Exceptional Sequences on Rational C*-Surfaces

Inspired by Bondal's conjecture, we study the behavior of exceptional sequences of line bundles on rational C*-surfaces under homogeneous degenerations. In particular, we provide a sufficient criterion for such a sequence to remain exceptional under a given degeneration. We apply our results to show that, for toric surfaces of Picard rank 3 or 4, all full exceptional sequences of line bundles may be constructed via augmentation. We also discuss how our techniques may be used to construct noncommutative deformations of derived categories.Comment: 30 pages, 11 figures. Some parts of this preprint originally appeared in arXiv:0906.4292v2 but have been revised and expanded upon. Minor changes, to appear in Manuscripta Mathematic

Food photographs in nutritional surveillance: errors in portion size estimation using drawings of bread and photographs of margarine and beverages consumption

Food photographs are widely used as instruments to estimate portion sizes of consumed foods. Several food atlases are available, all developed to be used in a specific context and for a given study population. Frequently, food photographs are adopted for use in other studies with a different context or another study population. In the present study, errors in portion size estimation of bread, margarine on bread and beverages by two-dimensional models used in the context of a Belgian food consumption survey are investigated. A sample of 111 men and women (age 45–65 years) were invited for breakfast; two test groups were created. One group was asked to estimate portion sizes of consumed foods using photographs 1–2 d after consumption, and a second group was asked the same after 4 d. Also, real-time assessment of portion sizes using photographs was performed. At the group level, large overestimation of margarine, acceptable underestimation of bread and only small estimation errors for beverages were found. Women tended to have smaller estimation errors for bread and margarine compared with men, while the opposite was found for beverages. Surprisingly, no major difference in estimation error was found after 4 d compared with 1–2 d. Individual estimation errors were large for all foods. The results from the present study suggest that the use of food photographs for portion size estimation of bread and beverages is acceptable for use in nutrition surveys. For photographs of margarine on bread, further validation using smaller amounts corresponding to actual consumption is recommended

Webs of Lagrangian Tori in Projective Symplectic Manifolds

For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperk\"ahler manifold is a fiber of an almost holomorphic Lagrangian fibration, giving an affirmative answer to a question of Beauville's. Our proof employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandt's theory of subnormal subgroups.Comment: 18 pages, minor latex problem fixe

Holomorphic symplectic geometry: a problem list

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

Predicting urinary creatinine excretion and its usefulness to identify incomplete 24h urine collections

Studies using 24 h urine collections need to incorporate ways to validate the completeness of the urine samples. Models to predict urinary creatinine excretion (UCE) have been developed for this purpose; however, information on their usefulness to identify incomplete urine collections is limited. We aimed to develop a model for predicting UCE and to assess the performance of a creatinine index using para-aminobenzoic acid (PABA) as a reference. Data were taken from the European Food Consumption Validation study comprising two non-consecutive 24 h urine collections from 600 subjects in five European countries. Data from one collection were used to build a multiple linear regression model to predict UCE, and data from the other collection were used for performance testing of a creatinine index-based strategy to identify incomplete collections. Multiple linear regression (n 458) of UCE showed a significant positive association for body weight (ß = 0·07), the interaction term sex × weight (ß = 0·09, reference women) and protein intake (ß = 0·02). A significant negative association was found for age (ß = - 0·09) and sex (ß = - 3·14, reference women). An index of observed-to-predicted creatinine resulted in a sensitivity to identify incomplete collections of 0·06 (95 % CI 0·01, 0·20) and 0·11 (95 % CI 0·03, 0·22) in men and women, respectively. Specificity was 0·97 (95 % CI 0·97, 0·98) in men and 0·98 (95 % CI 0·98, 0·99) in women. The present study shows that UCE can be predicted from weight, age and sex. However, the results revealed that a creatinine index based on these predictions is not sufficiently sensitive to exclude incomplete 24 h urine collections

Mixed Braid Group Actions From Deformations of Surface Singularities

We consider a set of toric Calabi-Yau varieties which arise as deformations of the small resolutions of type A surface singularities. By careful analysis of the heuristics of B-brane transport in the associated GLSMs, we predict the existence of a mixed braid group action on the derived category of each variety, and then prove that this action does indeed exist. This generalizes the braid group action found by Seidel and Thomas for the undeformed resolutions. We also show that the actions for different deformations are related, in a way that is predicted by the physical heuristics.Comment: 37 pages, including many figures and example

A functorial construction of moduli of sheaves

We show how natural functors from the category of coherent sheaves on a projective scheme to categories of Kronecker modules can be used to construct moduli spaces of semistable sheaves. This construction simplifies or clarifies technical aspects of existing constructions and yields new simpler definitions of theta functions, about which more complete results can be proved.Comment: 52 pp. Dedicated to the memory of Joseph Le Potier. To appear in Inventiones Mathematicae. Slight change in the definition of the Kronecker algebra in Secs 1 (p3) and 2.2 (p6), with corresponding small alterations elsewhere, to make the constructions work for non-reduced schemes. Section 6.5 rewritten. Remark 2.6 and new references adde

Bias in protein and potassium intake collected with 24-h recalls (EPIC-Soft) is rather comparable across European populations

Purpose: We investigated whether group-level bias of a 24-h recall estimate of protein and potassium intake, as compared to biomarkers, varied across European centers and whether this was influenced by characteristics of individuals or centers. Methods: The combined data from EFCOVAL and EPIC studies included 14 centers from 9 countries (n = 1,841). Dietary data were collected using a computerized 24-h recall (EPIC-Soft). Nitrogen and potassium in 24-h urine collections were used as reference method. Multilevel linear regression analysis was performed, including individual-level (e.g., BMI) and center-level (e.g., food pattern index) variables. Results: For protein intake, no between-center variation in bias was observed in men while it was 5.7% in women. For potassium intake, the between-center variation in bias was 8.9% in men and null in women. BMI was an important factor influencing the biases across centers (p <0.01 in all analyses). In addition, mode of administration (p = 0.06 in women) and day of the week (p = 0.03 in men and p = 0.06 in women) may have influenced the bias in protein intake across centers. After inclusion of these individual variables, between-center variation in bias in protein intake disappeared for women, whereas for potassium, it increased slightly in men (to 9.5%). Center-level variables did not influence the results. Conclusion: The results suggest that group-level bias in protein and potassium (for women) collected with 24-h recalls does not vary across centers and to a certain extent varies for potassium in men. BMI and study design aspects, rather than center-level characteristics, affected the biases across center