Cartan subalgebras of root-reductive Lie algebras

Root-reductive Lie algebras are direct limits of finite-dimensional reductive Lie algebras under injections which preserve the root spaces. It is known that a root-reductive Lie algebra is a split extension of an abelian Lie algebra by a direct sum of copies of finite-dimensional simple Lie algebras as well as copies of the three simple infinite-dimensional root-reductive Lie algebras sl_infty, so_infty, and sp_infty. As part of a structure theory program for root-reductive Lie algebras, Cartan subalgebras of the Lie algebra gl_infty were introduced and studied in a paper of Neeb and Penkov. In the present paper we refine and extend the results of [N-P] to the case of a general root-reductive Lie algebra g. We prove that the Cartan subalgebras of g are the centralizers of maximal toral subalgebras and that they are nilpotent and self-normalizing. We also give an explicit description of all Cartan subalgebras of the simple Lie algebras sl_infty, so_infty, and sp_infty. We conclude the paper with a characterization of the set of conjugacy classes of Cartan subalgebras of the Lie algebras gl_infty, sl_infty, so_infty, and sp_infty with respect to the group of automorphisms of the natural representation which preserve the Lie algebra.Comment: 28 pages, 1 figur

Hospital Board Infrastructure and Functions: The Role of Governance in Financial Performance

Increased stake of boards in the leadership of the hospitals makes them play a significant role in the financial health of their institutions. Understanding of the correct approach to successfully fulfill this purpose is critical for preparing their organizations for positioning adequately in the health care market. Governmental agencies and public companies, including insurers, will be interested in the extent to which hospital boards have adopted the provisions of accounting reform laws like those introduced by the Sarbanes-Oxley Act. It will remain for the boards to balance their oversight role for financial performance with the pressures of financial accountability

Formation and Evolution of Planetary Systems: Placing Our Solar System in Context with Spitzer

We summarize the progress to date of our Legacy Science Program entitled "The Formation and Evolution of Planetary Systems" (FEPS) based on observations obtained with the Spitzer Space Telescope during its first year of operation. In addition to results obtained from our ground-based preparatory program and our early validation program, we describe new results from a survey for near-infrared excess emission from the youngest stars in our sample as well as a search for cold debris disks around sun-like stars. We discuss the implications of our findings with respect to current understanding of the formation and evolution of our own solar system.Comment: 8 postscript pages including 3 figures. To appear in "Spitzer New Views of the Cosmos" ASP Conference Series, eds. L. Armus et al. FEPS website at http://feps.as.arizona.ed

The Woody Guthrie Centennial Bibliography

This bibliography updates two extensive works designed to include comprehensively all significant works by and about Woody Guthrie. Richard A. Reuss published A Woody Guthrie Bibliography, 1912–1967 in 1968 and Jeffrey N. Gatten\u27s article “Woody Guthrie: A Bibliographic Update, 1968–1986” appeared in 1988. With this current article, researchers need only utilize these three bibliographies to identify all English-language items of relevance related to, or written by, Guthrie

Predicting breast cancer response to neoadjuvant treatment using multi-feature MRI: results from the I-SPY 2 TRIAL.

Dynamic contrast-enhanced (DCE) MRI provides both morphological and functional information regarding breast tumor response to neoadjuvant chemotherapy (NAC). The purpose of this retrospective study is to test if prediction models combining multiple MRI features outperform models with single features. Four features were quantitatively calculated in each MRI exam: functional tumor volume, longest diameter, sphericity, and contralateral background parenchymal enhancement. Logistic regression analysis was used to study the relationship between MRI variables and pathologic complete response (pCR). Predictive performance was estimated using the area under the receiver operating characteristic curve (AUC). The full cohort was stratified by hormone receptor (HR) and human epidermal growth factor receptor 2 (HER2) status (positive or negative). A total of 384 patients (median age: 49 y/o) were included. Results showed analysis with combined features achieved higher AUCs than analysis with any feature alone. AUCs estimated for the combined versus highest AUCs among single features were 0.81 (95% confidence interval [CI]: 0.76, 0.86) versus 0.79 (95% CI: 0.73, 0.85) in the full cohort, 0.83 (95% CI: 0.77, 0.92) versus 0.73 (95% CI: 0.61, 0.84) in HR-positive/HER2-negative, 0.88 (95% CI: 0.79, 0.97) versus 0.78 (95% CI: 0.63, 0.89) in HR-positive/HER2-positive, 0.83 (95% CI not available) versus 0.75 (95% CI: 0.46, 0.81) in HR-negative/HER2-positive, and 0.82 (95% CI: 0.74, 0.91) versus 0.75 (95% CI: 0.64, 0.83) in triple negatives. Multi-feature MRI analysis improved pCR prediction over analysis of any individual feature that we examined. Additionally, the improvements in prediction were more notable when analysis was conducted according to cancer subtype

The NANOGrav 15-year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries

Evidence for a low-frequency stochastic gravitational wave background has recently been reported based on analyses of pulsar timing array data. The most likely source of such a background is a population of supermassive black hole binaries, the loudest of which may be individually detected in these datasets. Here we present the search for individual supermassive black hole binaries in the NANOGrav 15-year dataset. We introduce several new techniques, which enhance the efficiency and modeling accuracy of the analysis. The search uncovered weak evidence for two candidate signals, one with a gravitational-wave frequency of $\sim$4 nHz, and another at $\sim$170 nHz. The significance of the low-frequency candidate was greatly diminished when Hellings-Downs correlations were included in the background model. The high-frequency candidate was discounted due to the lack of a plausible host galaxy, the unlikely astrophysical prior odds of finding such a source, and since most of its support comes from a single pulsar with a commensurate binary period. Finding no compelling evidence for signals from individual binary systems, we place upper limits on the strain amplitude of gravitational waves emitted by such systems.Comment: 23 pages, 13 figures, 2 tables. Accepted for publication in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email [email protected]