Dynamics On Graphs

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 1139460889
Total Pages : 203 pages
Book Rating : 4.80/5 ( download)

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Download or read book Random Graph Dynamics written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-05-31 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.

Author : George Osipenko
Publisher : Springer
ISBN 13 : 3540355952
Total Pages : 286 pages
Book Rating : 4.53/5 ( download)

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Download or read book Dynamical Systems, Graphs, and Algorithms written by George Osipenko and published by Springer. This book was released on 2006-10-28 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes a family of algorithms for studying the global structure of systems. By a finite covering of the phase space we construct a directed graph with vertices corresponding to cells of the covering and edges corresponding to admissible transitions. The method is used, among other things, to locate the periodic orbits and the chain recurrent set, to construct the attractors and their basins, to estimate the entropy, and more.

Author : Erich Prisner
Publisher : CRC Press
ISBN 13 : 9780582286962
Total Pages : 252 pages
Book Rating : 4.64/5 ( download)

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Download or read book Graph Dynamics written by Erich Prisner and published by CRC Press. This book was released on 1995-11-22 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Study of "graph operators" or "graph-valued functions" such as the line graph, the clique graph, the complement, and powers, raises several immediate questions: Which graphs are fixed under the operator? Which graphs appear as images of graphs? What happens if the operator is iterated? Over the last 30 years these questions have been answered and methods developed for particular operators in literally hundreds of papers on the subject. Nowhere, however, could one find a comprehensive treatment-a unification of terminology, questions, and methods. Graph Dynamics provides that comprehensive treatment. Its purpose is threefold: it serves as an introductory textbook on the topic, offers an encyclopedic survey of the literature, and reports recent research-both new tools and results on concrete operators. Part I explicitly presents graph dynamics general theory, stating general principles illustrated by application to graph operators. Part 2 addresses the operators themselves. It lists all known graph operators grouped together in families and recounts, with complete references, all that is known about the dynamical behavior of these concrete operators. Graph Dynamics is the book you need if you are looking for information on a particular operator, need a text for advanced students, or want to review collected research results presented with a common terminology. It is clearly an essential resource for anyone working in or studying algebra, combinatorics, or graph theory.

Author : Forbes T. Brown
Publisher : CRC Press
ISBN 13 : 9780849396489
Total Pages : 1088 pages
Book Rating : 4.84/5 ( download)

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Download or read book Engineering System Dynamics written by Forbes T. Brown and published by CRC Press. This book was released on 2006-08-15 with total page 1088 pages. Available in PDF, EPUB and Kindle. Book excerpt: For today's students, learning to model the dynamics of complex systems is increasingly important across nearly all engineering disciplines. First published in 2001, Forbes T. Brown's Engineering System Dynamics: A Unified Graph-Centered Approach introduced students to a unique and highly successful approach to modeling system dynamics using bond graphs. Updated with nearly one-third new material, this second edition expands this approach to an even broader range of topics. What's New in the Second Edition? In addition to new material, this edition was restructured to build students' competence in traditional linear mathematical methods before they have gone too far into the modeling that still plays a pivotal role. New topics include magnetic circuits and motors including simulation with magnetic hysteresis; extensive new material on the modeling, analysis, and simulation of distributed-parameter systems; kinetic energy in thermodynamic systems; and Lagrangian and Hamiltonian methods. MATLAB® figures prominently in this edition as well, with code available for download from the Internet. This code includes simulations for problems that appear in the later chapters as well as code for selected thermodynamic substances. Using a step-by-step pedagogy accompanied by abundant examples, graphs, illustrations, case studies, guided exercises, and homework problems, Engineering System Dynamics: A Unified Graph-Centered Approach, Second Edition is a text that students will embrace and continue to use well into their careers. While the first half of the book is ideal for junior-level undergraduates, the entire contents are suited for more advanced students.

