W. J. Fitzgerald / University of Cambridge
R. L. Smith / University of North Carolina, Chapel Hill
A. T. Walden / Imperial College of Science, Technology and Medicine
P. C. Young / Lancaster University

Nonlinear and Nonstationary Signal Processing

Most currently employed methods that are used in various fields of data analysis are based on rather simplistic assumptions about linearity and stationarity, and are hence suboptimal in many situations. The chapters in this book introduce modern methods that have been developed in many fields of statistics, engineering, environmental science or finance, to address these shortcomings. The authors present state-of-the-art statistical methods, and discuss their applications in real-world situations. The chapters, taken together, provide a coherent and unique account of this active and important area.

Introduction; 1. Bayesian computational approaches to model selection C. Andrieu, A. Doucet, W. J. Fitzgerald and J. -M. Perez; 2. Sequential analysis of nonlinear dynamic systems using particles and mixtures Neil Gordon, Alan Marrs and David Salmond; 3. Stochastic, dynamic modelling and signal processing: time variable and state dependent parameter estimation Peter Young; 4. The use of generalised likelihood measures for uncertainty estimation in high-order models of environmental systems Keith Beven, Jim Freer, Barry Hankin and Karsten Schulz; 5. Spatial statistics in environmental science Richard L. Smith; 6. Useful lies: dynamics from data Alistair Mees; 7. A modelling framework for the prices and times of trades made on the New York Stock Exchange Tina Hviid Rydberg and Neil Shephard; 8. The sample autocorrelations of financial Time Series Models Richard A. Davis and Thomas Mikosch; 9. The many roads to time-frequency Patrick Flandrin; 10. Multiple Window time-varying spectrum estimation Metin Bayram and Richard Baraniuk; 11. Multitaper analysis of nonstationary and nonlinear Time Series Data David J. Thomson; 12. Signal and image denoising via wavelet thresholding: orthogonal and biorthogonal, scalar and multiple wavelet transforms Vasily Strela and Andrew Walden; 13. Wavestrapping time series: adaptive wavelet-based bootstrapping D. B. Percival, S. Sardy and A. C. Davison.

Neil Gershenfeld

The Physics of Information Technology

The Physics of Information Technology explores the familiar devices that we use to collect, transform, transmit, and interact with electronic information. Many such devices operate surprisingly close to very many fundamental physical limits. Understanding how such devices work, and how they can (and cannot) be improved, requires deep insight into the character of physical law as well as engineering practice. The book starts with an introduction to units, forces, and the probabilistic foundations of noise and signalling, then progresses through the electromagnetics of wired and wireless communications, and the quantum mechanics of electronic, optical, and magnetic materials, to discussions of mechanisms for computation, storage, sensing, and display. This self-contained volume will help both physical scientists and computer scientists see beyond the conventional division between hardware and software to understand the implications of physical theory for information manipulation.

Preface; 1. Introduction; 2. Interactions, units, and magnitudes; 3. Noise in physical systems; 4. Information in physical systems; 5. Electromagnetic fields and waves; 6. Circuits, transmission lines, and wave guides; 7. Multipoles and antennas; 8. Optics; 9. Lensless imaging and inverse problems; 10. Semiconductor materials and devices; 11. Generating, modulating, and detecting light; 12. Magnetic storage; 13. Measurement and coding; 14. Transducers; 15. Timekeeping and navigation; 16. Quantum computing and communications; Appendix 1. Problem solutions

Charles F. Dunkl and Yuan Xu

Orthogonal Polynomials of Several Variables

This is the first modern book on orthogonal polynomials of several variables, which are interesting both as objects of study and as tools used in multivariate analysis, including approximations and numerical integration. The book, which is intended both as an introduction to the subject and as a reference, presents the theory in elegant form and with modern concepts and notation. It introduces the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains such as the cube, the simplex, the sphere and the ball, or those of Gaussian type, for which fairly explicit formulae exist. The approach is a blend of classical analysis and symmetry-group-theoretic methods. Reflection groups are used to motivate and classify symmetries of weight functions and the associated polynomials. The book will be welcomed by research mathematicians and applied scientists, including applied mathematicians, physicists, chemists and engineers.

1. Background; 2. Examples of orthogonal polynomials; 3. General properties of orthogonal polynomials; 4. Root systems and Coxeter groups; 5. Spherical harmonics associated with reflection groups; 6. Classical and generalized classical orthogonal polynomials; 7. Summability of orthogonal polynomials; 8. Orthogonal polynomials associated with symmetric groups; 9. Orthogonal polynomials associated with octahedral groups; 10. Bibliography; Indexes.

Ron Blei

Analysis in Integer and Fractional Dimensions

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.

Preface; 1. A prologue: mostly historical; 2. Three classical inequalities; 3. A fourth inequality; 4. Elementary properties of the Frechet variation - an introduction to tensor products; 5. The Grothendieck factorization theorem; 6. An introduction to multidimensional measure theory; 7. An introduction to harmonic analysis; 8. Multilinear extensions of the Grothendieck inequality; 9. Product Frechet measures; 10. Brownian motion and the Wiener process; 11. Integrator; 12. A ・/2n- dimensional・Cartesian product; 13. The last chapter: leads and loose ends.