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Fitting Splines To A Parametric Function
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Book Synopsis Fitting Splines to a Parametric Function by : Alvin Penner
Download or read book Fitting Splines to a Parametric Function written by Alvin Penner and published by Springer. This book was released on 2019-02-23 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Brief investigates the intersections that occur between three different areas of study that normally would not touch each other: ODF, spline theory, and topology. The Least Squares Orthogonal Distance Fitting (ODF) method has become the standard technique used to develop mathematical models of the physical shapes of objects, due to the fact that it produces a fitted result that is invariant with respect to the size and orientation of the object. It is normally used to produce a single optimum fit to a specific object; this work focuses instead on the issue of whether the fit responds continuously as the shape of the object changes. The theory of splines develops user-friendly ways of manipulating six different splines to fit the shape of a simple family of epiTrochoid curves: two types of Bézier curve, two uniform B-splines, and two Beta-splines. This work will focus on issues that arise when mathematically optimizing the fit. There are typically multiple solutions to the ODF method, and the number of solutions can often change as the object changes shape, so two topological questions immediately arise: are there rules that can be applied concerning the relative number of local minima and saddle points, and are there different mechanisms available by which solutions can either merge and disappear, or cross over each other and interchange roles. The author proposes some simple rules which can be used to determine if a given set of solutions is internally consistent in the sense that it has the appropriate number of each type of solution.
Book Synopsis Curves and Surfaces for CAGD by : Gerald E. Farin
Download or read book Curves and Surfaces for CAGD written by Gerald E. Farin and published by Morgan Kaufmann. This book was released on 2002 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface -- Chapter 1 P. B̌ezier: How a Simple System Was Born -- Chapter 2 Introductory Material -- Chapter 3 Linear Interpolation -- Chapter 4 The de Casteljau Algorithm -- Chapter 5 The Bernstein Form of a B̌ezier Curve -- Chapter 6 B̌ezier Curve Topics -- Chapter 7 Polynomial Curve Constructions -- Chapter 8 B-Spline Curves -- Chapter 9 Constructing Spline Curves -- Chapter 10 W. Boehm: Differential Geometry I -- Chapter 11 Geometric Continuity -- Chapter 12 ConicSections -- Chapter 13 Rational B̌ezier and B-Spline Curves -- Chapter 14 Tensor Product Patches -- Chapter 15 Constructing Polynomial Patches -- Chapter 16 Composite Surfaces -- Chapter 17 B̌ezier Triangles -- Chapter 18 Practical Aspects of B̌ezier Triangles -- Chapter 19 W. Boehm: Differential Geometry II -- Chapter 20 GeometricContinuityforSurfaces -- Chapter 21 Surfaces with Arbitrary Topology -- Chapter 22 Coons Patches -- Chapter 23 Shape -- Chapter 24 Evaluation of Some Methods -- Appendix A Quick Reference of Curve ...
Book Synopsis The Theory of Splines and Their Applications by : J. H. Ahlberg
Download or read book The Theory of Splines and Their Applications written by J. H. Ahlberg and published by Elsevier. This book was released on 2016-06-03 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.
Book Synopsis Curve and Surface Fitting with Splines by : Paul Dierckx
Download or read book Curve and Surface Fitting with Splines written by Paul Dierckx and published by Oxford University Press. This book was released on 1995 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering, medicine, ...) with many interesting applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with (tensor product) splines. As such it gives a survey of possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular it is demonstrated in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothing software is illustrated with many examples, academic as well as taken from real life.
Book Synopsis Progress in Artificial Intelligence by : Nuno Moniz
Download or read book Progress in Artificial Intelligence written by Nuno Moniz and published by Springer Nature. This book was released on 2024-01-15 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNAI 14115 and 14116 constitutes the refereed proceedings of the 22nd EPIA Conference on Progress in Artificial Intelligence, EPIA 2023, held in Faial Island, Azores, in September 2023. The 85 full papers presented in these proceedings were carefully reviewed and selected from 163 submissions. The papers have been organized in the following topical sections: ambient intelligence and affective environments; ethics and responsibility in artificial intelligence; general artificial intelligence; intelligent robotics; knowledge discovery and business intelligence; multi-agent systems: theory and applications; natural language processing, text mining and applications; planning, scheduling and decision-making in AI; social simulation and modelling; artifical intelligence, generation and creativity; artificial intelligence and law; artificial intelligence in power and energy systems; artificial intelligence in medicine; artificial intelligence and IoT in agriculture; artificial intelligence in transportation systems; artificial intelligence in smart computing; artificial intelligence for industry and societies.
