arXiv subjects

Romualdo Pastor-Satorras

Publications and source records attributed to Romualdo Pastor-Satorras.

At least 91 records · Page 5Linked to original sources

arXiv2010

Irrelevance of information outflow in opinion dynamics models

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, that 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.

physics.soc-ph↗

arXiv2010

Thresholds for epidemic spreading in networks

We study the threshold of epidemic models in quenched networks with degree distribution given by a power-law. For the susceptible-infected-susceptible (SIS) model the activity threshold lambda_c vanishes in the large size limit on any network whose maximum degree k_max diverges with the system size, at odds with heterogeneous mean-field (HMF) theory. The vanishing of the threshold has not to do with the scale-free nature of the connectivity pattern and is instead originated by the largest hub in the system being active for any spreading rate lambda>1/sqrt{k_max} and playing the role of a self-sustained source that spreads the infection to the rest of the system. The susceptible-infected-removed (SIR) model displays instead agreement with HMF theory and a finite threshold for scale-rich networks. We conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.

cond-mat.stat-mech↗

arXiv2010

Mean-field diffusive dynamics on weighted networks

Diffusion is a key element of a large set of phenomena occurring on natural and social systems modeled in terms of complex weighted networks. Here, we introduce a general formalism that allows to easily write down mean-field equations for any diffusive dynamics on weighted networks. We also propose the concept of annealed weighted networks, in which such equations become exact. We show the validity of our approach addressing the problem of the random walk process, pointing out a strong departure of the behavior observed in quenched real scale-free networks from the mean-field predictions. Additionally, we show how to employ our formalism for more complex dynamics. Our work sheds light on mean-field theory on weighted networks and on its range of validity, and warns about the reliability of mean-field results for complex dynamics.

cond-mat.stat-mech↗

arXiv2009

Effects of mobility on ordering dynamics

Models of ordering dynamics allow 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 to study its effect on a large class of models, with implications in the understanding of evolutionary and social phenomena.

cond-mat.stat-mech↗

arXiv2009

Steady-State Dynamics of the Forest Fire Model on Complex Networks

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.

cond-mat.stat-mech↗

arXiv2009

Glass transition and random walks on complex energy landscapes

We present a simple mathematical model of glassy dynamics seen as a random walk in a directed, weighted network of minima taken as a representation of the energy landscape. Our approach gives a broader perspective to previous studies focusing on particular examples of energy landscapes obtained by sampling energy minima and saddles of small systems. We point out how the relation between the energies of the minima and their number of neighbors should be studied in connection with the network's global topology, and show how the tools developed in complex network theory can be put to use in this context.

cond-mat.stat-mech↗

arXiv2008

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

We study the dynamics of the contact-process, one of the simplest nonequilibrium stochastic processes, taking place on a scale-free network. We consider the network topology as annealed, i.e. all links are rewired at each microscopic time step, so that no dynamical correlation can build up. This is a practical implementation of the absence of correlations assumed by mean-field approaches. We present a detailed analysis of the contact process in terms of a Langevin equation, including explicitly the effects of stochastic fluctuations in the number of particles in finite networks. This allows us to determine analytically the survival time for spreading experiments and the density of active sites in surviving runs. The fluctuations in the topological structure induce anomalous scaling effects with respect to the system size when the degree distribution has an "hard" upper bound. When the upper bound is soft, the presence of outliers with huge connectivity perturbs the picture even more, inducing an apparent shift of the critical point. In light of these findings, recent theoretical and numerical results in the literature are critically reviewed.

cond-mat.dis-nn↗

arXiv2008

Random walks on complex trees

We study the properties of random walks on complex trees. We observe that the absence of loops reflects in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and the mean topological displacement from the origin present a considerable slowing down in the tree case. Second, the mean first passage time (MFPT) displays a logarithmic degree dependence, in contrast to the inverse degree shape exhibited in looped networks. This deviation can be ascribed to the dominance of source-target topological distance in trees. To show this, we study the distance dependence of a symmetrized MFPT and derive its logarithmic profile, obtaining good agreement with simulation results. These unique properties shed light on the recently reported anomalies observed in diffusive dynamical systems on trees.

cond-mat.stat-mech↗

arXiv2008

Routes to thermodynamic limit on scale-free networks

We show that there are two classes of finite size effects for dynamic models taking place on a scale-free topology. Some models in finite networks show a behavior that depends only on the system size N. Others present an additional distinct dependence on the upper cutoff k_c of the degree distribution. Since the infinite network limit can be obtained by allowing k_c to diverge with the system size in an arbitrary way, this result implies that there are different routes to the thermodynamic limit in scale-free networks. The contact process (in its mean-field version) belongs to this second class and thus our results clarify the recent discrepancy between theory and simulations with different scaling of k_c reported in the literature.

cond-mat.stat-mech↗

arXiv2008

Bosonic reaction-diffusion processes on scale-free networks

Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networks, such as transport processes or epidemic outbreaks. In most cases, however, they have been studied from a fermionic perspective, in which each vertex can be occupied by at most one particle. While still useful, this approach suffers from some drawbacks, the most important probably being the difficulty to implement reactions involving more than two particles simultaneously. Here we introduce a general framework for the study of bosonic reaction-diffusion processes on complex networks, in which there is no restriction on the number of interacting particles that a vertex can host. We describe these processes theoretically by means of continuous time heterogeneous mean-field theory and divide them into two main classes: steady state and monotonously decaying processes. We analyze specific examples of both behaviors within the class of one-species process, comparing the results (whenever possible) with the corresponding fermionic counterparts. We find that the time evolution and critical properties of the particle density are independent of the fermionic or bosonic nature of the process, while differences exist in the functional form of the density of occupied vertices in a given degree class k. We implement a continuous time Monte Carlo algorithm, well suited for general bosonic simulations, which allow us to confirm the analytical predictions formulated within mean-field theory. Our results, both at the theoretical and numerical level, can be easily generalized to tackle more complex, multi-species, reaction-diffusion processes, and open a promising path for a general study and classification of this kind of dynamical systems on complex networks.

