Maximizing antichains in the cube with fixed size of a shadow

In the n-dimensional cube, we determine the maximum size of antichains having a lower shadow of exactly m elements in the k-th level.     

A chemically sterilizable barrier for the protection of fermentors during automatic sampling into a low-injection system

Two three-way valves are connected by a short stainless steel tube and attached to a model fermentor. A sample can be drawn straight through the valves and into an analyzer for monitoring of oxygen or glucose. The valves are switched to an external solution after the sample has been taken. Solutions of 5% formaldehyde provide a barrier to the intrusion of micro-organisms into the fermentor, whereas water solutions are ineffective. With water in the barrier, infections occur after a few days when the system is provoked by a growing culture ofE.coli at the outlet. The concept of a chemically sterilizable barrier is particularly well suited for the intermittent needs of flow-injection systems used for process monitoring.     

Liquid phase synthesis of chiral quinoxalinones by microwave irradiation

Single mode microwave-assisted combinatorial synthesis of biologically interesting quinoxalinones is described. Chiral libraries of quinoxalinone were readily assembled utilizing S_NAr reactions, reduction and followed with concomitant cyclization under microwave irradiation. Enantiomeric 1,2,3,4-tetrahydroquinoxalinones were isolated in excellent yield and purity after cleavage.     

Estimating mean time to absorption for a markov chain with limited information

In many applications of absorbing Markov chains, solution of the problem at hand involves finding the mean time to absorption. Moreover, in almost all real world applications of Markov chains, accurate estimation of the elements of the probability matrix is a major concern. This paper develops a technique that provides close estimates of the mean number of stages before absorption with only the row sums of the transition matrix of transient states.     

Quantile regression for longitudinal data

The penalized least squares interpretation of the classical random effects estimator suggests a possible way forward for quantile regression models with a large number of “fixed effects”. The introduction of a large number of individual fixed effects can significantly inflate the variability of estimates of other covariate effects. Regularization, or shrinkage of these individual effects toward a common value can help to modify this inflation effect. A general approach to estimating quantile regression models for longitudinal data is proposed employing ?₁ regularization methods. Sparse linear algebra and interior point methods for solving large linear programs are essential computational tools.     

L 2-approximation by the translates of a function and related attenuation factors

Summary Let be thek-dimensional subspace spanned by the translates (·–2j/k),j=0, 1, ...,k–1, of a continuous, piecewise smooth, complexvalued, 2-periodic function . For a given functionfL ²(–, ), its least squares approximantS _kf from can be expressed in terms of an orthonormal basis. Iff is continuous,S _kf can be computed via its discrete analogue by fast Fourier transform. The discrete least squares approximant is used to approximate Fourier coefficients, and this complements the works of Gautschi on attenuation factors. Examples of include the space of trigonometric polynomials where is the de la Valleé Poussin kernel, algebraic polynomial splines where is the periodic B-spline, and trigonometric polynomial splines where is the trigonometric B-spline.