Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective

Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.

Matrix-Variate Statistical Distributions and Fractional Calculus

MSC 2010: 15A15, 15A52, 33C60, 33E12, 44A20, 62E15 Dedicated to Professor R. Gorenflo on the occasion of his 80th birthday

Properties of the Bellman Gamma Distribution

2000 Mathematics Subject Classification: 62H10.

Information Matrix for Beta Distributions

2000 Mathematics Subject Classification: 33C90, 62E99.

Matrix metalloproteinase (MMP)-9 genotypes and haplotypes in preeclampsia and gestational hypertension

Background: Abnormal production of matrix metalloproteinases (MMPs), especially MMP-9, may play a role in hypertensive disorders of pregnancy. These alterations may result from functional genetic polymorphisms in the promoter region of MMP-9 gene, which are known to change MMP-9 expression. We examined whether 2 MMP-9 polymorphisms (C(-) (1562) T and (CA)n) and haplotypes are associated with preeclampsia and/or gestational hypertension. Methods: We studied 476 pregnant women: 176 healthy pregnant (HP), 146 pregnant with gestational hypertension (GH), and 154 pregnant with preeclampsia (PE). Genomic DNA was extracted from whole blood and genotypes for C(- 1562) T and (CA)n polymorphisms were determined by PCR-RFLP. Haplotype frequencies were inferred using the PHASE ver. 2.1 program. Results: For the g.-90(CA)13-25 polymorphism, no significant differences were found in genotype and allele distributions when PE or GH groups were compared with HP group. However, the CT genotype and T allele for g.-1562C>T polymorphism were more commonly found in GH subjects compared with the HP group (both P<0.05). Conversely, we found no differences in genotypes or allele distributions for the g.-1562C>T polymorphism when the PE and the HP groups were compared. No significant differences were found in overall distributions of haplotype frequencies when the GH or the PE group was compared with the HP group. Conclusions: The C(- 1562) T polymorphism in MMP-9 gene is associated with gestational hypertension, but not with preeclampsia. These findings may help to explain the higher plasma MMP-9 levels previously reported in GH compared with HP. (C) 2010 Elsevier B.V. All rights reserved.

Thin films composed of gold nanoparticles dispersed in a dielectric matrix: the influence of the host matrix on the optical and mechanical responses

Gold nanoparticles were dispersed in two different dielectric matrices, TiO2 and Al2O3, using magnetron sputtering and a post-deposition annealing treatment. The main goal of the present work was to study how the two different host dielectric matrices, and the resulting microstructure evolution (including both the nanoparticles and the host matrix itself) promoted by thermal annealing, influenced the physical properties of the films. In particular, the structure and morphology of the nanocomposites were correlated with the optical response of the thin films, namely their localized surface plasmon resonance (LSPR) characteristics. Furthermore, and in order to scan the future application of the two thin film system in different types of sensors (namely biological ones), their functional behaviour (hardness and Young's modulus change) was also evaluated. Despite the similar Au concentrations in both matrices (~ 11 at.%), very different microstructural features were observed, which were found to depend strongly on the annealing temperature. The main structural differences included: (i) the early crystallization of the TiO2 host matrix, while the Al2O3 one remained amorphous up to 800 °C; (ii) different grain size evolution behaviours with the annealing temperature, namely an almost linear increase for the Au:TiO2 system (from 3 to 11 nm), and the approximately constant values observed in the Au:Al2O3 system (4–5 nm). The results from the nanoparticle size distributions were also found to be quite sensitive to the surrounding matrix, suggesting different mechanisms for the nanoparticle growth (particle migration and coalescence dominating in TiO2 and Ostwald ripening in Al2O3). These different clustering behaviours induced different transmittance-LSPR responses and a good mechanical stability, which opens the possibility for future use of these nanocomposite thin film systems in some envisaged applications (e.g. LSPR-biosensors).

Soporte geoespacial para modelos de distribución de especies (I): generalización del mapa de vegetación del Montseny apoyada en información de imágenes de satélite

Los mapas de vegetación son a menudo utilizados como proxis de una estratificación de hábitats para generar distribuciones geográficas contínuas de organismos a partir de datos discretos mediante modelos multi-variantes. Sin embargo, los mapas de vegetación suelen ser poco apropiados para ser directamente aplicados a este fin, pues sus categorías no se concibieron con la intención de corresponder a tipos de hábitat. En este artículo presentamos y aplicamos el método de Agrupamiento por Doble Criterio para generalizar un mapa de vegetación extraordinariamente detallado (350 clases) del Parque Natural del Montseny (Cataluña) en categorías que mantienen la coherencia tanto desde el punto de vista estructural (a través de una matriz de disimilaridad espectral calculada mediante una imágen del satélite SPOT-5) como en términos de vegetación (gracias a una matriz de disimilaridad calculada mediante propiedades de vegetación deducidas de la leyenda jerárquica del mapa). El método simplifica de 114 a 18 clases el 67% del área de estudio. Añadiendo otras agregaciones más triviales basadas exclusivamente en criterios de cubierta de suelo, el 73% del área de estudio pasa de 167 a 25 categorías. Como valor añadido, el método identifica el 10% de los polígonos originales como anómalos (a partir de comparar las propiedades espectrales de cada polígono con el resto de los de su clases), lo que implica cambios en la cubierta entre las fechas del soporte utilizado para generar el mapa original y la imagen de satélite, o errores en la producción de éste.

