INFERENCE FOR EIGENVALUES AND EIGENVECTORS OF GAUSSIAN SYMMETRIC MATRICES

This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3 x 3 and 2 x 2 symmetric positive definite matrices. The parameter sets involved in the inference problems for eigenvalues and eigenvectors are subsets of Euclidean space that are either affine subspaces, embedded submanifolds that are invariant under orthogonal transformations or polyhedral convex cones. We show that for a class of sets that includes the ones considered in this paper, the MLEs of the mean parameter do not depend on the covariance parameters if and only if the covariance structure is orthogonally invariant. Closed-form expressions for the MLEs and the associated LLRs are derived for this covariance structure.

Correlation between MMPs and their inhibitors in breast cancer tumor tissue specimens and in cell lines with different metastatic potential

Background: The metastatic disease rather than the primary tumor itself is responsible for death in most solid tumors, including breast cancer. The role of matrix metalloproteinases ( MMPs), tissue inhibitors of MMPs (TIMPs) and Reversion-inducing cysteine-rich protein with Kazal motifs ( RECK) in the metastatic process has previously been established. However, in all published studies only a limited number of MMPs/MMP inhibitors was analyzed in a limited number of cell lines. Here, we propose a more comprehensive approach by analyzing the expression levels of several MMPs (MMP-2, MMP-9 and MMP-14) and MMP inhibitors (TIMP-1, TIMP-2 and RECK) in different models ( five human breast cancer cell lines, 72 primary breast tumors and 30 adjacent normal tissues). Methods: We analyzed the expression levels of MMP-2, MMP-9 and MMP-14 and their inhibitors (TIMP-1, TIMP-2 and RECK) by quantitative RT-PCR (qRT-PCR) in five human breast cancer cell lines presenting increased invasiveness and metastatic potential, 72 primary breast tumors and 30 adjacent normal tissues. Moreover, the role of cell-extracellular matrix elements interactions in the regulation of expression and activity of MMPs and their inhibitors was analyzed by culturing these cell lines on plastic or on artificial ECM (Matrigel). Results: The results demonstrated that MMPs mRNA expression levels displayed a positive and statistically significant correlation with the transcriptional expression levels of their inhibitors both in the cell line models and in the tumor tissue samples. Furthermore, the expression of all MMP inhibitors was modulated by cell-Matrigel contact only in highly invasive and metastatic cell lines. The enzyme/inhibitor balance at the transcriptional level significantly favors the enzyme which is more evident in tumor than in adjacent non-tumor tissue samples. Conclusion: Our results suggest that the expression of MMPs and their inhibitors, at least at the transcriptional level, might be regulated by common factors and signaling pathways. Therefore, the multi-factorial analysis of these molecules could provide new and independent prognostic information contributing to the determination of more adequate therapy strategies for each patient.`

Polymer matrix sensitizing effect on photoluminescence properties of Eu(3+)-beta-diketonate complex doped into poly-beta-hydroxybutyrate (PHB) in film form

In this work is reported the sensitization effect by polymer matrices on the photoluminescence properties of diaquatris(thenoyltrifluoroacetonate)europium(III), [Eu(tta)(3)(H(2)O)(2)], doped into poly-beta-hydroxybutyrate (PHB) with doping percentage at 1, 3, 5, 7 and 10% (mass) in film form. TGA results indicated that the Eu(3+) complex precursor was immobilized in the polymer matrix by the interaction between the Eu(3+) complex and the oxygen atoms of the PHB polymer when the rare earth complex was incorporated in the polymeric host. The thermal behaviour of these luminescent systems is similar to that of the undoped polymer, however, the T(onset) temperature of decomposition decreases with increase of the complex doping concentration. The emission spectra of the Eu(3+) complex doped PHB films recorded at 298 K exhibited the five characteristic bands arising from the (5)D(0) -> (7)F(J) intraconfigurational transitions (J = 0-4). The fact that the quantum efficiencies eta of the doped film increased significantly revealed that the polymer matrix acts as an efficient co-sensitizer for Eu(3+) luminescent centres and therefore enhances the quantum efficiency of the emitter (5)D(0) level. The luminescence intensity decreases, however, with increasing precursor concentration in the doped polymer to greater than 5% where a saturation effect is observed at this specific doping percentage, indicating that changes in the polymeric matrix improve the absorption property of the film, consequently quenching the luminescent effect.

