Mean curvature flow in SE (2) and applications to visual perception

Our goal in this thesis is to provide a result of existence of the degenerate non-linear, non-divergence PDE which describes the mean curvature flow in the Lie group SE(2) equipped with a sub-Riemannian metric. The research is motivated by problems of visual completion and models of the visual cortex.

Curvature induced nanoscale rafts in lipid membranes

We present a coarse grained model for computer simulations of lipid mixtures, which we use to study generic mechanisms for the formation of nanoscale membrane structures (lipid rafts). We observe that even a two component system can separate into rafts of finite size, and we study these rafts and other membrane structures in detail. We look at the characteristics of our model that enable these phenomena and how they may relate to lipid-cholesterol or lipid-lipid mixtures. We propose an explanation for our findings using elastic theory to describe a possible mechanism of raft stabilization via curvature differences between coexisting lipid phases and we investigate whether this theory can be used to explain the results of our computer simulations.

Equivariant inverse spectral theory and toric orbifolds

Let O-2n be a symplectic toric orbifold with a fixed T-n-action and with a tonic Kahler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace Delta(g) operator on C-infinity(O) determines O up to symplectomorphism. In the setting of tonic orbifolds we shmilicantly improve upon our previous results and show that a generic tone orbifold is determined by its equivariant spectrum, up to two possibilities. This involves developing the asymptotic expansion of the heat trace on an orbifold in the presence of an isometry. We also show that the equivariant spectrum determines whether the toric Kahler metric has constant scalar curvature. (C) 2012 Elsevier Inc. All rights reserved.

Effect of constant and variable domain glycosylation on pharmacokinetics of therapeutic antibodies in mice

Previous studies on the effect of glycosylation on the elimination rate of antibodies have produced conflicting results. Here, we performed pharmacokinetic studies in mice with two preparations of a monoclonal IgG1 antibody enriched for complex type or high mannose type oligosaccharides at the Fc glycosylation site. No significant difference in the serum half-life was found between the two antibody glycoforms, nor was any difference observed in the serum half-lives of different complex type glycoforms. To evaluate the influence of glycosylation within the variable domain, a second monoclonal antibody, glycosylated in both the Fc and Fv domains, was separated into fractions containing different amounts of Fv-associated sialic acid and administered to mice. Again, no significant difference was found in the clearance rates of variants carrying different amounts of Fv-associated sialic acid or lacking Fv-glycosylation. These results suggest that glycosylation has little or no impact on the pharmacokinetic behavior of these two monoclonal antibodies in mice.

The Effect of Temperature on the Rate of Dissolution of Gold in Cyanide Solutions which have a Constant Oxygen Content.

Since the development of cyanidation into a highly efficient process for treating gold ores, many papers have been written on its various aspects. Although, there has been much work done on it, the chemistry of the reaction is not yet completely understood.

Stereoselective pharmacokinetics of ketamine and norketamine after constant rate infusion of a subanesthetic dose of racemic ketamine or S-ketamine in Shetland ponies

OBJECTIVE: To evaluate pharmacokinetics of ketamine and norketamine enantiomers after constant rate infusion (CRI) of a subanesthetic dose of racemic ketamine or S-ketamine in ponies. ANIMALS: Five 6-year-old Shetland pony geldings that weighed between 101 and 152 kg. PROCEDURES: In a crossover study, each pony received a CRI of racemic ketamine (loading dose, 0.6 mg/kg; CRI, 0.02 mg/kg/min) and S-ketamine (loading dose, 0.3 mg/kg; CRI, 0.01 mg/kg/min), with a 1-month interval between treatments. Arterial blood samples were collected before and at 5, 15, 30, 45, and 60 minutes during drug administration and at 5, 10, 30, and 60 minutes after discontinuing the CRI. Plasma ketamine and norketamine enantiomers were quantified by use of capillary electrophoresis. Individual R-ketamine and S-ketamine concentration-versus-time curves were analyzed by use of a monocompartmental model. Plasma disposition curves for R-norketamine and S-norketamine were described by estimating the area under the concentration-versus-time curve (AUC), maximum concentration (Cmax), and time until Cmax. RESULTS: Plasma concentrations of S-ketamine decreased and biodegradation products increased more rapidly after S-ketamine CRI, compared with results after racemic ketamine CRI. The R-norketamine was eliminated faster than was the S-norketamine. Significant differences between treatments were found for the AUC of S-ketamine and within the racemic ketamine CRI for the AUC and Cmax of norketamine isomers. CONCLUSIONS AND CLINICAL RELEVANCE: CRI of S-ketamine may be preferable over CRI of racemic ketamine in standing equids because the S-enantiomer was eliminated faster when infused alone instead of as part of a racemic mixture.