Formal deformations and their categorical general fibre

We study the general fibre of a formal deformation over the formal disk of a projective variety from the view point of abelian and derived categories. The abelian category of coherent sheaves of the general fibre is constructed directly from the formal deformation and is shown to be linear over the field of Laurent series. The various candidates for the derived category of the general fibre are compared. If the variety is a surface with trivial canonical bundle, we show that the derived category of the general fibre is again a linear triangulated category with a Serre functor given by the square of the shift functor

The 3-fold vertex via stable pairs

The theory of stable pairs in the derived category yields an enumerative geometry of curves in 3-folds. We evaluate the equivariant vertex for stable pairs on toric 3-folds in terms of weighted box counting. In the toric Calabi-Yau case, the result simplifies to a new form of pure box counting. The conjectural equivalence with the DT vertex predicts remarkable identities. The equivariant vertex governs primary insertions in the theory of stable pairs for toric varieties. We consider also the descendent vertex and conjecture the complete rationality of the descendent theory for stable pairs.Comment: Typos fixed. 40 pages, 8 figure

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

Numerical prediction of ship resistance and squat in confined waters

Accurate prediction of hydrodynamic forces opposing a ship displacement in restricted waterways is necessary in order to improve energy efficiency of inland transport. When a ship moves in restricted waterways, a significant increase in ship squat (combination of sinkage and trim) and resistance occurs compared to a movement in open waters. In this paper, a 3D numerical model based on fluid-structure coupling is presented and used to investigate the effect of limited water depth and channel width on ship resistance and squat

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

A new spatially and temporally variable sigma parameter in degree-day melt modelling of the Greenland Ice Sheet 1870–2013

The degree-day based method of calculating ice-/snow-melt across the Greenland Ice Sheet (GrIS) commonly includes the temperature parameter sigma (σ) accounting for temperature variability on short (sub-monthly down to hourly) timescales, in order to capture melt in months where the mean temperature is below 0 °C. Sigma is typically assumed to be constant in space and time, with values ranging from ~ 2.5 to 5.5 °C. It is unclear in many cases how these values were derived and little sensitivity analysis or validation has been conducted. Here we determine spatially and temporally varying monthly values of σ for the unique, extended 1870–2013 timescale based on downscaled, corrected European Centre for Medium-Range Weather Forecasts (ECMWF) Interim (ERA-I) and Twentieth Century Reanalysis (20CR) meteorological reanalysis 2 m air temperatures on a 5 km × 5 km polar stereographic grid for the GrIS. The resulting monthly σ values reveal a distinct seasonal cycle. The mean summer σ value for the study period is ~ 3.2 °C, around 1 °C lower than the value of 4.2 °C commonly used in the literature. Sigma values for individual summers range from 1.7 to 5.9 °C. Since the summer months dominate the melt calculation, use of the new variable σ parameter would lead to a smaller melt area and a more positive surface mass balance for the GrIS. Validation of our new variable σ dataset shows good agreement with standard deviations calculated from automatic weather station observations across the ice sheet. Trend analysis shows large areas of the ice sheet exhibit statistically significant increasing temperature variability from 1870–2013 in all seasons, with notable exceptions around Summit in spring, and Summit and South Dome in winter. More recently, since 1990, σ has been decreasing, significantly so in the north-west during July. These interannual σ trends reflect climate change and variability processes operating across the ice sheet, several mechanisms of which are briefly discussed