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.     

Self-Organizing Maps and Support Vector Regression as aids to coupled chromatography: illustrated by predicting spoilage in apples using volatile organic compounds

The paper describes the application of SOMs (Self-Organizing Maps) and SVR (Support Vector Regression) to pattern recognition in GC-MS (gas chromatography-mass spectrometry). The data are applied to two groups of apples, one which is a control and one which has been inoculated with Penicillium expansum and which becomes spoiled over the 10-day period of the experiment. GC-MS of SPME (solid phase microextraction) samples of volatiles from these apples were recorded, on replicate samples, over time, to give 58 samples used for pattern recognition and a peak table obtained. A new approach for finding the optimum SVR parameters called differential evolution is described. SOMs are presented in the form of two-dimensional maps. This paper shows the potential of using machine learning methods for pattern recognition in analytical chemistry, particularly as applied to food chemistry and biology where trends are likely to be non-linear.     

Diffusion-driven pattern formation in ionic chemical solutions

The driving force in diffusion-driven pattern formation is the difference in the diffusional flux of the key species, which in the case of ionic systems builds up a local electric field at the concentration gradients. The arising additional migrational flux not only decreases but also enhances the instability of the base state, depending on the charge distribution among the components. The opposite charges on the slower diffusing autocatalyst and its reacting counterpart favor pattern formation and shift the onset of instability to a smaller difference in the diffusion coefficients. The same charges, in addition to having the opposite effect, may even lead to the complete stabilization of planar reaction fronts unstable in the neutral system.     

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.