Hardback (ISBN-13: 9780521880237)
15 line diagrams 39 exercises
Page extent: 240 pages
Size: 247 x 174 mm
Supersymmetry represents the culmination of the search for fundamental symmetries that has dominated particle physics for 50 years. Traditionally, the constituents of matter (fermions) were regarded as different from the particles (bosons) transmitting the forces between them. In supersymmetry, fermions and bosons are unified. Intended for graduate students in particle physics, and researchers in experimental and phenomenological supersymmetry, this is the first textbook to provide a simple introduction to a previously formidably technical field. Its elementary, practical treatment brings readers to the frontier of contemporary research, in particular the experiments at the Large Hadron Collider. Theories are constructed through an intuitive 'trial and error' approach. Basic elements of spinor formalism and superfields are introduced, allowing readers to access more advanced treatments. Emphasis is placed on physical understanding, and on detailed derivations of important steps. Many short exercises are included, making for a valuable and accessible self-study tool.
* Builds on information from standard relativistic quantum mechanics courses, and also introduces new topics from scratch, so useful to readers at all levels * Constructs theories using a ‘trial-and-error’ approach rather than a formal deductive one, allowing for an intuitive understanding of this formal subject * Contains many short exercises that are useful for self-study
Contents
1. Introduction and motivation; 2. Spinors: Weyl, Dirac and Majorana; 3. A simple supersymmetric Lagrangian, and a first glance at the MSSM; 4. The supersymmetry algebra and supermultiplets; 5. The Wess-Zumino model; 6. Superfields; 7. Vector (or gauge) supermultiplets; 8. The MSSM; 9. SUSY breaking; 10. The Higgs sector and electroweak symmetry breaking in the MSSM; 11. Sparticle masses in the MSSM; 12. Some simple tree-level calculations in the MSSM; References; Index.
Series: Frontiers in Applied Mathematics (No. 34)
Paperback (ISBN-13: 9780898716177)
Page extent: 292 pages
Size: 228 x 152 mm
Weight: 0.536 kg
This volume brings together the range of control processes involved in the effective regulation of human cardiovascular and respiratory control systems and develops modelling themes, strategies, and key clinical applications using contemporary mathematical and control methodologies. Readers will gain an appreciation of how analytical techniques and ideas from optimal control theory, systems theory and numerical analysis can be utilized to better understand the regulation processes in these systems.
Contents
Preface; 1. The cardiovascular system under an ergometric workload; 2. Respiratory modeling; 3. Cardio-Respiratory Modeling; 4. Blood volume and the venous system; 5. Future directions; Appendix A. Supplemental calculations; B. A Nonlinear feedback law; C. Retarded functional differential equations: Basic theory; Bibliography; Index.
Series: Lecture Notes in Logic (No. 28)
Hardback (ISBN-13: 9780521884259)
3 tables
Page extent: 288 pages
Size: 228 x 152 mm
The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of recent developments, and the rest of the papers are chosen to complement the invited talks. This volume includes surveys, tutorials, and selected research papers from the 2005 meeting. Highlights include three papers on different aspects of connections between model theory and algebra; a survey of recent major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of Bernay's philosophy of mathematics.
Contents
1. Thread algebra and risk assessment services Jan A. Bergstra, Inge Bethke, and Alban Ponse; 2. Covering definable manifolds by open definable subsets Mario J. Edmundo; 3. Isomorphisms and definable relations on computable models Sergei S. Goncharov; 4. Independence for types in algebraically closed valued fields Deirdre Haskell; 5. Simple groups of finite Morley rank Eric Jaligot; 6. Towards a logic of type-free modality and truth Hannes Leitgeb; 7. Structural analysis of Aronszajn trees Justin Tatch Moore; 8. Proof analysis in non-classical logics Sara Negri; 9. Paul Bernays' later philosophy of mathematics Charles Parsons; 10. Proofnets for S5: sequents and circuits for modal logic Greg Restall; 11. Recursion on the partial continuous functionals Helmut Schwichtenberg; 12. A transactional approach to the logic of truth Michael Sheard; 13. On some problems in computable topology Dieter Spreen; 14. Monotone inductive definitions and consistency of New Foundations Sergei Tupailo.
Hardback (ISBN-13: 9780521872829)
36 line diagrams
Page extent: 760 pages
Size: 253 x 177 mm
In the last few years game theory has had a substantial impact on computer science, especially on Internet- and e-commerce-related issues. Algorithmic Game Theory develops the central ideas and results of this new and exciting area in a clear and succinct manner. More than 40 of the top researchers in this field have written chapters that go from the foundations to the state of the art. Basic chapters on algorithmic methods for equilibria, mechanism design and combinatorial auctions are followed by chapters on important game theory applications such as incentives and pricing, cost sharing, information markets and cryptography and security. This definitive work will set the tone of research for the next few years and beyond. Students, researchers, and practitioners alike need to learn more about these fascinating theoretical developments and their widespread practical application.
