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.
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.
Groups And Graphs Designs And Dynamics
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Author : R. A. Bailey
language : en
Publisher: Cambridge University Press
Release Date : 2024-05-30
Groups And Graphs Designs And Dynamics written by R. A. Bailey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-30 with Mathematics categories.
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.
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.
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.
Spectral Algorithms
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Author : Ravindran Kannan
language : en
Publisher: Now Publishers Inc
Release Date : 2009
Spectral Algorithms written by Ravindran Kannan and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Computers categories.
Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the y" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.
Spectral Analysis Of Musical Sounds With Emphasis On The Piano
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Author : David M. Koenig
language : en
Publisher: Oxford University Press, USA
Release Date : 2015
Spectral Analysis Of Musical Sounds With Emphasis On The Piano written by David M. Koenig and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Music categories.
In this book the tools of spectral analysis are applied via graphics to musical sounds, especially those coming from a piano, with emphasis on the visualization of musical sounds rather than the mathematics behind it. The aim is to give a different and insightful view of musical instruments.
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.
Sampling Statistics In The Atlantic Menhaden Fishery
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Author : Alexander J. Chester
language : en
Publisher:
Release Date : 1984
Sampling Statistics In The Atlantic Menhaden Fishery written by Alexander J. Chester and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Atlantic menhaden categories.
Atlantic menhaden, Brevootia tyrannus, the object of a major purse-seine fishery along the U.S. east coast, are landed at plants from northern Florida to central Maine. The National Marine Fisheries Service has sampled these landings since 1955 for length, weight, and age. Together with records of landings at each plant, the samples are used to estimate numbers of fish landed at each age. This report analyzes the sampling design in terms of probability sampling theory. The design is classified as two-stage cluster sampling, the first stage consisting of purse-seine sets randomly selected from the population of all sets landed, and the second state consisting of fish randomly selected from each sample set. Implicit assumptions of this design are discussed with special attention to current sampling procedures. Methods are developed for estimating mean fish weight, numbers of fish landed, and age composition of the catch, with approximate 95% confidence intervals. Based on specific results from three ports (Port Monmouth, N.J., Reedville, Va., and Beaufort, N.C.) for the 1979 fishing season, recommendations are made for improving sampling procedures to comply more exactly with assumptions of the sampling design. These recommendations include adopting more formal methods for randomizing set and fish selection, increasing the number of sets sampled, considering the bias introduced by unequal set sizes, and developing methods to optimize the use of funds and personnel.
Quantum Probability
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Author : Marek Bożejko
language : en
Publisher:
Release Date : 2006
Quantum Probability written by Marek Bożejko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Probabilities categories.