Series: Cambridge Monographs on Applied and Computational
Mathematics (No. 23)
Hardback (ISBN-13: 9780521863704 | ISBN-10: 0521863708)
Many applications in science and engineering require a digital
model of a real physical object. Advanced scanning technology has
made it possible to scan such objects and generate point samples
on their boundaries. This book shows how to compute a digital
model from this point sample. After developing the basics of
sampling theory and its connections to various geometric and
topological properties, the author describes a suite of
algorithms that have been designed for the reconstruction
problem, including algorithms for surface reconstruction from
dense samples, from samples that are not adequately dense and
from noisy samples. Voronoi and Delaunay based techniques,
implicit surface based methods and Morse theory based methods are
covered. Scientists and engineers working in drug design, medical
imaging, CAD, GIS, and many other areas will benefit from this
first book on the subject.
* Provides fundamentals of point cloud data processing
* Algorithms with correctness proofs are presented
* Many figures, a set of exercises, and a brief history for each
chapter
Contents
1. Basics; 2. Curve reconstruction; 3. Surface samples; 4.
Surface reconstruction; 5. Undersampling; 6. Watertight
reconstructions; 7. Noisy Samples; 8. Noise and reconstruction; 9.
Implicit surface based reconstructions; 10. Morse theoretic
reconstructions.
Series: Cambridge Series in Statistical and Probabilistic
Mathematics (No. 20)
Hardback (ISBN-13: 9780521866569 | ISBN-10: 0521866561)
The notion of six degrees of separation - that any two people on
the planet can be connected by a short chain of people - inspired
Strogatz and Watts to define the small world random graph, where
each site is connected to close neighbours, but also has long
range connections. At about the same time, it was observed in
human social networks and on the internet that the number of
neighbours of an individual has a power law distribution. This
inspired Barabasi and Albert to define the preferential
attachment model, which has these properties. These two papers
led to an explosion of research, but much was nonrigorous and
relied on simulations. This book uses mathematical arguments to
obtain insights into these graphs. A unique feature of this book
is the interest in the dynamics of process taking place on the
graphs in addition to their geometric properties, like
correctness and diameter.
* The treatment exposes the reader to a wide variety of topics in
probability theory and mathematical techniques
* A number of open ended problems are mentioned
* The exposition concentrates on ideas behind proofs rather than
technical details
Contents
1. Overview; 2. Erdos-Renyi random graphs; 3. Fixed degree
distributions; 4. Power laws; 5. Small worlds; 6. Random walks; 7.
CHKNS model.
Series: Cambridge Monographs on Applied and Computational
Mathematics (No. 21)
Hardback (ISBN-13: 9780521792110 | ISBN-10: 0521792118)
Spectral methods are well-suited to solve problems modeled by
time-dependent partial differential equations: they are fast,
efficient and accurate and widely used by mathematicians and
practitioners. This class-tested introduction, the first on the
subject, is ideal for graduate courses, or self-study. The
authors describe the basic theory of spectral methods, allowing
the reader to understand the techniques through numerous examples
as well as more rigorous developments. They provide a detailed
treatment of methods based on Fourier expansions and orthogonal
polynomials (including discussions of stability, boundary
conditions, filtering, and the extension from the linear to the
nonlinear situation). Computational solution techniques for
integration in time are dealt with by Runge-Kutta type methods.
Several chapters are devoted to material not previously covered
in book form, including stability theory for polynomial methods,
techniques for problems with discontinuous solutions, round-off
errors and the formulation of spectral methods on general grids.
These will be especially helpful for practitioners.
* Ideal for both graduate students and practitioners, including
both basic theory and more rigorous developments
* Written from material which has been thoroughly and
successfully class-tested by experienced authors
* No other text in print deals with this topic at a fundamental
level and it includes material never before covered in book form
Contents
Introduction; 1. From local to global approximation; 2.
Trigonometric polynomial approximation; 3. Fourier spectral
methods; 4. Orthogonal polynomials; 5. Polynomial expansions; 6.
