Ibrahim, J.G., Harvard School of Public Health, Boston, MA, USA
Chen, M.-H., Worcester Polytechnic Institute, Worcester, MA, USA
Sinha, D., University of New Hampshire, Durham, NH, USA

Bayesian Survival Analysis

2001. Approx. 490 pp. Hardcover
0-387-95277-2

Survival analysis arises in many fields of study including medicine, biology, engineering, public health, epidemiology, and economics. This book provides a comprehensive treatment of Bayesian survival analysis.
Several topics are addressed, including parametric models, semiparametric models based on prior processes, proportional and non-proportional hazards models, frailty models, cure rate models, model selection and comparison, joint models for longitudinal and survival data, models with time varying covariates, missing covariate data, design and monitoring of clinical trials, accelerated failure time models, models for mulitivariate survival data, and special types of hierarchial survival models. Also various censoring schemes are examined including right and interval censored data. Several additional topics are discussed, including noninformative and informative prior specificiations, computing posterior qualities of interest, Bayesian hypothesis testing, variable selection, model selection with nonnested models, model checking techniques using Bayesian diagnostic methods, and Markov chain Monte Carlo (MCMC) algorithms for sampling from the posteiror and predictive distributions.
The book presents a balance between theory and applications, and for each class of models discussed, detailed examples and analyses from case studies are presented whenever possible. The applications are all essentially from the health sciences, including cancer, AIDS, and the environment. The book is intended as a graduate textbook or a reference book for a one semester course at the advanced masters or Ph.D. level. This book would be most suitable for second or third year graduate students in statistics or biostatistics. It would also serve as a useful reference book for applied or theoretical researchers as well as practitioners.

Contents: Introduction.- Parametric Models.- Semiparametric Models.- Fraility Models.- Cure Rate Models.- Model Comparison.- Joint Models for Longitudinal and Survival Data.- Missing Covariate Data.- Design and Monitoring of Randomized Clinical Trials.- Other Topics.

Series: Springer Series in Statistics.

Pottmann, H., Technische Universita"t Wien, Austria
Wallner, J., Technische Universita"t Wien, Austria

Computational Line Geometry

2001. X, 565 pp. 264 figs., 17 in color. Hardcover
3-540-42058-4

The geometry of lines occurs naturally in such different areas as sculptured surface machining, computation of offsets and medial axes, surface reconstruction for reverse engineering, geometrical optics, kinematics and motion design, and modeling of developable surfaces. This book covers line geometry from various viewpoints and aims towards computation and visualization. Besides applications, it contains a tutorial on projective geometry and an introduction into the theory of smooth and algebraic manifolds of lines. It will be useful to researchers, graduate students, and anyone interested either in the theory or in computational aspects in general, or in applications in particular.

Keywords: line geometry, scientific computing, geometric design, visualization, kinematics

Tao, G., University of Virginia, Charlottesville, VA,  USA
Lewis, F.L., University of Texas at Arlington, Fort Worth, TX, USA (Eds.)

Adaptive Control of Nonsmooth Dynamic Systems

2001. Approx. 430 pp. 102 figs. Hardcover
1-85233-384-7

A complete reference to adaptive control of systems with nonsmooth industrial nonlinearities such as:
- backlash
- dead-zones
- component failure
- friction
- hysteresis
- saturation
- time delays.
These nonlinearities in industrial actuators cause severe problems in the motion control of industrial processes, particularly in view of modern requirements of speed and precision of movement such as occur in semiconductor manufacturing, precision machining, and elsewhere. Actuator nonlinearities are ubiquitous in engineering practice and limit control system performance.
While standard feedback control alone cannot handle these nonsmooth nonlinearities effectively, this book, with unified and systematic adaptive design methods developed in 16 chapters, shows how such nonlinear characteristics can be effectively compensated for by using adaptive and intelligent control techniques. This allows desired system performance to be achieved in the presence of uncertain nonlinearities.
With extensive surveys of literature and comprehensive summaries of various design methods, the authors of the book chapters, who are experts in their areas of interest, present new solutions to some important issues in adaptive control of systems with various sorts of nonsmooth nonlinearities.
In addition to providing solutions, the book is also aimed at motivating more research activities in the important field of adaptive control of nonsmooth nonlinear industrial systems by formulating several challenging open problems in related areas.

