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The first in a series of volumes dedicated to the study of continuum physics and partial differential equations. "This volume is a collection of papers by world experts in both homogenization and optimal structural design. The emphasis of all the papers is on applications and examples. The papers are of high quality, well written, and happily one need not be a specialist to gain insight from reading them. I recommend the collection to anyone interested in seeing what is happening on the applied side of homogenization and optimal structural design.
Brings together both the analytical and numerical sides of conservation law research. The objective is to examine recent trends in the investigation of systems of conservation laws and in particular to focus on the roles of dispersive and diffusion limits for singularly perturbed conservation laws. Special attention is devoted to the new ideas of compensated compactness and oscillation theory in the hope that these new methods may lead to new existence theorems for systems of conservation laws and perhaps provide a greater understanding of convergence of finite difference schemes.
Available knowledge of constitutive relations and environmental interactions may be limited; thus, many configurations may be compatible with the data. This volume addresses such incompletely posed questions and addresses a variety of issues as they are perceived by the material scientist and mathematician. They represent a portion of the significant activity which has been underway in recent years, from the experimental arena and physical theory to the analysis of differential equations and computations. While there is speculative character to much of this work, by grappling with specific problems, the authors provide experience from which one may aspire to abstract viable methods for the analysis and production of metastable behavior.
The behavior of matter and waves in a dynamical setting offers many challenging problems to the mathematician and the materials scientist alike. Under review in this volume are a variety of nonlinear phenomena whose consideration entails new perspectives, not commonly found in the literature. Attention has been given to the interaction of electromagnetic and mechanical properties of materials. Attempts are made to describe and to understand phenomena which are far from equilibrium or which suffer abrupt changes in behavior through tentative physical or analytical assumptions.
The diversity of experimental phenomena and the range of applications of liquid crystals present timely and challenging questions for experimentalists , mechanists, and mathematicians. The contents of this volume vary from descriptions of experimental phenomena to questions of a mathematical nature of efficient computation. Interest in this area is stimulated by problems relating to the many familiar devices as well as by questions which arise in the processing of high strength polymer fibers such as Kevlar. The objective of this volume is to foster improved theory and more effective computational methods through better mathematical understanding.
Experiences with amorphous polymers have supplied much of the motivation for developing novel kinds of molecular theory to deal with the more significant featuares of systems involving very large molecules with many degrees of freedom. Similarly, the observations of many unusual macroscopic phenomena has stimulated efforts to develop linear and nonlinear theories of viscoelasticity to describe them. This volume brings together research workers in chemistry, engineering, mathematics and physics from laboratory, industrial and academic environments. The objective is to devise techniques for finding equations capable of delivering definite and reliable predictions.
This volume brings together researchers who work in a broad area of applications and mathematical methodology related to random media. Papers represent a cross section of problems and methods that are currently of interest: Brownian motion, random PDE's, random Schrödinger operators, wave propagation, amorphous semiconductors, lattice models, diffusion processes, etc. One dimensional problems, such as Lyapunov indices, density of states, and localization, receive considerable attention. There is considerable progress in several dimensional problems as well, in particular on localization of cases in multidimensional random media. The volume should be of interest to chemists, physicists and mathematicians.
Percolation theory and infinite particle systems both deal with probability mode ls with great appeal to pure probabilists and to statistical physicists. The percolatio n model was invented about 30 years ago. One of its attractions is that it is extremely simple to state. It exhibits a phase transition, which turns out to be quite difficult to analyze. It is precisely this phase transition which makes the mod el interesting to physicists, because they have studied such phenomena for a much longer time in statistical mechanics (e.g. in models for magnetism). Infinite particle systems deal with the evolution of collections of interacting particles . The interaction is of course required if one wants to mimic any physical phenomenon, but it makes the mathematical problems challenging and difficult. Percolation theory and the study of infinite particle systems have many tools in common and there is a similarity of flavor between the two fields.
This volume contains the Proceedings of a workshop held at the Institute for Mathematics and its Applications, Minneapolis, in Feb. 1986. It reports recent results in the above fields (and some related ones) and gives an impression of the state of the art at the time of the workshop. There is a survey on fractal structures in percolation. Several papers prove new results completely; others merely state results, with proofs to appear in technical journals.
Fifteen papers are presented containing research in various directions currently being pursued on the hydrodynamic behavior of interacting particle systems. Papers are concerned with
This volume is the Proceedings of a Workshop on stochastic control and related topics in applied probability, held at the Institute for Mathematics and its Applications in June 1986. The choice of topics was deliberately made to obtain a mix of traditional areas of stochastic control theory and topics arising in newer areas of application. The papers included in this volume represent a diversity of approaches and viewpoints. They emphasize variously underlying mathematical theory, modelling issues and questions of computational implementation.
The volume will interest several audiences in mathematics, electrical/computer engineering, and management science. Mathematicians working in probability theory and related areas of partial differential equations would find of interest the papers on stochastic differential systems theory as well as those dealing with its application to stochastic control and nonlinear filtering. Among the newer areas emphasized are stochastic scheduling and queueing networks. These topics arise in analyses of computer networks and scheduling of complex manufacturing operations. Another newer area included is simulated annealing, which provides a stochastic algorithm for many kinds of large-scale optimization problems.
This volume is the Proceedings of a workshop on the numerical simulation of oil recovery held at the Institute for Mathematics and its Applications in December 1986. This volume contains a collection of articles by well known mathematicians, engineers, and scientists. The major research focus is the modeling of geologically realistic media. Several important topics discussed include heterogeneities, diffusion-dispersion, viscous fingering, three phase flow and fractures.
The audience for this volume would include researchers in production research in the petroleum industry (major oil companies), academia (applied mathematics, civil, petroleum, and chemical engineering departments), and government laboratories (DOE, EPA). In addition many of the articles are of interest to hydrologists and engineers modelling containment transport in ground water (U.S. Geological Survey).
This volume contains papers presented at the workshop on Computational Fluid Dynamics and Reacting Gas Flows held at the Institute for Mathematics and Its Applications during September, 1986. Computational fluid dynamics has become a research area of central importance to mathematics, science, and technology. It is a subject which brings together applied mathematics and numerical analysis to solve problems in fluid dynamics. Included in this volume is the description of new algorithms which can make possible the discovery of important new scientific phenomena and the development of new technological processes. This volume will be of interest to mathematicians, scientists, and engineers who are interested in the current research of international leaders in numerical analysis and scientific computing.
Parallel computers have the potential of providing additional memory and cpu cycles at low cost. They may completely revolutionize the outer limits of scientific computation. The papers in this volume represent simultaneous consideration of applied mathematical, computer science, and application aspects of parallel scientific computing. Such an interdisciplinary approach is likely to lead to the most rapid possible advances in multiprocessor architectures, parallel algorithm development and analysis, and parallel systems and programming languages.
This volume is the Proceedings of a Workshop on mathematical problems that arise from creating large scientific software systems. The topics lie at the interface between mathematics and computer science, yet some fundamental mathematical questions arise from efforts to understand scientific software. Papers in the volume include a lengthy overview of the area plus treatments of computational geometry, symbolic computation, performance evaluation issues and mathematical systems.
The volume will interest several audiences in mathematics plus the computationally oriented people in a variety of science and engineering disciplines. Of course, those computer scientists working on scientific software will also find the volume of interest.
This volume consists of the lectures at an IMA Workshop on Atomic and Molecular Structure and Dynamics. It focuses on areas where new mathematical developments are currently allowing for advances in computations and where further mathematical developements are required for important progress.
The volume begins with two introductory lectures; the following nine lecturers develope individual strains of research. The book should be of interest to students in mathematics, chemistry, and physics, as well as to senior researchers interested in new research topics. All chapters were specially prepared with this kind of audience in mind and with special emphasis on pedagogy. Emphasis is placed on frontier aspects of mathematical chemistry and physics where unsolved problems provide fertile ground for future research. The areas discussed include the theory of partial differential equations, integral equations, analytic continuation, quantum mechanics, molecular dynamics, and statistical mechanics.
The book is based on a seminar conducted by the author at the Institute for Mathematics and its Applications during 1987-88. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The consists of twenty-two chapters, each one being independent of the others. Each chapter is based on a presentation by one of the speakers; it includes the industrial background, relevant mathematical literature, a list of open mathematical problems and, in some cases, reference to a solution or a partial solution of the problem. Most of the problems, however, are still open and they are addressed to mathematicians. The topics of the book include scattering, control and coding, conservation laws, inverse problems, network optimization, fluid problems, and a variety of free boundary problems in fluid mechanics. The book will be of interest to mathematicians seeking to work on mathematical problems which arise in industry. It will also be of interest to mathematicians and scientists who would like to learn about the interaction between mathematics and industry, what type of problems arise, how they are modelled, etc. Scientists working in industry may also be interested in the book as they discover that some of the topics dealt with are connected to their own work.
This volume is the Proceedings of a Workshop on the applications of combinatorics and graph theory in the biological and social sciences, held at the Institute for Mathematics and its Applications in January 1988. Combinatorial and graph-theoretical methods are increasingly important in the biological and social sciences. The Workshop emphasized mathematical techniques and open problems arising in such fields as ecology, genetics, enzyme kinetics, economics, political science, sociology, and psychology.
Two illustrations will indicate the type of material in the volume. In biology, the Workshop paid considerable attention to the analysis of protein, DNA, and RNA sequences. This is an area where combinatorial analysis has historically played a very critical role, and where in the future it can be expected to be important as the United States undertakes the massive scientific project of mapping the human genome. In the social sciences, the Workshop paid considerable attention to the theory of measurement. Using both combinatorial and graph-theoretical methods, the Workshop explored the question: What kinds of statements using scales and index numbers can be meaningfully made? The answer to this question has applications to group decisionmaking, performance analysis of new technologies, the analysis of price indices, and so on.
Other areas of special emphasis in the biological sciences were the use of signed graphs in the analysis of stability in ecosystems if only patterns of interaction are known; analysis of competition in ecosystems in general through the use of competition graphs and niche overlap graphs; the use of tree structures in immunology; and combinatorial aspects of enzyme kinetics.
Other areas of special emphasis in the social sciences were the use of median rankings and spatial metrics in group choice and voting; the use of partially ordered sets to analyze knowledge spaces which describe how a person learns and the use of lattice structures to analyze concepts; the use of graphs and signed graphs to study small group behavior and social networks; and the use of signed graphs to study stability in economic models when only sign patterns are known.
The biological and social scientific applications described in the volume are closely related. Some of the uses of graph theory in the study of food webs in ecology are also used to model preference and indifference in psychology and economics. Some of the models used to describe how groups should make choices also have application to finding consensus structures in numerical taxonomy. The problems of measurement and classification discussed are common to the biological and social sciences, as are the methods for analyzing stability when only sign patterns are known.
The volume will interest audiences in mathematics, statistics, operations research, ecology genetics, kinetics, economics, psychology, sociology, and political science. Mathematicians working in graph theory, combinatorics, random discrete structures, lattice theory, partially ordered sets, and finite stochastic processes, should find this volume particularly interesting.
This volume is the proceedings of a workshop held for the Applied Combinatorics program in March, 1988. The central idea of the workshop is the recent interplay of the classical analysis of q-series, and the combinatorial analysis of partitions of integers. Many related topics are discussed, including orthogonal polynomials, the Macdonald conjectures for root systems, and related integrals. Those people interested in combinatorial enumeration and special functions will find this volume of interest. Recent applications of q-series (and related functions) to exactly solvable statistical mechanics models and to statistics makes this volume of interest to non-specialists. Included are several expository papers, and a series of papers on new work on the unimodality of the q-binomial coefficient.
This volume is the proceedings of a workshop held for the Applied Combinatorics program in March, 1988. The principal speaker was Gian-Carlo Rota, whose introductory lectures on invariant theory are included here. Several related topics are discussed in other papers: from recent applications of invariant theory to differential equations, to combinatorial questions on Coxeter groups and tableaux. Particularly noteworthy for non-specialists is a self-contained, elementary introduction to Young tableaux and the representations of the symmetric group.
