We investigate the assumption that sources have disjoint support in the time domain, time-frequency domain, or frequency domain. We call such signals disjoint orthogonal. The class of signals that approximately satisfies this assumption includes many synthetic signals, music and speech, as well as some biological signals. We measure the disjoint orthogonality of the benchmark signals in the ICA...

Orthogonality or near-orthogonality is an important property in the design of experiments. Supersaturated designs are natural when we wish to investigate the main effects for a large number of factors but are restricted to a small number of runs. These supersaturated designs, by definition, cannot satisfy pairwise orthogonality of all the factor columns in the designmatrix. Hence, we need amean...

In the downlink of WCDMA systems, multi-path propagation destroys the orthogonality of the user signals and causes multi-user interference (MUI). Chip-level equalization can restore the orthogonality and suppress the MUI. However, adaptive implementations of the chip-level equalizer receiver that can track time-varying multi-path channels are hard to realize in practice for two reasons : loss o...

In this paper we study the orthogonality conditions satisfied by Jacobi polynomials P (α,β) n when the parameters α and β are not necessarily > −1. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a number of con...

Abstract. In this paper we study the orthogonality conditions satisfied by Jacobi polynomials P (α,β) n when the parameters α and β are not necessarily > −1. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a num...

S.C. Zhang has put forward the idea that high-temperature-superconductors can be described in the framework of an SO(5)-symmetric theory in which the three components of the antiferromagnetic order-parameter and the two components of the two-particle condensate form a fivecomponent order-parameter with SO(5) symmetry. Interactions small in comparison to this strong interaction introduce anisotr...

The set of time series of spikes is expanded into a vector space, V , by taking all linear combinations. A definition is then given for an inner product on this vector space. This gives a definition of norm, of distance between time series, and of orthogonality. This also allows us to compute the best approximation to a given time series which can be formed by a linear combination of some given...

We present analytic and numerical studies based on Landauer theory of conductance antiresonances of molecular wires. Our analytic treatment is a solution of the Lippmann-Schwinger equation for the wire that includes the effects of the non-orthogonality of the atomic orbitals on different atoms exactly. The problem of non-orthogonality is treated by solving the transport problem in a new Hilbert...