11,954 research outputs found

    The Quantum McKay Correspondence for polyhedral singularities

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    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

    Letter from the Editors

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    Capacitor-type micrometeoroid detectors

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    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

    Heterogeneous Unit Clustering for Efficient Operational Flexibility Modeling for Strategic Models

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    The increasing penetration of wind generation has led to significant improvements in unit commitment models. However, long-term capacity planning methods have not been similarly modified to address the challenges of a system with a large fraction of generation from variable sources. Designing future capacity mixes with adequate flexibility requires an embedded approximation of the unit commitment problem to capture operating constraints. Here we propose a method, based on clustering units, for a simplified unit commitment model with dramatic improvements in solution time that enable its use as a submodel within a capacity expansion framework. Heterogeneous clustering speeds computation by aggregating similar but non-identical units thereby replacing large numbers of binary commitment variables with fewer integers that still capture individual unit decisions and constraints. We demonstrate the trade-off between accuracy and run-time for different levels of aggregation. A numeric example using an ERCOT-based 205-unit system illustrates that careful aggregation introduces errors of 0.05-0.9% across several metrics while providing several orders of magnitude faster solution times (400x) compared to traditional binary formulations and further aggregation increases errors slightly (~2x) with further speedup (2000x). We also compare other simplifications that can provide an additional order of magnitude speed-up for some problems

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

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    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

    Regrowth-related defect formation and evolution in 1 MeV amorphized (001) Ge

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    Geimplanted with 1MeV Si⁺ at a dose of 1×10¹⁵cm⁻² creates a buried amorphous layer that, upon regrowth, exhibits several forms of defects–end-of-range (EOR), regrowth-related, and clamshell defects. Unlike Si, no planar {311} defects are observed. The minimal EOR defects are small dotlike defects and are very unstable, dissolving between 450 and 550°C. This is in contrast to Si, where the EOR defects are very stable. The amorphous layer results in both regrowth-related defects and clamshell defects, which were more stable than the EOR damage.This work is supported by Semiconductor Research Corporation Contract No. 00057787

    Synthesis of Contemporary SAE Research 1994–2014

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    In the 1990s, a series of research syntheses were conducted regarding supervised agricultural experience. These syntheses included supervised agricultural experience (SAE) research from 1964 through 1993. With these past syntheses as the premise, contemporary SAE research was identified, synthesized, and coded into emerging themes. Inclusion criteria for this synthesis required articles to (a) be published in a peer-reviewed journal or national/regional American Association for Agricultural Education research conference proceedings, (b) include research specifically pertaining to SAE, (c) be available and accessible through the search procedures, and (d) be published between January 1994 and December 2014. An exhaustive search was conducted using library databases as well as digital journals and conference proceedings. Themes that emerged from this synthesis were (a) participation, (b) teacher education, (c) benefits, (d) professional development, (e) supervision, (f) scope/structure, (g) economic impact, (h) program quality, (i) learning theory, and (k) international settings. Similar to the previous syntheses, research conducted between 1994 and 2014 was primarily descriptive, conceptually broad, and often limited to relatively small populations such as single states. Additional multistate and national studies are recommended to describe the content and context of SAE instruction in teacher education and to refine quality indicators related to SAE practice
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