Coding Theory and Design Theory are areas of Combinatorics which found rich applications of algebraic structures. Combinatorial designs are generalizations of finite geometries. Probably, the history of Design Theory begins with the 1847 paper of Reverand T.P. Kirkman "On a problem of Combinatorics," Cambridge and Dublin Math. Journal. The great Statistician R.A. Fisher reinvented the concept of combinatorial 2-design in the twentieth century. Extensive application of algebraic structures for construction of 2-designs (balanced incomplete block designs) can be found in R.C. Bose's 1939 Annals of Eugenics paper, "On the construction of balanced incomplete block designs." Coding Theory and Design Theory are closely interconnected. Hamming codes can be found (in disguise) in R.C. Bose's 1947 Sankhyä paper "Mathematical theory of the symmetrical factorial designs." The same paper also introduced the packing problem in projective spaces - the central problem in the construction of optimum linear codes. Coding theory has developed into a rich and beautiful example of abstract sophisticated mathematics being applied successfully to solve real-life problems of communication. Applications of deep theorems of Algebraic Geometry for construction of linear codes by V.D. Goppa and others created much excitement. Much work remains to be done to make the algebraic geometric codes practical and implementable. Theory of $t$-designs for $t>2$ is in a state of rapid development. The 1987-88 Applied Combinatorics Program of IMA decided to devote the period from May 1, 1988 to June 25, 1988 to concentration on Design Theory and Coding Theory. It was particularly appropriate as many of the specialists that were invited worked in both of these areas.
The purpose of this section of the Applied Combinatorics Year was to bring together Coding Theorists, Design Theorists and Statisticians in the area of experimental designs, to exchange informations and ideas on the latest developments, to encourage interactions and to create an inspiring and stimulating research environment. This purpose was well served. Before the beginning of the workshops from May 1 to June 10, 1988 the pace was relaxed with plenty of time for research exchanges. During this period lectures of J.H. van Lint on Algebraic Geometric Codes was a particularly popular event. In this period there were also lectures by E. Assmus, R.A. Bailey, C-S. Cheng, M. Deza, A.S. Hedayat, S.L. Ma, V. Pless, D.K. Ray-Chaudhuri, N. Singhi, R.M. Wilson and L. Teirlinck. The periods of workshops, Coding Theory, June 13-17, 1988 and Design Theory, June 20-25, 1988 were much more intense with forty (40) lectures altogether. Symposium on Statistical theory of Experimental Designs attracted many statisticians with lively lectures by eight prominent statisticians. Most of the participants submitted their papers for publication in this volume on Coding Theory and Design Theory. Unfortunately a few fine lectures are not submitted for inclusion in these Proceedings.
See Volume 20 for description.
Contents: pdf postscript
The two volumes of Signal Processing are based on lectures delivered during a six week program held at the IMA during the summer of 1988. The first two weeks of the program dealt with general areas and methods of Signal Processing. The problem areas included imaging and analysis of recognition, x-ray crystallography, radar and sonar, signal analysis and 1-D signal processing, speech, vision, and VLSI implementation. The methods discussed included harmonic analysis and wavelets, operator theory, algorithm complexity, filtering and estimation, and inverse scattering. The topics of weeks three and four were digital filter, VLSI implementation, and integrable circuit modelling. In week five the concentration was on robust and nonlinear control with aerospace applications, and in week six the emphasis was on problems in radar, sonar and medical imaging.
Because of the large overlap between the various one-week and two-week segments of the program, we found it more convenient to divide the material somewhat differently. Part I deals with general signal process theory and Part II deals with (i) application of signal processing, (ii) control theory related themes.
Signal Processing is undergoing tremendous developments; it is our hope that these two volumes will serve as a source of information and stimulation to mathematical scientists who wish to get acquainted with this field.
See Volume 22 for description.
Contents: pdf postscript
The book is based on a seminar conducted by the author at the Institute for Mathematics and its Applications during 1988-89. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The book consists of nineteen chapters, each one being independent of the others. Each of the first eighteen chapters is based on a presentation by one of the speakers; it includes the industrial background, relevant mathematical literature, a list of open mathematical problems and, in some cases, reference to a solution or a partial solution of the problem. Most of the problems, however, are still open and they are addressed to mathematicians. The last chapter of the book contains references to solutions of problems presented in the previous volume of "Mathematics in Industrial Problems" published in the IMA series, as volume 16. The topics of the book include electro-chemical processes, magneto-optics, aerosol modeling, nonlinear optics, semiconductors and communication. The book will be of interest to mathematicians seeking to work on mathematical problems which arise in industry. It will also be of interest to mathematicians and scientists who would like to learn about the interaction between mathematics and industry, what type of problems arise, how they are modelled, etc. Scientists working in industry may also be interested in the book as they discover that some of the topics dealt with are connected to their own work.
This volume includes some of the lectures given at two workshops, Solitons in Physics and Mathematics" and "Solitons in Nonlinear Optics and Plasma Physics" held during the 1988-89 I.M.A. year on Nonlinear Waves. Since their discovery by Kruskal and Zabusky in the early 1960's, solitons have had a profound impact on many fields, ranging from engineering and physics to algebraic geometry. The present contributions represent only a fraction of these areas, but give the reader a good overview of several current research directions, including optics, fluid dynamics, inverse scattering, cellular automata, Backlund transformations, monodromy, Painlevé equations, symmetries and Hamiltonian systems.
This Workshop, held from January 3-10, 1989 at IMA, focused on the properties of materials which consist of many small particles or grains. These include granular materials, in which the particles interact through direct contact, and suspensions or two phase materials, in which particles interact through the influence of the surrounding viscous fluid. Such materials are important in many industrial and geological applications, especially fluidized beds.
This volume contains advanced scientific papers in this rapidly developing subject by authors from several different disciplines (e.g., engineering, physics, mathematics). Some papers attempt to derive continuum constitutive behavior from micromechanics. Others analyze theoretically or solve numerically the partial differential equations which result when an ad hoc constitutive law is assumed. Experimental phenomena exhibited by such materials are reported in other papers. Still others consider the application to fluidized beds.
This volume will be of interest to applied mathematicians, to researchers in Partial Differential Equations, and to Fluid Dynamicists and Numerical Analysts examining models for viscoelastic flows, porous medium and granular flows, and flows exhibiting phase transitions. As papers in this volume indicate, physical processes whose simplest models may involve change of type occur also in other dynamic contexts, such as in the simulation of oil reservoirs, involving multiphase flow in a porous medium, and in granular flow.
Since the dawn of the computer revolution the vast majority of scientific computation has dealt with a small cadre seeking precise solutions of equations and rigorous proofs of mathematical results. For example, the number theory and combinatorics have a long history of computer-assisted proofs; such methods are now well established in these fields. In analysis the use of computers to obtain exact results has been fragmented into several schools. This volume is the proceedings of a conference which brought together people in symbolic algebra and in interval arithmetic with some independent entrepreneurs who where interested in obtaining precise answers to questions in analysis by computer methods. There were mathematical physicists interested in the stability of matter, functional analyst computing norms in strange function spaces, celestial mechanists analyzing bifurcations, symbolic algebraists interested in exact integration, numerical analysts who had developed interval arithmetic, plus much more. The mix included developers and end users. The papers within reflect the heterogeneous background of the participants.
This volume is the proceedings of a two week workshop on multi-dimensional hyperbolic problems held during April 1989. The twenty-six papers in this volume emphasize the interdisciplinary nature of contemporary research in this field involving combinations of ideas from the theory of nonlinear partial differential equations, asymptotic methods, numerical computation and experiments. This volume incoudes several expository papers on asymptotic methods such as nonlinear geometric optics, a number of articles applying numerical algorithms such as higher order Godunov methods and front tracking to physical problems along with comparison to experimental data, and also several interesting papers on the rigorous mathematical theory of shock waves. In addition, there are two papers in the book devoted to open problems with this interdisciplinary emphasis. This book should be very interesting for any researcher pursuing modern developments in the theory and applications of hyperbolic conservation laws.
The behavior of linear hyperbolic waves has long been analyzed by decomposing the waves into pieces in space-time and into different frequencies. The linear nature of the equations involved allows the reassembling of the pieces in a simple fashion; the individual pieces do not interact. For nonlinear waves the interaction of the pieces seemed to preclude such an analysis, but in the late 1970s it was shown that a similar procedure could be undertaken in this case and would yield important information. The analysis of the decomposed waves, and of waves with special smoothness or size in certain directions, has been fruitful in describing a variety of the properties of nonlinear waves.
This volume presents a number of articles on topics of current interest which involve the use of the techniques described above. The results established include descriptions of the smoothness of such waves as determined by their geometry, the properties of solutions with high frequency oscillations, and the long-time smoothness and size estimates satisfied by nonlinear waves.
The book is based on a seminar conducted by the author at the Institute for Mathematics and its Applications during 1989-90. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The book consists of eighteen chapters each one being independent of the others. Each of the first seventeen chapters is based on a presentation by one of the speakers; it includes the industrial background, relevant mathematical literature, a list of open mathematical problems and, in some cases, reference to a solution or a partial solution of the problem. Most of the problems, however, are still open and they are addressed to mathematicians. The last chapter of the book contains references to solutions of problems presented in the previous volume of "Mathematics in Industrial Problems, Part 2" published in the IMA series, as volume 24. The topics of the book include electro-chemical processes, polymers, waveguides, diffractive optics, semiconductors and optimization. The book will be of interest to mathematicians seeking to work on mathematical problems which arise in industry. It will also be of interest to mathematicians and scientists who would like to learn about the interaction between mathematics and industry, what type of problems arise, how they are modelled, etc. Scientists working in industry may also be interested in the book as they discover that some of the topics dealt with are connected to their own work.
This volume contains the lecture notes from the three sets of tutorial lectures which were given during the first week of the IMA summer program RADAR AND SONAR, June 18-June 29, 1990. (The second week was devoted to research problems and the proceedings of that part of the program will appear in a second IMA volume.) The first week was run as a summer school with an audience consisting mainly of mathematicians and engineers. The tutorial topics were on mathematics (Topics in Harmonic Analysis with Applications to Radar and Sonar, by Willard Miller, Jr.), on the physical aspects of scattering (Sonar and Radar Echo Structure, by Calvin H. Wilcox), and on the engineering modelling and processing of the phenomena under consideration (Theory of Remote Surveillance Algorithms, by Richard E. Blahut), the famous 1960 technical report by Wilcox (The Synthesis Problem for Radar Ambiguity Functions) was featured prominently in the program and is also published here for the first time. A great effort was made by the lecturers to insure that the participants covered two or all three short courses in detail: mathematicians needed to spend more time and effort in the engineering and physical components and a corresponding distribution of effort was encouraged for engineers and physicists. One of the main goals of this effort was to ensure that people with different backgrounds would help each other, and learn in the process a bit about each others language and approach to problems in Radar and Sonar. We believe that the effort was a great success and offer these notes for the benefit of the wider mathematical sciences community.
Robust statistical procedures and diagnostics are complementary methodologies to deal with models which may be incomplete or incorrectly specified. These volumes contain the proceedings of a month long workshop on the two fields, held at the Institute for Mathematics and its Applications in Minneapolis in the Summer of 1989. They provide an overview of current directions in research in these two important areas of statistical theory and practice. Care has been taken to provide overview papers as well as easily accessible introductions to the more technical contributions.
These volumes are a point of reference for those researchers with a special interest in robust statistics and diagnostics as well as for other statisticians who have a general interest in these fields.
See Volume 33 for description.
This volume is the Proceedings of the Workshop of Dynamical Issues in Combustion, held at the Institute of Mathematics and its Applications in November, 1989. The world of combustion phenomena is rich in problems intriguing to the mathematical scientists, offering challenges on several fronts: mathematical modeling, devising appropriate asymptotic and computational methods, and developing sound mathematical theories.
Papers in the present volume describe how all these challenges have been met for particular examples within a number of common combustion scenarios: reactive shocks, low Mach number premised reactive flow, nonpremixed phenomena, and solid propellants.
The types of phenomena they examine are also diverse: properties of interfaces and shocks including curvature effects, the stability and other properties of steady structures, the long time dynamics of evolving solutions, and spatio-temporal patterns. These issues are foremost in combustion research; the papers collected here provide a good representative sampling of contemporary activity in this field.
This volume covers the computational part of IMA activities in statistics during the summer of 1989. The areas of statistical computing and graphics encompass a broad range of research, much of it representated here. The vigor of this research is probably best demonstrated by the fact that as of this writing two new journals are being launched, both entirely dedication to these areas.
