Brauer group of moduli spaces of pairs

We show that the Brauer group of any moduli space of stable pairs with fixed determinant over a curve is zero.Comment: 12 pages. Final version, accepted in Communications in Algebr

An Assessment of Basic Computer Proficiency Among Active Internet Users: Test Construction, Calibration, Antecedents and Consequences

The purpose of this article is to describe our efforts to create a test of basic computer proficiency, examine its properties using parametric test scoring methods, and identify some antecedents and consequences that accompany differences in performance. We also consider how much insight people have into their level of knowledge by examining the relationship between our tested measure of computer knowledge and self-rated knowledge scores collected at the same time. This research also adds to the large body of existing empirical work on computer literacy in the student population, by looking at computer literacy in a more general sample of the Internet-using population. A further purpose of this research, as a result, is to make our dataset available for future research

Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces

Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo invariant.Comment: v2: added due credits to the work of Burger, Iozzi and Wienhard. v3: corrected count of connected components for G=SU(p,q) (p \neq q); added due credits to the work of Xia and Markman-Xia; minor corrections and clarifications. 31 page

The dynamics of vortices on S^2 near the Bradlow limit

The explicit solutions of the Bogomolny equations for N vortices on a sphere of radius R^2 > N are not known. In particular, this has prevented the use of the geodesic approximation to describe the low energy vortex dynamics. In this paper we introduce an approximate general solution of the equations, valid for R^2 close to N, which has many properties of the true solutions, including the same moduli space CP^N. Within the framework of the geodesic approximation, the metric on the moduli space is then computed to be proportional to the Fubini- Study metric, which leads to a complete description of the particle dynamics.Comment: 17 pages, 9 figure

Cardiovascular magnetic resonance in pulmonary hypertension

Pulmonary hypertension represents a group of conditions characterized by higher than normal pulmonary artery pressures. Despite improved treatments, outcomes in many instances remain poor. In recent years, there has been growing interest in the use of Cardiovascular Magnetic Resonance (CMR) in patients with pulmonary hypertension. This technique offers certain advantages over other imaging modalities since it is well suited to the assessment of the right ventricle and the proximal pulmonary arteries. Reflecting the relatively sparse evidence supporting its use, CMR is not routinely recommended for patients with pulmonary hypertension. However, it is particularly useful in patient with pulmonary arterial hypertension associated with congenital heart disease. Furthermore, it has proven informative in a number of ways; illustrating how right ventricular remodeling is favorably reversed by drug therapies and providing explicit confirmation of the importance of the right ventricle to clinical outcome. This review will discuss these aspects and practical considerations before speculating on future applications

Closed-Form Bayesian Inferences for the Logit Model via Polynomial Expansions

Articles in Marketing and choice literatures have demonstrated the need for incorporating person-level heterogeneity into behavioral models (e.g., logit models for multiple binary outcomes as studied here). However, the logit likelihood extended with a population distribution of heterogeneity doesn't yield closed-form inferences, and therefore numerical integration techniques are relied upon (e.g., MCMC methods). We present here an alternative, closed-form Bayesian inferences for the logit model, which we obtain by approximating the logit likelihood via a polynomial expansion, and then positing a distribution of heterogeneity from a flexible family that is now conjugate and integrable. For problems where the response coefficients are independent, choosing the Gamma distribution leads to rapidly convergent closed-form expansions; if there are correlations among the coefficients one can still obtain rapidly convergent closed-form expansions by positing a distribution of heterogeneity from a Multivariate Gamma distribution. The solution then comes from the moment generating function of the Multivariate Gamma distribution or in general from the multivariate heterogeneity distribution assumed. Closed-form Bayesian inferences, derivatives (useful for elasticity calculations), population distribution parameter estimates (useful for summarization) and starting values (useful for complicated algorithms) are hence directly available. Two simulation studies demonstrate the efficacy of our approach.Comment: 30 pages, 2 figures, corrected some typos. Appears in Quantitative Marketing and Economics vol 4 (2006), no. 2, 173--20

A Statistical Look at Roger Clemens’ Pitching Career

A recent report (Hendricks Sports Management, LP, et al, 2008) issued by Hendricks Sports Management, LP, claims to provide evidence for the lack of use of performance-enhancing substances (PESs) by Hall-of-Fame caliber pitcher Roger Clemens, a claim based on an analysis of his career statistics (using ERA = earned run average, K rate = strikeout rate, innings pitched), both in isolation and in comparison to other power pitchers of his era (Randy Johnson, Nolan Ryan, and Curt Schilling). In this research, we re-examine Roger Clemens’ career using a more complete and stable set of pitching measures (WHIP = walks + hits per inning pitched, BAA = batting average against, ERA, BB rate = rate of walks per batter faced, K rate), and by using a broader (census) comparison set of pitchers with similar longevity in order to reduce the selection bias inherent in the Hendricks report. In contrast to Hendricks’ report, our analysis examines not only late career performance but also early- and mid-career trends. Our findings can be summarized as follows: Using simple quadratic functions, and an occasional spline to relate the above pitching measures to age, we demonstrate a number of empirical regularities: Roger Clemens’ career is atypical with respect to his peer group. While most pitchers with comparable longevity improve for the first half of their career, peaking just past the age of 30 and then declining (an inverted-U shape), Roger Clemens’ career statistics shows a decrease into his early thirties followed by a marked improvement late in his career (more of a U-shape). This pattern is consistent across most measures for Roger Clemens, yet for certain measures is not unique to him. That is, other pitchers have atypical patterns as well for some, but not all other tested measures. Our analyses suggest what we, as statisticians, have postulated all along: empirical association is not causation, and neither the Hendricks report nor ours can prove or disprove the use of PESs by any given player. This is because players are indeed unique, and due to the short-time series and sparseness of comparable players there is low power to assess specific hypotheses. However, our analyses clearly suggest that Roger Clemens’ career pitching trajectory is atypical