We investigate mutual dependencies of subexpressions of a computable expression, in orthogonal rewrite systems, and identify conditions for their concurrent independent computation. To this end, we introduce concepts familiar from ordinary Euclidean Geometry (such as basis, projection, distance, etc.) for reduction spaces. We show how a basis for an expression can be constructed so that any red...

This paper presents the theoretical aspects of a methodology for the design of robust orthogonal adaptive decision feedback equalizers. The dispersive transmission channel is assumed to have a transfer function type of description with small uncertainties in the parameters. A decision feedback equalizer is designed minimizing a mean square error objective function that takes into account the un...

To study orthogonal arrays and signed orthogonal arrays, Ray-Chaudhuri and Singhi (1988 and 1994) considered some module spaces. Here, using a linear algebraic approach we define an inclusion matrix and find its rank. In the special case of Latin squares we show that there is a straightforward algorithm for generating a basis for this matrix using the so-called intercalates. We also extend this...

We give a basis of bideterminants for the coordinate ring K[O(n)] of the orthogonal group O(n, K), where K is an infinite field of characteristic not 2. The bideterminants are indexed by pairs of Young tableaux which are O(n)-standard in the sense of King-Welsh. We also give an explicit filtration of K[O(n)] as an O(n, K)-bimodule, whose factors are isormorphic to the tensor product of orthogon...

The sum-product or belief propagation (BP) algorithm is a widely used message-passing technique for computing approximate marginals in graphical models. We introduce a new technique, called stochastic orthogonal series message-passing (SOSMP), for computing the BP fixed point in models with continuous random variables. It is based on a deterministic approximation of the messages via orthogonal ...

We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the matrix reproducing kernel. The key idea of the proof is to represent the differentiation operator matrix written in the basis of orthogonal polynomials as a...

We consider an approximation of L 2 0; 1) functions by linear combinations of exponentials fexp(? ` t)g. Having derived explicitly by Fourier transform techniques an orthogonal basis of exponentials, we specialize the discussion to the choicè = q ` , ` = 0; 1; : : :, where q 2 (0; 1). In that case the underlying orthogonal functions possess a particularly appealing form and they obey interestin...

In this paper we list some new orthogonal main e ects plans for three level designs for and factors in runs and compare them with designs obtained from the existing L orthogonal array We show that these new designs have better projection properties and can provide better parameter estimates for a range of possible models Additionally we study designs in other smaller run sizes when there are in...

An orthogonal double cover (ODC) of a complete graph is a collection of graphs such that every two of them share exactly one edge and every edge of the complete graph belongs to exactly two of the graphs. In this paper, we construct ODCs of Kn where all graphs are isomorphic to certain spanning subgraphs G (such as co-triangles, a star with cotriangles, and two other graph classes).

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