The topic of this paper is the (partial) minimal realization problem in the max algebra, which is one of the modeling frameworks that can be used to model discrete event systems. We use the fact that a system of multivariate max-algebraic polynomial equalities can be transformed into an Extended Linear Complementarity Problem to find all equivalent minimal state space realizations of a multiple...

This paper addresses three questions related to minimal triangulations of a 3-dimensional convex polytope P . • Can the minimal number of tetrahedra in a triangulation be decreased if one allows the use of interior points of P as vertices? • Can a dissection of P use fewer tetrahedra than a triangulation? • Does the size of a minimal triangulation depend on the concrete realization of P ? The m...

The topic of this paper is the (partial) minimal realization problem in the max algebra, which is one of the modeling frameworks that can be used to model discrete event systems. We use the fact that a system of multi-variate max-algebraic polynomial equalities can be transformed into an Extended Linear Complementarity Problem to nd all equivalent minimal state space realizations of a multiple ...

We discuss computationally efficient and numerically reliable algorithms to compute minimal proper nullspace bases of a rational or polynomial matrix. The underlying main computational tool is the orthogonal reduction to a Kronecker-like form of the system matrix of an equivalent descriptor system realization. A new algorithm is proposed to compute a simple minimal proper nullspace basis, start...

The posets of dimension 2 are those posets whose minimal realizations have two elements, that is, which may be obtained as the intersection of two of their linear extensions. Gallai's decomposition of a poset allows for a simple formula to count the number of the distinct minimal realizations of the posets of dimension 2. As an easy consequence, the characterization of M. El-Zahar and of N.W. S...

We review the realization of the Brout-Englert-Higgs mechanism in the electroweak theory and describe the experimental and theoretical constraints on the mass of the single Higgs boson expected in the minimal Standard Model. We also discuss the couplings of this Higgs boson and its possible decay modes as functions of its unknown mass. We then review the structure of the Higgs sector in the min...

Apart from controllability and observability an important concept in linear system theory is strong observability [1] — [4j. This latter concept appears naturally in the study of singular quadratic optimal control problems [4]. A strongly (alternatively perfectly) observable is that system for which an observer can determine the state vector x(0) = x0 with the knowledge of output y(t) only, inf...

We propose sentence chunking as a way to reduce the time and memory costs of realization of long sentences. During chunking we divide the semantic representation of a sentence into smaller components which can be processed and recombined without loss of information. Our meaning representation of choice is Dependency Minimal Recursion Semantics (DMRS). We show that realizing chunks of a sentence...