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.

Covariance structure in the skull of Catarrhini: a case of pattern stasis and magnitude evolution

The study of the genetic variance/covariance matrix (G-matrix) is a recent and fruitful approach in evolutionary biology, providing a window of investigating for the evolution of complex characters. Although G-matrix studies were originally conducted for microevolutionary timescales, they could be extrapolated to macroevolution as long as the G-matrix remains relatively constant, or proportional, along the period of interest. A promising approach to investigating the constancy of G-matrices is to compare their phenotypic counterparts (P-matrices) in a large group of related species; if significant similarity is found among several taxa, it is very likely that the underlying G-matrices are also equivalent. Here we study the similarity of covariance and correlation structure in a broad sample of Old World monkeys and apes (Catarrhini). We made phylogenetically structured comparisons of correlation and covariance matrices derived from 39 skull traits, ranging from between species to the superfamily level. We also compared the overall magnitude of integration between skull traits (r(2)) for all Catarrhim genera. Our results show that P-matrices were not strictly constant among catarrhines, but the amount of divergence observed among taxa was generally low. There was significant and positive correlation between the amount of divergence in correlation and covariance patterns among the 30 genera and their phylogenetic distances derived from a recently proposed phylogenetic hypothesis. Our data demonstrate that the P-matrices remained relatively similar along the evolutionary history of catarrhines, and comparisons with the G-matrix available for a New World monkey genus (Saguinus) suggests that the same holds for all anthropoids. The magnitude of integration, in contrast, varied considerably among genera, indicating that evolution of the magnitude, rather than the pattern of inter-trait correlations, might have played an important role in the diversification of the catarrhine skull. (C) 2009 Elsevier Ltd. All rights reserved.

PARTIAL STABILITY FOR A CLASS OF NONLINEAR SYSTEMS

This paper studies a nonlinear, discrete-time matrix system arising in the stability analysis of Kalman filters. These systems present an internal coupling between the state components that gives rise to complex dynamic behavior. The problem of partial stability, which requires that a specific component of the state of the system converge exponentially, is studied and solved. The convergent state component is strongly linked with the behavior of Kalman filters, since it can be used to provide bounds for the error covariance matrix under uncertainties in the noise measurements. We exploit the special features of the system-mainly the connections with linear systems-to obtain an algebraic test for partial stability. Finally, motivated by applications in which polynomial divergence of the estimates is acceptable, we study and solve a partial semistability problem.

Multifractality in the random parameter model for multivariate time series

The Random Parameter model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we explore the scaling properties of the model, as observed in the multifractal structure of the simulated time series. We use the Wavelet Transform Modulus Maxima technique to obtain the multifractal spectrum dependence with the parameters of the model. The model shows a scaling structure compatible with the stylized facts for a reasonable choice of the parameter values. (C) 2009 Elsevier B.V. All rights reserved.

Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline. (c) 2011 Elsevier Ltd. All rights reserved.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

The Evolution of Modularity in the Mammalian Skull I: Morphological Integration Patterns and Magnitudes

Morphological integration refers to the modular structuring of inter-trait relationships in an organism, which could bias the direction and rate of morphological change, either constraining or facilitating evolution along certain dimensions of the morphospace. Therefore, the description of patterns and magnitudes of morphological integration and the analysis of their evolutionary consequences are central to understand the evolution of complex traits. Here we analyze morphological integration in the skull of several mammalian orders, addressing the following questions: are there common patterns of inter-trait relationships? Are these patterns compatible with hypotheses based on shared development and function? Do morphological integration patterns and magnitudes vary in the same way across groups? We digitized more than 3,500 specimens spanning 15 mammalian orders, estimated the correspondent pooled within-group correlation and variance/covariance matrices for 35 skull traits and compared those matrices among the orders. We also compared observed patterns of integration to theoretical expectations based on common development and function. Our results point to a largely shared pattern of inter-trait correlations, implying that mammalian skull diversity has been produced upon a common covariance structure that remained similar for at least 65 million years. Comparisons with a rodent genetic variance/covariance matrix suggest that this broad similarity extends also to the genetic factors underlying phenotypic variation. In contrast to the relative constancy of inter-trait correlation/covariance patterns, magnitudes varied markedly across groups. Several morphological modules hypothesized from shared development and function were detected in the mammalian taxa studied. Our data provide evidence that mammalian skull evolution can be viewed as a history of inter-module parcellation, with the modules themselves being more clearly marked in those lineages with lower overall magnitude of integration. The implication of these findings is that the main evolutionary trend in the mammalian skull was one of decreasing the constraints to evolution by promoting a more modular architecture.

