Non-minimality of corners in subriemannian geometry

We give a short solution to one of the main open problems in subriemannian geometry. Namely, we prove that length minimizers do not have corner-type singularities. With this result we solve Problem II of Agrachev's list, and provide the first general result toward the 30-year-old open problem of regularity of subriemannian geodesics.Comment: 11 pages, final versio

Sets with constant normal in Carnot groups: properties and examples

We analyze subsets of Carnot groups that have intrinsic constant normal, as they appear in the blowup study of sets that have finite subRiemannian perimeter. The purpose of this paper is threefold. First, we prove some mild regularity and structural results in arbitrary Carnot groups. Namely, we show that for every constant-normal set in a Carnot group its subRiemannian-Lebesgue representative is regularly open, contractible, and its topological boundary coincides with the reduced boundary and with the measure-theoretic boundary. We infer these properties from a metric cone property. Such a cone will be a semisubgroup with nonempty interior that is canonically associated with the normal direction. We characterize the constant-normal sets exactly as those that are arbitrary unions of translations of such semisubgroups. Second, making use of such a characterization, we provide some pathological examples in the specific case of the free-Carnot group of step 3 and rank 2. Namely, we construct a constant normal set that, with respect to any Riemannian metric, is not of locally finite perimeter; we also construct an example with non-unique intrinsic blowup at some point, showing that it has different upper and lower subRiemannian density at the origin. Third, we show that in Carnot groups of step 4 or less, every constant-normal set is intrinsically rectifiable, in the sense of Franchi, Serapioni, and Serra Cassano

Could Dietary Goals and Climate Change Mitigation Be Achieved Through Optimized Diet? The Experience of Modeling the National Food Consumption Data in Italy

Objective: The aim of this study is to define a healthy and sustainable diet model with low GHGE, fulfilling dietary requirements, and considering current Italian food consumption patterns. Design: A duly designed database was developed, linking food nutritional composition and GHGE based on 921 food items consumed in Italy according to the last national food consumption survey (INRAN-SCAI 2005–2006). Linear programming was used to develop new diet plans separately for males and females, aged 18–60 years (n = 2,098 subjects), in order to minimize GHGE. The program is based on dietary goals and acceptability constraints as well as on 13 nutrient requirement constraints aiming to reach a healthy and acceptable diet for the Italian population. Results: Diet optimization resulted in a nutritionally adequate pattern minimizing GHGE values (4.0 vs. 1.9 kg CO2e/day for males and 3.2 vs. 1.6 kg CO2e/day for females). In both sexes, the nutrient intake of the optimized diet was at the established lower bound for cholesterol and calcium and at the established upper bound for free sugar and fiber. In males, intake of zinc was at the established lower bound whereas iron was at the established upper bound. Consumption of red meat and fruit and vegetables was at the established lower and upper bound, respectively, in both males and females. Despite the decrease in meat consumption, especially red meat, in the optimized diet with respect to the observed diet, levels of iron intake in females increased by 10% (10.3 vs. 11.3 mg/day) but remained below the adequate intake established in Italian national DRIs. Conclusions: An attainable healthy dietary pattern was developed that would lead to the reduction of GHGE by 48% for males and by 50% for females with respect to current food consumption in the Italian adult population. Health-promoting dietary patterns can substantially contribute to achieve related Sustainable Development Goals

Intrusion and extrusion of liquids in highly confining media: bridging fundamental research to applications

Wetting and drying of pores or cavities, made by walls that attract or repel the liquid, is a ubiquitous process in nature and has many technological applications including, for example, liquid separation, chromatography, energy damping, conversion, and storage. Understanding under which conditions intrusion/extrusion takes place and how to control/tune them by chemical or physical means are currently among the main questions in the field. Historically, the theory to model intrusion/extrusion was based on the mechanics of fluids. However, the discovery of the existence of metastable states, where systems are kinetically trapped in the intruded or extruded configuration, fostered the research based on modern statistical mechanics concepts and more accurate models of the liquid, vapor, and gas phases beyond the simplest sharp interface representation. In parallel, inspired by the growing number of technological applications of intrusion/extrusion, experimental research blossomed considering systems with complex chemistry and pore topology, possessing flexible frameworks, and presenting unusual properties, such as negative volumetric compressibility. In this article, we review recent theoretical and experimental progresses, presenting it in the context of unifying framework. We illustrate also emerging technological applications of intrusion/extrusion and discuss challenges ahead

