This new material is concerned with the theory and applications of probability, statistics and analysis of canonical moments. It provides a powerful tool for the determination of optimal experimental designs, for the calculation of the main characteristics of random walks, and for other moment problems appearing in probability and statistics.

This book is a comprehensive treatise on the theory and applications of moment functions in image analysis. Moment functions are widely used in various realms of computer vision and image processing. Numerous algorithms and techniques have been developed using image moments, in the areas of pattern recognition, object identification, three-dimensional object pose estimation, robot sensing, image coding and reconstruction. This book provides a compilation of the theoretical aspects related to different types of moment functions, and their applications in the above areas.The book is organized into two parts. The first part discusses the fundamental concepts behind important moments such as geometric moments, complex moments, Legendre moments, Zernike moments, and moment tensors. Most of the commonly used properties of moment functions and the mathematical framework for the derivation of basic theorems and results are discussed in detail. This includes the derivation of moment invariants, implementation aspects of moments, transform properties, and fast methods for computing the moment functions for both binary and gray-level images. The second part presents the key application areas of moments such as pattern recognition, object identification, image-based pose estimation, edge detection, clustering, segmentation, coding and reconstruction. Important algorithms in each of these areas are discussed. A comprehensive list of bibliographical references on image moments is also included.

Film is made of moments. In its earliest form, the cinema was a moment: mere seconds recorded and projected into the darkness. Even as film has developed into today's complex and intricate medium, it is the brief, temporary and transitory that combines to create the whole. Our memories of films are composed of the moments we deem to be crucial: touchstones for our understanding and appreciation. Moments matter. The 38 specially commissioned essays in Film Moments examine a wide selection of key scenes across a broad spectrum of national cinemas, historical periods and genres, featuring films by renowned auteurs including Alfred Hitchcock, Jean Renoir and Vincente Minnelli and important contemporary directors such as Pedro Costa, Zhang Ke Jia and Quentin Tarantino, addressing films including City Lights, Gone with the Wind, The Wizard of Oz, The Night of the Hunter, Wild Strawberries, 8 1?2, Bonnie and Clyde, Star Wars, Conte d'été, United 93 and Lord of the Rings: Return of the King. Film Moments provides both an enlightening introduction for students to the diversity of approaches and concerns in the study of film, and a dynamic and vibrant account of key film sequences for anyone interested in enhancing their understanding of cinema.

This advanced textbook provides a comprehensive and unified account of the moment problem. It covers the classical one-dimensional theory and its multidimensional generalization, including modern methods and recent developments. In both the one-dimensional and multidimensional cases, the full and truncated moment problems are carefully treated separately. Fundamental concepts, results and methods are developed in detail and accompanied by numerous examples and exercises. Particular attention is given to powerful modern techniques such as real algebraic geometry and Hilbert space operators. A wide range of important aspects are covered, including the Nevanlinna parametrization for indeterminate moment problems, canonical and principal measures for truncated moment problems, the interplay between Positivstellensätze and moment problems on semi-algebraic sets, the fibre theorem, multidimensional determinacy theory, operator-theoretic approaches, and the existence theory and important special topics of multidimensional truncated moment problems. The Moment Problem will be particularly useful to graduate students and researchers working on moment problems, functional analysis, complex analysis, harmonic analysis, real algebraic geometry, polynomial optimization, or systems theory. With notes providing useful background information and exercises of varying difficulty illustrating the theory, this book will also serve as a reference on the subject and can be used for self-study.

The theory of the muon anomalous magnetic moment is particle physics in a nutshell. It is an interesting, exciting and difficult subject, and this book provides a comprehensive review of it. The theory of the muon anomalous magnetic moment is at the cutting edge of current research in particle physics, and any deviation between the theoretical prediction and the experimental value might be interpreted as a signal of an as-yet-unknown new physics.

