Francisco A. Rodrigues

Characterization of complex networks : A survey of measurements

Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the proper application and interpretation of measurements.

Analyzing and modeling real-world phenomena with complex networks: a survey of applications

The success of new scientific areas can be assessed by their potential in contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with their sound theoretical basis being developed over the years and with a variety of applications. In this survey, we analyze the applications of complex networks to real-world problems and data, with emphasis in representation, analysis and modeling. A diversity of phenomena are surveyed, which may be classified into no less than 11 areas, providing a clear indication of the impact of the field of complex networks.

The Kuramoto model in complex networks

Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.

Cluster explosive synchronization in complex networks.

The emergence of explosive synchronization has been reported as an abrupt transition in complex networks of first-order Kuramoto oscillators. In this Letter we demonstrate that the nodes in a second-order Kuramoto model perform a cascade of transitions toward a synchronous macroscopic state, which is a novel phenomenon that we call cluster explosive synchronization. We provide a rigorous analytical treatment using a mean-field analysis in uncorrelated networks. Our findings are in good agreement with numerical simulations and fundamentally deepen the understanding of microscopic mechanisms toward synchronization.

A Systematic Comparison of Supervised Classifiers

Pattern recognition has been employed in a myriad of industrial, commercial and academic applications. Many techniques have been devised to tackle such a diversity of applications. Despite the long tradition of pattern recognition research, there is no technique that yields the best classification in all scenarios. Therefore, as many techniques as possible should be considered in high accuracy applications. Typical related works either focus on the performance of a given algorithm or compare various classification methods. In many occasions, however, researchers who are not experts in the field of machine learning have to deal with practical classification tasks without an in-depth knowledge about the underlying parameters. Actually, the adequate choice of classifiers and parameters in such practical circumstances constitutes a long-standing problem and is one of the subjects of the current paper. We carried out a performance study of nine well-known classifiers implemented in the Weka framework and compared the influence of the parameter configurations on the accuracy. The default configuration of parameters in Weka was found to provide near optimal performance for most cases, not including methods such as the support vector machine (SVM). In addition, the k-nearest neighbor method frequently allowed the best accuracy. In certain conditions, it was possible to improve the quality of SVM by more than 20% with respect to their default parameter configuration.

The structure and resilience of financial market networks.

Financial markets can be viewed as a highly complex evolving system that is very sensitive to economic instabilities. The complex organization of the market can be represented in a suitable fashion in terms of complex networks, which can be constructed from stock prices such that each pair of stocks is connected by a weighted edge that encodes the distance between them. In this work, we propose an approach to analyze the topological and dynamic evolution of financial networks based on the stock correlation matrices. An entropy-related measurement is adopted to quantify the robustness of the evolving financial market organization. It is verified that the network topological organization suffers strong variation during financial instabilities and the networks in such periods become less robust. A statistical robust regression model is proposed to quantity the relationship between the network structure and resilience. The obtained coefficients of such model indicate that the average shortest path length is the measurement most related to network resilience coefficient. This result indicates that a collective behavior is observed between stocks during financial crisis. More specifically, stocks tend to synchronize their price evolution, leading to a high correlation between pair of stock prices, which contributes to the increase in distance between them and, consequently, decrease the network resilience.

Complex networks: the key to systems biology

Though introduced recently, complex networks research has grown steadily because of its potential to represent, characterize and model a wide range of intricate natural systems and phenomena. Because of the intrinsic complexity and systemic organization of life, complex networks provide a specially promising framework for systems biology investigation. The current article is an up-to-date review of the major developments related to the application of complex networks in biology, with special attention focused on the more recent literature. The main concepts and models of complex networks are presented and illustrated in an accessible fashion. Three main types of networks are covered: transcriptional regulatory networks, protein-protein interaction networks and metabolic networks. The key role of complex networks for systems biology is extensively illustrated by several of the papers reviewed.

Beyond the average: Detecting global singular nodes from local features in complex networks

Deviations from the average can provide valuable insights about the organization of natural systems. The present article extends this important principle to the systematic identification and analysis of singular motifs in complex networks. Six measurements quantifying different and complementary features of the connectivity around each node of a network were calculated, and multivariate statistical methods applied to identify singular nodes. The potential of the presented concepts and methodology was illustrated with respect to different types of complex real-world networks, namely the US air transportation network, the protein-protein interactions of the yeast Saccharomyces cerevisiae and the Roget thesaurus networks. The obtained singular motifs possessed unique functional roles in the networks. Three classic theoretical network models were also investigated, with the Barabasi-Albert model resulting in singular motifs corresponding to hubs, confirming the potential of the approach. Interestingly, the number of different types of singular node motifs as well as the number of their instances were found to be considerably higher in the real-world networks than in any of the benchmark networks.

Collective behavior in financial markets

The financial market is an example of a complex system characterized by a highly intricate organization and the emergence of collective behavior. In this paper, this emergent dynamics in the financial market is quantified by using concepts of network synchronization. We consider networks constructed by the correlation matrix of asset returns and study the time evolution of the phase coherence among stock prices. It is verified that during a financial crisis a synchronous state emerges in the system, defining the markets direction. Furthermore, the paper proposes a statistical regression model able to identify the topological features that mostly influence such an emergence. The coefficients of the proposed model indicate that the average shortest path length is the measurement most related to network synchronization. Therefore, during an economic crisis, the stock prices present a similar evolution, which tends to shorten the distances between stocks indicating a collective dynamics.

Exploration of the antiplatelet activity profile of betulinic acid on human platelets

Betulinic acid, a natural pentacyclic triterpene acid, presents a diverse mode of biological actions including antiretroviral, antibacterial, antimalarial, and anti-inflammatory activities. The potency of betulinic acid as an inhibitor of human platelet activation was evaluated, and its antiplatelet profile against in vitro platelet aggregation, induced by several platelet agonists (adenosine diphosphate, thrombin receptor activator peptide-14, and arachidonic acid), was explored. Flow cytometric analysis was performed to examine the effect of betulinic acid on P-selectin membrane expression and PAC-1 binding to activated platelets. Betulinic acid potently inhibits platelet aggregation and also reduced PAC-1 binding and the membrane expression of P-selectin. Principal component analysis was used to screen, on the chemical property space, for potential common pharmacophores of betulinic acid with approved antithrombotic drugs. A common pharmacophore was defined between the NMR-derived structure of betulinic acid and prostacyclin agonists (PGI2), and the importance of its carboxylate group in its antiplatelet activity was determined. The present results indicate that betulinic acid has potential use as an antithrombotic compound and suggest that the mechanism underlying the antiplatelet effects of betulinic acid is similar to that of the PGI2 receptor agonists, a hypothesis that deserves further investigation.