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1 to 50 of 115 results
  • Networks in cognitive science

     Baronchelli, Andrea; Ferrer Cancho, Ramon; Pastor Satorras, Romualdo; Chatter, Nick; Christiansen, Morten H.
    Trends in cognitive sciences
    Date of publication: 2013-07-01
    Journal article

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    Networks of interconnected nodes have long played a key role in Cognitive Science, from artificial neural networks to spreading activation models of semantic memory. Recently, however, a new Network Science has been developed, providing insights into the emergence of global, system-scale properties in contexts as diverse as the Internet, metabolic reactions, and collaborations among scientists. Today, the inclusion of network theory into Cognitive Sciences, and the expansion of complex-systems science, promises to significantly change the way in which the organization and dynamics of cognitive and behavioral processes are understood. In this paper, we review recent contributions of network theory at different levels and domains within the Cognitive Sciences.

  • Topological properties of a time-integrated activity-driven network

     Starnini, Michele; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2013-06
    Journal article

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    Here we consider the topological properties of the integrated networks emerging from the activity-driven model, a temporal network model recently proposed to explain the power-law degree distribution empirically observed in many real social networks. By means of a mapping to a hidden-variable network model, we provide analytical expressions for the main topological properties of the integrated network, depending on the integration time and the distribution of activity potential characterizing the model. The expressions obtained, exacts in some cases, the results of controlled asymptotic expansions in others, are confirmed by means of extensive numerical simulations. Our analytical approach, which highlights the differences of the model with respect to the empirical observations made in real social networks, can be easily extended to deal with improved, more realistic modifications of the activity-driven network paradigm.

  • Mean-field analysis of the q-voter model on networks

     Moretti, Paolo; Liu, Suyu; Castellano, Claudio; Pastor Satorras, Romualdo
    Journal of statistical physics
    Date of publication: 2013-04-01
    Journal article

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    We present a detailed investigation of the behavior of the nonlinear q-voter model for opinion dynamics. At the mean-field level we derive analytically, for any value of the number q of agents involved in the elementary update, the phase diagram, the exit probability and the consensus time at the transition point. The mean-field formalism is extended to the case that the interaction pattern is given by generic heterogeneous networks. We finally discuss the case of random regular networks and compare analytical results with simulations.

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    Evolution in a changing environment  Open access

     Baronchelli, Andrea; Chater, Nick; Christiansen, Morten H.; Pastor Satorras, Romualdo
    PLoS one
    Date of publication: 2013-01-10
    Journal article

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    We propose a simple model for genetic adaptation to a changing environment, describing a fitness landscape characterized by two maxima. One is associated with “specialist” individuals that are adapted to the environment; this maximum moves over time as the environment changes. The other maximum is static, and represents “generalist” individuals not affected by environmental changes. The rest of the landscape is occupied by “maladapted” individuals. Our analysis considers the evolution of these three subpopulations. Our main result is that, in presence of a sufficiently stable environmental feature, as in the case of an unchanging aspect of a physical habitat, specialists can dominate the population. By contrast, rapidly changing environmental features, such as language or cultural habits, are a moving target for the genes; here, generalists dominate, because the best evolutionary strategy is to adopt neutral alleles not specialized for any specific environment. The model we propose is based on simple assumptions about evolutionary dynamics and describes all possible scenarios in a non-trivial phase diagram. The approach provides a general framework to address such fundamental issues as the Baldwin effect, the biological basis for language, or the ecological consequences of a rapid climate change.

  • Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks

     Boguñá, Marian; Castellano, Claudio; Pastor Satorras, Romualdo
    Physical review letters
    Date of publication: 2013-08-07
    Journal article

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    We develop an analytical approach to the susceptible-infected-susceptible epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance between the number of high degree nodes in the network and the topological distance between them dictates the existence or absence of such a threshold. In particular, small-world random networks with a degree distribution decaying slower than an exponential have a vanishing epidemic threshold in the thermodynamic limit.

