Graphs And Discrete Dirichlet Spaces
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Graphs And Discrete Dirichlet Spaces
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Author : Matthias Keller
language : en
Publisher: Springer Nature
Release Date : 2021-10-22
Graphs And Discrete Dirichlet Spaces written by Matthias Keller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-22 with Mathematics categories.
The spectral geometry of infinite graphs deals with three major themes and their interplay: the spectral theory of the Laplacian, the geometry of the underlying graph, and the heat flow with its probabilistic aspects. In this book, all three themes are brought together coherently under the perspective of Dirichlet forms, providing a powerful and unified approach. The book gives a complete account of key topics of infinite graphs, such as essential self-adjointness, Markov uniqueness, spectral estimates, recurrence, and stochastic completeness. A major feature of the book is the use of intrinsic metrics to capture the geometry of graphs. As for manifolds, Dirichlet forms in the graph setting offer a structural understanding of the interaction between spectral theory, geometry and probability. For graphs, however, the presentation is much more accessible and inviting thanks to the discreteness of the underlying space, laying bare the main concepts while preserving the deep insights of the manifold case. Graphs and Discrete Dirichlet Spaces offers a comprehensive treatment of the spectral geometry of graphs, from the very basics to deep and thorough explorations of advanced topics. With modest prerequisites, the book can serve as a basis for a number of topics courses, starting at the undergraduate level.
Graphs And Discrete Dirichlet Spaces
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Author : Matthias Keller
language : en
Publisher:
Release Date : 2021
Graphs And Discrete Dirichlet Spaces written by Matthias Keller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
The spectral geometry of infinite graphs deals with three major themes and their interplay: the spectral theory of the Laplacian, the geometry of the underlying graph, and the heat flow with its probabilistic aspects. In this book, all three themes are brought together coherently under the perspective of Dirichlet forms, providing a powerful and unified approach. The book gives a complete account of key topics of infinite graphs, such as essential self-adjointness, Markov uniqueness, spectral estimates, recurrence, and stochastic completeness. A major feature of the book is the use of intrinsic metrics to capture the geometry of graphs. As for manifolds, Dirichlet forms in the graph setting offer a structural understanding of the interaction between spectral theory, geometry and probability. For graphs, however, the presentation is much more accessible and inviting thanks to the discreteness of the underlying space, laying bare the main concepts while preserving the deep insights of the manifold case. Graphs and Discrete Dirichlet Spaces offers a comprehensive treatment of the spectral geometry of graphs, from the very basics to deep and thorough explorations of advanced topics. With modest prerequisites, the book can serve as a basis for a number of topics courses, starting at the undergraduate level.
Variational And Diffusion Problems In Random Walk Spaces
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Author : José M. Mazón
language : en
Publisher: Springer Nature
Release Date : 2023-08-04
Variational And Diffusion Problems In Random Walk Spaces written by José M. Mazón and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-04 with Mathematics categories.
This book presents the latest developments in the theory of gradient flows in random walk spaces. A broad framework is established for a wide variety of partial differential equations on nonlocal models and weighted graphs. Within this framework, specific gradient flows that are studied include the heat flow, the total variational flow, and evolution problems of Leray-Lions type with different types of boundary conditions. With many timely applications, this book will serve as an invaluable addition to the literature in this active area of research. Variational and Diffusion Problems in Random Walk Spaces will be of interest to researchers at the interface between analysis, geometry, and probability, as well as to graduate students interested in exploring these areas.
Scale Space And Variational Methods In Computer Vision
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Author : Tatiana A. Bubba
language : en
Publisher: Springer Nature
Release Date :
Scale Space And Variational Methods In Computer Vision written by Tatiana A. Bubba and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Markov Chains Theory And Applications
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Author :
language : en
Publisher: Elsevier
Release Date : 2025-03-28
Markov Chains Theory And Applications written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-28 with Mathematics categories.
