High performance computing consumes and generates vast amounts of data, and the storage, retrieval, and transmission of this data are major obstacles to effective use of computing power. Challenges inherent in all of these operations are security, speed, reliability, authentication and reproducibility. This workshop focused on a wide variety of technical results aimed at meeting these challenges. Topics ranging from the mathematics of coding theory to the practicalities of copyright preservation for Internet resources drew spirited discussion and interaction among experts in diverse but related fields. We hope this volume contributes to continuing this dialogue.

In information retrieval, Latent Semantic Mapping enables retrieval on the basis of conceptual content instead of merely matching words between queries and documents. It operates under the assumption that there is some latent semantic structure in the data, which is partially obscured by the randomness of word choice with respect to retrieval. Algebraic and/or statistical techniques are brought to bear to estimate this structure and get rid of the obscuring "noise." This results in a parsimonious continuous parameter description of words and documents, which then replaces the original parameterization in indexing and retrieval.This monograph gives a general overview of the framework and underscores the multi-faceted benefits it can bring to a number of problems in natural language understanding and spoken language processing. It concludes with a discussion of the inherent trade-offs associated with the approach and some perspectives on its general applicability to unsupervised information extraction.

This 121st IMA volume, entitled MATHEMATICAL MODELS FOR BIOLOGICAL PATTERN FORMATION is the first of a new series called FRONTIERS IN APPLICATION OF MATHEMATICS. The FRONTIERS volumes are motivated by IMA pro grams and workshops, but are specially planned and written to provide an entree to and assessment of exciting new areas for the application of mathematical tools and analysis. The emphasis in FRONTIERS volumes is on surveys, exposition and outlook, to attract more mathematicians and other scientists to the study of these areas and to focus efforts on the most important issues, rather than papers on the most recent research results aimed at an audience of specialists. The present volume of peer-reviewed papers grew out of the 1998-99 IMA program on "Mathematics in Biology," in particular the Fall 1998 em phasis on "Theoretical Problems in Developmental Biology and Immunol ogy." During that period there were two workshops on Pattern Formation and Morphogenesis, organized by Professors Murray, Maini and Othmer. James Murray was one of the principal organizers for the entire year pro gram. I am very grateful to James Murray for providing an introduction, and to Philip Maini and Hans Othmer for their excellent work in planning and preparing this first FRONTIERS volume. I also take this opportunity to thank the National Science Foundation, whose financial support of the IMA made the Mathematics in Biology pro gram possible.

This IMA Volume in Mathematics and its Applications MATHEMATICAL APPROACHES FOR EMERGING AND REEMERGING INFECTIOUS DISEASES: MODELS, AND THEORY METHODS is based on the proceedings of a successful one week workshop. The pro ceedings of the two-day tutorial which preceded the workshop "Introduction to Epidemiology and Immunology" appears as IMA Volume 125: Math ematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction. The tutorial and the workshop are integral parts of the September 1998 to June 1999 IMA program on "MATHEMATICS IN BI OLOGY. " I would like to thank Carlos Castillo-Chavez (Director of the Math ematical and Theoretical Biology Institute and a member of the Depart ments of Biometrics, Statistics and Theoretical and Applied Mechanics, Cornell University), Sally M. Blower (Biomathematics, UCLA School of Medicine), Pauline van den Driessche (Mathematics and Statistics, Uni versity of Victoria), and Denise Kirschner (Microbiology and Immunology, University of Michigan Medical School) for their superb roles as organizers of the meetings and editors of the proceedings. Carlos Castillo-Chavez, es pecially, made a major contribution by spearheading the editing process. I am also grateful to Kenneth L. Cooke (Mathematics, Pomona College), for being one of the workshop organizers and to Abdul-Aziz Yakubu (Mathe matics, Howard University) for serving as co-editor of the proceedings. I thank Simon A. Levin (Ecology and Evolutionary Biology, Princeton Uni versity) for providing an introduction.

The 1995-1996 program at the Institute for Mathematics and its Applications was devoted to mathematical methods in material science, and was attended by materials scientists, physicists, geologists, chemists engineers, and mathematicians. This volume contains chapters which emerged from four of the workshops, focusing on disordered materials; interfaces and thin films; mechanical response of materials from angstroms to meters; and phase transformation, composite materials and microstructure. The scales treated in these workshops ranged from the atomic to the macroscopic, the microstructures from ordered to random, and the treatments from "purely" theoretical to highly applied. Taken together, these results form a compelling and broad account of many aspects of the science of multi-scale materials, and will hopefully inspire research across the self-imposed barriers of twentieth century science.

The chapters in this book present an excellent exposition of recent developments in both robotics and nonlinear control centering around "hyper-redundancy", highly oscillatory inputs, optimal control, exterior differential systems, and the use of generic loops. The principal topics covered in the book are: adaptive control for a class of nonlinear systems, event-based motion planning, nonlinear control synthesis and path planning in robotics with special emphasis on nonholonomic and "hyper-redundant" robotic systems, control design and stabilization of driftless affine control systems (of the type arising in the kinematic control of nonholonomic robotic systems), control design methods for Hamiltonian systems and exterior differential systems. The chapter covering exterior differential systems contains a detailed introduction to the use of exterior differential methods, including the Goursat and extended Goursat normal forms and their application to path planning for nonholonomic systems.

Coding theory, system theory, and symbolic dynamics have much in common. A major new theme in this area of research is that of codes and systems based on graphical models. This volume contains survey and research articles from leading researchers at the interface of these subjects.

The IMA Hot Topics workshop on compatible spatialdiscretizations was held in 2004. This volume contains original contributions based on the material presented there. A unique feature is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science. Abstracts and presentation slides from the workshop can be accessed on the internet.

This volume contains papers based on invited talks given at the 2005 IMA Summer Workshop on Wireless Communications, held at the Institute for Mathematics and Its Applications, University of Minnesota, June 22 - July 1, 2005. It presents some of the highlights of the workshop, and collects papers covering a broad spectrum of important and pressing issues in wireless communications.

This IMA Volume in Mathematics and its Applications ALGORITHMS FOR PARALLEL PROCESSING is based on the proceedings of a workshop that was an integral part of the 1996-97 IMA program on "MATHEMATICS IN HIGH-PERFORMANCE COMPUTING. " The workshop brought together algorithm developers from theory, combinatorics, and scientific computing. The topics ranged over models, linear algebra, sorting, randomization, and graph algorithms and their analysis. We thank Michael T. Heath of University of lllinois at Urbana (Com puter Science), Abhiram Ranade of the Indian Institute of Technology (Computer Science and Engineering), and Robert S. Schreiber of Hewlett Packard Laboratories for their excellent work in organizing the workshop and editing the proceedings. We also take this opportunity to thank the National Science Founda tion (NSF) and the Army Research Office (ARO), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE The Workshop on Algorithms for Parallel Processing was held at the IMA September 16 - 20, 1996; it was the first workshop of the IMA year dedicated to the mathematics of high performance computing. The work shop organizers were Abhiram Ranade of The Indian Institute of Tech nology, Bombay, Michael Heath of the University of Illinois, and Robert Schreiber of Hewlett Packard Laboratories. Our idea was to bring together researchers who do innovative, exciting, parallel algorithms research on a wide range of topics, and by sharing insights, problems, tools, and methods to learn something of value from one another.