Linear variance bounds for particle approximations of time-homogeneous Feynman–Kac formulae

This article establishes sufficient conditions for a linear-in-time bound on the non-asymptotic variance for particle approximations of time-homogeneous Feynman–Kac formulae. These formulae appear in a wide variety of applications including option pricing in finance and risk sensitive control in engineering. In direct Monte Carlo approximation of these formulae, the non-asymptotic variance typically increases at an exponential rate in the time parameter. It is shown that a linear bound holds when a non-negative kernel, defined by the logarithmic potential function and Markov kernel which specify the Feynman–Kac model, satisfies a type of multiplicative drift condition and other regularity assumptions. Examples illustrate that these conditions are general and flexible enough to accommodate two rather extreme cases, which can occur in the context of a non-compact state space: (1) when the potential function is bounded above, not bounded below and the Markov kernel is not ergodic; and (2) when the potential function is not bounded above, but the Markov kernel itself satisfies a multiplicative drift condition.     

Synthetic talc as a solid base catalyst for condensation of aldehydes and ketones

Magnesium organo silicates (MOSs; synthetic talc) as such and with amine surface functionalities were synthesized by sol–gel method under non-hydrothermal conditions and characterized by spectroscopic techniques. The synthesized talc samples were observed to be thermally stable up to 200 °C in nitrogen atmosphere and used as catalysts for condensation of aldehydes and ketones. Application of synthetic talc as a solid base catalyst for condensation of aldehydes and ketones is being reported for the first time. The effect of solvent, solvent to reactant molar ratio, amount of catalyst and temperature was studied in detail for self-condensation of propanal. High conversion (86%) of propanal with 95% selectivity of 2-methylpentenal was achieved using dimethyl sulphoxide as a solvent. The kinetic study was carried out for the condensation of propanal catalyzed by amine functionalized MOS under optimum reaction conditions. Catalyst was re-used without significant loss in activity up to three cycles.     

Universality of the Stochastic Airy Operator

We introduce a new method for studying universality of random matrices. Let T_n be the Jacobi matrix associated to the Dyson beta ensemble with uniformly convex polynomial potential. We show that after scaling, T_n converges to the stochastic Airy operator. In particular, the top edge of the Dyson beta ensemble and the corresponding eigenvectors are universal. As a byproduct, these ideas lead to conjectured operator limits for the entire family of soft edge distributions.© 2015 Wiley Periodicals, Inc.     

A Sequential Algorithm for Fast Fitting of Dirichlet Process Mixture Models

In this article, we propose an improvement on the sequential updating and greedy search (SUGS) algorithm for fast fitting of Dirichlet process mixture models. The SUGS algorithm provides a means for very fast approximate Bayesian inference for mixture data which is particularly of use when datasets are so large that many standard Markov chain Monte Carlo (MCMC) algorithms cannot be applied efficiently, or take a prohibitively long time to converge. In particular, these ideas are used to initially interrogate the data, and to refine models such that one can potentially apply exact data analysis later on. SUGS relies upon sequentially allocating data to clusters and proceeding with an update of the posterior on the subsequent allocations and parameters which assumes this allocation is correct. Our modification softens this approach, by providing a probability distribution over allocations, with a similar computational cost; this approach has an interpretation as a variational Bayes procedure and hence we term it variational SUGS (VSUGS). It is shown in simulated examples that VSUGS can outperform, in terms of density estimation and classification, a version of the SUGS algorithm in many scenarios. In addition, we present a data analysis for flow cytometry data, and SNP data via a three-class Dirichlet process mixture model, illustrating the apparent improvement over the original SUGS algorithm.     

Synthesis and characterization of (S)-amino alcohol modified M41S as effective material for the enantioseparation of racemic compounds

A new chiral stationary phase (CSP) was synthesized based on (S)-1-anilino-3-propyl-2-propanol covalently bonded to the mesoporous semi-crystalline material M41S. Direct semipreparative enantioseparation of mandelic acid could be achieved using medium pressure chromatography. Partly separated could also be the enantiomers of 2,2'-dihydroxy-1,1'-binaphthalene, cyanochromene oxide, diethyl tartrate and 2-phenyl propionic acid. The characterization of CSP was accomplished by microanalysis, cross polarized magic angle spinning (CP-MAS) 13C NMR, powder X-ray diffraction (XRD), FTIR, thermo-gravimetric analysis (TGA), N2 adsorption-desorption isotherm, scanning electron microscopy (SEM) and solid reflectance UV-vis spectroscopy. Furthermore the stability of CSP was satisfactory as it could withstand three washing and reuse experiments of enantioseparation of mandelic acid without loss in its performance.     

Electrochemical behavior of zopiclone

The electrochemical properties of zopiclone, an anxiolytic and hypnotic drug, have been investigated by different techniques. The compound is reduced in two 2-electron steps in the pH range 0-12. The first step, which corresponds to the reduction of the pyrazine ring, is reversible in acidic and neutral solutions. Strong adsorption phenomena accompany the reduction process in acidic and neutral media. Zopiclone can be quantitatively measured over the entire pH range using DC polarography. However, the use of differential pulse and square-wave modes for quantitative measurements is more limited due to a slope modification in the current-concentration relationship. Adsorptive stripping voltammetry can be applied to the determination of low levels of the drug at pH 9, but only short deposition times may be used because large amounts of material accumulated under stirring conditions due to fast adsorption kinetics are rapidly released from the electrode surface. Detection limits are 1 x 10(-7)M and 2 x 10(-10)M for polarography and adsorptive stripping voltammetry, respectively. Only the first wave is of analytical interest for both techniques.