The major topics of statistical computing can be traced largely to problems in data analysis and to a lesser extent, in statistical theory. They involve integrated software systems, visualization of high-dimensional data and mathematical functions, numerical and combinatorial algorithms, tools for data handling, and simulation.
Problems arising in the development of integrated statistical software systems have lead to the adaptation of ideas from computer science, particularly programming environments, programming paradigms, and artificial intelligence. In this general area fall the papers by Dumouchel-O'Brien, Hurley-Oldford, McDonald-Pedersen, Nelder, Pedersen, and Young-Smith. Object-oriented programming has left a special mark in some of this research. Of growing importance for the future will be symbolic computing, especially if integrated eith data analyisis and simulation software (Cabrera).
Visualization has been an integral part of statistical methodology long before it became a major scientific initiative in recent years. What distinguishes the problems of statistics from many physical sciences is that they mostly concern genuine high-dimensional objects, such as multivariate data or functions of many variables. Along these lines is the work by Miller-Wegman, Scott, Stuetzle, and Young-Rheingans. A problem which fascinates with its simplicity and seeming intractability, is attacked in Wilkinson's paper on automatic methods for finding reasonable domains and ranges for plotting univariate functions.
Finally, we should point out the importance of numerical methods and Monte Carlo methods in statistics. Statistical problems are often messy and do require care (Grier). Computer intensive methodology has been at the forefront of statistics research in the last decade. Besides the bootstrap method, Bayesian inference and its associated integration problems have attracted much attention (Hesterberg).
This volume contains some of the lectures given at the workshop "Patterns and Dynamics in Reactive Media" held from October 16-20, 1989 as part of the year on Dynamical systems and their Applications at the Institute for Mathematics and its Applications, Minneapolis, Minnesota.
Ever since the seminal works on traveling waves and on morphogenesis by Fisher, by Kolmogorov, Petrovski & Piscunov, and by Turing, scientists from many disciplines have been fascinated by questions concerning the formation of steady or dynamic patterns in reactive media. The contributors to this volume include chemists, chemical engineers, mathematicians (both pure and applied), and physicists. Their contributions range from reports of experimental studies, through descriptions of numerical experiments, to rather abstract theoretical investigations, each exhibiting different aspects of a very diverse field. Although this small volume can hardly claim to cover the whole range of current research in patterns in reactive media, it nevertheless presents a representative sample.
The book is based on a seminar conducted by the author at the Institute for Mathematics and its applications during 1990-91. In this seminar, scientists from industry presented industrail problems to mathematicians, including the mathematical formulation of the problems. The book consists of twenty-one chapters, each one being independent of the others. Each of the first twenty chapters is based on a presentation by one of the speakers; it includes the industrial background, relevant mathematical literature, a list of open mathematical problems and in some cases, reference to a solution or a partial solution of the problem. Most of the problems however, are still open and they are addressed to mathematicians. The last chapter of the book contains references to solutions of problems presented in the previous volume of "Mathematics in Industrial Problems, Part 3" published in the IMA series, as volume 31. The topics of the book include semiconductor devices ahd processing; particles dynamics; polymer chains and electrophoresis; catalytic converte, robotics and CFD in the automobile industry, superconductivity, magnetic storage devices, signal processing, and experimental design.
The book will be of interest to mathematicians seeking to work on mathematical problems which arise in industry. It willl also be of interest to mathematicians and scientists who would like to learn about the interaction between mathematics and industry, what type of problems arise, how they are modelled, etc. Scientists working in industry may also be interested in the book as they discover that some of the topics dealt with are connected to their worn work.
This volume contains a representative discussion of mathematical problems that arise in radar and sonar and is based on the lectures that were given during the second week of the IMA summer program RADAR AND SONAR, June 18-June 29, 1990. (The first week was devoted to three sets of tutorial lectures and the lecture notes from that part of the program appear in an earlier IMA volume.) The second week was run as a workshop of contributed papers without formal review. The speakers were selected to cover a broad range of problems in this area.
The summer program was organized to stimulate a dialogue between engineers and applied mathematicians. The design of waveforms for radar and sonar and the development of algorithms for the processing of these waveforms lead to many interesting and difficult problems of applied mathematics. It is timely to separate these problems from the engineering tasks of radar and sonar so as to form a minitopic of applied mathematics. The range of such problems contained herein probably cannot be found in any other volume. There are applications of group theory, modern topics of signal processing, inverse problems, array processing and beamforming, estimation-theoretic imaging, and phase tracking. We believe the program was a great success. As these and related topics develop further a future sequel to this program will be a success as well.
"Nonlinear Phenomena in Athmospheric and Oceanic Sciences" is a collection of treatises contributed by distinguished physicists, mathematicians and geophysicists, concerning the fluid mechanical behavior of atmospheres, oceans and related systems. The primary emphasis is on a large scale dynamics, and accordingly, most of the chapters deal with the flow of two-dimensional or quasi-two-dimensional fluids. Topics covered include two-dimensional turbulence, fractal geometry and spectra, chaotic mixing, nonlinear stability theory, and coherent vortices. There are also contributions on convection, nonlinear stratified flow over obstacles, and chaotic eigenvalue problems appearing in dynamo theory. The geometric structures appearing in these flows are liberally illustrated through the use of color graphics.
This book will be of interest to mathematicians seeking to understand the range of problems of interest in geophysical fluid dynamics, and to geophysicists seeking to understand the range of modern mathematical techniques that can be brought to bear on geophysical fluid dynamics problems. It would be ideal as a text for graduate seminars intended to quickly bring students up to speed on this fascinating.
The subject matter of chaos and nonlinear dynamics has begun to spread to the geological sciences in the last several years. The articles from this book come from a workshop held at the University of Minnesota in June 1990 in which well-renowned geophysicists, geologists and applied mathematicians were in attendance. There were three areas of focus in the workshop: thermal convection as applied to the earth's mantle, magmatic dynamics and processes in geodynamo. The nonlinear nature of convection ws discussed especially in light of recent advances made in the physics community of the phenomenon of hard-turbulent convection. This book can be useful for graduate students and researchers in geophysics, applied mechanics, and applied mathematics. It should also of interest to workers in other areas of thermal convection.
In this volume we have collected articles presented at a workshop held at the University of Chicago, March 21-25, 1990. The articles address issues in the theoretical and applied aspects of partial differential equations with an emphasis on minimal smoothness.
This volume is the proceedings of a one week workshop on phase transitions held during September 1990. A primary goal of this workshop was to emphasize the interdisciplinary nature of contempomporary research in this field, research which involves ideas from nonlinear partial differential equations, asymptotic analysis, numerical computation and experiment. The ten papers in this volume span a wide cross-section of this research. Topics covered include the treatment of scaling laws that describe the coarsening or ripening behavior observed during the later stages of phase transitions; novel numerical methods for treating interface dynamics; the mathematical description of geometric models of interface dynamics; determination of the governing equations and interfacial boundary conditions in the context of fluid flow and elasticity. This book should be interesting for any researcher pursuing modern developments in the theory and applications of phase transitions and interface dynamics.
This is a collection of papers contributed by distinguished mathematicians and mathematical physicists on the dynamics of twist maps. Twist maps arise naturally in the study of stability questions in mechanical systems and applications in many areas of physical and mechanics.
This book contains many of the most recent developments by some of the leading figures in the field. It will be of interest to mathematicians, physicists, and engineers wishing to keep abreast of this fundamental and evolving area of classical mechanics.
Time Series Analysis is truly an interdisciplinary field, because development of its theory and methods requires interaction between the diverse disciplines in which it is applied. The goal of the IMA 1990 summer program from which these proceedings are drawn was to promote strong interaction among the diverse community of statisticians and other scientists whose research involves the analysis of time series data. The themes of the program were:
The time series volumes should be of interest to researchers in all of these fields.
See IMA Volume 45 for
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Contents: pdf postscript
This volume is the proceedings of the IMA workshop "Degenerate Diffusion" held at the University of Minnesota from May 13 to May 18, 1991.
The workshop consisted of two parts. The emphasis of the first four days was on current progress or new problems in nonlinear diffusions involving free boundaries or sharp interfaces. The analysts and geometers will find some of the mathematical models described in this volume interesting and the papers of more pure mathematical nature included here should provide applied mathematicians with powerful methods and useful techniques in handling singular perturbation problems as well as free boundary problems.
This volume contains some of the lectures given at the workshop Linear Algebra, Markov Chains, and Queueing Models held January 13-17, 1992, as part of the year of Applied Linear Algebra at the Institute for Mathematics and its applications.
Markov chains and queueing models play an increasingly important role in the understanding of complex systems such as computer, communication, and transportation systems. Linear algebra is an indispensable tool in such research, and this volume collects a selection of important papers in this area. The articles contained herein are representative of the underlying purpose of the workshop which was to bring together practitioners and researchers from the areas of linear algebra, numerical analysis, and queueing theory who share a common interest of analyzing and solving finite state Markov chains. The papers in this volume are grouped into three mejor categories-perturbation theory and error analysis, iterative methods, and applications regarding queueing models.
It is hoped that these contributions can provide the reader with an enlarged perspective of some of the major issues which are of current concern to both the pure and applied communities.
The book is based on a seminar conducted by the author at the Institute for Mathematics and its Applications during 1991-92. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The book consists of twenty chapters, each one being independent of the others. Each of the first nineteen chapters is based on a presentation by one of the speakers; it includes the industrial background, relevant mathematical literature, a list of open mathematical problems and, in some cases, reference to a solution or a partial solution of the problem. Most of the problems, however, are stilll open and they are addressed to mathematicians. The last chapter of the book contains references to solutions of problems presented in the previous volumes of "Mathematics in Industrial Problems, Parts 2, 3, and 4" published in the IMA series, as volume 24, volume 31, and volume 38. The topics included in Part 5 are imaging and visualization, diffusion in glassy and swelling polymers, composite materials, plastic flows, coating of fiber optics, communication, colloidal dispersion, stress in semiconductor, micromagnetics, photobleaching, and machine vision.
The book will be of interest to mathematicians seeking to work on mathematical roblems which arise in industry. It will also be of interest to mathematicians and scientists who would like to learn about the interaction between mathematics and industry, what type of problems arise, how they are modelled, etc. Scientists working in industry may also be interested in the book as they discover that some of the topics dealt with are connected to their own work.
This volume is the proceeding of a workshop on combinatorial and graphp-theoretical problems in linear algebra held during the week of November 11-15, 1991. A primary goal of the workshop was to foster interaction among the people who work on linear algebra problems in which combinatorial or graph-theoretical analysis is a major component and those that work on combinatorial or graph- theoretical problems for which linear algebra is a major tool. The fifteen papers in this volume span a wide cross-section of past and current research in the topic of the workshop. Specific topics covered in the papers include matrix problems and results in symbolic dynamics, block-triangular decompositions of mixed matrices, algebraic and geometric properties of Laplacian matrices of graphs, the use of eigenvalues in combinatorial optimization, eigenvalues and associated eigenspaces of graphs and tournaments, qualitative and combinatorial aspects of matrices, perturbation effects on rank and eigenvalues, and polynomial spaces. This book should be of interest to researchers in linear algebra, combinatorics and graph theory, and to anyone who wishes to get a glimpse of this fascinating area.
Dynamic phase transitions and the consequent issues of rapid solidification, liquification, and vaporization, gives rise to difficult experimental, physical and mathematical questions. The articles herein collected are from a workshop held at the University of Minnesota in October, 1990 and include presentations by some of the principal workkers in their respective fields on molecular dynamics, shear induced dynamic phase transitions, the Riemann problem for systems that allow change of type, adiabatic shear band formation, shock stability, and the implications of higher spatial gradients of deformation entering into the constitutive structure. The book should be of interest to physicists, mechanicians, and applied mathematicians.
Dynamic phase transitions and the consequent issues of rapid solidification, liquification, and vaporization, gives rise to difficult experimental, physical and mathematical questions. The articles herein collected are from a workshop held at the University of Minnesota in October, 1990 and include presentations by some of the principal workers in their respective fields on molecular dynamics, shear induced dynamic phase transitions, the Riemann problem for systems that allow change of type, adiabatic shear band formation, shock stability, and the implications of higher spatial gradients of deformation entering into the constitutive structure. The book should be of interest to physicists, mechanicians, and applied mathematicians.
