Splitting (complicated) surfaces is hard

Let be an orientable combinatorial surface. A cycle on is splitting if it has no self-intersections and it partitions into two components, neither of which is homeomorphic to a disk. In other words, splitting cycles are simple, separating, and non-contractible. We prove that finding the shortest splitting cycle on a combinatorial surface is NP-hard but fixed-parameter tractable with respect to the surface genus g and the number of boundary components b of the surface. Specifically, we describe an algorithm to compute the shortest splitting cycle in (g+b)^O(g+b)nlogn time, where n is the complexity of the combinatorial surface.     

Novel structural templates for estrogen-receptor ligands and prospects for combinatorial synthesis of estrogens

BACKGROUND: The development of estrogen pharmaceutical agents with appropriate tissue-selectivity profiles has not yet benefited substantially from the application of combinatorial synthetic approaches to the preparation of structural classes that are known to be ligands for the estrogen receptor (ER). We have developed an estrogen pharmacophore that consists of a simple heterocyclic core scaffold, amenable to construction by combinatorial methods, onto which are appended 3-4 peripheral substituents that embody substructural motifs commonly found in nonsteroidal estrogens. The issue addressed here is whether these heterocyclic core structures can be used to prepare ligands with good affinity for the ER. RESULTS: We prepared representative members of various azole core structures. Although members of the imidazole, thiazole or isoxazole classes generally have weak binding for the ER, several members of the pyrazole class show good binding affinity. The high-affinity pyrazoles bear close conformational relationship to the nonsteroidal ligand raloxifene, and they can be fitted into the ligand-binding pocket of the ER-raloxifene X-ray structure. CONCLUSIONS: Compounds such as these pyrazoles, which are novel ER ligands, are well suited for combinatorial synthesis using solid-phase methods.     

Molecular structure of AlH3[N(CH2CH2)3CH]2

Reaction of AlH₃[N(CH₂CH₂)₃CH] with hexamethyltrisiloxane, (OSiMe₂)₃, gives rise to the bis-quinuclidine complex AlH₃[N(CH₂CH₂)₃CH]₂, which has been characterized by ¹H and ¹³C NMR spectroscopy and X-ray crystallography. The molecular structure of AlH₃[N(CH₂CH₂)₃CH]₂ consists of a trigonal bipyramidal aluminum with axial coordination of the quinuclidine ligands. Crystal data: orthorhombic, space group Pbcn, a = 10.6895(9), b = 12.266(1), c = 12.3794(9) Å, V = 1623.2(2) ų, and Z = 4.     

On the orientation of ellipsoidal particles in a turbulent shear flow

Direct numerical simulation (DNS) of small prolate ellipsoidal particles suspended in a turbulent channel flow is reported. The coupling between the fluid and the particles is one-way. The particles are subjected to the hydrodynamic drag force and torque valid for creeping flow conditions. Six different particle cases with varying particle aspect ratios and equivalent response times are investigated. Results show that, in the near-wall region, ellipsoidal particles tend to align with the mean flow direction, and the alignment increases with increasing particle aspect ratio. When the particle inertia increases, the particles are less oriented in the spanwise direction and more oriented in the wall-normal direction. In the core region of the channel, the orientation becomes isotropic.     

An inviscid model for vortex shedding from a deforming body

An inviscid vortex sheet model is developed in order to study the unsteady separated flow past a two-dimensional deforming body which moves with a prescribed motion in an otherwise quiescent fluid. Following Jones (J Fluid Mech 496, 405–441, 2003) the flow is assumed to comprise of a bound vortex sheet attached to the body and two separate vortex sheets originating at the edges. The complex conjugate velocity potential is expressed explicitly in terms of the bound vortex sheet strength and the edge circulations through a boundary integral representation. It is shown that Kelvin’s circulation theorem, along with the conditions of continuity of the normal velocity across the body and the boundedness of the velocity field, yields a coupled system of equations for the unknown bound vortex sheet strength and the edge circulations. A general numerical treatment is developed for the singular principal value integrals arising in the solution procedure. The model is validated against the results of Jones (J Fluid Mech 496, 405–441, 2003) for computations involving a rigid flat plate and is subsequently applied to the flapping foil experiments of Heathcote et al. (AIAA J, 42, 2196–2204, 2004) in order to predict the thrust coefficient. The utility of the model in simulating aquatic locomotion is also demonstrated, with vortex shedding suppressed at the leading edge of the swimming body.      

