Symmetry in Complex Network Systems

Symmetry in Complex Network Systems

Author: Visarath In

Publisher: Springer

Published: 2017-09-05

Total Pages: 415

ISBN-13: 366255545X

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This book bridges the current gap between the theory of symmetry-based dynamics and its application to model and analyze complex systems. As an alternative approach, the authors use the symmetry of the system directly to formulate the appropriate models, and also to analyze the dynamics. Complex systems with symmetry arise in a wide variety of fields, including communication networks, molecular dynamics, manufacturing businesses, ecosystems, underwater vehicle dynamics, celestial and spacecraft dynamics and continuum mechanics. A general approach for their analysis has been to derive a detailed model of their individual parts, connect the parts and note that the system contains some sort of symmetry, then attempt to exploit this symmetry in order to simplify numerical computations. This approach can result in highly complicated models that are difficult to analyze even numerically. The alternative approach, while nonstandard, is not entirely new among the mathematics community. However, there is much less familiarity with the techniques of symmetry-breaking bifurcation, as they apply to the engineering, design and fabrication, of complex systems, in particular, nonlinear sensor devices with special emphasis on the conceptualization and development of new technologies of magnetic sensors such as fluxgate magnetometers and SQUID (Superconducting Quantum Interference Devices), E-- (electric-field) sensors, and communication and navigation systems that require multiple frequencies of operation, such as radar and antenna devices as well as gyroscopic systems.


Symmetry Measures on Complex Networks

Symmetry Measures on Complex Networks

Author: Angel Garrido

Publisher: MDPI

Published: 2018-07-09

Total Pages: 509

ISBN-13: 3038424986

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This book is a printed edition of the Special Issue "Symmetry Measures on Complex Networks" that was published in Symmetry


Modularity and Dynamics on Complex Networks

Modularity and Dynamics on Complex Networks

Author: Renaud Lambiotte

Publisher: Cambridge University Press

Published: 2022-02-03

Total Pages: 102

ISBN-13: 1108808654

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Complex networks are typically not homogeneous, as they tend to display an array of structures at different scales. A feature that has attracted a lot of research is their modular organisation, i.e., networks may often be considered as being composed of certain building blocks, or modules. In this Element, the authors discuss a number of ways in which this idea of modularity can be conceptualised, focusing specifically on the interplay between modular network structure and dynamics taking place on a network. They discuss, in particular, how modular structure and symmetries may impact on network dynamics and, vice versa, how observations of such dynamics may be used to infer the modular structure. They also revisit several other notions of modularity that have been proposed for complex networks and show how these can be related to and interpreted from the point of view of dynamical processes on networks.


Complex Networks IV

Complex Networks IV

Author: Gourab Ghoshal

Publisher: Springer

Published: 2013-02-19

Total Pages: 198

ISBN-13: 3642368441

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A network is a mathematical object consisting of a set of points (called vertices or nodes) that are connected to each other in some fashion by lines (called edges). Turns out this simple description corresponds to a bewildering array of systems in the real world, ranging from technological ones such as the Internet and World Wide Web, biological networks such as that of connections of the nervous systems or blood vessels, food webs, protein interactions, infrastructural systems such as networks of roads, airports or the power-grid, to patterns of social acquaintance such as friendship, network of Hollywood actors, connections between business houses and many more. Recent years have witnessed a substantial amount of interest within the scientific community in the properties of these networks. The emergence of the internet in particular, coupled with the widespread availability of inexpensive computing resources has facilitated studies ranging from large scale empirical analysis of networks in the real world, to the development of theoretical models and tools to explore the various properties of these systems. The study of networks is broadly interdisciplinary and central developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together a collection of cutting-edge research in the field from a diverse array of researchers ranging from physicists to social scientists, and presents them in a coherent fashion, highlighting the strong interconnections between the different areas. Topics included are social networks and social media, opinion and innovation diffusion, syncronization, transportation networks and human mobility, as well as theory, modeling and metrics of Complex Networks.


Modeling, Dynamics, Optimization and Bioeconomics III

Modeling, Dynamics, Optimization and Bioeconomics III

Author: Alberto A. Pinto

Publisher: Springer

Published: 2018-04-25

Total Pages: 469

ISBN-13: 3319740865

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The research and review papers presented in this volume provide an overview of the main issues, findings, and open questions in cutting-edge research on the fields of modeling, optimization and dynamics and their applications to biology, economics, energy, finance, industry, physics and psychology. Given the scientific relevance of the innovative applications and emerging issues they address, the contributions to this volume, written by some of the world’s leading experts in mathematics, economics and other applied sciences, will be seminal to future research developments and will spark future works and collaborations. The majority of the papers presented in this volume were written by participants of the 4th International Conference on Dynamics, Games and Science: Decision Models in a Complex Economy (DGS IV), held at the National Distance Education University (UNED) in Madrid, Spain in June 2016 and of the 8th Berkeley Bioeconomy Conference: The Future of Biofuels, held at the UC Berkeley Alumni House in April 2015.


