Approx. 800 pages
Trim size 6 X 9 in
Hardcover, Reference
Expected Release Date: Jul 2008
Much like the Chicago Manual of Style, The Manual of Scientific Style addresses all stylistic matters in the relevant disciplines of physical and biological science, medicine, health, and technology. It presents consistent guidelines for text, data, and graphics, providing a comprehensive and authoritative style manual that can be used by the professional scientist, science editor, general editor, science writer, and researcher.
Anyone working with scientific vocabulary including contributors to scientific journal articles; authors/editors to scientific monographs, serials, and reference works; editors, writers, and designers preparing publications at all levels of readership
Part I. General Style Manuscript Preparation General Style Units of Measurement Citation of References Presentation of Data and Figures Part II. References, Citations and Quotations Standards for Clear and Proper Attribution Standard Citation Formats Text Sources Audiovisual Media Electronic Sources Part III. Style Issues for Specific Disciplines Mathematics Physics Chemistry Earth and Environmental Science Life Science Medicine Civil, Mechanical and Electrical Engineering Computer Science and Information Science Appendices: Scientific Organizations and Publications: Standard Abbreviations Classification Schemes in Science and Technology Standard Abbreviation Dictionary Difficult and Troublesome Terms and Words Comparative Standards for Shared Terms and Conventions Bibliography Index
Paperback (ISBN-13: 9780521064996)
Bayesian probability theory has emerged not only as a powerful tool for building computational theories of vision, but also as a general paradigm for studying human visual perception. This book provides an introduction to and critical analysis of the Bayesian paradigm. Leading researchers in computer vision and experimental vision science describe general theoretical frameworks for modelling vision, detailed applications to specific problems and implications for experimental studies of human perception. The book provides a dialogue between different perspectives both within chapters, which draw on insights from experimental and computational work, and between chapters, through commentaries written by the contributors on each others' work. Students and researchers in cognitive and visual science will find much to interest them in this thought-provoking collection.
* Unusual degree of cross-referencing and dialogue between contributors of different disciplines * Integrated coverage
1. Introduction D. C. Knill, D. Kersten and A. Yuille; 2. Pattern theory: a unifying perspective D. Mumford; 3. Modal structure and reliable inference A. Jepson, W. Richards and D. C. Knill; 4. Priors, preferences and categorical percepts W. Richards, A. Jepson and J. Feldman; 5. Bayesian decision theory and psychophysics A. L. Yuille and H. H. Bulthoff; 6. Observer theory, Bayes theory, and psychophysics B. M. Bennett, D. D. Hoffman, C. Prakash and S. N. Richman; 7. Implications of a Bayesian formulation D. C. Knill, D. Kersten and P. Mamassian; 8. Shape from texture: ideal observers and human psychophysics A. Blake, H. H. Bulthoff and D. Sheinberg; 9. A computational theory for binocular stereopsis P. N. Belhumeur; 10. The generic viewpoint assumption in a Bayesian framework W. T. Freeman; 11. Experiencing and perceiving visual surfaces K. Nakayama and S. Shimojo; 12. The perception of shading and reflectance E. H. Adelson and A. P. Pentland; 13. Banishing the Homunculus H. Barlow.
ISBN 978-3-03719-050-0
April 2008, 219 pages, softcover, 17 x 24 cm.
Differential geometry studies geometrical objects using analytical methods. Like modern analysis itself, differential geometry originates in classical mechanics. For instance, geodesics and minimal surfaces are defined via variational principles and the curvature of a curve is easily interpreted as the acceleration with respect to the path length parameter. Modern differential geometry in its turn strongly contributed to modern physics.
This book gives an introduction to the basics of differential geometry, keeping in mind the natural origin of many geometrical quantities, as well as the applications of differential geometry and its methods to other sciences.
The text is divided into three parts. The first part covers the basics of curves and surfaces, while the second part is designed as an introduction to smooth manifolds and Riemannian geometry. In particular, Chapter 5 contains short introductions to hyperbolic geometry and geometrical principles of special relativity theory. Here, only a basic knowledge of algebra, calculus and ordinary differential equations is required. The third part is more advanced and introduces into matrix Lie groups and Lie algebras, representation theory of groups, symplectic and Poisson geometry, and applications of complex analysis in surface theory.
The book is based on lectures the author held repeatedly at Novosibirsk State University. It is addressed to students as well as to anyone who wants to learn the basics of differential geometry.
Lecture Notes--Monograph Series, Volume 56
Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007.
163 pp.
This monograph deals with adaptive supervised classification, using tools borrowed from statistical mechanics and information theory, stemming from the PAC-Bayesian approach pioneered by David McAllester and applied to a conception of statistical learning theory forged by Vladimir Vapnik. Using convex analysis on the set of posterior probability measures, we show how to get local measures of the complexity of the classification model involving the relative entropy of posterior distributions with respect to Gibbs posterior measures. We then discuss relative bounds, comparing the generalization error of two classification rules, showing how the margin assumption of Mammen and Tsybakov can be replaced with some empirical measure of the covariance structure of the classification model. We show how to associate to any posterior distribution an effective temperature relating it to the Gibbs prior distribution with the same level of expected error rate, and how to estimate this effective temperature from data, resulting in an estimator whose expected error rate converges according to the best possible power of the sample size adaptively under any margin and parametric complexity assumptions. We describe and study an alternative selection scheme based on relative bounds between estimators, and present a two step localization technique which can handle the selection of a parametric model from a family of those. We show how to extend systematically all the results obtained in the inductive setting to transductive learning, and use this to improve Vapnikfs generalization bounds, extending them to the case when the sample is made of independent non-identically distributed pairs of patterns and labels. Finally we review briefly the construction of Support Vector Machines and show how to derive generalization bounds for them, measuring the complexity either through the number of support vectors or through the value of the transductive or inductive margin.
