Extensions of the Petal Method for Vehicle Routeing

The petal method for vehicle routeing imposes special structure on the form of a feasible route. In this paper we show that by extending the definition of a petal route, more general forms of vehicle route can be generated without invalidating the important underlying property that optimal petal solutions can be produced very easily. It will also be shown that the optimal generalized petal solution can be produced efficiently by multiple applications of a shortest path algorithm.     

New Computational Results with a Dynamic Programming Approach for Product Selection and Supermarket Shelf-Space Allocation

This study reports on new computational results relating to a dynamic programming approach that optimally selects among a given set of products and allocates integer shelf-space units to the products in supermarkets. The computational results are reported for large problems that have been solved on an IBM-PC AT microcomputer.     

A quality index for reference mass spectra

A numerical rating for evaluating the quality of reference mass spectra used for retrieval and interpretive applications is proposed. The overall quality index is the product of seven quality factors: (1) source of the spectrum; (2) ionization conditions; (3) higher molecular weight impurities; (4) illogical neutral losses; (5) isotopic abundance accuracy; (6) number of peaks; and (7) lower mass limit of peaks. For quality factor 6 the number of peaks of abundances ≥1% was found to correspond to 15 more than the number of atoms in the molecule with a correlation coefficient of 0.482. The program has been found useful in preparing a data base of 41429 mass spectra; for the majority of spectra judged to be unsatisfactory by the program this arose from a low quality factor 6 value (too few peaks).     

Isotropic C6, C8 and C10 interaction coefficients for CH4, C2H6, C3H8, n-C4H10 and cyclo-C3H6

The non-empirical generalized Kirkwood, Unsöld, and the single-Δ Unsöld methods (with double-zeta quality SCF wave-functions) are used to calculate isotropic dispersion (and induction) energy coefficients C_2n, with n ? 5, for interactions involving ground state CH₄, C₂H₆, C₃H₈, n-C₄H₁₀ and cyclo-C₃H₆. Results are also given for the related multipole polarizabilities α_l, multipole sums S₁/(0) and S₁(?1) which are evaluated using sum rules, and the permanent multipole moments. for l = 1 (dipole) to l = 3 (octupole). Estimates of the reliability of the non-empirical methods, for the type of molecules considered, are obtained by a comparison with accurate literature values of α₁S₁(?1) and C₆. This, and the asymptotic properties of the multipolar expansion of the dispersion energy, the use to discuss recommended representation for the isotropic long range interaction energies through R^?10 where R is the intermolecular separation.     

Generating Cuts from Surrogate Constraint Analysis for Zero-One and Multiple Choice Programming

This paper presents a new surrogate constraint analysis that givesrise to a family of strong valid inequalities calledsurrogate-knapsack (S-K) cuts. The analytical procedure presentedprovides a strong S-K cut subject to constraining the values ofselected cut coefficients, including the right-hand side. Ourapproach is applicable to both zero-one integer problems and problemshaving multiple choice (generalized upper bound) constraints. We alsodevelop a strengthening process that further tightens the S-K cutobtained via the surrogate analysis. Building on this, we develop apolynomial-time separation procedure that successfully generates anS-K cut that renders a given non-integer extreme point infeasible. Weshow how sequential lifting processes can be viewed in our framework,and demonstrate that our approach can obtain facets that are notavailable to standard lifting methods. We also provide a relatedanalysis for generating fast cuts. Finally, we presentcomputational results of the new S-K cuts for solving 0-1 integerprogramming problems. Our outcomes disclose that the new cuts arecapable of reducing the duality gap between optimal continuous andinteger feasible solutions more effectively than standard liftedcover inequalities, as used in modern codes such as the CPLEX mixed0-1 integer programming solver.     

An undecidable property of definite integrals

We show that it is undecidable whether the definite contour multiple integral of an elementary meromorphic function is zero over an everywhere real analytic manifold on which it is analytic.

     

Reconstitution of a new cysteine biosynthetic pathway in Mycobacterium tuberculosis

A new pathway for cysteine biosynthesis has been elucidated in Mycobacterium tuberculosis. This pathway involves a protein-bound thiocarboxylate (CysO-SH) as the sulfide donor, similar to thiamin biosynthesis. Cysteine synthase M (CysM) catalyzes the addition of cysteine to the carboxy terminus of the protein-bound thiocarboxylate to generate a CysO-cysteine adduct. A protease, Mec+, hydrolyzes the CysO-cysteine adduct to release cysteine and regenerate CysO. Mec+ contains a JAMM motif, and this work provides the first functional characterization of the JAMM motif in prokaryotes. MoeZ, a paralogue of ThiF, has been shown to transfer sulfur onto CysO.