The prize collecting Steiner tree problem: models and Lagrangian dual optimization approaches

We propose a generalized version of the Prize Collecting Steiner Tree Problem (PCSTP), which offers a fundamental unifying model for several well-known -hard tree optimization problems. The PCSTP also arises naturally in a variety of network design applications including cable television and local access networks. We reformulate the PCSTP as a minimum spanning tree problem with additional packing and knapsack constraints and we explore various nondifferentiable optimization algorithms for solving its Lagrangian dual. We report computational results for nine variants of deflected subgradient strategies, the volume algorithm (VA), and the variable target value method used in conjunction with the VA and with a generalized Polyak–Kelley cutting plane technique. The performance of these approaches is also compared with an exact stabilized constraint generation procedure.     

A parallel extended GCD algorithm

A new parallel extended GCD algorithm is proposed. It matches the best existing parallel integer GCD algorithms of Sorenson and Chor and Goldreich, since it can be achieved in O(n/logn) time using at most n¹⁺ processors on CRCW PRAM. Sorenson and Chor and Goldreich both use a modular approach which consider the least significant bits. By contrast, our algorithm only deals with the leading bits of the integers u and v, with uv. This approach is more suitable for extended GCD algorithms since the coefficients of the extended version a and b, such that au+bv=gcd(u,v), are deeply linked with the order of magnitude of the rational v/u and its continuants. Consequently, the computation of such coefficients is much easier.     

Positive Elements and Automatic Continuity of Algebra Morphisms

We use positive elements of Hermitian algebras to give results on automatic continuity of algebra morphisms. Consequences and applications are also given.      

Fluorine-Boosted Kinetic and Selective Molecular Sieving of C6 Derivatives

Porous molecular sorbents have excellent selectivity towards hydrocarbon separation with energy saving techniques. However, to realize commercialization, molecular sieving processes should be faster and more efficient compared to extended frameworks. In this work, we show that utilizing fluorine to improve the hydrophobic profile of leaning pillararenes affords a substantial kinetic selective adsorption of benzene over cyclohexane (20 : 1 for benzene). The crystal structure shows a porous macrocycle that acts as a perfect match for benzene in both the intrinsic and extrinsic cavities with strong interactions in the solid state. The fluorinated leaning pillararene surpasses all reported organic molecular sieves and is comparable to the extended metal–organic frameworks that were previously employed for this separation such as UIO-66. Most importantly, this sieving system outperformed the well-known zeolitic imidazolate frameworks under low pressure, which opens the door to new generations of molecular sieves that can compete with extended frameworks for more sustainable hydrocarbon separation.     

Clustering Six Electrons within “Dawson-Like” Polyoxometalate: An Open Route toward Its Post-functionalization

Super-reduction of polyoxometalates (POMs) in solution is of fundamental interest for designing innovative energy storage systems. In this article, we show that the “Dawson-like” POM can undergo a disproportionation process during its massive electron uptake, leading to species containing three metal-metal bonds as evidenced by X-ray diffraction, multi-nuclear magnetic resonance spectroscopy (¹H and ¹⁸³W NMR), extended X-ray absorption fine structure (EXAFS), UV/Vis, and voltammetry techniques. This result indicates that electron storing within metal-metal bonds is not a unique property of Keggin-type POM as postulated since the 70s. Besides, we demonstrate that the presence of an electron-rich triad in the “Dawson-like” POM allows its post-functionalization with additional tungstate ions, generating a chiral molecule that is also the largest W^IV-containing POMs known to date.     

Synthesis of new quinoxalinophenazinediones and tetrahydrobenzodipyrrolotetrones of biological interest

The reaction of two equivalents of sodium azide with diarylaminodibromo-p-benzoquinone (I) in DMF for 15–24 h produced quinoxalinophenazinediones together with a byproduct identified as diarylaminodiaminobenzoquinone. On the other hand, the reaction of bromanil with active methylenes, such as diethyl malonate and ethyl acetoacetate, resulted in disubstitution products which, on treatment with primary amines, cyclized into benzodipyrroletetrones. Comparative antifungal and antibacterial studies were made.     

