Improved Approximation Algorithms for Geometric Set Cover

Given a collection S of subsets of some set and the set cover problem is to find the smallest subcollection that covers that is, where denotes We assume of course that S covers While the general problem is NP-hard to solve, even approximately, here we consider some geometric special cases, where usually Combining previously known techniques [4], [5], we show that polynomial-time approximation algorithms with provable performance exist, under a certain general condition: that for a random subset and nondecreasing function f(·), there is a decomposition of the complement into an expected at most f(|R|) regions, each region of a particular simple form. Under this condition, a cover of size O(f(|C|)) can be found in polynomial time. Using this result, and combinatorial geometry results implying bounding functions f(c) that are nearly linear, we obtain o(log c) approximation algorithms for covering by fat triangles, by pseudo-disks, by a family of fat objects, and others. Similarly, constant-factor approximations follow for similar-sized fat triangles and fat objects, and for fat wedges. With more work, we obtain constant-factor approximation algorithms for covering by unit cubes in and for guarding an x-monotone polygonal chain.     

Polarization phase in aberration compensation

A phase/amplitude mask on the aperture of an imaging system results in a pupil function that is multiplicative with the lens function, resulting in a morphological transformation of the imaging wavefront. It was shown that such amplitude and phase functions can be implemented using polarization masks, with the advantage that the phase and amplitude can be controlled in real time and in some cases, independently of each other. The phase and amplitude variation over the mask can be controlled either by changing the polarization of the mask or by changing the input beam parameters. Wavefront tailoring using polarization-masked apertures is therefore feasible and may be utilized for focal shift and partial aberration compensation. For complete compensation of aberration, the phase distribution over the mask should be conjugate to that of the phase error of the aberrant wavefront, which necessitates the use of a continuously variable polarization mask. Since such a mask is difficult to implement, we have considered polarizing masks consisting of discrete polarized zones on the lens aperture, leading to polarization phase steps on the exit pupil of the imaging system. The simulation results presented in this paper show that effects of focal shift, partial compensation of primary spherical aberration and astigmatism can indeed be achieved by the proper use of polarization masked apertures.     

Effect of filter spacing on melody recognition: acoustic and electric hearing

This paper assesses the effect of filter spacing on melody recognition by normal-hearing (NH) and cochlear implant (CI) subjects. A new semitone filter spacing is proposed for music. The quality of melodies processed by the various filter spacings is also evaluated. Results from NH listeners showed nearly perfect melody recognition with only four channels of stimulation, and results from CI users indicated significantly higher scores with a 12-channel semitone spacing compared to the spacing used in their daily processor. The quality of melodies processed by the semitone filter spacing was preferred over melodies processed by the conventional logarithmic filter spacing.     

Tailoring of Electronic Structure and Thermoelectric Properties of a Topological Crystalline Insulator by Chemical Doping

Topological crystalline insulators (TCIs) are a new quantum state of matter in which linearly dispersed metallic surface states are protected by crystal mirror symmetry. Owing to its vanishingly small bulk band gap, a TCI like Pb_0.6Sn_0.4Te has poor thermoelectric properties. Breaking of crystal symmetry can widen the band gap of TCI. While breaking of mirror symmetry in a TCI has been mostly explored by various physical perturbation techniques, chemical doping, which may also alter the electronic structure of TCI by perturbing the local mirror symmetry, has not yet been explored. Herein, we demonstrate that Na doping in Pb_0.6Sn_0.4Te locally breaks the crystal symmetry and opens up a bulk electronic band gap, which is confirmed by direct electronic absorption spectroscopy and electronic structure calculations. Na doping in Pb_0.6Sn_0.4Te increases p‐type carrier concentration and suppresses the bipolar conduction (by widening the band gap), which collectively gives rise to a promising zT of 1 at 856 K for Pb_0.58Sn_0.40Na_0.02Te. Breaking of crystal symmetry by chemical doping widens the bulk band gap in TCI, which uncovers a route to improve TCI for thermoelectric applications.     

Tunable, colorimetric DNA-based pH sensors mediated by A-motif formation

A colorimetric pH sensor has been developed based on GNP aggregation mediated by A-motif formation under acidic conditions. The pH response of the sensor can be tuned in the range of pH 2-5.5 by changing the length and the sequence of the A-motif forming poly dA tracts.     

