Sparse partition universal graphs for graphs of bounded degree

In 1983, Chvatal, Trotter and the two senior authors proved that for any Delta there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph K(N) with N >= Bn vertices yields a monochromatic copy of any graph H that has n vertices and maximum degree Delta. We prove that the complete graph may be replaced by a sparser graph G that has N vertices and O(N(2-1/Delta)log(1/Delta)N) edges, with N = [B`n] for some constant B` that depends only on Delta. Consequently, the so-called size-Ramsey number of any H with n vertices and maximum degree Delta is O(n(2-1/Delta)log(1/Delta)n) Our approach is based on random graphs; in fact, we show that the classical Erdos-Renyi random graph with the numerical parameters above satisfies a stronger partition property with high probability, namely, that any 2-colouring of its edges contains a monochromatic universal graph for the class of graphs on n vertices and maximum degree Delta. The main tool in our proof is the regularity method, adapted to a suitable sparse setting. The novel ingredient developed here is an embedding strategy that allows one to embed bounded degree graphs of linear order in certain pseudorandom graphs. Crucial to our proof is the fact that regularity is typically inherited at a scale that is much finer than the scale at which it is assumed. (C) 2011 Elsevier Inc. All rights reserved.

Local influence in estimating equations

Local influence diagnostics based on estimating equations as the role of a gradient vector derived from any fit function are developed for repeated measures regression analysis. Our proposal generalizes tools used in other studies (Cook, 1986: Cadigan and Farrell, 2002), considering herein local influence diagnostics for a statistical model where estimation involves an estimating equation in which all observations are not necessarily independent of each other. Moreover, the measures of local influence are illustrated with some simulated data sets to assess influential observations. Applications using real data are presented. (C) 2010 Elsevier B.V. All rights reserved.

Cutpoint selection for discretizing a continuous covariate for generalized estimating equations

We consider consider the problem of dichotomizing a continuous covariate when performing a regression analysis based on a generalized estimation approach. The problem involves estimation of the cutpoint for the covariate and testing the hypothesis that the binary covariate constructed from the continuous covariate has a significant impact on the outcome. Due to the multiple testing used to find the optimal cutpoint, we need to make an adjustment to the usual significance test to preserve the type-I error rates. We illustrate the techniques on one data set of patients given unrelated hematopoietic stem cell transplantation. Here the question is whether the CD34 cell dose given to patient affects the outcome of the transplant and what is the smallest cell dose which is needed for good outcomes. (C) 2010 Elsevier BM. All rights reserved.

Recovery of DNA for the detection and genotyping of human papillomavirus from clinical cervical specimens stored for up to 2 years in a universal collection medium with denaturing reagent

The recovery and stability of DNA for the detection and genotyping of HPV in UCM-containing specimens, after exposure to denaturing reagents and stored for up to 2 years were evaluated. Samples were collected from 60 women who had cervical cytology specimens harboring cervical intraepithelial neoplasia (CIN) 2 or 3. All samples were stored in UCM and had been frozen at -20 degrees C following the addition of the denaturing reagent (sodium hydroxide) and the removal of the aliquot required for Hybrid Capture 2 testing for the identification of HPV DNA. The samples had been stored for 6, 12 and 24 months (20 samples for each storage time). HPV DNA extraction was performed according to a protocol designed specifically and the presence and quality of DNA was confirmed by human P-globin detection using the consensus primers G73 and G74. HPV DNA was amplified using the consensus primers PGMY09 and PGMY11, and reverse line-blot hybridization was used to detect type-specific amplicons for 37 HPV types. The DNA extracted from the denatured specimen was recovered in 57/60 (95%) of the samples. HPV DNA was detected in 56/57 (98%) of the recovered samples. Twenty-six of the 56 samples recovered (48%) were genotyped successfully. (c) 2007 Elsevier B.V. All rights reserved.

Metastable Periodic Patterns in Singularly Perturbed Delayed Equations

We consider the scalar delayed differential equation epsilon(x) over dot(t) = -x(t) + f(x(t-1)), where epsilon > 0 and f verifies either df/dx > 0 or df/dx < 0 and some other conditions. We present theorems indicating that a generic initial condition with sign changes generates a solution with a transient time of order exp(c/epsilon), for some c > 0. We call it a metastable solution. During this transient a finite time span of the solution looks like that of a periodic function. It is remarkable that if df/dx > 0 then f must be odd or present some other very special symmetry in order to support metastable solutions, while this condition is absent in the case df/dx < 0. Explicit epsilon-asymptotics for the motion of zeroes of a solution and for the transient time regime are presented.

Local solvability for a class of evolution equations

Motivated by the celebrated example of Y. Kannai of a linear partial differential operator which is hypoelliptic but not locally solvable, we consider it class of evolution operators with real-analytic coefficients and study their local solvability both in L(2) and in the weak sense. In order to do so we are led to propose a generalization of the Nirenberg-Treves condition (psi) which is suitable to our study. (C) 2009 Published by Elsevier Inc.

CONTINUITY OF GLOBAL ATTRACTORS FOR A CLASS OF NON LOCAL EVOLUTION EQUATIONS

In this work we prove that the global attractors for the flow of the equation partial derivative m(r, t)/partial derivative t = -m(r, t) + g(beta J * m(r, t) + beta h), h, beta >= 0, are continuous with respect to the parameters h and beta if one assumes a property implying normal hyperbolicity for its (families of) equilibria.