Splines And Compartment Models
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Splines And Compartment Models
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Author : Karl-Ernst Biebler
language : en
Publisher: World Scientific
Release Date : 2013-07-23
Splines And Compartment Models written by Karl-Ernst Biebler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-23 with Mathematics categories.
This book presents methods of mathematical modeling from two points of view. Splines provide a general approach while compartment models serve as examples for context related to modeling. The preconditions and characteristics of the developed mathematical models as well as the conditions surrounding data collection and model fit are taken into account. The substantial statements of this book are mathematically proven. The results are ready for application with examples and related program codes given. In this book, splines are algebraically developed such that the reader or user can easily understand and vary the numerical construction of the different kinds of spline functions. The classical compartment models of the pharmacokinetics are systematically analyzed and connected with lifetime distributions. As such, parameter estimation and model fit can be treated statistically with a varied minimum chi-square method. This method is applicable for single kinetics and also allows the calculation of average kinetics. Contents:Spline Models:Why Spline Functions?Interpolating Splines of Degree nInterpolating Cubic SplinesSmoothing Natural Cubic Splines and the Choice of the Smoothing ParameterInterpolating Quadratic SplinesInterpolating Quadratic Splines and ParabolasSmoothing Quadratic SplinesSplines and Average FunctionsCompartment Models:Concept of a Context Related Mathematical Pharmacokinetical ModelCompartment ModelsOther Deterministic ModelsCalculability and IdentifiabilityCompartment Models and Associated Residence Time DistributionsOther Stochastic ModelsCalculation Methods Related to Compartment ModelsSelection of Pharmacokinetic ModelsPharmacokinetics for Multiple ApplicationsMathematica® Programs for Selected Problems Readership: Graduate students in biomathematics, medicine, pharmacy and human biology. Professionals like bio-mathematicians, pharmacologists, clinical pharmacologists, pharmacists, doctors engaged in clinical research, scientists in pharmaceutical R&D and scientific staff in the life sciences. Keywords:Mathematical Modeling;Model Selection;Pharmacokinetics;Compartment Models;Minimum Chi-square Estimation;Pharmacokinetics for Multiple Applications;Residence Time DistributionsKey Features:This book treats modeling and data interpretation as a whole, and the qualities of the developed methods are mathematically characterizedNew application of the varied minimum chi-square method for the parameter calculation and the model choice in the pharmacokineticsThe developed methods are ready for application. The reader/user will be able to modify the given solutionsReviews: “Part 2 is very pleasant reading which is completely suited for both course segments in teaching numerical analysis and seminars on the topics in the curriculum of applied mathematicians… I warmly recommend the book for applied mathematicians working in collaboration with medical, pharmacological and chemical institutes. Also, it is an excellent auxiliary material in the education of numerical mathematics.” Acta Scientiarum Mathematicarum
Splines And Compartment Models
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FREE 30 Days
Author : Karl-Ernst Biebler
language : en
Publisher: World Scientific
Release Date : 2013
Splines And Compartment Models written by Karl-Ernst Biebler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with MATHEMATICS categories.
This book presents methods of mathematical modeling from two points of view. Splines provide a general approach while compartment models serve as examples for context related to modeling. The preconditions and characteristics of the developed mathematical models as well as the conditions surrounding data collection and model fit are taken into account. The substantial statements of this book are mathematically proven. The results are ready for application with examples and related program codes given. In this book, splines are algebraically developed such that the reader or user can easily understand and vary the numerical construction of the different kinds of spline functions. The classical compartment models of the pharmacokinetics are systematically analyzed and connected with lifetime distributions. As such, parameter estimation and model fit can be treated statistically with a varied minimum chi-square method. This method is applicable for single kinetics and also allows the calculation of average kinetics.