  • Immunization strategies for epidemic processes in time-varying contact networks

     Starnini, Michele; Machens, Anna; Cattuto, Ciro; Barrat, Alain; Pastor Satorras, Romualdo
    Journal of theoretical biology
    Date of publication: 2013
    Journal article

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    preading processes represent a very efficient tool to investigate the structural properties of networks and the relative importance of their constituents, and have been widely used to this aim in static networks. Here we consider simple disease spreading processes on empirical time-varying networks of contacts between individuals, and compare the effect of several immunization strategies on these processes. An immunization strategy is defined as the choice of a set of nodes (individuals) who cannot catch nor transmit the disease. This choice is performed according to a certain ranking of the nodes of the contact network.

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    Phase transitions with infinitely many absorbing states in complex networks  Open access

     Sander, Renan S; Ferreira, Silvio C.; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2013-02-27
    Journal article

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    We investigate the properties of the threshold contact process (TCP), a process showing an absorbing-state phase transition with infinitely many absorbing states, on random complex networks. The finite-size scaling exponents characterizing the transition are obtained in a heterogeneous mean-field (HMF) approximation and compared with extensive simulations, particularly in the case of heterogeneous scale-free networks. We observe that the TCP exhibits the same critical properties as the contact process, which undergoes an absorbing-state phase transition to a single absorbing state. The accordance among the critical exponents of different models and networks leads to conjecture that the critical behavior of the contact process in a HMF theory is a universal feature of absorbing-state phase transitions in complex networks, depending only on the locality of the interactions and independent of the number of absorbing states.

    We investigate the properties of the threshold contact process (TCP), a process showing an absorbing-state phase transition with infinitely many absorbing states, on random complex networks. The finite-size scaling exponents characterizing the transition are obtained in a heterogeneous mean-field (HMF) approximation and compared with extensive simulations, particularly in the case of heterogeneous scale-free networks. We observe that the TCP exhibits the same critical properties as the contact process, which undergoes an absorbing-state phase transition to a single absorbing state. The accordance among the critical exponents of different models and networks leads to conjecture that the critical behavior of the contact process in a HMF theory is a universal feature of absorbing-state phase transitions in complex networks, depending only on the locality of the interactions and independent of the number of absorbing states. The conditions for the applicability of the conjecture are discussed considering a parallel with the susceptible-infected-susceptible epidemic spreading model, which in fact belongs to a different universality class in complex networks.

  • Effects of local population structure in a reaction-diffusion model of a contact process on metapopulation networks

     de Souza Mata, Angelica; Ferreira, Silvio C.; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2013-10-30
    Journal article

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    We investigate the effects of local population structure in reaction-diffusion processes representing a contact process (CP) on metapopulations represented as complex networks. Considering a model in which the nodes of a large scale network represent local populations defined in terms of a homogeneous graph, we show by means of extensive numerical simulations that the critical properties of the reaction-diffusion system are independent of the local population structure, even when this one is given by a ordered linear chain. This independence is confirmed by the perfect matching between numerical critical exponents and the results from a heterogeneous mean-field theory suited, in principle, to describe situations of local homogeneous mixing. The analysis of several variations of the reaction-diffusion process allows us to conclude the independence from population structure of the critical properties of CP-like models on metapopulations, and thus of the universality of the reaction-diffusion description of this kind of models.

  • Modeling human dynamics of face-to-face interaction networks

     Starnini, Michele; Baronchelli, Andrea; Pastor Satorras, Romualdo
    Physical review letters
    Date of publication: 2013-04-15
    Journal article

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    Face-to-face interaction networks describe social interactions in human gatherings, and are the substrate for processes such as epidemic spreading and gossip propagation. The bursty nature of human behavior characterizes many aspects of empirical data, such as the distribution of conversation lengths, of conversations per person, or of interconversation times. Despite several recent attempts, a general theoretical understanding of the global picture emerging from data is still lacking. Here we present a simple model that reproduces quantitatively most of the relevant features of empirical face-to-face interaction networks. The model describes agents that perform a random walk in a two-dimensional space and are characterized by an attractiveness whose effect is to slow down the motion of people around them. The proposed framework sheds light on the dynamics of human interactions and can improve the modeling of dynamical processes taking place on the ensuing dynamical social networks.

