Let S ⊆ {0, 1} and R be any polytope contained in [0, 1] with R ∩ {0, 1} = S. We prove that R has bounded Chvátal-Gomory rank (CG-rank) provided that S has bounded pitch and bounded gap, where the pitch is the minimum integer p such that all p-dimensional faces of the 0/1-cube have a nonempty intersection with S, and the gap is a measure of the size of the facet coefficients of conv(S). Let H [...

Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor data which only approximately fulfils the low-rank requirement. To address these two issues, we develop a data-adaptive tensor completion model which explici...

The symmetry preserving singular value decomposition (SPSVD) produces the best symmetric (low rank) approximation to a set of data. These symmetric approximations are characterized via an invariance under the action of a symmetry group on the set of data. The symmetry groups of interest consist of all the non-spherical symmetry groups in three dimensions. This set includes the rotational, refle...

We determine the Waring rank and a Waring decomposition of the fundamental skew invariant of any complex reflection group whose highest degree is a regular number. This includes all irreducible real reflection groups. Given a homogeneous polynomial f of degree d, the Waring rank of f , denoted r(f), is the smallest positive integer r such that there exist linear forms l1, . . . , lr with f = l ...

In AI and Web communities, many applications utilize PageRank. To obtain high PageRank score nodes, the original approach iteratively computes the PageRank score of each node until convergence by using the whole graph. If the graph is large, this approach is infeasible due to its high computational cost. The goal of this study is to find top-k PageRank score nodes efficiently for a given graph ...