Multivariate measurement error models based on scale mixtures of the skew-normal distribution

Scale mixtures of the skew-normal (SMSN) distribution is a class of asymmetric thick-tailed distributions that includes the skew-normal (SN) distribution as a special case. The main advantage of these classes of distributions is that they are easy to simulate and have a nice hierarchical representation facilitating easy implementation of the expectation-maximization algorithm for the maximum-likelihood estimation. In this paper, we assume an SMSN distribution for the unobserved value of the covariates and a symmetric scale mixtures of the normal distribution for the error term of the model. This provides a robust alternative to parameter estimation in multivariate measurement error models. Specific distributions examined include univariate and multivariate versions of the SN, skew-t, skew-slash and skew-contaminated normal distributions. The results and methods are applied to a real data set.

Nuclear elements of degree 6 in the free alternative algebra

We construct five new elements of degree 6 in the nucleus of the free alternative algebra. We use the representation theory of the symmetric group to locate the elements. We use the computer algebra system ALBERT and an extension of ALBERT to express the elements in compact form and to show that these new elements are not a consequence of the known clegree-5 elements in the nucleus. We prove that these five new elements and four known elements form a basis for the subspace of nuclear elements of degree 6. Our calculations are done using modular arithmetic to save memory and time. The calculations can be done in characteristic zero or any prime greater than 6, and similar results are expected. We generated the nuclear elements using prime 103. We check our answer using five other primes.

Representation type of Jordan algebras

The problem of classification of Jordan bit-nodules over (non-semisimple) finite dimensional Jordan algebras with respect to their representation type is considered. The notions of diagram of a Jordan algebra and of Jordan tensor algebra of a bimodule are introduced and a mapping Qui is constructed which associates to the diagram of a Jordan algebra J the quiver of its universal associative enveloping algebra S(J). The main results are concerned with Jordan algebras of semi-matrix type, that is, algebras whose semi-simple component is a direct sum of Jordan matrix algebras. In this case, criterion of finiteness and tameness for one-sided representations are obtained, in terms of diagram and mapping Qui, for Jordan tensor algebras and for algebras with radical square equals to 0. (c) 2010 Elsevier Inc. All rights reserved.

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.