On Seliger and Whitham`s variational principle for hydrodynamic systems from the point of view of `fictitious particles`

FAPESP, the Sao Paulo State Research Foundation[04/04611-5]

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

An integrated molecular map of yellow passion fruit based on simultaneous maximum-likelihood estimation of linkage and linkage phases

The development of genetic maps for auto-incompatible species, such as the yellow passion fruit (Passiflora edulis Sims f.flavicarpa Deg.) is restricted due to the unfeasibility of obtaining traditional mapping populations based on inbred lines. For this reason, yellow passion fruit linkage maps were generally constructed using a strategy known as two-way pseudo-testeross, based on monoparental dominant markers segregating in a 1:1 fashion. Due to the lack of information from these markers in one of the parents, two individual (parental) maps were obtained. However, integration of these maps is essential, and biparental markers can be used for such an operation. The objective of our study was to construct an integrated molecular map for a full-sib population of yellow passion fruit combining different loci configuration generated from amplified fragment length polymorphisms (AFLPs) and microsatellite markers and using a novel approach based on simultaneous maximum-likelihood estimation of linkage and linkage phases, specially designed for outcrossing species. Of the total number of loci, approximate to 76%, 21%, 0.7%, and 2.3% did segregate in 1:1, 3:1, 1:2:1, and 1:1:1:1 ratios, respectively. Ten linkage groups (LGs) were established with a logarithm of the odds (LOD) score >= 5.0 assuming a recombination fraction : <= 0.35. On average, 24 markers were assigned per LG, representing a total map length of 1687 cM, with a marker density of 6.9 cM. No markers were placed as accessories on the map as was done with previously constructed individual maps.

Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.

Does egg competition occur in marine broadcast-spawners?

When the availability of sperm limits female reproductive success, competition for sperm, may be an important broker of sexual selection. This is because sperm limitation can increase the variance in female reproductive success, resulting in strong selection on females to compete for limited fertilization opportunities. Sperm limitation is probably common in broadcast-spawning marine invertebrates, making these excellent candidates for investigating scramble competition between broods of eggs and its consequences for female reproductive success. Here, we report our findings from a series of experiments that investigate egg competition in the sessile, broadcast-spawning polychaete Galeolaria caespitosa. We initially tested whether the order in which eggs encounter sperm affects their fertilization success at two ecologically relevant current regimes. We used a split-clutch-split-ejaculate technique to compare the fertilization success of eggs from individual females that had either first access (competition-free treatment) or second access (egg competition treatment) to a batch of sperm. We found that fertilization success depended on the order in which eggs accessed sperm; eggs that were assigned to the competition-free treatment exhibited significantly higher fertilization rates than those assigned to the egg competition treatment at both current speeds. In subsequent experiments we found that prior exposure of sperm to eggs significantly reduced both the quantity and quality of sperm available to fertilize a second clutch of eggs, resulting in reductions in fertilization success at high and low sperm concentrations. These findings suggest that female traits that increase the likelihood of sperm-egg interactions (e.g. egg size) will respond to selection imposed by egg competition.

The "ethical anthropic principle" and the religious ethics of Levinas

Why did Levinas choose Isaiah 45:7 ("I make peace and create evil: I the Lord do all that") as a superscription of his essay on evil? This article explores the role of evil in Levinas's religious ethics. The author discusses the structure of evil as revealed phenomenologically and juxtaposes it to the structure of subjectivity found in the writings of Levinas. The idea of the "ethical anthropic principle," modeled upon the cosmic anthropic principle, is then used to link evil to the responsibility of the subject. The link is subsequently extended to God. This is proposed as one way of understanding the meaning of Isaiah 45:7. © 2001 Journal of Religious Ethics, Inc.

Maximum Likelihood Estimation of Mixture Densities for Binned and Truncated Multivariate Data

Binning and truncation of data are common in data analysis and machine learning. This paper addresses the problem of fitting mixture densities to multivariate binned and truncated data. The EM approach proposed by McLachlan and Jones (Biometrics, 44: 2, 571-578, 1988) for the univariate case is generalized to multivariate measurements. The multivariate solution requires the evaluation of multidimensional integrals over each bin at each iteration of the EM procedure. Naive implementation of the procedure can lead to computationally inefficient results. To reduce the computational cost a number of straightforward numerical techniques are proposed. Results on simulated data indicate that the proposed methods can achieve significant computational gains with no loss in the accuracy of the final parameter estimates. Furthermore, experimental results suggest that with a sufficient number of bins and data points it is possible to estimate the true underlying density almost as well as if the data were not binned. The paper concludes with a brief description of an application of this approach to diagnosis of iron deficiency anemia, in the context of binned and truncated bivariate measurements of volume and hemoglobin concentration from an individual's red blood cells.