A constant factor approximation algorithm for the fault-tolerant facility location problem

We consider a generalization of the classical facility location problem, where we require the solution to be fault-tolerant. In this generalization, every demand point j must be served by r_j facilities instead of just one. The facilities other than the closest one are “backup” facilities for that demand, and any such facility will be used only if all closer facilities (or the links to them) fail. Hence, for any demand point, we can assign nonincreasing weights to the routing costs to farther facilities. The cost of assignment for demand j is the weighted linear combination of the assignment costs to its r_j closest open facilities. We wish to minimize the sum of the cost of opening the facilities and the assignment cost of each demand j. We obtain a factor 4 approximation to this problem through the application of various rounding techniques to the linear relaxation of an integer program formulation. We further improve the approximation ratio to 3.16 using randomization and to 2.41 using greedy local-search type techniques.     

Tetranuclear [{Ni(HL3)}{W(CN)8}]2 square: a case of antiferromagnetic {NiIIWV} interactions

A tetranuclear cyano-bridged [{Ni(HL3)}{W(CN)8}]2 compound in a square geometry was formed by self-assembling of {W(CN)8}3- and {NiL3}2+ (L3=pentadentate ligand). The structure of the compound has been established by single crystal X-ray diffraction. The coordination sphere of the Ni ions is severely distorted with the macrocyclic ligand adopting a facial coordination with only four linkages to the metal center. The N atom of the pendant aminopropyl arm of L3 is no longer coordinated to the metal center but has undergone protonation during the assembling process. Magnetic measurements have revealed an unexpected antiferromagnetic behavior (J=-9 cm(-1)), which has been explained using a microscopic many-body electronic model Hamiltonian, based on DFT results. The many-body model is used to fit both the chiMT versus T and the M versus H plots obtained from experiments.     

Edge-enhanced spatiotemporal constrained reconstruction of undersampled dynamic contrast-enhanced radial MRI

Dynamic contrast-enhanced magnetic resonance imaging (MRI) is a technique used to study and track contrast kinetics in an area of interest in the body over time. Reconstruction of images with high contrast and sharp edges from undersampled data is a challenge. While good results have been reported using a radial acquisition and a spatiotemporal constrained reconstruction (STCR) method, we propose improvements from using spatially adaptive weighting and an additional edge-based constraint. The new method uses intensity gradients from a sliding window reference image to improve the sharpness of edges in the reconstructed image. The method was tested on eight radial cardiac perfusion data sets with 24 rays and compared to the STCR method. The reconstructions showed that the new method, termed edge-enhanced spatiotemporal constrained reconstruction, was able to reconstruct images with sharper edges, and there were a 36%±13.7% increase in contrast-to-noise ratio and a 24%±11% increase in contrast near the edges when compared to STCR. The novelty of this paper is the combination of spatially adaptive weighting for spatial total variation (TV) constraint along with a gradient matching term to improve the sharpness of edges. The edge map from a reference image allows the reconstruction to trade-off between TV and edge enhancement, depending on the spatially varying weighting provided by the edge map.     

Facile synthesis, fluorescence, and photochromism of novel helical pyrones and chromenes

[reaction: see text] Aryl coumaryl ethylenes undergo oxidative photocyclization readily to yield helical pyrone-annulated condensed aromatics. The pyrones are conveniently converted to the corresponding photochromic diphenylpyrans/chromenes. Both pyrones and chromenes exhibit helicity-dependent fluorescence efficiency and persistence, respectively.     

Effect of polarization on femtosecond pulsed laser ablation of surface relief gratings using a novel interferometer

In this paper, we report the effects of polarization state of individual beams in ablation of surface relief gratings using a two-beam interferometric technique. We have carried out ablation experiments on (1 1 1) silicon to form surface relief gratings by interfering two femtosecond laser beams under different polarization combinations. Four combinations of polarization were studied, i.e., s-: s-polarization, s-: p-polarization, p-: p-polarization and circular-: circular-polarization (c-: c-polarization). A novel interferometer was used for the investigation. The grating depths, surface roughness and ablation thresholds have been shown to depend on the polarization state of the interfering beams.     

Application of photogrammetry to surface flow visualization

The construction of three-dimensional surface flow fields is an extremely difficult task owing largely to the fragmented information available in the form of 2D images. Here, the method of photogrammetric resection based on a comprehensive camera model has been used to map oil flow visualization images on to the surface grid of the model. The data exported in the VRML format allow for user interaction in a manner not possible with 2D images. The technique is demonstrated here using the surface oil flow visualization images of a simplified landing gear model at low speed in a conventional wind tunnel without any specialized rigs for photogrammetry. The results are not limited to low-speed regimes and show that this technique can have significant impact on understanding the flow physics associated with the surface flow topology of highly three-dimensional separated flows on complex models.