Eating behavior associated with food intake in European adolescents participating in the HELENA study

Adolescence is recognized as a time of rapid physiological and behavioral change. In this transition, eating behavior is still being formed and remains an integral part of a person’s lifestyle throughout his or her life. This study aims to assess eating behavior and associations with food intake in European adolescents. We included 2194 adolescents (45.9% boys), aged 12.5 to 17.5 years, from the cross-sectional HELENA study, with two completed 24 h recalls and complete questionnaire data on their eating behavior (Eating Behavior and Weight Problems Inventory for Children- EWI-C). Three subscales of the EWI were evaluated; they measured Strength and motivation to eat (EWI 1), Importance and impact of eating (EWI 2), and Eating as a means of coping with emotional stress (EWI 3). Since these subscales were specially focused on eating behavior, participants were classified as either Low (=P75) or High (>P75) on each of the subscales. Our results showed a higher consumption of different types of food, in the EWI 1 scales, linked to the hunger and interest in eating, and we observed a relationship with the consumption of energy-dense products. This result was repeated in EWI 3, the subscale linked to emotional eating, where we also found higher consumption of energy-dense products. This study suggests that special features of eating behavior are associated with food intake in adolescents

Solution Structure and Dynamics of the I214V Mutant of the Rabbit Prion Protein

Background: The conformational conversion of the host-derived cellular prion protein (PrP C) into the disease-associated scrapie isoform (PrP Sc) is responsible for the pathogenesis of transmissible spongiform encephalopathies (TSEs). Various single-point mutations in PrP C s could cause structural changes and thereby distinctly influence the conformational conversion. Elucidation of the differences between the wild-type rabbit PrP C (RaPrP C) and various mutants would be of great help to understand the ability of RaPrP C to be resistant to TSE agents. Methodology/Principal Findings: We determined the solution structure of the I214V mutant of RaPrP C (91–228) and detected the backbone dynamics of its structured C-terminal domain (121–228). The I214V mutant displays a visible shift of surface charge distribution that may have a potential effect on the binding specificity and affinity with other chaperones. The number of hydrogen bonds declines dramatically. Urea-induced transition experiments reveal an obvious decrease in the conformational stability. Furthermore, the NMR dynamics analysis discloses a significant increase in the backbone flexibility on the pico- to nanosecond time scale, indicative of lower energy barrier for structural rearrangement. Conclusions/Significance: Our results suggest that both the surface charge distribution and the intrinsic backbone flexibility greatly contribute to species barriers for the transmission of TSEs, and thereby provide valuable hints fo

Relationship between self-reported dietary intake and physical activity levels among adolescents: The HELENA study

Background Evidence suggests possible synergetic effects of multiple lifestyle behaviors on health risks like obesity and other health outcomes. Therefore it is important to investigate associations between dietary and physical activity behavior, the two most important lifestyle behaviors influencing our energy balance and body composition. The objective of the present study is to describe the relationship between energy, nutrient and food intake and the physical activity level among a large group of European adolescents. Methods The study comprised a total of 2176 adolescents (46.2% male) from ten European cities participating in the HELENA (Healthy Lifestyle in Europe by Nutrition in Adolescence) study. Dietary intake and physical activity were assessed using validated 24-h dietary recalls and self-reported questionnaires respectively. Analyses of covariance (ANCOVA) were used to compare the energy and nutrient intake and the food consumption between groups of adolescents with different physical activity levels (1st to 3rd tertile). Results In both sexes no differences were found in energy intake between the levels of physical activity. The most active males showed a higher intake of polysaccharides, protein, water and vitamin C and a lower intake of saccharides compared to less active males. Females with the highest physical activity level consumed more polysaccharides compared to their least active peers. Male and female adolescents with the highest physical activity levels, consumed more fruit and milk products and less cheese compared to the least active adolescents. The most active males showed higher intakes of vegetables and meat, fish, eggs, meat substitutes and vegetarian products compared to the least active ones. The least active males reported the highest consumption of grain products and potatoes. Within the female group, significantly lower intakes of bread and cereal products and spreads were found for those reporting to spend most time in moderate to vigorous physical activity. The consumption of foods from the remaining food groups, did not differ between the physical activity levels in both sexes. Conclusion It can be concluded that dietary habits diverge between adolescents with different self-reported physical activity levels. For some food groups a difference in intake could be found, which were reflected in differences in some nutrient intakes. It can also be concluded that physically active adolescents are not always inclined to eat healthier diets than their less active peers.The HELENA study took place with the financial support of the European Community Sixth RTD Framework Programme (Contract FOOD-CT: 2005-007034). This work was also partially supported by the European Union, in the framework of the Public Health Programme (ALPHA project, Ref: 2006120), the Swedish Council for Working Life and Social Research (FAS), the Spanish Ministry of Education (EX-2007-1124, and EX-2008-0641), and the Spanish Ministry of Health, Maternal, Child Health and Development Network (number RD08/0072) (JPRL, LAM)

