Strong-field tidal distortions of rotating black holes: III. Embeddings in hyperbolic 3-space

In previous work, we developed tools for quantifying the tidal distortion of a black hole's event horizon due to an orbiting companion. These tools use techniques which require large mass ratios (companion mass $\mu$ much smaller than black hole mass $M$), but can be used for arbitrary bound orbits, and for any black hole spin. We also showed how to visualize these distorted black holes by embedding their horizons in a global Euclidean 3-space, ${\mathbb{E}}^3$. Such visualizations illustrate interesting and important information about horizon dynamics. Unfortunately, we could not visualize black holes with spin parameter $a_* > \sqrt{3}/2 \approx 0.866$: such holes cannot be globally embedded into ${\mathbb{E}}^3$. In this paper, we overcome this difficulty by showing how to embed the horizons of tidally distorted Kerr black holes in a hyperbolic 3-space, ${\mathbb{H}}^3$. We use black hole perturbation theory to compute the Gaussian curvatures of tidally distorted event horizons, from which we build a two-dimensional metric of their distorted horizons. We develop a numerical method for embedding the tidally distorted horizons in ${\mathbb{H}}^3$. As an application, we give a sequence of embeddings into ${\mathbb{H}}^3$ of a tidally interacting black hole with spin $a_*=0.9999$. A small amplitude, high frequency oscillation seen in previous work shows up particularly clearly in these embeddings.Comment: 10 pages, 6 figure

Asset Prices in the Measurement of Inflation

The debate over including asset prices in the construction of an inflation statistic has attracted renewed attention in recent years. Virtually all of this (and earlier) work on incorporating asset prices into an aggregate price statistic has been motivated by a presumed, but unidentified transmission mechanism through which asset prices are leading indicators of inflation at the retail level. In this paper, we take an alternative, longer-term perspective on the issue and argue that the exclusion of asset prices introduces an 'excluded goods bias' in the computation of the inflation statistic that is of interest to the monetary authority. We implement this idea using a relatively modern statistical technique, a dynamic factor index. This statistical algorithm allows us to see through the excessively 'noisy' asset price data that have frustrated earlier researchers who have attempted to integrate these prices into an aggregate measure. We find that the failure to include asset prices in the aggregate price statistic has introduced a downward bias in the U.S. Consumer Price Index on the order of magnitude of roughly 1/4 percentage point annually. Of the three broad assets categories considered here -- equities, bonds, and houses -- we find that the failure to include housing prices resulted in the largest potential measurement error. This conclusion is also supported by a cursory look at some cross-country evidence.

Modelling multivariate biomechanical measurements of the spine during a rowing exercise

Accepted versio

Improving the quality of the personalized electronic program guide

As Digital TV subscribers are offered more and more channels, it is becoming increasingly difficult for them to locate the right programme information at the right time. The personalized Electronic Programme Guide (pEPG) is one solution to this problem; it leverages artificial intelligence and user profiling techniques to learn about the viewing preferences of individual users in order to compile personalized viewing guides that fit their individual preferences. Very often the limited availability of profiling information is a key limiting factor in such personalized recommender systems. For example, it is well known that collaborative filtering approaches suffer significantly from the sparsity problem, which exists because the expected item-overlap between profiles is usually very low. In this article we address the sparsity problem in the Digital TV domain. We propose the use of data mining techniques as a way of supplementing meagre ratings-based profile knowledge with additional item-similarity knowledge that can be automatically discovered by mining user profiles. We argue that this new similarity knowledge can significantly enhance the performance of a recommender system in even the sparsest of profile spaces. Moreover, we provide an extensive evaluation of our approach using two large-scale, state-of-the-art online systems—PTVPlus, a personalized TV listings portal and Físchlár, an online digital video library system

Cold gas in group-dominant elliptical galaxies

We present IRAM 30m telescope observations of the CO(1-0) and (2-1) lines in a sample of 11 group-dominant elliptical galaxies selected from the CLoGS nearby groups sample. Our observations confirm the presence of molecular gas in 4 of the 11 galaxies at >4 sigma significance, and combining these with data from the literature we find a detection rate of 43+-14%, comparable to the detection rate for nearby radio galaxies, suggesting that group-dominant ellipticals may be more likely to contain molecular gas than their non-central counterparts. Those group-dominant galaxies which are detected typically contain ~2x10^8 Msol of molecular gas, and although most have low star formation rates (<1 Msol/yr) they have short depletion times, indicating that the gas must be replenished on timescales ~100 Myr. Almost all of the galaxies contain active nuclei, and we note while the data suggest that CO may be more common in the most radio-loud galaxies, the mass of molecular gas required to power the active nuclei through accretion is small compared to the masses observed. We consider possible origin mechanisms for the gas, through cooling of stellar ejecta within the galaxies, group-scale cooling flows, and gas-rich mergers, and find probable examples of each type within our sample, confirming that a variety of processes act to drive the build up of molecular gas in group-dominant ellipticals.Comment: 9 pages, 5 postscript figures, 4 tables, accepted by A&A. Revised throughout in response to referee's comments, including updates to Table 1 and Figure 4, and addition of Figure