Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

The geometric Birnbaum-Saunders regression model with cure rate

In this paper, we propose a cure rate survival model by assuming the number of competing causes of the event of interest follows the Geometric distribution and the time to event follow a Birnbaum Saunders distribution. We consider a frequentist analysis for parameter estimation of a Geometric Birnbaum Saunders model with cure rate. Finally, to analyze a data set from the medical area. (C) 2011 Elsevier B.V. All rights reserved.

GEOMETRIC RELATIONS BETWEEN SPACES OF NUCLEAR OPERATORS AND SPACES OF COMPACT OPERATORS

We extend and provide a vector-valued version of some results of C. Samuel about the geometric relations between the spaces of nuclear operators N(E, F) and spaces of compact operators K(E, F), where E and F are Banach spaces C(K) of all continuous functions defined on the countable compact metric spaces K equipped with the supremum norm. First we continue Samuel's work by proving that N(C(K-1), C(K-2)) contains no subspace isomorphic to K(C(K-3), C(K-4)) whenever K-1, K-2, K-3 and K-4 are arbitrary infinite countable compact metric spaces. Then we show that it is relatively consistent with ZFC that the above result and the main results of Samuel can be extended to C(K-1, X), C(K-2,Y), C(K-3, X) and C(K-4, Y) spaces, where K-1, K-2, K-3 and K-4 are arbitrary infinite totally ordered compact spaces; X comprises certain Banach spaces such that X* are isomorphic to subspaces of l(1); and Y comprises arbitrary subspaces of l(p), with 1 < p < infinity. Our results cover the cases of some non-classical Banach spaces X constructed by Alspach, by Alspach and Benyamini, by Benyamini and Lindenstrauss, by Bourgain and Delbaen and also by Argyros and Haydon.

Relationship Between Regional Brain Volumes and Cognitive Performance in the Healthy Aging: An MRI Study Using Voxel-Based Morphometry

The presence of cognitive impairment is a frequent complaint among elderly individuals in the general population. This study aimed to investigate the relationship between aging-related regional gray matter (rGM) volume changes and cognitive performance in healthy elderly adults. Morphometric magnetic resonance imaging (MRI) measures were acquired in a community-based sample of 170 cognitively-preserved subjects (66 to 75 years). This sample was drawn from the "Sao Paulo Ageing and Health" study, an epidemiological study aimed at investigating the prevalence and risk factors for Alzheimer's disease in a low income region of the city of Sao Paulo. All subjects underwent cognitive testing using a cross-culturally battery validated by the Research Group on Dementia 10/66 as well as the SKT (applied on the day of MRI scanning). Blood genotyping was performed to determine the frequency of the three apolipoprotein E allele variants (APOE epsilon 2/epsilon 3/epsilon 4) in the sample. Voxelwise linear correlation analyses between rGM volumes and cognitive test scores were performed using voxel-based morphometry, including chronological age as covariate. There were significant direct correlations between worse overall cognitive performance and rGM reductions in the right orbitofrontal cortex and parahippocampal gyrus, and also between verbal fluency scores and bilateral parahippocampal gyral volume (p < 0.05, familywise-error corrected for multiple comparisons using small volume correction). When analyses were repeated adding the presence of the APOE epsilon 4 allele as confounding covariate or excluding a minority of APOE epsilon 2 carriers, all findings retained significance. These results indicate that rGM volumes are relevant biomarkers of cognitive deficits in healthy aging individuals, most notably involving temporolimbic regions and the orbitofrontal cortex.

