splines and compartment models

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Splines And Compartment Models

Author : Karl-Ernst Biebler
ISBN : 9789814522243
Genre : Mathematics
File Size : 83. 87 MB
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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

Spline Functions

Author : Larry L. Schumaker
ISBN : 9781611973907
Genre : Science
File Size : 42. 81 MB
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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.

Comprehensive Biomedical Physics

Author :
ISBN : 9780444536334
Genre : Science
File Size : 81. 70 MB
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Comprehensive Biomedical Physics 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

Technometrics

Author :
ISBN : UOM:39015009679278
Genre : Experimental design
File Size : 76. 65 MB
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Spline Based Regression For Nonlinear Models With Multiple Responses

Author : Yuh-Wen Soo
ISBN : WISC:89035656008
Genre :
File Size : 34. 50 MB
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Chemica Scripta

Author :
ISBN : UVA:X004100727
Genre : Chemistry
File Size : 47. 61 MB
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S Plus 2000 Guide To Statistics

Author : Mathsoft, Inc. Data Analysis Products Division
ISBN : UCSD:31822029566874
Genre : Mathematics
File Size : 34. 27 MB
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Nonlinear Models In Medical Statistics

Author : James K. Lindsey
ISBN : 0198508123
Genre : Mathematics
File Size : 24. 73 MB
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'This book is a great introduction to the topic of nonlinear models and is probably the only book that deals with some of the concepts. Lindsey's writing style makes easy reading and very useful reference... this book is a must for those working in early phase clinical trials, particularly in the discipline of pharmacokinetics and pharmacodynamics.' -Pharmaceutical Statistics'The book would benefit primarily those statisticians working in exploratory fields, particularly early drug development. It would also benefit those working in pharmacokinetics and pharmacodynamics.' -Pharmaceutical StatisticsThis book provides an introduction to the use of nonlinear modelling in medical statistics, including worked through examples in most areas where such techniques are used. It is suitable for both professional and academic statisticians working in medical research. The data and computer code for the examples will be available on the authors web site.

Population Pharmacokinetic Models With Time Dependent Covariates

Author : Lang Li
ISBN : UOM:39015053365873
Genre :
File Size : 89. 53 MB
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Ber Die Erhaltung Der Kraft

Author : Hermann von Helmholtz
ISBN : BSB:BSB10927397
Genre : Force and energy
File Size : 26. 86 MB
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