Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

Effects of beverage alcohol taxes and prices on drinking: a meta-analysis of 1003 estimates from 112 studies

Aims: We conducted a systematic review of studies examining relationships between measures of beverage alcohol tax or price levels and alcohol sales or self-reported drinking. A total of 112 studies of alcohol tax or price effects were found, containing 1003 estimates of the tax/price–consumption relationship. Design: Studies included analyses of alternative outcome measures, varying subgroups of the population, several statistical models, and using different units of analysis. Multiple estimates were coded from each study, along with numerous study characteristics. Using reported estimates, standard errors, t-ratios, sample sizes and other statistics, we calculated the partial correlation for the relationship between alcohol price or tax and sales or drinking measures for each major model or subgroup reported within each study. Random-effects models were used to combine studies for inverse variance weighted overall estimates of the magnitude and significance of the relationship between alcohol tax/price and drinking. Findings: Simple means of reported elasticities are -0.46 for beer, -0.69 for wine and -0.80 for spirits. Meta-analytical results document the highly significant relationships (P < 0.001) between alcohol tax or price measures and indices of sales or consumption of alcohol (aggregate-level r = -0.17 for beer, -0.30 for wine, -0.29 for spirits and -0.44 for total alcohol). Price/tax also affects heavy drinking significantly (mean reported elasticity = -0.28, individual-level r = -0.01, P < 0.01), but the magnitude of effect is smaller than effects on overall drinking. Conclusions: A large literature establishes that beverage alcohol prices and taxes are related inversely to drinking. Effects are large compared to other prevention policies and programs. Public policies that raise prices of alcohol are an effective means to reduce drinking.

Assessing the accuracy of CME speed and trajectory estimates from STEREO observations through a comparison of independent methods

We have estimated the speed and direction of propagation of a number of Coronal Mass Ejections (CMEs) using single-spacecraft data from the STEREO Heliospheric Imager (HI) wide-field cameras. In general, these values are in good agreement with those predicted by Thernisien, Vourlidas, and Howard in Solar Phys. 256, 111 -aEuro parts per thousand 130 (2009) using a forward modelling method to fit CMEs imaged by the STEREO COR2 coronagraphs. The directions of the CMEs predicted by both techniques are in good agreement despite the fact that many of the CMEs under study travel in directions that cause them to fade rapidly in the HI images. The velocities estimated from both techniques are in general agreement although there are some interesting differences that may provide evidence for the influence of the ambient solar wind on the speed of CMEs. The majority of CMEs with a velocity estimated to be below 400 km s(-1) in the COR2 field of view have higher estimated velocities in the HI field of view, while, conversely, those with COR2 velocities estimated to be above 400 km s(-1) have lower estimated HI velocities. We interpret this as evidence for the deceleration of fast CMEs and the acceleration of slower CMEs by interaction with the ambient solar wind beyond the COR2 field of view. We also show that the uncertainties in our derived parameters are influenced by the range of elongations over which each CME can be tracked. In order to reduce the uncertainty in the predicted arrival time of a CME at 1 Astronomical Unit (AU) to within six hours, the CME needs to be tracked out to at least 30 degrees elongation. This is in good agreement with predictions of the accuracy of our technique based on Monte Carlo simulations.

Asymmetric adjustment in the City of London office market

Earlier estimates of the City of London office market are extended by considering a longer time series of data, covering two cycles, and by explicitly modeling of asymmetric space market responses to employment and supply shocks. A long run structural model linking real rental levels, office-based employment and the supply of office space is estimated and then rental adjustment processes are modeled using an error correction model framework. Rental adjustment is seen to be asymmetric, depending both on the direction of the supply and demand shocks and on the state of the space market at the time of the shock. Vacancy adjustment does not display asymmetries. There is also a supply adjustment equation. Two three-equation systems, one with symmetric rental adjustment and the other with asymmetric adjustment, are subjected to positive and negative shocks to employment. These illustrate differences in the two systems.

The effect of asymmetries on stock index return value-at-risk estimates

It is widely accepted that equity return volatility increases more following negative shocks rather than positive shocks. However, much of value-at-risk (VaR) analysis relies on the assumption that returns are normally distributed (a symmetric distribution). This article considers the effect of asymmetries on the evaluation and accuracy of VaR by comparing estimates based on various models.

On merging gradient estimation with mean-tracking techniques for cluster identification

This paper discusses how numerical gradient estimation methods may be used in order to reduce the computational demands on a class of multidimensional clustering algorithms. The study is motivated by the recognition that several current point-density based cluster identification algorithms could benefit from a reduction of computational demand if approximate a-priori estimates of the cluster centres present in a given data set could be supplied as starting conditions for these algorithms. In this particular presentation, the algorithm shown to benefit from the technique is the Mean-Tracking (M-T) cluster algorithm, but the results obtained from the gradient estimation approach may also be applied to other clustering algorithms and their related disciplines.

Clear-sky biases in satellite infrared estimates of upper tropospheric humidity and its trends

We use microwave retrievals of upper tropospheric humidity (UTH) to estimate the impact of clear-sky-only sampling by infrared instruments on the distribution, variability and trends in UTH. Our method isolates the impact of the clear-sky-only sampling, without convolving errors from other sources. On daily time scales IR-sampled UTH contains large data gaps in convectively active areas, with only about 20-30 % of the tropics (30 S­ 30 N) being sampled. This results in a dry bias of about -9 %RH in the area-weighted tropical daily UTH time series. On monthly scales, maximum clear-sky bias (CSB) is up to -30 %RH over convectively active areas. The magnitude of CSB shows significant correlations with UTH itself (-0.5) and also with the variability in UTH (-0.6). We also show that IR-sampled UTH time series have higher interannual variability and smaller trends compared to microwave sampling. We argue that a significant part of the smaller trend results from the contrasting influence of diurnal drift in the satellite measurements on the wet and dry regions of the tropics.

Evaluation of satellite-based and model re-analysis rainfall estimates for Uganda

The dependence of much of Africa on rain fed agriculture leads to a high vulnerability to fluctuations in rainfall amount. Hence, accurate monitoring of near-real time rainfall is particularly useful, for example in forewarning possible crop shortfalls in drought-prone areas. Unfortunately, ground based observations are often inadequate. Rainfall estimates from satellite-based algorithms and numerical model outputs can fill this data gap, however rigorous assessment of such estimates is required. In this case, three satellite based products (NOAA-RFE 2.0, GPCP-1DD and TAMSAT) and two numerical model outputs (ERA-40 and ERA-Interim) have been evaluated for Uganda in East Africa using a network of 27 rain gauges. The study focuses on the years 2001 to 2005 and considers the main rainy season (February to June). All data sets were converted to the same temporal and spatial scales. Kriging was used for the spatial interpolation of the gauge data. All three satellite products showed similar characteristics and had a high level of skill that exceeded both model outputs. ERA-Interim had a tendency to overestimate whilst ERA-40 consistently underestimated the Ugandan rainfall.