Hierarchical analysis of gravitational-wave measurements of binary black hole spin-orbit misalignments

Binary black holes may form both through isolated binary evolution and through dynamical interactions in dense stellar environments. The formation channel leaves an imprint on the alignment between the black hole spins and the orbital angular momentum. Gravitational waves from these systems directly encode information about the spin--orbit misalignment angles, allowing them to be (weakly) constrained. Identifying sub-populations of spinning binary black holes will inform us about compact binary formation and evolution. We simulate a mixed population of binary black holes with spin--orbit misalignments modelled under a range of assumptions. We then develop a hierarchical analysis and apply it to mock gravitational-wave observations of these populations. Assuming a population with dimensionless spin magnitudes of $\chi = 0.7$, we show that tens of observations will make it possible to distinguish the presence of subpopulations of coalescing binary black holes based on their spin orientations. With $100$ observations it will be possible to infer the relative fraction of coalescing binary black holes with isotropic spin directions (corresponding to dynamical formation in our models) with a fractional uncertainty of $\sim 40\%$. Meanwhile, only $\sim 5$ observations are sufficient to distinguish between extreme models---all binary black holes either having exactly aligned spins or isotropic spin directions.Comment: 12 pages, 9 figures. Updated to match version published in MNRAS as 10.1093/mnras/stx176

Geometric Properties of Quantum Phases

The Aharonov-Anandan phase is introduced from a physical point of view. Without reference to any dynamical equation, this phase is formulated by defining an appropriate connection on a specific fibre bundle. The holonomy element gives the phase. By introducing another connection, the Pancharatnam phase formula is derived following a different procedure.Comment: 9 page

Invasion percolation on the Poisson-weighted infinite tree

We study invasion percolation on Aldous' Poisson-weighted infinite tree, and derive two distinct Markovian representations of the resulting process. One of these is the $\sigma\to\infty$ limit of a representation discovered by Angel et al. [Ann. Appl. Probab. 36 (2008) 420-466]. We also introduce an exploration process of a randomly weighted Poisson incipient infinite cluster. The dynamics of the new process are much more straightforward to describe than those of invasion percolation, but it turns out that the two processes have extremely similar behavior. Finally, we introduce two new "stationary" representations of the Poisson incipient infinite cluster as random graphs on $\mathbb {Z}$ which are, in particular, factors of a homogeneous Poisson point process on the upper half-plane $\mathbb {R}\times[0,\infty)$.Comment: Published in at http://dx.doi.org/10.1214/11-AAP761 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Measuring physical inactivity:do current measures provide an accurate view of "sedentary" video game time?

BACKGROUND: Measures of screen time are often used to assess sedentary behaviour. Participation in activity-based video games (exergames) can contribute to estimates of screen time, as current practices of measuring it do not consider the growing evidence that playing exergames can provide light to moderate levels of physical activity. This study aimed to determine what proportion of time spent playing video games was actually spent playing exergames. METHODS: Data were collected via a cross-sectional telephone survey in South Australia. Participants aged 18 years and above (n = 2026) were asked about their video game habits, as well as demographic and socioeconomic factors. In cases where children were in the household, the video game habits of a randomly selected child were also questioned. RESULTS: Overall, 31.3% of adults and 79.9% of children spend at least some time playing video games. Of these, 24.1% of adults and 42.1% of children play exergames, with these types of games accounting for a third of all time that adults spend playing video games and nearly 20% of children's video game time. CONCLUSIONS: A substantial proportion of time that would usually be classified as "sedentary" may actually be spent participating in light to moderate physical activity

Adiabatic Berry Phase and Hannay Angle for Open Paths

We obtain the adiabatic Berry phase by defining a generalised gauge potential whose line integral gives the phase holonomy for arbitrary evolutions of parameters. Keeping in mind that for classical integrable systems it is hardly clear how to obtain open-path Hannay angle, we establish a connection between the open-path Berry phase and Hannay angle by using the parametrised coherent state approach. Using the semiclassical wavefunction we analyse the open-path Berry phase and obtain the open-path Hannay angle. Further, by expressing the adiabatic Berry phase in terms of the commutator of instantaneous projectors with its differential and using Wigner representation of operators we obtain the Poisson bracket between distribution function and its differential. This enables us to talk about the classical limit of the phase holonomy which yields the angle holonomy for open-paths. An operational definition of Hannay angle is provided based on the idea of classical limit of quantum mechanical inner product. A probable application of the open-path Berry phase and Hannay angle to wave-packet revival phenomena is also pointed out.Comment: Latex, no figures, 24 pages, submitted to Ann. Phy

Geometric phases and anholonomy for a class of chaotic classical systems

Berry's phase may be viewed as arising from the parallel transport of a quantal state around a loop in parameter space. In this Letter, the classical limit of this transport is obtained for a particular class of chaotic systems. It is shown that this ``classical parallel transport'' is anholonomic --- transport around a closed curve in parameter space does not bring a point in phase space back to itself --- and is intimately related to the Robbins-Berry classical two-form.Comment: Revtex, 11 pages, no figures

Estimation of Apartment Submarkets

The analysis of apartment sub-markets and the modelling of such markets have attracted a considerable degree of attention recently. This study compares apartment submarkets within a major European city. The price behaviour of the Dublin, Ireland apartment market is tested using hedonic models and aggregate and disaggregate data. The results strongly indicate that the modelling of apartment markets at the disaggregate level does result in significant improvements in estimation in comparison to estimations undertaken at an aggregate level. This particular apartment market is especially interesting, due to the introduction of fiscal incentives in inner-city locations. In order to fully understand the Dublin apartment market requires an appreciation of the role played by tax breaks for owner-occupiers and investors in urban renewal locations. The results show that different submarkets responded differently. The central city apartment market [urban renewal locations] saw a short-term stabilization of prices in the months following the fiscal changes, with price increases accelerating again shortly afterwards.

REVIEW - A reference data set for retinal vessel profiles

This paper describes REVIEW, a new retinal vessel reference dataset. This dataset includes 16 images with 193 vessel segments, demonstrating a variety of pathologies and vessel types. The vessel edges are marked by three observers using a special drawing tool. The paper also describes the algorithm used to process these segments to produce vessel profiles, against which vessel width measurement algorithms can be assessed. Recommendations are given for use of the dataset in performance assessment. REVIEW can be downloaded from http://ReviewDB.lincoln.ac.uk

On the Spinning Motion of the Hovering Magnetic Top

In this paper we analyze the spinning motion of the hovering magnetic top. We have observed that its motion looks different from that of a classical top. A classical top rotates about its own axis which precesses around a vertical fixed external axis. The hovering magnetic top, on the other hand, has its axis slightly tilted and moves rigidly as a whole about the vertical axis. We call this motion synchronous, because in a stroboscopic experiment we see that a point at the rim of the top moves synchronously with the top axis. We show that the synchronous motion may be attributed to a small deviation of the magnetic moment from the symmetry axis of the top. We calculate the minimum angular velocity required for stability in terms of the moments of inertia and magnetic field and show that it is different from that of a classical top. We also give experimental results that were taken with a top whose moment of inertia can be changed. These results show very good agreement with our calculations.Comment: 19 pages (including 3 figures named fig1.eps-fig3.eps), uses amssymb, epsf and amsbsy (AMSLaTeX