A GIT interpretration of the Harder-Narasimhan filtration

An unstable torsion free sheaf on a smooth projective variety gives a GIT unstable point in certain Quot scheme. To a GIT unstable point, Kempf associates a "maximally destabilizing" 1-parameter subgroup, and this induces a filtration of the torsion free sheaf. We show that this filtration coincides with the Harder-Narasimhan filtration.Comment: 19 pages; Comments of the referees and references added. The construction for holomorphic pairs (Sections 6 and 7 from previous version) will appear in a further publication. To appear in Rev. Mat Complutens

Turbulent marine bottom boundary layer by V t2-F turbulence model

In this work, we propose to implement the V2- f turbulence model rarely used in the marine environment to study the marine bottom boundary layer (MBBL). This model will complete the series of the turbulence models already implemented in the operational model 1DV-MoSeTT (1D Vertical Model of Sediment Transport and Turbu- lence) developed for the MBBL dynamics analysis . To show the performance of v/2 - f turbulence model first, we give a comparison between this model and q2 - q2σ model. This comparison is based in various laboratory data proposed in the literature and widely used by the scientific community. Second, and in comparison with in-situ suspended sediment transport measurements, we examine the impact of the v/2 - f and the q2 - q2σ turbulence models on the quantification of flux sediment at the bottom and on the estimation of the vertical profile of the suspended particle matter (SPM)

On the 0-dimensional cusps of the Kahler moduli of a K3 surface

Let S be a projective K3 surface. It is proved that the 0-dimensional cusps of the Kahler moduli of S are in one-to-one correspondence with the twisted Fourier-Mukai partners of S. This leads to a counting formula for the 0-dimensional cusps of the Kahler moduli. Applications to rational maps between K3 surfaces with large Picard numbers are given. When the Picard number of S is 1, the bijective correspondence is calculated explicitly.Comment: 24page

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

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

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

Reproducibility and validity of a diet quality index for children assessed using a FFQ

The diet quality index (DQI) for preschool children is a new index developed to reflect compliance with four main food-based dietary guidelines for preschool children in Flanders. The present study investigates: (1) the validity of this index by comparing DQI scores for preschool children with nutrient intakes, both of which were derived from 3d estimated diet records; (2) the reproducibility of the DQI for preschoolers based on a parentally reported forty-seven-item FFQ DQI, which was repeated after 5 weeks; (3) the relative validity of the FFQ DQI with 3d record DQI scores as reference. The study sample included 510 and 58 preschoolers (2-5-6.5 years) for validity and reproducibility analyses, respectively. Increasing 3d record DQI scores were associated with decreasing consumption of added sugars, and increasing intakes of fibre, water, Ca and many micronutrients. Mean FFQ DQI test-retest scores were not significantly different: 72 (so 11) v. 71 (Si) 10) (P-=0-218) out of a maximum of 100. Mean 3d record DQI score (66 (so 10)) was significantly lower than mean FFQ DQI (71 (so 10);

Holomorphic symplectic geometry: a problem list

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

Introduction to derived categories of coherent sheaves

In these notes, an introduction to derived categories and derived functors is given. The main focus is the bounded derived category of coherent sheaves on a smooth projective variety.Comment: 24 pages, minor changes, same content as published versio

Symplectic structures on moduli spaces of framed sheaves on surfaces

We provide generalizations of the notions of Atiyah class and Kodaira-Spencer map to the case of framed sheaves. Moreover, we construct closed two-forms on the moduli spaces of framed sheaves on surfaces. As an application, we define a symplectic structure on the moduli spaces of framed sheaves on some birationally ruled surfaces.Comment: v2: final version to appear in Centr. Eur. J. Math, section "Examples" improved: we obtain new examples of non-compact holomorphic symplectic varietie