Ron Blei's Books

Analysis in Integer and Fractional Dimensions

By: Ron Blei

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Analysis in Integer and Fractional Dimensions

By: Ron Blei

This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on 'dimension' as a basic counter of degrees of freedom, leading to precise relations between combinatorial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. The basic concepts of fractional Cartesian products and combinatorial dimension are introduced and linked to scales calibrated by harmonic-analytic and stochastic measurements. Topics include the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of randomness and Frechet measures in stochastic analysis. This book is primarily aimed at graduate students specialising in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable to be used as a textbook. It is also of interest to scientists from other disciplines, including computer scientists, physicists, statisticians, biologists and economists.

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Page Count

580

Publisher

Cambridge University Press

Published Date

ISBN 10

1139427938

ISBN 13

9781139427937

The Grothendieck Inequality Revisited

By: Ron Blei

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The Grothendieck Inequality Revisited

By: Ron Blei

The classical Grothendieck inequality is viewed as a statement about representations of functions of two variables over discrete domains by integrals of two-fold products of functions of one variable. An analogous statement is proved, concerning continuous functions of two variables over general topological domains. The main result is the construction of a continuous map $\Phi$ from $l^2(A)$ into $L^2(\Omega_A, \mathbb{P}_A)$, where $A$ is a set, $\Omega_A = \{-1,1\}^A$, and $\mathbb{P}_A$ is the uniform probability measure on $\Omega_A$.

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Page Count

102

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821898558

ISBN 13

9780821898550

Statistical Methods for Annotation Analysis

By: Silviu Paun,Ron Artstein,Massimo Poesio

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Statistical Methods for Annotation Analysis

By: Silviu Paun,Ron Artstein,Massimo Poesio

Labelling data is one of the most fundamental activities in science, and has underpinned practice, particularly in medicine, for decades, as well as research in corpus linguistics since at least the development of the Brown corpus. With the shift towards Machine Learning in Artificial Intelligence (AI), the creation of datasets to be used for training and evaluating AI systems, also known in AI as corpora, has become a central activity in the field as well. Early AI datasets were created on an ad-hoc basis to tackle specific problems. As larger and more reusable datasets were created, requiring greater investment, the need for a more systematic approach to dataset creation arose to ensure increased quality. A range of statistical methods were adopted, often but not exclusively from the medical sciences, to ensure that the labels used were not subjective, or to choose among different labels provided by the coders. A wide variety of such methods is now in regular use. This book is meant to provide a survey of the most widely used among these statistical methods supporting annotation practice. As far as the authors know, this is the first book attempting to cover the two families of methods in wider use. The first family of methods is concerned with the development of labelling schemes and, in particular, ensuring that such schemes are such that sufficient agreement can be observed among the coders. The second family includes methods developed to analyze the output of coders once the scheme has been agreed upon, particularly although not exclusively to identify the most likely label for an item among those provided by the coders. The focus of this book is primarily on Natural Language Processing, the area of AI devoted to the development of models of language interpretation and production, but many if not most of the methods discussed here are also applicable to other areas of AI, or indeed, to other areas of Data Science.

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Page Count

218

Publisher

Morgan & Claypool Publishers

Published Date

ISBN 10

1636392547

ISBN 13

9781636392547

Boneyard Nose Art

U.S. Military Aircraft Markings and Artwork

By: Nicholas A. Veronico,Jim Dunn,Ron Strong

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Boneyard Nose Art

U.S. Military Aircraft Markings and Artwork

By: Nicholas A. Veronico,Jim Dunn,Ron Strong

Another volume in the Stackpole Military Photo Series, Boneyard Nose Art gives readers a first-hand look at retired American military aircraft, emphasizing their nose art. Featuring aircraft from World War II, Korea, Vietnam, and the Gulf Wars, over 300 color photos detail fighters, bombers, tankers, and transports, such as the B-2, B-17, F-16, C-130, and more. An ideal reference for modelers, military history enthusiasts, and art buffs, this title is also a perfect complement to the narrative accounts in the Stackpole Military History Series, including Airborne Combat, Coast Watching in WWII, and Flying American Combat Aircraft.

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Page Count

210

Publisher

Stackpole Books

Published Date

ISBN 10

0811713083

ISBN 13

9780811713085

The Grothendieck Inequality Revisited

By: Ron Blei

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The Grothendieck Inequality Revisited

By: Ron Blei

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Solve jigsaw puzzle

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Page Count

102

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821898558

ISBN 13

9780821898550

Book's by Ron Blei

Analysis in Integer and Fractional Dimensions

Analysis in Integer and Fractional Dimensions

The Grothendieck Inequality Revisited

The Grothendieck Inequality Revisited

Statistical Methods for Annotation Analysis

Statistical Methods for Annotation Analysis

Boneyard Nose Art

Boneyard Nose Art

The Grothendieck Inequality Revisited

The Grothendieck Inequality Revisited

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