The Resource Splines and compartment models : an introduction, Karl-Ernst Biebler, Michael Wodny

Splines and compartment models : an introduction, Karl-Ernst Biebler, Michael Wodny

Label
Splines and compartment models : an introduction
Title
Splines and compartment models
Title remainder
an introduction
Statement of responsibility
Karl-Ernst Biebler, Michael Wodny
Creator
Contributor
Subject
Genre
Language
  • eng
  • eng
Summary
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 und
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Biebler, Karl-Ernst
Dewey number
511.8
Index
index present
Language note
English
LC call number
QA224
LC item number
.B54 2013
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Wodny, Michael
http://library.link/vocab/subjectName
  • Spline theory
  • Mathematical models
Label
Splines and compartment models : an introduction, Karl-Ernst Biebler, Michael Wodny
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliography and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
  • Preface; Contents; PART 1 Spline models; 1. Why spline functions?; 2. Interpolating splines of degree n; 3. Interpolating cubic splines; 3.1 Interpolating cubic splines with other extreme characteristics; 4. Smoothing natural cubic splines and the choice of the smoothing parameter; 4.1 Estimating the smoothing parameters; 5. Interpolating quadratic splines; 6. Interpolating quadratic splines and parabolas; 7. Smoothing quadratic splines; 7.1 Smoothing quadratic splines and the integral of the quadratic first derivative; 7.2 Quadratic splines smoothing the predefined first derivatives
  • 8. Splines and averaged functions8.1 Averaged splines in the case of common knots; 8.2 Averaged kinetics and reference ranges; 8.3 Growth curves and averaged splines without common knots; PART 2 Compartment models; 9. Concept of a context related mathematical pharmacokinetical model; 10. Compartment models; 10.1 One-compartment model; 10.2 Two-compartment models; 10.3 More-compartment models; 11. Other deterministic models; 11.1 Compartment models with delay; 11.2 Nonlinear kinetics; 12. Calculability and identifiability; 13. Compartment models and associated residence time distributions
  • 13.1 Unbounded residence times13.2 Properties of distributions of unbounded residence times; 13.3 Truncation; 14. Other stochastic models; 14.1 Stochastic differential equations; 14.2 Stochastic processes; 14.3 Regression attempts; 15. Calculation methods related to compartment models; 15.1 Method of least squares parameter calculations; 15.2 Statistical parameter estimation for an individual kinetics; 15.2.1 Varied minimum- X2-estimation; 15.2.2 Qualities of the varied minimum- X2-estimator; 15.3 The varied minimum- X2-method applied to population kinetics
  • 16. Selection of pharmacokinetic models17. Pharmacokinetics for multiple applications; PART 3 Mathematica® programs for selected problems; Program list; Bibliography; Index
Dimensions
unknown
Extent
1 online resource (349 p.)
Form of item
online
Isbn
9789814522236
Media category
computer
Media type code
  • c
Specific material designation
remote
System control number
  • (CKB)2550000001114708
  • (EBL)1389084
  • (OCoLC)858763088
  • (SSID)ssj0001168611
  • (PQKBManifestationID)11644972
  • (PQKBTitleCode)TC0001168611
  • (PQKBWorkID)11164428
  • (PQKB)10975119
  • (MiAaPQ)EBC1389084
  • (WSP)00008855
  • (EXLCZ)992550000001114708
Label
Splines and compartment models : an introduction, Karl-Ernst Biebler, Michael Wodny
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliography and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
  • Preface; Contents; PART 1 Spline models; 1. Why spline functions?; 2. Interpolating splines of degree n; 3. Interpolating cubic splines; 3.1 Interpolating cubic splines with other extreme characteristics; 4. Smoothing natural cubic splines and the choice of the smoothing parameter; 4.1 Estimating the smoothing parameters; 5. Interpolating quadratic splines; 6. Interpolating quadratic splines and parabolas; 7. Smoothing quadratic splines; 7.1 Smoothing quadratic splines and the integral of the quadratic first derivative; 7.2 Quadratic splines smoothing the predefined first derivatives
  • 8. Splines and averaged functions8.1 Averaged splines in the case of common knots; 8.2 Averaged kinetics and reference ranges; 8.3 Growth curves and averaged splines without common knots; PART 2 Compartment models; 9. Concept of a context related mathematical pharmacokinetical model; 10. Compartment models; 10.1 One-compartment model; 10.2 Two-compartment models; 10.3 More-compartment models; 11. Other deterministic models; 11.1 Compartment models with delay; 11.2 Nonlinear kinetics; 12. Calculability and identifiability; 13. Compartment models and associated residence time distributions
  • 13.1 Unbounded residence times13.2 Properties of distributions of unbounded residence times; 13.3 Truncation; 14. Other stochastic models; 14.1 Stochastic differential equations; 14.2 Stochastic processes; 14.3 Regression attempts; 15. Calculation methods related to compartment models; 15.1 Method of least squares parameter calculations; 15.2 Statistical parameter estimation for an individual kinetics; 15.2.1 Varied minimum- X2-estimation; 15.2.2 Qualities of the varied minimum- X2-estimator; 15.3 The varied minimum- X2-method applied to population kinetics
  • 16. Selection of pharmacokinetic models17. Pharmacokinetics for multiple applications; PART 3 Mathematica® programs for selected problems; Program list; Bibliography; Index
Dimensions
unknown
Extent
1 online resource (349 p.)
Form of item
online
Isbn
9789814522236
Media category
computer
Media type code
  • c
Specific material designation
remote
System control number
  • (CKB)2550000001114708
  • (EBL)1389084
  • (OCoLC)858763088
  • (SSID)ssj0001168611
  • (PQKBManifestationID)11644972
  • (PQKBTitleCode)TC0001168611
  • (PQKBWorkID)11164428
  • (PQKB)10975119
  • (MiAaPQ)EBC1389084
  • (WSP)00008855
  • (EXLCZ)992550000001114708

