Convergence
Convergence

Author: National Research Council

Publisher: National Academies Press

Published: 2014-06-16

Total Pages: 234

ISBN-13: 0309301645

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Convergence of the life sciences with fields including physical, chemical, mathematical, computational, engineering, and social sciences is a key strategy to tackle complex challenges and achieve new and innovative solutions. However, institutions face a lack of guidance on how to establish effective programs, what challenges they are likely to encounter, and what strategies other organizations have used to address the issues that arise. This advice is needed to harness the excitement generated by the concept of convergence and channel it into the policies, structures, and networks that will enable it to realize its goals. Convergence investigates examples of organizations that have established mechanisms to support convergent research. This report discusses details of current programs, how organizations have chosen to measure success, and what has worked and not worked in varied settings. The report summarizes the lessons learned and provides organizations with strategies to tackle practical needs and implementation challenges in areas such as infrastructure, student education and training, faculty advancement, and inter-institutional partnerships.

Nonparametric Functional Estimation and Related Topics
Nonparametric Functional Estimation and Related Topics

Author: George Roussas

Publisher: Springer Science & Business Media

Published: 1991-04-30

Total Pages: 732

ISBN-13: 9780792312260

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About three years ago, an idea was discussed among some colleagues in the Division of Statistics at the University of California, Davis, as to the possibility of holding an international conference, focusing exclusively on nonparametric curve estimation. The fruition of this idea came about with the enthusiastic support of this project by Luc Devroye of McGill University, Canada, and Peter Robinson of the London School of Economics, UK. The response of colleagues, contacted to ascertain interest in participation in such a conference, was gratifying and made the effort involved worthwhile. Devroye and Robinson, together with this editor and George Metakides of the University of Patras, Greece and of the European Economic Communities, Brussels, formed the International Organizing Committee for a two week long Advanced Study Institute (ASI) sponsored by the Scientific Affairs Division of the North Atlantic Treaty Organization (NATO). The ASI was held on the Greek Island of Spetses between July 29 and August 10, 1990. Nonparametric functional estimation is a central topic in statistics, with applications in numerous substantive fields in mathematics, natural and social sciences, engineering and medicine. While there has been interest in nonparametric functional estimation for many years, this has grown of late, owing to increasing availability of large data sets and the ability to process them by means of improved computing facilities, along with the ability to display the results by means of sophisticated graphical procedures.

Variational Analysis
Variational Analysis

Author: R. Tyrrell Rockafellar

Publisher: Springer Science & Business Media

Published: 2009-06-26

Total Pages: 747

ISBN-13: 3642024319

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From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.

Local Minimization, Variational Evolution and Γ-Convergence
Local Minimization, Variational Evolution and Γ-Convergence

Author: Andrea Braides

Publisher: Springer

Published: 2014-07-08

Total Pages: 184

ISBN-13: 3319019821

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This book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed.

Constructive Nonsmooth Analysis and Related Topics
Constructive Nonsmooth Analysis and Related Topics

Author: Vladimir F. Demyanov

Publisher: Springer Science & Business Media

Published: 2013-11-12

Total Pages: 258

ISBN-13: 1461486157

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This volume contains a collection of papers based on lectures and presentations delivered at the International Conference on Constructive Nonsmooth Analysis (CNSA) held in St. Petersburg (Russia) from June 18-23, 2012. This conference was organized to mark the 50th anniversary of the birth of nonsmooth analysis and nondifferentiable optimization and was dedicated to J.-J. Moreau and the late B.N. Pshenichnyi, A.M. Rubinov, and N.Z. Shor, whose contributions to NSA and NDO remain invaluable. The first four chapters of the book are devoted to the theory of nonsmooth analysis. Chapters 5-8 contain new results in nonsmooth mechanics and calculus of variations. Chapters 9-13 are related to nondifferentiable optimization, and the volume concludes with four chapters containing interesting and important historical chapters, including tributes to three giants of nonsmooth analysis, convexity, and optimization: Alexandr Alexandrov, Leonid Kantorovich, and Alex Rubinov. The last chapter provides an overview and important snapshots of the 50-year history of convex analysis and optimization.

Topics In Classical Analysis And Applications In Honor Of Daniel Waterman
Topics In Classical Analysis And Applications In Honor Of Daniel Waterman

Author: Laura De Carli

Publisher: World Scientific

Published: 2008-10-08

Total Pages: 202

ISBN-13: 9814469998

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This book covers a wide range of topics, from orthogonal polynomials to wavelets. It contains several high-quality research papers by prominent experts exploring trends in function theory, orthogonal polynomials, Fourier series, approximation theory, theory of wavelets and applications. The book provides an up-to-date presentation of several important topics in Classical and Modern Analysis. The interested reader will also be able to find stimulating open problems and suggestions for future research.

Calculus of Variations and Geometric Evolution Problems
Calculus of Variations and Geometric Evolution Problems

Author: F. Bethuel

Publisher: Springer

Published: 2006-11-14

Total Pages: 299

ISBN-13: 3540488138

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The international summer school on Calculus of Variations and Geometric Evolution Problems was held at Cetraro, Italy, 1996. The contributions to this volume reflect quite closely the lectures given at Cetraro which have provided an image of a fairly broad field in analysis where in recent years we have seen many important contributions. Among the topics treated in the courses were variational methods for Ginzburg-Landau equations, variational models for microstructure and phase transitions, a variational treatment of the Plateau problem for surfaces of prescribed mean curvature in Riemannian manifolds - both from the classical point of view and in the setting of geometric measure theory.