Contents: 1. New Models and Identification Methods for Backlash and Gear Play.- 2. Adaptive Dead Zone Inverses for Possibly Nonlinear Control Systems.- 3. Deadzone Compensation in Motion Control Systems Using Augmented Multilayer Neural Networks.- 4. On-Line Fault Detection, Diagnosis, Isolation and Accomodation of Dynamical Systems with Actuator Failures.- 5. Adaptive Control of Systems with Actuator Failures.- 6. Multi-mode System Identification.- 7. On Feedback Control of Processes with "Hard" Nonlinearities.- 8. Adaptive Friction Compensation for Servo Mechanisms.- 9. Relaxed Controls and a Class of Active Material Actuator Models.- 10. Robust Adaptive Control of Nonlinear Systems with Dynamic Backlash-like Hysteresis.- 11. Adaptive Control of a Class of Time-delay Systems in the Presence of Saturation.- 12. Adaptive Control for Systems with Input Constraints: A Survey.- 13. Robust Adaptive Control of Input Rate Saturation Constrained Discrete Time Systems.- 14. Adaptive Control of Linear Systems with Poles in the Closed LHP with Constrained Inputs.- 15. Adaptive Control with Input Saturation Constraints.- 16. Adaptive Control of Linear Systems with Unknown Time Delay.

Levin, A.L., The Open University of Israel, Tel Aviv, Israel
Lubinsky, D.S., Witwatersrand University, Wits, South Africa

Orthogonal Polynomials for Exponential Weights

2001. Approx. 490 pp. 1 fig. Hardcover
0-387-98941-2

The analysis of orthogonal polynomials associated with general weights was a major theme in classical analysis in the twentieth century, and undoubtedly will continue to grow in importance in the future.
In this monograph, the authors investigate orthogonal polynomials for exponential weights defined on a finite or infinite interval. The interval should contain 0, but need not be symmetric about 0; likewise the weight need not be even. The authors establish bounds and asymptotics for orthonormal and extremal polynomials, and their associated Christoffel functions. They deduce bounds on zeros of extremal and orthogonal polynomials, and also establish Markov- Bernstein and Nikolskii inequalities.
The authors have collaborated actively since 1982 on various topics, and have published many joint papers, as well as a Memoir of the American Mathematical Society. The latter deals with a special case of the weights treated in this book. In many ways, this book is the culmination of 18 years of joint work on orthogonal polynomials, drawing inspiration from the works of many researchers in the very active field of orthogonal polynomials.

Contents: .Introduction and Results.- Weighted Potential Theory: The Basics.- Basic Estimates for Q, at .- Restricted Range Inequalities.- Estimates for Measure and Potential.- Smoothness of /rho t.- Weighted Polynomial Approximation.- Asymptotics of Extremal Errors.- Christoffel Functions.- Markov-Bernstein and Nikolskii Inequalities.- Zeros of Orthogonal Polynomials.- Bounds on Orthogonal Polynomials.- Further Bounds and Applications.- Asymptotics of Extremal Polynomials.- Asymptotics of Orthonormal Polynomials.

Series: CMS Books in Mathematics.VOL. 4

Kushner, H.J., Brown University, Providence, RI, USA

Heavy Traffic Analysis of Controlled Queueing and Communication Networks

2001. Approx. 540 pp. 50 figs. Hardcover
0-387-95264-0

This book provides a thorough development of the powerful methods of heavy traffic analysis and approximations with applications to a wide variety of stochastic (e.g. queueing and communication) networks, for both controlled and uncontrolled systems.
The approximating models are reflected stochastic differential equations. The analytical and numerical methods yield considerable simplifications and insights and good approximations to both path properties and optimal controls under broad conditions on the data and structure.
The general theory is developed, with possibly state dependent parameters, and specialized to many different cases of practical interest.
Control problems in telecommunications and applications to scheduling, admissions control, polling, and elsewhere are treated. The necessary probability background is reviewed, including a detailed survey of reflected stochastic differential equations, weak convergence theory, methods for characterizing limit processes, and ergodic problems.

Contents: Models and applications.- Martingales and weak convergence.- Stochastic differential equations.- Invariant measures and the ergodic problem.- The single processor problem.- Uncontrolled networks.- Uncontrolled networks, continued.- State dependence.- Bounded controls.- Singular controls.- Polling and control of polling.- Multiclass scheduling.- References.- Symbol index.- Index.

Series: Applications of Mathematics.VOL. 47

Blowey, J., / Coleman, J.P.,/ Craig, A.W., University of Durham, UK (Eds.)

Theory and Numerics of Differential Equations

2001. X, 280 pp. Hardcover
3-540-41846-6

This book contains detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succinct and accurate account of recent research in areas parallel to their own, and graduates in mathematical sciences.

Keywords: Stochastic and hyperbolic partial differential equations, spectral and high order methods, microstructure, multigrid MSC 2000 : 35LXX, 65-XX

Contents: C. Bernardi, Y. Maday: Spectral, spectral element and mortar element methods.- S. Cyganowski, L. Gru"ne, P.E. Kloeden: MAPLE for Stochastic Differential Equations.- K.-S. Moon, A. Szepessy, R. Tempone, G. Zouraris: Hyperbolic Differential Equations and Adaptive Numerics.- R. Kornhuber: Nonlinear Multigrid Techniques.- C. Carstensen: Mathematical and Numerical Aspects in the Numerical Analysis of Microstructure.

Series: Universitext.