# 학술행사

세미나

## Extremal Positive Semidefinite Matrices for Weakly Bipartite Graphs

• 발표자  Ruriko Yoshida (University of Kentucky)
• 개최일시  2015-07-23 11:00
• 장소  수학원리응용센터 중형세미나실

NIMS 초청세미나

연사: Ruriko Yoshida (University of Kentucky)

일시: 2015년 7월 25일 11:00

장소: 국가수리과학연구소 CAMP 중형세미나실

제목: Extremal Positive Semidefinite Matrices for Weakly Bipartite Graphs

For a graph $G$ with $p$ vertices the cone of concentration matrices consists of all real positive semidefinite $p\times p$ matrices with zeros in the off-diagonal entries corresponding to nonedges of~$G$.

The extremal rays of this cone and their associated ranks have applications to matrix completion problems, maximum likelihood estimation in Gaussian graphical models in statistics, and Gauss elimination for sparse matrices.

For a weakly bipartite graph $G$, we show that the normal vectors to the facets of the $(\pm1)$- polytope of $G$ specify the off-diagonal entries of extremal matrices in $\K_G$.

We also prove that the constant term of the linear equation of each facet-supporting hyperplane is the rank of its corresponding extremal matrix in $\K_G$.

Furthermore, we show that if $G$ is series-parallel then this gives a complete characterization of all possible extremal ranks of $\K_G$, consequently solving the sparsity order problem for series-parallel graphs.  This is joint work with Liam Solus and Caroline Uhler.

이 페이지에서 제공하는 정보에 대해 만족하십니까?

Ranking TOP5
코로나19 확산 예측
코로나19 확산 예측 레포트
생명 현상과 의료 문제의 수학적 모델링 연구
산업수학연구본부
조직도

TOP