Publications (37)84.7 Total impact
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ABSTRACT: It is not fully understood why we cooperate with strangers on a daily basis. In an increasingly global world, where interaction networks and relationships between individuals are becoming more complex, different hypotheses have been put forward to explain the foundations of human cooperation on a large scale and to account for the true motivations that are behind this phenomenon. In this context, population structure has been suggested to foster cooperation in social dilemmas, but theoretical studies of this mechanism have yielded contradictory results so far; additionally, the issue lacks a proper experimental test in large systems. We have performed the largest experiments to date with humans playing a spatial Prisoner's Dilemma on a lattice and a scalefree network (1,229 subjects). We observed that the level of cooperation reached in both networks is the same, comparable with the level of cooperation of smaller networks or unstructured populations. We have also found that subjects respond to the cooperation that they observe in a reciprocal manner, being more likely to cooperate if, in the previous round, many of their neighbors and themselves did so, which implies that humans do not consider neighbors' payoffs when making their decisions in this dilemma but only their actions. Our results, which are in agreement with recent theoretical predictions based on this behavioral rule, suggest that population structure has little relevance as a cooperation promoter or inhibitor among humans.Proceedings of the National Academy of Sciences 07/2012; 109(32):129226. DOI:10.1073/pnas.1206681109  [Show abstract] [Hide abstract]
ABSTRACT: During the last few years, much research has been devoted to strategic interactions on complex networks. In this context, the Prisoner's Dilemma has become a paradigmatic model, and it has been established that imitative evolutionary dynamics lead to very different outcomes depending on the details of the network. We here report that when one takes into account the real behavior of people observed in the experiments, both at the meanfield level and on utterly different networks the observed level of cooperation is the same. We thus show that when human subjects interact in an heterogeneous mix including cooperators, defectors and moody conditional cooperators, the structure of the population does not promote or inhibit cooperation with respect to a well mixed population.Scientific Reports 01/2012; 2. DOI:10.1038/srep00325  [Show abstract] [Hide abstract]
ABSTRACT: Eigen's quasispecies model describes viruses as ensembles of different mutants of a high fitness "master" genotype. Mutants are assumed to have lower fitness than the master type, yet they coexist with it forming the quasispecies. When the mutation rate is sufficiently high, the master type no longer survives and gets replaced by a wide range of mutant types, thus destroying the quasispecies. It is the socalled "error catastrophe". But natural selection acts on phenotypes, not genotypes, and huge amounts of genotypes yield the same phenotype. An important consequence of this is the appearance of beneficial mutations which increase the fitness of mutants. A model has been recently proposed to describe quasispecies in the presence of beneficial mutations. This model lacks the error catastrophe of Eigen's model and predicts a steady state in which the viral population grows exponentially. Extinction can only occur if the infectivity of the quasispecies is so low that this exponential is negative. In this work I investigate the transient of this model when infection is started from a small amount of low fitness virions. I prove that, beyond an initial regime where viral population decreases (and can go extinct), the growth of the population is superexponential. Hence this population quickly becomes so huge that selection due to lack of host cells to be infected begins to act before the steady state is reached. This result suggests that viral infection may widespread before the virus has developed its optimal form.Mathematical and Computer Modelling 11/2010; 54(7). DOI:10.1016/j.mcm.2010.11.055  [Show abstract] [Hide abstract]
ABSTRACT: Ecosystems often undergo abrupt regime shifts in response to gradual external changes. These shifts are theoretically understood as a regime switch between alternative stable states of the ecosystem dynamical response to smooth changes in external conditions. Usual models introduce nonlinearities in the macroscopic dynamics of the ecosystem that lead to different stable attractors among which the shift takes place. Here we propose an alternative explanation of catastrophic regime shifts based on a recent model that pictures ecological communities as systems in continuous fluctuation, according to certain transition probabilities, between different microstates in the phase space of viable communities. We introduce a spontaneous extinction rate that accounts for gradual changes in external conditions, and upon variations on this control parameter the system undergoes a regime shift with similar features to those previously reported. Under our microscopic viewpoint we recover the main results obtained in previous theoretical and empirical work (anomalous variance, hysteresis cycles, trophic cascades). The model predicts a gradual loss of species in trophic levels from bottom to top near the transition. But more importantly, the spectral analysis of the transition probability matrix allows us to rigorously establish that we are observing the fingerprints, in a finite size system, of a true phase transition driven by background extinctions.Journal of Statistical Mechanics Theory and Experiment 10/2010; 2010(10):P10003. DOI:10.1088/17425468/2010/10/P10003  [Show abstract] [Hide abstract]