Polynomial approximations theory for smooth functions; 7.
Polynomial spectral methods; 8. Stability of polynomial spectral
methods; 9. Spectral methods for non-smooth problems; 10.
Discrete stability and time integration; 11. Computational
aspects; 12. Spectral methods on general grids; Bibliography.
Paperback (ISBN-13: 9780521033114 | ISBN-10: 052103311X)
The control and data flow of a program can be represented using
continuations, a concept from denotational semantics that has
practical application in real compilers. This book shows how
continuation-passing style is used as an intermediate
representation on which to perform optimisations and program
transformations. Continuations can be used to compile most
programming languages. The method is illustrated in a compiler
for the programming language Standard ML. However, prior
knowledge of ML is not necessary, as the author carefully
explains each concept as it arises. This is the first book to
show how concepts from the theory of programming languages can be
applied to the producton of practical optimising compilers for
modern languages like ML. This book will be essential reading for
compiler writers in both industry and academe, as well as for
students and researchers in programming language theory.
* Shows how continuations can be used to compile most programming
languages
* The method is illustrated with examples from the language
Standard ML
* All the nitty-gritty details of copilation to really good
machine code are covered
* Will be essential reading for compilers in industry and academe
Contents
Acknowledgments; 1. Overview; 2. Continuation-passing style; 3.
Semantics of the CPS; 4. ML-specific optimizations; 5. Conversion
into CPS; 6. Optimization of the CPS; 7. Beta-expansion; 8.
Hoisting; 9. Common subexpressions; 10. Closure conversion; 11.
Register spilling; 12. Space complexity; 13. The abstract
machine; 14. Machine code generation; 15. Performance evaluation;
16. The runtime system; 17. Parallel programming; 18. Future
directions.
Series: Mathematics, Finance and Risk (No. 5)
Hardback (ISBN-13: 9780521861700 | ISBN-10: 0521861705)
Optimization models play an increasingly important role in
financial decisions. This is the first textbook devoted to
explaining how recent advances in optimization models, methods
and software can be applied to solve problems in computational
finance more efficiently and accurately. Chapters discussing the
theory and efficient solution methods for all major classes of
optimization problems alternate with chapters illustrating their
use in modeling problems of mathematical finance. The reader is
guided through topics such as volatility estimation, portfolio
optimization problems and constructing an index fund, using
techniques such as nonlinear optimization models, quadratic
programming formulations and integer programming models
respectively. The book is based on Master's courses in financial
engineering and comes with worked examples, exercises and case
studies. It will be welcomed by applied mathematicians,
operational researchers and others who work in mathematical and
computational finance and who are seeking a text for self-learning
or for use with courses.
* The book is based on a successful Master's course at Carnegie
Mellon University and comes with worked examples, exercises and
case studies
* Cutting edge material - chapters on conic and robust
optimization are unique for any optimization text
* Ideal for applied mathematicians, operational researchers and
others working in mathematical and computational finance
* The chapters alternate between operational research and
financial applications, which is a unique approach
Contents
1. Introduction; 2. Linear programming: theory and algorithms; 3.
LP models: asset/liability cash flow matching; 4. LP models:
asset pricing and arbitrage; 5. Nonlinear programming: theory and
algorithms; 6. NLP volatility estimation; 7. Quadratic
programming: theory and algorithms; 8. QP models: portfolio
optimization; 9. Conic optimization tools; 10. Conic optimization
models in finance; 11. Integer programming: theory and
algorithms; 12. IP models: constructing an index fund; 13.
Dynamic programming methods; 14. DP models: option pricing; 15.
DP models: structuring asset backed securities; 16. Stochastic
programming: theory and algorithms; 17. SP models: value-at-risk;
18. SP models: asset/liability management; 19. Robust
optimization: theory and tools; 20. Robust optimization models in
finance; Appendix A. Convexity; Appendix B. Cones; Appendix C. A
probability primer; Appendix D. The revised simplex method;
Bibliography; Index.