Download or read book Symmetry in Complex Network Systems written by Visarath In and published by Springer. This book was released on 2017-09-05 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Symmetry in Complex Systems written by J. A. Tenreiro Machado and published by MDPI. This book was released on 2021-01-21 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex systems with symmetry arise in many fields, at various length scales, including financial markets, social, transportation, telecommunication and power grid networks, world and country economies, ecosystems, molecular dynamics, immunology, living organisms, computational systems, and celestial and continuum mechanics. The emergence of new orders and structures in complex systems means symmetry breaking and transitions from unstable to stable states. Modeling complexity has attracted many researchers from different areas, dealing both with theoretical concepts and practical applications. This Special Issue fills the gap between the theory of symmetry-based dynamics and its application to model and analyze complex systems.
Download or read book Symmetry Measures on Complex Networks written by Angel Garrido and published by MDPI. This book was released on 2018-07-09 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Symmetry Measures on Complex Networks" that was published in Symmetry
Download or read book Symmetry Measures on Complex Networks written by Angel Garrido (Ed.) and published by . This book was released on 2017 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry is found everywhere, to a greater or lesser degree. It is essential in all sciences and also as the basic substrate in all arts. The same happens with Complex Networks, which are the majority of all those that interest for advanced knowledge, that is, for research. That is why these two themes have been unified here, whose intersection we are dealing with: in its first part, of fundamentals, and in its second part of applications, which are multiple in the world today.
Download or read book Symmetry in Complex Systems written by J. A. Tenreiro Machado and published by . This book was released on 2020 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex systems with symmetry arise in many fields, at various length scales, including financial markets, social, transportation, telecommunication and power grid networks, world and country economies, ecosystems, molecular dynamics, immunology, living organisms, computational systems, and celestial and continuum mechanics. The emergence of new orders and structures in complex systems means symmetry breaking and transitions from unstable to stable states. Modeling complexity has attracted many researchers from different areas, dealing both with theoretical concepts and practical applications. This Special Issue fills the gap between the theory of symmetry-based dynamics and its application to model and analyze complex systems.
Download or read book Higher Order Networks written by Ginestra Bianconi and published by Cambridge University Press. This book was released on 2021-12-23 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Higher-order networks describe the many-body interactions of a large variety of complex systems, ranging from the the brain to collaboration networks. Simplicial complexes are generalized network structures which allow us to capture the combinatorial properties, the topology and the geometry of higher-order networks. Having been used extensively in quantum gravity to describe discrete or discretized space-time, simplicial complexes have only recently started becoming the representation of choice for capturing the underlying network topology and geometry of complex systems. This Element provides an in-depth introduction to the very hot topic of network theory, covering a wide range of subjects ranging from emergent hyperbolic geometry and topological data analysis to higher-order dynamics. This Elements aims to demonstrate that simplicial complexes provide a very general mathematical framework to reveal how higher-order dynamics depends on simplicial network topology and geometry.
Download or read book Modularity and Dynamics on Complex Networks written by Renaud Lambiotte and published by Cambridge University Press. This book was released on 2022-02-03 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topological Aspects Of Critical Systems And Networks With Cd rom Proceedings Of The International Symposium written by Kousuke Yakubo and published by World Scientific. This book was released on 2007-06-21 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gives an interdisciplinary discussion on the topological aspects of general networks and critical systems for physicists, chemists, biologists, mathematicians, medical scientists, social scientists, and other related researchers. Subjects as diverse as the general properties of complex networks, complexity in social science, patterns in biological objects, and criticality in pure and applied physics are represented. The book is essential for researchers in a wide range of scientific and technological fields related to these areas.
Download or read book Symmetry and Universal Critical Properties of a Class of Discrete State Networks written by Shabnam Hossein and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we study the statistical mechanics of Boolean networks as a simple model in class of heterogeneous complex systems. Boolean networks are used as generic models of complex systems of many interacting units, such as gene and protein interaction systems, neural networks and economical systems. They are particularly good examples of complex systems to study because they are relatively simple, yet have a nontrivial dynamical phase transition. We investigate the statistical mechanics of how this model behaves and dynamical properties of random Boolean networks at criticality. First we study the dynamics of critical random Boolean networks and find what the symmetry of the dynamics is. We propose a symmetry group, the \textit{canalization preserving group}, that describes the symmetry observed. The orbits of this symmetry group consist of Boolean functions that have the same canalization values. Canalization is a form of robustness in which a subset of the input values control the behavior of a node regardless of the remaining inputs. We show that the same symmetry governs critical random discrete multi-state networks dynamics with higher number of output values for each node. We investigate the criticality of random multi-state networks, and show that the same canalization preserving symmetry governs the critical multi-state networks dynamics as well. We also study a particular dynamical property of critical random Boolean networks: their attractor length distribution. Using a known result that nodes relevant to the dynamics on attractors at criticality can be divided into separate components, we analyze the structure of these relevant components and how their dynamics combine to find the distribution of attractor lengths. This is accomplished by mapping the problem to the enumeration of binary Lyndon words. Using analytical arguments we show that the attractor length distribution becomes scale-free in the large network limit with a decay described by a critical exponent of 1. The universal nature of this behavior is demonstrated by comparison to that of the evolved critical state achieved through the playing of an adaptive game that selects for diversity of node's behavior, and that of the attractor length distribution of critical multi-state networks.
