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

Achieving Small World Properties using Bio-Inspired Techniques in Wireless Networks

It is highly desirable and challenging for a wireless ad hoc network to have self-organization properties in order to achieve network wide characteristics. Studies have shown that Small World properties, primarily low average path length and high clustering coefficient, are desired properties for networks in general. However, due to the spatial nature of the wireless networks, achieving small world properties remains highly challenging. Studies also show that, wireless ad hoc networks with small world properties show a degree distribution that lies between geometric and power law. In this paper, we show that in a wireless ad hoc network with non-uniform node density with only local information, we can significantly reduce the average path length and retain the clustering coefficient. To achieve our goal, our algorithm first identifies logical regions using Lateral Inhibition technique, then identifies the nodes that beamform and finally the beam properties using Flocking. We use Lateral Inhibition and Flocking because they enable us to use local state information as opposed to other techniques. We support our work with simulation results and analysis, which show that a reduction of up to 40% can be achieved for a high-density network. We also show the effect of hopcount used to create regions on average path length, clustering coefficient and connectivity.Comment: Accepted for publication: Special Issue on Security and Performance of Networks and Clouds (The Computer Journal

Evolutionary Poisson Games for Controlling Large Population Behaviors

Emerging applications in engineering such as crowd-sourcing and (mis)information propagation involve a large population of heterogeneous users or agents in a complex network who strategically make dynamic decisions. In this work, we establish an evolutionary Poisson game framework to capture the random, dynamic and heterogeneous interactions of agents in a holistic fashion, and design mechanisms to control their behaviors to achieve a system-wide objective. We use the antivirus protection challenge in cyber security to motivate the framework, where each user in the network can choose whether or not to adopt the software. We introduce the notion of evolutionary Poisson stable equilibrium for the game, and show its existence and uniqueness. Online algorithms are developed using the techniques of stochastic approximation coupled with the population dynamics, and they are shown to converge to the optimal solution of the controller problem. Numerical examples are used to illustrate and corroborate our results

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Predictive Analytics Lead to Smarter Self-Organizing Directional Wireless Backbone Networks

Directional wireless systems are becoming a cost-effective approach towards providing a high-speed, reliable, broadband connection for the ubiquitous mobile wireless devices in use today. The most common of these systems consists of narrow-beam radio frequency (RF) and free-space-optical (FSO) links, which offer speeds between 100Mbps and 100Gbps while offering bit-error-rates comparable to fixed fiber optic installations. In addition, spatial and spectral efficiencies are accessible with directional wireless systems that cannot be matched with broadcast systems. The added benefits of compact designs permit the installation of directional antennas on-board unmanned autonomous systems (UAS) to provide network availability to regions prone to natural disasters, in maritime situations, and in war-torn countries that lack infrastructure security. In addition, through the use of intelligent network-centric algorithms, a flexible airborne backbone network can be established to dodge the scalability limitations of traditional omnidirectional wireless networks. Assuring end-to-end connectivity and coverage is the main challenge in the design of directional wireless backbone (DWB) networks. Conflating the duality of these objectives with the dynamical nature of the environment in which DWB networks are deployed, in addition to the standardized network metrics such as latency-minimization and throughput maximization, demands a rigorous control process that encompasses all aspects of the system. This includes the mechanical steering of the directional point-to-point link and the monitoring of aggregate network performance (e.g. dropped packets). The inclusion of processes for topology control, mobility management, pointing, acquisition, and tracking of the directional antennas, alongside traditional protocols (e.g. IPv6) provides a rigorous framework for next-generation mobile directional communication networks. This dissertation provides a novel approach to increase reliability in reconfigurable beam-steered directional wireless backbone networks by predicating optimal network reconfigurations wherein the network is modeled as a giant molecule in which the point-to-point links between two UASs are able to grow and retract analogously to the bonds between atoms in a molecule. This cross-disciplinary methodology explores the application of potential energy surfaces and normal mode analysis as an extension to the topology control optimization. Each of these methodologies provides a new and unique ability for predicting unstable configurations of DWB networks through an understanding of second-order principle dynamics inherent within the aggregate configuration of the system. This insight is not available through monitoring individual link performance. Together, the techniques used to model the DWB network through molecular dynamics are referred to as predictive analytics and provide reliable results that lead to smarter self-organizing reconfigurable beam-steered DWB networks. Furthermore, a comprehensive control architecture is proposed that complements traditional network science (e.g. Internet protocol) and the unique design aspects of DWB networks. The distinct ability of a beam-steered DWB network to adjust the direction of its antennas (i.e. reconfigure) in response to degraded effects within the atmosphere or due to an increased separation of nodes, is not incorporated in traditional network processes such re-routing mechanism, and therefore, processes for reconfiguration can be abstracted which both optimize the physical interconnections while maintaining interoperability with existing protocols. This control framework is validated using network metrics for latency and throughput and compared to existing architectures which use only standard re-routing mechanisms. Results are shown that validate both the analogous molecular modeling of a reconfigurable beam-steered directional wireless backbone network and a comprehensive control architecture which coalesces the unique capabilities of reconfiguration and mobility of mobile wireless backbone networks with existing protocols for networks such as IPv6