High finesse opto-mechanical cavity with a movable thirty-micron-size mirror

We report on the demonstration of a high finesse micro-optomechanical system and identify potential applications ranging from optical cooling to weak force detection to massive quantum superpositions. The system consists of a high quality diameter flat dielectric mirror cut from a larger substrate with a focused ion beam and attached to an atomic force microscope cantilever. Cavity ring-down measurements performed on a 25 mm long Fabry-Pérot cavity with the 30 microm mirror at one end show an optical finesse of 2100. Numerical calculations show that the finesse is not diffraction limited and that orders of magnitude higher finesse should be possible. A mechanical quality factor of more than 10(5) at pressures below 10(-3) mbar is demonstrated for the cantilever with a mirror attached.     

DTI at 7 and 3 T: systematic comparison of SNR and its influence on quantitative metrics

Diffusion tensor imaging (DTI) and advanced related methods such as diffusion spectrum and kurtosis imaging are limited by low signal-to-noise ratio (SNR) at conventional field strengths. DTI at 7 T can provide increased SNR; however, B0 and B1 inhomogeneity and shorter T2? still pose formidable challenges. The purpose of this study was to quantify and compare SNR at 7 and 3 T for different parallel imaging reduction factors, R, and TE, and to evaluate SNRs influences on fractional anisotropy (FA) and apparent diffusion coefficient (ADC). We found that R>4 at 7 T and R≥2 at 3 T were needed to reduce geometric distortions due to B0 inhomogeneity. For these R at 7 T, SNR was 70-90 for b=0 s/mm² and 22-28 for b=1000s/mm² in central brain regions. SNR was lower at 3 T (40 for b=0 s/mm² and 15 for b=1000 s/mm²) and in lateral brain regions at 7 T due to B1 inhomogeneity. FA and ADC did not change with MRI field strength, SENSE factor or TE in the tested range. However, the coefficient of variation for FA increased for SNR <15 and for SNR <10 in ADC, consistent with published theoretical studies. Our study demonstrates that 7 T is advantageous for DTI and lays the groundwork for further development. Foremost, future work should further address challenges with B0 and B1 inhomogeneity to take full advantage for the increased SNR at 7 T.     

The cascadic multigrid method for elliptic problems

Summary. The paper deals with certain adaptive multilevel methods at the confluence of nested multigrid methods and iterative methods based on the cascade principle of [10]. From the multigrid point of view, no correction cycles are needed; from the cascade principle view, a basic iteration method without any preconditioner is used at successive refinement levels. For a prescribed error tolerance on the final level, more iterations must be spent on coarser grids in order to allow for less iterations on finer grids. A first candidate of such a cascadic multigrid method was the recently suggested cascadic conjugate gradient method of [9], in short CCG method, whichused the CG method as basic iteration method on each level. In [18] it has been proven, that the CCG method is accurate with optimal complexity for elliptic problems in 2D and quasi-uniform triangulations. The present paper simplifies that theory and extends it to more general basic iteration methods like the traditional multigrid smoothers. Moreover, an adaptive control strategy for the number of iterations on successive refinement levels for possibly highly non-uniform grids is worked out on the basis of a posteriori estimates. Numerical tests confirm the efficiency and robustness of the cascadic multigrid method. Received November 12, 1994 / Revised version received October 12, 1995     

Auto-tuning unit norm frames

Finite unit norm tight frames provide Parseval-like decompositions of vectors in terms of redundant components of equal weight. They are known to be robust against additive noise and erasures, and as such, have great potential as encoding schemes. Unfortunately, up to this point, these frames have proven notoriously difficult to construct. Indeed, though the set of all unit norm tight frames, modulo rotations, is known to contain manifolds of nontrivial dimension, we have but a small finite number of known constructions of such frames. In this paper, we present a new iterative algorithm—gradient descent of the frame potential—for increasing the degree of tightness of any finite unit norm frame. The algorithm itself is easy to implement, and it preserves certain group structures present in the initial frame. In the special case where the number of frame elements is relatively prime to the dimension of the underlying space, we show that this algorithm converges to a unit norm tight frame at a linear rate, provided the initial unit norm frame is already sufficiently close to being tight. By slightly modifying this approach, we get a similar, but weaker, result in the non-relatively-prime case, providing an explicit answer to the Paulsen problem: “How close is a frame which is almost tight and almost unit norm to some unit norm tight frame?”     

