Related papers: Array Orthogonality in Higher Dimensions

Orthogonal arrays are arguably one of the most fascinating and important statistical tools for efficient data collection. They have a simple, natural definition, desirable properties when used as fractional factorials, and a rich and…

We present a $N$-dimensional generalization of the two-dimensional block-circulant perfect array construction by \cite{Blake2013}. As in \cite{Blake2013}, the families of $N$-dimensional arrays possess pairwise \textit{good} zero…

Orthogonal arrays play a fundamental role in many applications. However, constructing orthogonal arrays with the required parameters for an application usually is extremely difficult and, sometimes, even impossible. Hence there is an…

We introduce several new constructions for perfect periodic autocorrelation sequences and arrays over the unit quaternions. This paper uses both mathematical proofs and com- puter experiments to prove the (bounded) array constructions have…

Orthogonal array and a large set of orthogonal arrays are important research objects in combinatorial design theory, and they are widely applied to statistics, computer science, coding theory and cryptography. In this paper, some new series…

Orthogonal array, a classical and effective tool for collecting data, has been flourished with its applications in modern computer experiments and engineering statistics. Driven by the wide use of computer experiments with both qualitative…

We introduce a construction for families of 2n-dimensional arrays with asymptotically optimal pairwise cross-correlation. These arrays are constructed using a circulant array of n-dimensional Legendre arrays. We also introduce an…

In this paper, we show how certain three-class association schemes and orthogonal arrays give rise to partial geometric designs. We also investigate the connections between partial geometric designs and certain regular graphs having three…

Sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. Among the known sequences, cyclotomic families have the optimal autocorrelation property. In this paper, we…

The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…

We present a relation between convergence of multiple and single orthogonal series. This relation implies a complete characterization of all multiple sequences $(a_{n_1...n_d})_{n_1,...,n_d\in\bb N}$ such that for all orthonormal…

Connecting curves have been shown to organize the rotational structure of strange attractors in three-dimensional dynamical systems. We extend the description of connecting curves and their properties to higher dimensions within the special…

Orthogonal Fractional Factorial Designs and in particular Orthogonal Arrays are frequently used in many fields of application, including medicine, engineering and agriculture. In this paper we present a methodology and an algorithm to find…

Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…

We produce two-dimensional contiguous relations for generalized hypergeometric functions by starting with linearization coefficients for some continuous generalized hypergeometric orthogonal polynomials in the Askey-scheme.

In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…

This article studies a large, general class of orthogonal polytopes which we may call "generic orthotopes". These objects emerged from a desire to represent a Coxeter complex by an orthogonal polytope that is particularly nice with respect…

This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…

For an integer $p\geq 2$ we construct vertical and horizontal one-pth Riordan arrays from a Riordan array. When $p=2$, one-pth Riordan arrays reduced to well known half Riordan arrays. The generating functions of the $A$-sequences of…

Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the…