Generating highly balanced sudoku problems as hard problems

Sudoku problems are some of the most known and enjoyed pastimes, with a never diminishing popularity, but, for the last few years those problems have gone from an entertainment to an interesting research area, a twofold interesting area, in fact. On the one side Sudoku problems, being a variant of Gerechte Designs and Latin Squares, are being actively used for experimental design, as in Bailey et al. (Am. Math. Mon. 115:383–404, 2008; J. Agron. Crop Sci. 165:121–130, 1990), Morgan (Latin squares and related experimental designs. Wiley, New York, 2008) and Vaughan (Electron. J. Comb. 16, 2009). On the other hand, Sudoku problems, as simple as they seem, are really hard structured combinatorial search problems, and thanks to their characteristics and behavior, they can be used as benchmark problems for refining and testing solving algorithms and approaches. Also, thanks to their high inner structure, their study can contribute more than studies of random problems to our goal of solving real-world problems and applications and understanding problem characteristics that make them hard to solve. In this work we use two techniques for solving and modeling Sudoku problems, namely, Constraint Satisfaction Problem (CSP) and Satisfiability Problem (SAT) approaches. To this effect we define the Generalized Sudoku Problem (GSP), where regions can be of rectangular shape, problems can be of any order, and solution existence is not guaranteed. With respect to the worst-case complexity, we prove that GSP with block regions of m rows and n columns with m≠n is NP-complete. For studying the empirical hardness of GSP, we define a series of instance generators, that differ in the balancing level they guarantee between the constraints of the problem, by finely controlling how the holes are distributed in the cells of the GSP. Experimentally, we show that the more balanced are the constraints, the higher the complexity of solving the GSP instances, and that GSP is harder than the Quasigroup Completion Problem (QCP), a problem generalized by GSP. Finally, we provide a study of the correlation between backbone variables—variables with the same value in all the solutions of an instance—and hardness of GSP.     

Synthesis and glycosidase inhibitory activity of isourea-type bicyclic sp2-iminosugars related to galactonojirimycin and allonojirimycin

A series of sp²-iminosugars featuring a fused piperidine–isourea bicyclic core and hydroxylation profiles of stereochemical complementarity with the ‘classical’ iminosugars galactonojirimycin and allonojirimycin have been prepared and their inhibitory activity evaluated against a panel of commercial glycosidases. The synthetic methodology involves 2-aminooxazoline pseudo-C-nucleosides, accessible from vic-hydroxycarbodiimide precursors, as key intermediates and is compatible with molecular diversity-oriented strategies. Alkyl, aryl and glycosyl substituents have been incorporated in order to assess the potential of non-glyconic interactions to modulate the enzyme selectivity. All the galactonojirimycin derivatives behaved as potent competitive inhibitors of β-glucosidases. The inhibition potency was higher for aliphatic substituents (in the nM range), but the highest selectivity within β-glucosidase isoenzymes was achieved for a N′-glucopyranosyl pseudodisaccharide analogue. Going from d-galacto to d-allo configuration further increased enzyme selectivity, but strongly penalized the inhibition potency.     

Synthesis of High‐Mannose Oligosaccharide Analogues through Click Chemistry: True Functional Mimics of Their Natural Counterparts Against Lectins?

Terminal “high‐mannose oligosaccharides” are involved in a broad range of biological and pathological processes, from sperm‐egg fusion to influenza and human immunodeficiency virus infections. In spite of many efforts, their synthesis continues to be very challenging and actually represents a major bottleneck in the field. Whereas multivalent presentation of mannopyranosyl motifs onto a variety of scaffolds has proven to be a successful way to interfere in recognition processes involving high‐mannose oligosaccharides, such constructs fail at reproducing the subtle differences in affinity towards the variety of protein receptors (lectins) and antibodies susceptible to binding to the natural ligands. Here we report a family of functional high‐mannose oligosaccharide mimics that reproduce not only the terminal mannopyranosyl display, but also the core structure and the branching pattern, by replacing some inner mannopyranosyl units with triazole rings. Such molecular design can be implemented by exploiting “click” ligation strategies, resulting in a substantial reduction of synthetic cost. The binding affinities of the new “click” high‐mannose oligosaccharide mimics towards two mannose specific lectins, namely the plant lectin concanavalin A (ConA) and the human macrophage mannose receptor (rhMMR), have been studied by enzyme‐linked lectin assays and found to follow identical trends to those observed for the natural oligosaccharide counterparts. Calorimetric determinations against ConA, and X‐ray structural data support the conclusion that these compounds are not just another family of multivalent mannosides, but real “structural mimics” of the high‐mannose oligosaccharides.     

