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13 results on '"Mena, Robert"'

1. Markov Chains for Collaboration

Author

Mena, Robert and Murray, Will

Subjects
Mathematics - Probability, Mathematics - Combinatorics
Abstract

Consider a system of \(n\) players in which each initially starts on a different team. At each time step, we select an individual winner and an individual loser randomly and the loser joins the winner's team. The resulting Markov chain and stochastic matrix clearly have one absorbing state, in which all players are on the same team, but the combinatorics along the way are surprisingly elegant. The expected number of time steps until each team is eliminated is a ratio of binomial coefficients. When a team is eliminated, the probabilities that the players are configured in various partitions of \(n\) into \(t\) teams are given by multinomial coefficients. The expected value of the time to absorbtion is \((n-1)^2\) steps. The results depend on elementary combinatorics, linear algebra, and the theory of Markov chains.

Published
2014
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5. Amusements in the History of Mathematics.

Author

Gray, Shirley B. and Mena, Robert A.

Abstract

Presents activities that engage students and promote discussion emphasizing the history of mathematics, diversity, and multiculturalism. Six activities included are Crossword Puzzle, Date of Event, Quotes Matching, Famous Mathematical Expressions, Calendar Scramble, and Map Puzzle. Also lists related World Wide Web sites. Contains 15 references. (Author/ASK)

Published
1997

6. Optimal interleaving schemes for two-dimensional arrays

Author

Golomb, S.W., Mena, Robert, and Xu, Wen-Qing

Subjects
Algorithm, Algorithms -- Usage, Error-correcting codes -- Research
Abstract

Given an m x n array of k single random error correction (or erasure) codewords, each having length l such that mn = kl, we construct optimal interleaving schemes that provide the maximum burst error correction power such that an arbitrarily shaped error burst of size t can be corrected for the largest possible value of t. We show that for all such m x n arrays, the maximum possible interleaving distance, or equivalently, the largest value of t such that an arbitrary error burst of size up to t can be corrected, is bounded by [??][summation of 2k][??] if k [less than or equal to] [??]min{m,n})2/2[??], and by min{m,n} + [??]k - [??](min{m,n})2/2[??])/min{m,n}[??] if k [greater than or equal to] [??](min{m,n})2/2[??]. We generalize the cyclic shifting algorithm developed by the authors in a previous paper and construct, in several special cases, optimal interleaving arrays achieving these upper bounds. Additionally, for codewords of variable lengths, we solve a related array coloring problem for which the same upper bounds hold and can he achieved. Index Terms--Cluster errors, cyclic shifting, interleaving, random error-correcting codes, sphere packing.

Published
2006

7. E2592

Author

Hausner, Melvin, Barr, Michael, Erlebach, Lee, Foster, Lorraine, Goldstein, Richard, Greening, M. G., Lossers, O. P., and Mena, Robert

Published
1977
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8. Selección clonal de germoplasma élite de Ananas comosus L. «piña de castilla del Chocó» para la obtención de material de siembra para el establecimiento de cultivos comerciales, vía cultivo in vitro

Author

Medina, Miguel Angel, Mena, Robert, Medina, Miguel Angel, and Mena, Robert

Abstract

In order to perform clonal selection of the best individuals, pineapple, Ananas comusus «Pineapple of castilla from Chocó», buds of apices extracted from basal shoots were multiplied in vitro. These buds were transferred into a semisolid medium of Murashige and Skoog (MS), applying eight different types of hormonal treatments: No growth regulators; 0.25 mg/l of naftaleneacetic acid (NAA) + 0.5 mg/l of benzylaminopurine (BA), 0.1 mg/l de ANA+0.8 mg/l de BA, 0.3 mg/l de ANA+1 mg/l de 6-BA, 0.5 mg/l de ANA+1.5 mg/l de 6-BA, 0.8 mg/l de ANA+1.8 mg/ de 6-BA, 1 mg/l de ANA+2 mg/l de 6-BA, 0.3 mg/l de ANA+1 mg/l de 6-BA+2 mg/l gibberellic acid (AG3). Sixty day later, the number of shoots per explant (295.5) was greater when using 1 mg/l of NAA+2 mg/l of BA; also the number of shoots with height between 0.5 and 1 cm (9.5) and >1 cm (200.6) was greater, the rooting was ex vitro, at thirty days the plants had eight root of 1.5 cm., Con el propósito de realizar la selección clonal de los mejores individuos de Ananas comosus, piña de castilla del Chocó, se multiplicaron in vitro brotes provenientes de ápices caulinares extraídos de hijos basales, que se subcultivaron en un medio semisólido de Murashige y Skoog (MS), adicionando ocho tratamientos hormonales: sin reguladores de crecimiento, 0.25 mg/l de ANA+0.5 mg/l (6-BA), 0.1 mg/l de ANA+0.8 mg/l de BA, 0.3 mg/l de ANA+1.0 mg/l de 6-BA, 0.5 mg/l de ANA+1.5 mg/l de 6-BA, 0.8 mg/ l de ANA+1.8 mg/ de 6-BA, 1 mg/l de ANA+2 mg/l de 6-BA, 0.3 mg/l de ANA+1 mg/l de 6-BA+2 mg/l de ácido giberélico (AG3). A los 60 días, el número de brotes por explante (295.5) fue superior al usar 1 mg/l de ANA+2 mg/l de BA; también el número de brotes cuyo tamaño fue >1 cm (200.6) y de 0.5 a 1 cm (9.5) fueron mayores, el enraizamiento fue ex vitro y a los 30 días las plantas tenían en promedio ocho raíces de 1.5 cm.

Published
2011

13. JUNK MAIL.

Author

Fritcher, Chad and Mena, Robert

Subjects
LETTERS to the editor, MOTORSPORTS
Abstract

Presents letters to the editor published in a 2005 issue of the periodical "Dirtsports" about issues related to motorsports.

Published
2005

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