A note on the eigenvalues of a special class of matrices

In the analysis of stability of a variant of the Crank-Nicolson (C-N) method for the heat equation on a staggered grid a class of non-symmetric matrices appear that have an interesting property: their eigenvalues are all real and lie within the unit circle. In this note we shall show how this class of matrices is derived from the C-N method and prove that their eigenvalues are inside [-1, 1] for all values of m (the order of the matrix) and all values of a positive parameter a, the stability parameter sigma. As the order of the matrix is general, and the parameter sigma lies on the positive real line this class of matrices turns out to be quite general and could be of interest as a test set for eigenvalue solvers, especially as examples of very large matrices. (C) 2010 Elsevier B.V. All rights reserved.

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.

HOMEOMORPHISMS OF THE ANNULUS WITH A TRANSITIVE LIFT II

Let f be a homeomorphism of the closed annulus A that preserves the orientation, the boundary components and that has a lift (f) over tilde to the in finite strip (A) over tilde which is transitive. We show that, if the rotation number of (f) over tilde restricted to both boundary components of A is strictly positive, then there exists a closed nonempty connected set Gamma subset of (A) over tilde such that Gamma subset of] - infinity,0] x [0,1], Gamma is unbounded, the projection of to Gamma A is dense, Gamma - (1, 0) subset of Gamma and (f) over tilde(Gamma) subset of Gamma. Also, if p(1) is the projection on the first coordinate of (A) over tilde, then there exists d > 0 such that, for any (z) over tilde is an element of Gamma, lim sup (n ->infinity) p(1)((f) over tilde (n) ((Z) over tilde)) - p(1) ((Z) over tilde)/n < -d.

Homeomorphisms of the annulus with a transitive lift

Let f be a homeomorphism of the closed annulus A that preserves the orientation, the boundary components and that has a lift (f) over tilde to the infinite strip (A) over tilde which is transitive. We show that, if the rotation numbers of both boundary components of A are strictly positive, then there exists a closed nonempty unbounded set B(-) subset of (A) over tilde such that B(-) is bounded to the right, the projection of B to A is dense, B - (1, 0) subset of B and (f) over tilde (B) subset of B. Moreover, if p(1) is the projection on the first coordinate of (A) over tilde, then there exists d > 0 such that, for any (z) over tilde is an element of B(-), lim sup (n ->infinity) p1((f) over tilde (n)((z) over tilde)) - p(1) ((z) over tilde)/n < - d. In particular, using a result of Franks, we show that the rotation set of any homeomorphism of the annulus that preserves orientation, boundary components, which has a transitive lift without fixed points in the boundary is an interval with 0 in its interior.

Incorporation of Real-Time PCR into Routine Public Health Surveillance of Culture Negative Bacterial Meningitis in Sao Paulo, Brazil

Real-time (RT)-PCR increases diagnostic yield for bacterial meningitis and is ideal for incorporation into routine surveillance in a developing country. We validated a multiplex RT-PCR assay for Streptococcus pneumoniae, Neisseria meningitidis, and Haemophilus influenzae in Brazil. Risk factors for being culture-negative, RT-PCR positive were determined. The sensitivity of RT-PCR in cerebrospinal fluid (CSF) was 100% (95% confidence limits, 96.0%-100%) for N. meningitidis, 97.8% (85.5%-99.9%) for S. pneumoniae, and 66.7% (9.4%-99.2%) for H. influenzae. Specificity ranged from 98.9% to 100%. Addition of RT-PCR to routine microbiologic methods increased the yield for detection of S. pneumoniae, N. meningitidis, and H. influenzae cases by 52%, 85%, and 20%, respectively. The main risk factor for being culture negative and RT-PCR positive was presence of antibiotic in CSF (odds ratio 12.2, 95% CI 5.9-25.0). RT-PCR using CSF was highly sensitive and specific and substantially added to measures of meningitis disease burden when incorporated into routine public health surveillance in Brazil.

