Distributive inverse semigroups and non-commutative Stone dualities

We develop the theory of distributive inverse semigroups as the analogue of distributive lattices without top element and prove that they are in a duality with those etale groupoids having a spectral space of identities, where our spectral spaces are not necessarily compact. We prove that Boolean inverse semigroups can be characterized as those distributive inverse semigroups in which every prime filter is an ultrafilter; we also provide a topological characterization in terms of Hausdorffness. We extend the notion of the patch topology to distributive inverse semigroups and prove that every distributive inverse semigroup has a Booleanization. As applications of this result, we give a new interpretation of Paterson's universal groupoid of an inverse semigroup and by developing the theory of what we call tight coverages, we also provide a conceptual foundation for Exel's tight groupoid.Comment: arXiv admin note: substantial text overlap with arXiv:1107.551

EVS: Head-up or Head Down? Evaluation of Crew Procedure and Human Factors for Enhanced Vision Systems

Feasibility of an EVS head-down procedure is examined that may provide the same operational benefits under low visibility as the FAA rule on Enhanced Flight Visibility that requires the use of a head-up display (HUD). The main element of the described EVS head-down procedure is the crew procedure within cockpit for flying the approach. The task sharing between Pilot-Flying and Pilot-Not-Flying is arranged such that multiple head-up/head-down transitions can be avoided. The pilot-flying is using the head-down display for acquisition of the necessary visual cues in the EVS image. The pilot-not-flying is monitoring the instruments and looking for the outside visual cues

Uniform existence of the integrated density of states for random Schr\"odinger operators on metric graphs over Zd\mathbb{Z}^d

We consider ergodic random magnetic Schr\"odinger operators on the metric graph $\mathbb{Z}^d$ with random potentials and random boundary conditions taking values in a finite set. We show that normalized finite volume eigenvalue counting functions converge to a limit uniformly in the energy variable. This limit, the integrated density of states, can be expressed by a closed Shubin-Pastur type trace formula. It supports the spectrum and its points of discontinuity are characterized by existence of compactly supported eigenfunctions. Among other examples we discuss percolation models.Comment: 17 pages; typos removed, references updated, definition of subgraph densities explaine

Stochastic Methods for Zero Energy Quantum Scattering

We investigate the use of stochastic methods for zero energy quantum scattering based on a path integral approach. With the application to the scattering of a projectile from a nuclear many body target in mind, we use the potential scattering of a particle as a test for the accuracy and efficiency of several methods. To be able to deal with complex potentials, we introduce a path sampling action and a modified scattering observable. The approaches considered are the random walk, where the points of a path are sequentially generated, and the Langevin algorithm, which updates an entire path. Several improvements are investigated. A cluster algorithm for dealing with scattering problems is finally proposed, which shows the best accuracy and stability.Comment: 40 pages LaTeX, 1 Postscript file containig 20 figures; execute main.tex file, which automatically will include other file

Probing the environment of emerin by Enhanced ascorbate peroxidase 2 (APEX2)-mediated proximity labeling.

Emerin is one of the best characterized proteins of the inner nuclear membrane, but can also occur at the level of the endoplasmic reticulum. We now use enhanced ascorbate peroxidase 2 (APEX2) to probe the environment of emerin. APEX2 can be used as a genetic tag that produces short-lived yet highly reactive biotin species, allowing the modification of proteins that interact with or are in very close proximity to the tagged protein. Biotinylated proteins can be isolated using immobilized streptavidin and analyzed by mass spectrometry. As an alternative to the standard approach with a genetic fusion of APEX2 to emerin, we also used RAPIDS (rapamycin- and APEX-dependent identification of proteins by SILAC), a method with improved specificity, where the peroxidase interacts with the protein of interest (i.e., emerin) only upon addition of rapamycin to the cells. We compare these different approaches, which, together, identify well-known interaction partners of emerin like lamin A and the lamina associated polypeptide 1 (LAP1), as well as novel proximity partners

Coding over Sets for DNA Storage

In this paper, we study error-correcting codes for the storage of data in synthetic deoxyribonucleic acid (DNA). We investigate a storage model where data is represented by an unordered set of $M$ sequences, each of length $L$. Errors within that model are losses of whole sequences and point errors inside the sequences, such as substitutions, insertions and deletions. We propose code constructions which can correct these errors with efficient encoders and decoders. By deriving upper bounds on the cardinalities of these codes using sphere packing arguments, we show that many of our codes are close to optimal.Comment: 5 page

Invariant means on Boolean inverse monoids

The classical theory of invariant means, which plays an important role in the theory of paradoxical decompositions, is based upon what are usually termed `pseudogroups'. Such pseudogroups are in fact concrete examples of the Boolean inverse monoids which give rise to etale topological groupoids under non-commutative Stone duality. We accordingly initiate the theory of invariant means on arbitrary Boolean inverse monoids. Our main theorem is a characterization of when a Boolean inverse monoid admits an invariant mean. This generalizes the classical Tarski alternative proved, for example, by de la Harpe and Skandalis, but using different methods