A Single Statistic for Monitoring the Covariance Matrix of Bivariate Processes

In this article, we present a new control chart for monitoring the covariance matrix in a bivariate process. In this method, n observations of the two variables were considered as if they came from a single variable (as a sample of 2n observations), and a sample variance was calculated. This statistic was used to build a new control chart specifically as a VMIX chart. The performance of the new control chart was compared with its main competitors: the generalized sampled variance chart, the likelihood ratio test, Nagao's test, probability integral transformation (v(t)), and the recently proposed VMAX chart. Among these statistics, only the VMAX chart was competitive with the VMIX chart. For shifts in both variances, the VMIX chart outperformed VMAX; however, VMAX showed better performance for large shifts (higher than 10%) in one variance.

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.

MODULARITY, NOISE, AND NATURAL SELECTION

Most biological systems are formed by component parts that are to some degree interrelated. Groups of parts that are more associated among themselves and are relatively autonomous from others are called modules. One of the consequences of modularity is that biological systems usually present an unequal distribution of the genetic variation among traits. Estimating the covariance matrix that describes these systems is a difficult problem due to a number of factors such as poor sample sizes and measurement errors. We show that this problem will be exacerbated whenever matrix inversion is required, as in directional selection reconstruction analysis. We explore the consequences of varying degrees of modularity and signal-to-noise ratio on selection reconstruction. We then present and test the efficiency of available methods for controlling noise in matrix estimates. In our simulations, controlling matrices for noise vastly improves the reconstruction of selection gradients. We also perform an analysis of selection gradients reconstruction over a New World Monkeys skull database to illustrate the impact of noise on such analyses. Noise-controlled estimates render far more plausible interpretations that are in full agreement with previous results.

Short communication: Principal components and factor analytic models for test-day milk yield in Brazilian Holstein cattle

A total of 46,089 individual monthly test-day (TD) milk yields (10 test-days), from 7,331 complete first lactations of Holstein cattle were analyzed. A standard multivariate analysis (MV), reduced rank analyses fitting the first 2, 3, and 4 genetic principal components (PC2, PC3, PC4), and analyses that fitted a factor analytic structure considering 2, 3, and 4 factors (FAS2, FAS3, FAS4), were carried out. The models included the random animal genetic effect and fixed effects of the contemporary groups (herd-year-month of test-day), age of cow (linear and quadratic effects), and days in milk (linear effect). The residual covariance matrix was assumed to have full rank. Moreover, 2 random regression models were applied. Variance components were estimated by restricted maximum likelihood method. The heritability estimates ranged from 0.11 to 0.24. The genetic correlation estimates between TD obtained with the PC2 model were higher than those obtained with the MV model, especially on adjacent test-days at the end of lactation close to unity. The results indicate that for the data considered in this study, only 2 principal components are required to summarize the bulk of genetic variation among the 10 traits.

Genetic Variants in Matrix Metalloproteinase-9 Gene Modify Metalloproteinase-9 Levels in Black Subjects

Altered matrix metalloproteinases (MMPs) levels are involved in cardiovascular diseases and increased MMP-9 levels enhance the cardiovascular risk in apparently healthy subjects. We investigated the effects of MMP-9 gene polymorphisms and haplotypes on the circulating MMP-9 levels in healthy black subjects and the effects of an MMP-2 polymorphism on the plasma MMP-2 concentrations. We studied 190 healthy subjects, nonsmokers, self-reported as blacks (18-63 years). Genotypes for the MMP-2 C-1306T polymorphism and the MMP-9 C-1562T, 90(CA)(14-24) and Q279R polymorphisms (rs243865, rs3918242, rs2234681, and rs17576, respectively) were determined by TaqMan (R) Allele Discrimination assay and real-time polymerase chain reaction or restriction fragment length polymorphism. Alleles for the 90(CA)(14-24) polymorphism were grouped as low (L) when there were < 21 and high (H) when there were >= 21 CA repeats. The plasma levels of MMP-2 and MMP-9 were determined by gelatin zymography. The software PHASE 2.1 was used to estimate the haplotypes frequencies. Although we found no effects of the MMP-9 C-1562T or the Q279R polymorphisms on MMP-9 levels, higher MMP-9 levels were associated with the HH genotype for the -90(CA)(14-24) polymorphism compared with the HL or LL genotypes. Lower MMP-9 levels were found in carriers of the CRL haplotype (combining the C, R, and L alleles for the MMP-9 polymorphisms) compared with the CRH haplotype. Consistent with this finding, the CRL haplotype was more commonly found in subjects with low MMP-9 levels. The MMP-2 C-1306T polymorphism had no effects on the plasma MMP-2 levels. Our results show that MMP-9 genetic variations modify MMP-9 levels in black subjects and may offer biochemical evidence implicating MMP-9 in the pathogenesis of cardiovascular diseases in blacks.

Comprehensive Evaluation of the Effects of Enalapril on Matrix Metalloproteinases Levels in Hypertension

Angiotensin-converting enzyme inhibitors (ACEi) may downregulate matrix metalloproteinases (MMPs). We examined whether enalapril affects MMP-2, MMP-8, and MMP-9 levels and activity, and their endogenous inhibitors (tissue inhibitors of MMPs, TIMP-1 and TIMP-2) levels in hypertensive patients. Moreover, we assessed the effects of enalaprilat on MMP-9 and TIMP-1 secretion by human endothelial cells (HUVECs). Thirty-eight hypertensive patients received enalapril for 8 weeks and were compared with thirty-eight normotensive controls. Blood samples were collected at baseline and after treatment. Plasma ACE activity was determined by a fluorimetric assay. Plasma MMP-2, MMP-8, MMP-9, TIMP-1, and TIMP-2 were measured by ELISA and gelatin zymography. A fluorogenic peptide cleavage assay was used to measure MMP activity. HUVECs cells were stimulated by phorbol-12-myristate-13-acetate (PMA) and the effects of enalaprilat (10(-10) to 10(-6) M) on MMP-9 and TIMP-1 levels were determined. Enalapril decreased blood pressure and ACE activity in hypertensive patients (P < 0.05), but had no effects on plasma MMP-2, MMP-8, MMP-9, TIMP-1, and TIMP-2 levels, or MMP activity. Enalaprilat had no effects on PMA-induced increases in MMP-9 and TIMP-1 secretion by HUVECs or on MMP activity. We show consistent evidence, both in vivo and in vitro, that enalapril does not affect MMPs and TIMPs levels in hypertensive patients.

The full Fisher matrix for galaxy surveys

Starting from the Fisher matrix for counts in cells, we derive the full Fisher matrix for surveys of multiple tracers of large-scale structure. The key step is the classical approximation, which allows us to write the inverse of the covariance of the galaxy counts in terms of the naive matrix inverse of the covariance in a mixed position-space and Fourier-space basis. We then compute the Fisher matrix for the power spectrum in bins of the 3D wavenumber , the Fisher matrix for functions of position (or redshift z) such as the linear bias of the tracers and/or the growth function and the cross-terms of the Fisher matrix that expresses the correlations between estimations of the power spectrum and estimations of the bias. When the bias and growth function are fully specified, and the Fourier-space bins are large enough that the covariance between them can be neglected, the Fisher matrix for the power spectrum reduces to the widely used result that was first derived by Feldman, Kaiser & Peacock. Assuming isotropy, a fully analytical calculation of the Fisher matrix in the classical approximation can be performed in the case of a constant-density, volume-limited survey.