On the existence of quantum representations for two dichotomic measurements

Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics. The solution uses methods from the theory of operator algebras and the theory of moment problems. The ensuing conditions reveal surprisingly simple relations between certain quantum-mechanical probabilities. It also shown that generally, none of these relations holds in general probabilistic models. This result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories.Comment: 16+7 pages, presentation improved and minor errors correcte

Creating immersive, play-anywhere handheld augmented reality stories, through remote user testing

This thesis outlines new instances of Extended Reality (XR) stories as well as associated user studies with them, to create more immersive story experiences delivered at a user’s choice of location through a mobile phone. This extends prior work on Location Based Experiences (LBEs), which have typically been designed to offer a game or story at a pre-determined location. A play-anywhere experience offers potential to open up LBEs to a wider audience, as well as to those may prefer to take part individually or closer to home, such attitude shifts becoming increasingly more common. The current research adopted an in the wild approach combining practice, studies and theory, with most user data being collected remotely. Each story application developed is subsequently referred to as an app, with each app offering a bespoke story incorporating Augmented Reality (AR) features, to better bring users’ location inline with the narrative. Testing the apps across various locations matched their intended use, and resulted in new guidelines for both incorporating AR into such LBEs, as well as for conducting remote user studies. A final app offered a site-specific curated story, with all study participants taking part under similar conditions at the same location, the ability to observe them using the app providing additional insights. The story apps used available local map data alongside Handheld Augmented Reality (HAR), to overlay interactable virtual objects on top of the physical environment, and visible on the phone’s display. Guidelines from related methodologies were used to better allow for the variety of factors that might influence different users’ immersion and engagement. These included the implementation of the AR features, the story itself, real world activity, and personal preferences including onboarding requirements. The approach taken contributed a reverse methodology to a lot of related research, that would typically begin with laboratory testing before moving to public spaces. User studies with the five mobile apps contributed guidelines for such experiences, that could benefit both practitioners and researchers in related fields. In the later case, a need was identified to develop new research tools specifically suited to the subtleties of handheld play-anywhere LBEs, such issues explored within the apps tested. The guidelines identified for offering more effective XR LBEs were also implemented in the creation of a new open source Unity project, called Map Story Engine. This offers a tool to test new features, as well as providing a fully customisable template for practitioners to author their own play-anywhere HAR stories and games

On some fundamental results about higher-rank graphs and their C*-algebras

Results of Fowler and Sims show that every k-graph is completely determined by its k-coloured skeleton and collection of commuting squares. Here we give an explicit description of the k-graph associated to a given skeleton and collection of squares and show that two k-graphs are isomorphic if and only if there is an isomorphism of their skeletons which preserves commuting squares. We use this to prove directly that each k-graph {\Lambda} is isomorphic to the quotient of the path category of its skeleton by the equivalence relation determined by the commuting squares, and show that this extends to a homeomorphism of infinite-path spaces when the k-graph is row finite with no sources. We conclude with a short direct proof of the characterisation, originally due to Robertson and Sims, of simplicity of the C*-algebra of a row-finite k-graph with no sources.Comment: 21 pages, two pictures prepared using TiK

Isometric Representations of Totally Ordered Semigroups

Let S be a subsemigroup of an abelian torsion-free group G. If S is a positive cone of G, then all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic. Proved by Murphy, this statement generalized the well-known theorems of Coburn and Douglas. In this note we prove the reverse. If all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic, then S is a positive cone of G. Also we consider G = Z\times Z and prove that if S induces total order on G, then there exist at least two unitarily not equivalent irreducible isometrical representation of S. And if the order is lexicographical-product order, then all such representations are unitarily equivalent.Comment: February 21, 2012. Kazan, Russi

Gut dysfunction in patients with multiple sclerosis and the role of spinal cord involvement in the disease.

