Exceptional Sequences of Line Bundles and Spherical Twists - a Toric Example

Exceptional sequences of line bundles on a smooth projective toric surface are automatically full when they can be constructed via augmentation. By using spherical twists, we give examples that there are also exceptional sequences which can not be constructed this way but are nevertheless full.Comment: 12 pages, 3 figure

Holomorphic symplectic geometry: a problem list

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

Fracture Risk in Relation to Serum 25-Hydroxyvitamin D and Physical Activity: Results from the EPIC-Norfolk Cohort Study.

Vitamin D deficiency and physical inactivity have been associated with bone loss and fractures, but their combined effect has scarcely been studied either in younger or older adults. Therefore, we aimed to assess the associations between physical activity, age and 25-hydroxyvitamin D (25(OH)D) status separately and in combination with the incidence of fracture risk in the EPIC-Norfolk cohort study. Baseline (1993-1998) self-reported physical activity and serum 25(OH)D concentrations at follow-up (1998-2000) were collected in 14,624 men and women (aged 42-82 y between 1998 and 2000). Fracture incidence was ascertained up to March 2015. Cox proportional hazard model was used to determine HRs of fractures by plasma 25(OH)D (90 nmol/L), age (65 y) and physical activity (inactive and active) categories, by follow-up time per 20 nmol/L increase in serum 25(OH)D and to explore age-25(OH)D and physical activity-25(OH)D interactions. The age-, sex-, and month-adjusted HRs (95% CIs) for all fractures (1183 fractures) by increasing vitamin D category were not significantly different. With additional adjustment for body mass index, smoking status, alcohol intake, supplement use and history of fractures, the fracture risk was 29% lower in those participants with 50 to 70 nmol/L compared with those in the lowest quintile (<30 nmol/L). Physical inactivity based on a single baseline assessment was not associated with fracture risk. Vitamin D status appeared inversely related to fractures in middle aged adults. In older adults, the relationship between vitamin D status and fracture risk was observed to be J-shaped. Clinical and public health practice in vitamin D supplementation could partially explain these findings, although definitive conclusions are difficult due to potential changes in exposure status over the long follow up period.This work was supported by Medical Research Council (MRC) - MKS/S16 (RG19715) / Sponsor Funding Ref: G9502233; Cancer Research UK (CRUK) - MKS/R07 (RG14230) / Sponsor Funding Ref: SP2024/0201; and Cancer Research UK (CRUK) - MKS/T21 (RG23772) / Sponsor Funding Ref: SP2024/0204. CJA received a Grant FPU13/00421 from the Government of Spain “Ministerio de Educación, Cultura y Deporte”

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

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

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

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

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

Curve counting via stable pairs in the derived category

For a nonsingular projective 3-fold $X$, we define integer invariants virtually enumerating pairs $(C,D)$ where $C\subset X$ is an embedded curve and $D\subset C$ is a divisor. A virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of $X$. The resulting invariants are conjecturally equivalent, after universal transformations, to both the Gromov-Witten and DT theories of $X$. For Calabi-Yau 3-folds, the latter equivalence should be viewed as a wall-crossing formula in the derived category. Several calculations of the new invariants are carried out. In the Fano case, the local contributions of nonsingular embedded curves are found. In the local toric Calabi-Yau case, a completely new form of the topological vertex is described. The virtual enumeration of pairs is closely related to the geometry underlying the BPS state counts of Gopakumar and Vafa. We prove that our integrality predictions for Gromov-Witten invariants agree with the BPS integrality. Conversely, the BPS geometry imposes strong conditions on the enumeration of pairs.Comment: Corrected typos and duality error in Proposition 4.6. 47 page