Congruences on Menger algebras

We discuss some types of congruences on Menger algebras of rank $n$, which are generalizations of the principal left and right congruences on semigroups. We also study congruences admitting various types of cancellations and describe their relationship with strong subsets

Hopping magneto-transport via nonzero orbital momentum states and organic magnetoresistance

In hopping magnetoresistance of doped insulators, an applied magnetic field shrinks the electron (hole) s-wave function of a donor or an acceptor and this reduces the overlap between hopping sites resulting in the positive magnetoresistance quadratic in a weak magnetic field, B. We extend the theory of hopping magnetoresistance to states with nonzero orbital momenta. Different from s-states, a weak magnetic field expands the electron (hole) wave functions with positive magnetic quantum numbers, m > 0, and shrinks the states with negative m in a wide region outside the point defect. This together with a magnetic-field dependence of injection/ionization rates results in a negative weak-field magnetoresistance, which is linear in B when the orbital degeneracy is lifted. The theory provides a possible explanation of a large low-field magnetoresistance in disordered pi-conjugated organic materials (OMAR).Comment: 4 pages, 3 figure

Dynamical Semigroups for Unbounded Repeated Perturbation of Open System

We consider dynamical semigroups with unbounded Kossakowski-Lindblad-Davies generators which are related to evolution of an open system with a tuned repeated harmonic perturbation. Our main result is the proof of existence of uniquely determined minimal trace-preserving strongly continuous dynamical semigroups on the space of density matrices. The corresponding dual W *-dynamical system is shown to be unital quasi-free and completely positive automorphisms of the CCR-algebra. We also comment on the action of dynamical semigroups on quasi-free states

Real-Time RGB-D Camera Pose Estimation in Novel Scenes using a Relocalisation Cascade

Camera pose estimation is an important problem in computer vision. Common techniques either match the current image against keyframes with known poses, directly regress the pose, or establish correspondences between keypoints in the image and points in the scene to estimate the pose. In recent years, regression forests have become a popular alternative to establish such correspondences. They achieve accurate results, but have traditionally needed to be trained offline on the target scene, preventing relocalisation in new environments. Recently, we showed how to circumvent this limitation by adapting a pre-trained forest to a new scene on the fly. The adapted forests achieved relocalisation performance that was on par with that of offline forests, and our approach was able to estimate the camera pose in close to real time. In this paper, we present an extension of this work that achieves significantly better relocalisation performance whilst running fully in real time. To achieve this, we make several changes to the original approach: (i) instead of accepting the camera pose hypothesis without question, we make it possible to score the final few hypotheses using a geometric approach and select the most promising; (ii) we chain several instantiations of our relocaliser together in a cascade, allowing us to try faster but less accurate relocalisation first, only falling back to slower, more accurate relocalisation as necessary; and (iii) we tune the parameters of our cascade to achieve effective overall performance. These changes allow us to significantly improve upon the performance our original state-of-the-art method was able to achieve on the well-known 7-Scenes and Stanford 4 Scenes benchmarks. As additional contributions, we present a way of visualising the internal behaviour of our forests and show how to entirely circumvent the need to pre-train a forest on a generic scene.Comment: Tommaso Cavallari, Stuart Golodetz, Nicholas Lord and Julien Valentin assert joint first authorshi