cond-mat.stat-mech↗

arXiv2006

Correlations in weighted networks

We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of structural constraints. We also introduce an algorithm for generating maximally random weighted networks with arbitrary $P(k,s)$ to be used as null models. The application of our measures to real networks reveals the importance of weights in a correct understanding and modeling of these heterogeneous systems.

cond-mat.dis-nn↗

arXiv2006

Zero temperature Glauber dynamics on complex networks

We study the Glauber dynamics at zero temperature of spins placed on the vertices of an uncorrelated network with a power-law degreedistribution. Application of mean-field theory yields as main prediction that for symmetric disordered initial conditions the mean time to reach full order is finite or diverges as a logarithm of the system size N, depending on the exponent of the degree distribution. Extensive numerical simulations contradict these results and clearly show that the mean-field assumption is not appropriate to describe this problem.

cond-mat.stat-mech↗

arXiv2006

Non mean-field behavior of the contact process on scale-free networks

We present an analysis of the classical contact process on scale-free networks. A mean-field study, both for finite and infinite network sizes, yields an absorbing-state phase transition at a finite critical value of the control parameter, characterized by a set of exponents depending on the network structure. Since finite size effects are large and the infinite network limit cannot be reached in practice, a numerical study of the transition requires the application of finite size scaling theory. Contrary to other critical phenomena studied previously, the contact process in scale-free networks exhibits a non-trivial critical behavior that cannot be quantitatively accounted for by mean-field theory.

cond-mat.stat-mech↗

arXiv2004

Analytic solution of a static scale-free network model

We present a detailed analytical study of a paradigmatic scale-free network model, the Static Model. Analytical expressions for its main properties are derived by using the hidden variables formalism. We map the model into a canonic hidden variables one, and solve the latter. The good agreement between our predictions and extensive simulations of the original model suggests that the mapping is exact in the infinite network size limit. One of the most remarkable findings of this study is the presence of relevant disassortative correlations, which are induced by the physical condition of absence of self and multiple connections.

cond-mat.stat-mech↗

arXiv2004

Rate equation approach for correlations in growing network models

We propose a rate equation approach to compute two vertex correlations in scale-free growing network models based in the preferential attachment mechanism. The formalism, based on previous work of Szabó \textit{et al.} [Phys. Rev. E \textbf{67} 056102 (2002)] for the clustering spectrum, measuring three vertex correlations, is based on a rate equation in the continuous degree and time approximation for the average degree of the nearest neighbors of vertices of degree $k$, with an appropriate boundary condition. We study the properties of both two and three vertex correlations for linear preferential attachment models, and also for a model yielding a large clustering coefficient. The expressions obtained are checked by means of extensive numerical simulations. The rate equation proposed can be generalized to more sophisticated growing network models, and also extended to deal with related correlation measures. As an example, we consider the case of a recently proposed model of weighted networks, for which we are able to compute a weighted two vertex correlation function, taking into account the strength of the interactions between connected vertices.

cond-mat.stat-mech↗

arXiv2004

Dynamical patterns of epidemic outbreaks in complex heterogeneous networks

We present a thorough inspection of the dynamical behavior of epidemic phenomena in populations with complex and heterogeneous connectivity patterns. We show that the growth of the epidemic prevalence is virtually instantaneous in all networks characterized by diverging degree fluctuations, independently of the structure of the connectivity correlation functions characterizing the population network. By means of analytical and numerical results, we show that the outbreak time evolution follows a precise hierarchical dynamics. Once reached the most highly connected hubs, the infection pervades the network in a progressive cascade across smaller degree classes. Finally, we show the influence of the initial conditions and the relevance of statistical results in single case studies concerning heterogeneous networks. The emerging theoretical framework appears of general interest in view of the recently observed abundance of natural networks with complex topological features and might provide useful insights for the development of adaptive strategies aimed at epidemic containment.

cond-mat.dis-nn↗

arXiv2004

Self-organization of collaboration networks

We study collaboration networks in terms of evolving, self-organizing bipartite graph models. We propose a model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration networks. The model depends exclusively on basic properties of the network, such as the total number of collaborators and acts of collaboration, the mean size of collaborations, etc. The simplest model defined within this framework already allows us to describe many of the main topological characteristics (degree distribution, clustering coefficient, etc.) of one-mode projections of several real collaboration networks, without parameter fitting. We explain the observed dependence of the local clustering on degree and the degree--degree correlations in terms of the ``aging'' of collaborators and their physical impossibility to participate in an unlimited number of collaborations.

cond-mat.stat-mech↗

arXiv2004

Characterization and Modeling of weighted networks

We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical infrastructures and social systems, respectively. The main empirical results are (i) the broad distributions of various quantities and (ii) the existence of weight-topology correlations. These measurements show that weights are relevant and that in general the modeling of complex networks must go beyond topology. We review a model which provides an explanation for the features observed in several real-world networks. This model of weighted network formation relies on the dynamical coupling between topology and weights, considering the rearrangement of weights when new links are introduced in the system.

cond-mat.stat-mech↗