Refinement

This book provides a comprehensive overview of automatic model refinement, which helps readers close the gap between initial textual specification and its desired implementation. The authors enable readers to follow two “directions” for refinement: Vertical refinement, for adding detail and precision to single description for a given model and Horizontal refinement, which considers several views on one level of abstraction, refining the system specification by dedicated descriptions for structure or behavior. The discussion includes several methods which support designers of electronic systems in this refinement process, including verification methods to check automatically whether a refinement has been conducted as intended.

Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing.

Provides an integrated coverage of random/probabilistic algorithms, assertion-based program reasoning, and refinement programming models, providing a focused survey on probabilistic program semantics. This book illustrates, by examples, the typical steps necessary to build a mathematical model of any programming paradigm.

A musician’s journey never ends, and the work is often solitary. Fortunately for bassoonists, Solitary Refinement can be a trusted companion throughout their musical career, replete with exercises adaptable by bassoon students who are still developing their skills, all the way to virtuosi seeking to perfect their craft. Drawing on her extensive career as a professional bassoonist and teacher, Nadina Mackie Jackson has assembled a comprehensive volume of technical exercises for the serious bassoonist. This book covers chromatic scales in many permutations and intervals, diatonic scales and chords, and exercises designed to strengthen fundamental basics, such as fingering, embouchure, double tonguing, vibrato, tuning and tone quality. In elegant, accessible prose, Nadina Mackie Jackson also shares her wisdom on the importance and philosophy of technical practice, with sensible advice on how to build good habits. Beyond the exercises, this book also serves as a guide for bassoonists on how to set personal goals and develop a sustained practice that will nurture their musical growth over a lifetime. Solitary Refinement is designed for the seriously committed bassoonist of any age to maintain, develop and expand their command of the bassoon, and will inspire players to see themselves in a world that combines musical passion and fundamental discipline.

Almost 50 years have passed since the famous papers of Hugo Rietveld from the late sixties where he describes a method for the refinement of crystal structures from neutron powder diffraction data. Soon after, the potential of the method for laboratory X-ray powder diffraction was discovered. Although the method is now widely accepted, there are still many pitfalls in the theoretical understanding and in practical daily use. This book closes the gap with a theoretical introduction for each chapter followed by a practical approach. The flexible macro type language of the Topas Rietveld software can be considered as the defacto standard.

The goal of this book is to provide a comprehensive and systematic introduction to the important and highly applicable method of data refinement and the simulation methods used for proving its correctness. The authors concentrate in the first part on the general principles needed to prove data refinement correct. They begin with an explanation of the fundamental notions, showing that data refinement proofs reduce to proving simulation. The book's second part contains a detailed survey of important methods in this field, which are carefully analysed, and shown to be either incomplete, with counterexamples to their application, or to be always applicable whenever data refinement holds. This is shown by proving, for the first time, that all these methods can be described and analysed in terms of two simple notions: forward and backward simulation. The book is self-contained, going from advanced undergraduate level and taking the reader to the state of the art in methods for proving simulation.

Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.