In this paper we extend the framework of combinatorial and conceptual worlds to allow arbitrary relations. Conceptual worlds of properties provide a framework for knowledge representation, reasoning, and in particular for conceptual belief revision. However, it is desirable to consider such worlds where relations are not restricted to properties. Firstly, we discuss foundations of the conceptua...

The present article contains a short introduction to Modular Theory for von Neumann algebras with a cyclic and separating vector. It includes the formulation of the central result in this area, the Tomita-Takesaki theorem, and several of its consequences. We illustrate this theory through several elementary examples. We also present more elaborate examples and compute modular objects for a disc...

We present a general method using kernel canonical correlation analysis to learn a semantic representation to web images and their associated text. The semantic space provides a common representation and enables a comparison between the text and images. In the experiments, we look at two approaches of retrieving images based on only their content from a text query. We compare orthogonalization ...

We use kernel Canonical Correlation Analysis to learn a semantic representation of web images and their associated text. In the application we look at two approaches of retrieving images based only on their content from a text query. The semantic space provides a common representation and enables a comparison between the text and image. We compare the approaches against a standard cross-represe...

In this paper an affirmati5e answer is given to a question of D. Kazhdan on the existence of a canonical Hilbert spaces attached to symplectic vector spaces over finite fields. This result suggest a solution to a discrete analogue of a well known problem in geometric quantization where a naive canonical Hilbert space does not exist. As a result, a canonical model for the Weil representation of ...

Discrete symmetries in grand canonical ensembles and in ensembles canonical with respect to triality are investigated. We speculate about the general phase structure of finite temperature gauge theories with discrete Z(N) symmetry. Low and high temperature phases turn out to be different in both ensembles even for infinite systems. It is argued that gauge theories with matter fields in the fund...

The Rabi Hamiltonian, describing the coupling of a two-level system to a single quantized boson mode, is studied in the Bargmann-Fock representation. The corresponding system of differential equations is transformed into a canonical form in which all regular singu-larities between zero and infinity have been removed. The canonical or Birkhoff-transformed equations give rise to a two-dimensional...

In the canonical approach to Lorentzian Quantum General Relativity in four spacetime dimensions an important step forward has been made by Ashtekar, Isham and Lewandowski some eight years ago through the introduction of a Hilbert space structure which was later proved to be a faithful representation of the canonical commutation and adjointness relations of the quantum field algebra of diffeomor...

We relate the canonical basis of the Fock space representation of the quantum affine algebra Uq(ĝln), as defined by Leclerc and Thibon [LT], to the canonical basis of its restriction to Uq(sln), regarded as a based module in the sense of Lusztig. More generally we consider the restriction to any Levi subalgebra. We deduce results on decomposition numbers and branching coefficients of Schur alge...