Spectral Analysis Of Growing Graphs

Author : Nobuaki Obata
Publisher : Springer
Page : 138 pages
File Size : 49,5 Mb
Release : 2017-02-17
Category : Science
ISBN : 9789811035067

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Spectral Analysis of Growing Graphs by Nobuaki Obata Pdf

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 : Unknown
Page : 138 pages
File Size : 40,5 Mb
Release : 2017
Category : Distribution (Probability theory)
ISBN : 9811035075

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Spectral Analysis of Growing Graphs by Nobuaki Obata Pdf

Author : Akihito Hora,Nobuaki Obata
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 43,5 Mb
Release : 2007-07-05
Category : Science
ISBN : 9783540488637

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Quantum Probability and Spectral Analysis of Graphs by Akihito Hora,Nobuaki Obata Pdf

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 : Gene Cheung,Enrico Magli
Publisher : John Wiley & Sons
Page : 322 pages
File Size : 52,6 Mb
Release : 2021-08-31
Category : Computers
ISBN : 9781789450286

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Graph Spectral Image Processing by Gene Cheung,Enrico Magli Pdf

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
Page : 205 pages
File Size : 46,5 Mb
Release : 2018-08-29
Category : Science
ISBN : 9783319982670

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Progress in Nanophotonics 5 by Takashi Yatsui Pdf

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.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 190 pages
File Size : 48,6 Mb
Release : 2008
Category : Mathematical analysis
ISBN : 0821839284

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Selected Papers on Analysis and Related Topics by Anonim Pdf

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.

Author : Ljubiša Stanković,Ervin Sejdić
Publisher : Springer
Page : 507 pages
File Size : 55,9 Mb
Release : 2018-12-01
Category : Technology & Engineering
ISBN : 9783030035747

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Vertex-Frequency Analysis of Graph Signals by Ljubiša Stanković,Ervin Sejdić Pdf

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.

Author : Takeyuki Hida,Kimiaki Saito
Publisher : World Scientific
Page : 230 pages
File Size : 47,5 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812774835

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Quantum Information V by Takeyuki Hida,Kimiaki Saito Pdf

Sample Chapter(s). Chapter 1: Recognition and Teleportation (494 KB). Contents: Recognition and Teleportation (M Ohya et al.); Quantum Information and Spacetime Structure (I V Volovich); On Gaussian and Poisson White Noises (N Asai); Renormalization, Orthogonalization, and Generating Functions (N Asai et al.); Insider Trading in Continuous Time (E Barucci et al.); Existence, Uniqueness, Consistency and Dependency on Diffusion Coefficients of Generalized Solutions of Nonlinear Diffusion Equations in Colombeau''s Algebra (H Deguchi); On Mathematical Treatment of Quantum Communication Gate on Fock Space (W Freudenberg et al.); A Frontier of White Noise Analysis (T Hida); An Interacting Fock Space with Periodic Jacobi Parameter Obtained from Regular Graphs in Large Scale Limit (A Hora & N Obata); Error Exponents of Codings for Stationary Gaussian Channels (S Ihara); White Noise Analysis on Classical Wiener Space Revisited (Y-J Lee & H-H Shih); Fractional Brownian Motions and the L(r)vy Laplacian (K Nishi et al.); Jump Finding of a Stable Process (Si Si et al.); On Entropy Production of a One-Dimensional Lattice Conductor (S Tasaki). Readership: Researchers in probability & statistics, mathematical physics, functional analysis and mathematical biology.

Author : Anthony J. Petrillo
Publisher : Unknown
Page : 68 pages
File Size : 55,8 Mb
Release : 1976
Category : Conservation of natural resources
ISBN : UCR:31210024943548

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What's the Use of Land by Anthony J. Petrillo Pdf

Author : Eli Ben-Naim,Hans Frauenfelder,Zoltan Toroczkai
Publisher : Springer Science & Business Media
Page : 548 pages
File Size : 53,5 Mb
Release : 2004-09-01
Category : Science
ISBN : 3540223541

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Complex Networks by Eli Ben-Naim,Hans Frauenfelder,Zoltan Toroczkai Pdf

This volume is devoted to the applications of techniques from statistical physics to the characterization and modeling of complex networks. The first two parts of the book concern theory and modeling of networks, the last two parts survey applications to a wide variety of natural and artificial networks. The tutorial reviews that form this book are aimed at students and newcomers to the field, and will also constitute a modern and comprehensive reference for experts. To this aim, all contributions have been carefully peer-reviewed not only for scientific content but also for self-consistency and readability.

