The representation theory of reductive algebraic groups and related finite reductive groups has many applications. The articles in this volume provide introductions to various aspects of the subject, including algebraic groups and Lie algebras, reflection groups, abelian and derived categories, the Deligne-Lusztig representation theory of finite reductive groups, Harish-Chandra theory and its generalizations, quantum groups, subgroup structure of algebraic groups, intersection cohomology, and Lusztig's conjectured character formula for irreducible representations in prime characteristic. The...

On-line learning is one of the most commonly used techniques for training neural networks. Though it has been used successfully in many real-world applications, most training methods are based on heuristic observations. The lack of theoretical support damages the credibility as well as the efficiency of neural networks training, making it hard to choose reliable or optimal methods. This book presents a coherent picture of the state of the art in the theoretical analysis of on-line learning. An introduction relates the subject to other developments in neural networks and explains the overall...

This volume represents a comprehensive record of research into the theory of dynamos.

This book is the first major synthesis of theory and empirical knowledge regarding the ecology and epidemiology of infectious diseases in natural, unmanaged, animal and plant populations. Throughout the book, the contributors develop a dialogue between the patterns observed in empirical studies of disease in natural populations and the mathematical models used to dissect and examine the observed epidemiological patterns. The book is divided into a number of reviews and group reports by experts in various fields. Two sections synthesize important issues relating to the dynamics of...

A survey of idempotency, the developing area of mathematics.

The problems of understanding and controlling disease present a range of mathematical challenges, from broad theoretical issues to specific practical ones, making epidemiology one of the most vibrant branches of applied biology. Progress in this field requires collaboration among leading researchers with a wide range of mathematical expertise and close involvement in applied fields across the social, medical and biological sciences. This volume surveys the current state of epidemic modeling in relation to basic aims such as understanding, prediction, and evaluation and implementation of...

Most object-oriented or functional languages are higher order languages, ones in which the means of manipulation can itself be manipulated. This important reference contains a collection of original articles about recent developments in operational semantics for higher order programming languages by some of the leading researchers in the field. Operational techniques are important because they are closer to implementations and language definitions than more abstract mathematical techniques such as denotational semantics. One of the exciting developments recounted in the book is that...

Dynamo theory is the study of the generation and maintenance of magnetic fields by fluid motion. It is important in many areas of physics, ranging from stellar and galactic dynamics, through solar physics and geomagnetism to reactor physics. This volume is the only modern introduction to the subject, and is comprised of the lectures given by leading specialists for an intensive course held at the Newton Institute in Cambridge, U.K. as part of a NATO Advanced Study Institute. Topics covered include planetary and solar dynamos, fast dynamos, and the use of symmetry principles to derive...

Many fundamental theories of modern physics can be considered as descriptions of dynamical systems subjected to constraints. The study of these constrained dynamical systems, and in particular the problems of formulating them as quantum systems, has many profound links with geometry. These links were explored in the Symposium on Geometry and Gravity held at the Newton Institute in 1994. This book, which arose from a conference held during that symposium, is a collection of papers devoted to problems such as Chern-Simons theory, sigma-models, gauge invariance and loop quantization, general...

This is the first systematic introduction to electromagnetic duality and its generalizations. The authors, leading figures in this exciting new area of mathematical physics, describe the fundamental ideas, latest developments, and some earlier work whose significance has only recently become apparent. This volume will be essential reading for all those working in mathematical physics.