Sural nerve involvement in experimental hypertension: morphology and morphometry in male and female normotensive Wistar-Kyoto (WKY) and spontaneously hypertensive rats (SHR)

Background: The sural nerve has been widely investigated in experimental models of neuropathies but information about its involvement in hypertension was not yet explored. The aim of the present study was to compare the morphological and morphometric aspects of different segments of the sural nerve in male and female spontaneously hypertensive (SHR) and normotensive Wistar-Kyoto (WKY) rats. Rats aged 20 weeks (N = 6 in each group) were investigated. After arterial pressure and heart rate recordings in anesthetized animals, right and left sural nerves were removed and prepared for epoxy resin embedding and light microscopy. Morphometric analysis was performed with the aid of computer software, and took into consideration the fascicle area and diameter, as well as myelinated fiber number, density, area and diameter. Results: Significant differences were observed for the myelinated fiber number and density, comparing different genders of WKY and SHR. Also, significant differences for the morphological (thickening of the endoneural blood vessel walls and lumen reduction) and morphometric (myelinated fibers diameter and G ratio) parameters of myelinated fibers were identified. Morphological exam of the myelinated fibers suggested the presence of a neuropathy due to hypertension in both SHR genders. Conclusions: These results indicate that hypertension altered important morphometric parameters related to nerve conduction of sural nerve in hypertensive animals. Moreover the comparison between males and females of WKY and SHR allows the conclusion that the morphological and morphometric parameters of sural nerve are not gender related. The morphometric approach confirmed the presence of neuropathy, mainly associated to the small myelinated fibers. In conclusion, the present study collected evidences that the high blood pressure in SHR is affecting the sural nerve myelinated fibers.

Sperm head morphometry in ejaculates of adult marmosets (Callithrix jacchus): a model for studying sperm subpopulations and among-donor variations

In humans and other mammals, sperm morphology has been considered one of the most important predictive parameters of fertility. The objective was to determine the presence and distribution of sperm head morphometric subpopulations in a nonhuman primate model (Callithrix jacchus), using an objective computer analysis system and principal component analysis (PCA) methods to establish the relationship between the subpopulation distribution observed and among-donor variation. The PCA method revealed a stable number of principal components in all donors studied, that represented more than 85% of the cumulative variance in all cases. After cluster analysis, a variable number (from three to seven) sperm morphometric subpopulations were identified with defined sperm dimensions and shapes. There were differences in the distribution of the sperm morphometric subpopulations (P < 0.001) in all ejaculates among the four donors analyzed. In conclusion, in this study, computerized sperm analysis methods combined with PCA cluster analyses were useful to identify, classify, and characterize various head sperm morphometric subpopulations in nonhuman primates, yielding considerable biological information. In addition, because all individuals were kept in the same conditions, differences in the distribution of these subpopulations were not attributed to external or management factors. Finally, the substantial information derived from subpopulation analyses provided new and relevant biological knowledge which may have a practical use for future studies in human and nonhuman primate ejaculates, including identifying individuals more suitable for assisted reproductive technologies. (c) 2012 Elsevier Inc. All rights reserved.

Longitudinal brain volumetric changes during one year in non-elderly healthy adults: a voxel-based morphometry study

Previous cross-sectional magnetic resonance imaging (MRI) studies of healthy aging in young adults have indicated the presence of significant inverse correlations between age and gray matter volumes, although not homogeneously across all brain regions. However, such cross-sectional studies have important limitations and there is a scarcity of detailed longitudinal MRI studies with repeated measures obtained in the same individuals in order to investigate regional gray matter changes during short periods of time in non-elderly healthy adults. In the present study, 52 healthy young adults aged 18 to 50 years (27 males and 25 females) were followed with repeated MRI acquisitions over approximately 15 months. Gray matter volumes were compared between the two times using voxel-based morphometry, with the prediction that volume changes would be detectable in the frontal lobe, temporal neocortex and hippocampus. Voxel-wise analyses showed significant (P < 0.05, family-wise error corrected) relative volume reductions of gray matter in two small foci located in the right orbitofrontal cortex and left hippocampus. Separate comparisons for males and females showed bilateral gray matter relative reductions in the orbitofrontal cortex over time only in males. We conclude that, in non-elderly healthy adults, subtle gray matter volume alterations are detectable after short periods of time. This underscores the dynamic nature of gray matter changes in the brain during adult life, with regional volume reductions being detectable in brain regions that are relevant to cognitive and emotional processes.