arXiv subjects

M. Angeles Serrano

Publications and source records attributed to M. Angeles Serrano.

35 records · Page 2Linked to original sources

arXiv2007

Structural efficiency of percolation landscapes in flow networks

Complex networks characterized by global transport processes rely on the presence of directed paths from input to output nodes and edges, which organize in characteristic linked components. The analysis of such network-spanning structures in the framework of percolation theory, and in particular the key role of edge interfaces bridging the communication between core and periphery, allow us to shed light on the structural properties of real and theoretical flow networks, and to define criteria and quantities to characterize their efficiency at the interplay between structure and functionality. In particular, it is possible to assess that an optimal flow network should look like a "hairy ball", so to minimize bottleneck effects and the sensitivity to failures. Moreover, the thorough analysis of two real networks, the Internet customer-provider set of relationships at the autonomous system level and the nervous system of the worm Caenorhabditis elegans --that have been shaped by very different dynamics and in very different time-scales--, reveals that whereas biological evolution has selected a structure close to the optimal layout, market competition does not necessarily tend toward the most customer efficient architecture.

cond-mat.dis-nn↗

arXiv2007

Interfaces and the edge percolation map of random directed networks

The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in the strongly connected component and those in the in- and out-components. Formal equations for the relative sizes in number of edges of these giant structures are derived for arbitrary joint degree distributions in the presence of local and two-point correlations. The uncorrelated null model is fully solved analytically and compared against simulations, finding an excellent agreement between the theoretical predictions and the edge percolation map of synthetically generated networks with exponential or scale-free in-degree distribution and exponential out-degree distribution. Interfaces, and their internal organization giving place from "hairy ball" percolation landscapes to bottleneck straits, could bring new light to the discussion of how structure is interwoven with functionality, in particular in flow networks.

cond-mat.dis-nn↗

arXiv2007

Patterns of dominant flows in the world trade web

The large-scale organization of the world economies is exhibiting increasingly levels of local heterogeneity and global interdependency. Understanding the relation between local and global features calls for analytical tools able to uncover the global emerging organization of the international trade network. Here we analyze the world network of bilateral trade imbalances and characterize its overall flux organization, unraveling local and global high-flux pathways that define the backbone of the trade system. We develop a general procedure capable to progressively filter out in a consistent and quantitative way the dominant trade channels. This procedure is completely general and can be applied to any weighted network to detect the underlying structure of transport flows. The trade fluxes properties of the world trade web determines a ranking of trade partnerships that highlights global interdependencies, providing information not accessible by simple local analysis. The present work provides new quantitative tools for a dynamical approach to the propagation of economic crises.

q-fin.GN↗

arXiv2007

Phase transition in the globalization of trade

Globalization processes interweave economic structures at a worldwide scale, trade playing a central role as one of the elemental channels of interaction among countries. Despite the significance of such phenomena, measuring economic globalization still remains an open problem. More quantitative treatments could improve the understanding of globalization at the same time that help a formal basis for comparative economic history. In this letter, we investigate the time evolution of the statistical properties of bilateral trade imbalances between countries in the trade system. We measure their cumulative probability distribution at different moments in time to discover a sudden transition circa 1960 from a regime where the distribution was always represented by a steady characteristic function to a new state where the distribution dilates as time goes on. This suggests that the rule that was governing the statistical behavior of bilateral trade imbalances until the 60's abruptly changed to a new form persistent in the last decades. In the new regime, the figures for the different years collapse into a universal master curve when rescaled by the corresponding global gross domestic product value. This coupling points to an increased interdependence of world economies and its onset corresponds in time with the starting of the last globalization wave.

physics.soc-ph↗

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

Percolation and Epidemic Thresholds in Clustered Networks

We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant connected component, it cannot restore a finite percolation threshold. In turn, this implies the absence of an epidemic threshold in this class of networks extending, thus, this result to a wide variety of real scale-free networks which shows a high level of transitivity. Our findings are in good agreement with numerical simulations.

cond-mat.dis-nn↗

arXiv2006

Clustering in complex networks. II. Percolation properties

The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows to find the critical threshold and the size of the giant component. Numerical simulations confirm the accuracy of our results. In more general terms, we show that weak clustering hinders the onset of the giant component whereas strong clustering favors its appearance. This is a direct consequence of the differences in the $k$-core structure of the networks, which are found to be totally different depending on the level of clustering. An empirical analysis of a real social network confirms our predictions.

