Orthogonal rational functions and quadrature on an interval

AbstractRational functions with real poles and poles in the complex lower half-plane, orthogonal on the real line, are well known. Quadrature formulas similar to the Gauss formulas for orthogonal polynomials have been studied. We generalize to the case of arbitrary complex poles and study orthogonality on a finite interval. The zeros of the orthogonal rational functions are shown to satisfy a quadratic eigenvalue problem. In the case of real poles, these zeros are used as nodes in the quadrature formulas

Eu3+ multicenter formation and luminescent properties of Ca3Sc2Si3O12:Eu and Ca2YScMgSiO12:Eu single crystalline films

The work is dedicated to the investigation of Eu3+ multicenter formation and luminescent properties of Ca3Sc2Si3O12:Eu (CSSG:Eu) and Ca2YScMgSiO12:Eu (CYMSSG:Eu) single crystalline film (SCF) phosphors, grown by liquid phase epitaxy method onto Gd3Ga2.5Al2.5O12 (GAGG) and Y3Al5O12 (YAG) substrates, respectively. We have found notable differences in the luminescent properties of CSSG:Eu and CYMSSG:Eu SCFs caused by the Eu3+ multicenter formation in both garnets due to the different local surrounding of Eu3+ ions in the dodecahedral positions by the non-isovalent Sc3+/Mg2+ and Si4+ cations in the octahedral and tetrahedral positions of garnet hosts, respectively. A feature of the Eu3+ center creation in CYMSSG:Eu garnet in comparison with CSSG:Eu counterpart is the possibility of localization of Eu3+ ions in dodecahedral sites of both Ca2+ and Y3+ cations. However, based on the obtained results, we have presupposed preferable localization of the Eu3+ ions mainly in the Y3+ positions of this garnet

Near-infrared Fourier transform room-temperature photoluminescence of erbium complexes

A modified Fourier transform (FT) Raman bench spectrometer designed for the detection of weak light emission in the 800–1700 nm wavelength region has been used to demonstrate the advantages of FT spectroscopy for measuring near-infrared photoluminescence spectra of lanthanide complexes with a good resolution and very good sensitivity. This apparatus has been tested with an ultraviolet laser source (325 nm) on three standard erbium complexes. The 4I13/24I15/2 emission of tris-(acetylacetonato) (1,10 phenanthroline) erbium [Er(acac)3(phen)], tris-(4,4,4,-trifluoro-1-(2 thenoyl)-1,3-butenedione) (1,10 phenanthroline) erbium [Er(TTFA)3(phen)] and tris(8-hydroxyquinolinato) erbium [Erq3] has thus been recorded in solution and in the solid state and compared with literature. ©2003 American Institute of Physics

PCovR2:A flexible principal covariates regression approach to parsimoniously handle multiple criterion variables

Principal covariates regression (PCovR) allows one to deal with the interpretational and technical problems associated with running ordinary regression using many predictor variables. In PCovR, the predictor variables are reduced to a limited number of components, and simultaneously, criterion variables are regressed on these components. By means of a weighting parameter, users can flexibly choose how much they want to emphasize reconstruction and prediction. However, when datasets contain many criterion variables, PCovR users face new interpretational problems, because many regression weights will be obtained and because some criteria might be unrelated to the predictors. We therefore propose PCovR2, which extends PCovR by also reducing the criteria to a few components. These criterion components are predicted based on the predictor components. The PCovR2 weighting parameter can again be flexibly used to focus on the reconstruction of the predictors and criteria, or on filtering out relevant predictor components and predictable criterion components. We compare PCovR2 to two other approaches, based on partial least squares (PLS) and principal components regression (PCR), that also reduce the criteria and are therefore called PLS2 and PCR2. By means of a simulated example, we show that PCovR2 outperforms PLS2 and PCR2 when one aims to recover all relevant predictor components and predictable criterion components. Moreover, we conduct a simulation study to evaluate how well PCovR2, PLS2 and PCR2 succeed in finding (1) all underlying components and (2) the subset of relevant predictor and predictable criterion components. Finally, we illustrate the use of PCovR2 by means of empirical data