Bowel and bladder symptoms are highly prevalent in patients with multiple sclerosis (MS). Bladder dysfunction (affecting 75% of these patients) is caused by disease in the spinal cord, whilst the pathophysiology of bowel dysfunction is unknown. Pathways regulating both the organs lie in close proximity to the spinal cord, and coexistence of their dysfunction might be the result of a common pathophysiology. If so, the prevalence of bladder symptoms should be greater in patients with MS and bowel symptoms. This hypothesis is tested in the study. We also evaluated how patient-reported symptoms quantify bowel dysfunction

Magnetotransport properties of iron microwires fabricated by focused electron beam induced autocatalytic growth

We have prepared iron microwires in a combination of focused electron beam induced deposition (FEBID) and autocatalytic growth from the iron pentacarbonyl, Fe(CO)5, precursor gas under UHV conditions. The electrical transport properties of the microwires were investigated and it was found that the temperature dependence of the longitudinal resistivity (rhoxx) shows a typical metallic behaviour with a room temperature value of about 88 micro{\Omega} cm. In order to investigate the magnetotransport properties we have measured the isothermal Hall-resistivities in the range between 4.2 K and 260 K. From these measurements positive values for the ordinary and the anomalous Hall coefficients were derived. The relation between anomalous Hall resistivity (rhoAN) and longitudinal resistivity is quadratic, rhoAN rho^2 xx, revealing an intrinsic origin of the anomalous Hall effect. Finally, at low temperature in the transversal geometry a negative magnetoresistance of about 0.2 % was measured

Homology and K--Theory Methods for Classes of Branes Wrapping Nontrivial Cycles

We apply some methods of homology and K-theory to special classes of branes wrapping homologically nontrivial cycles. We treat the classification of four-geometries in terms of compact stabilizers (by analogy with Thurston's classification of three-geometries) and derive the K-amenability of Lie groups associated with locally symmetric spaces listed in this case. More complicated examples of T-duality and topology change from fluxes are also considered. We analyse D-branes and fluxes in type II string theory on ${\mathbb C}P^3\times \Sigma_g \times {\mathbb T}^2$ with torsion $H-$flux and demonstrate in details the conjectured T-duality to ${\mathbb R}P^7\times X^3$ with no flux. In the simple case of $X^3 = {\mathbb T}^3$, T-dualizing the circles reduces to duality between ${\mathbb C}P^3\times {\mathbb T}^2 \times {\mathbb T}^2$ with $H-$flux and ${\mathbb R}P^7\times {\mathbb T}^3$ with no flux.Comment: 27 pages, tex file, no figure

Exchange Leavitt path algebras and stable rank

We characterize those Leavitt path algebras which are exchange rings in terms of intrinsic properties of the graph and show that the values of the stable rank for these algebras are 1, 2 or ∞. Concrete criteria in terms of properties of the underlying graph are given for each case

Wavelets and graph C∗C^*-algebras

Here we give an overview on the connection between wavelet theory and representation theory for graph $C^{\ast}$-algebras, including the higher-rank graph $C^*$-algebras of A. Kumjian and D. Pask. Many authors have studied different aspects of this connection over the last 20 years, and we begin this paper with a survey of the known results. We then discuss several new ways to generalize these results and obtain wavelets associated to representations of higher-rank graphs. In \cite{FGKP}, we introduced the "cubical wavelets" associated to a higher-rank graph. Here, we generalize this construction to build wavelets of arbitrary shapes. We also present a different but related construction of wavelets associated to a higher-rank graph, which we anticipate will have applications to traffic analysis on networks. Finally, we generalize the spectral graph wavelets of \cite{hammond} to higher-rank graphs, giving a third family of wavelets associated to higher-rank graphs

Perturbations of nuclear C*-algebras

Kadison and Kastler introduced a natural metric on the collection of all C*-subalgebras of the bounded operators on a separable Hilbert space. They conjectured that sufficiently close algebras are unitarily conjugate. We establish this conjecture when one algebra is separable and nuclear. We also consider one-sided versions of these notions, and we obtain embeddings from certain near inclusions involving separable nuclear C*-algebras. At the end of the paper we demonstrate how our methods lead to improved characterisations of some of the types of algebras that are of current interest in the classification programme.Comment: 45 page