Quantitative analysis of crystal/grain sizes and their distributions in 2D and 3D

We review methods to estimate the average crystal (grain) size and the crystal (grain) size distribution in solid rocks. Average grain sizes often provide the base for stress estimates or rheological calculations requiring the quantification of grain sizes in a rock's microstructure. The primary data for grain size data are either 1D (i.e. line intercept methods), 2D (area analysis) or 3D (e.g., computed tomography, serial sectioning). These data have been used for different data treatments over the years, whereas several studies assume a certain probability function (e.g., logarithm, square root) to calculate statistical parameters as the mean, median, mode or the skewness of a crystal size distribution. The finally calculated average grain sizes have to be compatible between the different grain size estimation approaches in order to be properly applied, for example, in paleo-piezometers or grain size sensitive flow laws. Such compatibility is tested for different data treatments using one- and two-dimensional measurements. We propose an empirical conversion matrix for different datasets. These conversion factors provide the option to make different datasets compatible with each other, although the primary calculations were obtained in different ways. In order to present an average grain size, we propose to use the area-weighted and volume-weighted mean in the case of unimodal grain size distributions, respectively, for 2D and 3D measurements. The shape of the crystal size distribution is important for studies of nucleation and growth of minerals. The shape of the crystal size distribution of garnet populations is compared between different 2D and 3D measurements, which are serial sectioning and computed tomography. The comparison of different direct measured 3D data; stereological data and direct presented 20 data show the problems of the quality of the smallest grain sizes and the overestimation of small grain sizes in stereological tools, depending on the type of CSD. (C) 2011 Published by Elsevier Ltd.

Properties and Inference on the Skew-Curved-Symmetric Family of Distributions

In this article, we study some results related to a specific class of distributions, called skew-curved-symmetric family of distributions that depends on a parameter controlling the skewness and kurtosis at the same time. Special elements of this family which are studied include symmetric and well-known asymmetric distributions. General results are given for the score function and the observed information matrix. It is shown that the observed information matrix is always singular for some special cases. We illustrate the flexibility of this class of distributions with an application to a real dataset on characteristics of Australian athletes.

QUASISTATIONARY DISTRIBUTIONS AND FLEMING-VIOT PROCESSES IN FINITE SPACES

Consider a continuous-time Markov process with transition rates matrix Q in the state space Lambda boolean OR {0}. In In the associated Fleming-Viot process N particles evolve independently in A with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Lambda is finite, we show that the empirical distribution of the particles at a fixed time converges as N -> infinity to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N -> infinity to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1/N.

Covariance matrix formula for Birnbaum-Saunders regression models

The Birnbaum-Saunders regression model is commonly used in reliability studies. We derive a simple matrix formula for second-order covariances of maximum-likelihood estimators in this class of models. The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors. Some simulation results show that the second-order covariances can be quite pronounced in small to moderate sample sizes. We also present empirical applications.

A Note on the Prior Distributions of Weibull Parameters for the Reliability Function

In Bayesian Inference it is often desirable to have a posterior density reflecting mainly the information from sample data. To achieve this purpose it is important to employ prior densities which add little information to the sample. We have in the literature many such prior densities, for example, Jeffreys (1967), Lindley (1956); (1961), Hartigan (1964), Bernardo (1979), Zellner (1984), Tibshirani (1989), etc. In the present article, we compare the posterior densities of the reliability function by using Jeffreys, the maximal data information (Zellner, 1984), Tibshirani's, and reference priors for the reliability function R(t) in a Weibull distribution.

Off-Diagonal Quark Distributions in Pions in the Effective Single-Instanton Approximation

Nonperturbative functions that parametrize off-diagonal hadronic matrix elements of the light-cone leading-twist quark operators are considered. These functions are calculated within the proposed relativistic quark model allowing for the nontrivial structure of the QCD vacuum, special attention being given to gauge invariance. Hadrons are treated as bound states of quarks; strong-interaction quark-pion vertices are described by effective interaction Lagrangians generated by instantons. The parameters of the instanton vacuum, such as the effective radius of the instanton and the quark mass, are related to the vacuum expectation values of the quark-gluon operators of the lowest dimension and to low-energy pion observables. © 2000 MAIK Nauka/Interperiodica.

Rapidity distributions in exclusive Z plus jet and gamma plus jet events in pp collisions at root s=7 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)