cond-mat.dis-nn↗

arXiv2006

Clustering in complex networks. I. General formalism

We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in that it involves the properties of two --and not just one-- vertices. The formalism is completed with the definition of a three-vertex correlation function, which is the fundamental quantity describing the properties of clustered networks. The formalism suggests new metrics that are able to thoroughly characterize transitive relations. A rigorous analysis of several real networks, which makes use of the new formalism and the new metrics, is also provided. It is also found that clustered networks can be classified into two main groups: the {\it weak} and the {\it strong transitivity} classes. In the first class, edge multiplicity is small, with triangles being disjoint. In the second class, edge multiplicity is high and so triangles share many edges. As we shall see in the following paper, the class a network belongs to has strong implications in its percolation properties.

cond-mat.dis-nn↗

arXiv2006

Detecting rich-club ordering in complex networks

Uncovering the hidden regularities and organizational principles of networks arising in physical systems ranging from the molecular level to the scale of large communication infrastructures is the key issue for the understanding of their fabric and dynamical properties [1-5]. The ``rich-club'' phenomenon refers to the tendency of nodes with high centrality, the dominant elements of the system, to form tightly interconnected communities and it is one of the crucial properties accounting for the formation of dominant communities in both computer and social sciences [4-8]. Here we provide the analytical expression and the correct null models which allow for a quantitative discussion of the rich-club phenomenon. The presented analysis enables the measurement of the rich-club ordering and its relation with the function and dynamics of networks in examples drawn from the biological, social and technological domains.

physics.data-an↗

arXiv2006

Decoding the structure of the WWW: facts versus sampling biases

The understanding of the immense and intricate topological structure of the World Wide Web (WWW) is a major scientific and technological challenge. This has been tackled recently by characterizing the properties of its representative graphs in which vertices and directed edges are identified with web-pages and hyperlinks, respectively. Data gathered in large scale crawls have been analyzed by several groups resulting in a general picture of the WWW that encompasses many of the complex properties typical of rapidly evolving networks. In this paper, we report a detailed statistical analysis of the topological properties of four different WWW graphs obtained with different crawlers. We find that, despite the very large size of the samples, the statistical measures characterizing these graphs differ quantitatively, and in some cases qualitatively, depending on the domain analyzed and the crawl used for gathering the data. This spurs the issue of the presence of sampling biases and structural differences of Web crawls that might induce properties not representative of the actual global underlying graph. In order to provide a more accurate characterization of the Web graph and identify observables which are clearly discriminating with respect to the sampling process, we study the behavior of degree-degree correlation functions and the statistics of reciprocal connections. The latter appears to enclose the relevant correlations of the WWW graph and carry most of the topological information of theWeb. The analysis of this quantity is also of major interest in relation to the navigability and searchability of the Web.

cs.NI↗

arXiv2005

Modeling the Internet

We model the Internet as a network of interconnected Autonomous Systems which self-organize under an absolute lack of centralized control. Our aim is to capture how the Internet evolves by reproducing the assembly that has led to its actual structure and, to this end, we propose a growing weighted network model driven by competition for resources and adaptation to maintain functionality in a demand and supply ``equilibrium''. On the demand side, we consider the environment, a pool of users which need to transfer information and ask for service. On the supply side, ASs compete to gain users, but to be able to provide service efficiently, they must adapt their bandwidth as a function of their size. Hence, the Internet is not modeled as an isolated system but the environment, in the form of a pool of users, is also a fundamental part which must be taken into account. ASs compete for users and big and small come up, so that not all ASs are identical. New connections between ASs are made or old ones are reinforced according to the adaptation needs. Thus, the evolution of the Internet can not be fully understood if just described as a technological isolated system. A socio-economic perspective must also be considered.

physics.soc-ph↗

arXiv2005

Tuning clustering in random networks with arbitrary degree distributions

We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the clustering coefficient for each class of nodes of degree $k$ are fixed ad hoc and a priori. The algorithm generates corresponding topologies by applying first a closure of triangles and secondly the classical closure of remaining free stubs. The procedure unveils an universal relation among clustering and degree-degree correlations for all networks, where the level of assortativity establishes an upper limit to the level of clustering. Maximum assortativity ensures no restriction on the decay of the clustering coefficient whereas disassortativity sets a stronger constraint on its behavior. Correlation measures in real networks are seen to observe this structural bound.

