Quantization of energy and writhe in self-repelling knots

Probably the most natural energy functional to be considered for knotted strings is that given by electrostatic repulsion. In the absence of counter-charges, a charged, knotted string evolving along the energy gradient of electrostatic repulsion would progressively tighten its knotted domain into a point on a perfectly circular string. However, in the presence of charge screening self-repelling knotted strings can be stabilized. It is known that energy functionals in which repulsive forces between repelling charges grow inversely proportionally to the third or higher power of their relative distance stabilize self-repelling knots. Especially interesting is the case of the third power since the repulsive energy becomes scale invariant and does not change upon Mobius transformations (reflections in spheres) of knotted trajectories. We observe here that knots minimizing their repulsive Mobius energy show quantization of the energy and writhe (measure of chirality) within several tested families of knots.

Impact of physical activity on energy balance, food intake and choice in normal weight and obese children in the setting of acute social stress: a randomized controlled trial.

BACKGROUND: Psychological stress negatively influences food intake and food choices, thereby contributing to the development of childhood obesity. Physical activity can also moderate eating behavior and influence calorie intake. However, it is unknown if acute physical activity influences food intake and overall energy balance after acute stress exposure in children. We therefore investigated the impact of acute physical activity on overall energy balance (food intake minus energy expenditure), food intake, and choice in the setting of acute social stress in normal weight (NW) and overweight/obese (OW/OB) children as well as the impact of psychological risk factors. METHOD: After receiving written consent from their parents, 26 NW (BMI < 90(th) percentile) and 24 7-to 11-year-old OW (n = 5)/OB (n = 19, BMI ≥ 90(th) percentile) children were randomly allocated using computer-generated numbers (1:1, after stratification for weight status) to acute moderate physical or to sedentary activity for 30 min. Afterwards, all children were exposed to an acute social stressor. Children and their parents completed self-report questionnaires. At the end of the stressor, children were allowed to eat freely from a range of 12 different foods (6 sweet/6 salty; each of low/high caloric density). Energy balance, food intake/choice and obesity-related psychological risk factors were assessed. RESULTS: Lower overall energy balance (p = 0.019) and a decreased choice of low density salty foods (p < 0.001) in NW children compared with OW/OB children was found after acute moderate physical activity but not sedentary activity. Independent of their allocation, OW/OB children ate more high density salty foods (104 kcal (34 to 173), p = 0.004) following stress. They scored higher on impulsive behavior (p = 0.005), restrained eating (p < 0.001) and parental corporal punishment (p = 0.03), but these psychological factors were not related to stress-induced food intake/choice. Positive parenting tended to be related to lower intake of sweet high density food (-132 kcal, -277 to 2, p = 0.054). CONCLUSIONS: In the setting of stress, acute moderate physical activity can address energy balance in children, a benefit which is especially pronounced in the OW/OB. Positive parenting may act as a protective factor preventing stress-induced eating of comfort food. TRIAL REGISTRATION: clinicaltrials.gov NCT01693926 The study was a pilot study of a project funded by the Swiss National Science Foundation (CRSII3_147673).

Association between smoking and total energy expenditure in a multi-country study.

BACKGROUND: The association between smoking and total energy expenditure (TEE) is still controversial. We examined this association in a multi-country study where TEE was measured in a subset of participants by the doubly labeled water (DLW) method, the gold standard for this measurement. METHODS: This study includes 236 participants from five different African origin populations who underwent DLW measurements and had complete data on the main covariates of interest. Self-reported smoking status was categorized as either light (<7 cig/day) or high (≥7 cig/day). Lean body mass was assessed by deuterium dilution and physical activity (PA) by accelerometry. RESULTS: The prevalence of smoking was 55% in men and 16% in women with a median of 6.5 cigarettes/day. There was a trend toward lower BMI in smokers than non-smokers (not statistically significant). TEE was strongly correlated with fat-free mass (men: 0.70; women: 0.79) and with body weight (0.59 in both sexes). Using linear regression and adjusting for body weight, study site, age, PA, alcohol intake and occupation, TEE was larger in high smokers than in never smokers among men (difference of 298 kcal/day, p = 0.045) but not among women (162 kcal/day, p = 0.170). The association became slightly weaker in men (254 kcal/day, p = 0.058) and disappeared in women (-76 kcal/day, p = 0.380) when adjusting for fat-free mass instead of body weight. CONCLUSION: There was an association between smoking and TEE among men. However, the lack of an association among women, which may be partly related to the small number of smoking women, also suggests a role of unaccounted confounding factors.

Metabolic predictors of obesity. Contribution of resting energy expenditure, thermic effect of food, and fuel utilization to four-year weight gain of post-obese and never-obese women.

This prospective study was designed to identify abnormalities of energy expenditure and fuel utilization which distinguish post-obese women from never-obese controls. 24 moderately obese, postmenopausal, nondiabetic women with a familial predisposition to obesity underwent assessments of body composition, fasting and postprandial energy expenditure, and fuel utilization in the obese state and after weight loss (mean 12.9 kg) to a post-obese, normal-weight state. The post-obese women were compared with 24 never-obese women of comparable age and body composition. Four years later, without intervention, body weight was reassessed in both groups. Results indicated that all parameters measured in the post-obese women were similar to the never-obese controls: mean resting energy expenditure, thermic effect of food, and fasting and postprandial substrate oxidation and insulin-glucose patterns. Four years later, post-obese women regained a mean of 10.9 kg while control subjects remained lean (mean gain 1.7 kg) (P < 0.001 between groups). Neither energy expenditure nor fuel oxidation correlated with 4-yr weight changes, whereas self-reported physical inactivity was associated with greater weight regain. The data suggest that weight gain in obesity-prone women may be due to maladaptive responses to the environment, such as physical inactivity or excess energy intake, rather than to reduced energy requirements.

Under-reporting of dietary energy intake in five populations of the African diaspora.

Studies on the role of diet in the development of chronic diseases often rely on self-report surveys of dietary intake. Unfortunately, many validity studies have demonstrated that self-reported dietary intake is subject to systematic under-reporting, although the vast majority of such studies have been conducted in industrialised countries. The aim of the present study was to investigate whether or not systematic reporting error exists among the individuals of African ancestry (n 324) in five countries distributed across the Human Development Index (HDI) scale, a UN statistic devised to rank countries on non-income factors plus economic indicators. Using two 24 h dietary recalls to assess energy intake and the doubly labelled water method to assess total energy expenditure, we calculated the difference between these two values ((self-report - expenditure/expenditure) × 100) to identify under-reporting of habitual energy intake in selected communities in Ghana, South Africa, Seychelles, Jamaica and the USA. Under-reporting of habitual energy intake was observed in all the five countries. The South African cohort exhibited the highest mean under-reporting ( - 52·1% of energy) compared with the cohorts of Ghana ( - 22·5%), Jamaica ( - 17·9%), Seychelles ( - 25·0%) and the USA ( - 18·5%). BMI was the most consistent predictor of under-reporting compared with other predictors. In conclusion, there is substantial under-reporting of dietary energy intake in populations across the whole range of the HDI, and this systematic reporting error increases according to the BMI of an individual.