This volume contains articles based on lectures given at the workshop "Variational and Free Boundary Problems'' held April 1990 as a part of the year of Phase Transitions and Free Boundaries at the Institute for Mathematics and its Applications. The book provides a wide cross section of current research in far growing area. The articles are based on models which arise in phase transitions, in elastic/plastic contact problems, Hele-Shaw cells, crystal growth, variational formulation of computer vision models, magneto-hydrodynamics, bubble growth, hydrodynamics (jets and cavities), and in stochastic control and economics. They present mathematical methods which hopefully can be further extended and developed for other models. The book should be of interest both to mathematicians and to engineers who are working with mathematical models.
Much of our traditional knowledge of materials and processes is achieved by observation and analysis of small departures from equilibrium. Many materials, especially modern alloys, ceramics, and their composites, experience not only larger but more dramatic changes, such as the occurrence of phase transitions and the creation of defect structures, when viewed at the microscopic scale. How is this observed, how can it be interpreted, and how does it influence macroscopic behavior? These are the principle concerns of this volume, which constitute the proceedings of an IMA workshop dedicated to these issues.
The Institute of Mathematical Applications workshop on a Dynamical System Approach to Turbulence in Fluid Flows was one of a trio of workshops which closed the year-long program on Dynamical Systems and their Applications. The papers contained in this volume represent various approaches for studying the interrelated concepts of turbulence and long-time dynamics of the Navier-Stokes equations and related problems.
When reality is modeled by computation, matrices are often the connection between the continuous physical world and the finite algorithmic one. Usually, the more detailed the model, the bigger the matrix, the better the answer. Efficiency demands that every possible advantage be exploited: sparse structure, advanced computer architectures, efficient algorithms. Therefore sparse matrix computation knits together threads from linear algebra, parallel computing, data structures, geometry, and both numerical and discrete algorithms. One of the strongest threads is graph theory, which has been ubiquitous in sparse matrix computation ever since Seymour Parter used undirected graphs to model symmetric Gaussian elimination more than 30 years ago.
The Institute for Mathematics and Its Applications held a workshop on "Sparse Matrix Computations: Graph Theory Issues and Algorithms," organized by the editors of this volume, from October 14 to 18, 1991. The workshop included fourteen invited and several contributed talks, software demonstrations, an open problem session, and a great deal of stimulating discussion between mathematicians, numerical analysts, and theoretical computer scientists. After the workshop we invited some of the participants to submit papers for this collection. We intend the result to be a resource for the researcher or advanced student of either graphs or sparse matrices who wants to explore their connections. Therefore we asked the authors to undertake the challenging task of making current research accessible to both communities.
This is the sixth volume in Avner Friedman's collection of Mathematics in Industrial Problems. These books aim to foster interaction between industry and mathematics at the "grass root" level of specific problems. The problems presented in this book arise from models developed by industrial scientists engaged in research and development of new or improved products. The author's sources are affiliated with a variety of industrial enterprises including Eastman Kodak Company, Ford Motor Company, 3M, General Motors, Paramax, IBM/T.J. Watson Research Center, Xerox Corporation/Webster Research Center, Cray Research Inc., and Motorola.
The topics explored in this volume include magnetization in recording media; effective medium theory for color, particle simulation in xerography; amorphous semiconductors, small device semiconductor, and smart power device; dopant diffusion in network; reaction-diffusion and dissolution of crystals in solution; permeation through flawed surfaces; statistical quality control; glassy polymers; wettability for heterogeneous surfaces; electrorheological fluids; remote sensing and data fusion; micromechanical structures, and sensors. Open problems and references to mathematical literature are incorporated into many chapters. The final chapter contains solutions to problems raised in parts of the preceding volumes of Mathematics in Industrial Problems, published in the IMA Volumes in Mathematics and its Applications.
Semiconductor and integrated-circuit modeling are an important part of the high-technology "chip" industry, whose high-performance, low-cost microprocessors and high-density memory designs form the basis for supercomputers, engineering workstations, laptop computers, and other modern information appliances. There are a variety of differential equation problems that must be solved to facilitate such modeling.
During July 15-August 9, 1991, the Institute for Mathematics and its Applications at the University of Minnesota ran a special program on "Semiconductors." The four weeks were broken into three major topic areas:
This organization was natural since process modeling provides the geometry and impurity doping characteristics that are prerequisites for device modeling; device modeling, in turn, provides static current and transient charge characteristics needed to specify the so-called compact models employed by circuit simulators. The goal of this program was to bring together scientists and mathematicians to discuss open problems, algorithms to solve such, and to form bridges between the diverse disciplines involved.
The program was championed by Farouk Odeh of the IBM T.J. Watson Research Center. Sadly, Dr. Odeh met an untimely death. We have dedicated the proceedings volumes to him.
In this volume, we have combined the papers from the process modeling (week 1) and circuit simulation (week 4) portions of the program.
In 1991, semiconductor device modeling for practical engineering problems was largely based on the so-called drift-diffusion equations, a Poisson equation for the electrostatic potential coupled with advection-diffusion transport equations for the electrons and holes (in silicon, for example). Another popular model equation is the Boltzmann transport equation ( bte) of which the drift-diffusion equations are an approximation. For sufficiently small structures or iii-v (like GaAs) devices, some of the assumptions of the drift-diffusion model are incorrect. Alternate derivatives of the bte, such as energy-balance (or energy-transport) and hydrodynamic models, are of considerable interest. In fact, Dr. Odeh made a number of influential contributions to the hydrodynamic model and algorithms for it. The papers in this volume describe a variety of models and effectual techniques for dealing with them.
The solution of very large sparse or structured linear algebra problems is an integral part of many scientific computations. Direct methods for solving such problems are often infeasible because of computation time and memory requirements, and so iterative techniques are used instead. In recent years much research has focussed on the efficient solution of large systems of linear equations, least squares problems, and eigenvalue problems using iterative methods. The IMA Workshop on Iterative Methods for Sparse and Structured Problems brought together researchers from all over the world to discuss topics of current research. Areas addressed included the development of efficient iterative techniques for solving nonsymmetric linear systems and eigenvalue problems, estimating the convergence rate of such algorithms, and constructing efficient preconditioners for special classes of matrices such as Toeplitz and Hankel matrices. Iteration strategies and preconditioners that could exploit parallelism were of special interest. The papers in this volume represent the latest results of mathematical and computational research into the development and analysis of robust iterative methods for numerical linear algebra problems.
It is increasingly the case that models of natural phenomena and materials processing systems involve viscous flows with free surfaces. These free boundaries are interfaces of the fluid with either second immiscible fluids or else deformable solid boundaries. The deformation can be due to mechanical displacement or as is the case here, due to phase transformation; the solid can melt or freeze. This volume of the IMA Proceedings highlights a broad range of subjects on interfacial phenomena. There is an overview of the mathematical description of viscous free-surface flows, a description of the current understanding of mathematical issues that arise in these models and a discussion of high-order-accuracy boundary-integral methods for the solution of viscous free surface flows. There is the mathematical analysis of particular flows: long-wave instabilities in viscous-film flows, analysis of long-wave instabilities leading to Marangoni convection, and descriptions of the interaction of convection with morphological stability during directional solidification.
During the past decade the interaction between control theory and linear algebra has been ever increasing, giving rise to new results in both areas. As a consequence it was quite natural to include in the Applied Linear Algebra Year held at the IMA, a workshop dedicated to this interdisciplinary area.
This volume contains invited papers presented at this Workshop on Linear Algebra for Control Theory. The cross-fertilization between control and linear algebra can be found in subfields as Numerical Linear Algebra, Canonical Forms, Ring-theoretic Methods, Matrix Theory, and Robust Control.
The challenge of the workshop was to present the latest results in these areas and to find points of common interest. The present volume reflects very nicely this interaction: the range of topics seems very wide indeed but the basic problems and techniques are always closely connected. And the common denominator in all this is of course linear algebra.
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 volume contains the proceedings of the International Conference on Hamiltonian Dynamical Systems held at the University of Cincinnati in March of 1992. Its contents reflect the wide scope and increasing influence of Hamiltonian methods, with contributions from a whole spectrum of researchers in mathematics and physics from more than half a dozen countries, as well as several researchers in the history of science. With the inclusion of several historical articles, these proceedings are a slice not only of state-of-the-art methodology in Hamiltonian dynamics, but also of the bigger picture in which that methodology is embedded.
The articles in this book are from a workshop on power systems held at the Institute of Mathematics and its Applications at the University of Minnesota. Their topics include power system model reduction, transient and voltage stability, nonlinear control, robust stability, computation and optimization. The articles are authored by some of the leading researchers in these areas. The book should be of interest to power and control engineers, and applied mathematicians.
This volume is the Proceedings of the Workshop on Mathematical Finance held at the Institute for Mathematics and its Applications, June 14-18, 1993. A workshop on mathematical finance can be held only because of two revolutions that have taken place on Wall Street in the latter half of the twentieth century. The first revolution, which was the introduction of quantitative methods to the black art of equity fund management, began with the 1952 publication of his PhD dissertation "Portfolio Selection" by Harry Markowitz. The second revolution in finance began with the 1973 publication of the solution by Fischer Black and Myron Scholes (in consultation with Robert Merton) to the option pricing problem. The Black-Scholes formula brought to the finance industry the modern methodology of martingales and stochastic calculus, methodology which enables investment banks to produce, price and hedge an endless variety of "derivative securities." These two revolutions in finance have created a stream of practical problems whose solutions require the expertise of research mathematicians. This workshop addressed a number of these problems.
Robust control is motivated by the need to cope with systems with modeling uncertainty. Uncertainty is always present, fundamentally because no mathematical system can exactly model a physical system. For example, there are always uncertain parameters and unmodeled dynamics; simplifying assumptions are often made; only incomplete or inexact data from identification experiments is available. Robust control theory is a central subfield of control theory and deals with the analysis and synthesis of control systems in the face of plant uncertainty.
The 1992 IMA Workshop on Robust Control Theory brought together leading experts and covered most major research directions in the field of robust control This volume contains papers based on some of the talks that were presented.
This is the seventh volume in Avner Friedman's collection of Mathematics in Industrial Problems. These books aim to foster interaction between industry and mathematics at the "grass root" level of specific problems. The problems presented in this book arise from models developed by industrial scientists engaged in research and development of new or improved products. The author's sources are affiliated with a variety of industrial enterprises including General Motors, Eastman Kodak, Ford Motor Company, Oak Ridge National Laboratory, Bellcore, 3M, IBM, Siemens, Honeywell, UNISYS and Motorola.
The topics explored in this volume include heat sensors for automobiles, battery cells, colloidal dispersions, polymers, crack propagation, coating by electrostatic sprayers, neural networks, head-tape interaction in magnetic tapes, layered manufacturing, image analysis, landmarks identification by robots, communication for multi-users, data fusion, doping profile in semiconductors, effective medium estimates, and scattering by electromagnetic waves.
Open problems and references to mathematical literature are incorporated into most of the chapters. The final chapter contains solutions to problems raised in parts of the preceding volumes of Mathematics in Industrial Problems, published in the IMA Volumes in Mathematics and its Applications.
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This volume contains the proceedings of the Period of Concentration in Flow
Control held at the IMA in November, 1992. This gathering of engineers and
mathematicians was especially timely as it coincided with the emergence
of the role of mathematics and systematic engineering analysis in flow control
and optimization. Since this meeting, this role has significantly expanded
to the point where now sophisticated mathematical and computational tools
are being increasingly applied to the control and optimization of fluid
flows. Thus, these proceedings serve as a valuable record of some important
work that has gone on to influence the practical, everyday design of flows.
Moreover, they also represent very nearly the state of the art in the formulation,
analysis, and computation of flow control problems.
This volume contains papers by leading researchers on recent advances in linear algebra for signal processing. The papers address the following five areas (1) updating SVD and eigendecompositions; (2) adaptive filtering; (3) structured matrix problems; (4) wavelets and multirate signal processing; and (5) linear algebra architectures (parallel/vector and other high performance machines/designs). The papers explore innovative concepts that will be of great interest to anyone working in the general area of matrix based signal processing.