Improved testing inference in mixed linear models

Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Often, the number of observations is small, and it is thus important to use inference strategies that incorporate small sample corrections. In this paper, we develop modified versions of the likelihood ratio test for fixed effects inference in mixed linear models. In particular, we derive a Bartlett correction to such a test, and also to a test obtained from a modified profile likelihood function. Our results generalize those in [Zucker, D.M., Lieberman, O., Manor, O., 2000. Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood. Journal of the Royal Statistical Society B, 62,827-838] by allowing the parameter of interest to be vector-valued. Additionally, our Bartlett corrections allow for random effects nonlinear covariance matrix structure. We report simulation results which show that the proposed tests display superior finite sample behavior relative to the standard likelihood ratio test. An application is also presented and discussed. (C) 2008 Elsevier B.V. All rights reserved.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

Evaluation of in vitro human gingival fibroblast seeding on acellular dermal matrix

The acellular dermal matrix (ADM) was introduced in periodontology as a substitute for the autogenous grafts, which became restricted because of the limited source of donor's tissue. The aim of this study was to investigate, in vitro, the distribution, proliferation and viability of human gingival fibroblasts seeded onto ADM. ADM was seeded with human gingival fibroblasts for up to 21 days. The following parameters were evaluated: cell distribution, proliferation and viability. Results revealed that, at day 7, fibroblasts were adherent and spread on ADM surface, and were unevenly distributed, forming a discontinuous single cell layer; at day 14, a confluent fibroblastic monolayer lining ADM surface was noticed. At day 21, the cell monolayer exhibited a reduction in cell density. At 7 days, about to 90% of adherent cells on ADM surface were cycling while at 14 and 21 days this proportion was significantly reduced. A high proportion of viable cell was detected on AMD surface both on 14 and 21 days. The results suggest that fibroblast seeding onto ADM for 14 days can allow good conditions for cell adhesion and spreading on the matrix; however, migration inside the matrix was limited.

Metronidazole release using natural rubber latex as matrix

Natural Rubber Latex (NRL) can be used successfully in controlled release drug delivery due to their excellent matrix forming properties. Recently, NRL has shown to stimulate angiogenesis, cellular adhesion and the formation of extracellular matrix, promoting the replacement and regeneration of tissue. A dermatological delivery system comprising a topically acceptable, inert support impregnated with a metronidazole (MET) solution was developed. MET 2-(2- methyl- 5-nitro- 1H- imidazol- 1-yl) ethanol, has been widely used for the treatment of protozoa and anaerobic bacterial infections. MET is a nitroimidazole anti-infective medication used mainly in the treatment of infections caused by susceptible organisms, particularly anaerobic bacteria and protozoa. In a previous study, we have tested NRL as an occlusive membrane for GBR with promising results. One possible way to decrease the inflammatory process, it was incorporated the MET in NRL. MET was incorporated into the NRL, by mixing it in solution for in vitro protein delivery experiments. The solutions of latex and MET were polymerized at different temperatures, from -100 to 40 °C, in order to control the membrane morphology. SEM microscopy analysis showed that the number, size and distribution of pores in NRL membranes varied depending on polymerization temperature, as well as its overall morphology. Results demonstrated that the best drug-delivery system was the membrane polymerized at -100 °C, which does release 77,1% of its MET content for up 310 hours.

Modulation of extracellular matrix by nutritional hepatotrophic factors in thioacetamide-induced liver cirrhosis in the rat

Nutritional substances associated to some hormones enhance liver regeneration when injected intraperitoneally, being denominated hepatotrophic factors (HF). Here we verified if a solution of HF (glucose, vitamins, salts, amino acids, glucagon, insulin, and triiodothyronine) can revert liver cirrhosis and how some extracellular matrices are affected. Cirrhosis was induced for 14 weeks in 45 female Wistar rats (200 mg) by intraperitoneal injections of thioacetamide (200 mg/kg). Twenty-five rats received intraperitoneal HF twice a day for 10 days (40 mL·kg-1·day-1) and 20 rats received physiological saline. Fifteen rats were used as control. The HF applied to cirrhotic rats significantly: a) reduced the relative mRNA expression of the genes: Col-α1 (-53%), TIMP-1 (-31.7%), TGF-β1 (-57.7%), and MMP-2 (-41.6%), whereas Plau mRNA remained unchanged; b) reduced GGT (-43.1%), ALT (-17.6%), and AST (-12.2%) serum levels; c) increased liver weight (11.3%), and reduced liver collagen (-37.1%), regenerative nodules size (-22.1%), and fibrous septum thickness. Progranulin protein (immunohistochemistry) and mRNA (in situ hybridization) were found in fibrous septa and areas of bile duct proliferation in cirrhotic livers. Concluding, HF improved the histology and serum biochemistry of liver cirrhosis, with an important reduction of interstitial collagen and increased extracelullar matrix degradation by reducing profibrotic gene expression.

