ISBN: 978-0-470-58171-1
Hardcover
360 pages
December 2011
There has been enormous interest and development in Bayesian adaptive designs, especially for early phases of clinical trials. nevertheless, for phase III trials, frequentist methods still play a dominant role through controlling type I and type II errors in the hypothesis testing framework. This book provides an overview of the fundamentals of clinical trials, the key terminologies and concepts, and a brief review and comparison on Bayesian and frequentist estimation and inference procedures. From the practical point of view, this book introduces various statistical methods that are commonly used for designing clinical trials and interim monitoring and analysis. Adaptation has a broad meaning in both Bayesian and frequentist perspectives, such as dose finding, trial early stopping for futility or superiority, dropping or adding an arm, seamless transitions between consecutive phases, group sequential methods, sample size re-estimation, adaptive randomization, and subpopulation enrichment, etc.
Comprehensive discussions on a variety of statistical designs, their properties, and operating characteristics for phase I, II, and III clinical trials are provided, as well as an introduction on phase IV trials. Many practical issues and challenges arising in clinical trials are addressed, and while the book mainly focuses on the Bayesian approaches for phase I and II trial designs, many important frequentist methods for phase III clinical trails are included. In addition, advanced and up-to-date topics such as jointly modeling toxicity and efficacy, seamless phase I/II trial designs, multiple testing, causal inference and noncompliance, adaptive randomization, issues associated with delayed outcomes, dose finding with combined drugs, and targeted therapy designs in personalized medicine development are discussed. Chapter coverage includes Fundamentals of Clinical Trials; Frequentist versus Bayesian Statistics; Phase I, II, and III Trial Designs, Adaptive Randomization, Late-onset Toxicity, Drug-combination Trials, and Targeted Therapy Design.
ISBN: 978-1-1182-0448-1
Hardcover
352 pages
February 2012
Writing with clear knowledge and affection for the subject, the author introduces and explores infinite sets, infinite cardinals, and ordinals, thus challenging the readers' intuitive beliefs about infinity. Requiring little mathematical training and a healthy curiosity, the book presents a user-friendly approach to ideas involving the infinite. Readers will discover the main ideas of infinite cardinals and ordinal numbers without experiencing in-depth mathematical rigor. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun your intuitive view of the world. Infinity, we are told, is as large as things get. This is not entirely true. This book does not refer to infinities, but rather to cardinals. This is to emphasize the point that what you thought you knew about infinity is probably incorrect or imprecise. Since the reader is assumed to be educated in mathematics, but not necessarily mathematically trained, an attempt has been made to convince the reader of the truth of a matter without resorting to the type of rigor found in professional journals. Therefore, the author has accompanied the proofs with illustrative examples. The examples are often a part of a larger proof. Important facts are included and their proofs have been excluded if the author has determined that the proof is beyond the scope of the discussion. For example, it is assumed and not proven within the book that a collection of cardinals is larger than any set or mathematical object. The topics covered within the book cannot be found within any other one book on infinity, and the work succeeds in being the only book on infinite cardinals for the high school educated person. Topical coverage includes: logic and sets; functions; counting infinite sets; infinite cardinals; well ordered sets; inductions and numbers; prime numbers; and logic and meta-mathematics.
Advanced Studies in Pure Mathematics, Volume: 61
2011; 441 pp; hardcover
ISBN-13: 978-4-931469-64-8
In 2007, Professor Akihiro Tsuchiya of Nagoya University reached the retirement age of sixty-three. He has played a significant role in mathematical physics over the decades, most particularly in the foundation of conformal field theory, which was the first nontrivial example of a mathematically rigorous quantum field theory.
This volume contains the proceedings of the international conference on the occasion of his retirement. Included are conformal field theories and related topics such as solvable statistical models, representation theory of affine algebras, monodromy preserving deformations, and string theories. Readers interested in these subjects will find exciting and stimulating insights and questions from these articles.
Graduate students and researchers interested in conformal field theories, representation theory of affine algebras, monodromy preserving deformations, and string theories.
