The Quantum McKay Correspondence for polyhedral singularities

Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity C^3/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar-Vafa invariants), our result can be stated as a correspondence: each positive root of R corresponds to one half of a genus zero BPS state. As an application, we use the crepant resolution conjecture to provide a full prediction for the orbifold Gromov-Witten invariants of [C^3/G].Comment: Introduction rewritten. Issue regarding non-uniqueness of conifold resolution clarified. Version to appear in Inventione

Capacitor-type micrometeoroid detectors

The metal oxide semiconductor (MOS) capacitor micrometeroid detector consists of a thin dielectric capacitor fabricated on a silicon wafer. In operation, the device is charged to a voltage level sufficiently near breakdown that micrometeoroid impacts will cause dielectric deformation or heating and subsequent arc-over at the point of impact. Each detector is capable of recording multiple impacts because of the self-healing characteristics of the device. Support instrumentation requirements consist of a voltage source and pulse counters that monitor the pulse of recharging current following every impact. An investigation has been conducted in which 0.5 to 5 micron diameter carbonized iron spheres traveling at velocities of 4 to 10 Km/sec were impacted on to detectors with either a dielectric thickness of 0.4 or 1.0 micron. This study demonstrated that an ion microprobe tuned to sufficiently high resolution can detect Fe remaining on the detector after the impact. Furthermore, it is also possible to resolve Fe ion images free of mass interferences from Si, for example, giving its spatial distribution after impact. Specifically this technique has shown that significant amounts of impacting particles remain in the crater and near it which can be analyzed for isotopic content. Further testing and calibration could lead to quantitive analysis. This study has shown that the capacitor type micrometeroid detector is capable of not only time and flux measurements but can also be used for isotopic analysis

LOX/GOX mechanical impact tester assessment

The performances of three existing high pressure oxygen mechanical impact test systems were tested at two different test sites. The systems from one test site were fabricated from the same design drawing, whereas the system tested at the other site was of different design. Energy delivered to the test sample for each test system was evaluated and compared. Results were compared to the reaction rates obtained

Progression from ocular hypertension to visual field loss in the English hospital eye service

Background There are more than one million National Health Service visits in England and Wales each year for patients with glaucoma or ocular hypertension (OHT). With the ageing population and an increase in optometric testing, the economic burden of glaucoma-related visits is predicted to increase. We examined the conversion rates of OHT to primary open-angle glaucoma (POAG) in England and assessed factors associated with risk of conversion. Methods Electronic medical records of 45 309 patients from five regionally different glaucoma clinics in England were retrospectively examined. Conversion to POAG from OHT was defined by deterioration in visual field (two consecutive tests classified as stage 1 or worse as per the glaucoma staging system 2). Cox proportional hazards models were used to examine factors (age, sex, treatment status and baseline intraocular pressure (IOP)) associated with conversion. Results The cumulative risk of conversion to POAG was 17.5% (95% CI 15.4% to 19.6%) at 5 years. Older age (HR 1.35 per decade, 95% CI 1.22 to 1.50, p<0.001) was associated with a higher risk of conversion. IOP-lowering therapy (HR 0.45, 95% CI 0.35 to 0.57, p<0.001) was associated with a lower risk of conversion. Predicted 5-year conversion rates for treated and untreated groups were 14.0% and 26.9%, respectively. Conclusion Less than one-fifth of OHT patients managed in glaucoma clinics in the UK converted to POAG over a 5-year period, suggesting many patients may require less intensive follow-up. Our study provides real-world evidence for the efficacy of current management (including IOP-lowering treatment) at reducing risk of conversion

Generating Cosmological Gaussian Random Fields

We present a generic algorithm for generating Gaussian random initial conditions for cosmological simulations on periodic rectangular lattices. We show that imposing periodic boundary conditions on the real-space correlator and choosing initial conditions by convolving a white noise random field results in a significantly smaller error than the traditional procedure of using the power spectrum. This convolution picture produces exact correlation functions out to separations of L/2, where L is the box size, which is the maximum theoretically allowed. This method also produces tophat sphere fluctuations which are exact at radii $R \le L/4$. It is equivalent to windowing the power spectrum with the simulation volume before discretizing, thus bypassing sparse sampling problems. The mean density perturbation in the volume is no longer constrained to be zero, allowing one to assemble a large simulation using a series of smaller ones. This is especially important for simulations of Lyman-$\alpha$ systems where small boxes with steep power spectra are routinely used. We also present an extension of this procedure which generates exact initial conditions for hierarchical grids at negligible cost.Comment: 12 pages incl 3 figures, accepted in ApJ Letter

Explaining the entropy excess in clusters and groups of galaxies without additional heating

The X-ray luminosity and temperature of clusters and groups of galaxies do not scale in a self-similar manner. This has often been interpreted as a sign that the intracluster medium has been substantially heated by non-gravitational sources. In this paper, we propose a simple model which, instead, uses the properties of galaxy formation to explain the observations. Drawing on available observations, we show that there is evidence that the efficiency of galaxy formation was higher in groups than in clusters. If confirmed, this would deplete the low-entropy gas in groups, increase their central entropy and decrease their X-ray luminosity. A simple, empirical, hydrostatic model appears to match both the luminosity-temperature relation of clusters and properties of their internal structure as well.Comment: 5 pages, 4 figures, accepted in ApJL; added one reference, otherwise unchange