In this volume we present the collected contributions to the November, 1992 {\em Workshop on Control and Optimal Design of Distributed Parameter Systems} at the Institute for Mathematics and its Applications, University of Minnesota, Minneapolis. These papers present original contributions in the areas of Control Theory for Partial Differential Equations, Identification and Optimal Design for such systems and Modelling of Advanced Materials. They follow on a quarter century of highly successful research in the control theory of linear partial differential equations to explore new directions for future research.
In the past decade the proliferation of local and global communication networks for computer and human communication, the development of parallel computers with large numbers of processors, and the design of flexible and robust manufacturing systems have spurred major advances in our understanding of queueing networks, and this volume reviews recent progress. While research on queueing networks uses many of the traditional queueing theory insights, it is more concerned with how network components interact than with detailed models of how an individual queue behaves. In the last few years there have been some surprises, in particular with regard to the conditions for stability of multiclass queueing networks, and this area forms a major theme of the volume. Other important themes concern the challenges reflected Brownian motion has set both as a mathematical object and as a modelling paradigm; the usefulness of ideas from the interacting particle system world; the application of large deviation theory; and the developing connections with optimization and dynamical systems theory.
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 recent 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 of articles. The techniques developed and surveyed in this volume are still undergoing rapid development, and many of the articles of the collection offer an expositionally pleasant entree into a research area of growing importance.
The areas of discrete event systems and queueing systems pose a number of challenging design, analysis and control problems. Application areas of special and topical interest include communication networks and manufacturing systems. The topics covered in this volume include: Modeling, design and analysis of discrete event systems, Design of scheduling policies for manufacturing systems, Optimal designs for queueing systems, and Analysis of queueing system models of manufacturing systems and communication networks.
The book covers key issues in analysis and design of adaptive systems for control and signal processing such as:
(i) Stability analysis
(ii) Asymptotic analysis of convergence and performance
(iii) Design methods for linear and nonlinear systems
(iv) Averaging methods.
It also covers the closely related topics:
(i) Identification of linear stochastic systems
(ii) Connections between adaptation and learning.
The topics span the entire gamut from analysis of adaptive systems to design. The broad spectrum of analytical approaches illustrate the wide range of mathematical methods available for the study of adaptive systems.
With considerations such as complex multi-dimensional geometries and nonlinearity, the computational solution of partial differential systems has become so involved that it is important to automate decisions that have been classically left to the individual. These include mesh generation, which must be linked to the software generating the domain geometry. Solution accuracy and reliability dictates that mesh selection must be linked to solution generation in an iterative, adaptive fashion. Reliability can be gaged by efficient estimates of local and global discretization errors that both appraise solution accuracy and to control the adaptive process. The material within this volume addresses these issues. Papers describe geometric modeling and its relation to mesh generation; adaptive computational strategies with an emphasis on high-order methods and hp-refinement; and a posteriori error estimation. Applications concentrate on computational fluid mechanics. Submissions involve mathematicians, numerical analysts, computer scientists, and engineers in an effort to stimulate interdisciplinary interaction between the diverse groups.
Fifteen papers from an IMA workshop present the state of the art in a variety of areas of discrete probability, including random walks on finite and infinite graphs, random trees, renewal sequences, Stein's method for Normal approximation and Kohonen-type self-organizing maps.
This volume is a collection of research papers in the area of nonlinear stochastic partial differential equations. The first part contains work on fundamental problems of hydrodynamic limit for particle systems and on random media. The second part groups together papers under the umbrella of the name "Burgers' turbulence," although a broader spectrum of stochastic problem for the Burgers' equation is actually addressed. Finally, the last part deals with the stochastic Navier-Stokes equation both from mathematical and physical perspective.
This volume contains the proceedings of the workshop on Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control held at the Institute for Mathematics and its Applications in February 8-17, 1993. The topics include both geometric and nonsmooth analysis techniques in various problems of optimal control and stabilization for nonlinear dynamical systems governed by ordinary and partial differential equations and differential inclusions.
Environmental protection has become an universal issue with world-wide support. Destruction of the stratospheric ozone-layer, global increase in carbon dioxide and other radiatively important trace gases, acid rain, urban smog, water pollution of various types, and improper disposal of toxic wastes have all been shown as pressing problems. Environmental studies have now bridged the realms of academic research and societal applications. Mathematical modeling and large-scale data collection and analysis lie at the core of all environmental studies. Unfortunately, scientists, mathematicians, and engineers immersed in developing and applying environmental models, computaional methods, statistical techniques and computational hardware advance with separate and often discordant paces. The IMA Summer Program on Environmental Studies Workshop was designed to provide a much needed interdisciplinary forum for joint exploration of recent advances in this field.
This IMA volume includes a collection of twenty papers which address recent advances in the formulation and application of (A) environmental models, (B) environmental data and assimilation, (C) stochastic modeling and optimization, (D) Global climate modeling.
This volume is an attempt to explore the interface between two diverse areas of applied mathematics which are both "customers " of the maximum likelihood methodology: emission tomography (on the one hand) and hidden Markov models as an approach to speech understanding (on the other hand). There are other areas where maximum likelihood is used, some of which are represented in this volume: parsing of text (Jelinek), microstructure of materials (Ji), DNA sequencing (Nelson). Most of the participants were in the main areas of speech or emission density reconstruction. Of course there are many other areas where maximum likelihood is used which are not represented here.
Genetic mapping, physical mapping and DNA sequencing are the three key components of the human and other genome projects. Statistics, mathematics and computing play important roles in all three, as well as in the uses to which the mapping and sequencing data are put. This volume reviews recent progress in the area, with an emphasis on the theory and application of genetic mapping.
The revolutionary progress in molecular biology within the last 30 years opens the way to full understanding of the molecular structures and mechanisms of living organisms. Interdisciplinary research in mathematics and molecular biology is driven by ever growing experimental, theoretical and computational power. The mathematical sciences accompany and support much of the progress achieved by experiments and computations, as well as provide insight into geometric and topological properties of biomolecular structures and processes. This volume consists of a representative sample of the papers presented during week 3 (Protein Structure and Dynamics, organized by Jill P. Mesirov and Klaus Schulten) and week 4 (Topology and Geometry of DNA and RNA, organized by De Witt Sumners) of the month-long IMA Summer 1994 Program in Molecular Biology. The papers in this volume cover the spectrum from experiment to computation to simulation to theory.
This is the eight volume in Avner Friedman's collection of Mathematics in Industrial Problems. These books aim to foster interaction between industry and mathematics at the "grass root" level of specific problems. The problems presented in this book arise from models developed by industrial scientists engaged in research and development of new or improved products. The author's sources are affiliated with a variety of industrial enterprises including IBM Research Center and Columbia University, Engineering Computer Corporation (Warrensville Hts., Ohio), Eastman Kodak, IBM Research (Yorktown Heights), Electronic Data Systems, Ford Motor Company, Schlumberger-Doll Research, IBM Thomas J. Watson Research Center, AT&T Bell Laboratories, North Carolina Supercomputing Center (Research Triangle Park), General Motors Research and Development Center, Motorola Advanced Custom Technologies, 3M Company, Alliant Techsystems
The topics explored in this volume include several issues in semiconductors such as etching/deposition, failure in metal lines, and randomized algorithms in printed circuit board, surface modeling and geometric variability in manufacturing, robots and mechanisms, cellular mobile radio, signal masking in chaotic dynamical systems, geophysical prospecting, fluid flow and aeroacoustic, crystal growth, chemical filtration, and deformation of metals.
Open problems and references to mathematical literature are incorporated into most of the chapters. The final chapter contains solutions to problems raised in Part 7, Mathematics in Industrial Problems Mathematics in Industrial Problems, published in the IMA Volumes in Mathematics and its Applications. Volume 67.
This volume contains most of the papers presented at the IMA workshop on Classical and Modern Branching Processes, June 13-17 1994. As the papers indicate, branching processes is an active area of research both with its own problems as well as a number of new applications such as Tree structures, Algorithms, Disordered systems, Data storage, Spinglass models, and Dependencies in biological population dynamics. Many open problems are indicated here that should make the present volume a catalyst for much future research in Branching Processes.
This volume contains edited proceedings of a workshop on Stochastic Models in Geosystems held during the week of May 16, 1994 at the Institute for Mathematics and Its Applications at the University of Minnesota. The authors represent a broad interdisciplinary spectrum including mathematics, statistics, physics, geophysics, astrophysics, atmospheric physics, fluid mechanics, seismology, and oceanography. The common underlying theme was stochastic modeling of geophysical phenomena and papers appearing in this volume reflect a number of research directions that are currently pursued in these areas. From the methodological mathematical viewpoint most of the contributions fall within the areas of wave propagation in random media, passive scalar transport in random velocity flows, dynamical systems with random forcing and self-similarity concepts, including multifractals.
The papers contained in this volume represent a snap-shot of current applied mathematical research in wave propagation and scattering. Although the mathematical underpinnings of the research contained herein are rooted in classical asymptotic and numerical analyses, each author is motivated by a complex technological problem which requires a resolution. The problems range from using underwater sound to monitor and predict global warming, to periodically embedding phase-sensitive amplifiers in optical fibers to insure long range digital communication. Such variety shows that wave propagation and scattering remain vital and important areas of mathematical and scientific endeavors.
This volume contains a series of papers devoted to the collection, interpretation and analysis of population genetic data. Among the topics included here are studies on human evolutionary history, molecular techniques for generating data, statistical and computational techniques for the interpretation of such data, and stochastic models for genealogy and population structure. The papers reflect the close interaction between experimental molecular biologists and theoreticians. The papers will be useful for specialists in the area, as well as mathematicians, statistician s, computer scientists and biologists wanting a brief overview of current problems in the field.
This is the ninth volume in Avner Friedman's collection of Mathematics in Industrial Problems. These books aim to foster interaction between industry and mathematics at the "grass root" level of specific problems. The problems presented in this book arise from models developed by industrial scientists engaged in research and development of new or improved products. The author's sources are affiliated with a variety of industrial enterprises including Lucent Industries, IBM, 3M, Ford Motor Company, Eastman Kodak, Honeywell, Motorola, Lockheed Martin, General Electric, and Schlumberger-Doll Research
The topics explored in this volume include diffusion in porous media and in rubber/glass transition, coating flows, solvation of molecules, semiconductor processing, optoelectronics, photographic images, density-functional theory, sphere packing, performance evaluation, causal networks, electrical well logging, general positioning system, sensor management, pursuit-evasion algorithms, and nonlinear viscoelasticity.
Open problems and references to mathematical literature are incorporated into most of the chapters. The final chapter contains solutions to problems raised in previous parts of the series Mathematics in Industrial Problems, published in the IMA Volumes in Mathematics and its Applications.
This volume presents the proceedings of a workshop held at the Institute for Mathematics and Its Applications. This institute is founded by the National Science Foundation to promote the interchange of ideas between applied mathematics and the other sciences. The present volume fits in that framework by bringing together ideas of mathematicians, physicists, and chemists in the area of multiparticle scattering theory. Scattering theory (or collision theory as it is often called) is a fundamental area of theory and computation in both physics and chemistry. The correct formulation of scattering theory for two-body collisions is now well worked out, but systems with three or more particles still present fundamental unmet challenges, both in the formulations of the problem and in the interpretation of computational results. A key issue in the mathematical foundations is asymptotic completenes, which says that any state of a quantum system is a superposition of bound and scattering states. Key issues on the physical side are concerned with boundary conditions, electromagnetic fields, effective potentials, and resonances.
The volume begins with two tutorials, one on mathematical issues, including cluster decompositions and asymptotic completeness, in N-body quantum systems and the other on computational approaches to quantum scattering. Later chapters are concerned with wavepacket quantum mechanics and time evolution operators, classical action, collisions in laser fields and in magnetic fields, laser-induced processes, barrier resonances, complex dilated expansions, effective potentials for nuclear collisions, long-range potentials, and the Pauli Principle.
The publisher and the symposium organizers hope that this volume will contribute to increasing dialog between mathematicians, physicists, and chemists interested in collisions and scattering in systems with three or more particles.
Inverse problems in wave propagation concern extraction of information about distant structural features from the measurements of scattered waves. Tasks of this nature arise in geophysics, ocean acoustics, civil and environmental engineering, ultrasonic nondestructive testing, biomedical ultrasonics, radar, astrophysics, and other areas of science and technology.