Response surface methodology as an approach to determine optimal activities of lipase entrapped in sol-gel matrix using different vegetable oils

The conditions for maximization of the enzymatic activity of lipase entrapped in sol-gel matrix were determined for different vegetable oils using an experimental design. The effects of pH, temperature, and biocatalyst loading on lipase activity were verified using a central composite experimental design leading to a set of 13 assays and the surface response analysis. For canola oil and entrapped lipase, statistical analyses showed significant effects for pH and temperature and also the interactions between pH and temperature and temperature and biocatalyst loading. For the olive oil and entrapped lipase, it was verified that the pH was the only variable statistically significant. This study demonstrated that response surface analysis is a methodology appropriate for the maximization of the percentage of hydrolysis, as a function of pH, temperature, and lipase loading.

Covalent attachment of Candida rugosa lipase on chemically modified hybrid matrix of polysiloxane-polyvinyl alcohol with different activating compounds

Candida rugosa lipase was immobilized by covalent binding on hybrid matrix of polysiloxane-polyvinyl alcohol chemically modified with different activating agents as glutaraldehyde, sodium metaperiodate and carbonyldiimidazole. The experimental results suggested that functional activating agents render different interactions between enzyme and support, producing consequently alterations in the optimal reaction conditions. Properties of the immobilized systems were assessed and their performance on hydrolytic and synthetic reactions were evaluated and compared with the free enzyme. In hydrolytic reactions using p-nitrophenyl palmitate as substrate all immobilized systems showed higher thermal stability and optima pH and temperature values in relation to the free lipase. Among the activating compounds, carbonyldiimidazole resulted in a total recovery of activity on the support and the highest thermal stability. For the butyl butyrate synthesis, the best performance (molar conversion of 95% and volumetric productivity of 2.33 g L-1 h(-1)) was attained with the lipase immobilized on POS-PVA activated with sodium metaperiodate. The properties of the support and immobilized derivatives were also evaluated by scanning electron microscopy (SEM), energy dispersive X-ray spectroscopies and chemical composition (FTIR). (c) 2007 Elsevier B.V. All rights reserved.

Redundancy and Observability Analysis of Conventional and PMU Measurements

This letter shows that the matrix can be used for redundancy and observability analysis of metering systems composed of PMU measurements and conventional measurements (power and voltage magnitude measurements). The matrix is obtained via triangular factorization of the Jacobian matrix. Observability analysis and restoration is carried out during the triangular factorization of the Jacobian matrix, and the redundancy analysis is made exploring the matrix structure. As a consequence, the matrix can be used for metering system planning considering conventional and PMU measurements. These features of the matrix will be outlined and illustrated by numerical examples.

On the use of Gram matrix in observability analysis

This letter presents some notes on the use of the Gram matrix in observability analysis. This matrix is constructed considering the rows of the measurement Jacobian matrix as vectors, and it can be employed in observability analysis and restoration methods. The determination of nonredundant pseudo-measurements (normally injections pseudo-measurements) for merging observable islands into an observable (single) system is carried out analyzing the pivots of the Gram matrix. The Gram matrix can also be used to verify local redundancy, which is important in measurement system planning. Some numerical examples` are used to illustrate these features. Others features of the Gram matrix are under study.

Dynamic Imaging in Electrical Impedance Tomography of the Human Chest With Online Transition Matrix Identification

One of the electrical impedance tomography objectives is to estimate the electrical resistivity distribution in a domain based only on electrical potential measurements at its boundary generated by an imposed electrical current distribution into the boundary. One of the methods used in dynamic estimation is the Kalman filter. In biomedical applications, the random walk model is frequently used as evolution model and, under this conditions, poor tracking ability of the extended Kalman filter (EKF) is achieved. An analytically developed evolution model is not feasible at this moment. The paper investigates the identification of the evolution model in parallel to the EKF and updating the evolution model with certain periodicity. The evolution model transition matrix is identified using the history of the estimated resistivity distribution obtained by a sensitivity matrix based algorithm and a Newton-Raphson algorithm. To numerically identify the linear evolution model, the Ibrahim time-domain method is used. The investigation is performed by numerical simulations of a domain with time-varying resistivity and by experimental data collected from the boundary of a human chest during normal breathing. The obtained dynamic resistivity values lie within the expected values for the tissues of a human chest. The EKF results suggest that the tracking ability is significantly improved with this approach.

