When an orthogonal array is projected on a small number of factors, as is done in screening experiments, the question of interest is the structure of the projected design, by which we mean its decomposition in terms of smaller arrays of the same strength. In this paper we investigate the decomposition of arrays of strength t having t + 1 factors. The decomposition problem is well-understood for...

We present a new scale-invariant cost function for non-orthogonal joint-diagonalization of a set of symmetric matrices with application to Independent Component Analysis (ICA). We derive two gradient minimization schemes to minimize this cost function. We also consider their performance in the context of an ICA algorithm based on non-orthogonal joint diagonalization.

We give a characterization of operators on a separable Hilbert space of norm less than one that can be represented as products of orthogonal projections and give an estimate on the number of factors. We also describe the norm closure of the set of all products of orthogonal projections.

In this paper we conjecture some regularity properties for the zeros of Wronskian and Casorati determinants whose entries are orthogonal polynomials. These determinants are formed by choosing orthogonal polynomials whose degrees run on a finite set F of nonnegative integers. The case when F is formed by consecutive integers was studied by Karlin and Szegő. 2010 Mathematics Subject Classificatio...

2014 Consideration of the eigenproblem of the synaptic matrix in Hopfield’s model of neural networks suggests to introduce a matrix built up from an orthogonal set, orthogonal to the original memories. With this new scheme, capacity storage is significantly enhanced and robustness at least conserved. Revue Phys. Appl. 22 (1987) 1321-1325 OCTOBRE 1987, PAGE Classification Physics Abstracts 42.30...