The papers in this volume represent most of these scientific and technical topics, together with fundamental mathematical investigations of the relation between waves and scatterers.
The study of singularities and oscillations of waves has progressed along several fronts. A key common feature is the presence of a small scale in the solutions. Recent emphasis has been on nonlinear waves. Nonlinear problems are generally less amenable than linear problems to broad unified approaches. As a result there is a justifiable tendency to concentrate on problems of particular geometric or physical interest. This volume contains a multiplicity of approaches brought to bear on problems varying from the formation of caustics and the propagation of waves at a boundary to the examination of viscous boundary layers. There is an examination of the foundations of the theory of high-frequency electromagnetic waves in a dielectric or semiconducting medium. Unifying themes are not entirely absent from nonlinear analysis. One paper here considers microlocal analysis, including paradifferential operator calculus, on Morrey spaces, and connections with various classes of partial differential equations.
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.
The workshop on optimization applications for design and control was made up of specialists in optimization and practitioners in the fields of aerospace engineering, chemical engineering, and fluid and solid mechanics. The major themes included an assessment of the state of the art in optimization algorithms as well as challenging applications in design and control, in the areas of process engineering and systems with partial differential equation models, The papers in this volume represent a balanced selection from the above application areas as well as contributions that survey the state of the art in relevent areas of nonlinear programming.
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 Parts I and II which appeared as IMA Volumes 92 and 93, respectively.
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 articles in this volume explore the various aspects of quasiclassical methods such as approximate theories for large Coulomb systems, Schr\"odinger operator with magnetic wells, ground state energy of heavy molecules in strong magnetic field, and methods with emphasis on coherent states. Included are also mathematical theories dealing with $h$-pseudodifferential operators, asymptotic distribution of eigenvalues in gaps, a proof of the strong Scott conjecture, Lieb-Thirring inequalities for the Pauli operator, and local trace formulae.
This volume combines the proceedings of two workshops. One devoted to wavelets, multigrid and other fast algorithms (multipole, FFT) and their use in wave propagation, and another devoted to waves in random waves and other complex media.
Majority of the chapters deal with the effects of inhomogeneities of wave propagation both theoretically and computationally. They include topics such as waves in random media, coherent effects in scattering for random systems with discrete spectrum, interaction of microwaves with sea ice, scattering in magnetic field, surface waves, seismograms envelopes, backscattering, polarization mode dispersions, and spatio-temporal distribution of seismic power. Several articles describes numerical methods, such as fast algorithm for solving electromagnetic scattering problems, and the panel clustering methods in 3-d BEM.
On August 22-24, 1996, an international group of researchers convened, under the auspices of the Institute for Mathematics and Its Applications (IMA), in Minneapolis, Minnesota, for a scientific workshop on the "Applications and Theory of Random Sets." The articles in this volume address theoretical and applied aspects of this field in diverse areas of applications such as Image Modeling and Analysis, Information/Data Fusion, and Theoretical Statistics and Expert Systems. Emphasis is given to potential applications in engineering problems of practical interest. This volume is of interest to mathematicians, engineers and scientists who are interested in the potential application of random set theory to practical problems in imaging, information fusion, and expert systems.
This volume presents the proceedings of a workshop held at the Institute for Mathematics and its Applications. This institute is founded by the National Science Foundation to promote the interchange of ideas between applied mathematics and the other sciences. The present volume fits in that framework by bringing together ideas of mathematicians and researchers in the physical scientists in the area of particulate flow and rheology.
Flow of particles in a fluid occur in food processing, catalytic processing, slurries, coating, paper manufacturing, particle injection molding and filter operation. In many of these processes, the rheology of such materials as they undergo transport and processing is important in design, operation, and efficiency. Consequently, using these materials represents a technological challenge.
In spite of the phenomenal advances in computation and computers, simulation of the motion of more than a few particles in a fluid is impractical. Therefore, effective media models and two-fluid models are important in the description of particle-fluid flows.
The volume offers papers addressing issues of ensemble averaging, microstructure behavior, and the analysis of two-continuua models. The span of practical to theoretical approaches to particulate flow makes this volume appeal to researchers interested in deriving or applying particulate flow models.
The publisher and the symposium organizers hope that this volume will contribute to increasing dialog between mathematicians and physical scientists interested in particulate flow.
Polycrystalline metals, porous rocks, colloidal suspensions, epitaxial thin films, gels, foams, granular aggregates, sea ice, shape-memory metals, magnetic materials, and electro-rheological fluids are all examples of materials where an understanding of the mathematics on the different length scales is a key to interpreting their physical behavior. In their analysis of these media, scientists coming from a number of disciplines have encountered similar mathematical problems, yet it is rare for researchers in the various fields to meet. The 1995-96 program at the Institute for Mathematics and its Applications was devoted to Mathematical Methods in Materials Science, and was attended by material scientists, physicists, geologists, chemists, engineers, and mathematicians. The present volume contains papers which have emerged from four of the workshops held during the year, focusing on the following areas: 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 microstructural to the macroscopic, the microstructures from ordered to random, and the treatments from "purely" theoretical to the highly applied. Taken together, these works form a compelling and broad account of many aspects of the science of multiscale materials, and will hopefully inspire research across the self-imposed barriers of twentieth century science.
This is the tenth volume in Avner Friedman's collection of Mathematics in Industrial Problems. These books aim to foster interaction between industry and mathematics at the "grass root" level of specific problems. The problems presented in this book arise from models developed by industrial scientists engaged in research and development of new or improved products. The author's sources are affiliated with a variety of industrial enterprises including Motorola, IBM, Ford Motor Company, Eastman Kodak, 3M, AT\&T Labs, Honeywell, and Schlumberger-Doll Research.
The topics explored in this volume include semiconductor devices and micro-accelerometers, computational aeroacoustics, coating flows, coalescence, electrorheological fluids, mass transport in particle-loaded beds, metal cutting processes, network traffic analysis, risk management, micromagnetics and cooling systems.
Open problems and references to mathematical literature are incorporated into most of the chapters. The final chapter contains solutions to problems raised in previous parts of the series Mathematics in Industrial Problems, published in the IMA Volumes in Mathematics and its Applications.
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 optical response of materials, how to predict laser-induced breakdown in efficient optical devices, and how to handle electron cloud distortion in femtosecond processes.
Polymers occur in many different states and their physical properties are strongly correlated with their conformations. The theoretical investigation of the conformational properties of polymers is a difficult task and numerical methods play an important role in this field. This book contains contributions from a workshop on numerical methods for polymeric systems, held at the IMA in May 1996, which brought together chemists, physicists, mathematicians, computer scientists and statisticians with a common interest in numerical methods.
The two major approaches used in the field are molecular dynamics and Monte Carlo methods, and the book includes reviews of both approaches as well as applications to particular polymeric systems. The molecular dynamics approach solves the Newtonian equations of motion of the polymer, giving direct information about the polymer dynamics as well as about static properties. The Monte Carlo approaches discussed in this book all involve sampling along a Markov chain defined on the configuration space of the system. 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.
The book is of interest to workers in polymer statistical mechanics and also to a wider audience interested in numerical methods and their application in polymeric systems.
This book contains contributions from a workshop on topology and geometry of polymers, held at the IMA in June 1996, which brought together topologists, combinatorialists, theoretical physicists and polymer scientists, with a common interest in polymer topology.
Polymers can be highly self-entangled even in dilute solution. In the melt the inter- and intra-chain entanglements can dominate the rheological properties and it is important to develop a deeper theoretical understanding of these phenomena. Although the possibility of knotting in ring polymers has been recognised for more than thirty years it is only recently that the powerful methods of algebraic topology have been used in treating models of polymers. This book contains a series of papers which review the current state of the field and give an up to date account of what is known and, perhaps more importantly, what is still unknown. The field abounds with open problems.
The book is of interest to workers in polymer statistical mechanics but will also be useful as an introduction to topological methods for polymer scientists, and will introduce mathematicians to an area of science where topological approaches are making a substantial contribution.
The chapters in this book present an excellent exposition of recent developments in both robotics and nonlinear control centering around (i) "hyper-redundancy", (ii) highly oscillatory inputs, (iii) optimal control, (iv) exterior differential systems, and (v) the use of generic loops. The principal topics covered in the book are:
This book's chapters offer a wide-ranging tour of recent developments in the very rapidly growing and changing field of parallel algorithms. They cover the following general areas:
In the past two decades, breakthroughs in computer technology have made a tremendous impact on optimization. In particular, availability of parallel computers has created substantial interest in exploring the use of parallel processing for solving discrete and global optimization problems. The collection of articles in this volume covers a broad spectrum of recent research in parallel processing of discrete and related problems. The topics discussed include distributed branch-and-bound algorithms, parallel genetic algorithms for large scale discrete problems, simulated annealing, parallel branch-and-bound search under limited-memory constraints, parallelization of greedy randomized adaptive search procedures, parallel optical models of computing, randomized parallel algorithms, general techniques for the design of parallel discrete algorithms, parallel algorithms for the solution of quadratic assignment and satisfiability problems. The book will be a valuable source of information to faculty, students and researchers in combinatorial optimization and related areas.
High performance computing consumes and generates vast amounts of data, and the storage, retrieval, and transmission of these 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.
Drug research and discovery are of critical importance in human health care. Computational approaches for drug lead discovery and optimization have proven successful in many recent research programs. These methods have grown in their effectiveness not only because of improved understanding of the basic science - the biological events and molecular interactions that define a target for therapeutic intervention - but also because of advances in algorithms, representations, and mathematical procedures for studying such processes. This volume surveys some of those advances. A broad landscape of high-profile topics in computer-assisted molecular design (CAMD) directed to drug design are included.
Subject areas represented in the volume include receptor-based applications such as binding energy approximations, molecular docking, and de novo design; non-receptor-based applications such as molecular similarity; molecular dynamics simulations; solvation and partitioning of a solute between aqueous and nonpolar media; graph theory; non-linear multidimensional optimization, processing of information obtained from simulation studies, global optimization and search strategies, and performance enhancement through parallel computing.
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. Yet other applications are still emerging - providing number theorists with some major new areas of opportunity.
The 1996 IMA summer program on Emerging Applications of Number Theory was aimed at stimulating further work with some of these newest (and most attractive) applications.
Concentration was on number theory's recent links with:
(a) wave phenomena in quantum mechanics (more specifically, quantum chaos); and
(b) graph theory (especially expander graphs and related spectral
This volume contains the contributed papers from that meeting and will be of interest to anyone intrigued by novel applications of modern number-theoretical techniques.
The articles collected in this volume are based on lectures at the IMA Workshop "Computational Radiology and Imaging: Therapy and Diagnostics," March 17-21, 1997. Introductory articles by the editors have been added. The focus is on inverse problems involving electromagnetic radiation and particle beams, with applications to X-ray tomography, nuclear medicine, near-infrared imaging, microwave imaging, electron microscopy, and radiation therapy planning.
Mathematical and computational tools and models which play important roles in this volume include the X-ray transform and other integral transforms, the linear Boltzmann equation and, for near-infrared imaging, its diffusion approximation, iterative methods for large linear and non-linear least-squares problems, iterative methods for linear feasibility problems, and optimization methods.
The volume is intended not only for mathematical scientists and engineers working on these and related problems, but also for non-specialists. It contains much introductory expository material, and a large number of references. Many unsolved computational and mathematical problems of substantial practical importance are pointed out.
The IMA Workshop on Evolutionary Algorithms brought together many of the top researchers working in the area of Evolutionary Computation for a week of intensive interaction. The field of Evolutionary Computation has developed significantly over the past 30 years and today consists a variety of subfields such as genetic algorithms, evolution strategies, evolutionary programming, and genetic programming, each with their own algorithmic perspectives and goals.
The workshop did a great deal to clarify the current state of the theory in Evolutionary Algorithms. The existing theory might be characterized as deriving from two principal approaches. There is a high level macro-theory that looks at the processing of "building blocks" and "schemata" that are shared by many good solutions when searching a problem space. There is also a low level micro-theory that builds exact Markov models of the search process. It is sometimes hard for researchers working at such different levels of abstraction to interact. The IMA workshop allowed researchers working at these different levels to present their points of view and to move toward common ground.