Properties of poly(styrene/alpha-tert-butoxy-omega-vinylbenzyl-polyglycidol) microspheres suspended in water. Effect of sodium chloride and temperature on particle diameters and electrophoretic mobility

Hydrodynamic and electrophoretic properties of core-shell poly(styrene/alpha- tert-butoxy-omega-vinylbenzyl-polyglycidol) (P(S/PGL)) microspheres suspended in water are described. The microspheres were obtained by surfactant-free emulsion copolymerization of styrene and alpha- tert-butoxy-omega-vinylbenzyl-polyglycidol macromonomer ( M n = 2800, M w/ M n = 1.05). The process yielded microspheres with number average diameter D n = 270 nm and with low diameter dispersity index D w/ D n = 1.01. Shells of P(S/PGL) microspheres were enriched in polyglycidol. Molar fraction of polyglycidol monomeric units in the shells (determined by X-ray photoelectron spectroscopy) was equal to 0.34, which is much higher than the average molar fraction of polyglycidol monomeric units in whole particles of 0.048. Influences of NaCl concentration and temperature on P(S/PGL) microsphere diameters and on their electrophoretic mobility were investigated. It was found that hydrodynamic diameter of P(S/PGL) microspheres, determined by photon correlation spectroscopy, decreased significantly when temperature did exceed a certain value (transition temperature, T t). It has been found that the decrease is more pronounced for higher concentrations of NaCl in the medium. For microspheres suspended in 10 (-1) M NaCl, the hydrodynamic diameter decreased by 8% whereas for the same particles in pure water the diameter decreased by 5.2%. The process of shrinkage was fully reversible. Values of T t for P(S/PGL) microspheres were lower for higher concentrations of NaCl. Adjustment of salt concentration allowed controlling T t in a range from 44.4 to 49.9 degrees C. 13C NMR relaxation time measurements (T 1) for carbon atoms in polyglycidol macromonomer revealed that T 1 did increase with increasing temperature (in temperature range from 25 to 75 degrees C) indicating higher motion of chains at higher temperature. Addition of NaCl did not induce a substantial change of T 1 in the mentioned temperature range. The swelling-deswelling properties of P(S/PGL) microspheres' interfacial layer affected adsorption of P(S/PGL) particles on modified with (3-aminopropyl)triethoxysilane mica. It was shown that the deposition of P(S/PGL) microspheres at 25 degrees C on mica led to formation of two-dimensional crystal-shape assemblies, whereas at 60 degrees C (far above T t = 49.8 degrees C in H2O) the microspheres were randomly adsorbed without formation of colloidal crystal assemblies.     

Conformational preferences of the aglycon moiety in models and analogs of GlcNAc-Asn linkage: crystal structures and ab initio quantum chemical calculations of N-(beta-D-glycopyranosyl)haloacetamides

The biological addition of oligosaccharide structures to asparagine residues of N-glycoproteins influences the properties and bioactivities of these macromolecules. The linkage region constituents, 2-acetamino-2-deoxy-beta-D-glucopyranose monosaccharide (GlcNAc) and L-asparagine amino acid (Asn), are conserved in the N-glycoproteins of all eukaryotes. In order to gain information about the structure and dynamics of glycosylated proteins, two chloroacetamido sugars, Glc betaNAcNHCOCH2Cl and Man betaNHCOCH2Cl, have been synthesized, and their crystal structures have been solved. Structural comparison with a series of other models and analogs gives insight about the influence of the N-acetyl group at position C2 on the conformation of the glycan-peptide linkage at C1. Interestingly, this N-acetyl group also influences the packing and network of hydrogen bonds with involvement in weak hydrogen bonds C-H...X that are of biological importance. DFT ab initio calculations performed on a series of models and analogs also confirm that the GlcNAc derivatives present different preferred conformation about the N-CO-CH2-X (chi2) torsion angle of the glycan-peptide linkage, when compared to other monosaccharide derivatives. The energy profiles that have been obtained will be useful for parametrization of molecular mechanics force-field. The conjunction of crystallographic and computational chemistry studies provides arguments for the structural effect of the N-acetyl group at C2 in establishing an extended conformation that presents the oligosaccharide away from the protein surface.