Masujima, M., M.H. Company Ltd., Tokyo, Japan

Path Integral Quantization and Stochastic Quantization

2000. XII, 282 pp.
3-540-66542-0

The book gives an overview of path integral quantization and stochastic quantization of classical
mechanics and field theory. The non-Abelian gauge field, the gravitational field, and the path integral
representation of quantum statistical mechanics and stochastic quantization are described.

Keywords: Path Integral Quantization, Gravitational Field, Stochastic Quantization

Series: Springer Tracts in Modern Physics.VOL. 165

Fields: Quantum Physics; Elementary Particles and Fields

Written for: Physicists
Book category: Monograph
Publication language: English

Ritter, K., Technische Universitat Darmstadt, Germany

Average-Case Analysis of Numerical Problems

2000. IX, 254 pp.
3-540-67449-7

The average-case analysis of numerical problems is the counterpart of the more traditional worst-case
approach. The analysis of average error and cost leads to new insight on numerical problems as well as to
new algorithms. The book provides a survey of results that were mainly obtained during the last 10 years
and also contains new results. The problems under consideration include approximation/optimal recovery
and numerical integration of univariate and multivariate functions as well as zero-finding and global
optimization. Background material, e.g. on reproducing kernel Hilbert spaces and random fields, is provided.

Keywords: Bayesian numerical analysis, information-based complexity, optimal numerical methods, spatial
statistics

Series: Lecture Notes in Mathematics.VOL. 1733

Hirvensalo, M., University of Turku, Finland

Quantum Computing

2000. Approx. 180 pp.
3-540-66783-0

The book is devoted to quantum computing, a new, multidisciplinary research area crossing quantum
mechanics, theoretical computer science and mathematics. It contains an introduction to quantum
computing as well as the most important recent results on the topic. Two famous algorithms, fast
factorization and Grover search, are presented in separate chapters because these inventions are important
structurally and developmentally.
Unlike previous books which are mainly physics-oriented this book presents the topic in a computer
science-oriented uniform way. This makes the theory of quantum computation accessible to a larger
audience, including also the mathematics-oriented readers.

Keywords: Quantum computation, algorithms, probabilistic computation

Series: Natural Computing Series.

Kaneko, K., University of Tokyo, Japan
Tsuda, I., Hokkaido University, Sapporo, Japan

Complex Systems: Chaos and Beyond
A Constructive Approach with Applications in Life Sciences

2000. XIV, 273 pp. 113 figs.
3-540-67202-8

Chaos in science has always been a fascinating realm since it challenges the usual scientific approach of
reductionism. While carefully distinguishing between complexity, holism, randomness, incompleteness,
nondeterminism and stochastic behaviour the authors show that, although many aspects of chaos have
been phenomenologically understood, most of its defining principles are still difficult to grasp and
formulate. Demonstrating that chaos escapes all traditional methods of description, the authors set out to
find new methods to deal with this phenomenon and illustrate their constructive approach with many
examples from physics, biology and information technology. While maintaining a high level of rigour, an
overly complicated mathematical apparatus is avoided in order to make this book accessible, beyond the
specialist level, to a wider interdisciplinary readership.

Keywords: Chaos, complex systems, nonlinear dynamics, stochastic processes

Contents: Preface.- Necessity for a Science of Complex Systems.- Observation Problems from an
Information Theoretical Viewpoint.- CML: Constructive Approach to Spatiotemporal Chaos.- Network of
Chaotic Elements.- Significance of Coupled Chaotic Systems to Biological Networks.- Chaotic Information
Processing in the Brain.

Mazanec, J., Wirtschaftuniversitat Wien, Austria Vienna, Austria
Strasser, H., Wirtschaftsuniversitat Wien, Austria Vienna, Austria

A Nonparametric Approach to Perceptions-Based Market Segmentation
: Foundations

2000. IV, 195 pp. 29 figs.
3-211-83473-7

The new series edited by the Jubilamsstiftung of the Wirtschaftsuniversitat Wien aims at presenting results of
interdisciplinary research conducted at one of the largest business schools in Europe. Volumes 1 and 2 focus on recent results gained by a group of mathematicians and marketing scientists. It is a unique feature that the writing style adopted for this series makes the findings accessible for members of both research communities.
It is also targeted to practitioners in marketing management with an interest in optimally exploiting their consumer survey and panel data. Market segmentation and product positioning are major strategic
issues in a company's marketing decision making. The analytical tools highlighted in the Foundations and Applications Volumes are new instruments for exploratory and inferential market structure analysis based on consumer brand perceptions and choice. Unlike the majority of contemporary marketing modeling these methods operate nonparametrically thus avoiding the rigorous assumptions which are rarely satisfied by real-world data.

Contents: Perceptual market structure and strategy formation (J. A. Mazanec): Market segmentation; Getting prepared for PBMS; The analytical challenges; Conventional methodology; Implementing
PBMS.- Statistical Foundations (H. Strasser): Reduction of Complexity; Analysis of Consumer Perceptions.

Kallel, L., Ecole Polytechnique, Palaiseau, France
Naudts, B., Universiteit Antwerpen, Belgium
Rogers, A., University of Southampton, UK
(Eds.)

Theoretical Aspects of Evolutionary Computing

2000. Approx. 500 pp.
3-540-67396-2

This book is the first in the field to provide extensive, entry level tutorials to the theory of Evolutionary
Computing, covering the main approaches to understanding the dynamics of Evolutionary Algorithms. It
combines this with recent, previously unpublished research papers based on the material of the tutorials.
The outcome is a book which is self-contained to a large degree, attractive both to graduate students and
researchers from other fields who want to get acquainted with the theory of Evolutionary Computing, and
to active researchers in the field who can use this book as a reference and a source of recent results.

Keywords: Evolutionary Algorithms ; Genetic Algorithms ; Evolutionary Strategy ; Evolutionary
Programming ; Population Dynamics ; Optimization ; Effects of Mutation, Crossover and Selection

Series: Natural Computing Series.