Related papers: Array Orthogonality in Higher Dimensions

Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…

Orthogonal array based space-filling designs (Owen [Statist. Sinica 2 (1992a) 439-452]; Tang [J. Amer. Statist. Assoc. 88 (1993) 1392-1397]) have become popular in computer experiments, numerical integration, stochastic optimization and…

Hypergraphs capture multi-way relationships in data, and they have consequently seen a number of applications in higher-order network analysis, computer vision, geometry processing, and machine learning. In this paper, we develop…

In an early paper, He and Tang [Biometrika 100 (2013) 254-260] introduced and studied a new class of designs, strong orthogonal arrays, for computer experiments, and characterized such arrays through generalized orthogonal arrays. The…

We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…

The metric dimension of a graph is the smallest number of nodes required to identify all other nodes based on shortest path distances uniquely. Applications of metric dimension include discovering the source of a spread in a network,…

The general correlation function for the eigenvalues of $p$ complex hermitian matrices coupled in a chain is given as a single determinant. For this we use a slight generalization of a theorem of Dyson.

The space of derivations of finite dimensional evolution algebras associated to graphs over a field with characteristic zero has been completely characterized in the literature. In this work we generalize that characterization by describing…

We introduce two-dimensional toroidal arrays that are a variant of the de Bruijn tori. We call them nested perfect toroidal arrays. Instead of asking that every array of a given size has exactly one occurrence, we partition the positions in…

Complex structures are typical in machine learning. Tailoring learning algorithms for every structure requires an effort that may be saved by defining a generic learning procedure adaptive to any complex structure. In this paper, we propose…

We investigate graphs that have characteristic-dependent well-covered dimension and show how more of these graphs can be constructed from known ones.

We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.

A perfect matching in a 4-uniform hypergraph is a subset of $\lfloor\frac{n}{4}\rfloor$ disjoint edges. We prove that if $H$ is a sufficiently large 4-uniform hypergraph on $n=4k$ vertices such that every vertex belongs to more than…

We introduce a construction and an algorithm, both based on Topological Data Analysis (TDA), to tackle the problem of the isomorphism check of Orthogonal Arrays (OAs). Specifically, we associate to any binary OA a persistence diagram, one…

Standard statistical techniques often require transforming data to have mean $0$ and standard deviation $1$. Typically, this process of "standardization" or "normalization" is applied across subjects when each subject produces a single…

Fix a point in a finite-dimensional complex vector space and consider the sequence of iterates of this point under the composition of a unitary map with the orthogonal projection on the hyperplane orthogonal to the starting point. We prove…

In this paper, a sequence of linear combination of $R_{I}$ type polynomials such that the terms in this sequence have a common zero is constructed. A biorthogonality relation arising from such a sequence is discussed. Besides a sequence of…

For a more general notion of Cartan connection we define characteristic classes, we investigate their relation to usual characteristic classes.

Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…

This paper seeks to answer the question: as the (near-) orthogonality of weights is found to be a favorable property for training deep convolutional neural networks, how can we enforce it in more effective and easy-to-use ways? We develop…