Given a matrix U , using a deterministic method, we extract a "large" submatrix of Ũ (whose columns are obtained by normalizing those of U ) and estimate its smallest and largest singular value. We apply this result to the study of contact points of the unit ball with its maximal volume ellipsoid. We consider also the paving problem and give a deterministic algorithm to partition a matrix into ...

Order-Preserving SubMatrix (OPSM) has been proved to be important in modelling biologically meaningful subspace cluster, capturing the general tendency of gene expressions across a subset of conditions. Given an OPSM query based on row or column keywords, it is desirable to retrieve OPSMs quickly from a large gene expression dataset or OPSM data via indices. However, the time of OPSM mining fro...

Let A be a k-dimensional matrix of size d 1 :::d k : By a contiguous submatrix B of A we understand the matrix B = fa i 1

The point-plane, the point-line, and plane-line incidence matrices of $$\mathrm {PG}(3,q)$$ are interest in combinatorics, finite geometry, graph theory group theory. Some properties these their submatrices related with interplay orbits points, lines planes under action subgroups {PGL}(4,q)$$ . A remarkable particular case is subgroup $$G\cong \mathrm {PGL}(2,q)$$ , viewed as stabilizer twisted...

This paper presents a new construction of matrices with no singular square submatrix. This construction allows designing erasure codes over finite fied with fast encoding and decoding algorithms. 1 Systematic MDS Erasure Codes It is well known that a [n, k, d]-error correcting code is Maximum Distance Separable (MDS) if and only if its k × n-generator matrix does not contain any singular k×k-sq...

High throughput biomedical measurements normally capture multiple overlaid biologically relevant signals and often also signals representing different types of technical artefacts like e.g. batch effects. Signal identification and decomposition are accordingly main objectives in statistical biomedical modeling and data analysis. Existing methods, aimed at signal reconstruction and deconvolution...

We consider the poset of all submatrices of a given matrix, ordered by containment. The unique rank function for this poset is given by r(M) = R(M)+C(M)?1, where R(M) and C(M) denote the number of rows and columns of a nonempty matrix M, respectively, and the rank of the empty matrix is 0. For xed k and i our objective is to nd a set M of submatrices M 1 ; M 2 ; : : :; M k such that r(M j) = i ...

The heavy demand for large volumes of digital data has increased the interest in matrix-like representation. Matrices are well organized data structures which are suitable to store uniform data in order to simplify data access and manipulation. For several applications, the need is critical to efficiently search for a specific pattern in matrix structures. A pattern can be represented as an ndi...

Let F be a k×` (0,1)-matrix. We say a (0,1)-matrix A has F as a configuration if there is a submatrix of A which is a row and column permutation of F . In the language of sets, a configuration is a trace and in the language of hypergraphs a configuration is a subhypergraph. Let F be a given k × ` (0,1)-matrix. We define a matrix to be simple if it is a (0,1)-matrix with no repeated columns. The...