Covariate Selection in High-Dimensional Generalized Linear Models With Measurement Error

In many problems involving generalized linear models, the covariates are subject to measurement error. When the number of covariates p exceeds the sample size n, regularized methods like the lasso or Dantzig selector are required. Several recent papers have studied methods which correct for measurement error in the lasso or Dantzig selector for linear models in the p > n setting. We study a correction for generalized linear models, based on Rosenbaum and Tsybakov’s matrix uncertainty selector. By not requiring an estimate of the measurement error covariance matrix, this generalized matrix uncertainty selector has a great practical advantage in problems involving high-dimensional data. We further derive an alternative method based on the lasso, and develop efficient algorithms for both methods. In our simulation studies of logistic and Poisson regression with measurement error, the proposed methods outperform the standard lasso and Dantzig selector with respect to covariate selection, by reducing the number of false positives considerably. We also consider classification of patients on the basis of gene expression data with noisy measurements. Supplementary materials for this article are available online.     

A unifying coordinate family for the Kerr–Newman metric

A new unified metric form is presented for the Kerr–Newman geometry. The new form is a generalization of the Boyer–Lindquist metric involving an arbitrary gauge function of the spheroidal radial variable. Each choice of the gauge function corresponds to a coordinate system including four of the most important coordinate systems for Kerr–Newman (Boyer–Lindquist, Kerr, Kerr–Schild and Doran coordinates). The representation is given in terms of a single Minkowski frame together with the gauge function. This Minkowski frame arises by boosting a static orthonormal frame which is adapted to spheroidal coordinates. Properties of the boost reflect the rotating nature of the Kerr–Newman solution including an identification of the angular velocities of the disk and the horizon matching previously known values obtained in other ways.     

Positive shrinkage, improved pretest and absolute penalty estimators in partially linear models

Shrinkage estimators of a partially linear regression parameter vector are constructed by shrinking estimators in the direction of the estimate which is appropriate when the regression parameters are restricted to a linear subspace. We investigate the asymptotic properties of positive Stein-type and improved pretest semiparametric estimators under quadratic loss. Under an asymptotic distributional quadratic risk criterion, their relative dominance picture is explored analytically. It is shown that positive Stein-type semiparametric estimators perform better than the usual Stein-type and least square semiparametric estimators and that an improved pretest semiparametric estimator is superior to the usual pretest semiparametric estimator. We also consider an absolute penalty type estimator for partially linear models and give a Monte Carlo simulation comparisons of positive shrinkage, improved pretest and the absolute penalty type estimators. The comparison shows that the shrinkage method performs better than the absolute penalty type estimation method when the dimension of the parameter space is much larger than that of the linear subspace.     

Coordination Polymers Constructed from Paddle-Wheel Building Units

The two structurally related coordination polymers [Cu(ndc)(pyridine)], CPO-2-Cu, and [Zn(ndc)(3,4-lutidine)], CPO-2-Zn, were obtained by hydrothermal reactions between 2,6-naphthalenedicarboxylic acid (ndc), pyridine and copper(II) nitrate (CPO-2-Cu) and ndc, 3,4-lutidine and zinc(II) nitrate (CPO-2-Zn), respectively. The compounds are based on the binuclear paddle-wheel building unit. In both compounds these building units are connected into 2D sheets by naphthalene rings. In the third dimension there are weaker interactions involving the axial ligands pyridine and 3,4-lutidine. The sheets are stacked so that large 1D channels are formed into which the axial ligands protrude. The crystal structure of CPO-2-Cu was solved from synchrotron powder X-ray data, while the crystal structure of CPO-2-Zn was solved from conventional single-crystal X-ray data. Crystal data for CPO-2-Cu: Monoclinic space group C2/m (No. 12), a=10.2252(2), b=19.0915(4), c=8.0521(2) Å, β=98.824(1)°, V=1553.30(7) ų and Z=4. Crystal data for CPO-2-Zn: Triclinic space group P−1 (No. 2), a=7.540(1), b=10.711(1), c=11.196(2) Å, α=66.490(5)°, β=87.265(6)°, χ=88.470(6)°, V=828.2(2) ų and Z=2. The thermal properties of both compounds were investigated as well as the magnetic properties of CPO-2-Cu.     

