Nonlocal Continuum Limits Of P Laplacian Problems On Graphs
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Nonlocal Continuum Limits Of P Laplacian Problems On Graphs
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Author : Imad El Bouchairi
language : en
Publisher: Cambridge University Press
Release Date : 2023-05-11
Nonlocal Continuum Limits Of P Laplacian Problems On Graphs written by Imad El Bouchairi 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 2023-05-11 with Computers categories.
In this Element, the authors consider fully discretized p-Laplacian problems (evolution, boundary value and variational problems) on graphs. The motivation of nonlocal continuum limits comes from the quest of understanding collective dynamics in large ensembles of interacting particles, which is a fundamental problem in nonlinear science, with applications ranging from biology to physics, chemistry and computer science. Using the theory of graphons, the authors give a unified treatment of all the above problems and establish the continuum limit for each of them together with non-asymptotic convergence rates. They also describe an algorithmic framework based proximal splitting to solve these discrete problems on graphs.
Image And Signal Processing
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Author : Alamin Mansouri
language : en
Publisher: Springer
Release Date : 2018-06-29
Image And Signal Processing written by Alamin Mansouri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-29 with Computers categories.
This book constitutes the refereed proceedings of the 8th International Conference on Image and Signal Processing, ICISP 2018, held in Cherbourg, France, in July 2018. The 58 revised full papers were carefully reviewed and selected from 122 submissions. The contributions report on the latest developments in image and signal processing, video processing, computer vision, multimedia and computer graphics, and mathematical imaging and vision.
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.
Latent Modes Of Nonlinear Flows
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Author : Ido Cohen
language : en
Publisher: Cambridge University Press
Release Date : 2023-06-29
Latent Modes Of Nonlinear Flows written by Ido Cohen 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 2023-06-29 with Computers categories.
Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is essential for their analysis and modeling. In this Element the authors attempt to provide a consistent framework through Koopman theory and its related popular discrete approximation - dynamic mode decomposition (DMD). They investigate the conditions to perform appropriate linearization, dimensionality reduction and representation of flows in a highly general setting. The essential elements of this framework are Koopman eigenfunctions (KEFs) for which existence conditions are formulated. This is done by viewing the dynamic as a curve in state-space. These conditions lay the foundations for system reconstruction, global controllability, and observability for nonlinear dynamics. They examine the limitations of DMD through the analysis of Koopman theory and propose a new mode decomposition technique based on the typical time profile of the dynamics.
Active Particles Volume 4
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Author : José Antonio Carrillo
language : en
Publisher: Springer Nature
Release Date : 2024-12-12
Active Particles Volume 4 written by José Antonio Carrillo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-12 with Mathematics categories.
This edited volume collects nine surveys that present the state-of-the-art in modeling, qualitative analysis, and simulation of active particles, focusing on specific applications in the natural sciences. As in the preceding Active Particles volumes, it blends diverse applications that demonstrate the interdisciplinary nature of the subject and the various mathematical tools available. Contributions were selected with the aim of covering a variety of viewpoints, from modeling the interactions in collective dynamics of animals and in population dynamics; through neural-networks, semi-supervised learning, and Monte Carlo methods in optimization; to kinetic and continuum theories with applications to aggregations and birth-and-death processes. Mathematicians and other members of the scientific community interested in active matter and its many applications will find this volume to be a timely, authoritative, and valuable resource.
Processing Analyzing And Learning Of Images Shapes And Forms Part 2
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Author :
language : en
Publisher: Elsevier
Release Date : 2019-10-16
Processing Analyzing And Learning Of Images Shapes And Forms Part 2 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 2019-10-16 with Mathematics categories.
Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Volume 20, surveys the contemporary developments relating to the analysis and learning of images, shapes and forms, covering mathematical models and quick computational techniques. Chapter cover Alternating Diffusion: A Geometric Approach for Sensor Fusion, Generating Structured TV-based Priors and Associated Primal-dual Methods, Graph-based Optimization Approaches for Machine Learning, Uncertainty Quantification and Networks, Extrinsic Shape Analysis from Boundary Representations, Efficient Numerical Methods for Gradient Flows and Phase-field Models, Recent Advances in Denoising of Manifold-Valued Images, Optimal Registration of Images, Surfaces and Shapes, and much more. - Covers contemporary developments relating to the analysis and learning of images, shapes and forms - Presents mathematical models and quick computational techniques relating to the topic - Provides broad coverage, with sample chapters presenting content on Alternating Diffusion and Generating Structured TV-based Priors and Associated Primal-dual Methods
Nonlocal Modeling Analysis And Computation
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Author : Qiang Du
language : en
Publisher: SIAM
Release Date : 2019-03-20
Nonlocal Modeling Analysis And Computation written by Qiang Du and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Science categories.
Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.
Continuum Limits Of Evolution And Variational Problems On Graphs
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Author : Yosra Hafiene
language : en
Publisher:
Release Date : 2018
Continuum Limits Of Evolution And Variational Problems On Graphs written by Yosra Hafiene and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
The non-local p-Laplacian operator, the associated evolution equation and variational regularization, governed by a given kernel, have applications in various areas of science and engineering. In particular, they are modern tools for massive data processing (including signals, images, geometry), and machine learning tasks such as classification. In practice, however, these models are implemented in discrete form (in space and time, or in space for variational regularization) as a numerical approximation to a continuous problem, where the kernel is replaced by an adjacency matrix of a graph. Yet, few results on the consistency of these discretization are available. In particular it is largely open to determine when do the solutions of either the evolution equation or the variational problem of graph-based tasks converge (in an appropriate sense), as the number of vertices increases, to a well-defined object in the continuum setting, and if yes, at which rate. In this manuscript, we lay the foundations to address these questions.Combining tools from graph theory, convex analysis, nonlinear semigroup theory and evolution equa- tions, we give a rigorous interpretation to the continuous limit of the discrete nonlocal p-Laplacian evolution and variational problems on graphs. More specifically, we consider a sequence of (determin- istic) graphs converging to a so-called limit object known as the graphon. If the continuous p-Laplacian evolution and variational problems are properly discretized on this graph sequence, we prove that the solutions of the sequence of discrete problems converge to the solution of the continuous problem governed by the graphon, as the number of graph vertices grows to infinity. Along the way, we provide a consistency/error bounds. In turn, this allows to establish the convergence rates for different graph models. In particular, we highlight the role of the graphon geometry/regularity. For random graph se- quences, using sharp deviation inequalities, we deliver nonasymptotic convergence rates in probability and exhibit the different regimes depending on p, the regularity of the graphon and the initial data.
Nonlocal Modeling Analysis And Computation
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Author : Qiang Du
language : en
Publisher: SIAM
Release Date : 2019-03-20
Nonlocal Modeling Analysis And Computation written by Qiang Du and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Science categories.
Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.
Nonlocal Diffusion Problems
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Author : Fuensanta Andreu-Vaillo
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Nonlocal Diffusion Problems written by Fuensanta Andreu-Vaillo 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 2010 with Mathematics categories.
Nonlocal diffusion problems arise in a wide variety of applications, including biology, image processing, particle systems, coagulation models, and mathematical finance. These types of problems are also of great interest for their purely mathematical content. This book presents recent results on nonlocal evolution equations with different boundary conditions, starting with the linear theory and moving to nonlinear cases, including two nonlocal models for the evolution of sandpiles. Both existence and uniqueness of solutions are considered, as well as their asymptotic behaviour. Moreover, the authors present results concerning limits of solutions of the nonlocal equations as a rescaling parameter tends to zero. With these limit procedures the most frequently used diffusion models are recovered: the heat equation, the $p$-Laplacian evolution equation, the porous media equation, the total variation flow, a convection-diffusion equation and the local models for the evolution of sandpiles due to Aronsson-Evans-Wu and Prigozhin. Readers are assumed to be familiar with the basic concepts and techniques of functional analysis and partial differential equations. The text is otherwise self-contained, with the exposition emphasizing an intuitive understanding and results given with full proofs. It is suitable for graduate students or researchers. The authors cover a subject that has received a great deal of attention in recent years. The book is intended as a reference tool for a general audience in analysis and PDEs, including mathematicians, engineers, physicists, biologists, and others interested in nonlocal diffusion problems.