Enhancing community detection using a network weighting strategy

A community within a network is a group of vertices densely connected to each other but less connected to the vertices outside. The problem of detecting communities in large networks plays a key role in a wide range of research areas, e.g. Computer Science, Biology and Sociology. Most of the existing algorithms to find communities count on the topological features of the network and often do not scale well on large, real-life instances. In this article we propose a strategy to enhance existing community detection algorithms by adding a pre-processing step in which edges are weighted according to their centrality w.r.t. the network topology. In our approach, the centrality of an edge reflects its contribute to making arbitrary graph tranversals, i.e., spreading messages over the network, as short as possible. Our strategy is able to effectively complements information about network topology and it can be used as an additional tool to enhance community detection. The computation of edge centralities is carried out by performing multiple random walks of bounded length on the network. Our method makes the computation of edge centralities feasible also on large-scale networks. It has been tested in conjunction with three state-of-the-art community detection algorithms, namely the Louvain method, COPRA and OSLOM. Experimental results show that our method raises the accuracy of existing algorithms both on synthetic and real-life datasets.Comment: 28 pages, 2 figure

Synchronization in complex networks

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.Comment: Final version published in Physics Reports. More information available at http://synchronets.googlepages.com

Computer architecture for efficient algorithmic executions in real-time systems: New technology for avionics systems and advanced space vehicles

Improvements and advances in the development of computer architecture now provide innovative technology for the recasting of traditional sequential solutions into high-performance, low-cost, parallel system to increase system performance. Research conducted in development of specialized computer architecture for the algorithmic execution of an avionics system, guidance and control problem in real time is described. A comprehensive treatment of both the hardware and software structures of a customized computer which performs real-time computation of guidance commands with updated estimates of target motion and time-to-go is presented. An optimal, real-time allocation algorithm was developed which maps the algorithmic tasks onto the processing elements. This allocation is based on the critical path analysis. The final stage is the design and development of the hardware structures suitable for the efficient execution of the allocated task graph. The processing element is designed for rapid execution of the allocated tasks. Fault tolerance is a key feature of the overall architecture. Parallel numerical integration techniques, tasks definitions, and allocation algorithms are discussed. The parallel implementation is analytically verified and the experimental results are presented. The design of the data-driven computer architecture, customized for the execution of the particular algorithm, is discussed

Recent Techniques for Regularization in Partial Differential Equations and Imaging

abstract: Inverse problems model real world phenomena from data, where the data are often noisy and models contain errors. This leads to instabilities, multiple solution vectors and thus ill-posedness. To solve ill-posed inverse problems, regularization is typically used as a penalty function to induce stability and allow for the incorporation of a priori information about the desired solution. In this thesis, high order regularization techniques are developed for image and function reconstruction from noisy or misleading data. Specifically the incorporation of the Polynomial Annihilation operator allows for the accurate exploitation of the sparse representation of each function in the edge domain. This dissertation tackles three main problems through the development of novel reconstruction techniques: (i) reconstructing one and two dimensional functions from multiple measurement vectors using variance based joint sparsity when a subset of the measurements contain false and/or misleading information, (ii) approximating discontinuous solutions to hyperbolic partial differential equations by enhancing typical solvers with l1 regularization, and (iii) reducing model assumptions in synthetic aperture radar image formation, specifically for the purpose of speckle reduction and phase error correction. While the common thread tying these problems together is the use of high order regularization, the defining characteristics of each of these problems create unique challenges. Fast and robust numerical algorithms are also developed so that these problems can be solved efficiently without requiring fine tuning of parameters. Indeed, the numerical experiments presented in this dissertation strongly suggest that the new methodology provides more accurate and robust solutions to a variety of ill-posed inverse problems.Dissertation/ThesisDoctoral Dissertation Mathematics 201

Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

From Dynamics to Structure of Complex Networks: Exploiting Heterogeneity in the Sakaguchi-Kuramoto Model

