论文标题
部分可观测时空混沌系统的无模型预测
On Minimally Non-Firm Binary Matrices
论文作者
论文摘要
对于二进制矩阵X，布尔等级BR（x）是最小的整数k，x等于k stark-1二进制矩阵的布尔总和，隔离数i（x）是1S的最大数量1s，其中两个在同一行，列，列，列，列和a 2x2 submatrix中。在本文中，我们继续Lubiw对固定矩阵的研究。据说如果i（x）= br（x），则x是坚定的，并且这种平等为其所有一键。我们表明，X的超级固定的概念等同于X的矩形盖构图中没有奇数孔，其中Br（X）和I（X）和I（X）分别转化为集团封面和独立数。如果二进制矩阵不是确定的，那么二进制矩阵是最小的，但其所有适当的子膜都是。我们介绍了两个矩阵操作，这些操作导致广义二进制矩阵，并使用这些操作来得出四个无限类别的微型矩阵。我们希望我们的工作可以通过禁止的子膜铺平稳固矩阵的铺平道路。
For a binary matrix X, the Boolean rank br(X) is the smallest integer k for which X equals the Boolean sum of k rank-1 binary matrices, and the isolation number i(X) is the maximum number of 1s no two of which are in a same row, column and a 2x2 submatrix of all 1s. In this paper, we continue Lubiw's study of firm matrices. X is said to be firm if i(X)=br(X) and this equality holds for all its submatrices. We show that the stronger concept of superfirmness of X is equivalent to having no odd holes in the rectangle cover graph of X, the graph in which br(X) and i(X) translate to the clique cover and the independence number, respectively. A binary matrix is minimally non-firm if it is not firm but all of its proper submatrices are. We introduce two matrix operations that lead to generalised binary matrices and use these operations to derive four infinite classes of minimally non-firm matrices. We hope that our work may pave the way towards a complete characterisation of firm matrices via forbidden submatrices.