Some infinite series related to Feynman diagrams

Results are presented for some infinite series appearing in Feynman diagram calculations, many of which are similar to the Euler series. These include both one-, two- and three-dimensional series. The sums of these series can be evaluated with the help of various integral representations for hypergeometric functions, and expressed in terms of ζ(2),ζ(3), the Catalan constant G and Cl₂(π/3) where Cl₂(θ) is Clausen's function.     

Mass spectrometry of onium compounds-XVIII: Evaporation of N-arylpyridinium-3-oxides

Comparision of the fragmentation patterns and ionisation potentials for 3-hydroxy-2-phenylpyridine and N-arylpyridinium-3-oxides shows that the latter are evaporated as mesoins. The 2,4-dinitrophenyl derivative constitutes an exception in that transarylation to the corresponding ether takes place before evaporation.     

Probing BSA binding to citrate-coated gold nanoparticles and surfaces

The interaction of bovine serum albumin (BSA) with gold colloids and surfaces was studied using zeta-potential and quartz crystal microbalance (QCM) measurements, respectively, to determine the surface charge and coverage. The combination of these two measurements suggests that BSA binding to gold nanoparticles and gold surfaces occurs by an electrostatic mechanism when citrate is present. The binding of BSA to bare gold is nearly two times greater than the binding of BSA to a citrate-coated gold surface, suggesting that protein spreading (denaturation) on the surface may occur followed by secondary protein binding. On the other hand, binding to citrate-coated gold surfaces can be fit to a Langmuir isotherm model to obtain a maximum surface coverage of (3.7 +/- 0.2) x 10(12) molecules/cm(2) and a binding constant of 1.0 +/- 0.3 microM(-1). The zeta-potential measurements show that the stabilization of colloids by BSA has a significant contribution from a steric mechanism because the colloids are stable, even at their isoelectric point (pI approximately 4.6). To be consistent with the observed phenomena, the electrostatic interactions between BSA and citrate must consist of salt-bridges, for example, of the carboxylate-ammonium type, between the citrate and the lysine on the protein surface. The data support the role of strong electrostatic binding but do not exclude contributions from steric or hydrophobic interactions with the surface adlayer.     

Free and total para-aminobenzoic acid analysis in plants with high-performance liquid chromatography/tandem mass spectrometry

para-Aminobenzoic acid (PABA), a precursor in the synthesis of folates in plants, is determined by liquid chromatography/tandem mass spectrometry (LC/MS/MS). In plants PABA can be converted into its beta-D-glucopyranosyl ester (PABA-Glc) and can also exist in its free form. In this work, we developed and validated a quantitative method to study free and total PABA in plants. The total PABA (free PABA plus PABA-Glc) can be evaluated after acid hydrolysis at 80 degrees C for 2 hours. The plant material is homogenized and the PABA content is quantified using the standard addition procedure. The validated method is selective, sensitive, simple, accurate, has a recovery between 99.6 to 102.5%, is reproducible (RSD between 1.4 and 4.4%), and is linear between 2.5 and 1538 ng/mL. Free and total PABA determinations in five vegetables showed that different plant species had different amounts of free and total PABA, and that the ratios of total versus free PABA were also variable. This new method could be valuable for studies of folate synthesis in plants.     

Activation of crystalline cellulose surfaces through the chemoenzymatic modification of xyloglucan

Cellulose constitutes an important raw material for many industries. However, the superb load-bearing properties of cellulose are accompanied by poor chemical reactivity. The hydroxyl groups on cellulose surfaces can be reacted but usually not without loss of fiber integrity and strength. Here, we describe a novel chemoenzymatic approach for the efficient incorporation of chemical functionality onto cellulose surfaces. The modification is brought about by using a transglycosylating enzyme, xyloglucan endotranglycosylase, to join chemically modified xyloglucan oligosaccharides to xyloglucan, which has a naturally high affinity to cellulose. Binding of the chemically modified hemicellulose molecules can thus be used to attach a wide variety of chemical moieties without disruption of the individual fiber or fiber matrix.     

Calculation of wetting angles in crude oil/water/quartz systems

A method for the determination of water-advancing wetting angles has been developed and tested. The method allows measurements in black oils, as opposed to traditional techniques which substitute transparent model oils prior to measurements. The method is based on the Laplace equation and axisymmetric drop shape analysis. The main source of error is the determination of the drop volume. Results in transparent systems are comparable to results using other techniques. Wetting angles are determined for water in two different crude oil systems, using quartz as the substrate. The quartz surfaces are water wet over large pH ranges, but it is possible to accurately identify pH intervals where the surfaces are intermediate or oil wet.