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Full-Text Articles in Physical Sciences and Mathematics
Population Genetics: Estimation Of Distributions Through Systems Of Non-Linear Differential Equations, Nacer E. Abrouk, Robert J. Lopez
Population Genetics: Estimation Of Distributions Through Systems Of Non-Linear Differential Equations, Nacer E. Abrouk, Robert J. Lopez
Mathematical Sciences Technical Reports (MSTR)
In stochastic population genetics, the fundamental quantity used for describing the genetic composition of a Mendelian population is the gene frequency. The process of change in the gene frequency is generally modeled as a stochastic process satisfying a stochastic differential equation. The drift and diffusion coefficients in this equation reflect such mechanisms as mutation, selection, and migration that affect the population. Except in very simple cases, it is difficult to determine the probability law of the stochastic process of change in gene frequency. We present a method for obtaining approximations of this process, enabling us to study models more realistic …
A Variable Time-Step Midpoint Scheme For Hamiltonian Systems, Yosi Shibberu
A Variable Time-Step Midpoint Scheme For Hamiltonian Systems, Yosi Shibberu
Mathematical Sciences Technical Reports (MSTR)
A smooth time-step selection formula for the midpoint method is derived which minimize deviations in the Hamiltonian function along piecewise-linear phase space trajectories of autonomous Hamiltonian systems. The time-step formula is implemented in a second order predictor/corrector scheme and applied to Kepler's problem. The formula significantly improves energy conservation as well as the accuracy of the configuration space trajectory. Peak errors in position and momentum coordinates are not significantly reduced, but the time behavior of the errors is markedly more regular.
An Elementary Proof That Finite Groups Lack Unique Product Structures, Matthew Cushman
An Elementary Proof That Finite Groups Lack Unique Product Structures, Matthew Cushman
Mathematical Sciences Technical Reports (MSTR)
We provide an elementary proof that no nontrivial finite group has a unique m-element product structure for any m greater than or equal to 2.