Double Aztec diamonds and the tacnode process

Discrete and continuous non-intersecting random processes have given rise to critical “infinite-dimensional diffusions”, like the Airy process, the Pearcey process and variations thereof. It has been known that domino tilings of very large Aztec diamonds lead macroscopically to a disordered region within an inscribed ellipse (arctic circle in the homogeneous case), and a regular brick-like region outside the ellipse. The fluctuations near the ellipse, appropriately magnified and away from the boundary of the Aztec diamond, form an Airy process, run with time tangential to the boundary.     

Characterization of surfactant complex mixtures using Raman spectroscopy and signal extraction methods: Application to laundry detergent deformulation

This paper presents the analysis of surfactants in complex mixtures using Raman spectroscopy combined with signal extraction (SE) methods. Surfactants are the most important component in laundry detergents. Both their identification and quantification are required for quality control and regulation purposes. Several synthetic mixtures of four surfactants contained in an Ecolabel laundry detergent were prepared and analyzed by Raman spectroscopy. SE methods, Independent Component Analysis and Multivariate Curve Resolution, were then applied to spectral data for surfactant identification and quantification. The influence of several pre-processing treatments (normalization, baseline correction, scatter correction and smoothing) on SE performances were evaluated by experimental design. By using optimal pre-processing strategy, SE methods allowed satisfactorily both identifying and quantifying the four surfactants. When applied to the pre-processed Raman spectrum of the Ecolabel laundry detergent sample, SE models remained robust enough to predict the surfactant concentrations with sufficient precision for deformulation purpose. Comparatively, a supervised modeling technique (PLS regression) was very efficient to quantify the four surfactants in synthetic mixtures but appeared less effective than SE methods when applied to the Raman spectrum of the detergent sample. PLS seemed too sensitive to the other components contained in the laundry detergent while SE methods were more robust. The results obtained demonstrated the interest of SE methods in the context of deformulation.     

A rapid and selective HPLC‐UV method for the quantitation of efavirenz in plasma from patients on concurrent HIV/AIDS and tuberculosis treatments

Owing to heterogeneity in therapeutic response, efavirenz is of research and clinical interest. There is a need to quantitate it using noncostly and selective methods. A method for efavirenz quantitation in plasma containing HIV and tuberculosis drugs was developed. Chromatographic separation was carried out using a C₁₈ column. The mobile phase consisted of 0.1% formic acid and acetonitrile, and was pumped at a flow rate of 0.3 mL/min. Efavirenz and ritonavir (internal standard) were monitored at 247 nm. Plasma proteins were precipitated by centrifugation. The analysis time was 6 min. The response was linear (r = 0.9997). The accuracy ranged between 98 and 115% (intraday) and between 99 and 117% (interday). The precision ranged from 1.670 to 4.087% (intraday) and from 3.447 to 13.347% (interday). Recovery ranged from 98 to 132%. Stability ranged between 99 and 123%. The selectivity was proven by analysis of drugs used for the management of HIV/AIDS and tuberculosis. Plasma sample analysis showed an efavirenz retention time of 5.57 min and a peak plasma concentration of 2.4 µg/mL occurring at 2 h. This method is rapid and selective, and thus suitable for monitoring efavirenz in patients with HIV/AIDS alone or co‐infected with tuberculosis in a less resourced setting. Copyright © 2013 John Wiley & Sons, Ltd.     

Practical Syntheses of Functionalized 1-Oxo-L,2,3,4-Tetrahydro-β-carboline-3-carboxylic Acid Esters

Three methods have been proposed for the preparation of functionalized 1-oxo-1,2,3,4-tetrahydro-β-carboline-3 carboxylates (3) from which the “acylazide formation-Curtius rearrangement-acid catalyzed ring closure” sequence starling from hemi-ester hemi-acids (8) seemed to be quite general.     

A Note on Convergence of the Equi-Energy Sampler

This paper studies maximum likelihood estimation for a parameterised elliptic diffusion in a manifold. The focus is on asymptotic properties of maximum likelihood estimates obtained from continuous time observation. These are well known when the underlying manifold is a Euclidean space. However, no systematic study exists in the case of a general manifold. The starting point is to write down the likelihood function and equation. This is achieved using the tools of stochastic differential geometry. Consistency, asymptotic normality and asymptotic optimality of maximum likelihood estimates are then proved, under regularity assumptions. Numerical computation of maximum likelihood estimates is briefly discussed.