A description of generalized coherent states and geometric phases in the light of the general theory of smooth loops is given.

Even and odd q-deformed charge coherent states are constructed , their (over)completeness proved and their generation explored. A D-algebra realization of the SU q (1,1) generators is given in terms of them. They are shown to exhibit SU q (1,1) squeezing and two-mode q-antibunching, but neither one-mode, nor two-mode q-squeezing.

Walley’s theory of coherent lower previsions builds upon the former theory by Williams with the explicit aim to make it deal with conglomerability. We show that such a construction has been only partly successful because Walley’s founding axiom of joint coherence does not entirely capture the implications of conglomerability. As a way to fully achieve Walley’s original aim, we propose then the ...

A classification of Hermitian representations for the recently introduced fuzzy torus algebra is presented. This is carried out by regarding the fuzzy torus algebra as a q-deformation of parafermion. In addition to the known representations, new representations of both finite and infinite dimension are found. Using the infinite dimensional representation, coherent state for the fuzzy torus is c...

The enhancement and detection of elongated structures in noisy image data is relevant for many biomedical applications. To handle complex crossing structures in 2D images, 2D orientation scores U : R × S → R were introduced, which already showed their use in a variety of applications. Here we extend this work to 3D orientation scores U : R × S → R. First, we construct the orientation score from...

In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is geometric and involves coherent states and semi-classical calculus.

John E. Gough, ∗ Matthew R. James, 3, † Hendra I. Nurdin, ‡ and Joshua Combes 4, § Institute for Mathematics and Physics, Aberystwyth University, SY23 3BZ, Wales, United Kingdom ARC Centre for Quantum Computation and Communication Technology Research School of Engineering, Australian National University, Canberra, ACT 0200, Australia Department of Physics and Astronomy, University of New Mexico...