Predicting random effects with an expanded finite population mixed model

Prediction of random effects is an important problem with expanding applications. In the simplest context, the problem corresponds to prediction of the latent value (the mean) of a realized cluster selected via two-stage sampling. Recently, Stanek and Singer [Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 119-130] developed best linear unbiased predictors (BLUP) under a finite population mixed model that outperform BLUPs from mixed models and superpopulation models. Their setup, however, does not allow for unequally sized clusters. To overcome this drawback, we consider an expanded finite population mixed model based on a larger set of random variables that span a higher dimensional space than those typically applied to such problems. We show that BLUPs for linear combinations of the realized cluster means derived under such a model have considerably smaller mean squared error (MSE) than those obtained from mixed models, superpopulation models, and finite population mixed models. We motivate our general approach by an example developed for two-stage cluster sampling and show that it faithfully captures the stochastic aspects of sampling in the problem. We also consider simulation studies to illustrate the increased accuracy of the BLUP obtained under the expanded finite population mixed model. (C) 2007 Elsevier B.V. All rights reserved.

Geodesics and Almost Geodesic Cycles in Random Regular Graphs

A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and v in C, the distance d(G)(u, v) is at least d(C)(u, v) - e(n). Let omega(n) be any function tending to infinity with n. We consider a random d-regular graph on n vertices. We show that almost all pairs of vertices belong to an almost geodesic cycle C with e(n)= log(d-1)log(d-1) n+omega(n) and vertical bar C vertical bar =2 log(d-1) n+O(omega(n)). Along the way, we obtain results on near-geodesic paths. We also give the limiting distribution of the number of geodesics between two random vertices in this random graph. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 66: 115-136, 2011

Asymmetric Ramsey Properties of Random Graphs Involving Cliques

Consider the following problem: Forgiven graphs G and F(1),..., F(k), find a coloring of the edges of G with k colors such that G does not contain F; in color i. Rodl and Rucinski studied this problem for the random graph G,,, in the symmetric case when k is fixed and F(1) = ... = F(k) = F. They proved that such a coloring exists asymptotically almost surely (a.a.s.) provided that p <= bn(-beta) for some constants b = b(F,k) and beta = beta(F). This result is essentially best possible because for p >= Bn(-beta), where B = B(F, k) is a large constant, such an edge-coloring does not exist. Kohayakawa and Kreuter conjectured a threshold function n(-beta(F1,..., Fk)) for arbitrary F(1), ..., F(k). In this article we address the case when F(1),..., F(k) are cliques of different sizes and propose an algorithm that a.a.s. finds a valid k-edge-coloring of G(n,p) with p <= bn(-beta) for some constant b = b(F(1),..., F(k)), where beta = beta(F(1),..., F(k)) as conjectured. With a few exceptions, this algorithm also works in the general symmetric case. We also show that there exists a constant B = B(F,,..., Fk) such that for p >= Bn(-beta) the random graph G(n,p) a.a.s. does not have a valid k-edge-coloring provided the so-called KLR-conjecture holds. (C) 2008 Wiley Periodicals, Inc. Random Struct. Alg., 34, 419-453, 2009

Dinuclear Azide-Bridged Copper(II) Complex as Building Block for the Assembly of a 2D-Supramolecular Array

A novel Schiff base-copper(II) complex [Cu(2)L(2)(N(3))(2)](ClO(4))(2) 1, where L = (4-imidazolyl)ethylene-2-amino-1-ethylpyridine (apyhist), containing azide-bridges between adjacent copper ions in a dinuclear arrangement was isolated and characterized both in the solid state and in solution by X-ray crystallography and different spectroscopic techniques. Azide binding constants were estimated from titrations of the precursor [CuL(H(2)O)(2)](2+) solutions with sodium azide, giving rise to the azido-bridged species, [Cu(2)L(2)(N(3))(2)](2+). Raman spectra showed asymmetric stretching band at 2060 cm(-1), indicating the presence of azido ligands with a symmetric mu(1,) (1) binding geometry. EPA spectra, in frozen methanol/water solutions at 77 K, exhibited characteristic features of copper centers in tetragonal pyramidal coordination geometry, exhibiting magnetic interactions between them. Further, in solid state, two different values for magnetic coupling in this species were obtained, J/k = -(5.14 +/- 0.02) cm(-1) attributed to the mu(1, 1) azide-bridge mode, and J`z`/k = -(2.94 +/- 0.11) cm(-1) for the interaction between dinuclear moieties via water/perchorate bridges. Finally, an attempt was made to correlate structure and magnetic data for this dinuclear asymmetric end-on azido bridged-copper(II) 1 complex with those of another correlated dinuclear system, complex [Cu(2)L(2)Cl(2)](ClO(4))(2) 2, containing the same tridentate diimine ligand, but with chloro-bridged groups between the copper centres.