  • Generalized voter-like models on heterogeneous networks

     Moretti, Paolo; Baronchelli, Andrea; Starnini, Michele; Pastor Satorras, Romualdo
    Date of publication: 2013
    Book chapter

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    This Chapter presents a generalized model of consensus formation, which is able to encompass all previous formulations of copy/invasion processes inspired by variations on the voter model and the Moran process. It considered the implementation of such generalized dynamics on a heterogeneous contact pattern, represented by a complex network, and derived the theoretical predictions for the relevant dynamical quantities, within the assumptions of the heterogeneous mean-field theory. The chapter provides a brief review of previous results that can be recovered by this generalized formalism, and considers a novel application to the case of opinion formation in a social network. In particular, it addressed the case in which the opinion strength of an individual is related to his/her degree centrality in the network.

  • FET-Proactive Project MULTIPLEX

     Caldarelli, Guido; Pastor Satorras, Romualdo
    Participation in a competitive project

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    Percolation analysis of force networks in anisotropic granular matter  Open access

     Pastor Satorras, Romualdo; Miguel Lopez, Maria del Carmen
    Journal of statistical mechanics: Theory and experiment
    Date of publication: 2012-02-09
    Journal article

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    We study the percolation properties of force networks in an anisotropic model for granular packings, the so-called q-model. Following the original recipe of Ostojic et al (2006 Nature 439 828), we consider a percolation process in which forces smaller than a given threshold f are deleted in the network. For a critical threshold fc, the system experiences a transition akin to percolation. We determine the point of this transition and its characteristic critical exponents applying a finite-size scaling analysis that takes explicitly into account the directed nature of the q-model. By means of extensive numerical simulations, we show that this percolation transition is strongly affected by the anisotropic nature of the model, yielding characteristic exponents which are neither those found in isotropic granular systems nor those in the directed version of standard percolation. The differences shown by the computed exponents can be related to the presence of strong directed correlations and mass conservation laws in the model under scrutiny.

    We study the percolation properties of force networks in an anisotropic model for granular packings, the so-called q-model. Following the original recipe of Ostojic et al (2006 Nature 439 828), we consider a percolation process in which forces smaller than a given threshold f are deleted in the network. For a critical threshold fc, the system experiences a transition akin to percolation. We determine the point of this transition and its characteristic critical exponents applying a finite-size scaling analysis that takes explicitly into account the directed nature of the q-model. By means of extensive numerical simulations, we show that this percolation transition is strongly affected by the anisotropic nature of the model, yielding characteristic exponents which are neither those found in isotropic granular systems nor those in the directed version of standard percolation. The differences shown by the computed exponents can be related to the presence of strong directed correlations and mass conservation laws in the model under scrutiny.

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    Universal and nonuniversal features of the generalized voter class for ordering dynamics in two dimensions  Open access

     Castellano, Claudio; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2012-11-21
    Journal article

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    By considering three different spin models belonging to the generalized voter class for ordering dynamics in two dimensions [ Dornic et al. Phys. Rev. Lett. 87 045701 (2001)], we show that they behave differently from the linear voter model when the initial configuration is an unbalanced mixture of up and down spins. In particular, we show that for nonlinear voter models the exit probability (probability to end with all spins up when starting with an initial fraction x of them) assumes a nontrivial shape. This is the first time a nontrivial exit probability is observed in two-dimensional systems. The change is traced back to the strong nonconservation of the average magnetization during the early stages of dynamics. Also the time needed to reach the final consensus state TN(x) has an anomalous nonuniversal dependence on x.

    By considering three different spin models belonging to the generalized voter class for ordering dynamics in two dimensions [ Dornic et al. Phys. Rev. Lett. 87 045701 (2001)], we show that they behave differently from the linear voter model when the initial configuration is an unbalanced mixture of up and down spins. In particular, we show that for nonlinear voter models the exit probability (probability to end with all spins up when starting with an initial fraction x of them) assumes a nontrivial shape. This is the first time a nontrivial exit probability is observed in two-dimensional systems. The change is traced back to the strong nonconservation of the average magnetization during the early stages of dynamics. Also the time needed to reach the final consensus state TN(x) has an anomalous nonuniversal dependence on x.

