Biomedical subjects

Romualdo Pastor-Satorras

Publications and source records attributed to Romualdo Pastor-Satorras.

17 recordsLinked to original sources

PubMed2006

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 nontrivial critical behavior that cannot be quantitatively accounted for by mean-field theory.

Epidemiologic Methods↗

PubMed2005

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.

Communicable Disease Control↗

PubMed2005

Diffusion-annihilation processes in complex networks.

We present a detailed analytical study of the A+A --> 0 diffusion-annihilation process in complex networks. By means of microscopic arguments, we derive a set of rate equations for the density of A particles in vertices of a given degree, valid for any generic degree distribution, and which we solve for uncorrelated networks. For homogeneous networks (with bounded fluctuations), we recover the standard mean-field solution, i.e., a particle density decreasing as the inverse of time. For heterogeneous (scale-free networks) in the infinite network size limit, we obtain instead a density decreasing as a power law, with an exponent depending on the degree distribution. We also analyze the role of finite size effects, showing that any finite scale-free network leads to the mean-field behavior, with a prefactor depending on the network size. We check our analytical predictions with extensive numerical simulations on homogeneous networks with Poisson degree distribution and scale-free networks with different degree exponents.

Journal Article↗

PubMed2005

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 on the preferential attachment mechanism. The formalism, based on previous work of Szabo [Phys. Rev. E. 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.

Journal Article↗

PubMed2005

Generation of uncorrelated random scale-free networks.

Uncorrelated random scale-free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable of generating random uncorrelated scale-free networks with no multiple and self-connections. The model is based on the classical configuration model, with an additional restriction on the maximum possible degree of the vertices. We check numerically that the proposed model indeed generates scale-free networks with no two- and three-vertex correlations, as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k , respectively.

Journal Article↗

PubMed2004

Models of social networks based on social distance attachment.

We propose a class of models of social network formation based on a mathematical abstraction of the concept of social distance. Social distance attachment is represented by the tendency of peers to establish acquaintances via a decreasing function of the relative distance in a representative social space. We derive analytical results (corroborated by extensive numerical simulations), showing that the model reproduces the main statistical characteristics of real social networks: large clustering coefficient, positive degree correlations, and the emergence of a hierarchy of communities. The model is confronted with the social network formed by people that shares confidential information using the Pretty Good Privacy (PGP) encryption algorithm, the so-called web of trust of PGP.

Algorithms↗

PubMed2004

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.

Journal Article↗

PubMed2004

Velocity and hierarchical spread of epidemic outbreaks in scale-free networks.

We study the effect of the connectivity pattern of complex networks on the propagation dynamics of epidemics. The growth time scale of outbreaks is inversely proportional to the network degree fluctuations, signaling that epidemics spread almost instantaneously in networks with scale-free degree distributions. This feature is associated with an epidemic propagation that follows a precise hierarchical dynamics. Once the highly connected hubs are reached, the infection pervades the network in a progressive cascade across smaller degree classes. The present results are relevant for the development of adaptive containment strategies.

Disease Outbreaks↗

PubMed2003

Class of correlated random networks with hidden variables.

We study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices. The expressions obtained are checked by means of numerical simulations in a particular example. The general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure. We also present an extension of the class, to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system.

Journal Article↗

PubMed2003

Evolving protein interaction networks through gene duplication.

The topology of the proteome map revealed by recent large-scale hybridization methods has shown that the distribution of protein-protein interactions is highly heterogeneous, with many proteins having few edges while a few of them are heavily connected. This particular topology is shared by other cellular networks, such as metabolic pathways, and it has been suggested to be responsible for the high mutational homeostasis displayed by the genome of some organisms. In this paper we explore a recent model of proteome evolution that has been shown to reproduce many of the features displayed by its real counterparts. The model is based on gene duplication plus re-wiring of the newly created genes. The statistical features displayed by the proteome of well-known organisms are reproduced and suggest that the overall topology of the protein maps naturally emerges from the two leading mechanisms considered by the model.

Animals↗

PubMed2003

Stochastic theory of synchronization transitions in extended systems.

