This paper defines reduction on derivations in the strict intersection type assignment system of [2], by generalising cut-elimination, and shows a strong normalisation result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterisation of normalisability using intersection types.

Normalization of expression levels applied to microarray data can help in reducing measurement error. Different methods, including cyclic loess, quantile normalization and median or mean normalization, have been utilized to normalize microarray data. Although there is considerable literature regarding normalization techniques for mRNA microarray data, there are no publications comparing normali...

Profiling miRNA levels in cells with miRNA microarrays is becoming a widely used technique. Although normalization methods for mRNA gene expression arrays are well established, miRNA array normalization has so far not been investigated in detail. In this study we investigate the impact of normalization on data generated with the Agilent miRNA array platform. We have developed a method to select...

Alrstract--We consider the robust stability problem for a class of uncertain neutral time-delay systems where the characteristic equations involve a polytope ~ of quasipolynomials of neutral type. Given a stability region D in the complex plane our goal is to find a constructive technique to verify the D-stability of ~ (i.e. to verify whether the roots of every quasipolynomial in ~ all belong t...

The ring decomposition technique of part I is extended to the case when the factors in the direct product decomposition are no longer fields but arbitrary chain rings. This includes not only the case of quasi-cyclic codes over rings but also the case of quasi-cyclic codes over fields whose co-index is no longer prime to the characteristic of the field. A new quaternary construction of the Leech...

We provide a method for constructing a class of multivariate copulas depending on a univariate function. We study some properties of this class and present several examples. The same circle of ideas is used in a similar construction of quasi–copulas.

We introduce the notion of a standard system in order to deal with quasi-hereditary algebras. We shall prove that a necessary and sufficient condition for a finite dimensional algebra to be quasi-hereditary is the existence of a full and divisible standard system. As a further application, we obtain a sufficient condition for a standardly stratified algebra. To Roger Carter on his 65th birthday

In this paper, we investigate approximation of quasi-projection operators in Besov spaces B p,q, μ > 0, 1 ≤ p, q ≤ ∞. Suppose I is a countable index set. Let (φi)i∈I be a family of functions in Lp(IR), and let (φ̃i)i∈I be a family of functions in Lp̃(IR), where 1/p+ 1/p̃ = 1. Let Q be the quasi-projection operator given by