Real-time Polymerase Chain Reaction Quantification of Porphyromonas gingivalis and Tannerella forsythia in Primary Endodontic Infections

Introduction: Porphyromonas gingivalis and Tannerella forsythia are anaerobic bacteria commonly involved in root canal infections. Although previous investigations have assessed these species by strictly qualitative approaches, accurate determination of their cell levels by a sensitive quantitative technique may contribute with additional information regarding relevance in pain of endodontic origin. Method: The root canal levels of P gingivalis, T forsythia, and total bacteria were investigated by a quantitative polymerase chain reaction (PCR) assay based on unique copy molecular markers. A total of 32 symptomatic (n = 14) and asymptomatic (n = 18) cases of endodontic infections were analyzed. Root canal samples were collected; genomic DNA was extracted and submitted to SYBR Green I real-time PCR targeting the rgpB (P gingivalis), bspA (T forsythia), and rpoB (total bacteria) single copy genes. Results: Overall, R gingivalis, T forsythia, and the coexistence of both species were encountered in 28%, 66%, and 22% of the subjects, respectively. P gingivalis and T forsythia levels ranged from 5.65 x 10(-6) to 1.20 x 10(-2) and from 5.76 x 10(-6) to 1.35 x 10(-1). T forsythia was highly prevalent and numerous in the study groups, whereas P gingivalis was moderately frequent and less abundant, displaying 19-fold lower average levels than the former. Conclusions: The endodontic levels of P gingivalis and T forsythia, individually or in conjunction, did not display significant associations with the manifestation of pain of endodontic origin. (J Endod 2009,35:1518-1524)

Quantification of Listeria monocytogenes in minimally processed leafy vegetables using a combined method based on enrichment and 16S rRNA real-time PCR

Modern lifestyle markedly changed eating habits worldwide, with an increasing demand for ready-to-eat foods, such as minimally processed fruits and leafy greens. Packaging and storage conditions of those products may favor the growth of psychrotrophic bacteria, including the pathogen Listeria monocytogenes. In this work, minimally processed leafy vegetables samples (n = 162) from retail market from Ribeirao Preto, Sao Paulo, Brazil, were tested for the presence or absence of Listeria spp. by the immunoassay Listeria Rapid Test, Oxoid. Two L. monocytogenes positive and six artificially contaminated samples of minimally processed leafy vegetables were evaluated by the Most Probable Number (MPN) with detection by classical culture method and also culture method combined with real-time PCR (RTi-PCR) for 16S rRNA genes of L monocytogenes. Positive MPN enrichment tubes were analyzed by RTi-PCR with primers specific for L. monocytogenes using the commercial preparation ABSOLUTET (TM) QPCR SYBR (R) Green Mix (ABgene, UK). Real-time PCR assay presented good exclusivity and inclusivity results and no statistical significant difference was found in comparison with the conventional culture method (p < 0.05). Moreover, RTi-PCR was fist and easy to perform, with MPN results obtained in ca. 48 h for RTi-PCR in comparison to 7 days for conventional method. (C) 2009 Elsevier Ltd. All rights reserved.

Real-time detection of pneumothorax using electrical impedance tomogyaphy

Objectives: Pneumothorax is a frequent complication during mechanical ventilation. Electrical impedance tomography (EIT) is a noninvasive tool that allows real-time imaging of regional ventilation. The purpose of this study was to 1) identify characteristic changes in the EIT signals associated with pneumothoraces; 2) develop and fine-tune an algorithm for their automatic detection; and 3) prospectively evaluate this algorithm for its sensitivity and specificity in detecting pneumothoraces in real time. Design: Prospective controlled laboratory animal investigation. Setting: Experimental Pulmonology Laboratory of the University of Sao Paulo. Subjects: Thirty-nine anesthetized mechanically ventilated supine pigs (31.0 +/- 3.2 kg, mean +/- SD). Interventions. In a first group of 18 animals monitored by EIT, we either injected progressive amounts of air (from 20 to 500 mL) through chest tubes or applied large positive end-expiratory pressure (PEEP) increments to simulate extreme lung overdistension. This first data set was used to calibrate an EIT-based pneumothorax detection algorithm. Subsequently, we evaluated the real-time performance of the detection algorithm in 21 additional animals (with normal or preinjured lungs), submitted to multiple ventilatory interventions or traumatic punctures of the lung. Measurements and Main Results: Primary EIT relative images were acquired online (50 images/sec) and processed according to a few imaging-analysis routines running automatically and in parallel. Pneumothoraces as small as 20 mL could be detected with a sensitivity of 100% and specificity 95% and could be easily distinguished from parenchymal overdistension induced by PEEP or recruiting maneuvers, Their location was correctly identified in all cases, with a total delay of only three respiratory cycles. Conclusions. We created an EIT-based algorithm capable of detecting early signs of pneumothoraces in high-risk situations, which also identifies its location. It requires that the pneumothorax occurs or enlarges at least minimally during the monitoring period. Such detection was operator-free and in quasi real-time, opening opportunities for improving patient safety during mechanical ventilation.