Series: Publications of the Scuola Normale Superiore
Subseries: Theses (Scuola Normale Superiore) , Vol. 6
2008, XIV, 107 p., Softcover
ISBN: 978-88-7642-325-3
The first-order theory of real exponentiation has been studied by many mathematicians in the last fifty years, in particular by model theorists, real geometers and number theorists. The aim of this work is to present the results obtained so far in this area and to improve and refine them. In the early 1990s A. Macintyre and A.J. Wilkie proved that the theory of real exponentiation is decidable, provided that Schanuelfs conjecture holds. In the proof of their result, they proposed a candidate for a complete and recursive axiomatization of the theory. While simplifying their axiomatization, the author of this book analyses (in the first three chapters) the model theory and geometry of a broad class of functions over real closed fields. Even though the methods used are elementary, the results hold in great generality. The last chapter is devoted solely to the decidability problem for the real exponential field.
Graduates and researchers in model theory, real analytic and algebraic geometry, quasi-analytic and o-minimal geometry or transcendental number theory
1. Definably complete structures.- 2. Noetherian differential rings of functions.- 3. Effective o-minimality.- 4. Remarks on the decidability problem for the real exponential field.
(hardback)
ISBN-13: 978-0-19-920567-7
Publication date: 10 April 2008
448 pages, 68 line drawings, 234x156 mm
Series: International Series of Monographs on Physics number 140
'Numerical relativity has had many successes in the past few years, which is very timely with the major gravitational wave detectors collecting data. It is a good time for such a book, and the balance and coverage of the book are very good.' - Ian Hawke, University of Southampton
Self-contained and comprehensive introduction to the field of numerical relativity.
Discusses recent developments in the field, including simulation of black hole space-times.
Discusses several alternative formulations of the evolution equations.
Includes an introduction to relativistic hydrodynamics for non-experts.
Discusses techniques to extract gravitational wave information from numerical simulation with applications to gravitational wave detection.
This book introduces the modern field of 3+1 numerical relativity. The book has been written in a way as to be as self-contained as possible, and only assumes a basic knowledge of special relativity. Starting from a brief introduction to general relativity, it discusses the different concepts and tools necessary for the fully consistent numerical simulation of relativistic astrophysical systems, with strong and dynamical gravitational fields. Among the topics discussed in detail are the following: the initial data problem, hyperbolic reductions of the field equations, gauge conditions, the evolution of black hole space-times, relativistic hydrodynamics, gravitational wave extraction and numerical methods. There is also a final chapter with examples of some simple numerical space-times. The book is aimed at both graduate students and researchers in physics and astrophysics, and at those interested in relativistic astrophysics.
Readership: Graduate students and researchers in physics, general relativity, and astrophysics.
1. Brief Review of General Relativity
2. The 3+1 Formalism
3. Initial Data
4. Gauge Conditions
5. Hyperbolic Reductions of the Field Equations
6. Evolving Black Hole Spacetimes
7. Relativistic Hydrodynamics
8. Gravitational Wave Extraction
9. Numerical Methods
10. Examples of Numerical Spacetimes
A. Total Mass and Momentum in General Relativity
B. Spacetime Christoffel Symbols in 3+1 Language
C. BSSNOK with Natural Conformal Rescaling
D. Spin-weighted Spherical Harmonics
References
Index
Cloth | September 2008
1008 pp. | 8 x 10 | Black-and-white illustrations throughout | Cross-references, bibliographies, index
What is a modular form? What is the point of symplectic geometry? This one-of-a-kind reference illuminates modern pure mathematics in all its diversity. More than 200 articles, organized thematically and written by many of the world's leading mathematicians, explain the major ideas and branches of mathematics in a clear, accessible style. Presenting not only definitions but also motivation and context for concepts, methods, theorems, and other topics of mathematical study, this is an indispensable resource for everyone with a serious interest in the field.
1. What is Mathematics?
Introduces the language and grammar of mathematics
fundamental definitions
general goals of mathematical research
the subject matter of mathematics
2. The Fundamental Ideas of Mathematics
Explores algebra
algorithms
geometry
how analysis became rigorous
numbers
the crisis in the foundations of mathematics
the development of the idea of proof
3. Mathematical Objects
Defines and explains more than 75 mathematical objects, concepts, and buzzwords, from axiom of choice to zeta function
4. Branches of Mathematics
Includes detailed coverage of algebra
algebraic geometry
analysis
combinatorics
computation
geometry
logic and set theory
number theory
probability
5. Mathematicians
Profiles 70 mathematicians, from Apollonius to Weyl, who influenced the field
6. Theorems and Problems
Discusses notable theorems and open problems, from the four-color theorem to the Riemann hypothesis
7. The Influence of Mathematics
Covers the intellectual and practical influence of mathematics on other disciplines such as analytic philosophy, art, biology, chemistry, economics, finance, and music
8. Miscellaneous
Advice to a Young Mathematician
Chronology of Mathematics
Computer Experiments in Mathematics
The Art of Problem Solving
and more