Functional Quantization and Small Ball Probabilities for Gaussian Processes

Quantization consists in studying the L ^r -error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer⁽⁴⁾ and Dereich et al. ⁽³⁾ relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L ^r -quantization error from logarithmic small ball asymptotics and vice versa.     

Origins and predictions of stereoselective antibody catalysis: theoretical analysis of Diels-Alder catalysis by 39A11 and its germ-line antibody

The binding of enantiomeric haptens and transition states by the Schultz Diels-Alderase antibody 39A11 and its germ-line antibody were studied theoretically. The mechanisms by which one hapten and one transition state stereoisomer is recognized selectively are explored with docking simulations and quantum mechanical models. Transition states of the relevant Diels-Alder reaction were located with density functional theory. A prediction is made that the stereoselectivity of 39A11 will be achieved by two strategically placed hydrogen bonds and pi-stacking interactions of the maleimide with a binding-site tryptophan, arranged so as to coordinate one enantiomeric transition state. Binding of other ligands by antibody 39A11 and the germ-line antibody has also been investigated. The polyspecific nature of 39A11 and its germ-line precursor was found to originate from the general ability of the binding pockets to achieve hydrophobic binding of small organic substrates. Comparison of the highly homologous progesterone and Diels-Alderase antibodies (DB3, 1E9, and 39A11) highlights the fact that differences of several key residues in the binding pockets are sufficient to confer selectivity for different antigens.     

Liquid crystal mixtures for potential infrared applications

Liquid crystals (LCs) with diazo linkages have high dielectric and optical anisotropy. Two newly synthesized liquid crystalline compounds were dissolved in room temperature LC hosts, E7 and PTTP-24/36, to assess their properties. It was found that these mixtures have higher birefringence, larger dielectric anisotropy, and better elastic properties than the hosts. Satisfactory viscoelastic coefficients were also obtained for these mixtures, showing that they are promising LC materials for applications in the near IR region.     

Synthesis of (±)Dehydroxyglaupalol and Analogs

The natural furocoumarin dehydroxyglaupalol and two analogs were prepared by reaction of the appropriate 4-hydroxy-coumarin with 3-chloro-3-methylbutyne in basic medium, followed by catalytic hydrogenation of the exo double bond.     

Product Markovian Quantization of a Diffusion Process with Applications to Finance

Methodology and Computing in Applied Probability - We introduce a new methodology for the quantization of the Euler scheme for a d-dimensional diffusion process. This method is based on a Markovian...     

Diamond kinoform hard X‐ray refractive lenses: design,nanofabrication and testing

Motivated by the anticipated advantageous performance of diamond kinoform refractive lenses for synchrotron X‐ray radiation studies, this report focuses on progress in designing, nanofabricating and testing of their focusing performance. The method involves using lift‐off and plasma etching to reproduce a planar definition of numerically determined kinoform refractive optics. Tests of the focusing action of a diamond kinoform refractive lens at the APS 8‐ID‐I beamline demonstrate angular control of the focal spot.