A Toolbox for Digital Twins: From Model-Based to Data-Driven brings together the mathematical and numerical frameworks needed for developing digital twins (DTs). Starting from the basics-probability, statistics, numerical methods, optimization, and machine learning-and moving on to data assimilation, inverse problems, and Bayesian uncertainty ......
Presents a theory of indexing capable of ranking index terms, or subject identifiers in decreasing order of importance. This leads to the choice of good document representations, and also accounts for the role of phrases and of thesaurus classes in the indexing process. This study is typical of theoretical work in automatic information ......
Inverse problems need to be solved in order to properly interpret indirect measurements. Often, inverse problems are ill-posed and sensitive to data errors. Therefore one has to incorporate some sort of regularization to reconstruct significant information from the given data. This book presents the main achievements that have emerged in ......
This companion piece to the author's 2018 book, A Software Repository for Orthogonal Polynomials, focuses on Gaussian quadrature and the related Christoffel function. The book makes Gauss quadrature rules of any order easily accessible for a large variety of weight functions and for arbitrary precision. It also documents and illustrates known as ......
How I Learned to Stop Worrying and Love Measure Theory
Measure theory and measure-theoretic probability are fascinating subjects. Proofs describing profound ways to reason lead to results that are frequently startling, beautiful, and useful. Measure theory and probability also play roles in the development of pure and applied mathematics, statistics, engineering, physics, and finance. Indeed, it is ......
Adapted from a series of lectures given by the authors, this monograph focuses on radial basis functions (RBFs), a powerful numerical methodology for solving PDEs to high accuracy in any number of dimensions. This method applies to problems across a wide range of PDEs arising in fluid mechanics, wave motions, astro- and geosciences, mathematical ......
This textbook grew out of a course that the highly respected applied mathematician Lee Segel taught at the Weizmann Institute. This book represents the unique perspective on mathematical biology of Segel and his co-author Leah Edelstein-Keshet (author of the popular SIAM book, Mathematical Models in Biology). It introduces differential equations, ......
Designed to offer applied mathematicians, physicists, chemists, engineers, geophysicists, and other scientists an elementary level explanation of integral equations of the first kind. It maintains a casual, conversational approach. It emphasizes understanding, while deliberately avoiding special methods of highly limited application. Special ......
How does a marble manufacturer know that the colour will be consistent throughout the products he is making? How can you tell if the liquid at the bottom of a container is the same consistency as that at the top? How does a pellet manufacturer know if the pellets are consistently the same size? How does a chemical manufacturer know if the percent ......
