(Encyclopedia of Mathematics and Its Applications, vol.138)
Hardback ISBN: 9780521461931
205 pages
10 b/w illus.
Dimensions: 228 x 152 mm
Summary Look Inside Features Table of contents Excerpt Index Copyright Frontmatter Features
* Mathematical explanations are accessible to non-specialists
* Helps the reader to understand and visualise geometry in higher dimensions
* Contains applications to various fields, including electrical networks
1. A matricial approach to Euclidean geometry
2. Qualitative properties of the angles in a simplex
3. Special simplexes
4. Further geometric objects
5. Applications
Appendix
References
Index.
Series: Practical Guides to Biostatistics and Epidemiology
ISBN: 9780521875806 Hardback
ISBN: 9780521699099 Paperback
45 b/w illus. 25 tables
Dimensions: 247 x 174 mm
available from February 2011
This book is for anyone who has biomedical data and needs to identify variables that predict an outcome, for two-group outcomes such as tumor/not-tumor, survival/death, or response from treatment. Statistical learning machines are ideally suited to these types of prediction problems, especially if the variables being studied may not meet the assumptions of traditional techniques. Learning machines come from the world of probability and computer science but are not yet widely used in biomedical research. This introduction brings learning machine techniques to the biomedical world in an accessible way, explaining the underlying principles in nontechnical language and using extensive examples and figures. The authors connect these new methods to familiar techniques by showing how to use the learning machine models to generate smaller, more easily interpretable traditional models. Coverage includes single decision trees, multiple-tree techniques such as Random Forests?, neural nets, support vector machines, nearest neighbors and boosting.
Features
* Free open-source computer code is available online * Brings valuable new ideas from probability and computer science into the biomedical world to provide more accurate predictions * Plain-language approach makes the techniques more accessible
Preface
Acknowledgements
Part I. Introduction: 1. Prologue
2. The landscape of learning machines
3. A mangle of machines
4. Three examples and several machines
Part II. A Machine Toolkit: 5. Logistic regression
6. A single decision tree
7. Random forests ? trees everywhere
Part III. Analysis Fundamentals: 8. Merely two variables
9. More than two variables
10. Resampling methods
11. Error analysis and model validation
Part IV. Machine Strategies: 12. Ensemble methods ? let's take a vote
13. Summary and conclusions
References
Index.
Series: Cambridge Tracts in Mathematics (No. 78)
ISBN: 9780521183789 Paperback
Publication date: February 2011
342 pages
Dimensions: 216 x 140 mm
The purpose of this 1982 book is to present an introduction to developments which had taken place in finite group theory related to finite geometries. This book is practically self-contained and readers are assumed to have only an elementary knowledge of linear algebra. Among other things, complete descriptions of the following theorems are given in this book; the nilpotency of Frobneius kernels, Galois and Burnside theorems on permutation groups of prime degree, the Omstrom?Wagner theorem on projective planes, and the O'Nan and Ito theorems on characterizations of projective special linear groups. Graduate students and professionals in pure mathematics will continue to find this account of value.
Features
Part I. Introduction: 1. Notation and preliminaries
2. Groups
3. Algebraic structures
4. Vector spaces
5. Geometric structures
Part II. Fundamental Properties of Finite Groups: 1. The Sylow theorems
2. Direct products and semi-direct products
3. Normal series
4. Finite Abelian groups
5. p-groups
6. Groups with operators
7. Group extensions and the theorem of Schur?Zassenhaus
8. Normal ƒÎ-complements
9. Normal p-complements
10. Representation of finite groups
11. Frobenius groups
Part III. Fundamental Theory of Permutation Groups: 1. Permutations
2. Transitivity and intransitivity
3. Primitivity and imprimitivity
4. Multiple transitivity
5. Normal subgroups
6. Permutation groups of prime degree
7. Primitive permutation groups
Part IV. Examples - Symmetric Groups and General Linear Groups: 1. Conjugacy classes and composition series of the symmetric and alternating group
2. Conditions for being a symmetric or alternating group
3. Subgroups and automorphism groups of SĦ and AĦ
4. Generators and fundamental relations for Sn and An
5. The structure of general semi-linear groups
6. Properties of PSL(V) as a permutation group (dim V ? 3)
7. Symmetric groups and general linear groups of low order
Part V. Finite Projective Geometry: 1. Projective planes and affine planes
2. Higher-dimensional
projective geometry
3. Characterization of projective geometries
Part VI. Finite Groups and Finite Geometries: 1. Designs constructed from 2-transitive groups
2. Characterization of projective transformation
Epilogue
Index.
Series: Cambridge Monographs on Applied and Computational Mathematics
ISBN: 9780521782401 Hardback
145 b/w illus. 3 colour illus.
Dimensions: 228 x 152 mm
available from March 2011
Accurately predicting the behaviour of multiphase flows is a problem of immense industrial and scientific interest. Modern computers can now study the dynamics in great detail and these simulations yield unprecedented insight. This book provides a comprehensive introduction to direct numerical simulations of multiphase flows for researchers and graduate students. After a brief overview of the context and history the authors review the governing equations. A particular emphasis is placed on the 'one-fluid' formulation where a single set of equations is used to describe the entire flow field and interface terms are included as singularity distributions. Several applications are discussed, showing how direct numerical simulations have helped researchers advance both our understanding and our ability to make predictions. The final chapter gives an overview of recent studies of flows with relatively complex physics, such as mass transfer and chemical reactions, solidification and boiling, and includes extensive references to current work.
Features
* Authors are among the pioneers in the field and have extensive teaching experience * Gives a thorough treatment of the underlying mathematical formulation * Suitable for advanced graduate courses or to get individual students started on their dissertations
Preface
1. Introduction
2. Fluid mechanics with interfaces
3. Numerical solutions of the Navier?Stokes equations
4. Advecting a fluid interface
5. The volume-of-fluid method
6. Advecting marker points - front tracking
7. Surface tension
8. Disperse bubbly flows
9. Atomization and breakup
10. Droplet collision, impact and splashing
11. Extensions
Appendix A. Interfaces: description and definitions
Appendix B. Distributions on the interface
Appendix C. Cube-chopping
Appendix D. Dynamics of liquid sheets
Bibliography
Index.