*Peter Hall*

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566540
- eISBN:
- 9780191718038
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566540.003.0007
- Subject:
- Mathematics, Probability / Statistics

This chapter describes some contemporary topics in non-parametric statistics and outlines their relation to computation, particularly some topics on pure mathematics. It opens with a brief comparison ...
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This chapter describes some contemporary topics in non-parametric statistics and outlines their relation to computation, particularly some topics on pure mathematics. It opens with a brief comparison of parametric and non-parametric views of the same statistical problems and some comments on the ‘two cultures’ sometimes said to exist within statistical modeling. The impact of computational advances on non-parametric statistics is discussed, and the view that raw computer power can replace theoretical consideration of a problem is firmly rebutted. The discussion then turns to the relation between mathematics, particularly pure mathematics, and statistics. The contributions made by number theory, algebraic geometry, and operator theory to some statistical problems are exemplified in the contexts of digitizing data on a lattice, estimating multiperiodic functions, errors in variables, mixture modeling, and functional principal component analysis.Less

This chapter describes some contemporary topics in non-parametric statistics and outlines their relation to computation, particularly some topics on pure mathematics. It opens with a brief comparison of parametric and non-parametric views of the same statistical problems and some comments on the ‘two cultures’ sometimes said to exist within statistical modeling. The impact of computational advances on non-parametric statistics is discussed, and the view that raw computer power can replace theoretical consideration of a problem is firmly rebutted. The discussion then turns to the relation between mathematics, particularly pure mathematics, and statistics. The contributions made by number theory, algebraic geometry, and operator theory to some statistical problems are exemplified in the contexts of digitizing data on a lattice, estimating multiperiodic functions, errors in variables, mixture modeling, and functional principal component analysis.

*JAGDISH MEHRA and KIMBALL A. MILTON*

- Published in print:
- 2003
- Published Online:
- February 2010
- ISBN:
- 9780198527459
- eISBN:
- 9780191709593
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527459.003.0013
- Subject:
- Physics, History of Physics

As soon as Julian Schwinger burst upon the stage, one could hardly doubt that a Nobel Prize was in the offing. Certainly, after his solution of the problems of quantum electrodynamics in the late ...
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As soon as Julian Schwinger burst upon the stage, one could hardly doubt that a Nobel Prize was in the offing. Certainly, after his solution of the problems of quantum electrodynamics in the late 1940s the award of the Nobel Prize was just a matter of time. Yet years passed with no news of the award. Clarice Schwinger, his devoted wife, described waiting for the Prize and thought he would get it soon after they got married. When it did not happen, she then decided Julian simply was not going to get it. This chapter looks at Schwinger's winning the Nobel Prize for Physics in 1965 and the attention he received afterwards, his Nobel lecture entitled ‘Relativistic quantum field theory’ delivered in December 1965, his development of the source theory as an alternative to the operator quantum field theory, source theory calculation of the anomalous magnetic moment of the electron, Schwinger's research on chiral symmetry, his influence on Steven Weinberg with regards to effective Lagrangians, and his last years as a professor at Harvard University.Less

As soon as Julian Schwinger burst upon the stage, one could hardly doubt that a Nobel Prize was in the offing. Certainly, after his solution of the problems of quantum electrodynamics in the late 1940s the award of the Nobel Prize was just a matter of time. Yet years passed with no news of the award. Clarice Schwinger, his devoted wife, described waiting for the Prize and thought he would get it soon after they got married. When it did not happen, she then decided Julian simply was not going to get it. This chapter looks at Schwinger's winning the Nobel Prize for Physics in 1965 and the attention he received afterwards, his Nobel lecture entitled ‘Relativistic quantum field theory’ delivered in December 1965, his development of the source theory as an alternative to the operator quantum field theory, source theory calculation of the anomalous magnetic moment of the electron, Schwinger's research on chiral symmetry, his influence on Steven Weinberg with regards to effective Lagrangians, and his last years as a professor at Harvard University.

*Mihály Bakonyi and Hugo J. Woerdeman*

- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691128894
- eISBN:
- 9781400840595
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691128894.001.0001
- Subject:
- Mathematics, Computational Mathematics / Optimization

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly ...
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Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than two hundred exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to six hundred references from books and journals from a wide variety of disciplines.Less

Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than two hundred exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to six hundred references from books and journals from a wide variety of disciplines.