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Active Subspaces
Scientists and engineers use computer simulations to study relationships between a model's input parameters and its outputs. However, thorough parameter studies are challenging, if not impossible, when the simulation is expensive and the model has several inputs. To enable studies in these instances, the engineer may attempt to reduce the dimension of the model's input parameter space. Active subspaces are an emerging set of dimension reduction tools that identify important directions in the parameter space. This book describes techniques for discovering a model's active subspace and proposes methods for exploiting the reduced dimension to enable otherwise infeasible parameter studies. Readers will find new ideas for dimension reduction, easy-to-implement algorithms, and several examples of active subspaces in action.
A Mathematical Introduction to Electronic Structure Theory
Based on first principle quantum mechanics, electronic structure theory is widely used in physics, chemistry, materials science, and related fields and has recently received increasing research attention in applied and computational mathematics. This book provides a self-contained, mathematically oriented introduction to the subject and its associated algorithms and analysis. It will help applied mathematics students and researchers with minimal background in physics understand the basics of electronic structure theory and prepare them to conduct research in this area. The book begins with an elementary introduction of quantum mechanics, including the uncertainty principle and the Hartree?Fo...
Algorithms and Models for the Web-Graph
This book constitutes the refereed proceedings of the 5th International Workshop on Algorithms and Models for the Web-Graph, WAW 2007, held in San Diego, CA, USA, in December 2007 - colocated with WINE 2007, the Third International Workshop on Internet and Network Economics. The 13 revised full papers and five revised short papers presented were carefully reviewed and selected from a large pool of submissions for inclusion in the book. The papers address a wide variety of topics.
Myeloma Therapy
Therapeutic options for patients with myeloma have dramatically changed over the past 10 years. Beginning with the advances in therapy resulting from the use of high-dose therapy and autologous bone marrow or stem cell tra- plant, we have more than doubled the median survival for patients as a whole, and have now have a wealth of different biology -based treatment approaches for our patients in all disease stages. This book represents state-of-the-art information from many of the leaders in the plasma cell disorders world. Sections focusing on disease pathogenesis and biology, chemotherapy-based approaches, immune -based therapies, currently approved novel agents, developing targets, support...
Error Norm Estimation in the Conjugate Gradient Algorithm
The conjugate gradient (CG) algorithm is almost always the iterative method of choice for solving linear systems with symmetric positive definite matrices. This book describes and analyzes techniques based on Gauss quadrature rules to cheaply compute bounds on norms of the error. The techniques can be used to derive reliable stopping criteria. How to compute estimates of the smallest and largest eigenvalues during CG iterations is also shown. The algorithms are illustrated by many numerical experiments, and they can be easily incorporated into existing CG codes. The book is intended for those in academia and industry who use the conjugate gradient algorithm, including the many branches of science and engineering in which symmetric linear systems have to be solved.
Computational Modeling by Case Study
Mathematical models power the modern world; they allow us to design safe buildings, investigate changes to the climate, and study the transmission of diseases through a population. However, all models are uncertain: building contractors deviate from the planned design, humans impact the climate unpredictably, and diseases mutate and change. Modern advances in mathematics and statistics provide us with techniques to understand and quantify these sources of uncertainty, allowing us to predict and design with confidence. This book presents a comprehensive treatment of uncertainty: its conceptual nature, techniques to quantify uncertainty, and numerous examples to illustrate sound approaches. Several case studies are discussed in detail to demonstrate an end-to-end treatment of scientific modeling under uncertainty, including framing the problem, building and assessing a model, and answering meaningful questions. The book illustrates a computational approach with the Python package Grama, presenting fully reproducible examples that students and practitioners can quickly adapt to their own problems.
Iterative Solution of Symmetric Quasi-definite Linear Systems
Numerous applications, including computational optimization and fluid dynamics, give rise to block linear systems of equations said to have the quasi-definite structure. In practical situations, the size or density of those systems can preclude a factorization approach, leaving only iterative methods as the solution technique. Known iterative methods, however, are not specifically designed to take advantage of the quasi-definite structure.? This book discusses the connection between quasi-definite systems and linear least-squares problems, the most common and best understood problems in applied mathematics, and explains how quasi-definite systems can be solved using tailored iterative methods for linear least squares (with half as much work!). To encourage researchers and students to use the software, it is provided in MATLAB, Python, and Julia.? The authors provide a concise account of the most well-known methods for symmetric systems and least-squares problems, research-level advances in the solution of problems with specific illustrations in optimization and fluid dynamics, and a website that hosts software in three languages.?
Fuzzy Systems and Data Mining V
The Fuzzy Systems and Data Mining (FSDM) conference is an annual event encompassing four main themes: fuzzy theory, algorithms and systems, which includes topics like stability, foundations and control; fuzzy application, which covers different kinds of processing as well as hardware and architectures for big data and time series and has wide applicability; the interdisciplinary field of fuzzy logic and data mining, encompassing applications in electrical, industrial, chemical and engineering fields as well as management and environmental issues; and data mining, outlining new approaches to big data, massive data, scalable, parallel and distributed algorithms. The annual conference provides ...
Paul and Union with Christ
Paul and Union with Christ fills the gap for biblical scholars, theologians, and pastors pondering and debating the meaning of union with Christ. Following a selective survey of the scholarly work on union with Christ through the twentieth century to the present day, Greek scholar Constantine Campbell carefully examines every occurrence of the phrases ‘in Christ’, ‘with Christ’, ‘through Christ’, ‘into Christ,’ and other related expressions, exegeting each passage in context and taking into account the unique lexical contribution of each Greek preposition. Campbell then builds a holistic portrayal of Paul’s thinking and engages contemporary theological discussions about union with Christ by employing his evidence-based understanding of the theme. This volume combines high-level scholarship and a concern for practical application of a topic currently debated in the academy and the church. More than a monograph, this book is a helpful reference tool for students, scholars, and pastors to consult its treatment of any particular instance of any phrase or metaphor that relates to union with Christ in the Pauline corpus.
Constantine and Eusebius
Here is the fullest available narrative history of the reigns of Diocletian and Constantine, and a new assessment of the part Christianity played in the Roman world of the third and fourth centuries.