cond-mat.dis-nn↗

arXiv2004

Competition and adaptation in an Internet evolution model

We model the evolution of the Internet at the Autonomous System level as a process of competition for users and adaptation of bandwidth capability. We find the exponent of the degree distribution as a simple function of the growth rates of the number of autonomous systems and the total number of connections in the Internet, both empirically measurable quantities. This fact place our model apart from others in which this exponent depends on parameters that need to be adjusted in a model dependent way. Our approach also accounts for a high level of clustering as well as degree-degree correlations, both with the same hierarchical structure present in the real Internet. Further, it also highlights the interplay between bandwidth, connectivity and traffic of the network.

cond-mat.dis-nn↗

arXiv2003

Topology of the World Trade Web

Economy, and consequently trade, is a fundamental part of human social organization which, until now, has not been studied within the network modelling framework. Networks are mathematical tools used in the modelling of a wide variety of systems in social and natural science. Examples of these networks range from metabolic and cell networks to technological webs. Here we present the first empirical characterization of the world trade web, that is, the network built upon the trade relationships between different countries in the world. This network displays the typical properties of complex networks, namely, scale-free degree distribution, the {\it small world} property, a high clustering coefficient and, in addition, degree-degree correlation between different vertices. All these properties make the world trade web a complex network, which is far from being well-described through a classical random network description.

cond-mat.dis-nn↗

arXiv1999

Resonant Spheres: Multifrequency Detectors of Gravitational Waves

We discuss the capabilities of spherical antennæas single multifrequency detectors of gravitational waves. A first order theory allows us to evaluate the coupled spectrum and the resonators readouts when the first and the second quadrupole bare sphere frequencies are simultaneously selected for layout tuning. We stress the existence of non-tuning influences in the second mode coupling causing draggs in the frequency splittings. These URF effects are relevant to a correct physical description of resonant spheres, still more if operating as multifrequency appliances like our PHCA proposal.

gr-qc↗

arXiv1999

Multiple mode gravitational wave detection with a spherical antenna

Apart from omnidirectional, a solid elastic sphere is a natural multimode and multifrequency device for the detection of Gravitational Waves (GW). Motion sensing in a spherical GW detector thus requires a multiple set of transducers attached to it at suitable locations. Resonant transducers exert a significant back action on the larger sphere, and as a consequence the joint dynamics of the entire system has to be properly understood before reliable conclusions can be drawn from its readout. In this paper, we present and develop a mathematical formalism to analyse such dynamics, which generalises and enhances currently existing ones, and which clarifies their actual range of validity, thereby shedding light into the physics of the detector. In addition, the new formalism has enabled us to discover a new resonator layout (we call it PHC) which only requires five resonators per quadrupole mode sensed, and has mode channels, i.e., linear combinations of the transducers' readouts which are directly proportional to the GW amplitudes. The perturbative nature of our proposed approach makes it also very well adapted to systematically assess the consequences of small mistunings in the device parameters by robust analytic methods. These prove to be very powerful, not only theoretically but also practically: confrontation of our model's predictions with the experimental data of the LSU prototype detector TIGA reveals an agreement between both consistently reaching the fourth decimal place.

astro-ph↗

arXiv1997

Resonant transducers for a spherical Gravitational Wave antenna

Motion sensing in a spherical GW detector requires a multiple set of transducers attached to its surface at suitable locations. If transducers are of the resonant type then their motion couples to that of the sphere and the joint dynamics of the system has to be properly understood before reliable conclusions can be drawn from its readout. In this paper we address the problem of the coupled motion of a sphere and a set of resonators attached to it at arbitrary points. A remarkably elegant and powerful scheme emerges from the general equations which shows how coupling takes place as a power series in the small coupling constant ratio m(resonator)/M(sphere). We reasses in the new light the response of the highly symmetric TIGA and also present a new proposal (called PHC) which has less symmetry but which is based on 5 rather than 6 transducers per quadrupole mode sensed. We finally assess how the system charac- teristics are affected by slight departures from ideality, and find it to be quite robust to them. In particular we recover with full accuracy the reportedly measured frequencies of the LSU prototype TIGA.

gr-qc↗