An effective and simple heuristic for the set covering problem

This paper investigates the development of an effective heuristic to solve the set covering problem (SCP) by applying the meta-heuristic Meta-RaPS (Meta-heuristic for Randomized Priority Search). In Meta-RaPS, a feasible solution is generated by introducing random factors into a construction method. Then the feasible solutions can be improved by an improvement heuristic. In addition to applying the basic Meta-RaPS, the heuristic developed herein integrates the elements of randomizing the selection of priority rules, penalizing the worst columns when the searching space is highly condensed, and defining the core problem to speedup the algorithm. This heuristic has been tested on 80 SCP instances from the OR-Library. The sizes of the problems are up to 1000 rows × 10,000 columns for non-unicost SCP, and 28,160 rows × 11,264 columns for the unicost SCP. This heuristic is only one of two known SCP heuristics to find all optimal/best known solutions for those non-unicost instances. In addition, this heuristic is the best for unicost problems among the heuristics in terms of solution quality. Furthermore, evolving from a simple greedy heuristic, it is simple and easy to code. This heuristic enriches the options of practitioners in the optimization area.     

Number of irreducible polynomials and pairs of relatively prime polynomials in several variables over finite fields

We discuss several enumerative results for irreducible polynomials of a given degree and pairs of relatively prime polynomials of given degrees in several variables over finite fields. Two notions of degree, the total degree and the vector degree, are considered. We show that the number of irreducibles can be computed recursively by degree and that the number of relatively prime pairs can be expressed in terms of the number of irreducibles. We also obtain asymptotic formulas for the number of irreducibles and the number of relatively prime pairs. The asymptotic formulas for the number of irreducibles generalize and improve several previous results by Carlitz, Cohen and Bodin.     

High-field magnetic resonance imaging using solenoid radiofrequency coils

High-resolution magnetic resonance imaging using dedicated high-field radiofrequency micro-coils at 16.4 T (700 MHz) was investigated. Specific solenoid coils primarily using silver and copper as conductors with enamel and polyurethane coatings were built to establish which coil configuration produces the best image. Image quality was quantified using signal-to-noise ratio and signal variation over regions of interest. Benchmarking was conducted using 5-mm diameter coils, as this size is comparable to an established coil of the same size. Our 1.4-mm-diameter coils were compared directly to each other, from which we deduce performance as a function of conductor material and coating. A variety of materials and conductor coatings allowed us to choose an optimal design, which we used to image a kidney section at 10-micron resolution. We applied zero-fill extrapolation to achieve 5-micron resolution.     

Hypericin-Induced Phototoxicity in Cultured Fibroblasts and Swine Erythrocytes

Hypericin is a naturally occurring photosensitizer, whose presence in plants has been responsible for cutaneous phototoxicity in grazing animals. The photosensitizing properties of this agent have recently been exploited in models for anti-tumor and anti-viral activity. The cytotoxicity of hypericin and light was assessed in 3T3 mouse fibroblasts using the MTT [3-(4, 5-dimethylthiazol-2-yl)-2, 5-diphenyl tetrazolium bromide)] assay and the lactate dehydrogenase (LDH) leakage assay. Membrane damage was assessed in swine erythrocytes using hemolysis, potassium (K⁺) leakage and formation of lipid hydroperoxides. Concentration- and light-dependent decreases in fibroblast viability were seen starting at hypericin concentrations of 1.25 μM and light power flux levels of 24 J/cm² using a visible light source and at 0.417 μM hypericin and a similar light dose using a solar simulator, No LDH leakage was observed at hypericin concentrations up to 30 μM and visible light up to 144 J/cm². Light-and/or concentration-dependent increases in hemolysis, K⁺ leakage and formation of lipid hydroperoxides in red blood cell (RBC) membranes were observed, but at concentrations and light doses much greater than those required to induce cytotoxicity in fibroblasts. Lipid peroxidation and hemolysis occurred at 15 μM hypericin and 24 J/cm² (visible light source). Potassium ion leakage occurred at concentrations and light levels as low as 5 μM and 12 J/cm² or 15 μM and 4.8 J/cm² (visible light source) but was still a less sensitive indicator than fibroblast cytotoxicity. Evidence for both type I and type II reactions was shown in RBC membranes by TLC analysis of cholesterol products. In the absence of light, hypericin appears to be relatively nontoxic in the models tested.     

Novel syntheses of 3-anilino-pyrazin-2(1H)-ones and 3-anilino-quinoxalin-2-(1H)-ones via microwave-mediated Smiles rearrangement

In this Letter, we report a novel approach to the preparation of 3-anilino-pyrazin-2(1H)-ones and 3-anilino-quinoxalin-2(1H)-ones from the corresponding 3-halo pyrazin-2-amines and 3-haloquinoxalin-2-amines, using a microwave-mediated Smiles rearrangement.     

