Derived categories of cubic fourfolds

We discuss the structure of the derived category of coherent sheaves on cubic fourfolds of three types: Pfaffian cubics, cubics containing a plane and singular cubics, and discuss its relation to the rationality of these cubics.Comment: 18 page

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

Validity of Accelerometers for the Evaluation of Energy Expenditure in Obese and Overweight Individuals: A Systematic Review

Objective. Even though the validity of accelerometers for the measurement of energy expenditure (EE) has been demonstrated for normal-weight individuals, the applicability of this instrument in obese individuals remains controversial. This review aims to summarize the level of agreement between accelerometers and the gold standards (indirect calorimetry and doubly labelled water) for the measurement of energy expenditure (EE) in obese or overweight individuals. Methods. The literature search was limited to comparison studies assessing agreement in EE determination between accelerometers and indirect calorimetry (IC) or doubly labelled water (DLW). We searched in PubMed and in Scopus until March 1, 2019. The analysis was restricted to obese or overweight adult individuals. The following descriptive information was extracted for each study: sample size, characteristics of participants (sex, age, BMI, fat mass percentage, any pathological conditions, modality of recruitment in the study, and exclusion criteria), accelerometer description (model, type and body position), and type of gold standard and validity protocol (duration, conditions, and requirements during and before the experiment). Three review authors independently screened the obtained results, and the quality of the selected articles was assessed by the QUADAS-2 tool. Results. We obtained seventeen eligible articles, thirteen of which showed concerns for the applicability section, due to the patient selection. Regarding the accelerometers, nine devices were validated in the included studies with the BodyMedia SenseWear® (SWA) being the most frequently validated. Although correlations between accelerometers and the gold standard were high in some studies, agreement between the two methods was low, as shown by the Bland-Altman plots. Conclusions. Most accelerometer estimations of EE were inaccurate for obese/overweight subjects, and authors advise to improve the accuracy of algorithms for SWA software, or the predicted equations for estimating EE from other accelerometers

Holomorphic symplectic geometry: a problem list

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

Abel-Jacobi maps for hypersurfaces and non commutative Calabi-Yau's

It is well known that the Fano scheme of lines on a cubic 4-fold is a symplectic variety. We generalize this fact by constructing a closed p-form with p=2n-4 on the Fano scheme of lines on a (2n-2)-dimensional hypersurface Y of degree n. We provide several definitions of this form - via the Abel-Jacobi map, via Hochschild homology, and via the linkage class, and compute it explicitly for n = 4. In the special case of a Pfaffian hypersurface Y we show that the Fano scheme is birational to a certain moduli space of sheaves on a p-dimensional Calabi--Yau variety X arising naturally in the context of homological projective duality, and that the constructed form is induced by the holomorphic volume form on X. This remains true for a general non Pfaffian hypersurface but the dual Calabi-Yau becomes non commutative.Comment: 34 pages; exposition of Hochschild homology expanded; references added; introduction re-written; some imrecisions, typos and the orbit diagram in the last section correcte

Simply connected projective manifolds in characteristic p>0p>0 have no nontrivial stratified bundles

We show that simply connected projective manifolds in characteristic $p>0$ have no nontrivial stratified bundles. This gives a positive answer to a conjecture by D. Gieseker. The proof uses Hrushovski's theorem on periodic points.Comment: 16 pages. Revised version contains a more general theorem on torsion points on moduli, together with an illustration in rank 2 due to M. Raynaud. Reference added. Last version has some typos corrected. Appears in Invent.math

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

Usual energy and macronutrient intakes in 2-9-year-old European children

OBJECTIVE: Valid estimates of population intakes are essential for monitoring trends as well as for nutritional interventions, but such data are rare in young children. In particular, the problem of misreporting in dietary data is usually not accounted for. Therefore, this study aims to provide accurate estimates of intake distributions in European children. DESIGN: Cross-sectional setting-based multi-centre study. SUBJECTS: A total of 9560 children aged 2-9 years from eight European countries with at least one 24-h dietary recall (24-HDR). METHODS: The 24-HDRs were classified in three reporting groups based on age- and sex-specific Goldberg cutoffs (underreports, plausible reports, overreports). Only plausible reports were considered in the final analysis (N=8611 children). The National Cancer Institute (NCI)-Method was applied to estimate population distributions of usual intakes correcting for the variance inflation in short-term dietary data. RESULTS: The prevalence of underreporting (9.5%) was higher compared with overreporting (3.4%). Exclusion of misreports resulted in a shift of the energy and absolute macronutrient intake distributions to the right, and further led to the exclusion of extreme values, that is, mean values and lower percentiles increased, whereas upper percentiles decreased. The distributions of relative macronutrient intakes (% energy intake from fat/carbohydrates/proteins) remained almost unchanged when excluding misreports. Application of the NCI-Method resulted in markedly narrower intake distributions compared with estimates based on single 24-HDRs. Mean percentages of usual energy intake from fat, carbohydrates and proteins were 32.2, 52.1 and 15.7%, respectively, suggesting the majority of European children are complying with common macronutrient intake recommendations. In contrast, total water intake (mean: 1216.7 ml per day) lay below the recommended value for >90% of the children. CONCLUSION: This study provides recent estimates of intake distributions of European children correcting for misreporting as well as for the daily variation in dietary data. These data may help to assess the adequacy of young children's diets in Europe

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