K. Nagatomo and A. Tsuchiya -- The triplet vertex operator algebra W(p) and the restricted quantum group bar{U}_q(sl_2) at q=e^{pi i/p}
T. Arakawa -- Representation theory of W-algebras, II
V. V. Bazhanov -- Chiral Potts model and the discrete Sine-Gordon model at roots of unity
T. Eguchi, Y. Sugawara, and A. Taormina -- Modular forms and elliptic genera for ALE spaces
B. Feigin, E. Feigin<, and I. Tipunin -- Fermionic formulas for characters of (1,p) logarithmic model in Phi_{2,1} quasiparticle realisation
B. Feigin< and E. Frenkel -- Quantization of soliton systems and Langlands duality
K. Hasegawa< -- Quantizing the Backlund transformations of Painleve equations and the quantum discrete Painleve VI equation
G. Kuroki -- Quantum groups and quantization of Weyl group symmetries of Painleve systems
W. Nakai and T. Nakanishi -- On Frenkel-Mukhin algorithm for q-character of quantum affine algebras
H. Nakajima and K. Yoshioka -- Perverse coherent sheaves on blow-up. I. A quiver description
K. Takasaki -- Differential Fay identities and auxiliary linear problem of integrable hierarchies
ISBN: 978-81-8487-162-3
Publication Year: 2011
Pages: 166
Binding: Hard Back
Dimension: 160mm x 240mm
Geometric Invariant Theory (GIT), developed in the 1960s by David Mumford, is the theory of quotients by group actions in Algebraic Geometry. Its principal application is to the construction of various moduli spaces. Peter Newstead gave a series of lectures in 1975 at the Tata Institute of Fundamental Research, Mumbai on GIT and its application to the moduli of vector bundles on curves. It was a masterful yet easy to follow exposition of important material, with clear proofs and many examples. The notes, published as a volume in the TIFR lecture notes series, became a classic, and generations of algebraic geometers working in these subjects got their basic introduction to this area through these lecture notes. Though continuously in demand, these lecture notes have been out of print for many years. The Tata Institute is happy to re-issue these notes in a new print.
Preliminaries / The Concept of Moduli: Families / Moduli Spaces / Remarks / Endomorphisms of Vector Spaces: Families of Endomorphisms / Semi-Simple Endomorphisms / Cyclic Endomorphisms / Moduli and Quotients / Quotients: Actions of Algebraic Groups / Proof of Theorem / Affine Quotients / Linearisation / Historical Note / Examples: Elementary Examples / A Criterion for Stability / Binary Forms / Plane Cubics / N Ordered Points on a Line / Sequences of Linear Subspaces / Vector Bundles Over a Curve: Generalities and Historical Remarks / Coherent Sheaves Over X / Locally Universal Families for Semi-stable Bundles / Construction of the Quotient / Existence of a Fine Moduli Space / Proof of Theorem / Bundles Over a Singular Curve / Bibliography / List of Symbols / Index.
Postgraduate Students, Teachers & Researchers in Mathematics
ISBN13: 9780199740444
Paperback, 280 pages
Sep 2011,
While many think of algorithms as specific to computer science, at its core algorithmic thinking is defined by the use of analytical logic to solve problems. This logic extends far beyond the realm of computer science and into the wide and entertaining world of puzzles. In Algorithmic Puzzles, Anany and Maria Levitin use many classic brainteasers as well as newer examples from job interviews with major corporations to show readers how to apply analytical thinking to solve puzzles requiring well-defined procedures.
The book's unique collection of puzzles is supplemented with carefully developed tutorials on algorithm design strategies and analysis techniques intended to walk the reader step-by-step through the various approaches to algorithmic problem solving. Mastery of these strategies--exhaustive search, backtracking, and divide-and-conquer, among others--will aid the reader in solving not only the puzzles contained in this book, but also others encountered in interviews, puzzle collections, and throughout everyday life. Each of the 150 puzzles contains hints and solutions, along with commentary on the puzzle's origins and solution methods.
The only book of its kind, Algorithmic Puzzles houses puzzles for all skill levels. Readers with only middle school mathematics will develop their algorithmic problem-solving skills through puzzles at the elementary level, while seasoned puzzle solvers will enjoy the challenge of thinking through more difficult puzzles.
The only puzzle book to focus on algorithmic puzzles
Interprets puzzle solutions as illustrations of general methods of algorithmic problem solving
Contains a tutorial explaining the main ideas of algorithm design and analysis for a general reader
Preface
List of Puzzles
Tutorial Puzzles
Main Section Puzzles
1. Tutorials
General Strategies for Algorithm Design
Analysis Techniques
2. Puzzles
Easier Puzzles (#1 - #50)
Medium Dic culty Puzzles (51 - 110)
Harder Puzzles (#111 - 150)
3. Hints
4. Solutions
References
Design Strategy and Analysis Index
Index of Terms and Names