Rank two quadratic pairs and surface group representations

Let $X$ be a compact Riemann surface. A quadratic pair on $X$ consists of a holomorphic vector bundle with a quadratic form which takes values in fixed line bundle. We show that the moduli spaces of quadratic pairs of rank 2 are connected under some constraints on their topological invariants. As an application of our results we determine the connected components of the $\mathrm{SO}_0(2,3)$-character variety of $X$.Comment: 37 pages, 1 figur

Drugs used in cardiological practice

A medical journal article on drugs used in cardiology in the 1950's.It is manifestly impossible to deal with all the drugs used in cardio- logical practice. There are some 400 medical journals in tile English language published annually, and these contain some 800 articles on cardiology, so that it is merely possible to touch on the fringe of the subject

The K\"ahler Potential of Abelian Higgs Vortices

We calculate the K\"ahler potential for the Samols metric on the moduli space of Abelian Higgs vortices on \mathbbm{R}^{2}, in two different ways. The first uses a scaling argument. The second is related to the Polyakov conjecture in Liouville field theory. The K\"ahler potential on the moduli space of vortices on \mathbbm{H}^{2} is also derived, and we are led to a geometrical reinterpretation of these vortices. Finally, we attempt to find the K\"ahler potential for vortices on \mathbbm{R}^{2} in a third way by relating the vortices to SU(2) Yang-Mills instantons on \mathbbm{R}^{2}\times S^{2}. This approach does not give the correct result, and we offer a possible explanation for this.Comment: 25 page

Moduli of vortices and Grassmann manifolds

We use the framework of Quot schemes to give a novel description of the moduli spaces of stable n-pairs, also interpreted as gauged vortices on a closed Riemann surface with target Mat(r x n, C), where n >= r. We then show that these moduli spaces embed canonically into certain Grassmann manifolds, and thus obtain natural Kaehler metrics of Fubini-Study type; these spaces are smooth at least in the local case r=n. For abelian local vortices we prove that, if a certain "quantization" condition is satisfied, the embedding can be chosen in such a way that the induced Fubini-Study structure realizes the Kaehler class of the usual L^2 metric of gauged vortices.Comment: 22 pages, LaTeX. Final version: last section removed, typos corrected, two references added; to appear in Commun. Math. Phy

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

Effectiveness of computer-based auditory training in improving the perception of noise-vocoded speech

Five experiments were designed to evaluate the effectiveness of “high-variability” lexical training in improving the ability of normal-hearing subjects to perceive noise-vocoded speech that had been spectrally shifted to simulate tonotopic misalignment. Two approaches to training were implemented. One training approach required subjects to recognize isolated words, while the other training approach required subjects to recognize words in sentences. Both approaches to training improved the ability to identify words in sentences. Improvements following a single session (lasting 1–2 h) of auditory training ranged between 7 and 12 %pts and were significantly larger than improvements following a visual control task that was matched with the auditory training task in terms of the response demands. An additional three sessions of word- and sentence-based training led to further improvements, with the average overall improvement ranging from 13 to 18 %pts. When a tonotopic misalignment of 3 mm rather than 6 mm was simulated, training with several talkers led to greater generalization to new talkers than training with a single talker. The results confirm that computer-based lexical training can help overcome the effects of spectral distortions in speech, and they suggest that training materials are most effective when several talkers are included

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

Topological Reduction of 4D SYM to 2D σ\sigma--Models

By considering a (partial) topological twisting of supersymmetric Yang-Mills compactified on a 2d space with `t Hooft magnetic flux turned on we obtain a supersymmetric $\sigma$-model in 2 dimensions. For N=2 SYM this maps Donaldson observables on products of two Riemann surfaces to quantum cohomology ring of moduli space of flat connections on a Riemann surface. For N=4 SYM it maps $S$-duality to $T$-duality for $\sigma$-models on moduli space of solutions to Hitchin equations.Comment: 30 pages, harvma

Glucocorticoid Effects on Contact Hypersensitivity and on the Cutaneous Response to Ultraviolet Light in the Mouse

A single exposure to 254nm ultraviolet irradiation (UV) can systemically suppress experimental sensitization to the simple allergen 2,4-dinitro, 1-chlorobenzene (DNCB) in the mouse. We show here that topical application at the site of irradiation of the 21-oic acid methyl ester derivative of the synthetic glucocorticoid triamcinolone acetonide (TAme) prevents UV suppression of sensitization. That is, mice painted with TAme at the site of UV exposure developed normal contact hypersensitivity (CH); mice exposed to UV only, like mice treated with the parent compound triamcinolone acetonide (TA), failed to be sensitized by DNCB applied to a distal site. TAme is inactivated rapidly by plasma esterases, so its effect is thought to be confined to the skin. Apparently, TAme blocked the cutaneous signal(s) for systemic suppression of CH. Histologically, irradiated skin exhibited mild inflammation and hyperproliferation, but these effects were greatly exaggerated and prolonged in the UV + TAme-treated skin, independent of sensitization at the distal site. The infiltrate consisted mostly of neutrophils and lacked the round cells characteristic of cell-mediated immunity. Apparently, normal immune suppression by UV prevented this vigorous reaction to irradiated skin. Applied together with DNCB, TAme blocked sensitization. It also prevented response to challenge by DNCB in previously sensitized animals. However, unlike the parent compound triamcinolone acetonide (TA), Budesonide or Beclomethasone diproprionate, each of which can penetrate the epidermis in active form, TAme had no effect on sensitization when applied at a distal site. Likewise, TAme did not affect plasma B (17-desoxycortisol) levels, whereas the other three compounds reduced plasma B tenfold, as expected of compounds causing adrenal-pituitary suppression. The results as a whole show that glucocorticoids can specifically inhibit cutaneous steps in induction of cell-mediated immunity or its suppression, and can, at the site of challenge, prevent its expression in CH

A Bivariate Timing Model of Customer Acquisition and Retention

Two widely recognized components, central to the calculation of customer value, are acquisition and retention propensities. However, while extant research has incorporated such components into different types of models, limited work has investigated the kinds of associations that may exist between them. In this research, we focus on the relationship between a prospective customer\u27s time until acquisition of a particular service and the subsequent duration for which he retains it, and examine the implications of this relationship on the value of prospects and customers. To accomplish these tasks, we use a bivariate timing model to capture the relationship between acquisition and retention. Using a split-hazard model, we link the acquisition and retention processes in two distinct yet complementary ways. First, we use the Sarmonov family of bivariate distributions to allow for correlations in the observed acquisition and retention times within a customer; next, we allow for differences across customers using latent classes for the parameters that govern the two processes. We then demonstrate how the proposed methodology can be used to calculate the discounted expected value of a subscription based on the time of acquisition, and discuss possible applications of the modeling framework to problems such as customer targeting and resource allocation