More efficient time integration for Fourier pseudospectral DNS of incompressible turbulence

Time integration of Fourier pseudospectral DNS is usually performed using the classical fourth-order accurate Runge-Kutta method or other second- or third-order methods, with a fixed step size. We investigate the use of higher-order Runge-Kutta pairs and automatic step size control based on local error estimation. We find that the fifth-order accurate Runge-Kutta pair of Bogacki and Shampine gives much greater accuracy at a significantly reduced computational cost. Specifically, we demonstrate speedups of 2× to 10× for the same accuracy. Numerical tests (including the Taylor-Green vortex, Rayleigh-Taylor instability, and homogeneous isotropic turbulence) confirm the reliability and efficiency of the method. We also show that adaptive time stepping provides a significant computational advantage for some problems (like the development of a Rayleigh-Taylor instability) without compromising accuracy.     

On the analytic model of a class of semi-hyponormal operators

The analytic model of a class of semi-hyponormal operators is derived using three kernal functions. In addition, explicit forms of the kernal functions are given and the Pincus principal functions of the operators are calculated.     

Collisional Cross-Sections with T-Wave Ion Mobility Spectrometry without Experimental Calibration

A method for relating traveling-wave ion mobility spectrometry (TWIMS) drift times with collisional cross-sections using computational simulations is presented. This method is developed using SIMION modeling of the TWIMS potential wave and equations that describe the velocity of ions in gases induced by electric fields. The accuracy of this method is assessed by comparing the collisional cross-sections of 70 different reference ions obtained using this method with those obtained from static drift tube ion mobility measurements. The cross-sections obtained here with low wave velocities are very similar to those obtained using static drift (average difference?=?0.3%) for ions formed from both denaturing and buffered aqueous solutions. In contrast, the cross-sections obtained with high wave velocities are significantly greater, especially for ions formed from buffered aqueous solutions. These higher cross-sections at high wave velocities may result from high-order factors not accounted for in the model presented here or from the protein ions unfolding during TWIMS. Results from this study demonstrate that collisional cross-sections can be obtained from single TWIMS drift time measurements, but that low wave velocities and gentle instrument conditions should be used in order to minimize any uncertainties resulting from high-order effects not accounted for in the present model and from any protein unfolding that might occur. Thus, the method presented here eliminates the need to calibrate TWIMS drift times with collisional cross-sections measured using other ion mobility devices.

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Factors influencing the DNA nuclease activity of iron, cobalt, nickel, and copper chelates

A library of complexes that included iron, cobalt, nickel, and copper chelates of cyclam, cyclen, DOTA, DTPA, EDTA, tripeptide GGH, tetrapeptide KGHK, NTA, and TACN was evaluated for DNA nuclease activity, ascorbate consumption, superoxide and hydroxyl radical generation, and reduction potential under physiologically relevant conditions. Plasmid DNA cleavage rates demonstrated by combinations of each complex and biological co-reactants were quantified by gel electrophoresis, yielding second-order rate constants for DNA(supercoiled) to DNA(nicked) conversion up to 2.5 × 10(6) M(-1) min(-1), and for DNA(nicked) to DNA(linear) up to 7 × 10(5) M(-1) min(-1). Relative rates of radical generation and characterization of radical species were determined by reaction with the fluorescent radical probes TEMPO-9-AC and rhodamine B. Ascorbate turnover rate constants ranging from 3 × 10(-4) to 0.13 min(-1) were determined, although many complexes demonstrated no measurable activity. Inhibition and Freifelder-Trumbo analysis of DNA cleavage supported concerted cleavage of dsDNA by a metal-associated reactive oxygen species (ROS) in the case of Cu(2+)(aq), Cu-KGHK, Co-KGHK, and Cu-NTA and stepwise cleavage for Fe(2+)(aq), Cu-cyclam, Cu-cyclen, Co-cyclen, Cu-EDTA, Ni-EDTA, Co-EDTA, Cu-GGH, and Co-NTA. Reduction potentials varied over the range from -362 to +1111 mV versus NHE, and complexes demonstrated optimal catalytic activity in the range of the physiological redox co-reactants ascorbate and peroxide (-66 to +380 mV).