From the 1 of 13 linked papers with an AI index.
8 papers · 1 filter
Biquadratic SOS Rank and Augmented Zarankiewicz Number
Liqun Qi, Chunfeng Cui, Yi Xu
This paper introduces the concepts of the augmented Zarankiewicz number and the limited augmented Zarankiewicz number , which are natural combinatorial extensi…
Narrowing the Gap: SOS Ranks of Biquadratic Forms and a Lower Bound of
Yi Xu, Chunfeng Cui, Liqun Qi
We investigate the maximum sum-of-squares (SOS) rank of biquadratic forms in the critical case of variables, where the general bounds are currently $7 \leq \mathrm{BSR…
Sum of Squares Rank of Biquadratic Forms and The Zarankiewicz Number
Chunfeng Cui, Liqun Qi, Yi Xu
Denote the maximum sos rank of sum of squares (SOS) biquadratic forms by . In this paper, we show that and conjecture that $BSR(m, n…
On the SOS Rank of Simple and Diagonal Biquadratic Forms
Yi Xu, Chufeng Cui, Liqun Qi
We study the sum-of-squares (SOS) rank of simple and diagonal biquadratic forms. For simple biquadratic forms in variables, we show that the maximum SOS rank is exactl…
Sum of Squares Decompositions and Rank Bounds for Biquadratic Forms
Liqun Qi, Chunfeng Cui, Yi Xu
We study SOS properties of biquadratic forms. For the class of partially symmetric biquadratic forms, we establish necessary and sufficient conditions for positive semi-definitenes…
Sum of Squares Decompositions for Structured Biquadratic Forms
Yi Xu, Chunfeng Cui, Liqun Qi
This paper studies sum-of-squares (SOS) representations for structured biquadratic forms. We prove that diagonally dominated symmetric biquadratic tensors are always SOS. For the s…