Bøger i The IMA Volumes in Mathematics and its Applications serien

Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions.

This IMA Volume in Mathematics and its Applications STOCHASTIC NETWORKS is based on the proceedings of a workshop that was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability."

This IMA Volume in Mathematics and its Applications LARGE-SCALE OPTIMIZATION WITH APPLICATIONS, PART II: OPTIMAL DESIGN AND CONTROL is one of the three volumes based on the proceedings of the 1995 IMA three­ week Summer Program on "Large-Scale Optimization with Applications to Inverse Problems, Optimal Control and Design, and Molecular and Struc­ tural Optimization." The other two related proceedings appeared as Vol­ ume 92: Large-Scale Optirpization with Applications, Part I: Optimization in Inverse Problems and Design and Volume 94: Large-Scale Optimization with Applications, Part III: Molecular Structure and Optimization. We would like to thank Lorenz T. Biegler, Thomas F. Coleman, An­ drew R. Conn, and Fadil N. Santosa for their excellent work as organizers of the meetings and for editing the proceedings. We also take this opportunity to thank the National Science Founda­ tion (NSF), the Department of Energy (DOE), and the Alfred P. Sloan support made the workshops possible.

Inverse problems in wave propagation occur in geophysics, ocean acoustics, civil and environmental engineering, ultrasonic non-destructive testing, biomedical ultrasonics, radar, astrophysics, as well as other areas of science and technology.

This IMA Volume in Mathematics and its Applications MULTIPARTICLE QUANTUM SCATTERING WITH APPLICATIONS TO NUCLEAR, ATOMIC AND MOLECULAR PHYSICS is based on the proceedings of a workshop with the same title, which was an integral part of the 1994-1995 IMA program on "Waves and Scattering." We would like to thank Donald G. Truhlar and Barry Simon for their ex­ cellent work as organizers of this meeting and as editors of the proceedings. We also take this opportunity to thank the National Science Foundation (NSF), the Army Research Office (ARO), and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE The workshop on Multiparticle Quantum Scattering with Applications to Nuclear, Atomic, and Molecular Physics was held June 12-16, 1995 at the Institute for Mathematics and Its Applications in the University of Min­ nesota Twin Cities campus as part of the 1994-95 Program on Waves and Scattering. There were about seventy participants including the plenary lecturers whose contributions are included in this volume. The workshop was preceded by a two-day tutorial featuring lectures by Donald J. Kouri and Gian Michele Graf, and we are pleased that both Professors Graf and Kouri were able to write up their tutorials as opening chapters of this volume.

An important feature of the book is the treatment of Monte Carlo methods, including umbrella sampling and multiple Markov chain methods, which are useful for strongly interacting systems such as polymers at low temperatures and in compact phases.

This IMA Volume in Mathematics and its Applications WAVE PROPAGATION IN COMPLEX MEDIA is based on the proceedings of two workshops: * Wavelets, multigrid and other fast algorithms (multipole, FFT) and their use in wave propagation and * Waves in random and other complex media.

Most people tend to view number theory as the very paradigm of pure mathematics. With the advent of computers, however, number theory has been finding an increasing number of applications in practical settings, such as in cryptography, random number generation, coding theory, and even concert hall acoustics.

This IMA Volume in Mathematics and its Applications EVOLUTIONARY ALGORITHMS 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."

Proceedings of a Workshop

This IMA Volume in Mathematics and its Applications DEGENERATE DIFFUSIONS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries".

Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few.

The area of adaptive systems, which encompasses recursive identification, adaptive control, filtering, and signal processing, has been one of the most active areas of the past decade.

Proceedings of one of a series of IMA workshops held during 1984-1985

Genetics mapping, physical mapping and DNA sequencing are the three key components of the human and other genome projects. This volume edited by key researchers Mike Waterman and Terry Speed reviews recent progress in the area, with an emphasis on the theory and application of genetic mapping.

Mathematical methods play a significant role in the rapidly growing field of nonlinear optical materials.

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."

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 parallel computers) for computing approximate global minimizers. The purpose of the sessions represented in this volume was to discuss the new algorithmic advances for global minimization in the context of protein folding and related molecular minimization problems. Emphasis was on practical shortcomings of current approaches, outstanding problems and questions, and the use of high-performance parallel computers.

The two volumes of Signal Processing are based on lectures delivered during a six week program held at the IMA from June 27 to August 5, 1988. Part I deals with general signal process theory and Part II deals with (i) application of signal processing, (ii) control theory related themes.

The field of discontinuous Galerkin finite element methods has attracted considerable recent attention from scholars in the applied sciences and engineering.

Khasminskii, on his seventy-fifth birthday, for his contributions to stochastic processes and nonparametric estimation theory an IMA participating institution conference entitled "Conference on Asymptotic Analysis in Stochastic Processes, Nonparametric Estimation, and Related Problems" was held.

From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics, some of which were literally created along the way.

This IMA Volume in Mathematics and its Applications SEMICONDUCTORS, PART II is based on the proceedings of the IMA summer program "Semiconductors."

Computational Challenges in the Geosciences addresses a cross-section of grand challenge problems arising in geoscience applications, including groundwater and petroleum reservoir simulation, hurricane storm surge, oceanography, volcanic eruptions and landslides, and tsunamis.

Inverse problems and optimal design have come of age as a consequence of the availability of better, more accurate, and more efficient simulation packages. Many of these simulators, which can run on small workstations, can capture the complicated behavior of the physical systems they are modeling, and have become commonplace tools in engineering and science. There is a great desire to use them as part of a process by which measured field data are analyzed or by which design of a product is automated. A major obstacle in doing precisely this is that one is ultimately confronted with a large-scale optimization problem. This volume contains expository articles on both inverse problems and design problems formulated as optimization. Each paper describes the physical problem in some detail and is meant to be accessible to researchers in optimization as well as those who work in applied areas where optimization is a key tool. What emerges in the presentations is that there are features about the problem that must be taken into account in posing the objective function, and in choosing an optimization strategy. In particular there are certain structures peculiar to the problems that deserve special treatment, and there is ample opportunity for parallel computation. THIS IS BACK COVER TEXT!!! Inverse problems and optimal design have come of age as a consequence of the availability of better, more accurate, and more efficient, simulation packages. The problem of determining the parameters of a physical system from

This IMA Volume in Mathematics and its Applications RANDOM SETS: THEORY AND APPLICATIONS is based on the proceedings of a very successful 1996 three-day Summer Program on "Application and Theory of Random Sets." " - Henri Poincare Random set theory was independently conceived by D.G.