Hardback
ISBN:9781107005044
103 b/w illus.
Dimensions: 246 x 189 mm
available from March 2012
Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to topological quantum computation. The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way. Relevant calculations are fully explained, and numerous worked examples and exercises support and aid understanding. Special emphasis is given to the motivation and physical intuition behind every mathematical concept. Demystifying difficult topics by using accessible language, this book has broad appeal and is ideal for graduate students and researchers from various disciplines who want to get into this new and exciting research field.
* First authored book on the subject of topological quantum computing; combines a variety of different topics for the first time
* Keeps high-level and technical language to a minimum, making the book accessible to non-specialists and to researchers from a variety of sub-disciplines
* Includes detailed calculations of many essential cases, along with numerous examples and exercises to support understandingPrinter Friendly Version
Part I. Preliminaries: 1. Introduction
2. Geometric and topological phases
3. Quantum computation
4. Computational power of anyons
Part II. Topological Models: 5. Quantum double models
6. Kitaev's honeycomb lattice model
7. Chern?Simons quantum field theories
Part III. Quantum Information Perspectives: 8. The Jones polynomial algorithm
9. Topological entanglement entropy
10. Outlook
Index.
Hardback
Series: Institute of Mathematical Statistics Monographs(No. 2)
ISBN:9781107019584
20 b/w illus.
Dimensions: 228 x 152 mm
available from March 2012
This book introduces in a systematic manner a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important and varied applications in medical diagnostics, image analysis, and machine vision. An early chapter of examples establishes the effectiveness of the new methods and demonstrates how they outperform their parametric counterparts. Inference is developed for both intrinsic and extrinsic Frechet means of probability distributions on manifolds, then applied to shape spaces defined as orbits of landmarks under a Lie group of transformations
in particular, similarity, reflection similarity, affine and projective transformations. In addition, nonparametric Bayesian theory is adapted and extended to manifolds for the purposes of density estimation, regression and classification. Ideal for statisticians who analyze manifold data and wish to develop their own methodology, this book is also of interest to probabilists, mathematicians, computer scientists and morphometricians with mathematical training.
1. Introduction
2. Examples
3. Location and spread on metric spaces
4. Extrinsic analysis on manifolds
5. Intrinsic analysis on manifolds
6. Landmark-based shape spaces
7. Kendall's similarity shape spaces ƒ°km
8. The planar shape space ƒ°k2
9. Reflection similarity shape spaces Rƒ°km
10. Stiefel manifolds
11. Affine shape spaces Aƒ°km
12. Real projective spaces and projective shape spaces
13. Nonparametric Bayes inference
14. Regression, classification and testing
i. Differentiable manifolds
ii. Riemannian manifolds
iii. Dirichlet processes
iv. Parametric models on Sd and ƒ°k2
References
Subject index.
Afterword: John F. TuringForeword: Lyn Irvine
Hardback
ISBN:9781107020580
7 b/w illus.
Dimensions: 228 x 152 mm
available from March 2012
In a short life he accomplished much, and to the roll of great names in the history of his particular studies added his own.' So is described one of the greatest figures of the twentieth century, yet Alan Turing's name was not widely recognised until his contribution to the breaking of the German Enigma code became public in the 1970s. The story of Turing's life fascinates and in the years since his suicide, Turing's reputation has only grown, as his contributions to logic, mathematics, computing, artificial intelligence and computational biology have become better appreciated. To commemorate the centenary of Turing's birth, this republication of his mother's biography is enriched by a new foreword by Martin Davis and a never-before-published memoir by Alan's older brother. The contrast between this memoir and the original biography reveals tensions and sheds new light on Turing's relationship with his family, and on the man himself.
* Never-before-published contribution from Alan's brother, John Turing
* Unique personal insights from family, friends, teachers and colleagues
* Charts Turing's life from early childhood through to his death in 1954
Foreword to the Second Edition Martin Davis
Foreword to the First Edition Lyn Irvine
Preface
Part I. Mainly Biographical: 1. Family background
2. Childhood and early boyhood
3. At Sherborne school
4. At Cambridge
5. At the Graduate College, Princeton
6. Some characteristics
7. War work in the foreign office
8. At the National Physical Laboratory, Teddington
9. Work with the Manchester Automatic Digital Machine
10. Morphogenesis
11. Relaxation
12. Last days and some tributes
Part II. Containing Computing Machinery and Morphogenesis: 13. Computing machinery
14. Chemical theory of morphogenesis considered
Afterword John Turing
Bibliography
Index.
Series: De Gruyter Textbook
(to be published May 2012)
Contains proofs including intermediate steps and necessary explanations to make them easily understandable
Written by an applied person for the applied community
Serves as a reference-cum-text book of the applied people
This book grew out of a course taught in the Department of Mathematics, Indian Institute of Technology, Delhi, which was tailored to the needs of the applied community of mathematicians, engineers, physicists etc., who were interested to study the problems of mathematical physics in general and their approximate solutions on computer in particular.
Almost all topics which will be essential for the study of Sobolev spaces and their applications in the elliptic boundary value problems and their finite element approximations are presented. Also many additional topics of interests for specific applied disciplines and engineering, for example, elementary solutions, derivatives of discontinuous functions of several variables, delta-convergent sequences of functions, Fourier series of distributions, convolution system of equations etc. have been included along with many interesting examples.
Series: De Gruyter Series in Nonlinear Analysis and Applications 16
(to be published May 2012)
This monograph aims to give a self-contained introduction into the whole field of topological analysis: Requiring essentially only basic knowledge of elementary calculus and linear algebra, it provides all required background from topology, analysis, linear and nonlinear functional analysis, and multivalued maps, containing even basic topics like separation axioms, inverse and implicit function theorems, the Hahn-Banach theorem, Banach manifolds, or the most important concepts of continuity of multivalued maps. Thus, it can be used as additional material in basic courses on such topics. The main intention, however, is to provide also additional information on some fine points which are usually not discussed in such introductory courses.
The selection of the topics is mainly motivated by the requirements for degree theory which is presented in various variants, starting from the elementary Brouwer degree (in Euclidean spaces and on manifolds) with several of its famous classical consequences, up to a general degree theory for function triples which applies for a large class of problems in a natural manner. Although it has been known to specialists that, in principle, such a general degree theory must exist, this is the first monograph in which the corresponding theory is developed in detail.
Series: De Gruyter Studies in Mathematical Physics 4
(to be published September 2012)
Conveys a thorough treatment of the Dirac equations and their applications
This work is a must-have for scientists involved with relativistic quantum mechanics and quantum electrodynamics
Offers rigorous treatment of the underlying equations
Written by an highly experienced book author
Dirac equations are of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly.
In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.