Approximation of the steepest descent direction for the O-D matrix adjustment problem

In this paper, a method to approximate the directions of Clarke's generalized gradient of the upper level function for the demand adjustment problem on traffic networks is presented. Its consistency is analyzed in detail. The theoretical background on which this method relies is the known property of proximal subgradients of approximating subgradients of proximal bounded and lower semicountinuous functions using the Moreau envelopes. A double penalty approach is employed to approximate the proximal subgradients provided by these envelopes. An algorithm based on partial linearization is used to solve the resulting nonconvex problem that approximates the Moreau envelopes, and a method to verify the accuracy of the approximation to the steepest descent direction at points of differentiability is developed, so it may be used as a suitable stopping criterion. Finally, a set of experiments with test problems are presented, illustrating the approximation of the solutions to a steepest descent direction evaluated numerically. Research supported under Spanish CICYT project TRA99-1156-C02-02.     

On the Iterated Biclique Operator

A biclique of a graph G is a maximal induced complete bipartite subgraph of G. The biclique graph of G, denoted by , is the intersection graph of the bicliques of G. We say that a graph G diverges (or converges or is periodic) under an operator F whenever ( for some m, or for some k and , respectively). Given a graph G, the iterated biclique graph of G, denoted by , is the graph obtained by applying the biclique operator k successive times to G. In this article, we study the iterated biclique graph of G. In particular, we classify the different behaviors of when the number of iterations k grows to infinity. That is, we prove that a graph either diverges or converges under the biclique operator. We give a forbidden structure characterization of convergent graphs, which yield a polynomial time algorithm to decide if a given graph diverges or converges. This is in sharp contrast with the situsation for the better known clique operator, where it is not even known if the corresponding problem is decidable. © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 181–190, 2013     

Design, synthesis, and biological evaluation of platensimycin analogues with varying degrees of molecular complexity

The molecular design, chemical synthesis, and biological evaluation of two distinct series of platensimycin analogues with varying degrees of complexity are described. The first series of compounds probes the biological importance of the benzoic acid subunit of the molecule, while the second series explores the tetracyclic cage domain. The biological data obtained reveal that, while the substituted benzoic acid domain of platensimycin is a highly conserved structural motif within the active compounds with strict functional group requirements, the cage domain of the molecule can tolerate considerable structural modifications without losing biological action. These findings refine our present understanding of the platensimycin pharmacophore and establish certain structure-activity relationships from which the next generation of designed analogues of this new antibiotic may emerge.     

H2‐Fueled ATP Synthesis on an Electrode: Mimicking Cellular Respiration

ATP, the molecule used by living organisms to supply energy to many different metabolic processes, is synthesized mostly by the ATPase synthase using a proton or sodium gradient generated across a lipid membrane. We present evidence that a modified electrode surface integrating a NiFeSe hydrogenase and a F₁F₀‐ATPase in a lipid membrane can couple the electrochemical oxidation of H₂ to the synthesis of ATP. This electrode‐assisted conversion of H₂ gas into ATP could serve to generate this biochemical fuel locally when required in biomedical devices or enzymatic synthesis of valuable products.     

Gas‐Phase Infrared Spectroscopy of Substituted Cyanobutadiynes: Roles of the Bromine Atom and Methyl Group as Substituents

The IR spectra of 5‐bromo‐2,4‐pentadiynenitrile (Br?C≡C?C≡C?CN) and 2,4‐hexadiynenitrile (CH₃?C≡C?C≡C?CN), a compound of interstellar interest, have been recorded within the 4000–500 cm^?1 spectral region and calculated by means of high‐level ab initio and density functional calculations. Although the calculated structures of both compounds are rather similar, there are very subtle differences, mainly in the strength of the C≡C bond not directly bound to the substituent. These subtle bonding differences are reflected in small, but not negligible, differences in the electron density at the corresponding bond critical points, and, more importantly, are reflected in the IR spectra. Indeed, the IR spectrum for the bromine derivative presents two well‐differentiated strong bands around 2250 cm^?1, whereas for the methyl derivative both absorptions coalesce in a single band. These bands correspond in both cases to the coupling between C≡C and C≡N stretching displacements. A third, very weak, band also associated with C≡C and C≡N coupled stretches is observed for the bromine derivative, but not for the methyl one, owing to its extremely low intensity.     

Tetrahydroxy-p-benzoquinone as a source of polydentate O-donor ligands. Synthesis, crystal structure, and magnetic properties of the [Cu(bpy)(dhmal)]2 dimer and the two-dimensional [{SiW12O40}{Cu2(bpy)2(H2O)(ox)}2].16H2O inorganic-metalorganic hybrid

The use of tetrahydroxy-p-benzoquinone as a slow source of dihydroxymalonato and oxalato ligands led to the isolation under open-air mild reaction conditions of five different compounds, two of them prepared for the first time: [Cu(bpy)(dhmal)]2 (1) and [{SiW12O40}{Cu2(bpy)2(H2O)(ox)}2].16H2O (5) (bpy, 2,2'-bipyridine; dhmal, dihydroxymalonate; ox, oxalate). A possible mechanism for the oxidation of the benzoquinone to give the croconate dianion, which undergoes further ring-opening oxidation to decompose into dihydroxymalonate and oxalate, is proposed. All compounds have been characterized by elemental analysis, thermogravimetry, infrared spectroscopy, and powder X-ray diffraction. Single-crystal X-ray diffraction, electron paramagnetic resonance, and magnetic susceptibility measurements have been performed for compounds 1 and 5. A complete band assignment of the experimental FT-IR spectra is given through comparison with the ones calculated using density functional theory (DFT). The neutral dimer 1 constitutes the first structurally characterized example of a transition metal-dhmal complex, and it contains two copper atoms bridged by two dihydroxymalonato ligands acting in a mu2-kappa3O,O',O":kappa1O coordination fashion, so that an equatorial-axial Cu2(mu2-O)2 rhomboid core is formed. On the other hand, the inorganic-metalorganic hybrid compound 5 shows a two-dimensional arrangement of Keggin polyanions linked by one of the Cu atoms of the oxalate cationic dimers to give layers parallel to the (10) plane, the remaining ox-Cu-bpy fragments acting as interlamellar separators. In both cases, magnetic and EPR results are discussed with respect to the crystal structure of the compounds and, for compound 1, also with respect to DFT calculations of the exchange coupling constant.     

Synthesis and Crystal Structure of Peptide‐2,2′‐Biphenyl Hybrids

1,1′‐Biphenyl derivatives with amino acid/peptide substitution at C(2) and C(2′) (‘peptide‐biphenyl hybrids', 6 – 8 ) have been prepared by direct N‐acylation of amino acid/peptide derivatives with 1,1′‐biphenyl‐2,2′‐dicarbonyl dichloride ( 5 ). Both conformers, which arise from the rotation around the aryl aryl bond, have been detected by ¹H‐NMR spectroscopy. Single atropisomers of each 6 ((R)‐configuration at the stereogenic axis) and 7 ((S)‐configuration at the stereogenic axis) have been obtained in quantitative yield by slow evaporation of methanolic solutions. The procedures are dynamic atropselective resolutions (asymmetric transformations of the second kind). The crystal structures of the peptide‐biphenyl hybrids 6 and 7 show highly ordered molecular and supramolecular structures with extensive intramolecular and intermolecular H‐bonding.