constituent excitable units, may present diversity-induced resonance.
    No preview · Article · Oct 2015 · Chaos Solitons & Fractals
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    Adrián Carro · Raúl Toral · Maxi San Miguel
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    ABSTRACT: We focus on the influence of external sources of information upon financial markets. In particular, we develop a stochastic agent-based market model characterized by a certain herding behavior as well as allowing traders to be influenced by an external dynamic signal of information. This signal can be interpreted as a time-varying advertising, public perception or rumor, in favor or against one of two possible trading behaviors, thus breaking the symmetry of the system and acting as a continuously varying exogenous shock. As an illustration, we use a well-known German Indicator of Economic Sentiment as information input and compare our results with Germany's leading stock market index, the DAX, in order to calibrate some of the model parameters. We study the conditions for the ensemble of agents to more accurately follow the information input signal. The response of the system to the external information is maximal for an intermediate range of values of a market parameter, suggesting the existence of three different market regimes: amplification, precise assimilation and undervaluation of incoming information.
    Full-text · Article · Jun 2015 · PLoS ONE
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    C. Van den Broeck · R. Toral
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    ABSTRACT: Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative detailed fluctuation theorem is derived, expressed solely in terms of forward statistics. It is illustrated for a linear kinetic equation with kangaroo rates.
    Preview · Article · Mar 2015 · Physical Review E
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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.
    Full-text · Article · Dec 2014
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    ABSTRACT: We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not eliminated. Relaxation stronger than linear suppresses long tails immediately, but may lead to strong transient peaks in the probability distribution. A delta function initial distribution under stronger than linear decay displays not one but two different regimes of diffusive spreading.
    Full-text · Article · Aug 2014 · Physical Review E
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    ABSTRACT: We introduce multikangaroo Markov processes and provide a general procedure for evaluating a certain type of stochastic functional. We calculate analytically the large deviation properties. We apply our results to zero-crossing statistics and to stochastic thermodynamics, including the derivation of the fluctuation theorem and the large deviation properties for the stochastic entropy production in a typical solid state device.
    No preview · Article · Jun 2014 · Physical Review E
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    ABSTRACT: In this work we study the stochastic process of two-species coagulation. This process consists in the aggregation dynamics taking place in a ring. Particles and clusters of particles are set in this ring and they can move either clockwise or counterclockwise. They have a probability to aggregate forming larger clusters when they collide with another particle or cluster. We study the stochastic process both analytically and numerically. Analytically, we derive a kinetic theory which approximately describes the process dynamics. One of our strongest assumptions in this respect is the so called well-stirred limit, that allows neglecting the appearance of spatial coordinates in the theory, so this becomes effectively reduced to a zeroth dimensional model. We determine the long time behavior of such a model, making emphasis in one special case in which it displays self-similar solutions. In particular these calculations answer the question of how the system gets ordered, with all particles and clusters moving in the same direction, in the long time. We compare our analytical results with direct numerical simulations of the stochastic process and both corroborate its predictions and check its limitations. In particular, we numerically confirm the ordering dynamics predicted by the kinetic theory and explore properties of the realizations of the stochastic process which are not accessible to our theoretical approach.
    Preview · Article · Apr 2014 · Kinetic and Related Models
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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.
    Preview · Article · Apr 2014 · Physical Review E
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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.
    Full-text · Article · Mar 2014 · Physical Review E
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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.
    Preview · Article · Jan 2014 · Physical Review E
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    C. Van den Broeck · R. Toral
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    ABSTRACT: We calculate analytically the large deviation properties for a generalized kangaroo Markov process. Applications include zero-crossing statistics and stochastic thermodynamics.
    Preview · Article · Jan 2014 · Physical Review E

  • No preview · Article · Jan 2014
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    Luis F. Lafuerza · Raul 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.
    Preview · Article · Sep 2013 · Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences
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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.
    Full-text · Article · Sep 2013 · Physics of Condensed Matter
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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 to calculate steady state probabilities of order $10^{-300}$ and reproduce Arrhenius law for rates of order $10^{-280}$. Special attention is payed to the simulation of non-potential 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 algorithms efficiency with standard Brownian dynamics simulations and other WE methods.
    Full-text · Article · Jun 2013 · Physical Review E
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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.
    Full-text · Article · Mar 2013 · Proceedings of The Royal Society A
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    Adrián Carro · Raúl Toral · Maxi San Miguel
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    ABSTRACT: A thoroughly revised and updated version of this work has been published as "Markets, Herding and Response to External Information" in PLOS ONE 10(7), June 2015, with DOI: 10.1371/journal.pone.0133287.
    Preview · Article · Feb 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.
    Preview · Article · Feb 2013 · Scientific Reports
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    Adrian Carro · Raul Toral · Maxi San Miguel
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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.
    Full-text · Article · Aug 2012 · Journal of Statistical Physics

Publication Stats

4k Citations
469.18 Total Impact Points

Institutions

  • 2007-2015
    • Institute for Cross-Disciplinary Physics and Complex Systems
      Palma, Balearic Islands, Spain
  • 2014
    • Drew University
      Мадисон, New Jersey, United States
  • 1989-2014
    • University of the Balearic Islands
      • • Institute for Cross-Disciplinary Physics and Complex Systems (IFISC)
      • • Departamento de Física
      Palma, Balearic Islands, Spain
  • 2000-2013
    • Mediterranean Institute for Advanced Studies (IMEDEA)
      Esporles, Balearic Islands, Spain
  • 2010
    • Université Libre de Bruxelles
      Bruxelles, Brussels Capital Region, Belgium
  • 1993-2006
    • University of Porto
      • • Faculdade de Ciências
      • • Departamento de Engenharia Física
      Porto, Distrito do Porto, Portugal
    • Spanish National Research Council
      • Department of Molecular Physics
      Madrid, Madrid, Spain
  • 1986-2000
    • The University of Edinburgh
      Edinburgh, Scotland, United Kingdom
  • 1983-2000
    • University of Barcelona
      • • Department of Structure and Constituents of Matter
      • • Facultad de Física
      Barcino, Catalonia, Spain
  • 1998
    • University of Granada
      Granata, Andalusia, Spain
  • 1989-1998
    • Lehigh University
      • Department of Physics
      Bethlehem, PA, United States
  • 1994
    • Kansas State University
      • Department of Physics
      Kansas, United States
  • 1988-1989
    • Temple University
      • Department of Physics
      Philadelphia, Pennsylvania, United States