Lax entwining structures,groupoid algebras and cleft extensions

For an algebra A, a coalgebra C and a lax entwining structure (A, C, ψ), in this paper we introduce the notions of lax C-Galois extension with normal basis and lax C-cleft extension and we prove that these notions are equivalent if the functor A ? — preserve coequalizers.     

Influence of Ester versus Amide Linkers on the Supramolecular Polymerization Mechanisms of Planar BODIPY Dyes

We report the H‐type supramolecular polymerization of two new hydrophobic BODIPY derivatives equipped with ester and amide linkages. Whereas the ester‐containing BODIPY derivative undergoes an isodesmic supramolecular polymerization in which the monomers are parallel‐oriented, the replacement of the ester by amide groups leads to a highly cooperative self‐assembly process into H‐type aggregates with a rotational displacement of the dye molecules within the stack. The dye organization imposed by simultaneous π–π and hydrogen bonding interactions is the driving force for the cooperative supramolecular polymerization, whereas the absence of additional hydrogen bonds for the ester‐containing moiety does not suffice to induce cooperative phenomena.     

The outstanding ability of nanosilica to stabilize dispersions of Nylon 6 droplets in a polypropylene matrix

The effectiveness of hydrophobically modified nanosilica (NS) as interfacial modifying agent for immiscible polymer blends is evaluated. Blends of polypropylene (PP) with 20% of polyamide 6 (PA) and 5% hydrophobic NS were prepared by melt mixing. Compression molded sheets and extruded films were evaluated by scanning electron microscopy, transmission electron microscopy, tensile testing, and rheological measurements. Hydrophobic NS particles strongly reduce the polydispersity and droplet size of the dispersed phase, as a result of their preferential location at the interface. NS promotes outstanding stability of blend dispersion regardless of the processing or post‐processing technique employed. The viscoelastic terminal zone shows a plateau for PP/PA/NS, which corresponds to a suspension‐like behavior. Under large amplitude oscillatory shear, the increment in the non‐linearity parameter Q evidences the interactions between NS and blend components. Therefore, NS is an excellent morphological stabilizer that prevents coalescence, but cannot promote interfacial adhesion between immiscible PP and PA phases. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1567–1579     

GRASP and Path Relinking for the Clustered Prize-collecting Arc Routing Problem

The Clustered Prize-collecting Arc Routing Problem is an arc routing problem where each demand edge is associated with a profit which is collected once if the edge is serviced, independently of the number of times it is traversed. It is further required that if a demand edge is serviced, then all the demand edges of its component are also serviced. This paper presents GRASP and Path Relinking heuristics for the Clustered Prize-collecting Arc Routing Problem. For the constructive phase of the GRASP two different strategies are considered. One of them follows a bottom-up style whereas the other one is a top-down procedure. The best solutions obtained with both strategies are used as elite solutions for the Path Relinking. The results of extensive computational experiments are presented and analyzed.     

Magnetic Anisotropy in “Scorpionate” First‐Row Transition‐Metal Complexes: A Theoretical Investigation

In this work we have analyzed in detail the magnetic anisotropy in a series of hydrotris(pyrazolyl)borate (Tp^?) metal complexes, namely [VTpCl]⁺, [CrTpCl]⁺, [MnTpCl]⁺, [FeTpCl], [CoTpCl], and [NiTpCl], and their substituted methyl and tert‐butyl analogues with the goal of observing the effect of the ligand field on the magnetic properties. In the [VTpCl]⁺, [CrTpCl]⁺, [CoTpCl], and [NiTpCl] complexes, the magnetic anisotropy arises as a consequence of out‐of‐state spin–orbit coupling, and covalent changes induced by the substitution of hydrogen atoms on the pyrazolyl rings does not lead to drastic changes in the magnetic anisotropy. On the other hand, much larger magnetic anisotropies were predicted in complexes displaying a degenerate ground state, namely [MnTpCl]⁺ and [FeTpCl], due to in‐state spin–orbit coupling. The anisotropy in these systems was shown to be very sensitive to perturbations, for example, chemical substitution and distortions due to the Jahn–Teller effect. We found that by substituting the hydrogen atoms in [MnTpCl]⁺ and [FeTpCl] by methyl and tert‐butyl groups, certain covalent contributions to the magnetic anisotropy energy (MAE) could be controlled, thereby achieving higher values. Moreover, we showed that the selection of ion has important consequences for the symmetry of the ground spin–orbit term, opening the possibility of achieving zero magnetic tunneling even in non‐Kramers ions. We have also shown that substitution may also contribute to a quenching of the Jahn–Teller effect, which could significantly reduce the magnetic anisotropy of the complexes studied.