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    Random walks on temporal networks  Open access

     Starnini, Michele; Baronchelli, Andrea; Barrat, Alain; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2012
    Journal article

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    Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various time scales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis of the temporal patterns characterizing dynamic networks are still recent, so that many questions remain open. Here, we study how random walks, as a paradigm of dynamical processes, unfold on temporally evolving networks. To this aim, we use empirical dynamical networks of contacts between individuals, and characterize the fundamental quantities that impact any general process taking place upon them. Furthermore, we introduce different randomizing strategies that allow us to single out the role of the different properties of the empirical networks. We show that the random walk exploration is slower on temporal networks than it is on the aggregate projected network, even when the time is properly rescaled. In particular, we point out that a fundamental role is played by the temporal correlations between consecutive contacts present in the data. Finally, we address the consequences of the intrinsically limited duration of many real world dynamical networks. Considering the fundamental prototypical role of the random walk process, we believe that these results could help to shed light on the behavior of more complex dynamics on temporally evolving networks.

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    The biological origin of linguistic diversity  Open access

     Baronchelli, Andrea; Chater, Nick; Pastor Satorras, Romualdo; Christiansen, Morten H.
    PLoS one
    Date of publication: 2012-10-30
    Journal article

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    In contrast with animal communication systems, diversity is characteristic of almost every aspect of human language. Languages variously employ tones, clicks, or manual signs to signal differences in meaning; some languages lack the noun-verb distinction (e.g., Straits Salish), whereas others have a proliferation of fine-grained syntactic categories (e.g., Tzeltal); and some languages do without morphology (e.g., Mandarin), while others pack a whole sentence into a single word (e.g., Cayuga). A challenge for evolutionary biology is to reconcile the diversity of languages with the high degree of biological uniformity of their speakers. Here, we model processes of language change and geographical dispersion and find a consistent pressure for flexible learning, irrespective of the language being spoken. This pressure arises because flexible learners can best cope with the observed high rates of linguistic change associated with divergent cultural evolution following human migration. Thus, rather than genetic adaptations for specific aspects of language, such as recursion, the coevolution of genes and fast-changing linguistic structure provides the biological basis for linguistic diversity. Only biological adaptations for flexible learning combined with cultural evolution can explain how each child has the potential to learn any human language.

  • Competing activation mechanisms in epidemics on networks

     Castellano, Claudio; Pastor Satorras, Romualdo
    Scientific reports
    Date of publication: 2012-04-20
    Journal article

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  • Slow dynamics and rare-region effects in the contact process on weighted tree networks

     Odor, G.; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2012-08-28
    Journal article

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    Random walks and search in time-varying networks  Open access

     Perra, Nicola; Mocanu, Delia R.; Baronchelli, Andrea; Gonçalves, Bruno; Pastor Satorras, Romualdo; Vespignani, Alessandro
    Physical review letters
    Date of publication: 2012-12-04
    Journal article

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    The random walk process underlies the description of a large number of real-world phenomena. Here we provide the study of random walk processes in time-varying networks in the regime of time-scale mixing, i.e., when the network connectivity pattern and the random walk process dynamics are unfolding on the same time scale. We consider a model for time-varying networks created from the activity potential of the nodes and derive solutions of the asymptotic behavior of random walks and the mean first passage time in undirected and directed networks. Our findings show striking differences with respect to the well-known results obtained in quenched and annealed networks, emphasizing the effects of dynamical connectivity patterns in the definition of proper strategies for search, retrieval, and diffusion processes in time-varying networks.

    The random walk process underlies the description of a large number of real-world phenomena. Here we provide the study of random walk processes in time-varying networks in the regime of time-scale mixing, i.e., when the network connectivity pattern and the random walk process dynamics are unfolding on the same time scale. We consider a model for time-varying networks created from the activity potential of the nodes and derive solutions of the asymptotic behavior of random walks and the mean first passage time in undirected and directed networks. Our findings show striking differences with respect to the well-known results obtained in quenched and annealed networks, emphasizing the effects of dynamical connectivity patterns in the definition of proper strategies for search, retrieval, and diffusion processes in time-varying networks.

