Relative hyperbolicity and Artin groups

This paper considers the question of relative hyperbolicity of an Artin group with regard to the geometry of its associated Deligne complex. We prove that an Artin group is weakly hyperbolic relative to its finite (or spherical) type parabolic subgroups if and only if its Deligne complex is a Gromov hyperbolic space. For a two-dimensional Artin group the Deligne complex is Gromov hyperbolic precisely when the corresponding Davis complex is Gromov hyperbolic, that is, precisely when the underlying Coxeter group is a hyperbolic group. For Artin groups of FC type we give a sufficient condition for hyperbolicity of the Deligne complex which applies to a large class of these groups for which the underlying Coxeter group is hyperbolic. The key tool in the proof is an extension of the Milnor-Svarc Lemma which states that if a group G admits a discontinuous, co-compact action by isometries on a Gromov hyperbolic metric space, then G is weakly hyperbolic relative to the isotropy subgroups of the action.      

On Estimation in Interception Endgames

The paper presents an overview of the different errors created in an interception endgame by the measurement noise and the need of using an estimator in the guidance loop. Approaches for reducing the effects of the estimation error are described and some directions for further investigations are pointed out.     

Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function

A novel and robust automated docking method that predicts the bound conformations of flexible ligands to macromolecular targets has been developed and tested, in combination with a new scoring function that estimates the free energy change upon binding. Interestingly, this method applies a Lamarckian model of genetics, in which environmental adaptations of an individual's phenotype are reverse transcribed into its genotype and become heritable traits (sic). We consider three search methods, Monte Carlo simulated annealing, a traditional genetic algorithm, and the Lamarckian genetic algorithm, and compare their performance in dockings of seven protein–ligand test systems having known three-dimensional structure. We show that both the traditional and Lamarckian genetic algorithms can handle ligands with more degrees of freedom than the simulated annealing method used in earlier versions of AUTO DOCK , and that the Lamarckian genetic algorithm is the most efficient, reliable, and successful of the three. The empirical free energy function was calibrated using a set of 30 structurally known protein–ligand complexes with experimentally determined binding constants. Linear regression analysis of the observed binding constants in terms of a wide variety of structure-derived molecular properties was performed. The final model had a residual standard error of 9.11 kJ mol⁻¹ (2.177 kcal mol⁻¹) and was chosen as the new energy function. The new search methods and empirical free energy function are available in AUTO DOCK , version 3.0. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1639–1662, 1998     

Fenchone Derivatives as a Novel Class of CB2 Selective Ligands: Design,Synthesis, X-ray Structure and Therapeutic Potential

A series of novel cannabinoid-type derivatives were synthesized by the coupling of (1S,4R)-(+) and (1R,4S)-(−)-fenchones with various resorcinols/phenols. The fenchone-resorcinol derivatives were fluorinated using Selectfluor and demethylated using sodium ethanethiolate in dimethylformamide (DMF). The absolute configurations of four compounds were determined by X-ray single crystal diffraction. The fenchone-resorcinol analogs possessed high affinity and selectivity for the CB2 cannabinoid receptor. One of the analogues synthesized, 2-(2′,6′-dimethoxy-4′-(2″-methyloctan-2″-yl)phenyl)-1,3,3-trimethylbicyclo[2.2.1]heptan-2-ol (1d), had a high affinity (K_i = 3.51 nM) and selectivity for the human CB2 receptor (hCB2). In the [³⁵S]GTPγS binding assay, our lead compound was found to be a highly potent and efficacious hCB2 receptor agonist (EC₅₀ = 2.59 nM, E_(max) = 89.6%). Two of the fenchone derivatives were found to possess anti-inflammatory and analgesic properties. Molecular-modeling studies elucidated the binding interactions of 1d within the CB2 binding site.     

The order-disorder transformation at supercooled melt/crystal transition region of binary melts (I) the master equation

Binary melts crystallizing with almost perfectly ordered structures if exposed to conditions close to thermodynamic equilibrium exhibit an increasing tendency to form metastable crystals with increasing disorder when these alloys crystallize on the growth conditions of supercooling. Based on the model of a two-phase transition zone separating a growing crystal from its non-solid surrounding a kinetic master equation is formulated describing the kinetics of competitive atomic exchange processes within the transition region. The theory considers the case of simple cubic structure with equal particle numbers of two components that form a NaCl-type lattice at the state of perfect order. In a subsequent paper solutions of the master equation obtained for steady-state conditions are discussed.     

N‐Nitrosomelatonin

The title compound, N‐[2‐(5‐methoxy‐1‐nitro­so‐1H‐indol‐3‐yl)­ethyl]­acet­amide, C₁₃H₁₅N₃O₃, an N‐nitroso derivative of melatonin, crystallizes in the monoclinic C2/c space group. The mol­ecules are arranged in such a way that the aromatic rings are in a planar conformation, with the alkyl­amide side chains in a different plane, at a dihedral angle of 108.60 (6)°. The alkyl­amide chains are interconnected by hydrogen bonds, constituting an infinite array.