Qualitative and Quantitative Real Time Myocardial Contrast Echocardiography for Detecting Hibernating Myocardium

Background: Real time myocardial contrast echocardiography (RTMCE) is an emerging imaging modality for assessing myocardial perfusion that allows for noninvasive quantification of regional myocardial blood flow (MBF). Aim: We sought to assess the value of qualitative analysis of myocardial perfusion and quantitative assessment of myocardial blood flow (MBF) by RTMCE for predicting regional function recovery in patients with ischemic heart disease who underwent coronary artery bypass grafting (CABG). Methods: Twenty-four patients with coronary disease and left ventricular systolic dysfunction (ejection fraction < 45%) underwent RTMCE before and 3 months after CABG. RTMCE was performed using continuous intravenous infusion of commercially available contrast agent with low mechanical index power modulation imaging. Viability was defined by qualitative assessment of myocardial perfusion as homogenous opacification at rest in >= 2 segments of anterior or >= 1 segment of posterior territory. Viability by quantitative assessment of MBF was determined by receiver-operating characteristics curve analysis. Results: Regional function recovery was observed in 74% of territories considered viable by qualitative analysis of myocardial perfusion and 40% of nonviable (P = 0.03). Sensitivity, specificity, positive and negative predictive values of qualitative RTMCE for detecting regional function recovery were 74%, 60%, 77%, and 56%, respectively. Cutoff value of MBF for predicting regional function recovery was 1.76 (AUC = 0.77; 95% CI = 0.62-0.92). MBF obtained by RTMCE had sensitivity of 91%, specificity of 50%, positive predictive value of 75%, and negative predictive value of 78%. Conclusion: Qualitative and quantitative RTMCE provide good accuracy for predicting regional function recovery after CABG. Determination of MBF increases the sensitivity for detecting hibernating myocardium. (Echocardiography 2011;28:342-349).

Real-time quantitative PCR in cerebral toxoplasmosis diagnosis of Brazilian human immunodeficiency virus-infected patients

Cerebral toxoplasmosis is the most common cerebral mass lesion in AIDS patients in Brazil, and results in high mortality and morbidity, despite free access to HAART (highly active antiretroviral treatment). Molecular diagnosis based on conventional PCR (cnPCR) or real-time quantitative PCR (qrtPCR) has been indispensable for definitive diagnosis. We report here the evaluation of qrtPCR with blood and cerebrospinal fluid (CSF) samples from AIDS patients in Brazil. This prospective study was conducted for 2 years, analysing DNA samples extracted from 149 AIDS patients (98 blood and 51 CSF samples) with confirmed clinical and radiological diagnosis The laboratory diagnosis included cnPCR (with the B22/B23 primer set) and indirect immunofluorescence (IF). For qrtPCR, two primer sets were simultaneously designed based on described genes and using a 6-carboxyfluorescein dye-labelled TaqMan MGB (minor groove binder) probe One was Bug, which amplified a sequence from the B1 gene The other was the RETg, which amplified a PCR product of the 529 bp sequence. The overall cnPCR and qrtPCR results were positive results were observed in 33.6% (50) patients The sensitivities were 98% for cnPCR (B22/B23), and 86 and 98% for qrtPCR (B1Tg and RETg, respectively). Negative reactions were observed in 66 4% patients. The specificities were 97% for cnPCR and qrtPCR (B1Tg). and 88.8% for RETg These data show that RETg PCR is highly sensitive as it amplifies a repeat region with many copies; however, its specificity is lower than the other markers However, B1Tg PCR had good specificity, but lower sensitivity Among the patients, 20 had blood and CSF collected simultaneously Thus, their results permitted us to analyse and compare molecular, serological and clinical diagnosis for a better understanding of the different scenarios of laboratorial and clinical diagnosis. For nine patients with confirmed cerebral toxoplasmosis diagnosis, four scenarios were observed: (i) and (ii) negative molecular diagnosis for CSF and positive for blood with variable IF titres for the sera and CSF (negative or positive), (iii) positive molecular diagnosis with CSF and negative with blood, and (iv) positive molecular diagnosis in both samples. In the latter two situations, normally the IF titres in sera and CSF are variable. Other opportunistic infections were shown in 11 patients Despite the IF titres in sera and CSF being variable, all of them had negative molecular diagnosis for both samples qrtPCR allows for a rapid identification of Toxoplasma gondii DNA in patient samples; in a minority of cases discrepancies occur with the cnPCR.

