Spectral Analysis Of Growing Graphs
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Spectral Analysis Of Growing Graphs
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Author : Nobuaki Obata
language : en
Publisher: Springer
Release Date : 2017-02-17
Spectral Analysis Of Growing Graphs written by Nobuaki Obata and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-17 with Science categories.
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.
Spectral Analysis Of Growing Graphs
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Author : Nobuaki Obata
language : en
Publisher:
Release Date : 2017
Spectral Analysis Of Growing Graphs written by Nobuaki Obata and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Distribution (Probability theory) categories.
Quantum Probability And Spectral Analysis Of Graphs
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Author : Akihito Hora
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-05
Quantum Probability And Spectral Analysis Of Graphs written by Akihito Hora and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-05 with Science categories.
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.
Graph Spectra For Complex Networks
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Author : Piet Van Mieghem
language : en
Publisher:
Release Date : 2011
Graph Spectra For Complex Networks written by Piet Van Mieghem and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Electronic book categories.
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.
Vertex Frequency Analysis Of Graph Signals
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Author : Ljubiša Stanković
language : en
Publisher: Springer
Release Date : 2018-12-01
Vertex Frequency Analysis Of Graph Signals written by Ljubiša Stanković and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-01 with Technology & Engineering categories.
This book introduces new methods to analyze vertex-varying graph signals. In many real-world scenarios, the data sensing domain is not a regular grid, but a more complex network that consists of sensing points (vertices) and edges (relating the sensing points). Furthermore, sensing geometry or signal properties define the relation among sensed signal points. Even for the data sensed in the well-defined time or space domain, the introduction of new relationships among the sensing points may produce new insights in the analysis and result in more advanced data processing techniques. The data domain, in these cases and discussed in this book, is defined by a graph. Graphs exploit the fundamental relations among the data points. Processing of signals whose sensing domains are defined by graphs resulted in graph data processing as an emerging field in signal processing. Although signal processing techniques for the analysis of time-varying signals are well established, the corresponding graph signal processing equivalent approaches are still in their infancy. This book presents novel approaches to analyze vertex-varying graph signals. The vertex-frequency analysis methods use the Laplacian or adjacency matrix to establish connections between vertex and spectral (frequency) domain in order to analyze local signal behavior where edge connections are used for graph signal localization. The book applies combined concepts from time-frequency and wavelet analyses of classical signal processing to the analysis of graph signals. Covering analytical tools for vertex-varying applications, this book is of interest to researchers and practitioners in engineering, science, neuroscience, genome processing, just to name a few. It is also a valuable resource for postgraduate students and researchers looking to expand their knowledge of the vertex-frequency analysis theory and its applications. The book consists of 15 chapters contributed by 41 leading researches in the field.
The Spectral Analysis Of Time Series
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Author : Lambert Herman Koopmans
language : en
Publisher:
Release Date : 1974
The Spectral Analysis Of Time Series written by Lambert Herman Koopmans and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
The Spectral Analysis of Time Series ...
Graph Spectral Image Processing
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Author : Gene Cheung
language : en
Publisher: John Wiley & Sons
Release Date : 2021-08-31
Graph Spectral Image Processing written by Gene Cheung and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-31 with Computers categories.
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.
Progress In Nanophotonics 5
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Author : Takashi Yatsui
language : en
Publisher: Springer
Release Date : 2018-08-29
Progress In Nanophotonics 5 written by Takashi Yatsui and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-29 with Science categories.
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.
Recent Results In The Theory Of Graph Spectra
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Author : D. M. Cvetkovic
language : en
Publisher: North Holland
Release Date : 1988-01-01
Recent Results In The Theory Of Graph Spectra written by D. M. Cvetkovic and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
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.
Selected Papers On Analysis And Related Topics
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Selected Papers On Analysis And Related Topics written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematical analysis categories.
This volume contains translations of papers that originally appeared in the Japanese journal 'Sugaku'. The papers range over a variety of topics, including operator algebras, analysis, and statistics.