An Application of Computer Algebra to Pharmacokinetics: The Bateman Equation

SIAM Review ◽  
2006 ◽  
Vol 48 (1) ◽  
pp. 133-146 ◽  
Author(s):  
Eugenio Roanes-Lozano ◽  
Alfonso González-Bermejo ◽  
Eugenio Roanes-Macías ◽  
Justo Cabezas
Keyword(s):  
Computer Algebra ◽  
Bateman Equation

An Application of Computer Algebra to Pharmacokinetics: The Bateman Equation

2006 ◽  
Vol 37 (4) ◽  
pp. 326
Author(s):  
Raymond N. Greenwell ◽  
Eugenio Roanes-Lozano ◽  
Alfonso González-Bermije ◽  
Eugenio Roanes-Macías ◽  
Justo Cabezas
Keyword(s):  
Computer Algebra ◽  
Bateman Equation

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark
Keyword(s):  
Monte Carlo ◽  
Decision Trees ◽  
Computer Algebra ◽  
Taylor Series ◽  
Computer Algebra System ◽  
Random Variable ◽  
Monte Carlo Analysis ◽  
Normal Random Variable ◽  
Medical Decision ◽  
Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

Computer Simulation and Computer Algebra

1989 ◽  
Author(s):  
Dietrich Stauffer ◽  
Friedrich W. Hehl ◽  
Volker Winkelmann ◽  
John G. Zabolitzky
Keyword(s):  
Computer Simulation ◽  
Computer Algebra

Computer Simulation and Computer Algebra

1988 ◽  
Author(s):  
Dietrich Stauffer ◽  
Friedrich W. Hehl ◽  
Volker Winkelmann ◽  
John G. Zabolitzky
Keyword(s):  
Computer Simulation ◽  
Computer Algebra
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