Quantization dimension and temperature function for bi-Lipschitz mappings

The quantization dimension function for a probability measure supported on the limit set generated by a set of contractive bi-Lipschitz mappings is determined. The relationship between the quantization dimension function and the temperature function of the thermodynamic formalism arising in multifractal analysis is established.     

On Structured Surfaces with Defects: Geometry,Strain Incompatibility,Stress Field,and Natural Shapes

In this paper we study the stress and deformation fields generated by nonlinear inclusions with finite eigenstrains in anisotropic solids. In particular, we consider finite eigenstrains in transversely isotropic spherical balls and orthotropic cylindrical bars made of both compressible and incompressible solids. We show that the stress field in a spherical inclusion with uniform pure dilatational eigenstrain in a spherical ball made of an incompressible transversely isotropic solid such that the material preferred direction is radial at any point is uniform and hydrostatic. Similarly, the stress in a cylindrical inclusion contained in an incompressible orthotropic cylindrical bar is uniform hydrostatic if the radial and circumferential eigenstrains are equal and the axial stretch is equal to a value determined by the axial eigenstrain. We also prove that for a compressible isotropic spherical ball and a cylindrical bar containing a spherical and a cylindrical inclusion, respectively, with uniform eigenstrains the stress in the inclusion is uniform (and hydrostatic for the spherical inclusion) if the radial and circumferential eigenstrains are equal. For compressible transversely isotropic and orthotropic solids, we show that the stress field in an inclusion with uniform eigenstrain is not uniform, in general. Nevertheless, in some special cases the material can be designed in order to maintain a uniform stress field in the inclusion. As particular examples to investigate such special cases, we consider compressible Mooney-Rivlin and Blatz-Ko reinforced models and find analytical expressions for the stress field in the inclusion.     

Growth and characterization of semiconducting cadmium selenide thin films

Semiconducting thin films of cadmium selenide have been grown by conventional thermal evaporation technique. The effect of various growth parameters like rate of deposition and deposition temperature has been studied in detail. Films deposited at room temperature are cadmium rich with segregated selenium globules. A deposition temperature of 453 K has been found to yield stoichiometric, homogeneous films. The films have been analysed for optical band gap and thermal activation energies. Films of low electrical resistivity have been obtained for possible applications.     

Coefficient of volume expansion and thermoacoustic parameters in certain alkoxy benzylidene butylanilines — IB

Using the coefficient of volume expansion certain thermoacoustic parameters like isobaric (K), isothermal (K″), isochoric (K″) acoustic parameters, free volume (V_a/V) and two new dimensionless acoustic parameters A* and B* are estimated in certain alkoxy benzylidene butylanilines, in their isotropic- and mesophases as well as at and in the immediate vicinity of the phase transition temperatures following the method which was suggested by Sharma, for non-mesomorphic systems.     

Stability‐indicating HPLC assay for lysine–proline–valine (KPV) in aqueous solutions and skin homogenates

A simple, sensitive and stability‐indicating high‐performance liquid chromatographic (HPLC) assay method was developed and validated for a bioactive peptide, lysine–proline–valine (KPV) in aqueous solutions and skin homogenates. Chromatographic separation was achieved on a reversed phase Phenomenex C₁₈ column (4.6 × 250 mm, packed with 5 µm silica particles) with a gradient mobile phase consisting of 0.1% trifluoroacetic acid (TFA) in water (A) and 0.1% TFA in acetonitrile (B). The proposed HPLC method was validated with respect to accuracy, precision, linearity, repeatability, limit of detection (LOD) and limit of quantitation (LOQ). The calibration curve was linear with a correlation coefficient (r) of 0.9999. Relative standard deviation values of accuracy and precision experiments were <2. The LOD and LOQ of KPV were 0.01 and 0.25 µg/mL, respectively. Under stress conditions (acid, alkali and hydrogen peroxide) KPV yielded lys–pro–diketopiperazine as major degradation product, which was identified by flow injection MS analysis. The developed HPLC method was found to be efficient in separating the active peptide from its degradation products generated under various stress conditions. Also, the validated method was able to separate KPV from other peaks arising from endogenous components of the skin homogenate. Copyright © 2014 John Wiley & Sons, Ltd.