In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of Type-2 Theory of Effectivity. This gives rise to a natural representation of the set M(X) of Borel probability measures on X. We compare this representation to a canonically constructed representation which encodes a Borel pro...

Non-highest weight representations of the current algebra so(1, n), and Laplace Operators. Abstract We constructed canonical non-highest weight unitary irreducible representation of so(1, n) current algebra as well as canonical non-highest weight non-unitary representations, We constructed certain Laplacian operators as elements of the universal enveloping algebra, acting in representation spac...

We review the recently proposed method of Relevance Vector Machines which is a supervised training method related to Support Vector Machines. We also review the statistical technique of Canonical Correlation Analysis and its implementation in a Feature Space. We show how the technique of Relevance Vectors may be applied to the method of Kernel Canonical Correlation Analysis to gain a very spars...

By means of a proper notion of periodic cyclic matrix, we study the possibility of transforming a given periodic system into a canonical companion form. The passage from such form to an input-output periodic representation is straightforward. We characterize the structural properties of a system in canonical form in terms of coprimeness of the two periodic polynomials appearing in the input-out...

Symmetries of a Place/Transition-net can be exploited during the reachability analysis by considering only one representative marking in each orbit induced by the symmetries. In this report, three new algorithms for transforming a marking into a symmetric canonical representative marking are described. All the algorithms depend on the precalculation of a SchreierSims representation for the symm...

We describe an alternative construction of an existing canonical representation for definite Horn theories, the Guigues-Duquenne basis (or GD basis), which minimizes a natural notion of implicational size. We extend the canonical representation to general Horn, by providing a reduction from definite to general Horn CNF. We show how this representation relates to two topics in query learning the...

A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices of a unitary representation to canonical form, give a certain description of the representations of canonical form, and reduce the problem of classifying Eu...