There was real progress was in communication between theorist and practitioners in the evolutionary computation field. Speakers presented applications across a wide range of problem areas. In some of those cases, theoretically motivated methods work quite well. In other cases, practitioners used domain-based methods to obtain better performance than could be achieved by using a "pure" evolutionary algorithm. Individuals on both sides went away with a better appreciation of the successes and failures of current theory. The workshop should help to change what practitioners say about the current state of theory in the field.
This volume contains refereed papers from a workshop on Statistics in Genetics held as part of the six-week symposium on Statistics in the Health Sciences held by the Institute of Mathematics and its Applications in the summer of 1997. The week on genetics provided a forum for lively discussion among an unusual mix of statistical scientists and population geneticists.
The field of statistical genetics is growing and expanding. Though the Genome Project will eventually result in the sequencing of the human genome, as well as the genomes of several other organisms, there will still be a need for good statistics for family studies of complex diseases. Of special interest is the growing recognition of the potential role of interaction of mitochondrial genes with nuclear genes to produce many chronic or degenerative disorders. There is still much room for improving model building in phylogenetics analysis, particularly in understanding inference in this arena. The use of statistics for assessing identification in criminal and paternity cases through DNA is also becoming more widespread. The controversy over these methods are likely to rage for many years to come.
The papers in this volume are contributions by some of the leading researchers in the field to the current topics in in statistical genetics. One section deals with DNA sequence matching and issues related to forensics. Another group of papers deals with statistical problems of modeling phylogenies and inferential difficulties related to the complex tree structures produced, as well as the method of coalecence. Another group of papers are concerned with human genetics, including the identification of disease genes, and the genetics of cancer.
The papers in this volume are based on lectures given at the IMA Workshop on Grid Generation and Adaptive Algorithms held during April 28-May 2, 1997. Grid generation is a common feature of many computational tasks which require the discretization and representation of space and surfaces. The papers in this volume discuss how the geometric complexity of the physical object or the non-uniform nature of the solution variable make it impossible to use a uniform grid. Since an efficient grid requires knowledge of the computed solution, many of the papers in this volume treat how to construct grids that are adaptively computed with the solution.
This volume will be of interest to computational scientists and mathematicians working in a broad variety of applications including fluid mechanics, solid mechanics, materials science, chemistry, and physics. Papers treat residual-based error estimation and adaptivity, repartitioning and load balancing for adaptive meshes, data structures and local refinement methods for conservation laws, adaptivity for hp-finite element methods, the resolution of boundary layers in high Reynolds number flow, adaptive methods for elastostatic contact problems, the full domain partition approach to parallel adaptive refinement, the adaptive solution of phase change problems, and quality indicators for triangular meshes.
This volume contains refereed papers submitted by participants of the third week of a six week workshop on Statistics in the Health Sciences held by the Institute of Mathematics and its Applications in Minneapolis, Minnesota during July of 1997. This week was devoted to the closely related topics of Diagnosis and Prediction.
Theoretical and applied statisticians from Universities, Medical and Public Health Schools, government and private research institutions, and pharmaceutical companies involved in prediction problems in the life and social sciences and in diagnostic and screening tests were brought together to discuss and exchange new results and information on these important issues. A number of papers with applications were presented and especially lively discussions ensued involving the critical issues and difficulties in using and interpreting diagnostic tests and implementing mass screening programs. Both frequentist and Bayesian approaches were employed.
The importance of predicting or controlling future events such as survival, comparative survival and survival post intervention for a disease or even for certain biological or natural events is growing rapidly. This area of concern was also represented by participants who presented work that devised predictive methodology for a variety of problems mainly from a Bayesian perspective.
This volume contains a number of mini-review articles authored by speakers and attendees at the IMA workshop on Pattern Formation in Continuous and Coupled Systems. Pattern formation has been studied intensively for most of this century by both experimentalists and theoreticians. This workshop focused on new directions in the patterns literature. Systems that generate new types of pattern such as discrete coupled systems, systems with global coupling, and combustion experiments were stressed, as were new types of pattern.
The mini-reviews in this volume are intended to be pointers to the current literature for researchers at all levels and to have extensive bibliographies. They are also intended to discuss why certain subjects are currently exciting and worthy of additional research.
This volume contains refereed papers by participants in the two weeks on Clinical Trials and one week on Epidemiology and the Environment held as part of the six weeks workshop on Statistics in the Health Sciences at the Institute for Mathematics and its Application (IMA) in the summer 1997. Donald Berry was in charge of the weeks on clinical trials, and Elizabeth Halloran organized the week on epidemiology and the environment. The collection includes a major contribution from Jamie Robins, Andrea Rotnitzky, and Daniel Scharfstein on sensitivity analysis for selection bias and unmeasured confounding in missing data and causal inference models. In another paper, Jamie Robins presents a new class of causal models called marginal structural models. Alan Hubbard, Mark van der Laan, and Jamie Robins present a methodology for consistent and efficient estimation of treatment-specific survival functions in observational settings. Brian Leroux, Xingye Lei, and Norman Breslow present a new mixed model for spatial dependence for estimating disease rates in small areas. Andrew Lawson and Allan Clark demonstrate Markov Chain Monte Carlo methods for clustering in spatial epidemiology. Colin Chen, David Chock, and Sandra Winkler present a simulation study examining confounding in estimation of the epidemiologic effect of air pollution. Dalene Stangl discusses issues in the use of reference priors and Bayes factors in analyzing clinical trials. Stephen George reviews the role of surrogate endpoints in cancer clinical trials.
This volume contains papers from a workshop on Structured Adaptive Mesh Refinement (SAMR) held by the Institute of Mathematics and its Applications in the Spring of 1997.
Structured adaptive mesh refinement (SAMR) methods have matured over the past 20 years and are now the method of choice for certain difficult problems, such as compressible flow. SAMR presents difficult technical challenges, both in terms of the numerical techniques involved and the complexity of the programming effort, especially on parallel computers. In order to gain insight into managing these difficulties, much research effort has been directed at mesh generation, parallel computation, and improvements in accuracy, aimed primarily at refinement interfaces. A major stumbling block in this endeavor is that many of these techniques entail substantial amounts of problem specific detail. Standardization is highly unlikely, except within narrowly defined problem domains.
The papers presented in this collection are based on talks given at the Workshop on Structured Adaptive Mesh Refinement Grid Methods, held at the Institute for Mathematics and Its Applications, University of Minnesota, on March 12-13, 1997. They describe research to improve the general understanding of the application of SAMR to practical problems; identify issues critical to efficient and effective implementation on high performance computers; stimulate the development of a community code repository for software including benchmarks to assist in the evaluation of software and compiler technologies. The ten Chapters of this volume have been divided into two parts reflecting two major issues in the topic: (I) programming complexity of SAMR algorithms and (II) applicability and numerical challenges of SAMR methods. Part I presents three programming environments and two libraries that address the concerns of efficient execution and reduced software development times of SAMR applications. Part II describes an overview of applications that can benefit from SAMR methods, ranging from crack propagation and industrial boilers to the evolution of a cluster of galaxies.
The articles collected in this volume represent the contributions presented at the IMA workshop on "Dynamics of Algorithms" which took place in November 1997. The workshop was an integral part of the 1997-98 IMA program on "Emerging Applications of Dynamical Systems."
The interaction between algorithms and dynamical systems is mutually beneficial since dynamical methods can be used to study algorithms that are applied repeatedly. Convergence, asymptotic rates are indeed dynamical properties. On the other hand, the study of dynamical systems benefits enormously from having efficient algorithms to compute dynamical objects.
The Institute for Mathematics and its Applications (IMA) devoted its 1997-1998 program to Emerging Applications of Dynamical Systems. Dynamical systems theory and related numerical algorithms provide powerful tools for studying the solution behavior of differential equations and mappings. In the past 25 years computational methods have been developed for calculating fixed points, limit cycles, and bifurcation points. A remaining challenge is to develop robust methods for calculating more complicated objects, such as higher-codimension bifurcations of fixed points, periodic orbits, and connecting orbits, as well as the calculation of invariant manifolds. Another challenge is to extend the applicability of algorithms to the very large systems that result from discretizing partial differential equations. Even the calculation of steady states and their linear stability can be prohibitively expensive for large systems (e.g. 10^{3}-10^{6} equations) if attempted by simple direct methods.
Several of the papers in this volume treat computational methods for low and high dimensional systems and, in some cases, their incorporation into software packages. A few papers treat fundamental theoretical problems, including smooth factorization of matrices, self-organized criticality, and unfolding of singular heteroclinic cycles. Other papers treat applications of dynamical systems computations in various scientific fields, such as biology, chemical engineering, fluid mechanics, and mechanical engineering.
The papers in this volume are based on lectures given at the IMA workshop on the Parallel Solution of PDE during June 9-13, 1997. The numerical solution of partial differential equations has been of major importance to the development of many technologies and has been the target of much of the development of parallel computer hardware and software. Parallel computer offers the promise of greatly increased performance and the routine calculation of previously intractable problems.
This volume contains papers on the development and assessment of new approximation and solution techniques that can take advantage of parallel computers. It will be of interest to applied mathematicians, computer scientists, and engineers concerned with investigating the state-of-the-art and future directions in numerical computing. Topics include domain decomposition methods, parallel multi-grid methods, front tracking methods, sparse matrix techniques, adaptive methods, fictitious domain methods, and novel time and space discretizations. Applications discussed include fluid dynamics, radiative transfer, solid mechanics, and semiconductor simulation.
The formation of patterns in developing biological systems involves the spatio-temporal coordination of growth, cell-cell signalling, tissue movement, gene expression and cell differentiation. The interactions of these complex processes are generally nonlinear, and thus mathematical modelling and analysis are needed provide the framework in which to compute the outcome of different hypothesis on modes of interaction and to make experimentally testable predictions.
This collection contains papers exploring several aspects of the hierarchy of processes occurring during pattern fromation. A number of papers address the modelling of cell movement and deformation, with application to pattern formation within a collection of cells in response to external signalling cues. The results are considered in the context of pattern generation in {\em Dictyostelium discoideum} and bacterial colonies.
A number of models at the macroscopic level explore the possible mechanisms underlying spatio-temporal pattern generation in early development, focussing on primitive streak, somitogenesis, vertebrate limb development and pigmentation patterning. The latter two applications consider in detail the effects of growth on patterning.
The potential of models to generate more complex patterns are considered and models involving different modes of cell-cell signalling are investigated. Pattern selection is analysed in the context of chemical Turing patterns, which serve as a paradigm for morphogenesis and a model for vegetation patterns is presented.
Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neurobiological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations and jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role in the development of these techniques and one paper is directed specifically at applying geometric singular perturbation theory to reveal the synchrony in networks of neural oscillators.
Coding theory, system theory and symbolic dynamics have much in common. Among the central themes in each of these subjects are the construction of state space representations, understanding of fundamental structural properties of sequence spaces, construction of input/output systems, and understanding the special role played by algebraic structure. A major new theme in this active area of research is that of codes and systems based on graphical models.
This volume contains articles from leading researchers at the interface of these subjects. The book contains survey articles for non-specialists as well as original research papers. Many of these papers were presented at the 1999 IMA Summer Workshop on Codes, Systems, and Graphical Models.
This volume contains invited and refereed papers based upon presentations given in the IMA workshop on "Computational Modeling in Biological Fluid Dynamics" during January of 1999, which was part of the year-long program "Mathematics in Biology." This workshop brought together biologists, zoologists, engineers, and mathematicians working on a variety of issues in biological fluid dynamics.
A unifying theme in biological fluid dynamics is the interaction of elastic boundaries with a surrounding fluid. These moving boundary problems, coupled with the equations of incompressible, viscous fluid dynamics, pose formidible challenges to the computational scientist. In this volume, a variety of computational methods are presented, both in general terms, and within the context of applications including ciliary beating, blood flow, and insect flight.
Our hope is that this collection will allow others to become aware of and interested in the exciting accomplishments and challenges uncovered during this workshop.