ABSTRACT: We study the effect of a network of contacts on the emergence of cooperation on social dilemmas under myopic best response dynamics. We begin by summarizing the main features observed under less intellectually demanding dynamics, pointing out their most relevant general characteristics. Subsequently we focus on the new framework of best response. By means of an extensive numerical simulation program we show that, contrary to the rest of dynamics considered so far, best response is largely unaffected by the underlying network, which implies that, in most cases, no promotion of cooperation is found with this dynamics. We do find, however, nontrivial results differing from the wellmixed population in the case of coordination games on lattices, which we explain in terms of the formation of spatial clusters and the conditions for their advancement, subsequently discussing their relevance to other networks.The European Physical Journal B 10/2009; 71(4):587595. DOI:10.1140/epjb/e2009001890  [Show abstract] [Hide abstract]
ABSTRACT: Spatial structure is known to have an impact on the evolution of cooperation, and so it has been intensively studied during recent years. Previous work has shown the relevance of some features, such as the synchronicity of the updating, the clustering of the network, or the influence of the update rule. This has been done, however, for concrete settings with particular games, networks, and update rules, with the consequence that some contradictions have arisen and a general understanding of these topics is missing in the broader context of the space of 2x2 games. To address this issue, we have performed a systematic and exhaustive simulation in the different degrees of freedom of the problem. In some cases, we generalize previous knowledge to the broader context of our study and explain the apparent contradictions. In other cases, however, our conclusions refute what seems to be established opinions in the field, as for example the robustness of the effect of spatial structure against changes in the update rule, or offer new insights into the subject, e.g., the relation between the intensity of selection and the asymmetry between the effects on games with mixed equilibria.Physical Review E 10/2009; 80(4):046106.  [Show abstract] [Hide abstract]
ABSTRACT: This chapter deals with the applications of the density functional (DF) formalism to the study of inhomogeneous systems with hard core interactions. It includes a brief tutorial on the fundamentals of the method, and the exact free energy DF for onedimensional hard rods obtained by Percus. The development of DF approximations for the free energy of hard spheres (HS) is presented through its milestones in the weighted density approximation (WDA) and the fundamental measure theory (FMT). The extensions of these approaches to HS mixtures include the FMT treatment of polydisperse systems and the approximations for mixtures with nonadditive core radii. The DF treatment of nonspherical hard core systems is presented within the generic context of the study of liquid crystals phases. The chapter is directed to the potential users of these theoretical techniques, with clear explanations of the practical implementation details of the most successful approximations.Theory and Simulation of HardSphere Fluids and Related Systems, 1st edited by A. Mulero, 10/2008: chapter 7: pages 247341; Lecture Notes in Physics, Volume 753, SpringerVerlag Berlin Heidelberg., ISBN: 9783540787662  [Show abstract] [Hide abstract]
ABSTRACT: An analytic derivation of the spinodal of a polydisperse mixture is presented. It holds for fluids whose excess free energy can be accurately described by a function of a few moments of the size distribution. It is shown that one such mixture of hard spheres in the PercusYevick approximation never demixes, despite its size distribution. In the BoublíkMansooriCarnahanStarlingLeland approximation, though, it demixes for a sufficiently wide lognormal size distribution. The importance of this result is twofold: first, this distribution is unimodal, and yet it phase separates; and second, lognormal size distributions appear in many experimental contexts. The same phenomenon is shown to occur for the fluid of parallel hard cubes.EPL (Europhysics Letters) 01/2007; 46(2):197. DOI:10.1209/epl/i1999002446 
Article: Time Scales in Evolutionary Dynamics
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ABSTRACT: Evolutionary game theory has traditionally assumed that all individuals in a population interact with each other between reproduction events. We show that eliminating this restriction by explicitly considering the time scales of interaction and selection leads to dramatic changes in the outcome of evolution. Examples include the selection of the inefficient strategy in the Harmony and StagHunt games, and the disappearance of the coexistence state in the Snowdrift game. Our results hold for any population size and in more general situations with additional factors influencing fitness.Physical Review Letters 11/2006; 97(15):158701.  [Show abstract] [Hide abstract]
