Examples of covering properties of boundary points of space-times

The problem of classifying boundary points of space-time, for example singularities, regular points and points at infinity, is an unexpectedly subtle one. Due to the fact that whether or not two boundary points are identified or even "nearby" is dependant on the way the space-time is embedded, difficulties occur when singularities are thought of as an inherently local aspect of a space-time, as an analogy with electromagnetism would imply. The completion of a manifold with respect to a pseudo-Riemannian metric can be defined intrinsically, [SS94]. This is done via an equivalence relation, formalising which boundary sets cover other sets. This paper works through the possibilities, providing examples to show that all covering relations not immediately ruled out by the definitions are possible

Stable Lengths on the pants graph are rational

For the pants graph, there is little known about the behaviour of geodesics, as opposed to quasigeodesics. Brock-Masur-Minsky showed that geodesics or geodesic segments connecting endpoints satisfying a bounded combinatorics condition, such as the stable/unstable laminations of a pseudo-Anosov, all have bounded combinatorics, \textit{outside of annuli}. In this paper it is shown that there exist geodesics that also have bounded combinatorics within annuli. These geodesics are shown to have finiteness properties analogous to those of tight geodesics in the complex of curves, from which rationality of stable lengths of pseudo-Anosovs acting on the pants graph then follows from the arguments of Bowditch for the curve complex.Comment: No mathematical changes; had to add the number of the grant that funded this wor

Lifts of simple curves in finite regular coverings of closed surfaces

Suppose $S$ is a closed orientable surface and $\tilde{S}$ is a finite sheeted regular cover of $S$. The following question was posed by Juli\'{e}n March\'{e} in Mathoverflow: Do the lifts of simple curves from $S$ generate $H_{1}(\tilde{S},\mathbb{Z})$? A family of examples is given for which the answer is "no".Comment: Final rewrit

Resonant scattering by magnetic impurities as a model for spin relaxation in bilayer graphene

We propose that the observed spin-relaxation in bilayer graphene is due to resonant scattering by magnetic impurities. We analyze a resonant scattering model due to adatoms on both dimer and non-dimer sites, finding that only the former give narrow resonances at the charge neutrality point. Opposite to single-layer graphene, the measured spin-relaxation rate in graphene bilayer increases with carrier density. Although it has been commonly argued that a different mechanism must be at play for the two structures, our model explains this behavior rather naturally in terms of different broadening scales for the same underlying resonant processes. Not only our results---using robust and first-principles inspired parameters---agree with experiment, they also predict an experimentally testable sharp decrease of the spin-relaxation rate at high carrier densities.Comment: 6 pages, 3 figures + 2 pages Suppl. Materia

A study of online and blockwise updating of the EM algorithm for Gaussian mixtures.

A variant of the EM algorithm for the estimation of multivariate Gaussian mixtures, which allows for online as well as blockwise updating of sequentially obtained parameter estimates, is investigated. Several dierent update schemes are considered and compared, and the benets of articially performing EM in batches, even though all data are available, are discussed