splines and compartment models

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Splines And Compartment Models

Author : Karl-Ernst Biebler
ISBN : 9789814522243
Genre : Mathematics
File Size : 66. 8 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 : 72. 23 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.

Compartmental Modeling And Tracer Kinetics

Author : David H. Anderson
ISBN : 9783642518614
Genre : Science
File Size : 20. 13 MB
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This monograph is concerned with mathematical aspects of compartmental an alysis. In particular, linear models are closely analyzed since they are fully justifiable as an investigative tool in tracer experiments. The objective of the monograph is to bring the reader up to date on some of the current mathematical prob lems of interest in compartmental analysis. This is accomplished by reviewing mathematical developments in the literature, especially over the last 10-15 years, and by presenting some new thoughts and directions for future mathematical research. These notes started as a series of lectures that I gave while visiting with the Division of Applied ~1athematics, Brown University, 1979, and have developed in to this collection of articles aimed at the reader with a beginning graduate level background in mathematics. The text can be used as a self-paced reading course. With this in mind, exercises have been appropriately placed throughout the notes. As an aid in reading the material, the e~d of a proof is indicated by ~. Sub section titles are utilized to make it easier for the reader to skim over detailed material on a first reading and make the entire manuscript somewhat more accessible, especially to nonmathematicians in the biosciences. The preparation of this monograph has been a long task that would not have been completed without the influence of a number of individuals. I am especially indebted to H. T. Banks, J. W. Drane, J. Eisenfe1d, J. A. Jacquez, D. J.

Spline Based Regression For Nonlinear Models With Multiple Responses

Author : Yuh-Wen Soo
ISBN : WISC:89035656008
Genre :
File Size : 21. 6 MB
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Conference Record

Author : Institute of Electrical and Electronics Engineers
ISBN : 0780387007
Genre : Nuclear engineering
File Size : 27. 89 MB
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Technometrics

Author :
ISBN : UOM:39015009679278
Genre : Experimental design
File Size : 45. 76 MB
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Chemica Scripta

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ISBN : UVA:X004100727
Genre : Chemistry
File Size : 76. 97 MB
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An Introduction To Differential Equations

Author : Anil G Ladde
ISBN : 9789814397391
Genre : Mathematics
File Size : 22. 40 MB
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Volume 1: Deterministic Modeling, Methods and Analysis For more than half a century, stochastic calculus and stochastic differential equations have played a major role in analyzing the dynamic phenomena in the biological and physical sciences, as well as engineering. The advancement of knowledge in stochastic differential equations is spreading rapidly across the graduate and postgraduate programs in universities around the globe. This will be the first available book that can be used in any undergraduate/graduate stochastic modeling/applied mathematics courses and that can be used by an interdisciplinary researcher with a minimal academic background. An Introduction to Differential Equations: Volume 2 is a stochastic version of Volume 1 (“An Introduction to Differential Equations: Deterministic Modeling, Methods and Analysis”). Both books have a similar design, but naturally, differ by calculi. Again, both volumes use an innovative style in the presentation of the topics, methods and concepts with adequate preparation in deterministic Calculus. Errata Errata (32 KB)

Journal Of The American Statistical Association

Author :
ISBN : UOM:39015085199381
Genre : Statistics
File Size : 37. 54 MB
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Dissertation Abstracts International

Author :
ISBN : STANFORD:36105110578775
Genre : Science
File Size : 78. 75 MB
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