Download or read book A Principle of Symmetry in Networks written by Ron Aharoni and published by . This book was released on 1979 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Symmetry Measures on Complex Networks written by and published by . This book was released on 19?? with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Structural Analysis of Complex Networks written by Matthias Dehmer and published by Springer Science & Business Media. This book was released on 2010-10-14 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: Filling a gap in literature, this self-contained book presents theoretical and application-oriented results that allow for a structural exploration of complex networks. The work focuses not only on classical graph-theoretic methods, but also demonstrates the usefulness of structural graph theory as a tool for solving interdisciplinary problems. Applications to biology, chemistry, linguistics, and data analysis are emphasized. The book is suitable for a broad, interdisciplinary readership of researchers, practitioners, and graduate students in discrete mathematics, statistics, computer science, machine learning, artificial intelligence, computational and systems biology, cognitive science, computational linguistics, and mathematical chemistry. It may also be used as a supplementary textbook in graduate-level seminars on structural graph analysis, complex networks, or network-based machine learning methods.
Download or read book Introduction to Complex Network Theory written by Niloy Ganguly and published by Birkhäuser. This book was released on 2016-01-06 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex network theory is rapidly becoming recognized as a crucial tool for analyzing various dynamics and phenomena of large-scale networks across a spectrum of diverse disciplines. This textbook is the first to provide a multidisciplinary examination of common problems in systems exhibiting a complex network structure and includes: thorough explanations given both conceptually and mathematically, illustrative examples and exercises included in each chapter, large-scale network visualization software and algorithms, and a comprehensive set of glossaries. The text is intended for use by senior undergraduate and graduate students who are new to the field of complex network theory but is also structured to provide straightforward access to topics of specific interest and may be used as a reference by researchers.
Download or read book Dynamics On and Of Complex Networks III written by Fakhteh Ghanbarnejad and published by Springer. This book was released on 2019-05-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book bridges the gap between advances in the communities of computer science and physics--namely machine learning and statistical physics. It contains diverse but relevant topics in statistical physics, complex systems, network theory, and machine learning. Examples of such topics are: predicting missing links, higher-order generative modeling of networks, inferring network structure by tracking the evolution and dynamics of digital traces, recommender systems, and diffusion processes. The book contains extended versions of high-quality submissions received at the workshop, Dynamics On and Of Complex Networks (doocn.org), together with new invited contributions. The chapters will benefit a diverse community of researchers. The book is suitable for graduate students, postdoctoral researchers and professors of various disciplines including sociology, physics, mathematics, and computer science.
Download or read book Waves and Oscillations in Complex Networks written by Jason Michael Hindes and published by . This book was released on 2015 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Network theory has proven a powerful and general framework for studying the effects of complex interaction topology on the dynamics of many real systems in biology, physics and the social sciences, which show a variety of heterogeneous and multi-scale connectivity patterns. Although much work has been done in this field, many open questions remain about what role network topology plays in influencing the behaviors of complex systems. This dissertation examines the effects of complex network structure on the formation of collective oscillations and waves. In particular we study the propagation of epidemic fronts in multi-scale networks, the interplay between mutual and driven synchronization in heterogeneous oscillator networks, and the emergence of collective transport waves in driven randomly pinned oscillator networks. Qualitatively new behavior is found, and new reduction and analysis techniques are developed which allow us to understand the relationship between connectivity structure and the dynamics in these processes. Broadly, this work makes unique contributions to the exploration of fully non-equilibrium pattern formation and nonlinear dynamics in complex networks.
Download or read book Energy Transmission and Synchronization in Complex Networks written by Nicolás Rubido and published by Springer. This book was released on 2015-08-20 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work tackles the problems of understanding how energy is transmitted and distributed in power-grids as well as in determining how robust this transmission and distribution is when modifications to the grid or power occur. The most important outcome is the derivation of explicit relationships between the structure of the grid, the optimal transmission and distribution of energy, and the grid’s collective behavior (namely, the synchronous generation of power). These relationships are extremely relevant for the design of resilient power-grid models. To allow the reader to apply these results to other complex systems, the thesis includes a review of relevant aspects of network theory, spectral theory, and novel analytical calculations to predict the existence and stability of periodic collective behavior in complex networks of phase oscillators, which constitute a paradigmatic model for many complex systems.
Download or read book Dynamical Processes on Complex Networks written by Alain Barrat and published by Cambridge University Press. This book was released on 2008-10-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: An in-depth account on complex connectivity patterns for graduates and researchers in statistical mechanics, mathematical biology and information science.