Dynamics and Bifurcation in Networks

Dynamics and Bifurcation in Networks

Author: Martin Golubitsky

Publisher: SIAM

Published: 2023-04-24

Total Pages: 867

ISBN-13: 1611977339

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In recent years, there has been an explosion of interest in network-based modeling in many branches of science. This book synthesizes some of the common features of many such models, providing a general framework analogous to the modern theory of nonlinear dynamical systems. How networks lead to behavior not typical in a general dynamical system and how the architecture and symmetry of the network influence this behavior are the book’s main themes. Dynamics and Bifurcation in Networks: Theory and Applications of Coupled Differential Equations is the first book to describe the formalism for network dynamics developed over the past 20 years. In it, the authors introduce a definition of a network and the associated class of “admissible” ordinary differential equations, in terms of a directed graph whose nodes represent component dynamical systems and whose arrows represent couplings between these systems. They also develop connections between network architecture and the typical dynamics and bifurcations of these equations and discuss applications of this formalism to various areas of science, including gene regulatory networks, animal locomotion, decision-making, homeostasis, binocular rivalry, and visual illusions. This book will be of interest to scientific researchers in any area that uses network models, which includes many parts of biology, physics, chemistry, computer science, electrical and electronic engineering, psychology, and sociology.


Fundamentals of Circuits and Filters

Fundamentals of Circuits and Filters

Author: Wai-Kai Chen

Publisher: CRC Press

Published: 2018-10-08

Total Pages: 1034

ISBN-13: 1351835025

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This volume, drawn from the Circuits and Filters Handbook, focuses on mathematics basics; circuit elements, devices, and their models; and linear circuit analysis. It examines Laplace transformation, Fourier methods for signal analysis and processing, z-transform, and wavelet transforms. It also explores network laws and theorems, terminal and port represetnation, analysis in the frequency domain, and more.


Symmetry and Complexity

Symmetry and Complexity

Author: Klaus Mainzer

Publisher: World Scientific

Published: 2005

Total Pages: 448

ISBN-13: 9812561927

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Cosmic evolution leads from symmetry to complexity by symmetry breaking and phase transitions. The emergence of new order and structure in nature and society is explained by physical, chemical, biological, social and economic self-organization, according to the laws of nonlinear dynamics. All these dynamical systems are considered computational systems processing information and entropy. Are symmetry and complexity only useful models of science or are they universals of reality? Symmetry and Complexity discusses the fascinating insights gained from natural, social and computer sciences, philosophy and the arts. With many diagrams and pictures, this book illustrates the spirit and beauty of nonlinear science. In the complex world of globalization, it strongly argues for unity in diversity.


Vulnerable Systems

Vulnerable Systems

Author: Wolfgang Kröger

Publisher: Springer Science & Business Media

Published: 2011-06-22

Total Pages: 212

ISBN-13: 0857296558

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The safe management of the complex distributed systems and critical infrastructures which constitute the backbone of modern industry and society entails identifying and quantifying their vulnerabilities to design adequate protection, mitigation, and emergency action against failure. In practice, there is no fail-safe solution to such problems and various frameworks are being proposed to effectively integrate different methods of complex systems analysis in a problem-driven approach to their solution. Vulnerable Systems reflects the current state of knowledge on the procedures which are being put forward for the risk and vulnerability analysis of critical infrastructures. Classical methods of reliability and risk analysis, as well as new paradigms based on network and systems theory, including simulation, are considered in a dynamic and holistic way. Readers of Vulnerable Systems will benefit from its structured presentation of the current knowledge base on this subject. It will enable graduate students, researchers and safety and risk analysts to understand the methods suitable for different phases of analysis and to identify their criticalities in application.


Soft Computing Applications in Sensor Networks

Soft Computing Applications in Sensor Networks

Author: Sankar K. Pal

Publisher: CRC Press

Published: 2016-10-03

Total Pages: 235

ISBN-13: 1315354713

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This book uses tutorials and new material to describe the basic concepts of soft-computing which potentially can be used in real-life sensor network applications. It is organized in a manner that exemplifies the use of an assortment of soft-computing applications for solving different problems in sensor networking. Written by worldwide experts, the chapters provide a balanced mixture of different problems concerning channel access, routing, coverage, localization, lifetime maximization and target tracking using emerging soft-computing applications.