  • Heterogenous mean-field analysis of a generalized voter-like model on networks

     Moretti, Paolo; Liu, S.Y.; Baronchelli, Andrea; Pastor Satorras, Romualdo
    European physical journal B
    Date of publication: 2012-03
    Journal article

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    Epidemic thresholds of the susceptible-infected-susceptible model on networks: a comparison of numerical and theoretical results  Open access

     Ferreira, Silvio C.; Castellano, Claudio; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2012-10-15
    Journal article

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    Recent work has shown that different theoretical approaches to the dynamics of the susceptible-infected-susceptible (SIS) model for epidemics lead to qualitatively different estimates for the position of the epidemic threshold in networks. Here we present large-scale numerical simulations of the SIS dynamics on various types of networks, allowing the precise determination of the effective threshold for systems of finite size N. We compare quantitatively the numerical thresholds with theoretical predictions of the heterogeneous mean-field theory and of the quenched mean-field theory. We show that the latter is in general more accurate, scaling with N with the correct exponent, but often failing to capture the correct prefactor.

    Recent work has shown that different theoretical approaches to the dynamics of the susceptible-infected-susceptible (SIS) model for epidemics lead to qualitatively different estimates for the position of the epidemic threshold in networks. Here we present large-scale numerical simulations of the SIS dynamics on various types of networks, allowing the precise determination of the effective threshold for systems of finite size N. We compare quantitatively the numerical thresholds with theoretical predictions of the heterogeneous mean-field theory and of the quenched mean-field theory. We show that the latter is in general more accurate, scaling with N with the correct exponent, but often failing to capture the correct prefactor.

  • Ordering dynamics of the multi-state voter model

     Starnini, Michele; Baronchelli, Andrea; Pastor Satorras, Romualdo
    Journal of statistical mechanics: Theory and experiment
    Date of publication: 2012-10
    Journal article

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  • Activity driven modeling of time varying networks

     Perra, Nicola; Gonçalves, Bruno; Pastor Satorras, Romualdo; Vespignani, Alessandro
    Scientific reports
    Date of publication: 2012-06-25
    Journal article

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    Network modeling plays a critical role in identifying statistical regularities and structural principles common to many systems. The large majority of recent modeling approaches are connectivity driven. The structural patterns of the network are at the basis of the mechanisms ruling the network formation. Connectivity driven models necessarily provide a time-aggregated representation that may fail to describe the instantaneous and fluctuating dynamics of many networks. We address this challenge by defining the activity potential, a time invariant function characterizing the agents' interactions and constructing an activity driven model capable of encoding the instantaneous time description of the network dynamics. The model provides an explanation of structural features such as the presence of hubs, which simply originate from the heterogeneous activity of agents. Within this framework, highly dynamical networks can be described analytically, allowing a quantitative discussion of the biases induced by the time-aggregated representations in the analysis of dynamical processes.

  • Premi ICREA Acadèmia

     Pastor Satorras, Romualdo; Ginebra Molins, Maria Pau; Arroyo Balaguer, Marino; Camps Carmona, Adriano Jose; Aleman Llanso, Carlos Enrique
    Award or recognition

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  • Voter models on weighted networks

     Baronchelli, Andrea; Castellano, Claudio; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2011-06-29
    Journal article

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    Irrelevance of information outflow in opinion dynamics models  Open access

     Castellano, Claudio; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2011-01-27
    Journal article

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    The Sznajd model for opinion dynamics has attracted a large interest as a simple realization of the psychological principle of social validation. As its most salient feature, it has been claimed that the Sznajd model is qualitatively different from other ordering processes because it is the only one featuring outflow of information as opposed to inflow. We show that this claim is unfounded by presenting a generalized zero-temperature Glauber type of dynamics, which yields results indistinguishable from those of the Sznajd model. In one dimension, we also derive an exact expression for the exit probability of the Sznajd model, which turns out to coincide with the result of an analytical approach based on the Kirkwood approximation. This observation raises interesting questions about the applicability and limitations of this approach.

