Asymptotic normality in mixtures of power series distributions

The problem of estimating the individual probabilities of a discrete distribution is considered. The true distribution of the independent observations is a mixture of a family of power series distributions. First, we ensure identifiability of the mixing distribution assuming mild conditions. Next, the mixing distribution is estimated by non-parametric maximum likelihood and an estimator for individual probabilities is obtained from the corresponding marginal mixture density. We establish asymptotic normality for the estimator of individual probabilities by showing that, under certain conditions, the difference between this estimator and the empirical proportions is asymptotically negligible. Our framework includes Poisson, negative binomial and logarithmic series as well as binomial mixture models. Simulations highlight the benefit in achieving normality when using the proposed marginal mixture density approach instead of the empirical one, especially for small sample sizes and/or when interest is in the tail areas. A real data example is given to illustrate the use of the methodology.

Dual-specificity phosphatases in the hypo-osmotic stress response of keratin-defective epithelial cell lines

Although mutations in intermediate filament proteins cause many human disorders, the detailed pathogenic mechanisms and the way these mutations affect cell metabolism are unclear. In this study, selected keratin mutations were analysed for their effect on the epidermal stress response. Expression profiles of two keratin-mutant cell lines from epidermolysis bullosa simplex patients (one severe and one mild) were compared to a control keratinocyte line before and after challenge with hypo-osmotic shock, a common physiological stress that transiently distorts cell shape. Fewer changes in gene expression were found in cells with the severely disruptive mutation (55 genes altered) than with the mild mutation (174 genes) or the wild type cells (261 genes) possibly due to stress response pre-activation in these cells. We identified 16 immediate-early genes contributing to a general cell response to hypo-osmotic shock, and 20 genes with an altered expression pattern in the mutant keratin lines only. A number of dual-specificity phosphatases (MKP-1, MKP-2, MKP-3, MKP-5 and hVH3) are differentially regulated in these cells, and their downstream targets p-ERK and p-p38 are significantly up-regulated in the mutant keratin lines. Our findings strengthen the case for the expression of mutant keratin proteins inducing physiological stress, and this intrinsic stress may affect the cell responses to secondary stresses in patients' skin.

Oestrogenic activity of p-hydroxybenzoic acid (common metabolite of paraben esters) and methylparaben in human breast cancer cell lines

This paper addresses the question of whether p-hydroxybenzoic acid, the common metabolite of parabens, possesses oestrogenic activity in human breast cancer cell lines. The alkyl esters of p-hydroxybenzoic acid (parabens) are used widely as preservatives in consumer products to which the human population is exposed and have been shown previously to possess oestrogenic activity and to be present in human breast tumour tissue, which is an oestrogen-responsive tissue. Recent work has shown p-hydroxybenzoic acid to give an oestrogenic response in the rodent uterotrophic assay. We report here that p-hydroxybenzoic acid possesses oestrogenic activity in a panel of assays in human breast cancer cell lines. p-Hydroxybenzoic acid was able to displace [H-3]oestradiol from cytosolic oestrogen receptor of MCF7 human breast cancer cells by 54% at 5 x 10(6)-fold molar excess and by 99% at 10(7)-fold molar excess. It was able to increase the expression of a stably integrated oestrogen responsive reporter gene (ERE-CAT) at a concentration of 5 x 10(-4) M in MCF7 cells after 24 h and 7 days, which could be inhibited by the anti-oestrogen ICI 182 780 (Faslodex, fulvestrant). Proliferation of two human breast cancer cell lines (MCF7, ZR-75-1) could be increased by 10(-5) M p-hydroxybenzoic acid. Following on from previous studies showing a decrease in oestrogenic activity of parabens with shortening of the linear alkyl chain length, this study has compared the oestrogenic activity of p-hydroxybenzoic acid where the alkyl grouping is no longer present with methylparaben, which has the shortest alkyl group. Intrinsic oestrogenic activity of p-hydroxybenzoic acid was similar to that of methylparaben in terms of relative binding to the oestrogen receptor but its oestrogenic activity on gene expression and cell proliferation was lower than that of methylparaben. It can be concluded that removal of the ester group from parabens does not abrogate its oestrogenic activity and that p-hydroxybenzoic acid can give oestrogenic responses in human breast cancer cells. Copyright (C) 2005 John Wiley & Sons, Ltd.

Global asymptotic stability in a class of Putnam-type equations

In this paper, we initiate the study of a class of Putnam-type equation of the form x(n-1) = A(1)x(n) + A(2)x(n-1) + A(3)x(n-2)x(n-3) + A(4)/B(1)x(n)x(n-1) + B(2)x(n-2) + B(3)x(n-3) + B-4 n = 0, 1, 2,..., where A(1), A(2), A(3), A(4), B-1, B-2, B-3, B-4 are positive constants with A(1) + A(2) + A(3) + A(4) = B-1 + B-2 + B-3 + B-4, x(-3), x(-2), x(-1), x(0) are positive numbers. A sufficient condition is given for the global asymptotic stability of the equilibrium point c = 1 of such equations. (c) 2005 Elsevier Ltd. All rights reserved.

Global asymptotic stability in a rational recursive sequence

In this paper, we study the global stability of the difference equation x(n) = a + bx(n-1) + cx(n-1)(2)/d - x(n-2), n = 1,2,....., where a, b greater than or equal to 0 and c, d > 0. We show that one nonnegative equilibrium point of the equation is a global attractor with a basin that is determined by the parameters, and every positive Solution of the equation in the basin exponentially converges to the attractor. (C) 2003 Elsevier Inc. All rights reserved.