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 9781009521451
Total Pages : 0 pages
Book Rating : 4.54/5 ( download)

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Download or read book Dynamics on Graphs written by Rick Durrett and published by Cambridge University Press. This book was released on 2024-10-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This extensive revision of the 2007 book 'Random Graph Dynamics,' covering the current state of mathematical research in the field, is ideal for researchers and graduate students. It considers a small number of types of graphs, primarily the configuration model and inhomogeneous random graphs. However, it investigates a wide variety of dynamics. The author describes results for the convergence to equilibrium for random walks on random graphs as well as topics that have emerged as mature research areas since the publication of the first edition, such as epidemics, the contact process, voter models, and coalescing random walk. Chapter 8 discusses a new challenging and largely uncharted direction: systems in which the graph and the states of their vertices coevolve.

Author : Igor A. Karnovsky
Publisher : McGraw Hill Professional
ISBN 13 : 0071394656
Total Pages : 560 pages
Book Rating : 4.59/5 ( download)

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Download or read book Formulas for Structural Dynamics: Tables, Graphs and Solutions written by Igor A. Karnovsky and published by McGraw Hill Professional. This book was released on 2000-11-01 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: * This information-rich reference book provides solutions to the architectural problem of vibrations in beams, arches and frames in bridges, highways, buildings and tunnels * A must-have for structural designers and civil engineers, especially those involved in the seismic design of buildings * Well-organized into problem-specific chapters, and loaded with detailed charts, graphs, and necessary formulas

Author : V.C. Barbosa
Publisher : CRC Press
ISBN 13 : 1420035738
Total Pages : 385 pages
Book Rating : 4.35/5 ( download)

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Download or read book An Atlas of Edge-Reversal Dynamics written by V.C. Barbosa and published by CRC Press. This book was released on 2000-08-23 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important resource offers the first in-depth account of the graph dynamics system SER (Scheduling by Edge Reversal),. In Part 1: Edge-Reversal Dynamics, the author discusses the main applications and properties of SER, provides data from statistics and correlations computed over several graph classes, and gives an overview of the algorithmic aspects of the construction of the catalogue. Part 2: The Atlas comprises the atlas proper-a catalogue of graphical representations of all basins of attraction generated by the SER mechanism for all graphs in selected classes.

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 9780521866569
Total Pages : 222 pages
Book Rating : 4.61/5 ( download)

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Download or read book Random Graph Dynamics written by Rick Durrett and published by Cambridge University Press. This book was released on 2006-10-23 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At about the same time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. While this literature is extensive, many of the papers are based on simulations and nonrigorous arguments. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature of this book is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.

Author : Mark R.T. Dale
Publisher : Cambridge University Press
ISBN 13 : 110708931X
Total Pages : 355 pages
Book Rating : 4.10/5 ( download)

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Download or read book Applying Graph Theory in Ecological Research written by Mark R.T. Dale and published by Cambridge University Press. This book was released on 2017-11-09 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book clearly describes the many applications of graph theory to ecological questions, providing instruction and encouragement to researchers.

Author : Christian Borgelt
Publisher : Springer
ISBN 13 : 3642302785
Total Pages : 378 pages
Book Rating : 4.87/5 ( download)

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Download or read book Towards Advanced Data Analysis by Combining Soft Computing and Statistics written by Christian Borgelt and published by Springer. This book was released on 2012-08-29 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Soft computing, as an engineering science, and statistics, as a classical branch of mathematics, emphasize different aspects of data analysis. Soft computing focuses on obtaining working solutions quickly, accepting approximations and unconventional approaches. Its strength lies in its flexibility to create models that suit the needs arising in applications. In addition, it emphasizes the need for intuitive and interpretable models, which are tolerant to imprecision and uncertainty. Statistics is more rigorous and focuses on establishing objective conclusions based on experimental data by analyzing the possible situations and their (relative) likelihood. It emphasizes the need for mathematical methods and tools to assess solutions and guarantee performance. Combining the two fields enhances the robustness and generalizability of data analysis methods, while preserving the flexibility to solve real-world problems efficiently and intuitively.