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This volume collects papers based on plenary and invited talks given at the 50th Barrett Memorial Lectures on Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models that was organized by the University of Tennessee, Knoxville and held virtually in May 2021. The three-day meeting brought together experts from the computational, scientific, engineering, and mathematical communities who work with nonlocal models. These proceedings collect contributions and give a survey of the state of the art in computational practices, mathematical analysis, applications of nonlocal models, and explorations of new application domains. The volume benefits from the mixture of contributions by computational scientists, mathematicians, and application specialists. The content is suitable for graduate students as well as specialists working with nonlocal models and covers topics on fractional PDEs, regularity theory for kinetic equations, approximation theory for fractional diffusion, analysis of nonlocal diffusion model as a bridge between local and fractional PDEs, and more.

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 2006 is one tangible indication of the interest.

This volume consists of selected essays by participants of the workshop Control at Large Scales: Energy Markets and Responsive Grids held at the Institute for Mathematics and its Applications, Minneapolis, Minnesota, U.S.A. from May 9-13, 2016. The workshop brought together a diverse group of experts to discuss current and future challenges in energy markets and controls, along with potential solutions. The volume includes chapters on significant challenges in the design of markets and incentives, integration of renewable energy and energy storage, risk management and resilience, and distributed and multi-scale optimization and control. Contributors include leading experts from academia and industry in power systems and markets as well as control science and engineering. This volume will be of use to experts and newcomers interested in all aspects of the challenges facing the creation of a more sustainable electricity infrastructure, in areas such as distributed and stochastic optimization and control, stability theory, economics, policy, and financial mathematics, as well as in all aspects of power system operation.

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

This 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.

Covers major themes that include an assessment of the optimization algorithms as well as challenging applications in design and control, and of process engineering and systems with partial differential equation models.

The articles in this volume 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.

Recent revolutions in the world of finance have created a need for the expertise of research mathematicians in solving problems. The articles in this volume are based on recent research in methods in mathematical finance.

Covers the major themes that include an assessment of the optimization algorithms as well as challenging applications in design and control, and of process engineering and systems with partial differential equation models.

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

This IMA Volume in Mathematics and its Applications IMAGE MODELS (AND THEIR SPEECH MODEL COUSINS) is based on the proceedings of a workshop that was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability."

This 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.

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

Signal processing applications have burgeoned in the past decade. it brings together the writings of signal processing engineers, computer engineers, and applied linear algebraists in an exchange of problems, theories, and techniques.

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

This superb explication of a complex subject presents the current state of the art of the mathematical theory of symmetric functionals on random matrices. The book provides a detailed description of the approach of symmetric function decompositions to the asymptotic theory of symmetric functionals, including the classical theory of U-statistics.

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.

Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume contains a collection of papers that were presented dur ing the Workshop on Time Series Analysis and Applications to Geophysical Systems at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota from November 12-15, 2001.

This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title.

The computational solution of partial differential systems has become so involved that it is important to automate decisions that have been left to the individual. This book covers such decisions: mesh generation with links to the software generating the domain geometry; and solution accuracy with mesh selection linked to solution generation.

A collection of papers from an IMA "Hot Topics" workshop in internet auctions. This work includes descriptions of real and proposed auctions, with mathematical model formulations, theoretical results, solution approaches, and computational studies. It also provides a mathematical programming perspective on open questions in auction theory.

The IMA was an ideal venue for the 2007-2008 IMA thematic year on Mathematics of Molecular and Cellular Biology. This work contains 15 papers contributed by workshop speakers, that overview mathematical approaches to the understanding of DNA structure and function, and the interaction of DNA with proteins that mediate vital life processes.

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.

This IMA Volume in Mathematics and its Applications FRACTALS IN MULTIMEDIA is a result of a very successful three-day minisymposium on the same title. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume grew out of a meeting on Fractals in Multimedia held at the IMA in January 2001.

This IMA Volume in Mathematics and its Applications MATHEMATICAL APPROACHES FOR EMERGING AND REEMERGING INFECTIOUS DISEASES: MODELS, AND THEORY METHODS is based on the proceedings of a successful one week workshop.

Recent revolutions in the world of finance have created a need for the expertise of research mathematicians in solving problems. The articles in this volume are based on recent research in methods in mathematical finance.

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.

Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA v PREFACE This volume contains a collection of papers that were presented dur ing the Workshop on Time Series Analysis and Applications to Geophysical Systems at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota from November 12-15, 2001.

This IMA Volume in Mathematics and its Applications GEOMETRIC METHODS IN INVERSE PROBLEMS AND PDE CONTROL contains a selection of articles presented at 2001 IMA Summer Program with the same title.

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.