Geometric Modeling
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Author : Hans Hagen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Modeling written by Hans Hagen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
This book is based on lectures presented at an international workshop on geometric modeling held at Hewlett Packard GmbH in Boblingen, FRG, in June 1990. International experts from academia and industry were selected to speak on the most interesting topics in geometric modeling. The resulting papers, published in this volume, give a state-of-the-art survey of the relevant problems and issues. The following topics are discussed: - Methods for constructing surfaces on surfaces: four different solutions to the multidimen sional problem of constructing an interpolant from surface data are provided. - Surfaces in solid modeling: current results on the implementation of free-fonn solids in three well established solid models are reviewed. - Box splines and applications: an introduction to box spline methods for the representation of surfaces is given. Basic properties of box splines are derived, and refinement and evaluation methods for box splines are presented in detail. Shape preserving properties, the construction of non-rectangular box spline surfaces, applications to surface modeling, and imbedding problems, are discussed. - Advanced computer graphics techniques for volume visualization: the steps to be executed in the visualization process of volume data are described and tools are discussed that assist in handling this data. - Rational B-splines: an introduction to the representation of curves and surfaces using rational B-splines is given, together with a critical evaluation of their potential for industrial application.
Spline Functions
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Author : Larry L. Schumaker
language : en
Publisher: SIAM
Release Date : 2015-01-01
Spline Functions written by Larry L. Schumaker and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-01 with Science categories.
This book describes in detail the key algorithms needed for computing with spline functions and illustrates their use in solving several basic problems in numerical analysis, including function approximation, numerical quadrature, data fitting, and the numerical solution of PDE's. The focus is on computational methods for bivariate splines on triangulations in the plane and on the sphere, although both univariate and tensor-product splines are also discussed. The book contains numerous examples and figures to illustrate the methods and their performance. All of the algorithms in the book have been coded in a separate MATLAB package available for license. The package can be used to run all of the examples in the book and also provides readers with the essential tools needed to create software for their own applications. In addition to the included bibliography, a list of over 100 pages of additional references can be found on the book's website.
Approximation And Modeling With B Splines
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Author : Klaus Hollig
language : en
Publisher: SIAM
Release Date : 2015-07-01
Approximation And Modeling With B Splines written by Klaus Hollig and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-01 with Mathematics categories.
B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.
Geometric Modeling With Splines
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Author : ELAINE AUTOR COHEN
language : en
Publisher: A K Peters Ltd
Release Date : 2001
Geometric Modeling With Splines written by ELAINE AUTOR COHEN and has been published by A K Peters Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.
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. They achieve a balance between mathematical rigor and broad applicability. Appropriate for readers with a moderate degree of mathematical maturity, this book is suitable as an undergraduate or graduate text, or particularly as a resource for self-study.
Comprehensive Biomedical Physics
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Author :
language : en
Publisher: Newnes
Release Date : 2014-07-25
Comprehensive Biomedical Physics written by and has been published by Newnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-25 with Science categories.
Comprehensive Biomedical Physics, Ten Volume Set is a new reference work that provides the first point of entry to the literature for all scientists interested in biomedical physics. It is of particularly use for graduate and postgraduate students in the areas of medical biophysics. This Work is indispensable to all serious readers in this interdisciplinary area where physics is applied in medicine and biology. Written by leading scientists who have evaluated and summarized the most important methods, principles, technologies and data within the field, Comprehensive Biomedical Physics is a vital addition to the reference libraries of those working within the areas of medical imaging, radiation sources, detectors, biology, safety and therapy, physiology, and pharmacology as well as in the treatment of different clinical conditions and bioinformatics. This Work will be valuable to students working in all aspect of medical biophysics, including medical imaging and biomedical radiation science and therapy, physiology, pharmacology and treatment of clinical conditions and bioinformatics. The most comprehensive work on biomedical physics ever published Covers one of the fastest growing areas in the physical sciences, including interdisciplinary areas ranging from advanced nuclear physics and quantum mechanics through mathematics to molecular biology and medicine Contains 1800 illustrations, all in full color
Modeling With Ambient B Splines
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Author : Nicole Lehmann
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2013
Modeling With Ambient B Splines written by Nicole Lehmann and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
The present thesis introduces a new approach for the generation of CK-approximants of functions defined on closed submanifolds for arbitrary k ∈ N. In case a function on a surface resembles the three coordinates of a topologically equivalent surface in R3, we even obtain Ck-approximants of closed surfaces of arbitrary topology. The key idea of our method is a constant extension of the target function into the submanifold's ambient space. In case the reference submanifolds are embedded and Ck, the usage of standard tensor product B-splines for the approximation of the extended function is straightforward. We obtain a Ck-approximation of the target function by restricting the approximant to the reference submanifold. We illustrate our method by an easy example in R2 and verify its practicality by application-oriented examples in R3. The first treats the approximation of the geoid, an important reference magnitude within geodesy and geophysics. The second and third example treat the approximation of geometric models. The usage of B-splines not only guarantees full approximation power but also allows a canonical access to adaptive refinement strategies. We elaborate on two hierarchical techniques and successfully apply them to the introduced examples. Concerning the modeling of surfaces by the new approach, we derive numerically robust formulas for the determination of normal vectors and curvature information of a target surface which only need the spline approximant as well as the normal vectors and curvature information of the reference surface.