Book Synopsis Richly Parameterized Linear Models by : James S. Hodges
Download or read book Richly Parameterized Linear Models written by James S. Hodges and published by CRC Press. This book was released on 2016-04-19 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Step toward a Unified Theory of Richly Parameterized Linear ModelsUsing mixed linear models to analyze data often leads to results that are mysterious, inconvenient, or wrong. Further compounding the problem, statisticians lack a cohesive resource to acquire a systematic, theory-based understanding of models with random effects.Richly Param
Book Synopsis Longitudinal Data Analysis by : Garrett Fitzmaurice
Download or read book Longitudinal Data Analysis written by Garrett Fitzmaurice and published by CRC Press. This book was released on 2008-08-11 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although many books currently available describe statistical models and methods for analyzing longitudinal data, they do not highlight connections between various research threads in the statistical literature. Responding to this void, Longitudinal Data Analysis provides a clear, comprehensive, and unified overview of state-of-the-art theory
Book Synopsis Multi-State Survival Models for Interval-Censored Data by : Ardo van den Hout
Download or read book Multi-State Survival Models for Interval-Censored Data written by Ardo van den Hout and published by CRC Press. This book was released on 2016-11-25 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-State Survival Models for Interval-Censored Data introduces methods to describe stochastic processes that consist of transitions between states over time. It is targeted at researchers in medical statistics, epidemiology, demography, and social statistics. One of the applications in the book is a three-state process for dementia and survival in the older population. This process is described by an illness-death model with a dementia-free state, a dementia state, and a dead state. Statistical modelling of a multi-state process can investigate potential associations between the risk of moving to the next state and variables such as age, gender, or education. A model can also be used to predict the multi-state process. The methods are for longitudinal data subject to interval censoring. Depending on the definition of a state, it is possible that the time of the transition into a state is not observed exactly. However, when longitudinal data are available the transition time may be known to lie in the time interval defined by two successive observations. Such an interval-censored observation scheme can be taken into account in the statistical inference. Multi-state modelling is an elegant combination of statistical inference and the theory of stochastic processes. Multi-State Survival Models for Interval-Censored Data shows that the statistical modelling is versatile and allows for a wide range of applications.
Book Synopsis EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization by : H.C. Rodrigues
Download or read book EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization written by H.C. Rodrigues and published by Springer. This book was released on 2018-09-13 with total page 1486 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume focus on the following topics: design optimization and inverse problems, numerical optimization techniques,efficient analysis and reanalysis techniques, sensitivity analysis and industrial applications. The conference EngOpt brings together engineers, applied mathematicians and computer scientists working on research, development and practical application of optimization methods in all engineering disciplines and applied sciences.
Book Synopsis Geometric Modeling with Splines by : Elaine Cohen
Download or read book Geometric Modeling with Splines written by Elaine Cohen and published by CRC Press. This book was released on 2001-07-18 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by researchers who have helped found and shape the field, this book is a definitive introduction to geometric modeling. The authors present all of the necessary techniques for curve and surface representations in computer-aided modeling with a focus on how the techniques are used in design.
Book Synopsis Design & Analysis of Clinical Trials for Economic Evaluation & Reimbursement by : Iftekhar Khan
Download or read book Design & Analysis of Clinical Trials for Economic Evaluation & Reimbursement written by Iftekhar Khan and published by CRC Press. This book was released on 2015-11-11 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic evaluation has become an essential component of clinical trial design to show that new treatments and technologies offer value to payers in various healthcare systems. Although many books exist that address the theoretical or practical aspects of cost-effectiveness analysis, this book differentiates itself from the competition by detailing
Book Synopsis Nonparametric Regression and Spline Smoothing, Second Edition by : Randall L. Eubank
Download or read book Nonparametric Regression and Spline Smoothing, Second Edition written by Randall L. Eubank and published by CRC Press. This book was released on 1999-02-09 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a unified account of the most popular approaches to nonparametric regression smoothing. This edition contains discussions of boundary corrections for trigonometric series estimators; detailed asymptotics for polynomial regression; testing goodness-of-fit; estimation in partially linear models; practical aspects, problems and methods for confidence intervals and bands; local polynomial regression; and form and asymptotic properties of linear smoothing splines.