ABSTRACT: We have applied the DFT formalism to the study of the orientational freezing of HCB and proved that through the ELA the most relevant theories proposed in the literature are recovered. This framework thus provides a connection between them and makes clear the assumptions under which they are obtained. The latter fact makes easier to improve them. When the formalism is applied in D > 2 the results are very satisfactory when compared to the simulations (in particular, the theory is exact in the limit D ). The IN transition predicted is first order in this case. However the results for D = 2 are not so good: the IN predicted is always continuous while the simulations show a change in the order of the transition. Its location is also too deviated from that obtained from simulations. Nevertheless the results for the equation of state are reasonably accurate, specially for low aspect ratios. We conclude that the simple factorisation arising from the approximation used for the DCF is not enough to account for such a complex behaviour. The possibility of a coupling with translational degrees of freedom is not ruled out as an explanation for the change of order of the transition, because this change happens when this transition is very close to the fluidsolid transition. Anyway an improvement of the isotropic DCF seems to be neccessary to get more accurate results.01/2006: pages 209219; 
Article: Cluster density functional theory for lattice models based on the theory of Mobius functions
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ABSTRACT: Rosenfeld's fundamental measure theory for lattice models is given a rigorous formulation in terms of the theory of Mobius functions of partially ordered sets. The freeenergy density functional is expressed as an expansion in a finite set of lattice clusters. This set is endowed a partial order, so that the coefficients of the cluster expansion are connected to its Mobius function. Because of this, it is rigorously proven that a unique such expansion exists for any lattice model. The lowdensity analysis of the freeenergy functional motivates a redefinition of the basic clusters (zerodimensional cavities) which guarantees a correct zerodensity limit of the pair and triplet direct correlation functions. This new definition extends Rosenfeld's theory to lattice model with any kind of shortrange interaction (repulsive or attractive, hard or soft, one or multicomponent...). Finally, a proof is given that these functionals have a consistent dimensional reduction, i.e. the functional for dimension d' can be obtained from that for dimension d (d'<d) if the latter is evaluated at a density profile confined to a d'dimensional subset. Comment: 21 pages, 2 figures, uses iopart.cls, as well as diagrams.sty (included)Journal of Physics A General Physics 04/2005; 38(34). DOI:10.1088/03054470/38/34/002 
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ABSTRACT: Inside living cells are complex mixtures of thousands of components. It is hopeless to try to characterize all the individual interactions in these mixtures. Thus, we develop a statistical approach to approximating them, and examine the conditions under which the mixtures phase separate. The approach approximates the matrix of secondvirial coefficients of the mixture by a random matrix, and determines the stability of the mixture from the spectrum of such random matrices.Physical Review Letters 01/2004; 91(24):245701. DOI:10.1103/PhysRevLett.91.245701  [Show abstract] [Hide abstract]
ABSTRACT: We use an extension of fundamental measure theory to lattice hardcore fluids to study the phase diagram of two different systems. First, twodimensional parallel hard squares with edgelength $\sigma=2$ in a simple square lattice. This system is equivalent to the lattice gas with first and second neighbor exclusion in the same lattice, and has the peculiarity that its close packing is degenerated (the system orders in sliding columns). A comparison with other theories is discussed. Second, a threedimensional binary mixture of parallel hard cubes with $\sigma_{\rm{L}}=6$ and $\sigma_{\rm{S}}=2$. Previous simulations of this model only focused on fluid phases. Thanks to the simplicity introduced by the discrete nature of the lattice we have been able to map out the complete phase diagram (both uniform and nonuniform phases) through a free minimization of the free energy functional, so the structure of the ordered phases is obtained as a result. A zoo of entropydriven phase transitions is found: one, two and threedimensional positional ordering, as well as fluidordered phase and solidsolid demixings. Comment: 14 pages, 16 figuresThe Journal of Chemical Physics 06/2003; 119(20). DOI:10.1063/1.1615511 
Article: Overcomplete free energy functional for D=1 particle systems with next neighbor interactions
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ABSTRACT: We deduce an overcomplete free energy functional for D=1 particle systems with next neighbor interactions, where the set of redundant variables are the local block densities $\varrho_i$ of $i$ interacting particles. The idea is to analyze the decomposition of a given pure system into blocks of $i$ interacting particles by means of a mapping onto a hard rod mixture. This mapping uses the local activity of component $i$ of the mixture to control the local association of $i$ particles of the pure system. Thus it identifies the local particle density of component $i$ of the mixture with the local block density $\varrho_i$ of the given system. Consequently, our overcomplete free energy functional takes on the hard rod mixture form with the set of block densities $\varrho_i$ representing the sequence of partition functions of the local aggregates of particle numbers $i$. The system of equations for the local particle density $\varrho$ of the original system is closed via a subsidiary condition for the block densities in terms of $\varrho$. Analoguous to the uniform isothermalisobaric technique, all our results are expressible in terms of effective pressures. We illustrate the theory with two standard examples, the adhesive interaction and the squarewell potential. For the uniform case, our proof of such an overcomplete format is based on the exponential boundedness of the number of partitions of a positive integer (HardyRamanujan formula) and on Varadhan's theorem on the asymptotics of a class of integrals. We also discuss the applicability of our strategy in higher dimensional space, as well as models suggested thereof.Journal of Statistical Physics 07/2002; 111(56). DOI:10.1023/A:1023096031180  [Show abstract] [Hide abstract]
