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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. .
Dynamics. --- Geometry, Differential. --- Mathematical optimization. --- Probabilities. --- Transportation problems (Programming). --- Mathematical optimization --- Transportation problems (Programming) --- Probabilities --- Dynamics --- Geometry, Differential --- Mathematics --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Calculus --- Operations Research --- Differential geometry --- Dynamical systems --- Kinetics --- Probability --- Statistical inference --- Transport problems (Programming) --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematics. --- Partial differential equations. --- Differential geometry. --- Calculus of variations. --- Partial Differential Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Differential Geometry. --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Linear programming --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Differential equations, partial. --- Global differential geometry. --- Partial differential equations --- Isoperimetrical problems --- Variations, Calculus of --- Optimisation mathématique --- Problèmes de transport (Programmation) --- Probabilités --- Dynamique --- Géométrie différentielle
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This book provides an overview of the role of AI in medicine and, more generally, of issues at the intersection of mathematics, informatics, and medicine. It is intended for AI experts, offering them a valuable retrospective and a global vision for the future, as well as for non-experts who are curious about this timely and important subject. Its goal is to provide clear, objective, and reasonable information on the issues covered, avoiding any fantasies that the topic “AI” might evoke. In addition, the book seeks to provide a broad kaleidoscopic perspective, rather than deep technical details. .
Artificial intelligence --- Medicine --- Medical applications. --- Data processing --- Computational intelligence. --- Artificial intelligence. --- Biomedical engineering. --- Health informatics. --- Computational Intelligence. --- Artificial Intelligence. --- Biomedical Engineering and Bioengineering. --- Health Informatics. --- Clinical informatics --- Health informatics --- Medical information science --- Information science --- Intelligence, Computational --- Soft computing --- Clinical engineering --- Medical engineering --- Bioengineering --- Biophysics --- Engineering --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers
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This book challenges the views put forward by Pierre Cartier, one of the anchors of the famous Bourbaki group, and Cédric Villani, one of the most brilliant mathematicians of his generation, who received the Fields Medal in 2010. Jean Dhombres, mathematician and science historian, and Gerhard Heinzmann, philosopher of science and also a specialist in mathematics engage in a fruitful dialogue with the two mathematicians, prompting readers to reflect on mathematical activity and its social consequences in history as well as in the modern world. Cédric Villani’s popular success proves once again that a common awareness has developed, albeit in a very confused way, of the major role of mathematics in the construction and efficiency of natural sciences, which are at the origin of our technologies. Despite this, the idea that mathematics cannot be shared remains firmly entrenched, a perceived failing that has even been branded a lack of culture by vocal forces in the media as well as cultural and political establishment. The authors explore three major directions in their dialogue: the highly complex relationship between mathematics and reality, the subject of many debates and opposing viewpoints; the freedom that the construction of mathematics has given humankind by enabling them to develop the natural sciences as well as mathematical research; and the responsibility with which the scientific community and governments should address the role of mathematics in research and education policies.
Mathematics. --- Applied mathematics. --- Engineering mathematics. --- History. --- Social sciences. --- History of Mathematical Sciences. --- Applications of Mathematics. --- Mathematics in the Humanities and Social Sciences. --- Math --- Engineering --- Engineering analysis --- Mathematics --- Science --- Mathematical analysis --- Annals --- Auxiliary sciences of history --- Behavioral sciences --- Human sciences --- Sciences, Social --- Social science --- Social studies --- Civilization
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Approcher la musique par des chemins de traverse : Karol Beffa propose de déplacer les termes du débat esthétique autour de la musique dans le monde contemporain en ouvrant la réflexion à d’autres disciplines, à d’autres pratiques, à d’autres regards, des mathématiques au théâtre ou au cinéma. Pour mieux cerner la musique, il est nécessaire de la penser en relation et de l’affranchir d’une conception, inaugurée par le romantisme allemand, qui l’absolutise et par là même tend à l’isoler. Les q...
Art --- Music --- Cultural studies --- art --- création --- création artistique --- création musicale --- esthétique --- modernisme --- musicologie --- musique --- perception
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This volume collects the notes of the CIME course "Nonlinear PDE’s and applications" held in Cetraro (Italy) on June 23–28, 2008. It consists of four series of lectures, delivered by Stefano Bianchini (SISSA, Trieste), Eric A. Carlen (Rutgers University), Alexander Mielke (WIAS, Berlin), and Cédric Villani (Ecole Normale Superieure de Lyon). They presented a broad overview of far-reaching findings and exciting new developments concerning, in particular, optimal transport theory, nonlinear evolution equations, functional inequalities, and differential geometry. A sampling of the main topics considered here includes optimal transport, Hamilton-Jacobi equations, Riemannian geometry, and their links with sharp geometric/functional inequalities, variational methods for studying nonlinear evolution equations and their scaling properties, and the metric/energetic theory of gradient flows and of rate-independent evolution problems. The book explores the fundamental connections between all of these topics and points to new research directions in contributions by leading experts in these fields.
Differential equations, Partial --- Differential equations, Nonlinear --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Calculus --- Applied Mathematics --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Functional analysis. --- Partial differential equations. --- Differential geometry. --- Calculus of variations. --- Analysis. --- Partial Differential Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Functional Analysis. --- Differential Geometry. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Differential geometry --- Partial differential equations --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Global analysis (Mathematics). --- Differential equations, partial. --- Mathematical optimization. --- Global differential geometry. --- Geometry, Differential --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Operations research --- Simulation methods --- System analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Nonlinear PDEs --- CIME
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L'écriture constitue-t-elle le trait d'union entre technique et culture, et par là entre science et culture ? Cet ouvrage donne des éléments de réponse à cette double question, à l'acuité renouvelée par le numérique. il fait donc appel aux anthropologues et philosophes (Jack Goody, Jens Brockmeier, David Olson…), aux spécialistes des pratiques lettrées de l'antiquité (Christophe Batsch, Flavia Carraro), de l'internet (Paul Mathias, Henri Desbois, Michael Heim…), de la physique et des mathématiques (Jean Dhombres, Patrick Flandrin, Cédric Villani). En ce sens, cet ouvrage poursuit les réflexions largement entamées avec Regards croisés sur l'internet (enssib, 2011). Mais en explorant des voies nouvelles : les relations particulières qu'entretiennent les mathématiciens, et, plus largement les scientifiques, avec l'écriture. Cette publication est issue d'un colloque international consacré à Jack Goody, qui s'est tenu à l'enssib du 24 au 26 janvier 2008, auquel il a contribué et qu'il a conclu.
Written communication --- Language and culture --- Writing --- Communication and technology --- Communication écrite --- Langage et culture --- Ecriture --- Communication et technologie --- Congresses. --- History. --- Congrès --- Histoire --- Goody, Jack. --- Communication écrite --- Congrès --- Library, Information & Communication sciences --- Jack Goody --- culture --- langage --- information --- communication --- communication écrite --- anthropologie
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