Markov Chains: Theory and Applications, Volume 52 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on topics such as Markov Chain Estimation, Approximation, and Aggregation for Average Reward Markov Decision Processes and Reinforcement Learning, Ladder processes: symmetric functions and semigroups, Continuous-time Markov Chains and Models: Study via Forward Kolmogorov System, Analysis of Data Following Finite-State Continuous-Time Markov Chains, Computational applications of poverty measurement through Markov model for income classes, and more.Other sections cover Estimation and calibration of continuous time Markov chains, Additive High-Order Markov Chains, The role of the random-product technique in the theory of Markov chains on a countable state space., On estimation problems based on type I Longla copulas, and Long time behavior of continuous time Markov chains. - Provides the latest information on Markov Chains: Theory And Applications - Offers outstanding and original reviews on a range of Markov Chains research topics - Serves as an indispensable reference for researchers and students alike
Systems Theory And Pdes
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Author : Felix L. Schwenninger
language : en
Publisher: Springer Nature
Release Date : 2024-09-20
Systems Theory And Pdes written by Felix L. Schwenninger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-20 with Science categories.
This volume presents recent advances and open problems in the cross section of infinite-dimensional systems theory and the modern treatment of PDEs. Chapters are based on talks and problem sessions from the first “Workshop on Systems Theory and PDEs” (WOSTAP), held at TU Bergakademie Freiberg in July 2022. The main topics covered include: Differential algebraic equations Port-Hamiltonian systems in both finite and infinite dimensions Highly nonlinear equations related to elasticity/plasticity Modeling of thermo-piezo-electromagnetism
Scale Space And Variational Methods In Computer Vision
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Author : Luca Calatroni
language : en
Publisher: Springer Nature
Release Date : 2023-05-09
Scale Space And Variational Methods In Computer Vision written by Luca Calatroni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-09 with Computers categories.
This book constitutes the proceedings of the 9th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2023, which took place in Santa Margherita di Pula, Italy, in May 2023. The 57 papers presented in this volume were carefully reviewed and selected from 72 submissions. They were organized in topical sections as follows: Inverse Problems in Imaging; Machine and Deep Learning in Imaging; Optimization for Imaging: Theory and Methods; Scale Space, PDEs, Flow, Motion and Registration.
Introduction To Analysis On Graphs
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Author : Alexander Grigor’yan
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-23
Introduction To Analysis On Graphs written by Alexander Grigor’yan 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 2018-08-23 with Mathematics categories.
A central object of this book is the discrete Laplace operator on finite and infinite graphs. The eigenvalues of the discrete Laplace operator have long been used in graph theory as a convenient tool for understanding the structure of complex graphs. They can also be used in order to estimate the rate of convergence to equilibrium of a random walk (Markov chain) on finite graphs. For infinite graphs, a study of the heat kernel allows to solve the type problem—a problem of deciding whether the random walk is recurrent or transient. This book starts with elementary properties of the eigenvalues on finite graphs, continues with their estimates and applications, and concludes with heat kernel estimates on infinite graphs and their application to the type problem. The book is suitable for beginners in the subject and accessible to undergraduate and graduate students with a background in linear algebra I and analysis I. It is based on a lecture course taught by the author and includes a wide variety of exercises. The book will help the reader to reach a level of understanding sufficient to start pursuing research in this exciting area.
Spectral Analysis On Graph Like Spaces
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Author : Olaf Post
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-06
Spectral Analysis On Graph Like Spaces written by Olaf Post 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 2012-01-06 with Mathematics categories.
Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new tools such as norm convergence of operators acting in different Hilbert spaces, an extension of the concept of boundary triples to partial differential operators, and an abstract definition of resonances via boundary triples. These tools are formulated in an abstract framework, independent of the original problem of graph-like spaces, so that they can be applied in many other situations where the spaces are perturbed.
Random Graphs And Complex Networks
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Author : Remco van der Hofstad
language : en
Publisher: Cambridge University Press
Release Date : 2017
Random Graphs And Complex Networks written by Remco van der Hofstad 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 2017 with Computers categories.
This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.