Some Issues on Ontology Integration

The word integration has been used with different meanings in the ontology field. This article aims at clarifying the meaning of the word “integration” and presenting some of the relevant work done in integration. We identify three meanings of ontology “integration”: when building a new ontology reusing (by assembling, extending, specializing or adapting) other ontologies already available; when building an ontology by merging several ontologies into a single one that unifies all of them; when building an application using one or more ontologies. We discuss the different meanings of “integration”, identify the main characteristics of the three different processes and proposethree words to distinguish among those meanings:integration, merge and use

On equivariant mirror symmetry for local P^2

We solve the problem of equivariant mirror symmetry for O(-3)->P^2 for the (three) cases of one independent equivariant parameter. This gives a decomposition of mirror symmetry for local P^2 into that of three subspaces, each of which may be considered independently. Finally, we give a new interpretation of mirror symmetry for O(k)+O(-2-k)->P^1.Comment: 26 pages, 4 figures. v2: minor correction in section

Scattering theory of discrete (pseudo) Laplacians on a Weyl chamber

To a crystallographic root system we associate a system of multivariate orthogonal polynomials diagonalizing an integrable system of discrete pseudo Laplacians on the Weyl chamber. We develop the time-dependent scattering theory for these discrete pseudo Laplacians and determine the corresponding wave operators and scattering operators in closed form. As an application, we describe the scattering behavior of certain hyperbolic Ruijsenaars-Schneider type lattice Calogero-Moser models associated with the Macdonald polynomials.Comment: 31 pages, LaTe

Multiscale Representations for Manifold-Valued Data

We describe multiscale representations for data observed on equispaced grids and taking values in manifolds such as the sphere $S^2$, the special orthogonal group $SO(3)$, the positive definite matrices $SPD(n)$, and the Grassmann manifolds $G(n,k)$. The representations are based on the deployment of Deslauriers--Dubuc and average-interpolating pyramids "in the tangent plane" of such manifolds, using the $Exp$ and $Log$ maps of those manifolds. The representations provide "wavelet coefficients" which can be thresholded, quantized, and scaled in much the same way as traditional wavelet coefficients. Tasks such as compression, noise removal, contrast enhancement, and stochastic simulation are facilitated by this representation. The approach applies to general manifolds but is particularly suited to the manifolds we consider, i.e., Riemannian symmetric spaces, such as $S^{n-1}$, $SO(n)$, $G(n,k)$, where the $Exp$ and $Log$ maps are effectively computable. Applications to manifold-valued data sources of a geometric nature (motion, orientation, diffusion) seem particularly immediate. A software toolbox, SymmLab, can reproduce the results discussed in this paper