Law of Large Numbers for a Class of Superdiffusions

Under spectral conditions, we prove a LLN type result for superdiffusions, where the convergence is meant in probability. The main tool is a space-time H-transformation

High-temperature oxidation and erosion-resistant refractory coatings

Various refractory coating systems were evaluated for rocket nozzle applications by actual rocket test firings. A reference is noted which identifies failure mechanisms and gives results of the firing tests for 18 coating systems. Iridium, iridium-rhenium, and hafnium oxide-zirconium oxide coatings show most promising results

Wigner function and quantum kinetic theory in curved space-time and external fields

A new definition of the Wigner function for quantum fields coupled to curved space--time and an external Yang--Mills field is studied on the example of a scalar and a Dirac fields. The definition uses the formalism of the tangent bundles and is explicitly covariant and gauge invariant. Derivation of collisionless quantum kinetic equations is carried out for both quantum fields by using the first order formalism of Duffin and Kemmer. The evolution of the Wigner function is governed by the quantum corrected Liouville--Vlasov equation supplemented by the generalized mass--shell constraint. The structure of the quantum corrections is perturbatively found in all adiabatic orders. The lowest order quantum--curvature corrections coincide with the ones found by Winter.Comment: 41 page

Preliminary assessment of cognitive impairments in canine idiopathic epilepsy

In humans, epilepsy can induce or accelerate cognitive impairment (CI). There is emerging evidence of CI in dogs with idiopathic epilepsy (IE) from recent epidemiological studies. The aim of our study was to assess CI in dogs with IE using two tests of cognitive dysfunction designed for use in a clinical setting. Dogs with IE (n=17) were compared against controls (n=18) in their performance in two tasks; a spatial working memory task and a problem-solving task. In addition, owners completed the Canine Cognitive Dysfunction Rating (CCDR) scale for their dog. The groups did not differ statistically with respect to age and breed. Dogs with IE performed significantly worse than controls on the spatial working memory task (P=0.016), but not on the problem solving task (P=0.683). CCDR scores were significantly higher in the IE group (P=0.016); however, no dogs reach the recommended threshold score for CCD diagnosis. Our preliminary data suggest that dogs with IE exhibit impairments in a spatial working memory task. Further research is required to explore the effect of IE on other cognitive abilities in dogs with a larger sample, characterising the age of onset, nature and progression of any impairments and the impact of anti-epileptic drugs

A synchronous program algebra: a basis for reasoning about shared-memory and event-based concurrency

This research started with an algebra for reasoning about rely/guarantee concurrency for a shared memory model. The approach taken led to a more abstract algebra of atomic steps, in which atomic steps synchronise (rather than interleave) when composed in parallel. The algebra of rely/guarantee concurrency then becomes an instantiation of the more abstract algebra. Many of the core properties needed for rely/guarantee reasoning can be shown to hold in the abstract algebra where their proofs are simpler and hence allow a higher degree of automation. The algebra has been encoded in Isabelle/HOL to provide a basis for tool support for program verification. In rely/guarantee concurrency, programs are specified to guarantee certain behaviours until assumptions about the behaviour of their environment are violated. When assumptions are violated, program behaviour is unconstrained (aborting), and guarantees need no longer hold. To support these guarantees a second synchronous operator, weak conjunction, was introduced: both processes in a weak conjunction must agree to take each atomic step, unless one aborts in which case the whole aborts. In developing the laws for parallel and weak conjunction we found many properties were shared by the operators and that the proofs of many laws were essentially the same. This insight led to the idea of generalising synchronisation to an abstract operator with only the axioms that are shared by the parallel and weak conjunction operator, so that those two operators can be viewed as instantiations of the abstract synchronisation operator. The main differences between parallel and weak conjunction are how they combine individual atomic steps; that is left open in the axioms for the abstract operator.Comment: Extended version of a Formal Methods 2016 paper, "An algebra of synchronous atomic steps

Localization and its consequences for quantum walk algorithms and quantum communication

The exponential speed-up of quantum walks on certain graphs, relative to classical particles diffusing on the same graph, is a striking observation. It has suggested the possibility of new fast quantum algorithms. We point out here that quantum mechanics can also lead, through the phenomenon of localization, to exponential suppression of motion on these graphs (even in the absence of decoherence). In fact, for physical embodiments of graphs, this will be the generic behaviour. It also has implications for proposals for using spin networks, including spin chains, as quantum communication channels.Comment: 4 pages, 1 eps figure. Updated references and cosmetic changes for v

Full security of quantum key distribution from no-signaling constraints

We analyze a cryptographic protocol for generating a distributed secret key from correlations that violate a Bell inequality by a sufficient amount, and prove its security against eavesdroppers, constrained only by the assumption that any information accessible to them must be compatible with the non-signaling principle. The claim holds with respect to the state-of-the-art security definition used in cryptography, known as universally-composable security. The non-signaling assumption only refers to the statistics of measurement outcomes depending on the choices of measurements; hence security is independent of the internal workings of the devices --- they do not even need to follow the laws of quantum theory. This is relevant for practice as a correct and complete modeling of realistic devices is generally impossible. The techniques developed are general and can be applied to other Bell inequality-based protocols. In particular, we provide a scheme for estimating Bell-inequality violations when the samples are not independent and identically distributed.Comment: 15 pages, 2 figur

Unusual hyperfine interaction of Dirac electrons and NMR spectroscopy in graphene

Theory of nuclear magnetic resonance (NMR) in graphene is presented. The canonical form of the electron-nucleus hyperfine interaction is strongly modified by the linear electronic dispersion. The NMR shift and spin-lattice relaxation time are calculated as function of temperature, chemical potential, and magnetic field and three distinct regimes are identified: Fermi-, Dirac-gas, and extreme quantum limit behaviors. A critical spectrometer assessment shows that NMR is within reach for fully 13C enriched graphene of reasonable size.Comment: 5 pages, 3 figure