C = network connectivity C = total journey cost D = matrix of maximum communication range between nodes (Rn×n) E = set of edges in G EG = subset of edges in G G = graph containing all nodes and edges G = evolving graph H = number of hops in a journey J = set of feasible journeys J = journey between nodes J = highest-value journey M = total number of edges in G m = number of edges in G N = total...

Many inference techniques for multivariate data analysis assume that the rows of the data matrix are realizations of independent and identically distributed random vectors. Such an assumption will be met, for example, if the rows of the data matrix are multivariate measurements on a set of independently sampled units. In the absence of an independent random sample, a relevant question is whethe...

An alternating sign matrix is a square matrix such that (i) all entries are 1,-1, or 0, (ii) every row and column has sum 1, and (iii) in every row and column the nonzero entries alternate in sign. Striking numerical evidence of a connection between these matrices and the descending plane partitions introduced by Andrews (Invent. Math. 53 (1979), 193-225) have been discovered, but attempts to p...

Sudoku puzzles are now popular among people in many countries across the world with simple constraints that no repeated digits in each row, each column, or each block. In this paper, we demonstrate that the Sudoku configuration provides us a new alternative way of matrix element representation by using block-grid pair besides the conventional row-column pair. Moreover, we discover six more matr...

New techniques are presented forthe manipulation of sparse matrices on parallel MIMD computers. We consider the following problems: matrix addition, matrix multiplication, row and column permutation, matrix transpose, matrix vector multiplication, and Gaussian elimination.

Sparse matrices are a core component in many numerical simulations, and their efficiency is essential to achieving high performance. Dynamic sparse-matrix allocation (insertion) can benefit a number of problems such as sparse-matrix factorization, sparse-matrix-matrix addition, static analysis (e.g., points-to analysis), computing transitive closure, and other graph algorithms. Existing sparse-...

Given a skew-symmetric matrix, the corresponding two-player symmetric zero-sum game is defined as follows: one player, the row player, chooses a row and the other player, the column player, chooses a column. The payoff of the row player is given by the corresponding matrix entry, the column player receives the negative of the row player. A randomized strategy is optimal if it guarantees an expe...

Results are proven on an inequality in max algebra and applied to theorems on the diagonal similarity scaling of matrices. Thus the set of all solutions to several scaling problems is obtained. Also introduced is the “full term rank” scaling of a matrix to a matrix with prescribed row and column maxima with the additional requirement that all the maxima are attained at entries each from a diffe...

We provide an inequality for absolute row and column sums of the powers of a complex matrix. This inequality generalizes several other inequalities. As a result, it provides an inequality that compares the absolute entry sum of the matrix powers to the sum of the powers of the absolute row/column sums. This provides a proof for a conjecture of London, which states that for all complex matrices ...

The Data Matrix The most important matrix for any statistical procedure is the data matrix. The observations form the rows of the data matrix and the variables form the columns. The most important requirement for the data matrix is that the rows of the matrix should be statistically independent. That is, if we pick any single row of the data matrix, then we should not be able to predict any oth...