Book Synopsis Economic Evaluation of Cancer Drugs by : Iftekhar Khan
Download or read book Economic Evaluation of Cancer Drugs written by Iftekhar Khan and published by CRC Press. This book was released on 2019-06-14 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cancer is a major healthcare burden across the world and impacts not only the people diagnosed with various cancers but also their families, carers, and healthcare systems. With advances in the diagnosis and treatment, more people are diagnosed early and receive treatments for a disease where few treatments options were previously available. As a result, the survival of patients with cancer has steadily improved and, in most cases, patients who are not cured may receive multiple lines of treatment, often with financial consequences for the patients, insurers and healthcare systems. Although many books exist that address economic evaluation, Economic Evaluation of Cancer Drugs using Clinical Trial and Real World Data is the first unified text that specifically addresses the economic evaluation of cancer drugs. The authors discuss how to perform cost-effectiveness analyses while emphasising the strategic importance of designing cost-effectiveness into cancer trials and building robust economic evaluation models that have a higher chance of reimbursement if truly cost-effective. They cover the use of real-world data using cancer registries and discuss how such data can support or complement clinical trials with limited follow up. Lessons learned from failed reimbursement attempts, factors predictive of successful reimbursement and the different payer requirements across major countries including US, Australia, Canada, UK, Germany, France and Italy are also discussed. The book includes many detailed practical examples, case studies and thought-provoking exercises for use in classroom and seminar discussions. Iftekhar Khan is a medical statistician and health economist and a lead statistician at Oxford Unviersity’s Center for Statistics in Medicine. Professor Khan is also a Senior Research Fellow in Health Economics at University of Warwick and is a Senior Statistical Assessor within the Licensing Division of the UK Medicine and Health Regulation Agency. Ralph Crott is a former professor in Pharmacoeconomics at the University of Montreal in Quebec, Canada and former head of the EORTC Health Economics Unit and former senior health economist at the Belgian HTA organization. Zahid Bashir has over twelve years experience working in the pharmaceutical industry in medical affairs and oncology drug development where he is involved in the design and execution of oncology clinical trials and development of reimbursement dossiers for HTA submission.
Book Synopsis Environmental Health Perspectives by :
Download or read book Environmental Health Perspectives written by and published by . This book was released on 1993 with total page 858 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pattern Recognition and Neural Networks by : Brian D. Ripley
Download or read book Pattern Recognition and Neural Networks written by Brian D. Ripley and published by Cambridge University Press. This book was released on 2007 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1996 book explains the statistical framework for pattern recognition and machine learning, now in paperback.
Book Synopsis Handbook of Chemical and Biological Sensors by : R.F Taylor
Download or read book Handbook of Chemical and Biological Sensors written by R.F Taylor and published by CRC Press. This book was released on 1996-01-01 with total page 1248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Chemical and Biological Sensors focuses on the development of sensors to recognize substances rather than physical quantities. This fully inclusive book examines devices that use a biological sensing element to detect and measure chemical and biological species as well as those that use a synthetic element to achieve a similar result. A first port of call for anyone with a specific interest, question, or problem relating to this area, this comprehensive source of reference serves as a guide for practicing scientists and as a text for many graduate courses. It presents relevant physics to chemists, chemistry to materials scientists, materials science to electronic engineers, and fabrication technology to all of the above. In addition, the handbook is useful both to newcomers and to experienced researchers who wish to broaden their knowledge of the constituent disciplines of this wide-ranging field.
Book Synopsis Biostatistics in the Study of Toxicology by :
Download or read book Biostatistics in the Study of Toxicology written by and published by . This book was released on 1994 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