Library Locations

  • Albert D. Cohen Management LibraryBorrow it
    181 Freedman Crescent, Winnipeg, MB, R3T 5V4, CA
    49.807878 -97.129961
  • Architecture/Fine Arts LibraryBorrow it
    84 Curry Place, Winnipeg, MB, CA
    49.807716 -97.136226
  • Archives and Special CollectionsBorrow it
    25 Chancellors Circle (Elizabeth Dafoe Library), Room 330, Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Bibliothèque Alfred-Monnin (Université de Saint-Boniface)Borrow it
    200, avenue de la Cathédrale, Local 2110, Winnipeg, MB, R2H 0H7, CA
    49.888861 -97.119735
  • Bill Larson Library (Grace Hospital)Borrow it
    300 Booth Drive, G-227, Winnipeg, MB, R3J 3M7, CA
    49.882400 -97.276436
  • Carolyn Sifton - Helene Fuld Library (St. Boniface General Hospital)Borrow it
    409 Tache Avenue, Winnipeg, MB, R2H 2A6, CA
    49.883388 -97.126050
  • Concordia Hospital LibraryBorrow it
    1095 Concordia Avenue, Winnipeg, MB, R2K 3S8, CA
    49.913252 -97.064683
  • Donald W. Craik Engineering LibraryBorrow it
    75B Chancellors Circle (Engineering Building E3), Room 361, Winnipeg, MB, R3T 2N2, CA
    49.809053 -97.133292
  • E.K. Williams Law LibraryBorrow it
    224 Dysart Road, Winnipeg, MB, R3T 5V4, CA
    49.811829 -97.131017
  • Eckhardt-Gramatté Music LibraryBorrow it
    136 Dafoe Road (Taché Arts Complex), Room 257, Winnipeg, MB, R3T 2N2, CA
    49.807964 -97.132222
  • Elizabeth Dafoe LibraryBorrow it
    25 Chancellors Circle, Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Fr. H. Drake Library (St. Paul's College)Borrow it
    70 Dysart Road, Winnipeg, MB, R3T 2M6, CA
    49.810605 -97.138184
  • J.W. Crane Memorial Library (Deer Lodge Centre)Borrow it
    2109 Portage Avenue, Winnipeg, MB, R3J 0L3, CA
    49.878000 -97.235520
  • Libraries Annex (not open to the public; please see web page for details)Borrow it
    25 Chancellors Circle (in the Elizabeth Dafoe Library), Winnipeg, MB, R3T 2N2, CA
    49.809961 -97.131878
  • Neil John Maclean Health Sciences LibraryBorrow it
    727 McDermot Avenue (Brodie Centre), 200 Level, Winnipeg, MB, R3E 3P5, CA
    49.903563 -97.160554
  • Sciences and Technology LibraryBorrow it
    186 Dysart Road, Winnipeg, MB, R3T 2M8, CA
    49.811526 -97.133257
  • Seven Oaks General Hospital LibraryBorrow it
    2300 McPhillips Street, Winnipeg, MB, R2V 3M3, CA
    49.955177 -97.148865
  • Sister St. Odilon Library (Misericordia Health Centre)Borrow it
    99 Cornish Avenue, Winnipeg, MB, R3C 1A2, CA
    49.879592 -97.160425
  • St. John's College LibraryBorrow it
    92 Dysart Road, Winnipeg, MB, R3T 2M5, CA
    49.811242 -97.137156
  • Victoria General Hospital LibraryBorrow it
    2340 Pembina Highway, Winnipeg, MB, R3T 2E8, CA
    49.806755 -97.152739
  • William R Newman Library (Agriculture)Borrow it
    66 Dafoe Road, Winnipeg, MB, R3T 2R3, CA
    49.806936 -97.135525
Processing Feedback ...