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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 goal of Optimal Transport (OT) is to define geometric tools that are useful to compare probability distributions. Their use dates back to 1781. Recent years have witnessed a new revolution in the spread of OT, thanks to the emergence of approximate solvers that can scale to sizes and dimensions that are relevant to data sciences. Thanks to this newfound scalability, OT is being increasingly used to unlock various problems in imaging sciences (such as color or texture processing), computer vision and graphics (for shape manipulation) or machine learning (for regression, classification and density fitting). This monograph reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of these applications. Computational Optimal Transport presents an overview of the main theoretical insights that support the practical effectiveness of OT before explaining how to turn these insights into fast computational schemes. Written for readers at all levels, the authors provide descriptions of foundational theory at two-levels. Generally accessible to all readers, more advanced readers can read the specially identified more general mathematical expositions of optimal transport tailored for discrete measures. Furthermore, several chapters deal with the interplay between continuous and discrete measures, and are thus targeting a more mathematically-inclined audience. This monograph will be a valuable reference for researchers and students wishing to get a thorough understanding of Computational Optimal Transport, a mathematical gem at the interface of probability, analysis and optimization.
This textbook includes all 13 chapters of Français interactif. It accompanies www.laits.utexas.edu/fi, the web-based French program developed and in use at the University of Texas since 2004, and its companion site, Tex's French Grammar (2000) www.laits.utexas.edu/tex/ Français interactif is an open acess site, a free and open multimedia resources, which requires neither password nor fees. Français interactif has been funded and created by Liberal Arts Instructional Technology Services at the University of Texas, and is currently supported by COERLL, the Center for Open Educational Resources and Language Learning UT-Austin, and the U.S. Department of Education Fund for the Improvement of Post-Secondary Education (FIPSE Grant P116B070251) as an example of the open access initiative.
Since its commercialization in 1971, the microprocessor, a modern and integrated form of the central processing unit, has continuously broken records in terms of its integrated functions, computing power, low costs and energy saving status. Today, it is present in almost all electronic devices. Sound knowledge of its internal mechanisms and programming is essential for electronics and computer engineers to understand and master computer operations and advanced programming concepts. This book in five volumes focuses more particularly on the first two generations of microprocessors, those that handle 4- and 8- bit integers. Microprocessor 1 the first of five volumes presents the computation function, recalls the memory function and clarifies the concepts of computational models and architecture. A comprehensive approach is used, with examples drawn from current and past technologies that illustrate theoretical concepts, making them accessible.
This book is a general presentation of complex systems, examined from the point of view of management. There is no standard formula to govern such systems, nor to effectively understand and respond to them. The interdisciplinary theory of self-organization is teeming with examples of living systems that can reorganize at a higher level of complexity when confronted with an external challenge of a certain magnitude. Modern businesses, considered as complex systems, ideally know how to flexibly and resiliently adapt to their environment, and also how to prepare for change via self-organization. Understanding sources of potential crisis is essential for leaders, though not all crises are necessarily bad news, as creative firms know how to respond to challenges through innovation: new products and markets, organizational learning for collective intelligence, and more.