Optimal Transport On Quantum Structures

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Optimal Transport On Quantum Structures

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Author : Jan Maas
language : en
Publisher: Springer Nature
Release Date : 2024-09-19

Optimal Transport On Quantum Structures written by Jan Maas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-19 with Mathematics categories.

The flourishing theory of classical optimal transport concerns mass transportation at minimal cost. This book introduces the reader to optimal transport on quantum structures, i.e., optimal transportation between quantum states and related non-commutative concepts of mass transportation. It contains lecture notes on classical optimal transport and Wasserstein gradient flows dynamics and quantum optimal transport quantum couplings and many-body problems quantum channels and qubits These notes are based on lectures given by the authors at the "Optimal Transport on Quantum Structures" School held at the Erdös Center in Budapest in the fall of 2022. The lecture notes are complemented by two survey chapters presenting the state of the art in different research areas of non-commutative optimal transport.

Credible Asset Allocation Optimal Transport Methods And Related Topics

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Author : Songsak Sriboonchitta
language : en
Publisher: Springer Nature
Release Date : 2022-07-29

Credible Asset Allocation Optimal Transport Methods And Related Topics written by Songsak Sriboonchitta and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-29 with Technology & Engineering categories.

This book describes state-of-the-art economic ideas and how these ideas can be (and are) used to make economic decision (in particular, to optimally allocate assets) and to gauge the results of different economic decisions (in particular, by using optimal transport methods). Special emphasis is paid to machine learning techniques (including deep learning) and to different aspects of quantum econometrics—when quantum physics and quantum computing models are techniques are applied to study economic phenomena. Applications range from more traditional economic areas to more non-traditional topics such as economic aspects of tourism, cryptocurrencies, telecommunication infrastructure, and pandemic. This book helps student to learn new techniques, practitioners to become better knowledgeable of the state-of-the-art econometric techniques, and researchers to further develop these important research directions

Noncommutative Geometry And Optimal Transport

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Author : Pierre Martinetti
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-10-26

Noncommutative Geometry And Optimal Transport written by Pierre Martinetti 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 2016-10-26 with Mathematics categories.

The distance formula in noncommutative geometry was introduced by Connes at the end of the 1980s. It is a generalization of Riemannian geodesic distance that makes sense in a noncommutative setting, and provides an original tool to study the geometry of the space of states on an algebra. It also has an intriguing echo in physics, for it yields a metric interpretation for the Higgs field. In the 1990s, Rieffel noticed that this distance is a noncommutative version of the Wasserstein distance of order 1 in the theory of optimal transport. More exactly, this is a noncommutative generalization of Kantorovich dual formula of the Wasserstein distance. Connes distance thus offers an unexpected connection between an ancient mathematical problem and the most recent discovery in high energy physics. The meaning of this connection is far from clear. Yet, Rieffel's observation suggests that Connes distance may provide an interesting starting point for a theory of optimal transport in noncommutative geometry. This volume contains several review papers that will give the reader an extensive introduction to the metric aspect of noncommutative geometry and its possible interpretation as a Wasserstein distance on a quantum space, as well as several topic papers.

An Invitation To Optimal Transport Wasserstein Distances And Gradient Flows

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Author : Alessio Figalli
language : en
Publisher: European Mathematical Society
Release Date : 2023-05-15

An Invitation To Optimal Transport Wasserstein Distances And Gradient Flows written by Alessio Figalli and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-15 with Mathematics categories.

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.

Research In Progress

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Author : United States. Army Research Office
language : en
Publisher:
Release Date : 1989

Research In Progress written by United States. Army Research Office and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Military research categories.

Vols. for 1977- consist of two parts: Chemistry, biological sciences, engineering sciences, metallurgy and materials science (issued in the spring); and Physics, electronics, mathematics, geosciences (issued in the fall).

Research In Progress

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Author :
language : en
Publisher:
Release Date : 1982

Research In Progress written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Military research categories.

Government Reports Announcements Index

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Author :
language : en
Publisher:
Release Date : 1995

Government Reports Announcements Index written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.

Optimal Transport For Applied Mathematicians

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Author : Filippo Santambrogio
language : en
Publisher: Birkhäuser
Release Date : 2015-10-17

Optimal Transport For Applied Mathematicians written by Filippo Santambrogio and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-17 with Mathematics categories.

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.

Optimal Transportation Networks

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Author : Marc Bernot
language : en
Publisher: Springer Science & Business Media
Release Date : 2009

Optimal Transportation Networks written by Marc Bernot 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 2009 with Business & Economics categories.

The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.

Nanomaterials And Supramolecular Structures

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Author : Anatoliy Petrovych Shpak
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-22

Nanomaterials And Supramolecular Structures written by Anatoliy Petrovych Shpak 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 2009-10-22 with Science categories.

The text features experimental investigations which use a variety of modern methods and theoretical modeling of surface structures and physicochemical processes which occur at solid surfaces. Nanomaterials and Supramolecular Structures: Physics, Chemistry, and Applications is intended for specialists experienced in the fields of Nanochemistry, Nanophysics, Surface Chemistry (and Physics), synthesis of new nanostructural functional materials and their practical applications. It will also prove useful to students, post-graduates, researchers, and lecturers.