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    Quasistationary simulations of the contact process on quenched networks  Open access

     Ferreira, Silvio C.; Ferreira, Ronan S.; Castellano, Claudio; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2011
    Journal article

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    We present high-accuracy quasistationary (QS) simulations of the contact process in quenched networks, built using the configuration model with both structural and natural cutoffs. The critical behavior is analyzed in the framework of the anomalous finite-size scaling which was recently shown to hold for the contact process on annealed networks. It turns out that the quenched topology does not qualitatively change the critical behavior, leading only (as expected) to a shift of the transition point. The anomalous finite-size scaling holds with exactly the same exponents of the annealed case, so we can conclude that heterogeneous mean-field theory works for the contact process on quenched networks, at odds with previous claims. Interestingly, topological correlations induced by the presence of the natural cutoff do not alter the picture.

  • Quasistationary analysis of the contact process on annealed scale-free networks

     Ferreira, Silvio C.; Ferreira, Ronan S.; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2011
    Journal article

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  • Complex networks and glassy dynamics: walks in the energy landscape

     Moretti, Paolo; Baronchelli, Andrea; Barrat, Alain; Pastor Satorras, Romualdo
    Journal of statistical mechanics: Theory and experiment
    Date of publication: 2010-03
    Journal article

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  • Mean-field diffusive dynamics on weighted networks

     Baronchelli, Andrea; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2010-07-12
    Journal article

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  • Steady-state dynamics of the forest fire model on complex networks

     Bancal, J. -D.; Pastor Satorras, Romualdo
    European physical journal B
    Date of publication: 2010-07
    Journal article

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    Many sociological networks, as well as biological and technological ones, can be represented in terms of complex networks with a heterogeneous connectivity pattern. Dynamical processes taking place on top of them can be very much influenced by this topological fact. In this paper we consider a paradigmatic model of non-equilibrium dynamics, namely the forest fire model, whose relevance lies in its capacity to represent several epidemic processes in a general parametrization. We study the behavior of this model in complex networks by developing the corresponding heterogeneous mean-field theory and solving it in its steady state. We provide exact and approximate expressions for homogeneous networks and several instances of heterogeneous networks. A comparison of our analytical results with extensive numerical simulations allows to draw the region of the parameter space in which heterogeneous mean-field theory provides an accurate description of the dynamics, and enlights the limits of validity of the mean-field theory in situations where dynamical correlations become important.

  • COMPLEX NETWORKS Patterns of complexity

     Pastor Satorras, Romualdo; Vespignani, Alessandro
    Nature physics
    Date of publication: 2010-07
    Journal article

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  • Thresholds for epidemic spreading in networks

     Castellano, Claudio; Pastor Satorras, Romualdo
    Physical review letters
    Date of publication: 2010
    Journal article

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  • Redes complejas y auto-organización en ecología, biodiversidad y neurociencia

     Pastor Satorras, Romualdo; Muñoz, Miguel Angel
    Participation in a competitive project

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  • Effects of mobility on ordering dynamics

     Baronchelli, Andrea; Pastor Satorras, Romualdo
    Journal of statistical mechanics: Theory and experiment
    Date of publication: 2009-11
    Journal article

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    Models of ordering dynamics allow us to understand natural systems in which an initially disordered population homogenizes some traits via local interactions. The simplest of these models, with wide applications ranging from evolutionary to social dynamics, are the Voter and Moran processes, usually defined in terms of static or randomly mixed individuals that interact with a neighbor to copy or modify a discrete trait. Here we study the effects of diffusion in Voter/Moran processes by proposing a generalization of ordering dynamics in a metapopulation framework, in which individuals are endowed with mobility and diffuse through a spatial structure represented as a graph of patches upon which interactions take place. We show that diffusion dramatically affects the time to reach the homogeneous state, independently of the underlying network’s topology, while the final consensus emerges through different local/global mechanisms, depending on the mobility strength. Our results highlight the crucial role played by mobility in ordering processes and set up a general framework that allows its effect to be studied on a large class of models, with implications in the understanding of evolutionary and social phenomena.

