Complete Reducibility in Good Characteristic

Let $G$ be a simple algebraic group of exceptional type, over an algebraically closed field of characteristic $p \ge 0$. A closed subgroup $H$ of $G$ is called $G$-completely reducible ($G$-cr) if whenever $H$ is contained in a parabolic subgroup $P$ of $G$, it is contained in a Levi subgroup of $P$. In this paper we determine the $G$-conjugacy classes of non-$G$-cr simple connected subgroups of $G$ when $p$ is good for $G$. For each such subgroup $X$, we determine the action of $X$ on the adjoint module $L(G)$ and the connected centraliser of $X$ in $G$. As a consequence we classify all non-$G$-cr connected reductive subgroups of $G$, and determine their connected centralisers. We also classify the subgroups of $G$ which are maximal among connected reductive subgroups, but not maximal among all connected subgroups.Comment: 66 pages. To appear in Trans. Amer. Math. So

Constraining the size of the narrow line region in distant quasars

We propose a proper method to measure the size of the narrow line region (NLR) in distant quasars. The apparent angular size of the NLR is, in general, too small to resolve technically. However, it is possible to map the NLR if with gravitational lensing. In our method, we directly compare the observed image of the NLR with the expected lensed images of the NLR for various source sizes and lens models. Seeking the best fit image via the comparison procedures, we can obtain the best-fit size and the best-fit lens model. We apply this method to the two-dimensional spectroscopic data of a famous lensed quasar, Q2237+0305. If the lens galaxy resembles the applied lens model, an upper limit to the NLR size can be set 750 pc. Further, we examine how the fitting results will be improved by future observations, taking into account the realistic observational effects, such as seeing. Future observations will provide us more stringent constraints on the size of the NLR and on the density profile of the lens galaxy.Comment: 17 pages including 4 figures, accepted to Ap

Estimating sufficient reductions of the predictors in abundant high-dimensional regressions

We study the asymptotic behavior of a class of methods for sufficient dimension reduction in high-dimension regressions, as the sample size and number of predictors grow in various alignments. It is demonstrated that these methods are consistent in a variety of settings, particularly in abundant regressions where most predictors contribute some information on the response, and oracle rates are possible. Simulation results are presented to support the theoretical conclusion.Comment: Published in at http://dx.doi.org/10.1214/11-AOS962 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Integrated Sachs-Wolfe Signal from BOSS Super-Structures

Cosmic structures leave an imprint on the microwave background radiation through the integrated Sachs-Wolfe effect. We construct a template map of the linear signal using the SDSS-III Baryon Acoustic Oscillation Survey at redshift 0.43 < z < 0.65. We verify the imprint of this map on the Planck CMB temperature map at the 97% confidence level and show consistency with the density-temperature cross-correlation measurement. Using this ISW reconstruction as a template we investigate the presence of ISW sources and further examine the properties of the Granett-Neyrinck-Szapudi supervoid and supercluster catalogue. We characterise the three-dimensional density profiles of these structures for the first time and demonstrate that they are significant structures. Model fits demonstrate that the supervoids are elongated along the line-of-sight and we suggest that this special orientation may be picked out by the void-finding algorithm in photometric redshift space. We measure the mean temperature profiles in Planck maps from public void and cluster catalogues. In an attempt to maximise the stacked ISW signal we construct a new catalogue of super-structures based upon local peaks and troughs of the gravitational potential. However, we do not find a significant correlation between these structures and the CMB temperature.Comment: Updated to match journal articl

Scaling study of Si and strained Si n-MOSFETs with different high-k gate stacks

Using ensemble Monte Carlo device simulations, this paper studies the impact of interface roughness and soft-optical phonon scattering on the performance of sub-100nm Si and strained Si MOSFETs with different high-k gate stacks. Devices with gate lengths down to 25nm have been investigated

Carbon Free Boston: Waste Technical Report

Part of a series of reports that includes: Carbon Free Boston: Summary Report; Carbon Free Boston: Social Equity Report; Carbon Free Boston: Technical Summary; Carbon Free Boston: Buildings Technical Report; Carbon Free Boston: Transportation Technical Report; Carbon Free Boston: Energy Technical Report; Carbon Free Boston: Offsets Technical Report; Available at http://sites.bu.edu/cfb/OVERVIEW: For many people, their most perceptible interaction with their environmental footprint is through the waste that they generate. On a daily basis people have numerous opportunities to decide whether to recycle, compost or throwaway. In many cases, such options may not be present or apparent. Even when such options are available, many lack the knowledge of how to correctly dispose of their waste, leading to contamination of valuable recycling or compost streams. Once collected, people give little thought to how their waste is treated. For Boston’s waste, plastic in the disposal stream acts becomes a fossil fuel used to generate electricity. Organics in the waste stream have the potential to be used to generate valuable renewable energy, while metals and electronics can be recycled to offset virgin materials. However, challenges in global recycling markets are burdening municipalities, which are experiencing higher costs to maintain their recycling. The disposal of solid waste and wastewater both account for a large and visible anthropogenic impact on human health and the environment. In terms of climate change, landfilling of solid waste and wastewater treatment generated emissions of 131.5 Mt CO2e in 2016 or about two percent of total United States GHG emissions that year. The combustion of solid waste contributed an additional 11.0 Mt CO2e, over half of which (5.9 Mt CO2e) is attributable to the combustion of plastic [1]. In Massachusetts, the GHG emissions from landfills (0.4 Mt CO2e), waste combustion (1.2 Mt CO2e), and wastewater (0.5 Mt CO2e) accounted for about 2.7 percent of the state’s gross GHG emissions in 2014 [2]. The City of Boston has begun exploring pathways to Zero Waste, a goal that seeks to systematically redesign our waste management system that can simultaneously lead to a drastic reduction in emissions from waste. The easiest way to achieve zero waste is to not generate it in the first place. This can start at the source with the decision whether or not to consume a product. This is the intent behind banning disposable items such as plastic bags that have more sustainable substitutes. When consumption occurs, products must be designed in such a way that their lifecycle impacts and waste footprint are considered. This includes making durable products, limiting the use of packaging or using organic packaging materials, taking back goods at the end of their life, and designing products to ensure compatibility with recycling systems. When reducing waste is unavoidable, efforts to increase recycling and organics diversion becomes essential for achieving zero waste. [TRUNCATED]Published versio

Multiple zero modes of the Dirac operator in three dimensions

One of the key properties of Dirac operators is the possibility of a degeneracy of zero modes. For the Abelian Dirac operator in three dimensions the construction of multiple zero modes has been sucessfully carried out only very recently. Here we generalise these results by discussing a much wider class of Dirac operators together with their zero modes. Further we show that those Dirac operators that do admit zero modes may be related to Hopf maps, where the Hopf index is related to the number of zero modes in a simple way.Comment: Latex file, 20 pages, no figure

Dwarf Archives: A Compendium of M, L, and T Dwarf Data

Dwarf Archives is an online archive containing astrometric, photometric, and spectroscopic information for all known L and T dwarfs (over 650 objects), as well as a select sample of over 500 M dwarfs. In this paper, we describe the specific data available in the archive, the interface for searching through it and discuss plans for future updates