scholarly journals Exhaustive search of symplectic integrators using computer algebra

1996 ◽  
pp. 103-119 ◽  
Author(s):  
P Koseleff
Keyword(s):  
Computer Algebra ◽  
Exhaustive Search ◽  
Symplectic Integrators

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

Hamilton-Jacobi Theory

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Bbgky Hierarchy ◽  
Distribution Functions ◽  
Symplectic Integrators ◽  
Partition Functions ◽  
Von Neumann ◽  
Equipartition Theorem ◽  
Recurrence Theorem ◽  
Phase Amplitude ◽  
Canonical Ensembles

This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.

1P285 Exhaustive search for protein surface similarities using a grid computing system

2005 ◽  
Vol 45 (supplement) ◽  
pp. S103
Author(s):  
R. Minai ◽  
M. Iwasaki ◽  
H. Murakmai ◽  
Y. Matsuo
Keyword(s):  
Grid Computing ◽  
Computing System ◽  
Exhaustive Search ◽  
Protein Surface
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