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.

Carbapenem stewardship: positive impact on hospital ecology

INTRODUCTION: Excessive group 2 carbapenem use may result in decreased bacterial susceptibility. OBJECTIVE: We evaluated the impact of a carbapenem stewardship program, restricting imipenem and meropenem use. METHODS: Ertapenem was mandated for ESBL-producing Enterobacteriaceae infections in the absence of non-fermenting Gram-negative bacilli (GNB) from April 2006 to March 2008. Group 2 carbapenems were restricted for use against GNB infections susceptible only to carbapenems and suspected GNB infections in unstable patients. Cumulative susceptibility tests were done for nosocomial pathogens before and after restriction using Clinical and Laboratory Standards Institute (CLSI) guide-lines.Vitek System or conventional identification methods were performed and susceptibility testing done by disk diffusion according to CLSI.Antibiotic consumption (t-test) and susceptibilities (McNemar's test) were determined. RESULTS: The defined daily doses (DDD) of group 2 carbapenems declined from 61.1 to 48.7 DDD/1,000 patient-days two years after ertapenem introduction (p = 0.027). Mean ertapenem consumption after restriction was 31.5 DDD/1,000 patient-days. Following ertapenem introduction no significant susceptibility changes were noticed among Gram-positive cocci. The most prevalent GNB were P. aeruginosa, Klebsiella pneumoniae, and Acinetobacter spp. There was no change in P. aeruginosa susceptibility to carbapenems. Significantly improved P. aeruginosa and K. pneumoniae ciprofloxacin susceptibilities were observed, perhaps due to decreased group 2 carbapenem use. K. pneumoniae susceptibility to trimethoprim-sulfamethoxazole improved. CONCLUSION: Preferential use of ertapenem resulted in reduced group 2 carbapenem use, with a positive impact on P. aeruginosa and K. pneumoniae susceptibility.

Porcine skin as a source of biodegradable matrices: alkaline treatment and glutaraldehyde crosslinking

In this work, the modifications promoted by alkaline hydrolysis and glutaraldehyde (GA) crosslinking on type I collagen found in porcine skin have been studied. Collagen matrices were obtained from the alkaline hydrolysis of porcine skin, with subsequent GA crosslinking in different concentrations and reaction times. The elastin content determination showed that independent of the treatment, elastin was present in the matrices. Results obtained from in vitro trypsin degradation indicated that with the increase of GA concentration and reaction time, the degradation rate decreased. From thermogravimetry and differential scanning calorimetry analysis it can be observed that the collagen in the matrices becomes more resistant to thermal degradation as a consequence of the increasing crosslink degree. Scanning electron microscopy analysis indicated that after the GA crosslinking, collagen fibers become more organized and well-defined. Therefore, the preparations of porcine skin matrices with different degradation rates, which can be used in soft tissue reconstruction, are viable.

Immediate reconstruction following breast-conserving surgery: management of the positive surgical margins and influence on secondary reconstruction

The efficacy of breast-conserving surgery for the local control of early breast cancer has been repeatedly evidenced. Although immediate reconstruction following breast-conserving surgery has been described, little information is available regarding surgical management in reoperative settings due to positive margins. We studied the influence of intraoperatively assessed and postoperatively controlled surgical margin status on the type of breast-conserving surgery and report our results regarding complications in a reoperative breast reconstruction scenario. All patients were seen by a multidisciplinary team who recommended breast-conserving surgery. According to the breast volume, ptosis and tumor size/location, the patients were also evaluated by a plastic surgeon, who recommended reconstruction with the appropriate technique. Intraoperative assessment of surgical margins was determined by histological examination of frozen sections. The mean follow-up time was 48months. Two hundred and eighteen patients (88.5 per cent ) underwent breast-conserving surgery and immediate reconstruction. Twelve (5.5 per cent ) patients had a positive tumor margin after review of the permanent section. All patients underwent re-exploration. In 1.3 per cent , a second reconstructive technique was indicated and in 2.2 per cent a skin-sparing mastectomy with total reconstruction was performed. Our findings support the important role of the intraoperative assessment of surgical margins and its interference in the selection of reconstruction techniques and negative margins; however, it will not guarantee complete excision of the tumor. Success depends on coordinated planning with the oncologic surgeon and careful intraoperative management

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.