* First book to cover the whole spectrum of algorithmic game theory * Contributions by all the major researchers in the field * Applied chapters by researchers and consultants at major firms such as Yahoo, Lehman Brothers, IBM and Microsoft
Contents
Introduction Noam Nisan, Tim Roughgarden, Eva Tardos and Vijay V. Vazirani; Part I. Computing in Games: 1. Basic solution concepts and computational issues Eva Tardos and Vijay V. Vazirani; 2. Algorithms for equilibria Christos Papadimitriou; 3. Equilibrium computation for games in strategic and extensive form Bernhard von Stengel; 4. Learning, regret minimization and correlated equilibria Avrim Blum and Yishay Mansour; 5. Graphical games Michael J. Kearns; 6. Cryptography and game theory Yevgeniy Dodis and Tal Rabin; 7. Combinatorial algorithms for market equilibria Vijay V. Vazirani; 8. Computation of market equilibria by convex programming Bruno Codenotti and Kasturi Varadarajan; Part II. Algorithmic Mechanism Design: 9. Introduction to mechanism design (for computer scientists) Noam Nisan; 10. Mechanism design without money James Schummer and Rakesh V. Vohra; 11. Combinatorial auctions Noam Nisan and Liad Blumrosen; 12. Computationally efficient approximation mechanisms Ron Lavi; 13. Profit maximization in mechanism design Jason Hartline and Anna Karlin; 14. Distributed algorithmic mechanism design Joan Feigenbaum, Michael Schapira and Scott Shenker; 15. Cost sharing Kamal Jain and Mohammad Mahdian; 16. On-line mechanisms David C. Parkes; Part III. Quantifying the Inefficiency of Equilibria: 17. Introduction to the inefficiency of equilibria Tim Roughgarden and Eva Tardos; 18. Routing games Tim Roughgarden; 19. Inefficiency of equilibria in network formation games Eva Tardos and Tom Wexler; 20. Selfish load-balancing Berthold Vocking; 21. Efficiency loss and the design of scalable resource allocation mechanisms Ramesh Johari; Part IV. Additional Topics: 22. Incentives and pricing in communication networks Asuman Ozdaglar and R. Srikant; 23. Incentives in peer-to-peer systems John Chuang, Michal Feldman and Moshe Babaioff; 24. Cascading behavior in networks: algorithmic and economic issues Jon Kleinberg; 25. Incentives and information security Ross Anderson, Tyler Moore, Shishir Nagaraja and Andy Ozment; 26. Computational aspects of information markets David M. Pennock and Rahul Sami; 27. Manipulation-resistant reputation systems Eric Friedman, Paul Resnick and Rahul Sami; 28. Sponsored search auctions Sebastien Lahaie, David M. Pennock, Amin Saberi and Rakesh V. Vohra; 29. Algorithmic issues in evolutionary game theory Michael Kearns and Siddharth Suri.
Paperback (ISBN-13: 9780521714778)
81 line diagrams 8 tables
Page extent: 283 pages
Size: 247 x 174 mm
Weight: 0.463 kg
This book describes the application of statistical physics and complex systems theory to the study of the evolution and structure of the Internet. Using a statistical physics approach the Internet is viewed as a growing system that evolves in time through the addition and removal of nodes and links. This perspective permits us to outline the dynamical theory required for a description of the macroscopic evolution of the Internet. The presence of such a theoretical framework appears to be a revolutionary and promising path towards our understanding of the Internet and the various processes taking place on this network, including, for example, the spread of computer viruses or resilience to random or intentional damages. This book will be of interest to graduate students and researchers in statistical physics, computer science and mathematics studying in this subject.
* Statistical physics and complex systems theory applied to the understanding of the Internet physical structure * Interdisciplinary approach to the study of the global Internet * A comprehensive presentation of the scientific characterization of the Internet
Contents
Preface; List of abbreviations; 1. A brief history of the Internet; 2. How the Internet works; 3. Measuring the global Internet; 4. The Internet's large-scale topology; 5. Modeling the Internet; 6. Internet robustness; 7. Virtual and social networks in the Internet; 8. Searching and walking on the Internet; 9. Epidemics in the Internet; 10. Beyond the Internet’s skeleton: traffic and global performance; 11. Outlook; Appendix I: graph theory applied to topology analysis; Appendix II: interface resolution and router topology; Appendix III: numerical analysis of heavy-tailed distributions; Appendix IV: degree correlations; Appendix V: scale-free networks: scaling relations; Appendix VI: the SIR model of virus propagation; References; Index.