ABSTRACT: We present the extension of Rosenfeld's fundamental measure theory to lattice models by constructing a density functional for ddimensional mixtures of parallel hard hypercubes on a simple hypercubic lattice. The onedimensional case is exactly solvable and two cases must be distinguished: all the species with the same lebgth parity (additive mixture), and arbitrary length parity (nonadditive mixture). At the best of our knowledge, this is the first time that the latter case is considered. Based on the onedimensional exact functional form, we propose the extension to higher dimensions by generalizing the zerodimensional cavities method to lattice models. This assures the functional to have correct dimensional crossovers to any lower dimension, including the exact zerodimensional limit. Some applications of the functional to particular systems are also shown. Comment: 22 pages, 7 figures, needs IOPP LaTeX styles filesJournal of Physics Condensed Matter 05/2002; 14(46). DOI:10.1088/09538984/14/46/314  [Show abstract] [Hide abstract]
ABSTRACT: Ideal bosons and a classical system of monomers that aggregate forming noninteracting ring polymers are known to have the same partition function. So, the ring polymers have a phase transition, the analogue of BoseEinstein condensation of bosons. At this phase transition macroscopic polymers are formed. The link between these systems is made via Feynman's path integrals: these integrals are the same for the trajectories of the bosons in imaginary time and for the configurations of the polymers. We show that a transition of this general form occurs within a whole class of aggregating systems. Examples are the lamellae formation in suspensions of disclike micelles or the emulsification failure observed in wateroilsurfactant emulsions. As with bosons, the transition occurs even when aggregates do not interact. The lambdatransition in 4He is believed to be BoseEinstein condensation modified by interatomic interactions. We suggest that interaggregate interactions too only modify the transition we have found.Physical Review E 04/2002; 65(3 Pt 1):031406. DOI:10.1103/PhysRevE.65.031406  [Show abstract] [Hide abstract]
ABSTRACT: In a previous paper (J. Zhang {\it et al.}, J. Chem. Phys. {\bf 110}, 5318 (1999)) we introduced a model for polydisperse hard sphere mixtures that is able to adjust its particlesize distribution. Here we give the explanation of the questions that arose in the previous description and present a consistent theory of the phase transition in this system, based on the PercusYevick equation of state. The transition is continuous, and like BoseEinstein condensation a macroscopic aggregate is formed due to the microscopic interactions. A BMCSLlike treatment leads to the same conclusion with slightly more accurate predictions. Comment: 7 pages including 5 figures in revtexThe Journal of Chemical Physics 03/2001; 115(2). DOI:10.1063/1.1380210  [Show abstract] [Hide abstract]
ABSTRACT: Ideal bosons and classical ring polymers formed via selfassembly, are known to have the same partition function, and so analogous phase transitions. In ring polymers, the analogue of BoseEinstein condensation occurs when a ring polymer of macroscopic size appears. We show that a transition of the same general form occurs within a whole class of systems with selfassembly, and illustrate it with the emulsification failure of a microemulsion phase of water, oil and surfactant. As with BoseEinstein condensation, the transition occurs even in the absence of interactions. Comment: 7 pages, 1 figure, typeset with EUROTeX, uses epsfigEPL (Europhysics Letters) 12/2000; 55(4). DOI:10.1209/epl/i2001004366  [Show abstract] [Hide abstract]
ABSTRACT: We study the phase behaviour of the Zwanzig model of suspensions of hard rods, allowing for polydispersity in the lengths of the rods. In spite of the simplified nature of the model (rods are restricted to lie along one of three orthogonal axes), the results agree qualitatively with experimental observations: the coexistence region broadens significantly as the polydispersity increases, and strong fractionation occurs, with long rods found preferentially in the nematic phase. These conclusions are obtained from an analysis of the exact phase equilibrium equations. In the second part of the paper, we consider the application of the recently developed ``moment free energy method'' to the polydisperse Zwanzig model. Even though the model contains nonconserved densities due to the orientational degrees of freedom, most of the exactness statements (regarding the onset of phase coexistence, spinodals, and critical points) derived previously for systems with conserved densities remain valid. The accuracy of the results from the moment free energy increases as more and more additional moments are retained in the description. We show how this increase in accuracy can be monitored without relying on knowledge of the exact results, and discuss an adaptive technique for choosing the extra moments optimally.The Journal of Chemical Physics 06/2000; DOI:10.1063/1.1290473
Publication Stats
829  Citations  
84.70  Total Impact Points  
Top Journals
Institutions

2012

University of Zaragoza
 Department of Theoretical Physics
Caesaraugusta, Aragon, Spain


1970–2012

University Carlos III de Madrid
 High Technical College
Getafe, Madrid, Spain


2006

Complutense University of Madrid
 Facultad de Ciencias Físicas
Madrid, Madrid, Spain
