M. Angeles Serrano
Universitat de Barcelona, Química Física, Department Member
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Research Interests: Information Systems, Computer Science, Distributed Computing, Statistical Analysis, Web Crawling, and 11 moreLibrary and Information Studies, World Wide Web, Comparative Analysis, Hyperlink, Web Measurement, Web Pages, Large Scale, Topological Properties, Data Gathering, Correlation function, and Navigability
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Research Interests: Engineering, Mathematics, Computer Science, Physics, Statistical Mechanics, and 15 moreSocial Networking, Applied Physics, Medicine, Multidisciplinary, Probability, Nature, Humans, Popularity, Escherichia coli, American physical society, Reproducibility of Results, Large Scale, Internet, Scale free Networks, and Similarity Geometry
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Clustering–the tendency for neighbors of nodes to be connected–quantifies the coupling of a complex network to its latent metric space. In random geometric graphs, clustering undergoes a continuous phase transition, separating a phase... more
Clustering–the tendency for neighbors of nodes to be connected–quantifies the coupling of a complex network to its latent metric space. In random geometric graphs, clustering undergoes a continuous phase transition, separating a phase with finite clustering from a regime where clustering vanishes in the thermodynamic limit. We prove this geometric to non-geometric phase transition to be topological in nature, with anomalous features such as diverging entropy as well as atypical finite-size scaling behavior of clustering. Moreover, a slow decay of clustering in the non-geometric phase implies that some real networks with relatively high levels of clustering may be better described in this regime.
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Significance Branching processes underpin the complex evolution of many real systems. However, network models typically describe network growth in terms of a sequential addition of nodes. Here, we measured the evolution of real... more
Significance Branching processes underpin the complex evolution of many real systems. However, network models typically describe network growth in terms of a sequential addition of nodes. Here, we measured the evolution of real networks—journal citations and international trade—over a 100-y period and found that they grow in a self-similar way that preserves their structural features over time. This observation can be explained by a geometric branching growth model that generates a multiscale unfolding of the network by using a combination of branching growth and a hidden metric space approach. Our model enables multiple practical applications, including the detection of optimal network size for maximal response to an external influence and a finite-size scaling analysis of critical behavior.
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One of the aspirations of network science is to explain the growth of real networks, often through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of... more
One of the aspirations of network science is to explain the growth of real networks, often through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or species. Here, we provide empirical evidence for self-similar branching growth in the evolution of real networks and present the Geometric Branching Growth model, which is designed to predict evolution and explain the symmetries observed. The model produces multiscale unfolding of a network in a sequence of scaled-up replicas. Practical applications in real instances include the tuning of network size for best response to external influence and finite-size scaling to assess critical behavior under random link failures.
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The increasing integration of world economies, which organize in complex multilayer networks of interactions, is one of the critical factors for the global propagation of economic crises. We adopt the network science approach to quantify... more
The increasing integration of world economies, which organize in complex multilayer networks of interactions, is one of the critical factors for the global propagation of economic crises. We adopt the network science approach to quantify shock propagation on the global trade-investment multiplex network. To this aim, we propose a model that couples a spreading dynamics, describing how economic distress propagates between connected countries, with an internal contagion mechanism, describing the spreading of such economic distress within a given country. At the local level, we find that the interplay between trade and financial interactions influences the vulnerabilities of countries to shocks. At the large scale, we find a simple linear relation between the relative magnitude of a shock in a country and its global impact on the whole economic system, albeit the strength of internal contagion is country-dependent and the inter-country propagation dynamics is non-linear. Interestingly,...
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Here, we present the World Trade Atlas 1870–2013, a collection of annual world trade maps in which distance combines economic size and the different dimensions that affect international trade beyond mere geography. Trade distances, based... more
Here, we present the World Trade Atlas 1870–2013, a collection of annual world trade maps in which distance combines economic size and the different dimensions that affect international trade beyond mere geography. Trade distances, based on a gravity model predicting the existence of significant trade channels, are such that the closer countries are in trade space, the greater their chance of becoming connected. The atlas provides us with information regarding the long-term evolution of the international trade system and demonstrates that, in terms of trade, the world is not flat but hyperbolic, as a reflection of its complex architecture. The departure from flatness has been increasing since World War I, meaning that differences in trade distances are growing and trade networks are becoming more hierarchical. Smaller-scale economies are moving away from other countries except for the largest economies; meanwhile those large economies are increasing their chances of becoming connect...
