The Generalized Arc Routing Problem

This paper focuses on the generalized arc routing problem. This problem is stated on an undirected graph in which some clusters are defined as pairwise-disjoint connected subgraphs, and a route is sought that traverses at least one edge of each cluster. Broadly speaking, the generalized arc routing problem is the arc routing counterpart of the generalized traveling salesman problem, where the set of vertices of a given graph is partitioned into clusters and a route is sought that visits at least one vertex of each cluster. A mathematical programming formulation that exploits the structure of the problem and uses only binary variables is proposed. Facets and families of valid inequalities are presented for the polyhedron associated with the formulation and the corresponding separation problem studied. The numerical results of a series of computational experiments with an exact branch and cut algorithm are presented and analyzed.     

Synthesis and Comprehensive Characterization of Hydrated Alkaline Earth Metal Salts of 5‐Amino‐1H‐tetrazole

Hydrated alkaline earth metal salts of 5‐amino‐1H‐tetrazole ( B ) were synthesized by reaction of B with a suitable metal hydroxide in water. All compounds were fully characterized by analytical (elemental analysis and mass spectrometry) and spectroscopic (IR, Raman, ¹H and ¹³C NMR) methods. Additionally, the crystal structures of the magnesium [ 1· 4H₂O: triclinic, P$\bar {1}$ , a = 5.940(1) Å, b = 7.326(1) Å,c = 7.383(1) Å, α = 106.10(1)°, β = 106.51(1)°, γ = 111.85(1)°, V = 258.0(1) ų], calcium [ 2· 6H₂O: monoclinic, P2₁/m, a = 6.904(1) Å,b = 6.828(1) Å, c = 10.952(2) Å, β = 94.50(2)°, V = 514.6(1) ų], and strontium [ 3· 6H₂O: orthorhombic, Cmcm, a = 6.987(1) Å, b = 28.394(2) Å, c = 7.007(1) Å, V = 1390.3(2) ų] were determined by low temperature X‐ray diffraction. Additionally, the (gas phase) structure of the 5‐amino‐1H‐tetrazole anion ([ B ]^–) was also studied by natural bond orbital (NBO) analysis [B3LYP/6‐31+G(d,p)]. Lastly, standard tests were used to determine the sensitivity towards impact, friction, and electrostatic discharge of the compounds and the thermal stability was assessed by differential scanning calorimetry (DSC) analysis.     

Total synthesis of the Amaryllidaceae alkaloid clivonine

Two syntheses of the Amaryllidaceae alkaloid clivonine (1) are described. Both employ previously reported 7-arylhydrindane 6 as an intermediate but differ in the method employed for subsequent introduction of what becomes the ring-B lactone carbonyl carbon (C7). The synthesis featuring a Bischler-Napieralski reaction for this transformation constitutes the first asymmetric synthesis of natural (+)-clivonine. Crystal structures for compounds (±)-13, (±)-16, (-)-20 and (±)-28 are also reported.     

Scoring by intermolecular pairwise propensities of exposed residues (SIPPER): a new efficient potential for protein-protein docking

A detailed and complete structural knowledge of the interactome is one of the grand challenges in Biology, and a variety of computational docking approaches have been developed to complement experimental efforts and help in the characterization of protein-protein interactions. Among the different docking scoring methods, those based on physicochemical considerations can give the maximum accuracy at the atomic level, but they are usually computationally demanding and necessarily noisy when implemented in rigid-body approaches. Coarser-grained knowledge-based potentials are less sensitive to details of atomic arrangements, thus providing an efficient alternative for scoring of rigid-body docking poses. In this study, we have extracted new statistical potentials from intermolecular pairs of exposed residues in known complex structures, which were then used to score protein-protein docking poses. The new method, called SIPPER (scoring by intermolecular pairwise propensities of exposed residues), combines the value of residue desolvation based on solvent-exposed area with the propensity-based contribution of intermolecular residue pairs. This new scoring function found a near-native orientation within the top 10 predictions in nearly one-third of the cases of a standard docking benchmark and proved to be also useful as a filtering step, drastically reducing the number of docking candidates needed by energy-based methods like pyDock.     

Analysis of the effects of N-substituents on some aspects of the aromaticity of imidazoles and pyrazoles

The influence of the N-substituent on the aromaticity of azoles is a subject that has not yet been addressed in detail, in contrast to the good understanding of the corresponding C-substitution. In the present work, we analyze the aromaticities of a series of 1,2- and 1,3-azoles (pyrazoles and imidazoles, respectively) with the N-substituents NH(2), OH, Cl, SH, H, NO(2), CN, SO(2)F, SO(2)CF(3), and N(SO(2)CF(3))(2), which are also compared with the aromaticities of the corresponding substituted benzene series. The larger stabilitiy of the imidazole ring is due not to a higher aromaticity, but rather to the weakness of the N-N bond in the pyrazole series. The aromaticity of azoles was found to be significantly less robust to N-substitutions than that of their C-substituted benzene counterparts.     

Alkaloids from Hippeastrum papilio

Galanthamine, an acetylcholinesterase inhibitor marketed as a hydrobromide salt (Razadyne?, Reminyl?) for the treatment of Alzheimer's disease (AD), is obtained from Amaryllidaceae plants, especially those belonging to the genera Leucojum, Narcissus, Lycoris and Ungernia. The growing demand for galanthamine has prompted searches for new sources of this compound, as well as other bioactive alkaloids for the treatment of AD. In this paper we report the isolation of the new alkaloid 11β-hydroxygalanthamine, an epimer of the previously isolated alkaloid habranthine, which was identified using NMR techniques. It has been shown that 11β-hydroxygalanthamine has an important in vitro acetylcholinesterase inhibitory activity. Additionally, Hippeastrum papilio yielded substantial quantities of galanthamine.     

Resonance tongues in the quasi-periodic Hill-Schrödinger equation with three frequencies

In this paper we investigate numerically the following Hill’s equation x″ + (a + bq(t))x = 0 where $ q(t) = \cos t + \cos \sqrt {2t} + \cos \sqrt {3t} $ is a quasi-periodic forcing with three rationally independent frequencies. It appears, also, as the eigenvalue equation of a Schrödinger operator with quasi-periodic potential. Massive numerical computations were performed for the rotation number and the Lyapunov exponent in order to detect open and collapsed gaps, resonance tongues. Our results show that the quasi-periodic case with three independent frequencies is very different not only from the periodic analogs, but also from the case of two frequencies. Indeed, for large values of b the spectrum contains open intervals at the bottom. From a dynamical point of view we numerically give evidence of the existence of open intervals of a, for large b, where the system is nonuniformly hyperbolic: the system does not have an exponential dichotomy but the Lyapunov exponent is positive. In contrast with the region with zero Lyapunov exponents, both the rotation number and the Lyapunov exponent do not seem to have square root behavior at endpoints of gaps. The rate of convergence to the rotation number and the Lyapunov exponent in the nonuniformly hyperbolic case is also seen to be different from the reducible case.