Splines and compartment models :: an introduction /
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...
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| Hauptverfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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[Hackensack] New Jersey :
World Scientific,
[2013]
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xiii, 334 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 319-330) and index. |
| ISBN: | 9789814522236 9814522236 1299833292 9781299833296 |
Internformat
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| 520 | 3 | |a 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. | |
| 504 | |a Includes bibliographical references (pages 319-330) and index. | ||
| 505 | 0 | |a Why spline functions? -- Interpolating splines of degree n -- Interpolating cubic splines -- Smoothing natural cubic splines and the choice of the smoothing parameter -- Interpolating quadratic splines -- Interpolating quadratic splines and paraboles -- Smoothing quadratic splines -- Splines and averaged functions -- Concept of a context related mathematical pharmacokinetical model -- Compartment models -- Other deterministic models -- Calculability and identifiability -- Compartment models and associated residence time distributions -- Other stochastic models -- Calculating methods related to compartment models -- Selection of pharmacokinetic models -- Pharmacokinetics for multiple applications -- Mathematica® programs for selected problems. | |
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| 650 | 6 | |a Théorie des splines. | |
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| author | Biebler, Karl-Ernst Wodny, Michael |
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| author_facet | Biebler, Karl-Ernst Wodny, Michael |
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| contents | Why spline functions? -- Interpolating splines of degree n -- Interpolating cubic splines -- Smoothing natural cubic splines and the choice of the smoothing parameter -- Interpolating quadratic splines -- Interpolating quadratic splines and paraboles -- Smoothing quadratic splines -- Splines and averaged functions -- Concept of a context related mathematical pharmacokinetical model -- Compartment models -- Other deterministic models -- Calculability and identifiability -- Compartment models and associated residence time distributions -- Other stochastic models -- Calculating methods related to compartment models -- Selection of pharmacokinetic models -- Pharmacokinetics for multiple applications -- Mathematica® programs for selected problems. |
| ctrlnum | (OCoLC)861528211 |
| dewey-full | 511.42 |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.42 |
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| discipline | Mathematik |
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| id | ZDB-4-EBA-ocn861528211 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:36Z |
| institution | BVB |
| isbn | 9789814522236 9814522236 1299833292 9781299833296 |
| language | English |
| oclc_num | 861528211 |
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| physical | 1 online resource (xiii, 334 pages) : illustrations |
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| spelling | Biebler, Karl-Ernst, author. http://id.loc.gov/authorities/names/n2010180548 Splines and compartment models : an introduction / Karl-Ernst Biebler, Michael Wodny. [Hackensack] New Jersey : World Scientific, [2013] ©2013 1 online resource (xiii, 334 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier 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. Includes bibliographical references (pages 319-330) and index. Why spline functions? -- Interpolating splines of degree n -- Interpolating cubic splines -- Smoothing natural cubic splines and the choice of the smoothing parameter -- Interpolating quadratic splines -- Interpolating quadratic splines and paraboles -- Smoothing quadratic splines -- Splines and averaged functions -- Concept of a context related mathematical pharmacokinetical model -- Compartment models -- Other deterministic models -- Calculability and identifiability -- Compartment models and associated residence time distributions -- Other stochastic models -- Calculating methods related to compartment models -- Selection of pharmacokinetic models -- Pharmacokinetics for multiple applications -- Mathematica® programs for selected problems. Print version record. Spline theory. http://id.loc.gov/authorities/subjects/sh85126830 Mathematical models. http://id.loc.gov/authorities/subjects/sh85082124 Models, Theoretical https://id.nlm.nih.gov/mesh/D008962 Théorie des splines. Modèles mathématiques. mathematical models. aat MATHEMATICS General. bisacsh Mathematical models fast Spline theory fast Wodny, Michael, author. http://id.loc.gov/authorities/names/no2013143319 has work: Splines and compartment models (Text) https://id.oclc.org/worldcat/entity/E39PCGkKfxpTWT9VWg3ydbfqFC https://id.oclc.org/worldcat/ontology/hasWork Print version: Biebler, Karl-Ernst. Splines and compartment models. Singapore ; Hackensack : World Scientific, [2013] 9814522228 (OCoLC)850182963 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=637074 Volltext |
| spellingShingle | Biebler, Karl-Ernst Wodny, Michael Splines and compartment models : an introduction / Why spline functions? -- Interpolating splines of degree n -- Interpolating cubic splines -- Smoothing natural cubic splines and the choice of the smoothing parameter -- Interpolating quadratic splines -- Interpolating quadratic splines and paraboles -- Smoothing quadratic splines -- Splines and averaged functions -- Concept of a context related mathematical pharmacokinetical model -- Compartment models -- Other deterministic models -- Calculability and identifiability -- Compartment models and associated residence time distributions -- Other stochastic models -- Calculating methods related to compartment models -- Selection of pharmacokinetic models -- Pharmacokinetics for multiple applications -- Mathematica® programs for selected problems. Spline theory. http://id.loc.gov/authorities/subjects/sh85126830 Mathematical models. http://id.loc.gov/authorities/subjects/sh85082124 Models, Theoretical https://id.nlm.nih.gov/mesh/D008962 Théorie des splines. Modèles mathématiques. mathematical models. aat MATHEMATICS General. bisacsh Mathematical models fast Spline theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85126830 http://id.loc.gov/authorities/subjects/sh85082124 https://id.nlm.nih.gov/mesh/D008962 |
| title | Splines and compartment models : an introduction / |
| title_auth | Splines and compartment models : an introduction / |
| title_exact_search | Splines and compartment models : an introduction / |
| title_full | Splines and compartment models : an introduction / Karl-Ernst Biebler, Michael Wodny. |
| title_fullStr | Splines and compartment models : an introduction / Karl-Ernst Biebler, Michael Wodny. |
| title_full_unstemmed | Splines and compartment models : an introduction / Karl-Ernst Biebler, Michael Wodny. |
| title_short | Splines and compartment models : |
| title_sort | splines and compartment models an introduction |
| title_sub | an introduction / |
| topic | Spline theory. http://id.loc.gov/authorities/subjects/sh85126830 Mathematical models. http://id.loc.gov/authorities/subjects/sh85082124 Models, Theoretical https://id.nlm.nih.gov/mesh/D008962 Théorie des splines. Modèles mathématiques. mathematical models. aat MATHEMATICS General. bisacsh Mathematical models fast Spline theory fast |
| topic_facet | Spline theory. Mathematical models. Models, Theoretical Théorie des splines. Modèles mathématiques. mathematical models. MATHEMATICS General. Mathematical models Spline theory |
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