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A large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength. In... more
A large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength. In recent years, the study of an increasing number of large-scale networks has highlighted the statistical heterogeneity of their interaction pattern, with degree and weight distributions that vary over many orders of magnitude. These features, along with the large number of elements and links, make the extraction of the truly relevant connections forming the network's backbone a very challenging problem. More specifically, coarse-graining approaches and filtering techniques come into conflict with the multiscale nature of large-scale systems. Here, we define a filtering method that offers a practical procedure to extract the relevant connection backbone in complex multiscale networks, preserving the edges that represent statistically significant dev...
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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... more
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.
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We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical an efficient algorithm alike the... more
We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical an efficient algorithm alike the Gillespie algorithm for Markovian processes, with the difference that now the occurrence rates of the events depend on the time elapsed since the event last took place. We use our non-Markovian generalized Gillespie stochastic simulation methodology to investigate the effects of non-exponential inter-event time distributions in the susceptible-infected-susceptible model of epidemic spreading. Strikingly, our results unveil the drastic effects that very subtle differences in the modeling of non-Markovian processes have on the global behavior of complex systems, with important implications for their understanding and prediction. We also assess our generalized Gillespie algorithm on a system of biochemical reactions with time delays. As compared to other...
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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... more
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.
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Identifying key players in collective dynamics remains a challenge in several research fields, from the efficient dissemination of ideas to drug target discovery in biomedical problems. The difficulty lies at several levels: how to single... more
Identifying key players in collective dynamics remains a challenge in several research fields, from the efficient dissemination of ideas to drug target discovery in biomedical problems. The difficulty lies at several levels: how to single out the role of individual elements in such intermingled systems, or which is the best way to quantify their importance. Centrality measures describe a node's importance by its position in a network. The key issue obviated is that the contribution of a node to the collective behavior is not uniquely determined by the structure of the system but it is a result of the interplay between dynamics and network structure. We show that dynamical influence measures explicitly how strongly a node's dynamical state affects collective behavior. For critical spreading, dynamical influence targets nodes according to their spreading capabilities. For diffusive processes it quantifies how efficiently real systems may be controlled by manipulating a single ...
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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... more
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.
Research Interests: Geophysics, Biophysics, Molecular Physics, Nuclear Physics, Electronics, and 15 moreNonlinear dynamics, Atomic Physics, High Energy Physics, Fluid Dynamics, Nanotechnology, Chemical Physics, Astrophysics, Nature, Condensed Matter, Cosmology, Mathematical Sciences, Complex network, Null Model, Nature Physics, and Dynamic Properties
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... more
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 wor...
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Natural numbers can be divided in two non-overlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as... more
Natural numbers can be divided in two non-overlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as building blocks remains elusive. Here, we propose a new approach to decoding the architecture of natural numbers based on complex networks and stochastic processes theory. We introduce a parameter-free non-Markovian dynamical model that naturally generates random primes and their relation with composite numbers with remarkable accuracy. Our model satisfies the prime number theorem as an emerging property and a refined version of Cram\'er's conjecture about the statistics of gaps between consecutive primes that seems closer to reality than the original Cram\'er's version. Regarding composites, the model helps us to derive the prime factors counting function, giving the probability of distinct prime factors for any integer. Probabilist...
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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... more
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 whi...
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Metabolism is a fascinating cell machinery underlying life and disease and genome-scale reconstructions provide us with a captivating view of its complexity. However, deciphering the relationship between metabolic structure and function... more
Metabolism is a fascinating cell machinery underlying life and disease and genome-scale reconstructions provide us with a captivating view of its complexity. However, deciphering the relationship between metabolic structure and function remains a major challenge. In particular, turning observed structural regularities into organizing principles underlying systemic functions is a crucial task that can be significantly addressed after endowing complex network representations of metabolism with the notion of geometric distance. Here, we design a cartographic map of metabolic networks by embedding them into a simple geometry that provides a natural explanation for their observed network topology and that codifies node proximity as a measure of hidden structural similarities. We assume a simple and general connectivity law that gives more probability of interaction to metabolite/reaction pairs which are closer in the hidden space. Remarkably, we find an astonishing congruency between the...
