Computational Methods for Applied Inverse Problems

Computational techniques have become indispensable tools in solving complex problems in transport phenomena. This book, first published in 1997, provides a clear, user-oriented introduction to the subject. Each self-contained chapter includes a detailed worked example and a discussion of the problem system equations. Also included are the numerical methods used; computer code for the solution of the problem system equations; discussion of the numerical solution with emphasis on physical interpretation; and when appropriate, a comparison of the numerical solution with an analytical solution or a discussion of how the numerical solution goes beyond what can be done analytically, especially for nonlinear problems. Intended for students and a broad range of scientists and engineers, the book includes computer code written in transportable Fortran so that readers can produce the numerical solutions and then extend them to other cases. The programs are also available on the author's web site

Explicates the mathematical theory of regularization methods and gives an account of currently available results about regularization methods for both linear and nonlinear ill-posed problems. Overview

The calculus of variations has been an active area of mathematics for over 300 years. Its main use is to find stable critical points of functions for the solution of problems. To find unstable values, new approaches (Morse theory and min-max methods) were developed, and these are still being refined to overcome difficulties when applied to the theory of partial differential equations. Here, Professor Ghoussoub describes a point of view that may help when dealing with such problems. Building upon min-max methods, he systematically develops a general theory that can be applied in a variety of situations. In so doing he also presents a whole array of duality and perturbation methods. The prerequisites for following this book are relatively few; an appendix sketching certain methods in analysis makes the book reasonably self-contained. Consequently, it should be accessible to all mathematicians, pure or applied, economists and engineers working in nonlinear analysis or optimization.

This book is designed to provide students, teachers, and researchers with a text that includes a full range of statistical methods available to address commonly encountered research problems. Many textbooks for introductory, intermediate, and advanced statistics courses focus heavily on parametric methods. However, in practice the assumptions underlying these methods are frequently not met, therefore calling into question their use. This book addresses this issue by presenting parametric, nonparametric, robust, and Bayesian techniques that are appropriate for research scenarios often encountered in practice and typically found in statistics courses. For each of these major topics, the standard parametric approach is presented, along with the assumptions underlying it and the methods used to assess the viability of these assumptions. Next, a set of alternative techniques for the research scenario is presented and applied to the motivating example that begins each chapter. Each chapter c

This book presents methods for the summation of infinite and finite series and the related identities and inversion relations. The summation includes the column sums and row sums of lower triangular matrices. The convergence of the summation of infinite series is considered. The author's focus is on symbolic methods and the Riordan array approach. In addition, this book contains hundreds summation formulas and identities, which can be used as a handbook for people working in computer science, applied mathematics, and computational mathematics, particularly, combinatorics, computational discrete mathematics, and computational number theory. The exercises at the end of each chapter help deepen understanding.Much of the materials in this book has never appeared before in textbook form. This book can be used as a suitable textbook for advanced courses for high lever undergraduate and lower lever graduate students. It is also an introductory self-study book for re- searchers interested in t

This monograph is a compilation of research on the inverse Gaussian distribution. It emphasizes the presentation of the statistical properties, methods, and applications of the two-parameter inverse G

Learn how to apply cognitive principles to the problems of computer vision Computational Models for Cognitive Vision formulates the computational models for the cognitive principles found in bio

Computational Non-coding RNA Biology is a resource for the computation of non-coding RNAs. The book covers computational methods for the identification and quantification of non-coding RNAs, including

Algebraic and Combinatorial Computational Biology introduces students and researchers to a panorama of powerful and current methods for mathematical problem-solving in modern computational biology. Pr

These proceedings highlight research on the latest trends and methods in experimental and behavioral economics. Featuring contributions presented at the 2017 Computational Methods in Experimental Econ

This book introduces and reviews all of the currently available methods being used for computational electroencephalogram (EEG) analysis, from the fundamentals through to the state-of-the-art. Th

Free-Surface Flow: Computational Methods presents a detailed analysis of numerical schemes for shallow-water waves. It includes practical applications for the numerical simulation of flow and transpor

Computational materials science is a fast growing field. It involves computational tools for solving problems related to materials science. Different mathematical models are used for developing a bett

