Pattern-based representation (PBR) is a novel sparse matrix representation that reduces the index overhead for many matrices without zero-filling and without requiring the identification of dense matrix blocks. The PBR analyzer identifies recurring block nonzero patterns, represents the submatrix consisting of all blocks of this pattern in block coordinate format, and generates custom matrix-ve...

We prove that every infinite sequence of skew-symmetric or symmetric matrices M1, M2, . . . over a fixed finite field must have a pair Mi, Mj (i < j) such that Mi is isomorphic to a principal submatrix of the Schur complement of a nonsingular principal submatrix in Mj , if those matrices have bounded rank-width. This generalizes three theorems on well-quasi-ordering of graphs or matroids admitt...

this study set out to investigate the distribution of the syntactic properties associatedwith the prodrop parameter by persian-speaking l2 learners of english in an attemptto examine the (un)attainability of native-like knowledge and (in)accessibility of ugin adult sla. to do so, 92 participants were assigned into different levels of l2knowledge based on their performances on the oxford placeme...

Abstract The Zarankiewicz problem asks for an estimate on z ( m , n ; s t ), the largest number of 1’s in × matrix with all entries 0 or 1 containing no submatrix consisting entirely 1’s. We show that a classical upper bound ) due to Kővári, Sós and Turán is tight up constant broad range parameters. proof relies new quantitative variant random algebraic method.

We initiate a systematic study of the Row Deletion(B) problem on matrices: For a fixed “forbidden submatrix” B, the question is, given an input matrix A (both A and B have entries chosen from a finite-size alphabet), to remove a minimum number of rows such that A has no submatrix which is equivalent to a row or column permutation of B. An application of this question can be found, e.g., in the ...

A new multilevel preconditioner is proposed for the iterative solution of two dimensional discrete second order elliptic PDEs. It is based a recursive block incomplete factorization of the system matrix partitioned in a two-by-two block form, in which the submatrix related to the rst block of unknowns in approximated by a MILU(0) factorization, and the Schur complement computed from a diagonal ...

Let A be a matrix over the integers, and let p be a positive integer. A submatrix B of A is zero-sum mod p if the sum of each row of B and the sum of each column of B is a multiple of p. Let M(p, k) denote the least integer m for which every square matrix of order at least m has a square submatrix of order k which is zero-sum mod p. In this paper we supply upper and lower bounds for M(p, k). In...

A binary matrix has the Consecutive Ones Property (C1P) for columns if there exists a permutation of its rows that leaves the 1’s consecutive in every column. The problem of Consecutive Ones Property for a matrix is a special variant of Consecutive Ones Submatrix problem in which a positive integer K is given and we want to know if there exists a submatrix B of A consisting of K columns of A wi...

We initiate a systematic study of the Row Deletion(B) problem on matrices: Given an input matrix A and a fixed “forbidden submatrix” B, the task is to remove a minimum number of rows from A such that no row or column permutation of B occurs as a submatrix in the resulting matrix. An application of this problem can be found, for instance, in the construction of perfect phylogenies. Establishing ...