Tests on categorical data from the unionintersection principle

Summary The union-intersection principle developed by S. N. Roy [13] has become an important tool in multivariate analysis. In this paper the union-intersection principle is applied to obtain some of the standard tests of hypothesis on categorical data, as well as a new test for homogeneity in anr×c table. In particular, tests of hypothesis on a single multinomial distribution and tests for the comparison of two multinomials are derived on the union-intersection principle and the corresponding simultaneous confidence intervals obtained. A test for homogeneity in anr×c table is derived on the union-intersection principle, and for the case of equal sample size from each of ther populations it is shown that the test statistic is distributed as the largest root of a central Wishart matrix.     

Wigner distribution of a transducer beam pattern within a multiple scattering formalism for heterogeneous solids

Diffuse ultrasonic backscatter measurements have been especially useful for extracting microstructural information and for detecting flaws in materials. Accurate interpretation of experimental data requires robust scattering models. Quantitative ultrasonic scattering models include components of transducer beam patterns as well as microstructural scattering information. Here, the Wigner distribution is used in conjunction with the stochastic wave equation to model this scattering problem. The Wigner distribution represents a distribution in space and time of spectral energy density as a function of wave vector and frequency. The scattered response is derived within the context of the Wigner distribution of the beam pattern of a Gaussian transducer. The source and receiver distributions are included in the analysis in a rigorous fashion. The resulting scattered response is then simplified in the single-scattering limit typical of many diffuse backscatter experiments. Such experiments, usually done using a modified pulse-echo technique, utilize the variance of the signals in space as the primary measure of microstructure. The derivation presented forms a rigorous foundation for the multiple scattering process associated with ultrasonic experiments in heterogeneous media. These results are anticipated to be relevant to ultrasonic nondestructive evaluation of polycrystalline and other heterogeneous solids.     

Radical reactions with 3H-quinazolin-4-ones: synthesis of deoxyvasicinone, mackinazolinone, luotonin A, rutaecarpine and tryptanthrin

Alkyl, aryl, heteroaryl and acyl radicals have been cyclised onto the 2-position of 3H-quinazolin-4-one. The side chains containing the radical precursors were attached to the nitrogen atom in the 3-position. The cyclisations take place by aromatic homolytic substitution hence retain the aromaticity of the 3H-quinazolin-4-one ring. The highest yields were obtained using hexamethylditin to facilitate cyclisation rather than reduction without cyclisation. The alkaloids deoxyvasicinone , mackinazolinone , tryptanthrin , luotonin A and rutaecarpine were synthesised by radical cyclisation onto 3H-quinazolin-4-one.     

Development and optimization of an LC-MS/MS-based method for simultaneous quantification of vitamin D2 , vitamin D3 , 25-hydroxyvitamin D2 and 25-hydroxyvitamin D3

Simultaneous and accurate measurement of vitamin D and 25-hydroxyvitamin D in biological samples is a barrier limiting our ability to define "optimal" vitamin D status. Thus, our goal was to optimize conditions and evaluate an LC-MS method for simultaneous detection and quantification of vitamin D(2) , vitamin D(3) , 25-hydroxyvitamin D(2) and 25-hydroxyvitamin D(3) in serum. Extraction and separation of vitamin D forms were achieved using acetone liquid-liquid extraction and by a reversed phase C8 column, respectively. Detection was performed on a triple quadrupole tandem mass spectrometer (QQQ-MS/MS) equipped with atmospheric pressure photo ionization source. The LOQs for all analytes tested were 1 ng/mL for hydroxylated molecules and 2 ng/mL for the parent vitamin Ds. RSD at lower LOQ (2 ng/mL) and in medium (80 ng/mL) and high (200 ng/mL) quality control samples did not exceed 20 and 15% CV, respectively. Accuracy of the method for determination of hydroxylated molecules was also validated using National Institutes of Standards and Technology standard samples and found to be in the range of 90.9-111.2%. In summary, a sensitive and reproducible method is reported for simultaneous quantification of vitamin D(2) , vitamin D(3) , 25-hydroxyvitamin D(2) and 25-hydroxyvitamin D(3) molecules in biological samples.     

Minkowski Length of 3D Lattice Polytopes

We study the Minkowski length L(P) of a lattice polytope P, which is defined to be the largest number of non-trivial primitive segments whose Minkowski sum lies in P. The Minkowski length represents the largest possible number of factors in a factorization of polynomials with exponent vectors in P, and shows up in lower bounds for the minimum distance of toric codes. In this paper we give a polytime algorithm for computing L(P) where P is a 3D lattice polytope. We next study 3D lattice polytopes of Minkowski length 1. In particular, we show that if Q, a subpolytope of P, is the Minkowski sum of L=L(P) lattice polytopes Q _i , each of Minkowski length 1, then the total number of interior lattice points of the polytopes Q ₁,??,Q _L is at most 4. Both results extend previously known results for lattice polygons. Our methods differ substantially from those used in the two-dimensional case.     

Determination of aflatoxins and ochratoxin A in ginseng and other botanical roots by immunoaffinity column cleanup and liquid chromatography with fluorescence detection

Mycotoxins are toxic secondary metabolites produced by certain molds and are common contaminants of many important food crops, such as grains, nuts, and spices. Some mycotoxins are found in fruits, vegetables, and botanical roots. These contaminants have a broad range of toxic effects, including carcinogenicity, immunotoxicity, neurotoxicity, and reproductive and developmental toxicity. The public health concerns related to both acute and chronic effects of mycotoxins in animals have prompted more than 100 countries to establish regulatory limits for some of the well-known mycotoxins, such as the aflatoxins (AFL). Our research focused on method development for 2 of these toxins, AFL and ochratoxin A (OTA), in ginseng and other selected botanical roots. Methods using an immunoaffinity column (IAC) cleanup, liquid chromatographic separation, and fluorescence detection were modified and evaluated. Two types of IAC cleanup were evaluated: IAC for AFL, and IAC for both AFL and OTA. Three derivatization techniques to enhance the fluorescence of the AFL were compared: precolumn trifluoroacetic acid, postcolumn bromination, and postcolumn ultraviolet irradiation. No derivatization was needed for OTA. Results for AFL using the single analyte IAC cleanup and the 3 derivatization techniques were all comparable for ginseng and for other roots such as ginger, licorice, and kava-kava. Recoveries of added AFL for ginseng at levels from 2 to 16 ng/g were about 80%. Using IAC cleanup for both AFL and OTA recoveries of added AFL for ginseng at 4-16 ng/g were about 70%, and for ginger, licorice, and kava-kava were about 60%. Recoveries of added OTA for ginseng, ginger, and echinacea at 4 ng/g were about 55%.     

Charged microbeads are not transported across the human stratum corneum in vitro by short high-voltage pulses

There have been several reports of particle transport due to high-voltage pulsing of human skin. Here, several different short, high-voltage pulsing protocols were used in vitro to study the possible transport of highly charged, fluorescent polystyrene particles (14 nm to 2.1 microns in diameter; surface charges of -4.05 x 10(3) e to -2.77 x 10(7) e) across the skin. Two different methods were used to trap and measure particles on the other side of the skin. The first used a polycarbonate membrane to trap the particles, determining the amount of transport by enumeration under a fluorescence microscope. The second used spectrofluorimetry to measure the amount of particles transported. After pulsing, particles were found in randomly distributed clusters on the surface of the skin. No detectable transport across the stratum corneum for any size particle was observed.