Applied Computational Physics is a graduate-level text stressing three essential elements: advanced programming techniques, numerical analysis, and physics. The goal of the text is to provide students

Applied Computational Physics is a graduate-level text stressing three essential elements: advanced programming techniques, numerical analysis, and physics. The goal of the text is to provide students

Complexity theory aims to understand and classify computational problems, especially decision problems, according to their inherent complexity. This book uses new techniques to expand the theory for use with counting problems. The authors present dichotomy classifications for broad classes of counting problems in the realm of P and NP. Classifications are proved for partition functions of spin systems, graph homomorphisms, constraint satisfaction problems, and Holant problems. The book assumes minimal prior knowledge of computational complexity theory, developing proof techniques as needed and gradually increasing the generality and abstraction of the theory. This volume presents the theory on the Boolean domain, and includes a thorough presentation of holographic algorithms, culminating in classifications of computational problems studied in exactly solvable models from statistical mechanics.

This new and completely updated edition gives a detailed description of radiative transfer processes at a level accessible to advanced students. The volume gives the reader a basic understanding of global warming and enhanced levels of harmful ultraviolet radiation caused by ozone depletion. It teaches the basic physics of absorption, scattering and emission processes in turbid media, such as the atmosphere and ocean, using simple semi-classical models. The radiative transfer equation, including multiple scattering, is formulated and solved for several prototype problems, using both simple approximate and accurate numerical methods. In addition, the reader has access to a powerful, state-of-the-art computational code for simulating radiative transfer processes in coupled atmosphere-water systems including snow and ice. This computational code can be regarded as a powerful educational aid, but also as a research tool that can be applied to solve a variety of research problems in environ

Science is fundamentally about learning from data, and doing so in the presence of uncertainty. This volume is an introduction to the major concepts of probability and statistics, and the computational tools for analysing and interpreting data. It describes the Bayesian approach, and explains how this can be used to fit and compare models in a range of problems. Topics covered include regression, parameter estimation, model assessment, and Monte Carlo methods, as well as widely used classical methods such as regularization and hypothesis testing. The emphasis throughout is on the principles, the unifying probabilistic approach, and showing how the methods can be implemented in practice. R code (with explanations) is included and is available online, so readers can reproduce the plots and results for themselves. Aimed primarily at undergraduate and graduate students, these techniques can be applied to a wide range of data analysis problems beyond the scope of this work.

Science is fundamentally about learning from data, and doing so in the presence of uncertainty. This volume is an introduction to the major concepts of probability and statistics, and the computational tools for analysing and interpreting data. It describes the Bayesian approach, and explains how this can be used to fit and compare models in a range of problems. Topics covered include regression, parameter estimation, model assessment, and Monte Carlo methods, as well as widely used classical methods such as regularization and hypothesis testing. The emphasis throughout is on the principles, the unifying probabilistic approach, and showing how the methods can be implemented in practice. R code (with explanations) is included and is available online, so readers can reproduce the plots and results for themselves. Aimed primarily at undergraduate and graduate students, these techniques can be applied to a wide range of data analysis problems beyond the scope of this work.

Applied Social Psychology combines the science of social psychology with the practical application of solving social problems that exist in the real world. This exciting textbook provides a thorough explanation of how social psychologists can contribute to the understanding and management of different social problems. A highly prestigious team of contributors from across Europe and the United States illustrate how social psychological theories, research methods and intervention techniques can be successfully applied to problems encountered in the fields of physical and mental health, immigration and integration, economic behaviour, political behaviour, environmental behaviour, organisations and the classroom. This expanded edition also features new chapters on the dynamic fields of consumer behaviour, traffic behaviour, criminal behaviour, sport and development aid. Each field studied features an overview of important problems, the role of human behaviour in these problems, the factors

