Spectral Analysis Of Growing Graphs PDF Download
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| Author | : Nobuaki Obata |
| Publisher | : Springer |
| Total Pages | : 141 |
| Release | : 2017-02-17 |
| Genre | : Science |
| ISBN | : 9811035067 |
Download Spectral Analysis of Growing Graphs Book in PDF, ePub and Kindle
This book is designed as a concise introduction to the recent achievements on spectral analysis of graphs or networks from the point of view of quantum (or non-commutative) probability theory. The main topics are spectral distributions of the adjacency matrices of finite or infinite graphs and their limit distributions for growing graphs. The main vehicle is quantum probability, an algebraic extension of the traditional probability theory, which provides a new framework for the analysis of adjacency matrices revealing their non-commutative nature. For example, the method of quantum decomposition makes it possible to study spectral distributions by means of interacting Fock spaces or equivalently by orthogonal polynomials. Various concepts of independence in quantum probability and corresponding central limit theorems are used for the asymptotic study of spectral distributions for product graphs.This book is written for researchers, teachers, and students interested in graph spectra, their (asymptotic) spectral distributions, and various ideas and methods on the basis of quantum probability. It is also useful for a quick introduction to quantum probability and for an analytic basis of orthogonal polynomials.
| Author | : Nobuaki Obata |
| Publisher | : |
| Total Pages | : 138 |
| Release | : 2017 |
| Genre | : Distribution (Probability theory) |
| ISBN | : 9789811035074 |
Download Spectral Analysis of Growing Graphs Book in PDF, ePub and Kindle
| Author | : Akihito Hora |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 384 |
| Release | : 2007-07-05 |
| Genre | : Science |
| ISBN | : 3540488634 |
Download Quantum Probability and Spectral Analysis of Graphs Book in PDF, ePub and Kindle
This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.
| Author | : |
| Publisher | : |
| Total Pages | : 8 |
| Release | : 1791 |
| Genre | : |
| ISBN | : |
Download Déclaration des sentimens des curés, vicaires & autres ecclésiastiques du doyenné de Fontenay, diocèse de Bayeux, adressée aux fidèles de leurs différentes paroisses, au sujet du serment exigé par l'Assemblée Nationale Book in PDF, ePub and Kindle
| Author | : R. A. Bailey |
| Publisher | : Cambridge University Press |
| Total Pages | : 452 |
| Release | : 2024-05-30 |
| Genre | : Mathematics |
| ISBN | : 1009465945 |
Download Groups and Graphs, Designs and Dynamics Book in PDF, ePub and Kindle
This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.
| Author | : D.M. Cvetkovic |
| Publisher | : Elsevier |
| Total Pages | : 319 |
| Release | : 1988-01-01 |
| Genre | : Mathematics |
| ISBN | : 0080867766 |
Download Recent Results in the Theory of Graph Spectra Book in PDF, ePub and Kindle
The purpose of this volume is to review the results in spectral graph theory which have appeared since 1978. The problem of characterizing graphs with least eigenvalue -2 was one of the original problems of spectral graph theory. The techniques used in the investigation of this problem have continued to be useful in other contexts including forbidden subgraph techniques as well as geometric methods involving root systems. In the meantime, the particular problem giving rise to these methods has been solved almost completely. This is indicated in Chapter 1. The study of various combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2. Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs.
| Author | : Piet van Mieghem |
| Publisher | : Cambridge University Press |
| Total Pages | : 363 |
| Release | : 2010-12-02 |
| Genre | : Technology & Engineering |
| ISBN | : 1139492276 |
Download Graph Spectra for Complex Networks Book in PDF, ePub and Kindle
Analyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained 2010 book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range of types of graphs and topics important to the analysis of complex systems, this guide provides the mathematical foundation needed to understand and apply spectral insight to real-world systems. In particular, the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. An ideal resource for researchers and students in communications networking as well as in physics and mathematics.
| Author | : Donald Pierantozzi |
| Publisher | : |
| Total Pages | : 536 |
| Release | : 2020-04-16 |
| Genre | : |
| ISBN | : |
Download Topics in Spectral Analysis Book in PDF, ePub and Kindle
Algebraic graph theory is the branch of mathematics that studies graphs by using algebraic properties of associated matrices. Spectral graph theory studies the relation between graph properties and the spectrum of the adjacency or Laplacian matrix.Google founders computed the Perron-Frobenius eigenvector of the web graph and became billionaires. The second largest eigenvalue of a graph gives information about expansion and randomness properties with smallest eigenvalue gives information about independence and chromatic number. Interlacing gives information about substructures. Eigenvalue multiplicities provides strong restrictions with the spectrum providing useful invariants.The standard material on spectra is first provided. Important applications of graph spectra involve the largest or second largest or smallest eigenvalue, or interlacing, topics are then presented. Special topics of trees, topological structures and spectral characterizations are discussed.Work herein is based on the PhD dissertation work at the University of Pennsylvania under the direction of former professors Bedrosian and Wilf with post-doctoral studies at Princeton University with professors Sarniak and Conway.DCP 11/19/19
| Author | : Gene Cheung |
| Publisher | : John Wiley & Sons |
| Total Pages | : 322 |
| Release | : 2021-08-31 |
| Genre | : Computers |
| ISBN | : 1789450284 |
Download Graph Spectral Image Processing Book in PDF, ePub and Kindle
Graph spectral image processing is the study of imaging data from a graph frequency perspective. Modern image sensors capture a wide range of visual data including high spatial resolution/high bit-depth 2D images and videos, hyperspectral images, light field images and 3D point clouds. The field of graph signal processing – extending traditional Fourier analysis tools such as transforms and wavelets to handle data on irregular graph kernels – provides new flexible computational tools to analyze and process these varied types of imaging data. Recent methods combine graph signal processing ideas with deep neural network architectures for enhanced performances, with robustness and smaller memory requirements. The book is divided into two parts. The first is centered on the fundamentals of graph signal processing theories, including graph filtering, graph learning and graph neural networks. The second part details several imaging applications using graph signal processing tools, including image and video compression, 3D image compression, image restoration, point cloud processing, image segmentation and image classification, as well as the use of graph neural networks for image processing.
| Author | : Takashi Yatsui |
| Publisher | : Springer |
| Total Pages | : 205 |
| Release | : 2018-08-29 |
| Genre | : Science |
| ISBN | : 3319982672 |
Download Progress in Nanophotonics 5 Book in PDF, ePub and Kindle
This book presents important topics in nanophotonics in review-style chapters written by world leading scientists. The book sketches the history of dressed photon science and technology and explains why advanced theories of dressed photons are required. To meet this requirement, the recent results of theoretical studies and the theory of dressed photons are displayed by modifying the conventional electromagnetic theory. The classical theoretical model of spatiotemporal vortex dynamics is explained by treating the dressed photon as a space-like virtual photon. Also discussed in the book is the energy transfer of dressed photons, based on a quantum walk model and a quantum mechanical measurement process of dressed photons for connecting the nano- and macro-systems. Dressed photons are explained as quantum fields by characterizing them in momentum space.
