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

GENOTYPE CHARACTERIZATION OF THE Haematobia irritans (DIPTERA: MUSCIDAE) FROM BRAZIL, DOMINICAN REPUBLIC AND COLOMBIA BASED ON RANDOMLY AMPLIFIED POLYMORPHIC DNA (RAPD) ANALYSIS

Blood-sucking flies are important parasites in animal production systems, especially regarding confinement conditions. Haematobia irritans, the horn fly, is one of the most troublesome species within bovine production systems, due to the intense stress imposed to the animals. H. irritans is one of the parasites of cattle that cause significant economic losses in many parts of the world, including South America. In the present work, Brazilian, Colombian and Dominican Republic populations of this species were studied by Random Amplified Polymorphic DNA(RAPD) to assess basically genetic variability between populations. Fifteen different decamer random primers were employed in the genomic DNA amplification, yielding 196 fragments in the three H. irritans populations. Among h. irritans samples, that from Colombia produced the smallest numbers of polymorphic hands. This high genetic homogeneity may be ascribed to its geographic origin, which causes high isolation, low gene flow, unlike the other American populations, from Brazil and Dominican Republic. Molecular marker fragments, which its produced exclusive bands, detected in every sample enabled the population origin to be characterized, but they are also potentially useful for further approaches such as the putative origin of Brazilian, Colombian and Dominican Republic populations of horn fly from South America. Similarity indices produced by chemo metric analysis showed the closest relationships between flies from Brazil and Dominican Republic, while flies from Colombia showed the greatest genotypic differentiation relative to the others populations.

Dynamic Solid Phase DNA Extraction and PCR Amplification in Polyester-Toner Based Microchip

A variety of substrates have been used for fabrication of microchips for DNA extraction, PCR amplification, and DNA fragment separation, including the more conventional glass and silicon as well as alternative polymer-based materials. Polyester represents one such polymer, and the laser-printing of toner onto polyester films has been shown to be effective for generating polyester-toner (PeT) microfluidic devices with channel depths on the order of tens of micrometers. Here, we describe a novel and simple process that allows for the production of multilayer, high aspect-ratio PeT microdevices with substantially larger channel depths. This innovative process utilizes a CO(2) laser to create the microchannel in polyester sheets containing a uniform layer of printed toner, and multilayer devices can easily be constructed by sandwiching the channel layer between uncoated cover sheets of polyester containing precut access holes. The process allows the fabrication of deep channels, with similar to 270 mu m, and we demonstrate the effectiveness of multilayer PeT microchips for dynamic solid phase extraction (dSPE) and PCR amplification. With the former, we found that (i) more than 65% of DNA from 0.6 mu L of blood was recovered, (ii) the resultant DNA was concentrated to greater than 3 ng/mu L., (which was better than other chip-based extraction methods), and (iii) the DNA recovered was compatible with downstream microchip-based PCR amplification. Illustrative of the compatibility of PeT microchips with the PCR process, the successful amplification of a 520 bp fragment of lambda-phage DNA in a conventional thermocycler is shown. The ability to handle the diverse chemistries associated with DNA purification and extraction is a testimony to the potential utility of PeT microchips beyond separations and presents a promising new disposable platform for genetic analysis that is low cost and easy to fabricate.

Estimation of Parameters in Random Effect Models with Incidence Matrix Uncertainty

Random effect models have been widely applied in many fields of research. However, models with uncertain design matrices for random effects have been little investigated before. In some applications with such problems, an expectation method has been used for simplicity. This method does not include the extra information of uncertainty in the design matrix is not included. The closed solution for this problem is generally difficult to attain. We therefore propose an two-step algorithm for estimating the parameters, especially the variance components in the model. The implementation is based on Monte Carlo approximation and a Newton-Raphson-based EM algorithm. As an example, a simulated genetics dataset was analyzed. The results showed that the proportion of the total variance explained by the random effects was accurately estimated, which was highly underestimated by the expectation method. By introducing heuristic search and optimization methods, the algorithm can possibly be developed to infer the 'model-based' best design matrix and the corresponding best estimates.

Dichlorvos exposure impedes extraction and amplification of DNA from insects in museum collections

Background: The insecticides dichlorvos, paradichlorobenzene and naphthalene have been commonly used to eradicate pest insects from natural history collections. However, it is not known how these chemicals affect the DNA of the specimens in the collections. We thus tested the effect of dichlorvos, paradichlorobenzene and naphthalene on DNA of insects (Musca domestica) by extracting and amplifying DNA from specimens exposed to insecticides in two different concentrations over increasing time intervals. Results: The results clearly show that dichlorvos impedes both extraction and amplification of mitochondrial and nuclear DNA after relatively short time, whereas paradichlorobenzene and naphthalene do not. Conclusion: Collections treated with paradichlorobenzene and naphthalene, are better preserved concerning DNA, than those treated with dichlorvos. Non toxic pest control methods should, however, be preferred due to physical damage of specimens and putative health risks by chemicals.