Abstract. Dirichlet density extends global asymptotic density in an additive number system A whose generating series A(x) diverges at its radius of convergence (see [1], p. 50). This note shows that the parallel result holds for a multiplicative number system A, namely if the abcissa of convergence α of the generating series A(x) is finite and A(α) = ∞ then Dirichlet density extends global asym...

We consider conditioned Galton–Watson trees and show asymptotic normality of additive functionals that are defined by toll functions that are not too large. This includes, as a special case, asymptotic normality of the number of fringe subtrees isomorphic to any given tree, and joint asymptotic normality for several such subtree counts. Another example is the number of protected nodes. The offs...

In this paper, we investigate the asymptotic theory for U -statistics based on sample spacings, i.e. the gaps between successive observations. The usual asymptotic theory for U -statistics does not apply here because spacings are dependent variables. However, under the null hypothesis, the uniform spacings can be expressed as conditionally independent Exponential random variables. We exploit th...

We investigate the formation of a locally naked singularity in the collapse of radiation shells in an expanding Vaidya-deSitter background. This is achieved by considering the behaviour of non-spacelike and radial geodesics originating at the singularity. A specific condition is determined for the existence of radially outgoing, null geodesics originating at the singularity which, when this con...

Among gastrointestinal distributed isozymes encoded at the UGT1 locus, UDP-glucuronosyltransferase 1A10 (UGT1A10) metabolizes a number of important chemicals. Similar to broad conversion of phytoestrogens (Basu, N. K., Ciotti, M., Hwang, M. S., Kole, L., Mitra, P. S., Cho, J. W., and Owens, I. S. (2004) J. Biol. Chem. 279, 1429-1441), UGT1A10 metabolized estrogens and their derivatives, whereas...

The null vector method, based on a simple linear algebraic concept, is proposed as a solution to the phase retrieval problem. In the case with complex Gaussian random measurement matrices, a non-asymptotic error bound is derived, yielding an asymptotic regime of accurate approximation comparable to that for the spectral vector method.

Mesp1 and Mesp2 are homologous basic helix-loop-helix (bHLH) transcription factors that are co-expressed in the anterior presomitic mesoderm (PSM) just prior to somite formation. Analysis of possible functional redundancy of Mesp1 and Mesp2 has been prevented by the early developmental arrest of Mesp1/Mesp2 double-null embryos. Here we performed chimera analysis, using either Mesp2-null cells o...

We use zero angular momentum null geodesics in the Kerr-de Sitter spacetime to transform metric a generalised Bondi coordinate system. write components explicitly. Next, we choose radial be areal and asymptotic Bondi-Sachs gauge.

This article describes the asymptotic properties of local polynomial regression estimators for univariate and additive models when observation weights are included. The implications of these ndings are discussed for local scoring estimators, a widely used class of estimators for generalized additive models described in Hastie and Tibshirani (1990).

In the multivariate regression setting, we propose a flexible varying coefficient model in which the regression coefficients of some predictors are additive functions of other predictors. Marginal integration estimators of the coefficients are developed and their asymptotic properties investigated. Under -mixing, it is found that the estimators of the parameters in the regression coefficients h...