Holomorphic symplectic geometry: a problem list

A list of open problems on holomorphic symplectic, contact and Poisson manifolds

Differential risk of death in older residents in nursing homes prescribed specific antipsychotic drugs: population based cohort study

Objective To assess risks of mortality associated with use of individual antipsychotic drugs in elderly residents in nursing homes

Lagrangian fibrations of holomorphic-symplectic varieties of K3^[n]-type

Let X be a compact Kahler holomorphic-symplectic manifold, which is deformation equivalent to the Hilbert scheme of length n subschemes of a K3 surface. Let L be a nef line-bundle on X, such that the 2n-th power of c_1(L) vanishes and c_1(L) is primitive. Assume that the two dimensional subspace H^{2,0}(X) + H^{0,2}(X), of the second cohomology of X with complex coefficients, intersects trivially the integral cohomology. We prove that the linear system of L is base point free and it induces a Lagrangian fibration on X. In particular, the line-bundle L is effective. A determination of the semi-group of effective divisor classes on X follows, when X is projective. For a generic such pair (X,L), not necessarily projective, we show that X is bimeromorphic to a Tate-Shafarevich twist of a moduli space of stable torsion sheaves, each with pure one dimensional support, on a projective K3 surface.Comment: 34 pages. v3: Reference [Mat5] and Remark 1.8 added. Incorporated improvement to the exposition and corrected typos according to the referees suggestions. To appear in the proceedings of the conference Algebraic and Complex Geometry, Hannover 201

Harnessing the Medicaid Analytic eXtract (MAX) to Evaluate Medications in Pregnancy: Design Considerations

Background: In the absence of clinical trial data, large post-marketing observational studies are essential to evaluate the safety and effectiveness of medications during pregnancy. We identified a cohort of pregnancies ending in live birth within the 2000–2007 Medicaid Analytic eXtract (MAX). Herein, we provide a blueprint to guide investigators who wish to create similar cohorts from healthcare utilization data and we describe the limitations in detail. Methods: Among females ages 12–55, we identified pregnancies using delivery-related codes from healthcare utilization claims. We linked women with pregnancies to their offspring by state, Medicaid Case Number (family identifier) and delivery/birth dates. Then we removed inaccurate linkages and duplicate records and implemented cohort eligibility criteria (i.e., continuous and appropriate enrollment type, no private insurance, no restricted benefits) for claim information completeness. Results: From 13,460,273 deliveries and 22,408,810 child observations, 6,107,572 pregnancies ending in live birth were available after linkage, cleaning, and removal of duplicate records. The percentage of linked deliveries varied greatly by state, from 0 to 96%. The cohort size was reduced to 1,248,875 pregnancies after requiring maternal eligibility criteria throughout pregnancy and to 1,173,280 pregnancies after further applying infant eligibility criteria. Ninety-one percent of women were dispensed at least one medication during pregnancy. Conclusions: Mother-infant linkage is feasible and yields a large pregnancy cohort, although the size decreases with increasing eligibility requirements. MAX is a useful resource for studying medications in pregnancy and a spectrum of maternal and infant outcomes within the indigent population of women and their infants enrolled in Medicaid. It may also be used to study maternal characteristics, the impact of Medicaid policy, and healthcare utilization during pregnancy. However, careful attention to the limitations of these data is necessary to reduce biases

Fibrations on four-folds with trivial canonical bundles

Four-folds with trivial canonical bundles are divided into six classes according to their holonomy group. We consider examples that are fibred by abelian surfaces over the projective plane. We construct such fibrations in five of the six classes, and prove that there is no such fibration in the sixth class. We classify all such fibrations whose generic fibre is the Jacobian of a genus two curve.Comment: 28 page

Period- and mirror-maps for the quartic K3

We study in detail mirror symmetry for the quartic K3 surface in P3 and the mirror family obtained by the orbifold construction. As explained by Aspinwall and Morrison, mirror symmetry for K3 surfaces can be entirely described in terms of Hodge structures. (1) We give an explicit computation of the Hodge structures and period maps for these families of K3 surfaces. (2) We identify a mirror map, i.e. an isomorphism between the complex and symplectic deformation parameters, and explicit isomorphisms between the Hodge structures at these points. (3) We show compatibility of our mirror map with the one defined by Morrison near the point of maximal unipotent monodromy. Our results rely on earlier work by Narumiyah-Shiga, Dolgachev and Nagura-Sugiyama.Comment: 29 pages, 3 figure

Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces

We perform a study of the moduli space of framed torsion-free sheaves on Hirzebruch surfaces by using localization techniques. We discuss some general properties of this moduli space by studying it in the framework of Huybrechts-Lehn theory of framed modules. We classify the fixed points under a toric action on the moduli space, and use this to compute the Poincare polynomial of the latter. This will imply that the moduli spaces we are considering are irreducible. We also consider fractional first Chern classes, which means that we are extending our computation to a stacky deformation of a Hirzebruch surface. From the physical viewpoint, our results provide the partition function of N=4 Vafa-Witten theory on total spaces of line bundles on P1, which is relevant in black hole entropy counting problems according to a conjecture due to Ooguri, Strominger and Vafa.Comment: 17 pages. This submission supersedes arXiv:0809.0155 [math.AG

Five-Brane Superpotentials, Blow-Up Geometries and SU(3) Structure Manifolds

We investigate the dynamics of space-time filling five-branes wrapped on curves in heterotic and orientifold Calabi-Yau compactifications. We first study the leading N=1 scalar potential on the infinite deformation space of the brane-curve around a supersymmetric configuration. The higher order potential is also determined by a brane superpotential which we compute for a subset of light deformations. We argue that these deformations map to new complex structure deformations of a non-Calabi-Yau manifold which is obtained by blowing up the brane-curve into a four-cycle and by replacing the brane by background fluxes. This translates the original brane-bulk system into a unifying geometrical formulation. Using this blow-up geometry we compute the complete set of open-closed Picard-Fuchs differential equations and identify the brane superpotential at special points in the field space for five-branes in toric Calabi-Yau hypersurfaces. This has an interpretation in open mirror symmetry and enables us to list compact disk instanton invariants. As a first step towards promoting the blow-up geometry to a supersymmetric heterotic background we propose a non-Kaehler SU(3) structure and an identification of the three-form flux.Comment: 95 pages, 4 figures; v2: Minor corrections, references update

Application of Headspace Solid-Phase Microextraction for Determination of Chloro-Organic Compounds in Sewage Samples

Solid phase microextraction (SPME) has been optimized and applied to the determination of the volatile halogenated compounds (VHCs) and semi-volatile halogenated compounds (SVHCs). Three types of SPME fiber coated with different stationary phases (PDMS–100 μm, CAR/PDMS-75 μm, PDMS/DVB–65 μm) were used to examine their extraction efficiencies for the compounds tested. Experimental parameters such as the selection of SPME coatings, extraction time, and addition of salts were studied. The carboxen-polydimethylsiloxane (CAR/PDMS) fiber appears to be the most suitable for the determination of VHCs. Analytical parameters such as linearity, limit of detection, and precision were also evaluated. Application of ECD detector for the determination of VHCs and SVHCs allows their determination on the low concentration level, ranging from 0.005 to 0.8 μg/L−1. The HS-SPME-GC/ECD procedure gave good analytical precision expressed as relative standard deviation (RSD) (ranged from 5.08% to 8.07%) for a concentration level of 5 μg/L−1 and good linearity (r2 > 0.98) in a wide calibration range. The applied HS-SPME-GC/ECD method was found to be a quick and effective technique for the determination of microtrace amounts of volatile and semi-volatile halogenated compounds in samples containing high amounts of various organic compounds

Association of heart rate and blood pressure among European adolescents with usual food consumption: the HELENA study

Background and aim: In adults, there is some evidence that improving diet reduces blood pressure (BP) and the subsequent risk of cardiovascular diseases (CVDs). However, studies that analyse this association in adolescents are still scarce. The objective of the present study was to examine the associations between heart rate, systolic (SBP), diastolic (DBP) and mean arterial blood pressure (MAP) among European adolescents and usual intake of vegetables, fruits, dairy products, meat, fish, high-sugar foods and savoury snacks. Methods and results: In total, 2283 adolescents from the HELENA-study (12.5-17.5 years old; 1253 girls) were included. Dietary intake was assessed using two computerized 24-hour dietary recalls. Age, sex, body mass index, maternal educational level, physical activity and Tanner stage were considered as confounders. Associations were examined by mixed model analysis stratified by sex. Tests for trend were assessed by tertiles of intake while controlling for the aforementioned confounders. Dairy products and fish intake were negatively associated with BP and heart rate. Significant decreasing trends were observed for heart rate and BP across tertiles of dairy products, fish intake and high-sugar foods intake (p < 0.05). Significant increasing trends were observed for SBP and MAP across tertiles of savoury snack intake (p < 0.05). Conclusion: Significant but small inverse associations between fish and dairy products consumption with blood pressure and heart rate have been found in European adolescents. Dietary intervention studies are needed to explore these associations in the context of the modification of several risk factors for the prevention of cardiovascular diseases