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Networks are natural geometric objects. Yet the discrete metric structure of shortest path lengths in a network, known as chemical distances, is definitely not the only reservoir of geometric distances that characterize many networks. The... more
Networks are natural geometric objects. Yet the discrete metric structure of shortest path lengths in a network, known as chemical distances, is definitely not the only reservoir of geometric distances that characterize many networks. The other forms of network-related geometries are the geometry of continuous latent spaces underlying many networks, and the effective geometry induced by dynamical processes in networks. A solid and rapidly growing amount of evidence shows that the three approaches are intimately related. Network geometry is immensely efficient in discovering hidden symmetries, such as scale-invariance, and other fundamental physical and mathematical properties of networks, as well as in a variety of practical applications, ranging from the understanding how the brain works, to routing in the Internet. Here, we review the most important theoretical and practical developments in network geometry in the last two decades, and offer perspectives on future research directi...
Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and... more
Real networks are finite metric spaces. Yet the geometry induced by shortest path distances in a network is definitely not its only geometry. Other forms of network geometry are the geometry of latent spaces underlying many networks, and the effective geometry induced by dynamical processes in networks. These three approaches to network geometry are all intimately related, and all three of them have been found to be exceptionally efficient in discovering fractality, scale-invariance, self-similarity, and other forms of fundamental symmetries in networks. Network geometry is also of great utility in a variety of practical applications, ranging from the understanding how the brain works, to routing in the Internet. Here, we review the most important theoretical and practical developments dealing with these approaches to network geometry in the last two decades, and offer perspectives on future research directions and challenges in this novel frontier in the study of complexity.
We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering,... more
We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering, scale-free graphs with finite clustering and metric structure, growing scale-free networks, and many real networks. The proof and the derivation of the giant component size do not require the assumption that networks are treelike. Our results rely only on the observation that self-similar networks possess a hierarchy of nested subgraphs whose average degree grows with their depth in the hierarchy. We conjecture that this property is pivotal for percolation in networks.
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We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering,... more
We provide a simple proof that graphs in a general class of self-similar networks have zero percolation threshold. The considered self-similar networks include random scale-free graphs with given expected node degrees and zero clustering, scale-free graphs with finite clustering and metric structure, growing scale-free networks, and many real networks. The proof and the derivation of the giant component size do not require the assumption that networks are treelike. Our results rely only on the observation that self-similar networks possess a hierarchy of nested subgraphs whose average degree grows with their depth in the hierarchy. We conjecture that this property is pivotal for percolation in networks.
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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... more
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 ...
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We discuss the capabilities of spherical antenn\ae as 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... more
We discuss the capabilities of spherical antenn\ae as 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.
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Pedro Almagro,1, ∗ Marián Boguñá,2, 3, † and M. Ángeles Serrano2, 3, 4, ‡ Departamento de Ciencias de la Computación e Inteligencia Artificial, Universidad de Sevilla, Spain Departament de Fı́sica de la Matèria Condensada, Universitat de... more
Pedro Almagro,1, ∗ Marián Boguñá,2, 3, † and M. Ángeles Serrano2, 3, 4, ‡ Departamento de Ciencias de la Computación e Inteligencia Artificial, Universidad de Sevilla, Spain Departament de Fı́sica de la Matèria Condensada, Universitat de Barcelona, Martı́ i Franquès 1, E-08028 Barcelona, Spain Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona, Spain Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluı́s Companys 23, E-08010 Barcelona, Spain
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We present a minimal motif model for transmembrane cell signaling. The model assumes signaling events taking place in spatially distributed nanoclusters regulated by a birth/death dynamics. The combination of these spatio-temporal aspects... more
We present a minimal motif model for transmembrane cell signaling. The model assumes signaling events taking place in spatially distributed nanoclusters regulated by a birth/death dynamics. The combination of these spatio-temporal aspects can be modulated to provide a robust and high-fidelity response behavior without invoking sophisticated modeling of the signaling process as a sequence of cascade reactions and fine-tuned parameters. Our results show that the fact that the distributed signaling events take place in nanoclusters with a finite lifetime regulated by local production is sufficient to obtain a robust and high-fidelity response.