Paperback (ISBN-13: 9780898716399)
Page extent: 450 pages
Size: 247 x 174 mm
This book provides a unified and accessible introduction to the basic theory of finite difference schemes applied to the numerical solution of partial differential equations. Originally published in 1989, its objective remains to clearly present the basic methods necessary to perform finite difference schemes and to understand the theory underlying these schemes. This is one of the few texts in the field to not only present the theory of stability in a rigorous and clear manner but also to discuss the theory of initial-boundary value problems in relation to finite difference schemes. In this updated edition the notion of a stability domain is now included in the definition of stability and is more prevalent throughout the book. The author has also added many new figures and tables to clarify important concepts and illustrate the properties of finite difference schemes.
* Provides an introduction that will enable students to progress to more advanced texts and to knowledgeably implement the basic methods ? Researchers in numerical analysis also will find it a useful reference for studying stability theory for finite difference schemes applied to linear partial differential equations * The author has added many new figures and tables to clarify important concepts and illustrate the properties of finite difference schemes
Contents
Preface to the second edition; Preface to the first edition; 1. Hyperbolic partial differential equations; 2. Analysis of finite difference Schemes; 3. Order of accuracy of finite difference schemes; 4. Stability for multistep schemes; 5. Dissipation and dispersion; 6. Parabolic partial differential equations; 7. Systems of partial differential equations in higher dimensions; 8. Second-order equations; 9. Analysis of well-posed and stable problems; 10. Convergence estimates for initial value problems; 11. Well-posed and stable initial-boundary value problems; 12. Elliptic partial differential equations and difference schemes; 13. Linear iterative methods; 14. The method of steepest descent and the conjugate gradient method; Appendix A. Matrix and vectoranalysis; Appendix B. A survey of real analysis; Appendix C. A Survey of results from complex analysis; References; Index.
Series: Cambridge Monographs on Mathematical Physics
Hardback (ISBN-13: 9780521842631)
25 line diagrams
Page extent: 784 pages
Size: 247 x 174 mm
Modern physics rests on two fundamental building blocks: general relativity and quantum theory. General relativity is a geometric interpretation of gravity while quantum theory governs the microscopic behaviour of matter. Since matter is described by quantum theory which in turn couples to geometry, we need a quantum theory of gravity. In order to construct quantum gravity one must reformulate quantum theory on a background independent way. Modern Canonical Quantum General Relativity provides a complete treatise of the canonical quantisation of general relativity. The focus is on detailing the conceptual and mathematical framework, on describing physical applications and on summarising the status of this programme in its most popular incarnation, called loop quantum gravity. Mathematical concepts and their relevance to physics are provided within this book which therefore can be read by graduate students with basic knowledge of quantum field theory or general relativity.
* Discusses all aspects of theory from the foundations to the frontiers of current research * Contains mathematical precision which reaches new levels of rigour * Designed to be an absolute reference text on the subject
Contents
Preface; Notation and conventions; Introduction; Part I. Classical Foundations, Interpretation and the Canonical Quantisation Programme: 1. Classical Hamiltonian formulation of general relativity; 2. The problem of time, locality and the interpretation of quantum mechanics; 3. The programme of canonical quantisation; 4. The new canonical variables of Ashtekar for general relativity; Part II. Foundations of Modern Canonical Quantum General Relativity: 5. Introduction; 6. Step I: the holonomy-flux algebra [P]; 7. Step II: quantum -algebra; 8. Step III: representation theory of [A]; 9. Step IV: 1. Implementation and solution of the kinematical constraints; 10. Step V: 2. implementation and solution of the Hamiltonian constraint; 11. Step VI: semiclassical analysis; Part III. Physical Applications: 12. Extension to standard matter; 13. Kinematical geometrical operators; 14. Spin foam models; 15. Quantum black hole physics; 16. Applications to particle physics and quantum cosmology; 17. Loop quantum gravity phenomenology; Part IV. Mathematical Tools and their Connection to Physics: 18. Tools from general topology; 19. Differential, Riemannian, symplectic and complex geometry; 20. Semianalytical category; 21. Elements of fibre bundle theory; 22. Holonomies on non-trivial fibre bundles; 23. Geometric quantisation; 24. The Dirac algorithm for field theories with constraints; 25. Tools from measure theory; 26. Elementary introduction to Gel’fand theory for Abelean C* algebras; 27. Bohr compactification of the real line; 28. Operatir -algebras and spectral theorem; 29. Refined algebraic quantisation (RAQ) and direct integral decomposition (DID); 30. Basics of harmonic analysis on compact Lie groups; 31. Spin network functions for SU(2); 32. + Functional analytical description of classical connection dynamics;