This book grew out of the discussions and presentations that began during the Workshop on Emerging and Reemerging Diseases (May 17-21, 1999) sponsored by the Institute for Mathematics and its Application (IMA) at the University of Minnesota with the support of NIH and NSF. The workshop started with a two-day tutorial session directed to ecologists, epidemiologists, immunologists, mathematicians and scientists interested in being exposed to some of the modeling and mathematical approaches used in the study of disease dynamics. The core of this first volume, Volume 125, covers tutorial and research contributions on the use of dynamical systems (deterministic discrete, delay, PDEs and ODEs models) and stochastic models in disease dynamics. The volume includes the study of Cancer, HIV, Pertusis and Tuberculosis.
Beginning graduate students in applied mathematics, scientists in the natural, social or health sciences or mathematicians who want to enter the fields of mathematical and theoretical epidemiology will find this book useful.
This book grew out of the discussions and presentations that began during the Workshop on Emerging and Reemerging Diseases (May 17-21, 1999) sponsored by the Institute for Mathematics and its Application (IMA) at the University of Minnesota with the support of NIH and NSF. The workshop started with a two-day tutorial session directed to ecologists, epidemiologists, immunologists, mathematicians and scientists interested in being exposed to some of the modeling and mathematical approaches used in the study of disease dynamics. The core of this second volume, Volume 126, includes research contributions on the use of dynamical systems (deterministic discrete, delay, PDEs and ODEs models) and stochastic models in disease dynamics. Contributions motivated by the study of diseases like Influenza, HIV, Tuberculosis and macro parasitic diseases like schistosomiasis are also included.
This second volume requires additional mathematical sophistication and graduate students in applied mathematics, scientists in the natural, social and health sciences or mathematicians who want to enter the field of mathematical or theoretical epidemiology will find it useful.
The collection of contributors includes many who have been in the forefront
of the development of the subject.
"Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling.
There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes.
There is also a growing appreciation of the role for the inclusion of stochastic effects in the modeling of complex systems. This has led to interesting new mathematical problems at the interface of probability, dynamical systems, numerical analysis, and partial differential equations.
This volume will be useful to researchers and graduate students interested in probabilistic methods, dynamical systems approaches and numerical analysis for mathematical modeling in the sciences and engineering.
The physics of soft matter -- materials such as elastomers, gels, foams and liquid crystals -- is an area of intense interest and contemporary study. Moreover, soft matter plays a role in a wide variety of important processes and application. For example, gel swelling and dynamics are an essential part of many biological and industrial processes, such as motility mechanisms in bacteria and the transport and absorption of drugs. Ferroelectrics, liquid crystals, and elastomers are being used to design ever faster switching devices. Experimental studies, such as scattering, optical and electron microscopy, have provided a great deal of detailed information on structures. But the integration of mathematical modeling and analysis with experimental approaches promises to greatly increase our understanding of structure-property relationships and constitutive equations. The workshop on Modeling of Soft Matter has taken such an integrated approach. It brought together researchers in applied and computational mathematical fields such as differential equations, dynamical systems, analysis, and fluid and solid mechanics, and scientists and engineers from a variety of disciplines relevant to soft matter physics. An important outcome of the workshop has been to identify beautiful and novel scientific problems arising in soft matter that are in need of mathematical modeling and appear amenable to it and so to set the stage for further research. This Volume presents a collection of papers representing the key aspects of the topics discussed at depth in the course of the workshop.
The IMA Hot Topics workshop on compatible spatial discretizations was held May 11-15, 2004 at the University of Minnesota. The purpose of the workshop was to bring together scientists at the forefront of the research in the numerical solution of PDEs to discuss recent advances and novel applications of geometrical and homological approaches to discretization. This volume contains original contributions based on the material presented at the workshop. A unique feature of the collection is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science. Compatible spatial discretizations are those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. The papers in this volume offer a snapshot of the current trends and developments in compatible spatial discretizations. The reader will find valuable insights on spatial compatibility from several different perspectives and important examples of applications of compatible discretizations in computational electromagnetics, geosciences, linear elasticity, eigenvalue approximations and MHD. The contributions collected in this volume will help to elucidate relations between different methods and concepts and to generally advance our understanding of compatible spatial discretizations for PDEs. Abstracts and presentation slides from the workshop can be accessed at http://www.ima.umn.edu/talks/workshops/5-11-15.2004/.
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. The workshop provided a great opportunity to facilitate the communications between academia and the industry, and to bridge the mathematical sciences, engineering, information theory, and communication communities. The emphases were on design and analysis of computationally efficient algorithms to better understand the behavior and to control the wireless telecommunication networks. As an achieve, this volume presents some of the highlights of the workshop, and collects papers covering a broad spectrum of important and pressing issues in wireless communications. All papers have been reviewed. One of the book's distinct features is highly multi-disciplinary. This book is useful for researchers and advanced graduate students working in communication networks, information theory, signal processing, and applied probability and stochastic processes, among others.
Symmetries in various forms pervade mathematics and physics. Globally, there are the symmetries of a homogeneous space induced by the action of a Lie group. Locally, there are the infinitesimal symmetries induced by differential operators, including not only those of first order but of higher order too. This three-week Summer Program considered the symmetries preserving various natural geometric structures. Often these structures are themselves derived from partial differential equations whilst their symmetries turn out to be constrained by overdetermined systems. This leads to further topics including separation of variables, conserved quantities, superintegrability, parabolic geometry, representation theory, the Bernstein-Gelfand-Gelfand complex, finite element schemes, exterior differential systems, and moving frames.
There are two parts to these Proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.
These Proceedings are dedicated to the memory of Thomas P. Branson who played a leading role in the conception and organization of this Summer Program but did not live to see its realization.
To assess the past achievement and to provide a road map for future research, an IMA participating institution conference entitled "Conference on Asymptotic Analysis in Stochastic Processes, Nonparametric Estimation, and Related Problems" was held at Wayne State University, September 15-17, 2006. This conference was also held to honor Professor Rafail Z. Khasminskii for his fundamental contributions to many aspects of stochastic processes and nonparametric estimation theory on the occasion of his seventy-fifth birthday. It assembled an impressive list of invited speakers, who are renowned leaders in the fields of probability theory, stochastic processes, stochastic differential equations, as well as in the nonparametric estimation theory, and related fields. A number of invited speakers were early developers of the fields of probability and stochastic processes, establishing the foundation of the Modern probability theory. After the conference, to commemorate this special event, an IMA volume dedicated to Professor Rafail Z. Khasminskii was put together. It consists of nine papers on various topics in probability and statistics. They include authoritative expositions as well significant research papers of current interest. It is conceivable that the volume will have a lasting impact on the further development of stochastic analysis and nonparametric estimation.
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The Workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its Applications on September 18–22, 2006 at the University of Minnesota is one tangible indication of the interest. One hundred ten participants from eleven countries and twenty states came to listen to the many talks; discuss mathematics; and pursue collaborative work on the many faceted problems and the algorithms, both symbolic and numeric, that illuminate them.
This volume of articles captures some of the spirit of the IMA Workshop.
Keywords: algebraic degree, algebraic set, component of solutions, connected component, deflation, diagonal homotopy, embedding, equation-by-equation solver, generic point, fewnomials, finite fields, flag, generic point, homotopy continuation, hypersurfaces, irreducible components, isolated singular solutions, join, k-ellipse, Littlewood-Richardson coefficients, matrices of fixed displacement rank, monodromy, multiplicity, Newton's method, numerical algebraic geometry, numerical irreducible decomposition, path following, permutation arrays, plane curves, polar varieties, polynomial systems, polynomial system solving, public key cryptography, reconditioning, Schubert varieties, secant, semidefinite representation, symbolic-numeric computations, tangent space, tensor sum, witness point, witness set, Zariski closure
The volume is a result of the authorsâ€™ collaborative effort initiated at the IMA during the Institute's 2003/04 annual program on "Probability and Statistics in Complex Systems: Genomics, Networks, and Finance Engineering." The volume content is drawn from the recent literature on the asymptotic behavior of random permanents and random matchings. In particular, the authors present an elegant connection between the problem of an asymptotic behavior for a certain family of functionals on random matrices and the asymptotic results in the classical theory of the so-called U-statistics &mdash objects of fundamental importance in the non-parametric statistical inference. The volume content has been augmented with a sizable amount of preliminary material, in order to make the text largely self-contained and accessible to any mathematics, statistics or engineering graduate student who has taken basic introductory courses in probability theory and mathematical statistics.
Dr. Grzegorz A. Rempała is a Professor of Statistics in the Department of Mathematics at the University of Louisville in Louisville, KY. Dr. Jacek Wesołowski is a Professor of Mathematics and Associate Dean for Research at the Faculty of Mathematics and Information Science, Warsaw University of Technology in Warsaw, Poland.
Algorithms in algebraic geometry go hand in hand with software packages that implement them. Together they have established the modern field of computational algebraic geometry which has come to play a major role in both theoretical advances and applications. Over the past fifteen years, several excellent general purpose packages for computations in algebraic geometry have been developed, such as CoCoA, Singular and Macaulay 2. While these packages evolve continuously, incorporating new mathematical advances, they both motivate and demand the creation of new mathematics and smarter algorithms.
This volume reflects the workshop "Software for Algebraic Geometry" held in the week from 23 to 27 October 2006, as the second workshop in the thematic year on Applications of Algebraic Geometry at the IMA. The papers in this volume describe the software packages Bertini, PHClab, Gfan, DEMiCs, SYNAPS, TrIm, Gambit, ApaTools, and the application of Risa/Asir to a conjecture on multiple zeta values. They offer the reader a broad view of current trends in computational algebraic geometry through software development and applications.
Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research.
The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on the burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.
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 was a tutorial on Mathematics of Nucleic Acids, followed by the workshop Mathematics of Molecular and Cellular Biology, held September 15–21 at the IMA. This volume is dedicated to the memory of Nicholas R. Cozzarelli, a dynamic leader who fostered research and training at the interface between mathematics and molecular biology. It contains a personal remembrance of Nick Cozzarelli, plus 15 papers contributed by workshop speakers. The papers give and overview of state-of-the-art mathematical approaches to the understanding of DNA structure and function, and the interaction of DNA with proteins that mediate vital life processes.
An original motivation for algebraic
geometry was to understand curves and surfaces
in three dimensions. Recent theoretical and technological
advances in
areas such as robotics, computer vision, computer-aided
geometric design and molecular biology,
together with the increased availability of computational
resources, have brought these original questions
once more into the forefront of research.
One particular challenge is to combine applicable methods from
algebraic geometry
with proven techniques from piecewise-linear computational
geometry
(such as Voronoi diagrams and hyperplane arrangements)
to develop tools for treating curved objects. These research
efforts
may be summarized under the term
nonlinear computational geometry.
This volume grew out of an IMA workshop on
Nonlinear Computational Geometry in May/June 2007
(organized by I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald)
which
gathered leading experts in this emerging field. The research
and
expository articles in the volume are intended to provide an
overview of
nonlinear computational geometry.
Since the topic involves
computational geometry,
algebraic geometry, and geometric modeling, the volume
has contributions from all of these areas.
By addressing a broad range
of issues from purely theoretical and algorithmic problems,
to implementation and practical applications
this volume conveys the spirit of the IMA workshop.
The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eys of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australian school of category theory, and a historical paper by Ross Street describes its development.
This volume contains the proceedings of the Summer Program
on Nonlinear Conservation Laws and Applications held at the
IMA on July 13-31, 2009.
Hyperbolic conservation laws is a classical subject, which has
experienced vigorous growth in recent years.
The present collection
provides a timely survey of
the state of the art in this exciting field,
and a comprehensive outlook on open problems.
Contributions of more theoretical nature cover the following
topics:
global existence and uniqueness theory of one-dimensional
systems,
multidimensional conservation laws in several space variables
and
approximations of their solutions,
mathematical analysis of fluid motion,
stability and dynamics of viscous shock waves,
singular limits for viscous systems,
basic principles in the modeling of turbulent mixing,
transonic flows past an obstacle and a fluid dynamic approach
for isometric
embedding in geometry, models of nonlinear elasticity, the
Monge problem,
and transport equations with rough coefficients.
In addition, there are a number of papers devoted to
applications.
These include:
models of blood flow, self-gravitating compressible fluids,
granular flow, charge transport in fluids,
and the modeling and control of traffic flow on networks.
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. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners -- including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers -- are interested in solving large-scale MINLP instances.