1. The generalized moment problem. 1.1. Formulations. 1.2. Duality theory. 1.3. Computational complexity. 1.4. Summary. 1.5. Exercises. 1.6. Notes and sources -- 2. Positive polynomials. 2.1. Sum of squares representations and semi-definite optimization. 2.2. Nonnegative versus s.o.s. polynomials. 2.3. Representation theorems : univariate case. 2.4. Representation theorems : mutivariate case. 2.5. Polynomials positive on a compact basic semi-algebraic set. 2.6. Polynomials nonnegative on real varieties. 2.7. Representations with sparsity properties. 2.8. Representation of convex polynomials. 2.9. Summary. 2.10. Exercises. 2.11. Notes and sources -- 3. Moments. 3.1. The one-dimensional moment problem. 3.2. The multi-dimensional moment problem. 3.3. The K-moment problem. 3.4. Moment conditions for bounded density. 3.5. Summary. 3.6. Exercises. 3.7. Notes and sources -- 4. Algorithms for moment problems. 4.1. The overall approach. 4.2. Semidefinite relaxations. 4.3. Extraction of solutions. 4.4. Linear relaxations. 4.5. Extensions. 4.6. Exploiting sparsity. 4.7. Summary. 4.8. Exercises. 4.9. Notes and sources. 4.10. Proofs -- 5. Global optimization over polynomials. 5.1. The primal and dual perspectives. 5.2. Unconstrained polynomial optimization. 5.3. Constrained polynomial optimization : semidefinite relaxations. 5.4. Linear programming relaxations. 5.5. Global optimality conditions. 5.6. Convex polynomial programs. 5.7. Discrete optimization. 5.8. Global minimization of a rational function. 5.9. Exploiting symmetry. 5.10. Summary. 5.11. Exercises. 5.12. Notes and sources -- 6. Systems of polynomial equations. 6.1. Introduction. 6.2. Finding a real solution to systems of polynomial equations. 6.3. Finding all complex and/or all real solutions : a unified treatment. 6.4. Summary. 6.5. Exercises. 6.6. Notes and sources -- 7. Applications in probability. 7.1. Upper bounds on measures with moment conditions. 7.2. Measuring basic semi-algebraic sets. 7.3. Measures with given marginals. 7.4. Summary. 7.5. Exercises. 7.6. Notes and sources -- 8. Markov chains applications. 8.1. Bounds on invariant measures. 8.2. Evaluation of ergodic criteria. 8.3. Summary. 8.4. Exercises. 8.5. Notes and sources -- 9. Application in mathematical finance. 9.1. Option pricing with moment information. 9.2. Option pricing with a dynamic model. 9.3. Summary. 9.4. Notes and sources -- 10. Application in control. 10.1. Introduction. 10.2. Weak formulation of optimal control problems. 10.3. Semidefinite relaxations for the OCP. 10.4. Summary. 10.5. Notes and sources -- 11. Convex envelope and representation of convex sets. 11.1. The convex envelope of a rational function. 11.2. Semidefinite representation of convex sets. 11.3. Algebraic certificates of convexity. 11.4. Summary. 11.5. Exercises. 11.6. Notes and sources -- 12. Multivariate integration 12.1. Integration of a rational function. 12.2. Integration of exponentials of polynomials. 12.3. Maximum entropy estimation. 12.4. Summary. 12.5. Exercises. 12.6. Notes and sources -- 13. Min-max problems and Nash equilibria. 13.1. Robust polynomial optimization. 13.2. Minimizing the sup of finitely many rational cunctions. 13.3. Application to Nash equilibria. 13.4. Exercises. 13.5. Notes and sources -- 14. Bounds on linear PDE. 14.1. Linear partial differential equations. 14.2. Notes and sources

Examines the ways that embracing socially awkward situations, even when they lead to embarrassment and self-conciousness, also provide the opportunity to test oneself and to recognize how people are connected to each other.

The New York Times bestselling authors of Switch and Made to Stick explore why certain brief experiences can jolt us and elevate us and change us—and how we can learn to create such extraordinary moments in our life and work. While human lives are endlessly variable, our most memorable positive moments are dominated by four elements: elevation, insight, pride, and connection. If we embrace these elements, we can conjure more moments that matter. What if a teacher could design a lesson that he knew his students would remember twenty years later? What if a manager knew how to create an experience that would delight customers? What if you had a better sense of how to create memories that matter for your children? This book delves into some fascinating mysteries of experience: Why we tend to remember the best or worst moment of an experience, as well as the last moment, and forget the rest. Why “we feel most comfortable when things are certain, but we feel most alive when they’re not.” And why our most cherished memories are clustered into a brief period during our youth. Readers discover how brief experiences can change lives, such as the experiment in which two strangers meet in a room, and forty-five minutes later, they leave as best friends. (What happens in that time?) Or the tale of the world’s youngest female billionaire, who credits her resilience to something her father asked the family at the dinner table. (What was that simple question?) Many of the defining moments in our lives are the result of accident or luck—but why would we leave our most meaningful, memorable moments to chance when we can create them? The Power of Moments shows us how to be the author of richer experiences.

Choice Outstanding Academic Title for 2015 Jean-Paul Sartre is often seen as the quintessential public intellectual, but this was not always the case. Until the mid-1940s he was not so well-known, even in France. Then suddenly, in a very short period of time, Sartre became an intellectual celebrity. How can we explain this remarkable transformation? The Existentialist Moment retraces Sartre's career and provides a compelling new explanation of his meteoric rise to fame. Baert takes the reader back to the confusing and traumatic period of the Second World War and its immediate aftermath and shows how the unique political and intellectual landscape in France at this time helped to propel Sartre and existentialist philosophy to the fore. The book also explores why, from the early 1960s onwards, in France and elsewhere, the interest in Sartre and existentialism eventually waned. The Existentialist Moment ends with a bold new theory for the study of intellectuals and a provocative challenge to the widespread belief that the public intellectual is a species now on the brink of extinction.