[eng] Most of the real-world complex systems are best described as complex networks and can be mathematically described as oscillatory systems, coupled with the neighbours through the connections of the network. The flashing of fireflies, the neuronal brain signals or the energy flow through the power grid are some examples. Yoshiki Kuramoto came up with a tractable mathematical model that could capture the phenomenology of collective synchronization by suggesting that oscillators were coupled by a sinusoidal function of their phase differences. Later, Yoshiki Kuramoto together with Hidetsugu Sakaguchi presented a generalization of the previous limit-cycle set of oscillators Kuramoto’s model which incorporated a constant phase lag between oscillators. Subsequent studies of the model included the network structure within the model together with the global shift. For a wide range of the phase lag values, the system becomes synchronized to a resulting frequency, i.e., the dynamics reaches a stationary state. In the original work of Kuramoto and Sakaguchi and in most of the consequent later studies, a uniform distribution of phase lag parameters is customarily assumed. However, the intrinsic properties of nodes – that assuredly represent the constituents of real systems – do not need be identical but distributed non-homogeneously among the population. This thesis contributes to the understanding of the Kuramoto-Sakaguchi model with a generalization for nonhomogeneous phase lag parameter distribution. Considering different scenarios concerning the distribution of the frustration parameter among the oscillators represents a major step towards the extension of the original model and provides significant novel insights into the structure and function of the considered network. The first setting that the present thesis considers consists in perturbing the stationary state of the system by introducing a non-zero phase lag shift into the dynamics of a single node. The aim of this work is to sort the nodes by their potential effect on the whole network when a change on their individual dynamics spreads over the entire oscillatory system by disrupting the otherwise synchronized state. In particular, we define functionability, a novel centrality measure that addresses the question of which are the nodes that, when individually perturbed, are best able to move the system away from the fully synchronized state. This issue may be relevant for the identification of critical nodes that are either beneficial – by enabling access to a broader spectrum of states – or harmful – by destroying the overall synchronization. The second scenario that the present thesis addresses considers a more general configuration in which the phase lag parameter is an intrinsic property of each node, not necessarily zero, and hence exploring the potential heterogeneity of the frustration among oscillators. We obtain the analytical solution of frustration parameters so as to achieve any phase configuration, by linearizing the most general model. We also address the fact that the question ’among all the possible solutions, which is the one that makes the system achieve a particular phase configuration with the minimum required cost?’ is of particular relevance when we consider the plausible real nature of the system. Finally, the homogenous distribution of phase lag parameters is revisited in the last scenario. As studied in the literature, a certain degree of symmetry is an attribute of real-world networks. Nevertheless, beyond structural or topological symmetry, one should consider the fact that real- world networks are exposed to fluctuations or errors, as well as mistaken insertions or removals. In the present thesis, we provide an alternative notion to approximate symmetries, which we call ‘Quasi-Symmetries’ and are defined such that they remain free to impose any invariance of a particular network property and are obtained from the stationary state of the Kuramoto-Sakaguchi model with a homogeneous phase lag distribution. A first contribution is exploring the distributions of structural similarity among all pairs of nodes. Secondly, we define the ‘dual network’, a weighted network –and its corresponding binarized counterpart– that effectively encloses all the information of quasi-symmetries in the original one.[cat] La major part dels sistemes complexos presents en la natura i la societat es poden descriure com a xarxes complexes. Molts d’aquests sistemes es poden modelitzar matemàticament com un sistema oscil·latori, on les unitats queden acoblades amb els components veïns a través de les connexions de la xarxa. Yoshiki Kuramoto i Hidetsugu Sakaguchi van presentar la generalització del ben conegut model d’oscil·ladors de Kuramoto, on s’incorporava un terme de desfasament entre parelles d’oscil·ladors. Aquesta tesi contribueix en la comprensió d’aquest model, tot considerant una distribució no homogènia d’aquest paràmetre de desfasament o frustració. S’han considerat tres escenaris diferents, tots ells donant lloc a resultats que permeten una millor descripció de l’estructura i funció de la xarxa que s’està considerant. Una primera configuració consisteix en pertorbar l’estat estacionari tot introduint un desfasament en la dinàmica d’un node de manera aïllada. Seguidament, definim la funcionabilitat, una mesura de centralitat única que respon a la pregunta de, quins nodes, quan són pertorbats individualment, són més capaços d’allunyar el sistema de l’estat sincronitzat. Aquest fet podria suposar un comportament beneficiós o perjudicial per sistemes reals. El segon escenari considera la configuració més flexible, explorant la potencial heterogeneïtat dels paràmetres de frustració dels diferents nodes. Obtenim la solució analítica d’aquesta distribució per tal d’assolir qualsevol configuració de les fases dels oscil·ladors, a través de la linearització del model. També contestem a la pregunta: “de totes les possibles solucions, quina és la que implica un menor cost per tal d’assolir una configuració en particular?”. Finalment, en l’últim escenari, proporcionem una definició alternativa al concepte de simetria aproximada d’una xarxa, i que anomenem “Quasi simetries”. Aquestes són definides sense imposar invariàncies en les propietats del sistema, sinó que s’obtenen de l’estat estacionari del model de Kuramoto-Sakaguchi model, tot considerant una distribució homogènia dels paràmetres de frustració

THE MODEL AND FUNCTION OF QUALITY ASSESSMENT OF IMPLEMENTATION OF DESIGN PATTERNS

One of the ways of providing high internal software quality (that is a source code) is using design patterns. The article aims at presenting a suggested model which enables one to assess the quality of implementation of design patterns. The model assumes verification of different aspects of the patterns and a numeric expression of the obtained results. The analysis of the obtained results may show the occurrence of certain problems which are difficult to be identified during code review or testing