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Full-Text Articles in Physical Sciences and Mathematics
Computational Insight With Monte Carlo Simulations, Boyan Kostadinov
Computational Insight With Monte Carlo Simulations, Boyan Kostadinov
Publications and Research
We introduce Monte Carlo simulations for estimating areas by playing a game of "darts". We also introduce simulations of random walks. We use compact, vectorized programming, based on the R language, for all computer simulations and visualizations, aimed at high school students. This presentation is based on the Invited, prime time lecture given at the summer camp for gifted high school students at City College of New York, July 13, 2011.
Dea With A Perfect Object: Analytical Solutions, Alexander Vaninsky
Dea With A Perfect Object: Analytical Solutions, Alexander Vaninsky
Publications and Research
For the main DEA models, adding a Perfect Object—that is, a virtual object that has the smallest inputs and greatest outputs—to a collection of actual objects permits obtaining solutions analytically. The paper derives formulas for the solutions and demonstrates that computations with them comprise simple operations with ratios of inputs and outputs while avoiding the use of linear programming (LP) algorithms. A numerical example illustrates the utility of the approach.