In this paper, we obtain expressions for the principal angles between the row spaces of input and output data block Hankel matrices of a linear stochastic model in terms of the model parameters. The canonical correlations of the corresponding processes are equal to the limiting values of the cosines of the principal angles. From these parametric expressions, the relations between the different ...

The Birkhoff (permutation) polytope, Bn, consists of the n × n nonnegative doubly stochastic matrices, has dimension (n− 1)2, and has n2 facets. A new analogue, the alternating sign matrix polytope, ASMn, is introduced and characterized. Its vertices are the Qn−1 j=0 (3j+1)! (n+j)! n × n alternating sign matrices. It has dimension (n− 1)2, has 4[(n− 2)2 +1] facets, and has a simple inequality d...

We study the averaging-based distributed optimization solvers over random networks. show a general result on convergence of such schemes using weight-matrices that are row-stochastic almost surely and column-stochastic in expectation for broad class dependent weight-matrix sequences. In addition to implying many previously known results this domain, our work shows robustness link-failure. Also,...

Position-weight matrices (PWMs) are broadly used to locate transcription factor binding sites in DNA sequences. The majority of existing PWMs provide a low level of both sensitivity and specificity. We present a new computational algorithm, a modification of the Staden-Bucher approach, that improves the PWM. We applied the proposed technique on the PWM of the GC-box, binding site for Sp1. The c...

We prove an asymptotic estimate for the number of m×n non-negative integer matrices (contingency tables) with prescribed row and column sums and, more generally, for the number of integer feasible flows in a network. Similarly, we estimate the volume of the polytope of m × n non-negative real matrices with prescribed row and column sums. Our estimates are solutions of convex optimization proble...

We study the calculation of the volume of the polytope Bn of n × n doubly stochastic matrices; that is, the set of real non-negative matrices with all row and column sums equal to one. We describe two methods. The first involves a decomposition of the polytope into simplices. The second involves the enumeration of “magic squares”, i.e., n×n non-negative integer matrices whose rows and columns a...