Structure dependent sampling in compressed sensing: Theoretical guarantees for tight frames

Many of the applications of compressed sensing have been based on variable density sampling, where certain sections of the sampling coefficients are sampled more densely. Furthermore, it has been observed that these sampling schemes are dependent not only on sparsity but also on the sparsity structure of the underlying signal. This paper extends the result of Adcock, Hansen, Poon and Roman (arXiv:1302.0561, 2013) [2] to the case where the sparsifying system forms a tight frame. By dividing the sampling coefficients into levels, our main result will describe how the amount of subsampling in each level is determined by the local coherences between the sampling and sparsifying operators and the localized level sparsities – the sparsity in each level under the sparsifying operator.     

Automated fringe pattern analysis for moiré interferometry

The theory of an automated fringe-pattern analysis using temporal phase stepping method for moiré interferometry is presented. The automated method provides a fast and accurate strain measurement for moiré interferometry. Measurements on a tapered composite specimen with a dropped ply are shown to highlight the capability of this technique to obtain the strain distribution, particularly around the region with a dropped ply.     

Principal Submatrices of a Hermitian Matrix

Suppose k 1 ,<, k m and n are positive integers such that k 1 + … + k m h n . We characterize those k i × k i Hermitian matrices A i , i = 1, < , m that can appear as diagonal blocks of an n × n Hermitian matrix C with prescribed eigenvalues. The characterization will be given in terms of the eigenvalues of C and A i , i = 1, <, m . Our results extend those of Thompson and Freede, Horn, Fan and Pall.     

The electronic structure of the nitridoosmate(VIII) ion,OsO3N-

The electronic spectrum of the nitridoosmate(VIII) ion, OsO₃N^-, has been measured at liquid helium temperatures for thin films of the n-tetrabutyl-ammonium salt and for oriented, doped LiClO₄. 3H₂O single crystals. Four structured band systems, all individually composed of superimposed A ₁ ← A ₁ and E←A ₁ transitions, are observed at energies comparable to those of the two lowest ¹ T ₂←¹ A ₁ transitions of OsO₄. Prominent vibronic structure assigned to ν(Os-N) is observed for all of the bands. The bands are assigned to transitions to completely spin-orbit mixed states. The highest filled orbitals of OsO₃N^- are oxygen-localized and π non-bonding. The nitrido ligand appears to ‘dominate’ the π-bonding in the ion.     

Damage accumulation and hysteretic behavior of MAX phase materials

The compressive response of fully dense and 10 vol% porous Ti₂AlC MAX phase materials subjected to quasi-static uniaxial and cyclic loading including their repeatable hysteretic behavior is presented. Damage accumulation in the form of kink bands and microcracking is characterized using ultrasonics and scanning electron microscopy under different levels of compressive loading. The observations and measurements are correlated quantitatively using a model based on friction between the crack faces, which is the main dissipation process. The model is shown to capture the hysteretic behavior of Ti₂AlC MAX phase and quantitatively reproduce the experimentally measured stress–strain curves.     

Synthesis of Rhenabenzenes from the Reactions of Rhenacyclobutadienes with Ethoxyethyne

Treatment of Na[Re(CO)₅] with RC?CCO₂Et (R=phenyl, naphthalen‐1‐yl, phenanthren‐9‐yl and pyren‐1‐yl) followed by reaction with acetyl chloride and ethanol afforded the rhenacyclobutadienes Re{‐C(R)?C(CO₂Et)C(OEt)?}(CO)₄. Reactions of these rhenacyclobutadienes with HC?COEt produced rhenabenzenes Re{‐C(R)?C(CO₂Et)C(OEt)?CHC(OEt)?}(CO)₄. Except for R=Ph, new rhenacyclobutadienes with pendant alkenyl substituents Re{‐C(R)?C(C(OEt)?CH(CO₂Et))C(OEt)?}(CO)₄ were also isolated from these reactions. The NMR spectroscopic and X‐ray structural data, as well as the aromatic stabilization energy (ASE) values suggest that the rhenabenzenes are aromatic, with extensive delocalized π character.     

Determination of avilamycin as dichloroisoeverninic acid in poultry and porcine muscles by isotope dilution liquid chromatography–tandem mass spectrometry

Avilamycin residue in food is regulated as its marker residue dichloroisoeverninic acid (DIA). An isotope dilution liquid chromatography–tandem mass spectrometry method is established for the accurate determination of DIA in animal muscles without any pre-extraction and preconcentration prior to alkaline hydrolysis. Optimization of the sample cleanup procedures such as liquid–liquid extraction and solid phase extraction was performed by fine-tuning several critical parameters to reduce the matrix effects. Quantification of DIA in edible muscle was accomplished by using matrix-matched calibration with dichloroisoeverninic acid-d₆ as internal standard. The method was validated with DIA and avilamycin-fortified poultry and porcine muscles at three different levels (25, 50, and 100 μg/kg). Conversion of avilamycin to DIA by alkaline hydrolysis was ≥92 %. The recoveries of DIA in both muscles at three fortification levels ranged from 94 to 106 % and RSDs were ≤11 % in all cases. The estimated limit of detection values in poultry and porcine muscles were 2.7 and 0.7 μg/kg, respectively. The estimated limit of quantitation values in poultry and porcine muscles were 8.3 and 2.4 μg/kg, respectively. This method is suitable for routine monitoring of avilamycin residue in food safety surveillance programs.     

Smooth over-parameterized solvers for non-smooth structured optimization

Mathematical Programming - Non-smooth optimization is a core ingredient of many imaging or machine learning pipelines. Non-smoothness encodes structural constraints on the solutions, such as...     

Microdroplet-etched highly birefringent low-loss fiber tapers

We use hydrofluoric acid microdroplets to directly etch highly birefringent biconical fiber tapers from standard single-mode fibers. The fiber tapers have micrometer-sized cross sections, which are controlled by the etching condition. The characteristic teardrop cross section leads to a high group birefringence of B(G)≈0.017 and insertion losses <0.7 dB over waist lengths of about 2.1 mm.     

Effect of ovariectomy on contrast agent diffusion into lumbar intervertebral disc: a dynamic contrast-enhanced MRI study in female rats

Purpose

The purpose was to study the effect of estrogen deficiency on contrast agent diffusion into intervertebral disc in a rat model.

Materials and Methods

Seven-month-old female Sprague–Dawley rats were used. Fourteen rats had ovariectomy, and nine rats had sham surgery. Magnetic resonance imaging (MRI) of sagittal midsection of lumbar spine was performed with a 1.5-T magnet. Dynamic MRI was performed after a bolus injection of Gd-DOTA (0.3 mmol/kg) through tail vein. Eight hundred images were acquired at 0.6 s per acquisition. Regions of interests were drawn over three discs per rat. Maximum enhancement (E_max) and enhancement slope (E_slope) were evaluated. MRI was carried out at baseline and 8 weeks postsurgery.

Result

All disc enhancements demonstrated an initial fast wash-in phase followed by a second slower wash-in phase. For initial wash-in phase, E¹_max and E¹_slope of all rats remained unchanged at the two time points. For second wash-in phase, E²_max and E²_slope of control rats remained unchanged, while with ovariectomized rats, E²_max showed reduction at 8 weeks (4.5%±5.6%) compared to baseline (10.3%±6.3%, P=.037), and E²_slope was lower at 8 weeks (0.015±0.017) than the baseline (0.029±0.022), although it was not statistically significant (P=.101).

Conclusion

Ovariectomy induced detectable decrease in second wash-in phase of contrast agent into lumbar disc.