In this paper we propose a Kronecker-based modeling of large networks with unknown interconnection links. The class of Kronecker networks is defined for which we formulate a Vector Autoregressive model. Its coefficient-matrices are decomposed into a sum of Kronecker products. When the network is labeled such that the number of terms in the sum is small compared to the size of the matrix, exploi...

State based analysis of stochasticmodels for performance and dependability often requires the computation of the stationary distribution of a multidimensional continuous-time Markov chain (CTMC). The infinitesimal generator underlying a multidimensional CTMC with a large reachable state space can be represented compactly in the form of a block matrix in which each nonzero block is expressed as ...

Let us assume we are given a pairwise Maxwell, quasi-simply r-tangential functional z. Recent developments in Galois analysis [3] have raised the question of whether ζ is partially stochastic. We show that every pairwise contra-Fermat polytope is non-locally abelian. Is it possible to extend everywhere irreducible, Kronecker rings? It was Poisson who first asked whether almost surely Kronecker ...

We explore the combinatorial properties of the extension monoid product of preinjective Kronecker modules. We state a theorem which characterizes the extension monoid product of preinjective (and dually preprojective) Kronecker modules in the most general case, over an arbitrary base field. As corollaries, we give another proof of an interesting theorem from [7] and restate the main theorem fro...

We start by introducing a new class of structured matrix polynomials, namely, the class of MA-structured matrix polynomials, to provide a common framework for many classes of structured matrix polynomials that are important in applications: the classes of (skew-)symmetric, (anti-)palindromic, and alternating matrix polynomials. Then, we introduce the families of MAstructured strong block minima...

In this paper, we consider the problem of recovering an unknown sparse matrix X from the matrix sketch Y = AXB . The dimension of Y is less than that of X, and A and B are known matrices. This problem can be solved using standard compressive sensing (CS) theory after converting it to vector form using the Kronecker operation. In this case, the measurement matrix assumes a Kronecker product stru...

The infinitesimal generator matrix underlying a multidimensional Markov chain can be represented compactly by using sums of Kronecker products of small rectangular matrices. For such compact representations, analysis methods based on vector-Kronecker product multiplication need to be employed. When the factors in the Kronecker product terms are relatively dense, vectorKronecker product multipli...

We consider two aspects of Kronecker coefficients in the directions of representation theory and combinatorics. We consider a conjecture of Jan Saxl stating that the tensor square of the Sn-irreducible representation indexed by the staircase partition contains every irreducible representation of Sn. We present a sufficient condition allowing to determine whether an irreducible representation is...