Applied Social Psychology combines the science of social psychology with the practical application of solving social problems that exist in the real world. This exciting textbook provides a thorough explanation of how social psychologists can contribute to the understanding and management of different social problems. A highly prestigious team of contributors from across Europe and the United States illustrate how social psychological theories, research methods and intervention techniques can be successfully applied to problems encountered in the fields of physical and mental health, immigration and integration, economic behaviour, political behaviour, environmental behaviour, organisations and the classroom. This expanded edition also features new chapters on the dynamic fields of consumer behaviour, traffic behaviour, criminal behaviour, sport and development aid. Each field studied features an overview of important problems, the role of human behaviour in these problems, the factors

This book emphasizes the increasingly important role that Computational Intelligence (CI) methods are playing in solving a myriad of entangled Wireless Sensor Networks (WSN) related problems. The book

The book covers the essentials of computational science and gives tools and techniques to solve materials science problems using molecular dynamics and first-principles methods. The new edition expand

This book explores the numerical algorithms underpinning modern finite element based computational mechanics software. It covers all the major numerical methods that are used in computational mechanic

The overall goal of the book is to provide access to the regularized solution of inverse problems relevant in geophysics without requiring more mathematical knowledge than is taught in undergraduate m

Before The Computational Brain was published in 1992, conceptual frameworks for brain function were based on the behavior of single neurons, applied globally. In The Computational Brain, Patricia Ch

Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 9 of the Proceedings of the 2016 SEM Annual Conference & Exposition on Experimental and

Focusing on five main groups of interdisciplinary problems, this book covers a wide range of topics in mathematical modeling, computational science and applied mathematics. It presents a wealth of new

Computational Approaches for Studying Enzyme Mechanism Part B, is the first of two volumes in the Methods in Enzymology series, focusses on computational approaches for studying enzyme mechanism. Th

Computational Approaches for Studying Enzyme Mechanism Part A, is the first of two volumes in the Methods in Enzymology series, focusses on computational approaches for studying enzyme mechanism. Th

An ideal introduction to statistical neurocomputing, this book examines current statistical methods for solving emerging problems in neuroscience. These methods have been applied to data involving mul

This book focuses on finding all ordinary differential equations that satisfy a given set of properties, thus dedicating itself to inverse problems of ordinary differential equations. The Nambu bracke

This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, includi

Computational and Statistical Methods for Analysing Big Data with Applications begins with an overview of the era of big data. It then goes on to explain different computational and statistical method

Research Methods in Applied Linguistics is designed to be the essential one-volume resource for students. The book includes:* qualitative, quantitative and mixed methods* research techniques and appro

Research Methods in Applied Linguistics is designed to be the essential one-volume resource for students. The book includes:* qualitative, quantitative and mixed methods* research techniques and appro

The recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fredholm integral equations of the second kind, ill-posed integral equations of the first kind and eigen-problems of compact integral operators. Theorems of functional analysis used throughout the book are summarised in the appendix. The book is an essential reference for practitioners wishing to use the new techniques. It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates.

Mathematical methods are essential tools for all physical scientists. This book provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students across the physical sciences. In contrast to more traditional textbooks, all the material is presented in the form of exercises. Within these exercises, basic mathematical theory and its applications in the physical sciences are well integrated. In this way, the mathematical insights that readers acquire are driven by their physical-science insight. This third edition has been completely revised: new material has been added to most chapters, and two completely new chapters on probability and statistics and on inverse problems have been added. This guided tour of mathematical techniques is instructive, applied, and fun. This book is targeted for all students of the physical sciences. It can serve as a stand-alone text, or as a source of exercises and examples to complement other textbooks.

Mathematical methods are essential tools for all physical scientists. This book provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students across the physical sciences. In contrast to more traditional textbooks, all the material is presented in the form of exercises. Within these exercises, basic mathematical theory and its applications in the physical sciences are well integrated. In this way, the mathematical insights that readers acquire are driven by their physical-science insight. This third edition has been completely revised: new material has been added to most chapters, and two completely new chapters on probability and statistics and on inverse problems have been added. This guided tour of mathematical techniques is instructive, applied, and fun. This book is targeted for all students of the physical sciences. It can serve as a stand-alone text, or as a source of exercises and examples to complement other textbooks.

This manuscript is devoted to a rigorous and detailed exposition of the spectral theory and associated forward and inverse scattering problems for the Laplace-Beltrami operators on asymptotically hype