Overcoming the boundary effects in surface spline interpolation

Surface spline interpolation when the domain is all of R^d isknown to converge much faster to the data function f than inthe case when the domain is the unit ball. This difference isunderstood to be due to boundary effects which, as will be shown,also affect the size of the surface spline's coefficients. Wepropose a modified form of surface spline interpolation which,to a great extent, overcomes these boundary effects. This modifiedsurface spline interpolant uses only the values of f at thegiven interpolation points.     

Pompeiu sets in compact Heisenberg manifolds

A necessary and sufficient condition is presented for a set to be a Pompeiu subset of any compact homogeneous space with a finite invariant measure. The condition, which is expressed in terms of the intertwining operators of each primary summand of the quasi-regular representation, is then interpreted in the case of the compact Heisenberg manifolds. Examples are presented demonstrating that the condition to be Pompeiu in these manifolds is quite different from the corresponding condition for a torus of the same dimension. This provides a contrast with the existing comparison between the Heisenberg group itself and Euclidean space in terms of Pompeiu sets. In addition, the closed linear span of all translates of any square integrable function on any compact homogeneous space is determined.     

Cycloisomerization of Olefins in Water

Preparative reactions that occur efficiently under dilute, buffered, aqueous conditions in the presence of biomolecules find application in ligation, peptide synthesis, and polynucleotide synthesis and sequencing. However, the identification of functional groups or reagents that are mutually reactive with one another, but unreactive with biopolymers and water, is challenging. Shown here are cobalt catalysts that react with alkenes under dilute, aqueous, buffered conditions and promote efficient cycloisomerization and formal Friedel–Crafts reactions. The constraining conditions of bioorthogonal chemistry are beneficial for reaction efficiency as superior conversion at low catalyst concentration is obtained and competent rates in dilute conditions are maintained. Efficiency at high dilution in the presence of buffer and nucleobases suggests that these reaction conditions may find broad application.     

In vivo MR evaluation of Gd-DTPA conjugated to dextran in normal rabbits.

A dextran-Gd-DTPA compound has been recently synthesized utilizing 70,800 Da molecular weight dextran. This polymeric contrast agent for magnetic resonance imaging has been found chemically to be very stable and to demonstrate in vitro improved relaxivities of 1.5 to 2.3 times that of monomeric Gd-DTPA at 100 MHz. This MR experiment examines the in vivo distribution and relaxivity of the 70,800 Da molecular weight dextran-Gd-DTPA compound in a rabbit model by measuring the change in signal-to-noise ratio of a variety of organs (renal cortex, renal medulla, liver, brain, and torcula herophile) compared to the preinjection state. Results demonstrate prolonged (beyond 60 min) enhancement of the renal cortex, renal medulla, liver and torcula, and no enhancement of brain parenchyma.     

Identification and quantification of anticarcinogens in garlic extract and licorice root extract powder

Nine organosulfur compounds present in an aged garlic extract and two isoflavonoids and one triterpenoid present in a licorice root extract powder have been identified and quantified. Quantification involved solvent extraction and gas chromatographic – mass spectrometric analysis (garlic extract) or hydrolysis, solvent extraction, and liquid chromatographic analysis (licorice root extract powder). Although the garlic extract proved to be unstable and the concentration of the organosulfur compounds varied with time, one analysis of the extract gave the following results: methyl disulfide (0.607 μg/g), methyl trisulfide (0.181 μg/g), allyl sulfide (2.02 μg/g), allyl disulfide (0.784 μg/g), allyl trisulfide (0.795 μg/g), allyl methyl sulfide (1.64 μg/g), allyl methyl disulfide (0.411 μg/g), allyl methyl trisulfide (0.695 μg/g), and ethyl 2-propenesulfinate (11.4 μg/g). The analysis of the licorice root extract powder gave the following results: formononetin (1.92 mg/g), isoliquiritigenin (9.61 mg/g), and 18β-glycyrrhetinic acid (43.9 mg/g). Methods were successfully developed to quantify the same compounds in the serum of test animals which had consumed feed spiked with garlic extract or licorice root extract powder. Only the 18β-glycyrrhetinic acid could be detected in the sera of such animals, however. An effort was also made to determine serum levels of prostaglandin E2 to correlate its inhibition with levels of the dietary components, but the prostaglandin E2 levels were too low to measure.     

Altered mitochondrial structure and motion dynamics in living cells with energy metabolism defects revealed by real time microscope imaging.

Using the real time microscope (RTM), a system applying new developments in light microscopy, we documented the spatial and temporal dynamics of mitochondrial behavior in human cultured skin fibroblasts. Without the use of stains or probes, we resolved fibroblast mitochondria as dark slender filaments of approximately 0.2 m wide and up to 10 m long, as well as a few smaller ovoid forms. In the living cell, the three most common mitochondrial movements were: (1) small oscillatory movements; (2) larger movements including filament extension, retraction, and branching as well as combinations of these actions; and (3) whole transit movements of single mitochondrial filaments. Skin fibroblasts from patients with mitochondrial complex I deficiency and normal fibroblasts during incubation with rotenone, or antimycin A, contained higher proportions of mitochondria in the swollen filamentous forms, nodal filaments, and ovoid forms rather than the slender filamentous forms in normal cells. Interestingly, decreased motility was observed with the more ovoid mitochondrial forms compared to the filamentous forms. We conclude that mitochondrial morphology and dynamic motion are strongly associated with changes in mitochondrial energy metabolism. Images documenting our observations are presented both at single time points and as QuickTime videos.