Gelfand-Zetlin Polytopes and the Geometry of Flag Varieties

Gelfand-Zetlin polytopes are important in the finite dimensional representation theory of SLn(C) and the symplectic geometry of coadjoint orbits of the unitary group. We examine the combinatorics of Gelfand-Zetlin polytopes in relation to the geometry of the flag variety of SLn(C). The two main contributions of the thesis are as follows: (1) we describe virtual Gelfand-Zetlin polytopes associated to non-dominant weights and (2) we identify the cohomology ring of the flag variety with a quotient of the subalgebra of the Chow cohomology ring of the Gelfand-Zetlin toric variety generated in degree one. More precisely, we take the largest quotient of this subalgebra that satisfies Poincare duality

Health-status outcomes with invasive or conservative care in coronary disease

BACKGROUND In the ISCHEMIA trial, an invasive strategy with angiographic assessment and revascularization did not reduce clinical events among patients with stable ischemic heart disease and moderate or severe ischemia. A secondary objective of the trial was to assess angina-related health status among these patients. METHODS We assessed angina-related symptoms, function, and quality of life with the Seattle Angina Questionnaire (SAQ) at randomization, at months 1.5, 3, and 6, and every 6 months thereafter in participants who had been randomly assigned to an invasive treatment strategy (2295 participants) or a conservative strategy (2322). Mixed-effects cumulative probability models within a Bayesian framework were used to estimate differences between the treatment groups. The primary outcome of this health-status analysis was the SAQ summary score (scores range from 0 to 100, with higher scores indicating better health status). All analyses were performed in the overall population and according to baseline angina frequency. RESULTS At baseline, 35% of patients reported having no angina in the previous month. SAQ summary scores increased in both treatment groups, with increases at 3, 12, and 36 months that were 4.1 points (95% credible interval, 3.2 to 5.0), 4.2 points (95% credible interval, 3.3 to 5.1), and 2.9 points (95% credible interval, 2.2 to 3.7) higher with the invasive strategy than with the conservative strategy. Differences were larger among participants who had more frequent angina at baseline (8.5 vs. 0.1 points at 3 months and 5.3 vs. 1.2 points at 36 months among participants with daily or weekly angina as compared with no angina). CONCLUSIONS In the overall trial population with moderate or severe ischemia, which included 35% of participants without angina at baseline, patients randomly assigned to the invasive strategy had greater improvement in angina-related health status than those assigned to the conservative strategy. The modest mean differences favoring the invasive strategy in the overall group reflected minimal differences among asymptomatic patients and larger differences among patients who had had angina at baseline

Initial invasive or conservative strategy for stable coronary disease

BACKGROUND Among patients with stable coronary disease and moderate or severe ischemia, whether clinical outcomes are better in those who receive an invasive intervention plus medical therapy than in those who receive medical therapy alone is uncertain. METHODS We randomly assigned 5179 patients with moderate or severe ischemia to an initial invasive strategy (angiography and revascularization when feasible) and medical therapy or to an initial conservative strategy of medical therapy alone and angiography if medical therapy failed. The primary outcome was a composite of death from cardiovascular causes, myocardial infarction, or hospitalization for unstable angina, heart failure, or resuscitated cardiac arrest. A key secondary outcome was death from cardiovascular causes or myocardial infarction. RESULTS Over a median of 3.2 years, 318 primary outcome events occurred in the invasive-strategy group and 352 occurred in the conservative-strategy group. At 6 months, the cumulative event rate was 5.3% in the invasive-strategy group and 3.4% in the conservative-strategy group (difference, 1.9 percentage points; 95% confidence interval [CI], 0.8 to 3.0); at 5 years, the cumulative event rate was 16.4% and 18.2%, respectively (difference, 121.8 percentage points; 95% CI, 124.7 to 1.0). Results were similar with respect to the key secondary outcome. The incidence of the primary outcome was sensitive to the definition of myocardial infarction; a secondary analysis yielded more procedural myocardial infarctions of uncertain clinical importance. There were 145 deaths in the invasive-strategy group and 144 deaths in the conservative-strategy group (hazard ratio, 1.05; 95% CI, 0.83 to 1.32). CONCLUSIONS Among patients with stable coronary disease and moderate or severe ischemia, we did not find evidence that an initial invasive strategy, as compared with an initial conservative strategy, reduced the risk of ischemic cardiovascular events or death from any cause over a median of 3.2 years. The trial findings were sensitive to the definition of myocardial infarction that was used

Problems in measuring the cash recovery rate and measurement error in estimates of the firm IRR

This paper considers the impact on estimates of the IRR derived from the cash recovery rate approach to the estimation of economic performance of an inability to observe the conceptually defined CRR from accounting data. In particular, it considers a typical proxy used in empirical applications of the CRR approach and asks the question — under what circumstances will this proxy fail to measure the true CRR? Two circumstances are identified. First, the empirical CRR will not measure the true CRR when advertising and research expenditures exist which should be treated as part of the composite investment (and, hence, as investment expenditures) but are expensed in the accounting records -referred to as the capitalize/expense case. Second, the empirical CRR will not measure the true CRR when the composite investment is made up of projects with different lives — referred to as the retirement case. For these two cases, relationships are developed between the proxy and the true CRR. From these relationships the impact of errors in measuring the CRR on estimates of the IRR are deduced. Analytically, it is demonstrated that, in the capitalize/expense case, the inability to measure the CRR produces measurement error in the IRR estimate that is monotonically and negatively related to the rate of investment growth. Further, as the proportion of expensed investment expenditures increases, measurement error increases if the investment growth rate is less than the IRR and decreases if the investment growth rate is greater than the IRR. In the retirement case, it is identified analytically that measurement error also will be monotonically and negatively related to the investment growth rate. This is the case even though the analyst is able to specify the basic relationship between investment outflows and subsequent cash inflows (the inability to spec ify this basic relationship is a problem considered in many papers on the CRR approach). Numerical examples suggest that these effects are not insignificant in size a priori.

Measurement of the ZZ production cross section and search for anomalous couplings in 2l2l' final states in pp collisions at sqrt(s)=7 TeV

Submitted to the Journal of High Energy Physics ; see paper for full list of authorsA measurement is presented of the ZZ production cross section in the ZZ to 2l 2l' decay mode with l = e, mu and l' = e, mu, tau in proton-proton collisions at sqrt(s) = 7 TeV with the CMS experiment at the LHC. Results are based on data corresponding to an integrated luminosity of 5.0 inverse femtobarns. The measured cross section sigma(pp to ZZ) = 6.24 [+0.86/-0.80] (stat.) [+0.41/-0.32] (syst.) +/- 0.14 (lumi.) pb is consistent with the standard model predictions. The following limits on ZZZ and ZZ gamma anomalous trilinear gauge couplings are set at 95% confidence level: -0.011 f[4;Z] < 0.012, -0.012 < f[5;Z] < 0.012, -0.013 < f[4;gamma] < 0.015, and -0.014 < f[5,gamma] < 0.014