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Author: Luigi Ambrosio
Publisher: Springer Science & Business Media
ISBN: 376438722X
Category : Mathematics
Languages : en
Pages : 333
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Book Description
The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
Author: Luigi Ambrosio
Publisher: Springer Science & Business Media
ISBN: 376438722X
Category : Mathematics
Languages : en
Pages : 333
Get Book Here
Book Description
The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
Author: Luigi Ambrosio
Publisher: Springer Science & Business Media
ISBN: 3764373091
Category : Mathematics
Languages : en
Pages : 330
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Book Description
This book is devoted to a theory of gradient ?ows in spaces which are not nec- sarily endowed with a natural linear or di?erentiable structure. It is made of two parts, the ?rst one concerning gradient ?ows in metric spaces and the second one 2 1 devoted to gradient ?ows in the L -Wasserstein space of probability measures on p a separable Hilbert space X (we consider the L -Wasserstein distance, p? (1,?), as well). The two parts have some connections, due to the fact that the Wasserstein space of probability measures provides an important model to which the “metric” theory applies, but the book is conceived in such a way that the two parts can be read independently, the ?rst one by the reader more interested to Non-Smooth Analysis and Analysis in Metric Spaces, and the second one by the reader more oriented to theapplications in Partial Di?erential Equations, Measure Theory and Probability.
Author: Karl-Theodor Sturm
Publisher: American Mathematical Society
ISBN: 1470466961
Category : Mathematics
Languages : en
Pages : 124
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Book Description
View the abstract.
Author: Ben Andrews
Publisher: Springer Science & Business Media
ISBN: 3642162851
Category : Mathematics
Languages : en
Pages : 306
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Book Description
This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.
Author: Alessio Figalli
Publisher: European Mathematical Society
ISBN: 3985470502
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this beautiful subject. The presentation focuses on the essential topics of the theory: Kantorovich duality, existence and uniqueness of optimal transport maps, Wasserstein distances, the JKO scheme, Otto's calculus, and Wasserstein gradient flows. At the end, a presentation of some selected applications of optimal transport is given. Suitable for a course at the graduate level, the book also includes an appendix with a series of exercises along with their solutions. The second edition contains a number of additions, such as a new section on the Brunn–Minkowski inequality, new exercises, and various corrections throughout the text.
Author: Luigi Ambrosio
Publisher: Springer Nature
ISBN: 3030721620
Category : Mathematics
Languages : en
Pages : 250
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Book Description
This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations.
Author: Filippo Santambrogio
Publisher: Birkhäuser
ISBN: 3319208284
Category : Mathematics
Languages : en
Pages : 376
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Book Description
This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource.
Author: Anna Esposito
Publisher: Springer Nature
ISBN: 981993592X
Category : Technology & Engineering
Languages : en
Pages : 358
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Book Description
This book provides an overview on the current progresses in artificial intelligence and neural nets in data science. The book is reporting on intelligent algorithms and applications modeling, prediction, and recognition tasks and many other application areas supporting complex multimodal systems to enhance and improve human–machine or human–human interactions. This field is broadly addressed by the scientific communities and has a strong commercial impact since investigates on the theoretical frameworks supporting the implementation of sophisticated computational intelligence tools. Such tools will support multidisciplinary aspects of data mining and data processing characterizing appropriate system reactions to human-machine interactional exchanges in interactive scenarios. The emotional issue has recently gained increasing attention for such complex systems due to its relevance in helping in the most common human tasks (like cognitive processes, perception, learning, communication, and even "rational" decision-making) and therefore improving the quality of life of the end users.
Author: Yann Ollivier
Publisher: Cambridge University Press
ISBN: 1139993623
Category : Mathematics
Languages : en
Pages : 317
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Book Description
The theory of optimal transportation has its origins in the eighteenth century when the problem of transporting resources at a minimal cost was first formalised. Through subsequent developments, particularly in recent decades, it has become a powerful modern theory. This book contains the proceedings of the summer school 'Optimal Transportation: Theory and Applications' held at the Fourier Institute in Grenoble. The event brought together mathematicians from pure and applied mathematics, astrophysics, economics and computer science. Part I of this book is devoted to introductory lecture notes accessible to graduate students, while Part II contains research papers. Together, they represent a valuable resource on both fundamental and advanced aspects of optimal transportation, its applications, and its interactions with analysis, geometry, PDE and probability, urban planning and economics. Topics covered include Ricci flow, the Euler equations, functional inequalities, curvature-dimension conditions, and traffic congestion.
Author: Tuncer Cebeci
Publisher: Butterworth-Heinemann
ISBN: 0080983391
Category : Computers
Languages : en
Pages : 465
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Book Description
Analysis of Turbulent Flows is written by one of the most prolific authors in the field of CFD. Professor of Aerodynamics at SUPAERO and Director of DMAE at ONERA, Professor Tuncer Cebeci calls on both his academic and industrial experience when presenting this work. Each chapter has been specifically constructed to provide a comprehensive overview of turbulent flow and its measurement. Analysis of Turbulent Flows serves as an advanced textbook for PhD candidates working in the field of CFD and is essential reading for researchers, practitioners in industry and MSc and MEng students. The field of CFD is strongly represented by the following corporate organizations: Boeing, Airbus, Thales, United Technologies and General Electric. Government bodies and academic institutions also have a strong interest in this exciting field. - An overview of the development and application of computational fluid dynamics (CFD), with real applications to industry - Contains a unique section on short-cut methods – simple approaches to practical engineering problems