Geometric Modeling
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Author : Hans Hagen
language : en
Publisher: Springer
Release Date : 1991-07-18
Geometric Modeling written by Hans Hagen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-07-18 with Computers categories.
This book is based on lectures presented at an international workshop on geometric modeling held at Hewlett Packard GmbH in Boblingen, FRG, in June 1990. International experts from academia and industry were selected to speak on the most interesting topics in geometric modeling. The resulting papers, published in this volume, give a state-of-the-art survey of the relevant problems and issues. The following topics are discussed: - Methods for constructing surfaces on surfaces: four different solutions to the multidimen sional problem of constructing an interpolant from surface data are provided. - Surfaces in solid modeling: current results on the implementation of free-fonn solids in three well established solid models are reviewed. - Box splines and applications: an introduction to box spline methods for the representation of surfaces is given. Basic properties of box splines are derived, and refinement and evaluation methods for box splines are presented in detail. Shape preserving properties, the construction of non-rectangular box spline surfaces, applications to surface modeling, and imbedding problems, are discussed. - Advanced computer graphics techniques for volume visualization: the steps to be executed in the visualization process of volume data are described and tools are discussed that assist in handling this data. - Rational B-splines: an introduction to the representation of curves and surfaces using rational B-splines is given, together with a critical evaluation of their potential for industrial application.
Autodesk Fusion 360 Introduction To Surface And T Spline Modeling
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Author : Sandeep Dogra
language : en
Publisher: CADArtifex
Release Date : 2021-09-08
Autodesk Fusion 360 Introduction To Surface And T Spline Modeling written by Sandeep Dogra and has been published by CADArtifex this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-08 with Computers categories.
Autodesk Fusion 360: Introduction to Surface and T-Spline Modeling textbook has been designed for instructor-led courses as well as self-paced learning. It is intended to help engineers and designers interested in learning Autodesk Fusion 360 for creating complex shape real-world models by using surface and T-Spline modeling techniques. This textbook is a great help for Autodesk Fusion 360 users who are new to surface and T-Spline modeling. It consists of a total of 232 pages covering the Surface and Form/Sculpt environments of Autodesk Fusion 360. It teaches users to use Autodesk Fusion 360 mechanical design software for creating complex shapes, three-dimensional surfaces and T-Spline models of zero thickness. This edition of textbook has been developed using Autodesk Fusion 360 software version: 2.0.10811 (August 2021 Product Update). This textbook not only focuses on the usage of the tools and commands of Autodesk Fusion 360 for creating surface and T-Spline models but also on the concept of design. Every chapter in this textbook contains Tutorials followed by theoretical description, that provide users with step-by-step instructions for creating surface designs and sculpting with T-Spline surfaces. Moreover, every chapter ends with Hands-on Test Drives which allow users to experience the user friendly and powerful capacities of Autodesk Fusion 360.