Diffusion dynamics on multiplex networks

We study the time scales associated to diffusion processes that take place on multiplex networks, i.e. on a set of networks linked through interconnected layers. To this end, we propose the construction of a supra-Laplacian matrix, which consists of a dimensional lifting of the Laplacian matrix of each layer of the multiplex network. We use perturbative analysis to reveal analytically the structure of eigenvectors and eigenvalues of the complete network in terms of the spectral properties of the individual layers. The spectrum of the supra-Laplacian allows us to understand the physics of diffusion-like processes on top of multiplex networks.Comment: 6 Pages including supplemental material. To appear in Physical Review Letter

Trade synchronization in the World Trade Web

In March 2008, the bankruptcy of Lehman Brothers marked for many the beginning of the global crisis. In an increasingly globalized world, the financial crisis spread relentlessly. Recent theories of financial fragility link globalization with economic cycles, i.e. when local crises coincide with bad credit regulation and failures in international monetary arrangements. The globalization process in recent years has been accelerated due to to the increase of international trade. Here we analyze how economic cycles can spread worldwide over the global trade network (WTW). We use the WTW network structure to simulate a network of Integrate-and-Fire oscillators for two different years, 1980 and 2000. The results reinforce the idea that globalization accelerates the global synchronization process

Nonequilibrium phase transition in a model for the propagation of innovations among economic agents

We characterize the different morphological phases that occur in a simple one-dimensional model of propagation of innovations among economic agents [X.\ Guardiola, {\it et. al.}, Phys. Rev E {\bf 66}, 026121 (2002)]. We show that the model can be regarded as a nonequilibrium surface growth model. This allows us to demonstrate the presence of a continuous roughening transition between a flat (system size independent fluctuations) and a rough phase (system size dependent fluctuations). Finite-size scaling studies at the transition strongly suggest that the dynamic critical transition does not belong to directed percolation and, in fact, critical exponents do not seem to fit in any of the known universality classes of nonequilibrium phase transitions. Finally, we present an explanation for the occurrence of the roughening transition and argue that avalanche driven dynamics is responsible for the novel critical behavior

Dynamical and spectral properties of complex networks

Dynamical properties of complex networks are related to the spectral properties of the Laplacian matrix that describes the pattern of connectivity of the network. In particular we compute the synchronization time for different types of networks and different dynamics. We show that the main dependence of the synchronization time is on the smallest nonzero eigenvalue of the Laplacian matrix, in contrast to other proposals in terms of the spectrum of the adjacency matrix. Then, this topological property becomes the most relevant for the dynamics.Comment: 14 pages, 5 figures, to be published in New Journal of Physic

Optimal network topologies for local search with congestion

The problem of searchability in decentralized complex networks is of great importance in computer science, economy and sociology. We present a formalism that is able to cope simultaneously with the problem of search and the congestion effects that arise when parallel searches are performed, and obtain expressions for the average search cost--written in terms of the search algorithm and the topological properties of the network--both in presence and abscence of congestion. This formalism is used to obtain optimal network structures for a system using a local search algorithm. It is found that only two classes of networks can be optimal: star-like configurations, when the number of parallel searches is small, and homogeneous-isotropic configurations, when the number of parallel searches is large.Comment: 4 pages. Final version accepted in PR

Ceruloplasmin and Coronary Heart Disease-A Systematic Review

Several studies indicate that oxidative stress might play a central role in the initiation and maintenance of cardiovascular diseases. It remains unclear whether ceruloplasmin acts as a passive marker of inflammation or as a causal mediator. To better understand the impact of ceruloplasmin blood levels on the risk of cardiovascular disease, and paying special attention to coronary heart disease, we conducted a search on the two most commonly used electronic databases (Medline via PubMed and EMBASE) to analyze current assessment using observational studies in the general adult population. Each study was quality rated using criteria developed by the US Preventive Services Task Force. Most of 18 eligible studies reviewed support a direct relationship between ceruloplasmin elevated levels and incidence of coronary heart disease. Our results highlight the importance of promoting clinical trials that determine the functions of ceruloplasmin as a mediator in the development of coronary heart disease and evaluate whether the treatment of elevated ceruloplasmin levels has a role in the prognosis or prevention of this condition

New approaches to model and study social networks

We describe and develop three recent novelties in network research which are particularly useful for studying social systems. The first one concerns the discovery of some basic dynamical laws that enable the emergence of the fundamental features observed in social networks, namely the nontrivial clustering properties, the existence of positive degree correlations and the subdivision into communities. To reproduce all these features we describe a simple model of mobile colliding agents, whose collisions define the connections between the agents which are the nodes in the underlying network, and develop some analytical considerations. The second point addresses the particular feature of clustering and its relationship with global network measures, namely with the distribution of the size of cycles in the network. Since in social bipartite networks it is not possible to measure the clustering from standard procedures, we propose an alternative clustering coefficient that can be used to extract an improved normalized cycle distribution in any network. Finally, the third point addresses dynamical processes occurring on networks, namely when studying the propagation of information in them. In particular, we focus on the particular features of gossip propagation which impose some restrictions in the propagation rules. To this end we introduce a quantity, the spread factor, which measures the average maximal fraction of nearest neighbors which get in contact with the gossip, and find the striking result that there is an optimal non-trivial number of friends for which the spread factor is minimized, decreasing the danger of being gossiped.Comment: 16 Pages, 9 figure

Comparing community structure identification

We compare recent approaches to community structure identification in terms of sensitivity and computational cost. The recently proposed modularity measure is revisited and the performance of the methods as applied to ad hoc networks with known community structure, is compared. We find that the most accurate methods tend to be more computationally expensive, and that both aspects need to be considered when choosing a method for practical purposes. The work is intended as an introduction as well as a proposal for a standard benchmark test of community detection methods.Comment: 10 pages, 3 figures, 1 table. v2: condensed, updated version as appears in JSTA

Role of Network Topology in the Synchronization of Power Systems

We study synchronization dynamics in networks of coupled oscillators with bimodal distribution of natural frequencies. This setup can be interpreted as a simple model of frequency synchronization dynamics among generators and loads working in a power network. We derive the minimum coupling strength required to ensure global frequency synchronization. This threshold value can be efficiently found by solving a binary optimization problem, even for large networks. In order to validate our procedure, we compare its results with numerical simulations on a realistic network describing the European interconnected high-voltage electricity system, finding a very good agreement. Our synchronization threshold can be used to test the stability of frequency synchronization to link removals. As the threshold value changes only in very few cases when aplied to the European realistic network, we conclude that network is resilient in this regard. Since the threshold calculation depends on the local connectivity, it can also be used to identify critical network partitions acting as synchronization bottlenecks. In our stability experiments we observe that when a link removal triggers a change in the critical partition, its limits tend to converge to national borders. This phenomenon, which can have important consequences to synchronization dynamics in case of cascading failure, signals the influence of the uncomplete topological integration of national power grids at the European scale.Comment: The final publication is available at http://www.epj.org (see http://www.springerlink.com/content/l22k574x25u6q61m/

On Synchronization in a Lattice Model of Pulse-Coupled Oscillators

We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interaction that ensures, in a general context, the existence of a fully synchronized regime. This condition turns out to be the same than the obtained for the globally coupled population. When the condition is not completely satisfied we find different spatial structures. This also gives some hints about self-organized criticality.Comment: 4 pages, RevTex, 1 PostScript available upon request, To appear in Phys. Rev. Let