Sorption and desorption of phenanthrene onto iron, copper, and silicon dioxide nanoparticles

The sorption and desorption of phenanthrene by three engineered nanoparticles including nanosize zerovalent iron (NZVI), copper (NZVC), and silicon dioxide (NSiO2) were investigated. The sorption of phenanthrene onto NSiO2 was linear and reversible due to the hydrophilic properties of NSiO2. In comparison, sorption of phenanthrene onto NZVI and NZVC was nonlinear and irreversible, which was potentially due to the existence of significantly heterogeneous surface energy distribution patterns detected by a standard molecular probe technique. Naphthalene exerted significant competitive sorption with phenanthrene for NZVI and NZVC, and the isotherm of phenanthrene changed from being significantly nonlinear to nearly linear when naphthalene was simultaneously absorbed. A surface adsorption mechanism was proposed to explain the observed sorption and competition of phenanthrene on both NZVI and NZVC. In contrast, no competition was observed for sorption onto NSiO2. The sorption of phenanthrene on all three nanoparticles significantly decreased with increasing pH. The sorption irreversibility of phenanthrene on NZVI and NZVC were significantly enhanced with decreasing pH. A pH-dependent hydrophobic effect and dipole interactions between the charged surface (electron acceptors) and phenanthrene with electron-rich pi systems (electron donors) were proposed to explain the observed pH-dependent sorption.     

Investigation of copper-azamacrocyclic complexes by high-performance liquid chromatography

The use of copper radioisotopes in imaging and therapy has prompted an increased interest in chelators which form stable copper complexes, such as Cu(II)-azamacrocyclic complexes. The effects of charge, stability and the size of the macrocyclic backbone of the Cu(II)-azamacrocyclic complexes on biological behavior have been evaluated. Here we report a reversed-phase high-performance liquid chromatography (HPLC) method to separate several Cu(II)-azamacrocyclic complexes, including Cu(II) complexes of 1,4,8,11-tetraazacyclotetradecane-1,4,8,11-tetraacetic acid (TETA), 4,11-bis(carboxymethyl)-1,4,8,11-tetraazabicyclo[6.6.2]hexadecane (CB-TE2A) and 4,10-bis(carboxymethyl)-1,4,7,10-tetraazabicyclo[5.5.2]tetradecane (CB-DO2A). Absorbance at 280 nm was used to monitor the complexes as they eluted from the reversed-phase column. The effects of the concentration of the buffer, the pH of the buffered mobile phase and the concentration of the organic modifier, methanol, on the separation were investigated. Separation of these copper complexes by ion-pair HPLC with the use of a mass spectrometry-compatible ion-pair reagent, triethylammonium acetate, in the mobile phase at pH 6.3 is also presented. The reversed-phase chromatographic conditions utilized also allow the pK(a)s of Cu-TETA and the log(k'w) values of Cu-CB-TE2A, Cu-TETA and Cu-CB-DO2A to be estimated.     

A systematic study of carboxylic acids in negative ion mode electrospray ionisation mass spectrometry providing a structural model for ion suppression

We report a systematic investigation of the effects and structural requirements for ion suppression in negative ion mode electrospray ionisation mass spectrometry of a series of carboxylic acids and present a structural model rationalising ion suppression effects.     

Approaches to open fullerenes: synthesis and thermal stability of cis-1 bis(isobenzofuran) Diels-Alder adducts of C60

In a quest to form wider openings within the cage of the fullerene C60 through controlled bond-breaking reactions, we have examined the double saturation of adjacent C=C bonds within a six-membered ring of C60. We have investigated the double Diels-Alder cycloaddition of two tethered isobenzofurans to the fullerene C60. We obtained cis-1 adducts in good yields after reacting the methylene- or quinoxaline-tethered bis(isobenzofuran) precursors 2a-k with parent 3,6-dihydro-1,2,4,5-tetrazine (3b). The X-ray structure of the methylene-tethered bis(isobenzofuran)-C60 adduct 4b has been obtained; four-eclipsed substituents are held rigidly by the bicyclic addends. The cis-1 bis(isobenzofuran) bisadducts 4b and 4e-j are kinetically far more stable toward thermal retro-Diels-Alder fragmentation than are mono(isobenzofuran) adducts of C60, in solution and in the solid state as determined by 1H NMR spectroscopy or thermogravimetric analysis. A methodology for the reversible solubilization of other fullerene derivatives based on this work is also presented.     

Novel heterocycles. 7. Reaction of 2-chloronicotinonitrile with thioureas. Synthesis of the pyrido[2,3-d]pyrimido-[2,1-b][1,3]thiazine ring system

N,N'-Dimethylthiourea and 3,4,5,6-tetrahydro-2-pyrimidinethiol were allowed to react with 2-chloro-nicotinonitrile ( 1 ) and their products investigated by standard methods and by carbon-13 nmr. In both instances, displacement of the chlorine occurred by nitrogen not the sulfur of the thioureas. Secondary cyclizations occurred by attack of nitrogen on the nitrile to furnish 3a , and by sulfur on the nitrile to give 4b , a new ring system. Tricyclic 4b was hydrolyzed in dilute acid to give 5 , or alkylated with methyl iodide in the presence of sodium hydride to give the ring opened product 6 .