We consider the set Σ(R, C) of all m×n matrices having 0-1 entries and prescribed row sums R = (r1, . . . , rm) and column sums C = (c1, . . . , cn). We prove an asymptotic estimate for the cardinality |Σ(R, C)| via the solution to a convex optimization problem. We show that if Σ(R, C) is sufficiently large, then a random matrix D ∈ Σ(R, C) sampled from the uniform probability measure in Σ(R, C...

In a typical MapReduce job, each map task processing one piece of the input file. If two input matrices are stored in separate HDFS files, one map task would not be able to access the two input matrices at the same time. To deal with this problem, we propose a efficient matrix multiplication in Hadoop. For dense matrices, we use plain row major order to store the matrices on HDFS; For sparse ma...

Generalizing the Bruhat order for permutations (so for permutation matrices), a Bruhat order is defined for the class of m by n (0, 1)-matrices with a given row and column sum vector. An algorithm is given for constructing a minimal matrix (with respect to the Bruhat order) in such a class. This algorithm simplifies in the case that the row and column sums are all equal to a constant k. When k ...

We show that the computation of the Popov form of Ore polynomial matrices can be formulated as a problem of computing the left nullspace of such matrices. While this technique is already known for polynomial matrices, the extension to Ore polynomial matrices is not immediate because multiplication of the matrix entries is not commutative. A number of results for polynomial matrices are extended...

this paper presents an approach for solving a nonlinear stochastic differential equations (nsdes) using a new basis functions (nbfs). these functions and their operational matrices areused for representing matrix form of the nbfs. with using this method in combination with the collocation method, the nsdes are reduced a stochastic nonlinear system of equations and unknowns. then, the error anal...

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fai...

We compute the spectral density for ensembles of of sparse symmetric random matrices using replica. Our formulation of the replica-symmetric ansatz shares the symmetries of the one suggested in a seminal paper by Rodgers and Bray (symmetry with respect to permutation of replica and rotation symmetry in the space of replica), but uses a different representation in terms of superpositions of Gaus...

An increasing number of applications is concerned with recovering a sparsity can be defined in terms of lq balls for q 2 [0, 2), defined as Bq(s) = { v = (vi) 2 R2 : n2 ∑

Orthogonal matrices over arbitrary elds are de ned together with their non-square analogs, which are termed row-orthogonal matrices. Antiorthogonal and self-orthogonal square matrices are introduced together with their non-square analogs. The relationships of these matrices to such codes as self-dual codes and linear codes with complementary duals are given.