Author : Pavel Exner,Jonathan P. Keating,Peter Kuchment,Toshikazu Sunada,Alexander Teplyaev
Publisher : American Mathematical Soc.
Page : 721 pages
File Size : 40,8 Mb
Release : 2008
Category : Combinatorial analysis
ISBN : 9780821844717

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Analysis on Graphs and Its Applications by Pavel Exner,Jonathan P. Keating,Peter Kuchment,Toshikazu Sunada,Alexander Teplyaev Pdf

This book addresses a new interdisciplinary area emerging on the border between various areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus here is on problems and techniques related to graphs, quantum graphs, and fractals that parallel those from differential equations, differential geometry, or geometric analysis. Also included are such diverse topics as number theory, geometric group theory, waveguide theory, quantum chaos, quantum wiresystems, carbon nano-structures, metal-insulator transition, computer vision, and communication networks.This volume contains a unique collection of expert reviews on the main directions in analysis on graphs (e.g., on discrete geometric analysis, zeta-functions on graphs, recently emerging connections between the geometric group theory and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide systems and modeling quantum graph systems with waveguides, control theory on graphs), as well as research articles.

Author : Marek Bożejko
Publisher : Unknown
Page : 334 pages
File Size : 49,8 Mb
Release : 2007
Category : Free probability theory
ISBN : UOM:39015075633761

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Noncommutative Harmonic Analysis with Applications to Probability by Marek Bożejko Pdf

Author : Marcello Pelillo
Publisher : Springer Science & Business Media
Page : 291 pages
File Size : 50,6 Mb
Release : 2013-11-26
Category : Computers
ISBN : 9781447156284

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Similarity-Based Pattern Analysis and Recognition by Marcello Pelillo Pdf

This accessible text/reference presents a coherent overview of the emerging field of non-Euclidean similarity learning. The book presents a broad range of perspectives on similarity-based pattern analysis and recognition methods, from purely theoretical challenges to practical, real-world applications. The coverage includes both supervised and unsupervised learning paradigms, as well as generative and discriminative models. Topics and features: explores the origination and causes of non-Euclidean (dis)similarity measures, and how they influence the performance of traditional classification algorithms; reviews similarity measures for non-vectorial data, considering both a “kernel tailoring” approach and a strategy for learning similarities directly from training data; describes various methods for “structure-preserving” embeddings of structured data; formulates classical pattern recognition problems from a purely game-theoretic perspective; examines two large-scale biomedical imaging applications.

Author : Jürgen Sander,Jörn Steuding,Rasa Steuding
Publisher : Springer
Page : 552 pages
File Size : 53,6 Mb
Release : 2016-12-29
Category : Mathematics
ISBN : 9783319282039

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From Arithmetic to Zeta-Functions by Jürgen Sander,Jörn Steuding,Rasa Steuding Pdf

This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on Elementary and Analytic Number Theory (ELAZ), held July 2014 in Hildesheim, Germany. Ranging from the theory of arithmetical functions to diophantine problems, to analytic aspects of zeta-functions, the various research and survey articles cover the broad interests of the well-known number theorist and cherished colleague Wolfgang Schwarz (1934-2013), who contributed over one hundred articles on number theory, its history and related fields. Readers interested in elementary or analytic number theory and related fields will certainly find many fascinating topical results among the contributions from both respected mathematicians and up-and-coming young researchers. In addition, some biographical articles highlight the life and mathematical works of Wolfgang Schwarz.

Author : William L. William L. Hamilton
Publisher : Springer Nature
Page : 141 pages
File Size : 48,6 Mb
Release : 2022-06-01
Category : Computers
ISBN : 9783031015885

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Graph Representation Learning by William L. William L. Hamilton Pdf

Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.