Matrix Method for Acoustic Levitation Simulation

A matrix method is presented for simulating acoustic levitators. A typical acoustic levitator consists of an ultrasonic transducer and a reflector. The matrix method is used to determine the potential for acoustic radiation force that acts on a small sphere in the standing wave field produced by the levitator. The method is based on the Rayleigh integral and it takes into account the multiple reflections that occur between the transducer and the reflector. The potential for acoustic radiation force obtained by the matrix method is validated by comparing the matrix method results with those obtained by the finite element method when using an axisymmetric model of a single-axis acoustic levitator. After validation, the method is applied in the simulation of a noncontact manipulation system consisting of two 37.9-kHz Langevin-type transducers and a plane reflector. The manipulation system allows control of the horizontal position of a small levitated sphere from -6 mm to 6 mm, which is done by changing the phase difference between the two transducers. The horizontal position of the sphere predicted by the matrix method agrees with the horizontal positions measured experimentally with a charge-coupled device camera. The main advantage of the matrix method is that it allows simulation of non-symmetric acoustic levitators without requiring much computational effort.

An Array Recursive Least-Squares Algorithm With Generic Nonfading Regularization Matrix

We present a novel array RLS algorithm with forgetting factor that circumvents the problem of fading regularization, inherent to the standard exponentially-weighted RLS, by allowing for time-varying regularization matrices with generic structure. Simulations in finite precision show the algorithm`s superiority as compared to alternative algorithms in the context of adaptive beamforming.

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 Kumaraswamy Weibull distribution with application to failure data

For the first time, we introduce and study some mathematical properties of the Kumaraswamy Weibull distribution that is a quite flexible model in analyzing positive data. It contains as special sub-models the exponentiated Weibull, exponentiated Rayleigh, exponentiated exponential, Weibull and also the new Kumaraswamy exponential distribution. We provide explicit expressions for the moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and Renyi entropy. The moments of the order statistics are calculated. We also discuss the estimation of the parameters by maximum likelihood. We obtain the expected information matrix. We provide applications involving two real data sets on failure times. Finally, some multivariate generalizations of the Kumaraswamy Weibull distribution are discussed. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

A positive growth response to NaCl applications in Eucalyptus plantations established on K-deficient soils

Contrasting responses of Eucalyptus trees to K fertilizer applications have been reported on soils with low K contents. A complete randomized block experiment was set up in Brazil to test the hypothesis that large atmospheric deposits of NaCl in coastal regions might lead to a partial substitution of K by Na in Eucalyptus physiology and enhance tree growth. Treatments with application of 1.5, 3.0, 4.5 kmol K ha(-1) (K(1.5), K(3.0), 1(4.5, respectively) as KCl, 3.0 kmol K ha(-1) applied as K(2)SO(4), 3.0 kmol Na ha(-1) (Na(3.0)) as NaCl commercialized for cattle feeding, and a mixture of 1.5 kmol K + 1.5 kmol Na ha(-1) (K(1.5) + Na(1.5)) were compared to a control treatment (C) with no K and Na applications. All the plots were fertilized with large amounts of the other nutrients. A positive effect of NaCl applications on the growth of E. grandis trees was observed. NaCl and KCl additions in treatments Na(3.0) and K(3.0) increased above-ground biomass by 56% and 130% three years after planting, respectively, in comparison with the C treatment. By contrast, accumulated litterfall up to age 3 years was not significantly modified. NaCl applications in the Na(3.0) treatment significantly increased Na accumulation in above-ground tree components but did not modify K accumulation, whatever the sampling age. A partial substitution of K by Na in tree physiology, as observed for various agricultural crops, might explain this behaviour. Our results suggest the possibility of applying inexpensive K fertilizers, which are less purified in Na, and explain why high yields are achieved without K fertilizer applications in areas with large dry depositions of marine aerosols. Further investigations are necessary to identify the processes involving Na in Eucalyptus tree physiology. (C) 2009 Elsevier B.V. All rights reserved.

Newcastle disease virus in penguins from King George Island on the Antarctic region

Here we report the isolation of Newcastle disease virus (NDV) from cloacal swabs obtained from penguins in the South Atlantic Antarctic region (62 degrees 08S, 58 degrees 25W). Samples of 100 penguins from King George Island were tested by real-time PCR, of which 2 (2%) were positive for NDV. The positive samples were isolated in embryonated chicken eggs and their matrix and fusion proteins genes were partially sequenced. This was complemented by the serological study performed on the blood of the same specimens, which resulted in a 33.3% rate of positivity. (C) 2010 Elsevier B.V. All rights reserved.