Fluorescent probes with malononitrile side group in methyl methacrylate copolymers

Fluorescent probes derivated from auramine, 1-aminopyrene, and 9-aminoacridine containing a malononitrile group are copolymerized with methyl methacrylate. These new fluorescent polymeric materials are studied in solution of different solvents by steady-state and time-resolved emission techniques. Their spectroscopic properties and excited state dynamics are driven by charge transfer from the aromatic group to the electron withdrawing CN groups, and this factor is responsible for the non-exponential emission decay behavior. (c) 2008 Elsevier B.V. All rights reserved.

Excited-state dynamics of polyfluorene derivatives in solution

The excited-state dynamics of two polyfluorene copolymers, one fully conjugated containing phenylene vinylene units alternated with 9,9`-dihexylfluorenyl groups and the other segmented by -(CH2)(8)- spacer, were studied in dilute solution of different solvents using a picosecond single-photon timing technique. The excited-state dynamics of the segmented copolymer follows the Forster resonant energy-transfer model which describes intrachain energy-transfer kinetics among random oriented chromophores. Energy transfer is confirmed by analysis of fluorescence anisotropy relaxation with the measurement of a short decay component of about 60 ps. The fluorescence decay surface of the fully conjugated copolymer is biexponential with decay times of about 470 and 900 ps, ascribed to deactivation of chain moieties containing trans and cis isomers already in a photostationary condition. Thus, energy transfer is very fast due to the conjugated nature and rigid-rod-like structure of this copolymer chain.

Evaluation of the light polymerization efficiency of copolymers used in dental formulations by differential scanning calorimetry

Different compositions of visible-light-curable triethylene glycol dimethacrylate/bisglycidyl methacrylate copolymers used in dental resin formulations were prepared through copolymerization photoinitiated by a camphorquinone/ethyl 4-dimethylaminobenzoate system irradiated with an Ultrablue IS light-emitting diode. The obtained copolymers were evaluated with differential scanning calorimetry. From the data for the heat of polymerization, before and after light exposure, obtained from exothermic differential scanning calorimetry curves, the light polymerization efficiency or degree of conversion of double bonds was calculated. The glass-transition temperature also was determined before and after photopolymerization. After the photopolymerization, the glass-transi-tion temperature was not well defined because of the breadth of the transition region associated with the properties of the photocured dimethacrylate. The glass-transition temperature after photopolymerization was determined experimentally and compared with the values determined with the Fox equation. In all mixtures, the experimental value was lower than the calculated value. Scanning electron microscopy was used to analyze the morphological differences in the prepared copolymer structures. (C) 2007 Wiley Periodicals, Inc.

Evaluation of Postpolymerization as a Function of the Storage Time of Triethylene Glycol Dimethacrylate/2,2-Bis[4-(2-Hydroxy-3-Methacryloxy-Prop-1-Oxy)-Phenyl]-propane Bisphenyl-alpha-Glycidyl Ether Dimethacrylate Copolymers Used in Dental Resins by Differential Scanning Calorimetry and Dynamic Mechanical Analysis

The aim of this work was to evaluate the effect of the storage time on the thermal properties of triethylene glycol dimethacrylate/2,2-bis[4-(2-hydroxy-3-methacryloxy-prop-1-oxy)-phenyl]propane bisphenyl-alpha-glycidyl ether dimethacrylate (TB) copolymers used in formulations of dental resins after photopolymerization. The TB copolymers were prepared by photopolymerization with an Ultrablue IS light-emitting diode, stored in the dark for 160 days at 37 degrees C, and characterized with differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), and Fourier transform infrared spectroscopy with attenuated total reflection. DSC curves indicated the presence of an exothermic peak, confirming that the reaction was not completed during the photopolymerization process. This exothermic peak became smaller as a function of the storage time and was shifted at higher temperatures. In DMA studies, a plot of the loss tangent versus the temperature initially showed the presence of two well-defined peaks. The presence of both peaks confirmed the presence of residual monomers that were not converted during the photopolymerization process. (C) 2009 Wiley Periodicals, Inc. J Appl Polym Sci 112: 679-684, 2009