The solution of chemical process simulation and optimization problems on today's high performance supercomputers requires algorithms that can take advantage of vector and parallel processing when solving the large, sparse matrices that arise. The frontal method can be highly e cient in this context due to its ability to make use of vectorizable dense matrix kernels on a relatively small frontal...

We consider the following matrix reachability problem: given r square matrices with entries in a semiring, is there a product of these matrices which attains a prescribed matrix? We define similarly the vector (resp. scalar) reachability problem, by requiring that the matrix product, acting by right multiplication on a prescribed row vector, gives another prescribed row vector (resp. when multi...

background: recurrence rate of rotator cuff tears is still high despite the improvements of surgical techniques, materials used and a better knowledge of the healing process of the rotator cuff tendons. large to massive rotator cuff tears are particularly associated with a high failure rate, especially in elderly. augmentation of rotator cuff repairs with extracellular matrix or synthetic patch...

This is a survey of the recent progress and open questions on the structure of the sets of 0-1 and non-negative integer matrices with prescribed row and column sums. We discuss cardinality estimates, the structure of a random matrix from the set, discrete versions of the Brunn-Minkowski inequality and the statistical dependence between row and column sums.

A matrix with positive row sums and all its off-diagonal elements bounded above by their corresponding row averages is called a B-matrix by J. M. Peña in References (SIAM J. Matrix Anal. Appl. 2001; 22:1027–1037) and (Numer. Math. 2003; 95:337–345). In this paper, it is generalized to more extended matrices—MB-matrices, which is proved to be a subclass of the class of P-matrices. Subsequently, ...

Papers by Goldman, Rivest and Schapire, and Goldman and War-muth contain worst case analyses for several polynomial time algorithms for predicting k-binary relations. Here we present an empirical study of the average-case performance of those algorithms, and also of two new methods which dominate them in this average-case setting. The better of the two methods uses a graph coloring heuristic to...

Let A be an m n matrix in which the entries of each row are all distinct. Drisko 4] showed that, if m 2n ? 1, then A has a transversal: a set of n distinct entries with no two in the same row or column. We generalize this to matrices with entries in a matroid. For such a matrix A, we show that if each row of A forms an independent set, then we can require the transversal to be independent as we...

We consider the problem of large-scale inference on the row or column variables of data in the form of a matrix. Many of these data matrices are transposable meaning that neither the row variables nor the column variables can be considered independent instances. An example of this scenario is detecting significant genes in microarrays when the samples may be dependent due to latent variables or...