Entangled matrix builders

Matrices are often built and designed by applying procedures from lower order matrices. Matrix tensor products, direct sums and multiplication of matrices retain certain properties of the lower order matrices; matrices produced by these procedures are said to be {\em separable}. {\em Entangled} matrices is the term used for matrices which are not separable. Here design methods for entangled matrices are derived. These can retain properties of lower order matrices or acquire new required properties. Entangled matrices are often required in practice and a number of applications of the designs are given. Methods with which to construct multidimensional entangled paraunitary matrices are derived; these have applications for wavelet and filter bank design. New entangled unitary matrices are designed; these are used in quantum information theory. Efficient methods for designing new full diversity constellations of unitary matrices with excellent {\em quality} (a defined term) for space time applications are given

The Hadamard circulant conjecture

It is shown that if $H$ is a circulant Hadamard 4n\ti 4n then $n=1$. This proves the Hadamard circulant conjecture.Comment: This is post publication revision of on-line Bull. London Math. Soc. version which changes subsection 3.

The ICON Challenge on Algorithm Selection

Algorithm selection is of increasing practical relevance in a variety of applications. Many approaches have been proposed in the literature, but their evaluations are often not comparable, making it hard to judge which approaches work best. The ICON Challenge on Algorithm Selection objectively evaluated many prominent approaches from the literature, making them directly comparable for the first time. The results show that there is still room for improvement, even for the very best approaches