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

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

Downlink and Uplink Decoupling: a Disruptive Architectural Design for 5G Networks

Cell association in cellular networks has traditionally been based on the downlink received signal power only, despite the fact that up and downlink transmission powers and interference levels differed significantly. This approach was adequate in homogeneous networks with macro base stations all having similar transmission power levels. However, with the growth of heterogeneous networks where there is a big disparity in the transmit power of the different base station types, this approach is highly inefficient. In this paper, we study the notion of Downlink and Uplink Decoupling (DUDe) where the downlink cell association is based on the downlink received power while the uplink is based on the pathloss. We present the motivation and assess the gains of this 5G design approach with simulations that are based on Vodafone's LTE field trial network in a dense urban area, employing a high resolution ray-tracing pathloss prediction and realistic traffic maps based on live network measurements.Comment: 6 pages, 7 figures, conference paper, submitted to IEEE GLOBECOM 201

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

The Differential Topology of the Thurston Spine of Teichm\"uller Space

In \cite{Thurston}, a short, simple and elegant construction of a mapping class group-equivariant deformation retraction of Teichm\"uller space of a closed compact surface was given. The preprint \cite{Thurston}, which unfortunately is not online, has not been broadly accepted. The purpose of this paper is to go through the construction in detail, resolve any questions that have arisen in the literature and in personal communications. An explicit example is given to show that one of the claims needs to be modified, and details of how to do this are given. A mapping class group-equivariant deformation retraction of the Thurston spine onto a complex of dimension equal to the virtual cohomological dimension of the mapping class group is then constructed.Comment: A complete reformulation. A shorter proof of the vcd result was given, and a claim in the Thurston construction was fixed. Some of the material was moved to the paper submit/534164