34 citations · 75 across the 22 of their papers we have counts for
22 papers
Exact Second-Order Zarankiewicz Numbers for Complete-Graph Incidence Families
Yannan Chen, Liqun Qi, Johan Löfberg
For , , let the complete-graph incidence family on have the vertices of as columns, its edges as rows, and the incidence graph as one-edge graph. Th…
Exact and Asymptotic Values for Weak Limited Augmented Zarankiewicz Numbers in the Case
Liqun Qi, Johan Löfberg, Yannan Chen
We determine the exact weak limited augmented Zarankiewicz numbers for all : \[ z_{wL}(m,3)= \begin{cases} m+3+\left\lceil \dfrac{m}{2}\right\rceil+1, & 9\le…
The SOS Rank of a Biquadratic Form via Orthogonality
Yannan Chen
Biquadratic forms arise naturally in polynomial optimization, tensor analysis, and quantum information theory. A key problem is determining the minimal number of squares needed in…
Even Order Pascal Tensors are Positive Definite
Chunfeng Cui, Liqun Qi, Yannan Chen
In this paper, we show that even order Pascal tensors are positive definite, and odd order Pascal tensors are strongly completely positive. The significance of these is that our in…
Multi-Linear Pseudo-PageRank for Hypergraph Partitioning
Yannan Chen, Wen Li, Jingya Chang
Motivated by the PageRank model for graph partitioning, we develop an extension of PageRank for partitioning uniform hypergraphs. Starting from adjacency tensors of uniform hypergr…
A Low Rank Quaternion Decomposition Algorithm and Its Application in Color Image Inpainting
Yannan Chen, Liqun Qi, Xinzhen Zhang +1
In this paper, we propose a lower rank quaternion decomposition algorithm and apply it to color image inpainting. We introduce a concise form for the gradient of a real function in…
A Tensor Rank Theory and Maximum Full Rank Subtensors
Liqun Qi, Xinzhen Zhang, Yannan Chen
A matrix always has a full rank submatrix such that the rank of this matrix is equal to the rank of that submatrix. This property is one of the corner stones of the matrix rank the…
Triple Decomposition and Tensor Recovery of Third Order Tensors
Liqun Qi, Yannan Chen, Mayank Bakshi +1
In this paper, we introduce a new tensor decomposition for third order tensors, which decomposes a third order tensor to three third order low rank tensors in a balanced way. We ca…
A Polynomially Irreducible Functional Basis of Elasticity Tensors
Zhenyu Ming, Yannan Chen, Liqun Qi +1
Tensor function representation theory is an essential topic in both theoretical and applied mechanics. For the elasticity tensor, Olive, Kolev and Auffray (2017) proposed a minimal…
Tensor Norm, Cubic Power and Gelfand Limit
Liqun Qi, Shenglong Hu, Xinzhen Zhang +1
We establish two inequalities for the nuclear norm and the spectral norm of tensor products. The first inequality indicates that the nuclear norm of the square matrix is a matrix n…
A Polynomially Irreducible Functional Basis of Hemitropic Invariants of Piezoelectric Tensors
Y. Chen, Z. Ming, L. Qi +1
For piezoelectric tensors, Olive (2014) proposed a minimal integrity basis of 495 hemitropic invariants, which is also a functional basis. In this article, we construct a new funct…
Two Irreducible Functional Bases of Isotropic Invariants of A Fourth Order Three-Dimensional Symmetric and Traceless Tensor
Zhongming Chen, Yannan Chen, Liqun Qi +1
The elasticity tensor is one of the most important fourth order tensors in mechanics. Fourth order three-dimensional symmetric and traceless tensors play a crucial role in the stud…
An Irreducible Polynomial Functional Basis of Two-dimensional Eshelby Tensors
Zhenyu Ming, Liping Zhang, Yannan Chen
Representation theorems for both isotropic and anisotropic functions are of prime importance in both theoretical and applied mechanics. The Eshelby inclusion problem is very fundam…
Irreducible Function Bases of Isotropic Invariants of A Third Order Three-Dimensional Symmetric and Traceless Tensor
Yannan Chen, Shenglong Hu, Liqun Qi +1
Third order three-dimensional symmetric and traceless tensors play an important role in physics and tensor representation theory. A minimal integrity basis of a third order three-d…
Spectral Analysis of Piezoelectric Tensors
Yannan Chen, Antal Jákli, Liqun Qi
A third order real tensor is called a piezoelectric-type tensor if it is partially symmetric with respect to its last two indices. The piezoelectric tensor is a piezoelectric-type…
Octupolar Tensors for Liquid Crystals
Yannan Chen, Liqun Qi, Epifanio G. Virga
A third-order three-dimensional symmetric traceless tensor, called the \emph{octupolar} tensor, has been introduced to study tetrahedratic nematic phases in liquid crystals. The oc…
Computing Eigenvalues of Large Scale Sparse Tensors Arising from a Hypergraph
Jingya Chang, Yannan Chen, Liqun Qi
The spectral theory of higher-order symmetric tensors is an important tool to reveal some important properties of a hypergraph via its adjacency tensor, Laplacian tensor, and signl…
Finding the maximum eigenvalue of a class of tensors with applications in copositivity test and hypergraphs
Haibin Chen, Yannan Chen, Guoyin Li +1
Finding the maximum eigenvalue of a symmetric tensor is an important topic in tensor computation and numerical multilinear algebra. This paper is devoted to a semi-definite program…
Computing Eigenvalues of Large Scale Hankel Tensors
Yannan Chen, Liqun Qi, Qun Wang
Large scale tensors, including large scale Hankel tensors, have many applications in science and engineering. In this paper, we propose an inexact curvilinear search optimization m…
Three Dimensional Strongly Symmetric Circulant Tensors
Liqun Qi, Qun Wang, Yannan Chen
In this paper, we give a necessary and sufficient condition for an even order three dimensional strongly symmetric circulant tensor to be positive semi-definite. In some cases, we…
Positive Semi-Definiteness and Sum-of-Squares Property of Fourth Order Four Dimensional Hankel Tensors
Yannan Chen, Liqun Qi, Qun Wang
A positive semi-definite (PSD) tensor which is not a sum-of-squares (SOS) tensor is called a PSD non-SOS (PNS) tensor. Is there a fourth order four dimensional PNS Hankel tensor? U…
An Explicit SOS Decomposition of A Fourth Order Four Dimensional Hankel Tensor with A Symmetric Generating Vector
Yannan Chen, Liqun Qi, Qun Wang
In this note, we construct explicit SOS decomposition of A Fourth Order Four Dimensional Hankel Tensor with A Symmetric Generating Vector, at the critical value. This is a suppleme…