On type II degenerations of hyperk\"ahler manifolds

We give a simple argument to prove Nagai's conjecture for type II degenerations of compact hyperk\"ahler manifolds and cohomology classes of middle degree. Under an additional assumption, the techniques yield the conjecture in arbitrary degree. This would complete the proof of Nagai's conjecture in general, as it was proved already for type I degenerations by Koll\'ar, Laza, Sacc\`a, and Voisin and independently by Soldatenkov, while it is immediate for type III degenerations. Our arguments are close in spirit to a recent paper by Harder proving similar results for the restrictive class of good degenerations

Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces

We construct a compactification $M^{\mu ss}$ of the Uhlenbeck-Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\gamma \colon M^{ss} \to M^{\mu ss}$, where $M^{ss}$ is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space $M^{\mu ss}$ has a natural set-theoretic stratification which allows one, via a Hitchin-Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.Comment: 18 pages. v2: a few very minor changes. v3: 27 pages. Several proofs have been considerably expanded, and more explanations have been added. v4: 28 pages. A few minor changes. Final version accepted for publication in Math.

Lagrangian fibrations

We review the theory of Lagrangian fibrations of hyperk ̈ahler manifoldsas initiated by Matsushita. We also discuss more recent work of Shen–Yin andHarder–Li–Shen–Yin. Occasionally, we give alternative arguments and comple-ment the discussion by additional observations

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

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

Factors controlling the last interglacial climate as simulated by LOVECLIM1.3

The last interglacial (LIG), also identified to the Eemian in Europe, began at approximately 130 kyr BP and ended at about 115 kyr BP (before present). More and more proxy-based reconstructions of the LIG climate are becoming more available even though they remain sparse. The major climate forcings during the LIG are rather well known and therefore models can be tested against paleoclimatic data sets and then used to better understand the climate of the LIG. However, models are displaying a large range of responses, being sometimes contradictory between them or with the reconstructed data. Here we would like to investigate causes of these differences. We focus on a single climate model, LOVECLIM, and we perform transient simulations over the LIG, starting at 135 kyr BP and run until 115 kyr BP. With these simulations, we test the role of the surface boundary conditions (the time-evolution of the Northern Hemisphere (NH) ice sheets) on the simulated LIG climate and the importance of the parameter sets (internal to the model, such as the albedos of the ocean and sea ice), which affect the sensitivity of the model. The magnitude of the simulated climate variations through the LIG remains too low compared to reconstructions for climate variables such as surface air temperature. Moreover, in the North Atlantic, the large increase in summer sea surface temperature towards the peak of the interglacial occurs too early (at ∼128 kyr BP) compared to the reconstructions. This feature as well as the climate simulated during the optimum of the LIG, between 131 and 121 kyr BP, does not depend on changes in surface boundary conditions and parameter sets. The additional freshwater flux (FWF) from the melting NH ice sheets is responsible for a temporary abrupt weakening of the North Atlantic meridional overturning circulation, which causes a strong global cooling in annual mean. However, the changes in the configuration (extent and albedo) of the NH ice sheets during the LIG only slightly impact the simulated climate. Together, configuration of and FWF from the NH ice sheets greatly increase the magnitude of the temperature variations over continents as well as over the ocean at the beginning of the simulation and reduce the difference between the simulated climate and the reconstructions. Lastly, we show that the contribution from the parameter sets to the climate response is actually very modest