Optimal Transport for Applied Mathematicians


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.




The Rhetoric of Roman Transportation


Book Description

Preamble : on the way -- Introduction : en route -- Making use : plaustrum -- Power steering : currus -- The other chariot : essedum -- Conveying women : carpentum -- Portable retreats : lectica -- Envoi : the end of the road.




Optimal Transport


Book Description

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.




Lectures on Optimal Transport


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.




Modelling Freight Transport


Book Description

Freight Transport Modelling is a unique new reference book that provides insight into the state-of-the-art of freight modelling. Focusing on models used to support public transport policy analysis, Freight Transport Modelling systematically introduces the latest freight transport modelling approaches and describes the main methods and techniques used to arrive at operational models. As freight transport has grown exponentially in recent decades, policymakers now need to include freight flows in quantitative evaluations of transport systems. Whereas early freight modelling practice was inspired by passenger transport models, by now it has developed its separate stream of methods and techniques inspired by disciplines such as economic geography and supply chain management. Besides summarizing the latest achievements in fundamental research, this book describes the state of practice and advises practitioners on how to cope with typical challenges such as limitations in data availability. Uniquely focused book exploring the key issues and logistics of freight transport modelling Highlights the latest approaches and describes the main methods and techniques used to arrive at operational models Summarizes fundamental research into freight transport modeling, as well as current practices and advice for practitioners facing day-to-day challenges










New Mobilities


Book Description

In New Mobilities: Smart Planning for Emerging Transportation Technologies, transportation expert Todd Litman examines 12 emerging transportation modes and services that are likely to significantly affect our lives: bike- and carsharing, micro-mobilities, ridehailing and micro-transit, public transit innovations, telework, autonomous and electric vehicles, air taxis, mobility prioritization, and logistics management. Public policies around New Mobilities can either help create heaven, a well-planned transportation system that uses new technologies intelligently, or hell, a poorly planned transportation system that is overwhelmed by conflicting and costly, unhealthy, and inequitable modes. His expert analysis will help planners, local policymakers, and concerned citizens to make informed choices about the New Mobility revolution.




Research on Transport Economics 2000


Book Description

The Annual Information Bulletin presents a survey of research in hand on the social and economic aspects of transport in over 400 specialised agencies which are mainly European (West and East) but in some cases American, Canadian or Australian.




Social Change and Sustainable Transport


Book Description

Transportation research has traditionally been dominated by engineering and logistics research approaches. This book integrates social, economic, and behavioral sciences into the transportation field. As its title indicates, emphasis is on socioeconomic changes, which increasingly govern the development of the transportation sector. The papers presented here originated at a conference on Social Change and Sustainable Transport held at the University of California at Berkeley in March 1999, under the auspices of the European Science Foundation and the National Science Foundation. The contributors, who represent a range of disciplines, including geography and regional science, economics, political science, sociology, and psychology, come from twelve different countries. Their subjects cover the consequences of environmentally sustainable transportation vs. the "business-as-usual" status quo, the new phenomenon of "edge cities," automobile dependence as a social problem, the influence of leisure or discretionary travel and of company cars, the problems of freight transport, the future of railroads in Europe, the imposition of electronic road tolls, potential transport benefits of e-commerce, and the electric car.