Optimal Transportation Networks
Title | Optimal Transportation Networks PDF eBook |
Author | Marc Bernot |
Publisher | Springer Science & Business Media |
Pages | 204 |
Release | 2009 |
Genre | Business & Economics |
ISBN | 3540693149 |
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.
Optimal Transportation Networks
Title | Optimal Transportation Networks PDF eBook |
Author | Marc Bernot |
Publisher | |
Pages | 0 |
Release | 2009 |
Genre | |
ISBN |
Optimal Urban Networks via Mass Transportation
Title | Optimal Urban Networks via Mass Transportation PDF eBook |
Author | Giuseppe Buttazzo |
Publisher | Springer |
Pages | 161 |
Release | 2008-11-09 |
Genre | Mathematics |
ISBN | 3540857990 |
Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. One assumes the distributions of population and of services/workplaces (i.e. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it. Both the long-term optimization and the short-term, "who goes where," optimization are considered. These models can also be adapted for the optimization of other types of networks, such as telecommunications, pipeline or drainage networks. In the monograph we study the most general problem settings, namely, when neither the shape nor even the topology of the network to be constructed is known a priori.
Optimal Transport Networks in Nature
Title | Optimal Transport Networks in Nature PDF eBook |
Author | Natalya Kizilova |
Publisher | World Scientific Publishing Company |
Pages | 200 |
Release | 2010 |
Genre | Medical |
ISBN | 9789812838735 |
This unique book presents a broad range of data on geometry and topology of long-distance liquid transport networks in nature including circulatory and respiratory systems of mammals, trophic fluid transport systems of animals, and conducting systems of higher plants. It is the very first book where evidence of the common design principles and optimal properties of the transportation networks of vascular plants and animals is provided. The book also provides a comprehensive comparative study of the recent measurement results and data analysis, including unique data obtained by the author to conduct systems of plant leaves of different shapes, sizes, venation types and evolutionary ages. It was shown that the mathematical solutions of the optimization problem for the animal and plant conducting systems lead to the same design principles, despite different physical conditions of the fluid transport.
Optimal Transport Methods in Economics
Title | Optimal Transport Methods in Economics PDF eBook |
Author | Alfred Galichon |
Publisher | Princeton University Press |
Pages | 184 |
Release | 2018-08-14 |
Genre | Business & Economics |
ISBN | 0691183465 |
Optimal Transport Methods in Economics is the first textbook on the subject written especially for students and researchers in economics. Optimal transport theory is used widely to solve problems in mathematics and some areas of the sciences, but it can also be used to understand a range of problems in applied economics, such as the matching between job seekers and jobs, the determinants of real estate prices, and the formation of matrimonial unions. This is the first text to develop clear applications of optimal transport to economic modeling, statistics, and econometrics. It covers the basic results of the theory as well as their relations to linear programming, network flow problems, convex analysis, and computational geometry. Emphasizing computational methods, it also includes programming examples that provide details on implementation. Applications include discrete choice models, models of differential demand, and quantile-based statistical estimation methods, as well as asset pricing models. Authoritative and accessible, Optimal Transport Methods in Economics also features numerous exercises throughout that help you develop your mathematical agility, deepen your computational skills, and strengthen your economic intuition. The first introduction to the subject written especially for economists Includes programming examples Features numerous exercises throughout Ideal for students and researchers alike
Designing Optimal Transportation Networks
Title | Designing Optimal Transportation Networks PDF eBook |
Author | Shieng-I. Tung |
Publisher | |
Pages | 27 |
Release | 1987 |
Genre | Expert systems (Computer science) |
ISBN |
Optimal Transport
Title | Optimal Transport PDF eBook |
Author | Cédric Villani |
Publisher | Springer Science & Business Media |
Pages | 970 |
Release | 2008-10-26 |
Genre | Mathematics |
ISBN | 3540710507 |
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.