We propose a general Langevin equation describing the universal properties of synchronization transitions in extended systems. By means of theoretical arguments and numerical simulations we show that the proposed equation exhibits, depending on parameter values: (i) a continuous transition in the bounded Kardar-Parisi-Zhang universality class, with a zero largest Lyapunov exponent at the critical point; (ii) a continuous transition in the directed percolation class, with a negative Lyapunov exponent, or (iii) a discontinuous transition (that is argued to be possibly just a transient effect). Cases (ii) and (iii) exhibit coexistence of synchronized and unsynchronized phases in a broad (fuzzy) region. This reproduces almost all of the reported features of synchronization transitions, providing a unified theoretical framework for the analysis of synchronization transitions in extended systems.

Fuzzy Logic↗

PubMed2003

Topology and correlations in structured scale-free networks.

We study a recently introduced class of scale-free networks showing a high clustering coefficient and nontrivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the model. We solve exactly the case of low average connectivity, providing also exact expressions for the clustering and degree correlation functions. The model also exhibits a lack of small-world properties in the whole parameter range. We discuss the physical properties of these networks in the light of the present detailed analysis.

Journal Article↗

PubMed2003

Absence of epidemic threshold in scale-free networks with degree correlations.

Random scale-free networks have the peculiar property of being prone to the spreading of infections. Here we provide for the susceptible-infected-susceptible model an exact result showing that a scale-free degree distribution with diverging second moment is a sufficient condition to have null epidemic threshold in unstructured networks with either assortative or disassortative mixing. Degree correlations result therefore irrelevant for the epidemic spreading picture in these scale-free networks. The present result is related to the divergence of the average nearest neighbor's degree, enforced by the degree detailed balance condition.

Epidemiologic Methods↗

PubMed2002

Epidemic spreading in correlated complex networks.

We study a dynamical model of epidemic spreading on complex networks in which there are explicit correlations among the node's connectivities. For the case of Markovian complex networks, showing only correlations between pairs of nodes, we find an epidemic threshold inversely proportional to the largest eigenvalue of the connectivity matrix that gives the average number of links, which from a node with connectivity k go to nodes with connectivity k('). Numerical simulations on a correlated growing network model provide support for our conclusions.

Journal Article↗

PubMed2002

Large-scale topological and dynamical properties of the Internet.

We study the large-scale topological and dynamical properties of real Internet maps at the autonomous system level, collected in a 3-yr time interval. We find that the connectivity structure of the Internet presents statistical distributions settled in a well-defined stationary state. The large-scale properties are characterized by a scale-free topology consistent with previous observations. Correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the Internet. The study of the Internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models. We compare the properties of growing network models with the present real Internet data analysis.

Journal Article↗

PubMed2002

Epidemic dynamics in finite size scale-free networks.

Many real networks present a bounded scale-free behavior with a connectivity cutoff due to physical constraints or a finite network size. We study epidemic dynamics in bounded scale-free networks with soft and hard connectivity cutoffs. The finite size effects introduced by the cutoff induce an epidemic threshold that approaches zero at increasing sizes. The induced epidemic threshold is very small even at a relatively small cutoff, showing that the neglection of connectivity fluctuations in bounded scale-free networks leads to a strong overestimation of the epidemic threshold. We provide the expression for the infection prevalence and discuss its finite size corrections. The present paper shows that the highly heterogeneous nature of scale-free networks does not allow the use of homogeneous approximations even for systems of a relatively small number of nodes.

Journal Article↗

PubMed2002

Immunization of complex networks.

Complex networks such as the sexual partnership web or the Internet often show a high degree of redundancy and heterogeneity in their connectivity properties. This peculiar connectivity provides an ideal environment for the spreading of infective agents. Here we show that the random uniform immunization of individuals does not lead to the eradication of infections in all complex networks. Namely, networks with scale-free properties do not acquire global immunity from major epidemic outbreaks even in the presence of unrealistically high densities of randomly immunized individuals. The absence of any critical immunization threshold is due to the unbounded connectivity fluctuations of scale-free networks. Successful immunization strategies can be developed only by taking into account the inhomogeneous connectivity properties of scale-free networks. In particular, targeted immunization schemes, based on the nodes' connectivity hierarchy, sharply lower the network's vulnerability to epidemic attacks.

Journal Article↗