This IMA Volume in Mathematics and its Applications TOWARDS HIGHER CATEGORIES contains expository and research papers based on a highly successful IMA Summer Program on n-Categories: Foundations and Applications. We are grateful to all the participants for making this occasion a very productive and stimulating one. We would like to thank John C. Baez (Department of Mathematics, University of California Riverside) and J. Peter May (Department of Ma- ematics, University of Chicago) for their superb role as summer program organizers and editors of this volume. We take this opportunity to thank...

Propelled by the success of the sequencing of the human and many related genomes, molecular and cellular biology has delivered significant scientific breakthroughs. Mathematics (broadly defined) continues to play a major role in this effort, helping to discover the secrets of life by working collaboratively with bench biologists, chemists and physicists.

Because of its outstanding record of interdisciplinary research and training, the IMA was an ideal venue for the 2007-2008 IMA thematic year on Mathematics of Molecular and Cellular Biology. The kickoff event for this thematic year...

Many important molecular conformation problems, such as protein folding, are expressed as global minimization problems. It is the fact that local minimization is insufficient, that markedly differentiates this volume from the previous two. Unfortunately, global minimization problems that result from models of molecular conformation are usually intractable. For example, simple 1-dimensional versions of distance conformation problems are NP-hard. Nevertheless, there has been significant recent progress in the design of promising heuristic strategies (often involving the use of high- performance...

Discrete probability theory and the theory of algorithms have become close partners over the last ten years, though the roots of this partnership go back much longer. The papers in this volume address the latest developments in this active field. They are from the IMA Workshops "Probability and Algorithms" and "The Finite Markov Chain Renaissance." They represent the current thinking of many of the world's leading experts in the field.

Researchers and graduate students in probability, computer science, combinatorics, and optimization theory will all be interested in this collection...

This IMA Volume in Mathematics and its Applications DYNAMICAL ISSUES IN COMBUSTION THEORY is based on the proceedings of a workshop which was an integral part of the 1989-90 IMA program on "Dynamical Systems and their Applications." The aim of this workshop was to cross-fertilize research groups working in topics of current interest in combustion dynamics and mathematical methods applicable thereto. We thank Shui-Nee Chow, Martin Golubitsky, Richard McGehee, George R. Sell, Paul Fife, Amable Liiian and Foreman Williams for organizing the meeting. We especially thank Paul Fife, Amable Liiilin...

This IMA Volume in Mathematics and its Applications STATISTICAL MODELS IN EPIDEMIOLOGY, THE ENVIRONMENT, AND CLINICAL TRIALS is a combined proceedings on "Design and Analysis of Clinical Trials" and "Statistics and Epidemiology: Environment and Health. " This volume is the third series based on the proceedings of a very successful 1997 IMA Summer Program on "Statistics in the Health Sciences. " I would like to thank the organizers: M. Elizabeth Halloran of Emory University (Biostatistics) and Donald A. Berry of Duke University (Insti- tute of Statistics and Decision Sciences and Cancer Center...

This IMA Volume in Mathematics and its Applications PATTERN FORMATION IN CONTINUOUS AND COUPLED SYSTEMS is based on the proceedings of a workshop with the same title, but goes be yond the proceedings by presenting a series of mini-review articles that sur vey, and provide an introduction to, interesting problems in the field. The workshop was an integral part of the 1997-98 IMA program on "EMERG ING APPLICATIONS OF DYNAMICAL SYSTEMS." I would like to thank Martin Golubitsky, University of Houston (Math ematics) Dan Luss, University of Houston (Chemical Engineering), and Steven H. Strogatz,...

Mathematical methods play a significant role in the rapidly growing field of nonlinear optical materials. This volume discusses a number of successful or promising contributions. The overall theme of this volume is twofold: (1) the challenges faced in computing and optimizing nonlinear optical material properties; and (2) the exploitation of these properties in important areas of application. These include the design of optical amplifiers and lasers, as well as novel optical switches. Research topics in this volume include how to exploit the magnetooptic effect, how to work with the nonlinear...

This is the eighth volume in the series "Mathematics in Industrial Prob lems." The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots level"; that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob lems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists....

This IMA Volume in Mathematics and its Applications CLASSICAL AND MODERN BRANCHING PROCESSES is based on the proceedings with the same title and was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability." We would like to thank Krishna B. Athreya and Peter J agers for their hard work in organizing this meeting and in editing the proceedings. We also take this opportunity to thank the National Science Foundation, the Army Research Office, and the National Security Agency, whose financial support made this workshop possible. A vner Friedman Robert Gulliver v...