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Learning Theory
The goal of learning theory is to approximate a function from sample values. To attain this goal learning theory draws on a variety of diverse subjects, specifically statistics, approximation theory, and algorithmics. Ideas from all these areas blended to form a subject whose many successful applications have triggered a rapid growth during the last two decades. This is the first book to give a general overview of the theoretical foundations of the subject emphasizing the approximation theory, while still giving a balanced overview. It is based on courses taught by the authors, and is reasonably self-contained so will appeal to a broad spectrum of researchers in learning theory and adjacent fields. It will also serve as an introduction for graduate students and others entering the field, who wish to see how the problems raised in learning theory relate to other disciplines.
Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science
The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manif...
Social Memory and State Formation in Early China
A thought-provoking book on the archaeology of power, knowledge, social memory, and the emergence of classical tradition in early China.
Foundations of Time-Frequency Analysis
Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in tim...
Prediction, Learning, and Games
This important text and reference for researchers and students in machine learning, game theory, statistics and information theory offers a comprehensive treatment of the problem of predicting individual sequences. Unlike standard statistical approaches to forecasting, prediction of individual sequences does not impose any probabilistic assumption on the data-generating mechanism. Yet, prediction algorithms can be constructed that work well for all possible sequences, in the sense that their performance is always nearly as good as the best forecasting strategy in a given reference class. The central theme is the model of prediction using expert advice, a general framework within which many related problems can be cast and discussed. Repeated game playing, adaptive data compression, sequential investment in the stock market, sequential pattern analysis, and several other problems are viewed as instances of the experts' framework and analyzed from a common nonstochastic standpoint that often reveals new and intriguing connections.
The Cambridge History of Ancient China
The Cambridge History of Ancient China provides a survey of the institutional and cultural history of pre-imperial China.
Ridge Functions
Presents the state of the art in the theory of ridge functions, providing a solid theoretical foundation.
Image Processing and Analysis
This book develops the mathematical foundation of modern image processing and low-level computer vision, bridging contemporary mathematics with state-of-the-art methodologies in modern image processing, whilst organizing contemporary literature into a coherent and logical structure. The authors have integrated the diversity of modern image processing approaches by revealing the few common threads that connect them to Fourier and spectral analysis, the machinery that image processing has been traditionally built on. The text is systematic and well organized: the geometric, functional, and atomic structures of images are investigated, before moving to a rigorous development and analysis of several image processors. The book is comprehensive and integrative, covering the four most powerful classes of mathematical tools in contemporary image analysis and processing while exploring their intrinsic connections and integration. The material is balanced in theory and computation, following a solid theoretical analysis of model building and performance with computational implementation and numerical examples.
California's Salmon and Steelhead
Millions upon millions of salmon and steelhead once filled California streams, providing a plentiful and sustainable food resource for the original peoples of the region. But over the years, dams and irrigation diversions have reduced natural spawning habitat from an estimated 6,000 miles to fewer than 300. River pollution has also hit hard at fish populations, which within recent decades have diminished by 80 percent. One species, the San Joaquin River spring chinook, became extinct soon after World War II. Other species are nearly extinct. This volume documents the reasons for the decline; it also offers practical suggestions about how the decline might be reversed. The California salmon s...
Substance and Non-substance Addiction
This book focuses on the similarities and differences between substance and non-substance addictions. It discusses in detail the mechanisms, diagnosis and treatment of substance and non-substance addictions, and addresses selected prospects that will shape future studies on addiction. Addiction is a global problem that costs millions of lives tremendous damage year after year. There are mainly two types of addition: substance addiction (e.g., nicotine, alcohol, cannabis, heroin, stimulants, etc.) and non-substance addiction (e.g., gambling, computer gaming, Internet, etc.). Based on existing evidence, both types of addiction produce negative impacts on individuals’ physical, mental, social and financial well-being, and share certain common mechanisms, which involve a dysfunction of the neural reward system and specific gene transcription factors. However, there are also key differences between these two types of addiction. Covering these aspects systematically, the book will provide researchers and graduate students alike a better understanding of drug and behavioral addictions.