Expression of matrix metalloproteinase 2 (MMP-2) and tissue inhibitor of metalloproteinase 2 (TIMP-2) in medullary thyroid carcinoma: Prognostic implications

Background: Metalloproteinase 2 (MMP-2) and tissue inhibitor of metalloproteinase 2 (TIMP-2) participate in the degeneration of the extracellular matrix and are associated with carcinogenesis. MMP-2 is one of the main metalloproteinases active in neoplasia and is a marker of the malignant phenotype. Since the biological behavior of medullary thyroid carcinoma (MTC) varies widely, the present study was undertaken to determine if there is a correlation between the clinical evolution of MTC and the immunohistochemically detected expression of these enzymes in thyroid surgical specimens containing MTC. If so, their expression would be a novel indicator of the prognosis of MTC. Methods: Thirty-seven patients with MTC who had undergone thyroid surgery were followed for an average of 73 months. Immunohistochemical staining for metalloproteinase-related enzymes was performed in surgical paraffin blocks. The clinical status of the patients after surgery and at the end of the study period was characterized to determine correlations between these and the immunohistochemical markers. A value of p < 0.05 was considered statistically significant. Results: At the end of the study period, 15 patients (40.5%) were alive and without evidence of MTC, 17 (45.9%) had persistent MTC, and 5 (13.5%) had a relapse of their neoplasia. Four patients (10.8%) died during the course of the study. There was a significant correlation (p = 0.0005) between the immunohistochemical staining for MMP-2 and the clinical condition of the patients at the end of the study period, and a correlation between the state of apparent cure compared to persistence of MTC after thyroid surgery (p = 0.0207). No significant correlations were observed between either TIMP-2 expression or immune marking of metastatic lymph nodes and the clinical variables studied. Conclusion: Immunohistochemical expression of MMP-2 in thyroid surgical specimens from patients with MTC is a novel indicator of the prognosis of this cancer.

Lsa21, a novel leptospiral protein binding adhesive matrix molecules and present during human infection

Background: It has been well documented over past decades that interaction of pathogens with the extracellular matrix (ECM) plays a primary role in host cell attachment and invasion. Adherence to host tissues is mediated by surface-exposed proteins expressed by the microorganisms during infection. The mechanisms by which pathogenic leptospires invade and colonize the host remain poorly understood since few virulence factors contributing to the pathogenesis of the disease have been identified. Whole-genome sequencing analysis of L. interrogans allowed identification of a repertoire of putative leptospiral surface proteins. Results: Here, we report the identification and characterization of a new leptospiral protein that exhibits extracellular matrix-binding properties, called as Lsa21 (leptospiral surface adhesin, 21 kDa). Compatible with its role in adhesion, the protein was shown to be surface-exposed by indirect immunofluorescence. Attachment of Lsa21 to laminin, collagen IV, and plasma fibronectin was specific and dose dependent. Laminin oxidation by sodium metaperiodate reduced the protein-laminin interaction in a concentration-dependent manner, indicating that laminin sugar moieties are crucial for this interaction. The gene coding for Lsa21 is present in pathogenic strains belonging to the L. interrogans species but was not found in the saprophytic L. biflexa serovar Patoc strain Patoc 1. Loss of gene expression occurs upon culture attenuation of pathogenic strains. Environmental factors such as osmolarity and temperature affect Lsa21 expression at the transcriptional level. Moreover, anti-Lsa21 serum labeled liver and kidney tissues of human fatal cases of leptospirosis. Conclusion: Our data suggest a role of Lsa21 in the pathogenesis of leptospirosis.

Interethnic Differences in the Distribution of Matrix Metalloproteinases Genetic Polymorphisms Are Consistent with Interethnic Differences in Disease Prevalence

Interethnic differences exist in disease prevalence, especially with regard to cancer and cardiovascular diseases, which involve altered expression or activity of matrix metalloproteinases (MMPs). The hypothesis being tested in this study is that interethnic differences exist between blacks and whites with regard to the distribution of genetic variants of MMP polymorphisms and haplotypes. We examined the distribution of polymorphisms of MMP-2 and MMP-9 genes in 177 black and 140 white subjects. We studied the following polymorphisms: the C(-1306)T in the promoter of the MMP-2 gene, the C(-1562)T and a microsatellite -90(CA)(14-24) in the promoter, and the Q279R in exon 6 of the MMP-9 gene. We have also compared our results with those from Hapmap or Seattle SNPs Projects and estimated the haplotype frequency in these two ethnic groups. The ""C'' allele for the C(-1306)T polymorphism was more common in blacks (91.5%) than in whites (80.4%; p<0.0001). The ""T'' allele for the C(-1562)T polymorphism was more common in blacks (15.0%) than in whites (8.9%; p=0.0279), as well as the alleles with >21 repeats for the -90(CA)(14-24) were more common in blacks than in whites (61.9% in blacks and 49.3% in whites; p=0.0017). We found no interethnic differences for the Q279R polymorphism. Moreover, two haplotypes that combine ""detrimental'' alleles were found at higher frequencies in blacks than in whites (31% vs. 16.4%, respectively; p<0.05). The interethnic differences being reported here replicate those previously found with smaller number of subjects in the Hapmap or Seattle SNPs data and may help explain the higher prevalence of cancer and cardiovascular diseases in blacks compared with whites. Our findings suggest a proportional significance of these polymorphisms in each ethnic group.