Rigidity of planar tilings

Summary Aperturbation of a tiling of a region inR ⁿ is a set of isometries, one applied to each tile, so that the images of the tiles tile the same region.We show that a locally finite tiling of an open region inR ² with tiles which are closures of their interiors isrigid in the following sense: any sufficiently small perturbation of the tiling must have only earthquake-type discontinuities, that is, the discontinuity set consists of straight lines and arcs of circles, and the perturbation near such a curve shifts points along the direction of that curve.We give an example to show that this type of rigidity does not hold inR ⁿ , forn>2.Using rigidity in the plane we show that any tiling problem with a finite number of tile shapes (which are topological disks) is equivalent to a polygonal tiling problem, i.e. there is a set of polygonal shapes with equivalent tiling combinatorics.Oblatum 19-III-1991     

Effect of microstructure on molecular oxygen permeation through condensed phospholipid monolayers

A method is presented that allows novel measurement of the effect of microstructure on the oxygen permeability of highly condensed, polycrystalline phospholipid monolayers. Oxygen permeability of the polycrystalline shell coating a stationary microbubble is measured directly using an apposing microelectrode in the induced transfer mode and modeling oxygen flux through the shell and intervening aqueous medium. Varying cooling rate through the phospholipid main phase transition permits control of shell microstructure by manipulation of crystalline domain size and shape. Domain boundary density, defined as the ratio of the mean domain perimeter to the mean domain area, of the microbubble shell is determined by fluorescence microscopy. Oxygen permeability was shown to increase linearly with domain boundary density at a constant phospholipid acyl chain length and, accordingly, was shown to decrease exponentially with increasing chain length at a constant domain boundary density. Modification of the energy barrier theory to account for microstructural effects, in terms of the domain boundary density, provides a general equation to model passive transport through polycrystalline monolayer films. Results from this method show promise in determining the gas transport kinetics of medical microbubbles and the gas exchange characteristics of biological monolayers.     

Fatty acid desaturation index in human plasma: comparison of different analytical methodologies for the evaluation of diet effects

Stearoyl-CoA desaturase 1 (SCD1) plays a role in the development of obesity and related conditions, such as insulin resistance, and potentially also in neurological and heart diseases. The activity of SCD1 can be monitored using the desaturation index (DI), the ratio of product (16:1n-7 and 18:1n-9) to precursor (16:0 and 18:0) fatty acids. Here, different analytical strategies were applied to identify the method which best supports SCD1 biology. A novel effective approach was the use of the SCD1-independent fatty acid (16:1n-10) as a negative control. The first approach was based on a simple extraction followed by neutral loss triglyceride fatty acid analysis. The second approach was based on the saponification of triglycerides followed by fatty acid analysis (specific for the position of the double bond within monounsaturated fatty acids (MUFAs)). In addition to the analytical LC-MS assays, different matrices (plasma total triglyceride fraction and the very low-density lipoprotein (VLDL) fraction) were investigated to identify the best for studying changes in SCD1 activity. Samples from volunteers on a high-carbohydrate diet were analyzed. Both ultra HPLC (UHPLC)-MS-based assays showed acceptable accuracies (75–125 % of nominal) and precisions (<20 %) for the analysis of DI-specific fatty acids in VLDL and plasma. The most specific assay for the analysis of the liver SCD activity was then validated for specificity and selectivity, intra- and interday accuracy and precision, matrix effects, dilution effects, and analyte stability. After 3 days of high-carbohydrate diet, only the specific fatty acids in human plasma VLDL showed a significant increase in DI and associated SCD1 activity.     

Decision strategies of hearing-impaired listeners in spectral shape discrimination

The ability to discriminate between sounds with different spectral shapes was evaluated for normal-hearing and hearing-impaired listeners. Listeners detected a 920-Hz tone added in phase to a single component of a standard consisting of the sum of five tones spaced equally on a logarithmic frequency scale ranging from 200 to 4200 Hz. An overall level randomization of 10 dB was either present or absent. In one subset of conditions, the no-perturbation conditions, the standard stimulus was the sum of equal-amplitude tones. In the perturbation conditions, the amplitudes of the components within a stimulus were randomly altered on every presentation. For both perturbation and no-perturbation conditions, thresholds for the detection of the 920-Hz tone were measured to compare sensitivity to changes in spectral shape between normal-hearing and hearing-impaired listeners. To assess whether hearing-impaired listeners relied on different regions of the spectrum to discriminate between sounds, spectral weights were estimated from the perturbed standards by correlating the listener's responses with the level differences per component across two intervals of a two-alternative forced-choice task. Results showed that hearing-impaired and normal-hearing listeners had similar sensitivity to changes in spectral shape. On average, across-frequency correlation functions also were similar for both groups of listeners, suggesting that as long as all components are audible and well separated in frequency, hearing-impaired listeners can use information across frequency as well as normal-hearing listeners. Analysis of the individual data revealed, however, that normal-hearing listeners may be better able to adopt optimal weighting schemes. This conclusion is only tentative, as differences in internal noise may need to be considered to interpret the results obtained from weighting studies between normal-hearing and hearing-impaired listeners.     

The Lévy-Hinčin representation for random compact convex subsets which are infinitely divisible under Minkowski addition

Summary This paper establishes the Lévy-Hinčin representation for all random compact convex subsets of ℝ which are infinitely divisible for Minkowski addition. Research partially supported by NSF grants No. MCS 8100728 and DMS-8318610 Research partially supported by NSF grant No. MCS 8301326     

Intrinsic vacancy-induced nanoscale wire structure in heteroepitaxial Ga2Se3/Si(001)

A highly anisotropic growth morphology is found for heteroepitaxial gallium sesquiselenide (Ga2Se3) on the lattice matched substrate, arsenic-terminated Si(001). Scanning tunneling microscopy of Ga2Se3 films reveals nanoscale, wirelike structures covering the surface in parallel lines, less than 1 nm wide and up to 30 nm long. Core-level photoemission spectroscopy and diffraction reveals the local structure of buried Ga and Se atoms to reflect the bulk, defected zinc-blende structure of beta-Ga2Se3, which contains ordered 110 arrays of Ga vacancies. These ordered vacancy lines are proposed to be responsible for the observed growth anisotropy in heteroepitaxial Ga2Se3.