Depending on the interpretation of the type of edges, a chain graph can represent different relations between variables and thereby independence models. Three interpretations, known by the acronyms LWF, MVR, and AMP, are prevalent. Multivariate regression (MVR) chain graphs were introduced by Cox and Wermuth in 1993. We review Markov properties for MVR chain graphs chronologically, and for the ...

In this paper, a new control scheme called repetitive control is proposed, in which the controlled variables follow periodic reference commands. A high accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period L into the closed-loop system. Sufficient conditions for the stability of repetitive control systems and modified repetitive ...

The large-N limit of SU(N) gauge theories is of considerable interest from the phenomenological point of view, and is one of our sources of understanding of non-perturbative QCD. The theoretical side is no less interesting, allowing e.g. to establish precise relationships between Yang-Mills theories and string theories. A crucial property of large-N field theories is factorization: connected Gr...

Fourier Analysis Cyclic Reduction is a class of very eecient methods for the solution of Poisson's equation on regular grids. We show that exploiting the numerical properties of the tridiagonal systems involved may reduce the factorization work required to a few percent of a normal factorization. We also show that exploiting this property on distributed memory parallel processor architectures m...

Bipartite graphs are used to describe the generalized Schur complements of real matrices having no square submatrix with two or more nonzero diagonals. For any matrix A with this property, including any nearly reducible matrix, the sign pattern of each generalized Schur complement is shown to be determined uniquely by the sign pattern of A. Moreover, if A has a normalized LU factorization A = L...

Abstract. The paper develops a necessary condition for the regularity of a multivariate refinable function in terms of a factorization property of the associated subdivision mask. The extension to arbitrary isotropic dilation matrices necessitates the introduction of the concepts of restricted and renormalized convergence of a subdivision scheme as well as the notion of subconvergence, i.e., th...

Overlapping clustering is a fundamental and widely studied subject that identifies all densely connected groups of vertices separates them from other in complex networks. However, most conventional algorithms extract modules directly the whole large-scale graph using various heuristics, resulting either high time consumption or low accuracy. To address this issue, we develop an overlapping comm...

Variational Bayesian (VB) learning is known to be a promising approximation to Bayesian learning with computational efficiency. However, in some applications, e.g., large-scale collaborative filtering and tensor factorization, VB is still computationally too costly. In such cases, looser approximations such as MAP estimation and partially Bayesian (PB) learning, where a part of the parameters a...

Semiseparable matrices and many other rank-structured matrices have been widely used in developing new fast matrix algorithms. In this paper, we generalize the hierarchically semiseparable (HSS) matrix representations and propose some fast algorithms for HSS matrices. We represent HSS matrices in terms of general binary HSS trees and use simplified postordering notation for HSS forms. Fast HSS ...

Matrices with off-diagonal decay appear in a variety of fields in mathematics and in numerous applications, such as signal processing, statistics, communications engineering, condensed matter physics, and quantum chemistry. Numerical algorithms dealing with such matrices often take advantage (implicitly or explicitly) of the empirical observation that this off-diagonal decay property seems to b...