Raúl Toral

Drew University, Мадисон, New Jersey, United States

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Publications (232)454.85 Total impact

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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.
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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.
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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.
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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.
    Physical Review E 08/2014; 91(1-1). DOI:10.1103/PhysRevE.91.012128 · 2.33 Impact Factor
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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.
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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.
    Kinetic and Related Models 04/2014; 7(2). DOI:10.3934/krm.2014.7.253 · 0.99 Impact Factor
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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.
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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 03/2014; 89(6-1). DOI:10.1103/PhysRevE.89.062802 · 2.33 Impact Factor
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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. DOI:10.1103/PhysRevE.89.012921 · 2.33 Impact Factor
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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.
    Physical Review E 01/2014; 89(6). DOI:10.1103/PhysRevE.89.062124 · 2.33 Impact Factor
  • 01/2014; 1:365-368. DOI:10.15248/proc.1.365
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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.
    Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 09/2013; 371(1999):20120458. DOI:10.1098/rsta.2012.0458 · 2.86 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). DOI:10.1140/epjb/e2013-40777-7 · 1.46 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 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.
    Physical Review E 06/2013; 87(6-1):063311. DOI:10.1103/PhysRevE.87.063311 · 2.33 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 03/2013; 460:2269–2284. DOI:10.1098/rspa.2004.1283 · 2.00 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.
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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 02/2013; 3:1189. DOI:10.1038/srep01189 · 5.58 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 (DTMC) analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs. Keywords: Parrondo’s paradox; Fokker-Planck equation; Brownian ratchet. 1.
  • Article: due to non
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    ABSTRACT: “Fuzzy ” stochastic resonance: robustness against noise tuning
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    ABSTRACT: The domain growth processes originating from noise-induced nonequilibrium phase transitions are analyzed, both for non-conserved and conserved dynamics. The existence of a dynamical scaling regime is established in the two cases, and the corresponding growth laws are determined. The resulting universal dynamical scaling scenarios are those of Allen-Cahn and Lifshitz-Slyozov, respectively. Additionally, the

Publication Stats

4k Citations
454.85 Total Impact Points

Institutions

  • 2014
    • Drew University
      Мадисон, New Jersey, United States
  • 2007–2014
    • Institute for Cross-Disciplinary Physics and Complex Systems
      Palma, Balearic Islands, Spain
  • 1989–2014
    • University of the Balearic Islands
      • • Institute for Cross-Disciplinary Physics and Complex Systems (IFISC)
      • • Department of Physics
      Palma, Balearic Islands, Spain
    • Temple University
      • Department of Physics
      Philadelphia, Pennsylvania, United States
  • 1999–2013
    • 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
      Porto, Distrito do Porto, Portugal
  • 2001–2002
    • Universidad de Cantabria
      Santander, Cantabria, Spain
  • 1983–2000
    • University of Barcelona
      • • Department of Structure and Constituents of Matter
      • • Facultad de Física
      Barcino, Catalonia, Spain
  • 1998
    • The University of Edinburgh
      Edinburgh, Scotland, United Kingdom
    • 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