Extending shelling orders and a hierarchy of functions of unimodal simple polytopes

Let P be a simplicial d-polytope with n facets ((d − 1)-dimensional faces) in R^d. A shelling of P is an ordering of the facets of P such that the intersection of each facet F with the union of all facets that precede it the ordering is a nonempty union of (d − 2)-faces of F. The following open question was raised by Tverberg and is recorded in [4]. Suppose for some k < n, there is an ordering of k of the facets of P so that the intersection of each of these facets with the union of all of the facets that precede it in the ordering is a nonempty union of (d − 2)-faces. Can this initial “segment” be extended to a shelling of all the facets? This question is open even in the case that P is the dual of the d-dimensional hypercube. The question in this case has resurfaced several times since G. Danaraj and V. Klee (1978) in a variety of forms. It is related to the hierarchies of completely unimodal pseudo-Boolean functions studied in P.L. Hammer et al. (1988), the author (1988) and D. Wiedemann (1986). (A pseudo-Boolean function is a function mapping the vertices of the d-dimensional hypercube into the reals). In this paper, the hierarchies are compared and combined. This hierarchy is then extended to general simple polytopes, and the relationship to the above open question is explained.     

Normals in a Minkowski Plane

In this paper we will establish bounds on the average number of normals through a point in a convex body in a Minkowski plane for certain classes of convex bodies. Also, a related Euler relation is discussed.     

A rare case of three rearrangements during the cycloaddition-elimination reaction of 4-methyl-5-phenylimino-Δ2-1,2,3,4-thiatriazoline with 2-pyridyl isothiocyanate

2-Pyridyl isothiocyanate ( 7 ), with its electrophilic and basic properties, gives a series of ring-transformation reactions with 4-methyl-5-phenylimino-1,2,3,4-thiatriazoline ( 1 ) at 60°. Two dithiazolidines, 8 and 10 , are formed as major products at an early stage of the reaction, whereas two thiadiazolidines, 9 and 11 , predominate at the end. The mechanism (Schemes II and III) has been elucidated by following the reaction course under a variety of conditions and by analyzing the products by ¹³C nmr spectroscopy.     

Use of modifiers in on-line and off-line supercritical fluid extraction

For many applications using supercritical fluid extraction (SFE), modifiers may be required.This paper will present some findings regarding the use of various modifiers including methanol, hexane, acetone, chloroform, dichloromethane, toluene, and tributylphosphate, in on-line and off-line SFE with cryogenic adsorbent trapping. The specific applications involved the extractions of petroleum hydrocarbons and pesticides from naturally incurred soils.     

Laser-induced breakdown detection combined with asymmetrical flow field-flow fractionation: application to iron oxi/hydroxide colloid characterization

The combination of asymmetrical flow field-flow fractionation (AsFlFFF) with the laser-induced breakdown detection (LIBD) is presented as a powerful tool for the determination of colloid size distribution at trace particle concentrations. Detection limits (D1) of 1, 4, and 20 microg/L have been determined for a mixture of polystyrene reference particles with 20, 50, and 100 nm in size, respectively. This corresponds to injected masses of 1, 4, and 20 pg, which is lower than found in a previous study with the symmetrical FlFFF (SyFlFFF). The improvement is mainly due to the lower colloid background discharged from the AsFlFFF channel. The combined method of AsFlFFF-LIBD is then applied to the analysis of iron oxi/hydroxide colloids being considered as potential carriers for the radionuclide migration from a nuclear waste repository. Our LIBD arrangement is less sensitive for iron colloid detection as compared to reference polystyrene particles which results in a detection limit of approximately 240 microg/L FeOOH for the AsFlFFF-LIBD analysis. This is superior to the detection via UV-Vis absorbance and comparable to ICP-MS detection. Size information (mean size 11-18 nm) for different iron oxi/hydroxide colloids supplied by the present method is comparable to that obtained by sequential ultrafiltration and dynamic light scattering. A combined on-line ICP-MS detection is used to gain insight into the colloid-borne main and trace elements.     

DEVELOPMENT OF A PLAQUE REDUCTION ASSAY AND APPLICATION TO THE STUDY OF PSORALEN-DAMAGED DNA

Abstract— We have developed a procedure called a plaque reduction assay to assess the biological activity of duplex circular DNA modified by covalent adduct formation with psoralen derivatives. The replicating form (RF) of bacteriophage DNA modified by photochemical addition of a psoralen derivative was introduced into bacterial cells using the CaCI₂ transfection method. The transfected cells. plated upon a confluent lawn of cells permissive for the bacteriophage in the inoculum, provided a measure of the reduction in infectivity of the RF DNA which resulted from its covalent modification. Use of this assay is illustrated in studies which screened and compared the activities of several recently synthesized psoralen derivatives. We describe two new compounds. β-(8-psoralenoxy)-ethanol and β-(8-psoralenoxy)ethylamine that are significantly more active than either 8-methoxypsoralen or trioxsalen in the biological assay     

A 3D QSAR pharmacophore model and quantum chemical structure--activity analysis of chloroquine(CQ)-resistance reversal

Using CATALYST, a three-dimensional QSAR pharmacophore model for chloroquine(CQ)-resistance reversal was developed from a training set of 17 compounds. These included imipramine (1), desipramine (2), and 15 of their analogues (3-17), some of which fully reversed CQ-resistance, while others were without effect. The generated pharmacophore model indicates that two aromatic hydrophobic interaction sites on the tricyclic ring and a hydrogen bond acceptor (lipid) site at the side chain, preferably on a nitrogen atom, are necessary for potent activity. Stereoelectronic properties calculated by using AM1 semiempirical calculations were consistent with the model, particularly the electrostatic potential profiles characterized by a localized negative potential region by the side chain nitrogen atom and a large region covering the aromatic ring. The calculated data further revealed that aminoalkyl substitution at the N5-position of the heterocycle and a secondary or tertiary aliphatic aminoalkyl nitrogen atom with a two or three carbon bridge to the heteroaromatic nitrogen (N5) are required for potent "resistance reversal activity". Lowest energy conformers for 1-17 were determined and optimized to afford stereoelectronic properties such as molecular orbital energies, electrostatic potentials, atomic charges, proton affinities, octanol-water partition coefficients (log P), and structural parameters. For 1-17, fairly good correlation exists between resistance reversal activity and intrinsic basicity of the nitrogen atom at the tricyclic ring system, frontier orbital energies, and lipophilicity. Significantly, nine out of 11 of a group of structurally diverse CQ-resistance reversal agents mapped very well on the 3D QSAR pharmacophore model.     

An automated, sheathless capillary electrophoresis-mass spectrometry platform for discovery of biomarkers in human serum

A capillary electrophoresis-mass spectrometry (CE-MS) method has been developed to perform routine, automated analysis of low-molecular-weight peptides in human serum. The method incorporates transient isotachophoresis for in-line preconcentration and a sheathless electrospray interface. To evaluate the performance of the method and demonstrate the utility of the approach, an experiment was designed in which peptides were added to sera from individuals at each of two different concentrations, artificially creating two groups of samples. The CE-MS data from the serum samples were divided into separate training and test sets. A pattern-recognition/feature-selection algorithm based on support vector machines was used to select the mass-to-charge (m/z) values from the training set data that distinguished the two groups of samples from each other. The added peptides were identified correctly as the distinguishing features, and pattern recognition based on these peptides was used to assign each sample in the independent test set to its respective group. A twofold difference in peptide concentration could be detected with statistical significance (p-value < 0.0001). The accuracy of the assignment was 95%, demonstrating the utility of this technique for the discovery of patterns of biomarkers in serum.