Graphs and Discrete Dirichlet Spaces PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Graphs and Discrete Dirichlet Spaces PDF full book. Access full book title Graphs and Discrete Dirichlet Spaces by Matthias Keller. Download full books in PDF and EPUB format.
Author: Matthias Keller
Publisher: Springer Nature
ISBN: 3030814599
Category : Mathematics
Languages : en
Pages : 675
Get Book Here
Book Description
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.
Author: Matthias Keller
Publisher: Springer Nature
ISBN: 3030814599
Category : Mathematics
Languages : en
Pages : 675
Get Book Here
Book Description
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.
Author: Matthias Keller
Publisher:
ISBN: 9783030814601
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
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.
Author: José M. Mazón
Publisher: Springer Nature
ISBN: 3031335848
Category : Mathematics
Languages : en
Pages : 396
Get Book Here
Book Description
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.
Author: Felix L. Schwenninger
Publisher: Springer Nature
ISBN: 3031649915
Category :
Languages : en
Pages : 262
Get Book Here
Book Description
Author: Luca Calatroni
Publisher: Springer Nature
ISBN: 3031319753
Category : Computers
Languages : en
Pages : 767
Get Book Here
Book Description
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.
Author: Olaf Post
Publisher: Springer Science & Business Media
ISBN: 3642238394
Category : Mathematics
Languages : en
Pages : 444
Get Book Here
Book Description
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.
Author: Rick Durrett
Publisher: Cambridge University Press
ISBN: 1139460889
Category : Mathematics
Languages : en
Pages : 203
Get Book Here
Book Description
The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
Author: Wolfgang Woess
Publisher: Cambridge University Press
ISBN: 0521552923
Category : Mathematics
Languages : en
Pages : 350
Get Book Here
Book Description
The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.
Author: Xian-Da Zhang
Publisher: Springer Nature
ISBN: 9811527709
Category : Computers
Languages : en
Pages : 844
Get Book Here
Book Description
Matrix algebra plays an important role in many core artificial intelligence (AI) areas, including machine learning, neural networks, support vector machines (SVMs) and evolutionary computation. This book offers a comprehensive and in-depth discussion of matrix algebra theory and methods for these four core areas of AI, while also approaching AI from a theoretical matrix algebra perspective. The book consists of two parts: the first discusses the fundamentals of matrix algebra in detail, while the second focuses on the applications of matrix algebra approaches in AI. Highlighting matrix algebra in graph-based learning and embedding, network embedding, convolutional neural networks and Pareto optimization theory, and discussing recent topics and advances, the book offers a valuable resource for scientists, engineers, and graduate students in various disciplines, including, but not limited to, computer science, mathematics and engineering.
Author: Gregory Berkolaiko
Publisher: American Mathematical Soc.
ISBN: 0821837656
Category : Mathematics
Languages : en
Pages : 322
Get Book Here
Book Description
This volume is a collection of articles dedicated to quantum graphs, a newly emerging interdisciplinary field related to various areas of mathematics and physics. The reader can find a broad overview of the theory of quantum graphs. The articles present methods coming from different areas of mathematics: number theory, combinatorics, mathematical physics, differential equations, spectral theory, global analysis, and theory of fractals. They also address various important applications, such as Anderson localization, electrical networks, quantum chaos, mesoscopic physics, superconductivity, optics, and biological modeling.
