Spectral properties of the Laplacian of multiplex networks.

One of the more challenging tasks in the understanding of dynamical properties of models on top of complex networks is to capture the precise role of multiplex topologies. In a recent paper, Gómez et al. [ Phys. Rev. Lett. 110 028701 (2013)], some of the authors proposed a framework for the study of diffusion processes in such networks. Here, we extend the previous framework to deal with general configurations in several layers of networks and analyze the behavior of the spectrum of the Laplacian of the full multiplex. We derive an interesting decoupling of the problem that allow us to unravel the role played by the interconnections of the multiplex in the dynamical processes on top of them. Capitalizing on this decoupling we perform an asymptotic analysis that allow us to derive analytical expressions for the full spectrum of eigenvalues. This spectrum is used to gain insight into physical phenomena on top of multiplex, specifically, diffusion processes and synchronizability

Mathematical formulation of multilayer networks

A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems are very rich. Achieving a deep understanding of such systems necessitates generalizing “traditional” network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multilayer complex systems. In this paper, we introduce a tensorial framework to study multilayer networks, and we discuss the generalization of several important network descriptors and dynamical processes—including degree centrality, clustering coefficients, eigenvector centrality, modularity, von Neumann entropy, and diffusion—for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multilayer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems

The physics of spreading processes in multilayer networks

The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (i.e., "multiplexity") among their constituent components and/or multiple interacting subsystems. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent "multilayer" approach for modeling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. On one hand, it allows one to couple different structural relationships by encoding them in a convenient mathematical object. On the other hand, it also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation. Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure.Comment: 25 pages, 4 figure

Effectiveness of the 13-valent pneumococcal conjugate vaccine in preventing invasive pneumococcal disease in children aged 7-59 months. A matched case-control study

Background The 13-valent pneumococcal conjugate vaccine (PCV13) was licensed based on the results of immunogenicity studies and correlates of protection derived from randomized clinical trials of the 7-valent conjugate pneumococcal vaccine. We assessed the vaccination effectiveness (VE) of the PCV13 in preventing invasive pneumococcal disease (IPD) in children aged 7-59 months in a population with suboptimal vaccination coverage of 55%. Methods The study was carried out in children with IPD admitted to three hospitals in Barcelona (Spain) and controls matched by hospital, age, sex, date of hospitalization and underlying disease. Information on the vaccination status was obtained from written medical records. Conditional logistic regression was made to estimate the adjusted VE and 95% confidence intervals (CI). Results 169 cases and 645 controls were included. The overall VE of ≥1 doses of PCV13 in preventing IPD due to vaccine serotypes was 75.8% (95% CI, 54.1-87.2) and 90% (95% CI, 63.9-97.2) when ≥2 doses before 12 months, two doses on or after 12 months or one dose on or after 24 months, were administered. The VE of ≥1 doses was 89% (95% CI, 42.7-97.9) against serotype 1 and 86.0% (95% CI, 51.2-99.7) against serotype 19A. Serotype 3 showed a non-statistically significant effectiveness (25.9%; 95% CI, -65.3 to 66.8). Conclusions The effectiveness of ≥1 doses of PCV13 in preventing IPD caused by all PCV13 serotypes in children aged 7-59 months was good and, except for serotype 3, the effectiveness of ≥1 doses against the most frequent PCV13 serotypes causing IPD was high when considered individually

Opinion formation in multiplex networks with general initial distributions

We study opinion dynamics over multiplex networks where agents interact with bounded confidence. Namely, two neighbouring individuals exchange opinions and compromise if their opinions do not differ by more than a given threshold. In literature, agents are generally assumed to have a homogeneous confidence bound. Here, we study analytically and numerically opinion evolution over structured networks characterised by multiple layers with respective confidence thresholds and general initial opinion distributions. Through rigorous probability analysis, we show analytically the critical thresholds at which a phase transition takes place in the long-term consensus behaviour, over multiplex networks with some regularity conditions. Our results reveal the quantitative relation between the critical threshold and initial distribution. Further, our numerical simulations illustrate the consensus behaviour of the agents in network topologies including lattices and, small-world and scale-free networks, as well as for structure-dependent convergence parameters accommodating node heterogeneity. We find that the critical thresholds for consensus tend to agree with the predicted upper bounds in Theorems 4 and 5 in this paper. Finally, our results indicate that multiplexity hinders consensus formation when the initial opinion configuration is within a bounded range and, provide insight into information diffusion and social dynamics in multiplex systems modeled by networks

Maintaining extensivity in evolutionary multiplex networks

In this paper, we explore the role of network topology on maintaining the extensive property of entropy. We study analytically and numerically how the topology contributes to maintaining extensivity of entropy in multiplex networks, i.e. networks of subnetworks (layers), by means of the sum of the positive Lyapunov exponents, HKS, a quantity related to entropy. We show that extensivity relies not only on the interplay between the coupling strengths of the dynamics associated to the intra (short-range) and inter (long-range) interactions, but also on the sum of the intra-degrees of the nodes of the layers. For the analytically treated networks of size N, among several other results, we show that if the sum of the intra-degrees (and the sum of inter-degrees) scales as N?+1, ? > 0, extensivity can be maintained if the intra-coupling (and the inter-coupling) strength scales as N??, when evolution is driven by the maximisation of HKS. We then verify our analytical results by performing numerical simulations in multiplex networks formed by electrically and chemically coupled neurons

Modelling the generalised median correspondence through an edit distance.

On the one hand, classification applications modelled by structural pattern recognition, in which elements are represented as strings, trees or graphs, have been used for the last thirty years. In these models, structural distances are modelled as the correspondence (also called matching or labelling) between all the local elements (for instance nodes or edges) that generates the minimum sum of local distances. On the other hand, the generalised median is a well-known concept used to obtain a reliable prototype of data such as strings, graphs and data clusters. Recently, the structural distance and the generalised median has been put together to define a generalise median of matchings to solve some classification and learning applications. In this paper, we present an improvement in which the Correspondence edit distance is used instead of the classical Hamming distance. Experimental validation shows that the new approach obtains better results in reasonable runtime compared to other median calculation strategies

Towards the estimation of feature-based semantic similarity using multiple ontologies

10.1016/j.knosys.2013.10.015A key application of ontologies is the estimation of the semantic similarity between terms. By means of this assessment, the comprehension and management of textual resources can be improved. However, most ontology-based similarity measures only support a single input ontology. If any of the compared terms do not belong to that ontology, their similarity cannot be assessed. To solve this problem, multiple ontologies can be considered. Even though there are methods that enable the multi-ontology similarity assessment by means of integrating concepts from different ontologies, most of them are based on simple terminological and/or partial matchings. This hampers similarity measures that exploit a broad set of taxonomic evidences of similarity, like feature-based ones. In this paper, we tackle this problem by proposing a method to identify all the suitable matchings between concepts of different ontologies that intervene in the similarity assessment. In addition to the obvious terminological matching, we exploit the ontological structure and the notion of concept subsumption to discover non-trivial equivalences between heterogeneous ontologies. Our final goal is to enable the accurate application of feature-based similarity measures in a multi-ontology setting. Our proposal is evaluated with regard human judgements of similarity for several benchmarks and ontologies. Results shows an improvement against related works, with similarity accuracies that even rival those obtained in an ideal mono-ontology setting