Control of antigen presentation with a photoreleasable agonist peptide

The immunological synapse is a specialized intercellular junction between a T cell and a target cell that orchestrates the engagement of receptors and ligands in space and time as a means of regulating function. Here we introduce a reagent for controlling the spatial and temporal presentation of natural antigen to T cells. Moth cytochrome c (88-103) peptide (MCC), an agonist to the murine T cell receptor AND when presented in the context of H2 IEk major histocompatibility complex (IEk), was synthesized with the side-chain amine of Lys99 conjugated to a photosensitive protecting group, 6-nitroveratryloxycarbonyl (NVOC). Cells plated on supported bilayers displaying mobile intercellular adhesion molecule-1 (ICAM-1) and NVOC-MCC loaded IEk did not form immunological synapses and exhibited low intracellular calcium levels, similar to cells presented with self-peptide. Irradiation with UV light was sufficient to restore agonist activity in situ.     

On the swelling behavior of poly(N-Isopropylacrylamide) hydrogels exposed to perfluoroalkyl acids

Per- and polyfluoroalkyl substances (PFAS) have rapidly accumulated in the environment due to their widespread use prior to commercial discussion in the early 21st century, and their slow degradation has magnified concerns of their potential toxicity. Monitoring their distribution is, therefore, necessary to evaluate and control their impact on the health of exposed populations. This investigation evaluates the capability of a simple polymeric detection scheme for PFAS based on crosslinked, thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) hydrogels. Surveying swelling perturbations induced by several hydrotropes and comparable hydrocarbon analogs, tetraethylammonium perfluorooctane sulfonate (TPFOS) showed a significantly higher swelling ratio on a mass basis (65.5 ± 8.8 at 15°C) than any of the other analytes tested. Combining swelling with the fluorimetric response of a solvachromatic dye, nile red, revealed the fluorosurfactant to initiate observable aggregation (i.e., its critical aggregation concentration) at 0.05 mM and reach saturation (i.e., its charge neutralization concentration) at 0.5 mM. The fluorosurfactant was found to homogeneously distribute throughout the polymer matrix with energy dispersive X-ray spectroscopy, marking the swelling response as a peculiar nexus of fluorinated interfacial positioning and delocalized electrostatic repulsion. Results from the current study hold promise for exploiting the physiochemical response of PNIPAM to assess TPFOS's concentration.     

Peptide microarrays for the determination of protease substrate specificity

A method is described for the preparation of substrate microarrays that allow for the rapid determination of protease substrate specificity. Peptidyl coumarin substrates, synthesized on solid support using standard techniques, are printed onto glass slides using DNA microarraying equipment. The linkage from the peptide to the slide is formed through a chemoselective reaction, resulting in an array of uniformly displayed fluorogenic substrates. The arrays can be treated with proteases to yield substrate specificity profiles. Standard instrumentation for visualization of microarrays can be used to obtain comparisons of the specificity constants for all of the prepared substrates. The utility of these arrays is demonstrated by the selective cleavage of preferred substrates with trypsin, thrombin, and granzyme B, and by assessing the extended substrate specificity of thrombin using a microarray of 361 different peptidyl coumarin substrates.     

Unconventional, highly selective CO2 adsorption in zeolite SSZ-13

Low-pressure adsorption of carbon dioxide and nitrogen was studied in both acidic and copper-exchanged forms of SSZ-13, a zeolite containing an 8-ring window. Under ideal conditions for industrial separations of CO(2) from N(2), the ideal adsorbed solution theory selectivity is >70 in each compound. For low gas coverage, the isosteric heat of adsorption for CO(2) was found to be 33.1 and 34.0 kJ/mol for Cu- and H-SSZ-13, respectively. From in situ neutron powder diffraction measurements, we ascribe the CO(2) over N(2) selectivity to differences in binding sites for the two gases, where the primary CO(2) binding site is located in the center of the 8-membered-ring pore window. This CO(2) binding mode, which has important implications for use of zeolites in separations, has not been observed before and is rationalized and discussed relative to the high selectivity for CO(2) over N(2) in SSZ-13 and other zeolites containing 8-ring windows.