  • Glass transition and random walks on complex energy landscapes

     Baronchelli, Andrea; Barrat, A; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2009-08
    Journal article

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  • Langevin approach for the dynamics of the contact process on annealed scale-free networks

     Boguna, M; Castellano, C; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2009-03
    Journal article

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    Nonlinear q-voter model  Open access

     Castellano, C; Muñoz, M A; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2009-10
    Journal article

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    We introduce a nonlinear variant of the voter model, the q-voter model, in which q neighbors (with possible repetition) are consulted for a voter to change opinion. If the q neighbors agree, the voter takes their opinion; if they do not have a unanimous opinion, still a voter can flip its state with probability ε. We solve the model on a fully connected network (i.e., in mean field) and compute the exit probability as well as the average time to reach consensus by employing the backward Fokker-Planck formalism and scaling arguments. We analyze the results in the perspective of a recently proposed Langevin equation aimed at describing generic phase transitions in systems with two (Z2-symmetric) absorbing states. In particular, by deriving explicitly the coefficients of such a Langevin equation as a function of the microscopic flipping probabilities, we find that in mean field the q-voter model exhibits a disordered phase for high ε and an ordered one for low ε with three possible ways to go from one to the other: (i) a unique (generalized-voter-like) transition, (ii) a series of two consecutive transitions, one (Ising-like) in which the Z2 symmetry is broken and a separate one (in the directed-percolation class) in which the system falls into an absorbing state, and (iii) a series of two transitions, including an intermediate regime in which the final state depends on initial conditions. This third (so far unexplored) scenario, in which a type of ordering dynamics emerges, is rationalized and found to be specific of mean field, i.e., fluctuations are explicitly shown to wash it out in spatially extended systems.

  • GRUP DE SIMULACIO PER ORDINADOR EN MATERIA CONDENSADA

     Pastor Satorras, Romualdo; Sese Castel, Gemma; Rey Oriol, Rosendo; Casulleras Ambros, Joaquin; Trullàs Simó, Joaquim; Bitrian Varea, Vicente; Baronchelli, Andrea; Osychenco, Oleg; Canales Gabriel, Manel; Boronat Medico, Jordi; Marti Rabassa, Jordi; Macia Rey, Adrian; Calvo Minguillon, Ausias March; Ortiz de Urbina Viade, Jordi; Mazzanti Castrillejo, Fernando Pablo; Astrakharchik, Grigori; Rota, Riccardo; Sala2 Viñas, Jonàs; Guardia Manuel, Elvira
    Participation in a competitive project

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  • PREMI ICREA ACADEMIA

     Pastor Satorras, Romualdo
    Participation in a competitive project

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  • Routes to thermodynamic limit on scale-free networks

     Pastor Satorras, Romualdo; Castellano, Claudio
    Physical review letters
    Date of publication: 2008-04
    Journal article

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  • Random walks on complex trees.

     Baronchelli, Andrea; Catanzaro, Michele; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2008-07
    Journal article

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  • Bosonic reaction-diffusion processes on scale-free networks

     Baronchelli, Andrea; Catanzaro, Michele; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2008-07
    Journal article

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  • DYNAMICAL PROCESSES IN COMPLEX NETWORKS

     Catanzaro, Michele
    Defense's date: 2008-07-10
    Department of Applied Physics, Universitat Politècnica de Catalunya
    Theses

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  • Reaction-diffusion processes and metapopulation models in heterogeneous networks

     Colizza, V; Pastor Satorras, Romualdo; Vespignani, Alessandro
    Nature physics
    Date of publication: 2007-04
    Journal article

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  • Comment on "Non-mean-field behavior of the contact process on scale-free networks" - Reply

     Castellano, C; Pastor Satorras, Romualdo
    Physical review letters
    Date of publication: 2007-01
    Journal article

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  • Correlations in complex networks

     Pastor Satorras, Romualdo; Serrano, M A; Boguñá, M; Vespignani, Alessandro
    Date of publication: 2007-01-01
    Book chapter

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  • Procesos dinámicos en sistemas físicos auto-ensamblados

     Pastor Satorras, Romualdo
    Participation in a competitive project

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  • Bosonic dynamics in complex networks

     Pastor Satorras, Romualdo
    International Workshop and Conference on Network Science NetSci'08
    Presentation's date: 2007-06-02
    Presentation of work at congresses

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  • Correlations in weighted networks - art. no. 055101

     Serrano, M A; Boguna, M; Pastor Satorras, Romualdo
    Physical review E: statistical, nonlinear, and soft matter physics
    Date of publication: 2006-11
    Journal article

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