Integrating functional genomics data using maximum likelihood based simultaneous component analysis

<p>Abstract</p> <p>Background</p> <p>In contemporary biology, complex biological processes are increasingly studied by collecting and analyzing measurements of the same entities that are collected with different analytical platforms. Such data comprise a number of data blocks that are coupled via a common mode. The goal of collecting this type of data is to discover biological mechanisms that underlie the behavior of the variables in the different data blocks. The simultaneous component analysis (SCA) family of data analysis methods is suited for this task. However, a SCA may be hampered by the data blocks being subjected to different amounts of measurement error, or noise. To unveil the true mechanisms underlying the data, it could be fruitful to take noise heterogeneity into consideration in the data analysis. Maximum likelihood based SCA (MxLSCA-P) was developed for this purpose. In a previous simulation study it outperformed normal SCA-P. This previous study, however, did not mimic in many respects typical functional genomics data sets, such as, data blocks coupled via the experimental mode, more variables than experimental units, and medium to high correlations between variables. Here, we present a new simulation study in which the usefulness of MxLSCA-P compared to ordinary SCA-P is evaluated within a typical functional genomics setting. Subsequently, the performance of the two methods is evaluated by analysis of a real life <it>Escherichia coli </it>metabolomics data set.</p> <p>Results</p> <p>In the simulation study, MxLSCA-P outperforms SCA-P in terms of recovery of the true underlying scores of the common mode and of the true values underlying the data entries. MxLSCA-P further performed especially better when the simulated data blocks were subject to different noise levels. In the analysis of an <it>E. coli </it>metabolomics data set, MxLSCA-P provided a slightly better and more consistent interpretation.</p> <p>Conclusion</p> <p>MxLSCA-P is a promising addition to the SCA family. The analysis of coupled functional genomics data blocks could benefit from its ability to take different noise levels per data block into consideration and improve the recovery of the true patterns underlying the data. Moreover, the maximum likelihood based approach underlying MxLSCA-P could be extended to custom-made solutions to specific problems encountered.</p

Performance of LED-Based Fluorescence Microscopy to Diagnose Tuberculosis in a Peripheral Health Centre in Nairobi.

Sputum microscopy is the only tuberculosis (TB) diagnostic available at peripheral levels of care in resource limited countries. Its sensitivity is low, particularly in high HIV prevalence settings. Fluorescence microscopy (FM) can improve performance of microscopy and with the new light emitting diode (LED) technologies could be appropriate for peripheral settings. The study aimed to compare the performance of LED-FM versus Ziehl-Neelsen (ZN) microscopy and to assess feasibility of LED-FM at a low level of care in a high HIV prevalence country

Stress induced Salmonella Typhimurium re-excretion by pigs is associated with cortisol induced increased intracellular proliferation in porcine macrophages

Infections of pigs with Salmonella enterica subspecies enterica serovar Typhimurium (Salmonella Typhimurium) often result in the development of carriers that intermittently excrete Salmonella in very low numbers. During periods of stress, recrudescence of Salmonella may occur

Evaluation of Combined LED-Fluorescence Microscopy and Bleach Sedimentation for Diagnosis of Tuberculosis at Peripheral Health Service Level

Sputum microscopy is the only diagnostic for tuberculosis (TB) available at peripheral levels of health service in resource-poor countries. Its sensitivity is reduced in high HIV-prevalence settings. Sodium hypochlorite (NaOCl) specimen sedimentation prior microscopy and light-emitting diode (LED)-fluorescence microscopy (FM) can individually improve performance of microscopy. This study aimed to evaluate the performance of combined LED-FM and NaOCl sputum sedimentation for TB detection at peripheral level of health services