Ideal cardiovascular health and inflammation in European adolescents: The HELENA study

Background and aims Inflammation plays a key role in atherosclerosis and this process seems to appear in childhood. The ideal cardiovascular health index (ICHI) has been inversely related to atherosclerotic plaque in adults. However, evidence regarding inflammation and ICHI in adolescents is scarce. The aim is to assess the association between ICHI and inflammation in European adolescents. Methods and results As many as 543 adolescents (251 boys and 292 girls) from the Healthy Lifestyle in Europe by Nutrition in Adolescence (HELENA) study, a cross-sectional multi-center study including 9 European countries, were measured. C-reactive protein (CRP), complement factors C3 and C4, leptin and white blood cell counts were used to compute an inflammatory score. Multilevel linear models and multilevel logistic regression were used to assess the association between ICHI and inflammation controlling by covariates. Higher ICHI was associated with a lower inflammatory score, as well as with several individual components, both in boys and girls (p < 0.01). In addition, adolescents with at least 4 ideal components of the ICHI had significantly lower inflammatory score and lower levels of the study biomarkers, except CRP. Finally, the multilevel logistic regression showed that for every unit increase in the ICHI, the probability of having an inflammatory profile decreased by 28.1% in girls. Conclusion Results from this study suggest that a better ICHI is associated with a lower inflammatory profile already in adolescence. Improving these health behaviors, and health factors included in the ICHI, could play an important role in CVD prevention

Dietary animal and plant protein intakes and their associations with obesity and cardio-metabolic indicators in European adolescents: The HELENA cross-sectional study

Background: Previous studies suggest that dietary protein might play a beneficial role in combating obesity and its related chronic diseases. Total, animal and plant protein intakes and their associations with anthropometry and serum biomarkers in European adolescents using one standardised methodology across European countries are not well documented. Objectives: To evaluate total, animal and plant protein intakes in European adolescents stratified by gender and age, and to investigate their associations with cardio-metabolic indicators (anthropometry and biomarkers). Methods: The current analysis included 1804 randomly selected adolescents participating in the HELENA study (conducted in 2006-2007) aged 12.5-17.5 y (47% males) who completed two non-consecutive computerised 24-h dietary recalls. Associations between animal and plant protein intakes, and anthropometry and serum biomarkers were examined with General linear Model multivariate analysis. Results: Average total protein intake exceeded the recommendations of World Health Organization and European Food Safety Authority. Mean total protein intake was 96 g/d (59% derived from animal protein). Total, animal and plant protein intakes (g/d) were significantly lower in females than in males and total and plant protein intakes were lower in younger participants (12.5-14.9 y). Protein intake was significantly lower in underweight subjects and higher in obese ones; the direction of the relationship was reversed after adjustments for body weight (g/(kg.d)). The inverse association of plant protein intakes was stronger with BMI z-score and body fat percentage (BF%) compared to animal protein intakes. Additionally, BMI and BF% were positively associated with energy percentage of animal protein. Conclusions: This sample of European adolescents appeared to have adequate total protein intake. Our findings suggest that plant protein intakes may play a role in preventing obesity among European adolescents. Further longitudinal studies are needed to investigate the potential beneficial effects observed in this study in the prevention of obesity and related chronic diseases