Recursion Operators for CBC system with reductions. Geometric theory

We discuss some recent developments of the geometric theory of the Recursion Operators (Generating Operators) for Caudrey-Beals-Coifman systems(CBC systems) on semisimple Lie algebras. As is well known the essence of this interpretation is that the Recursion Operators could be considered as adjoint to Nijenhuis tensors on certain infinite-dimensional manifolds. In particular, we discuss the case when there are Zp reductions of Mikhailov type

Assessing the Body Composition of 6-17 Year-old Black and White Girls in Field Studies

The purpose of the study was to develop ethnic-specific equations for fat-free mass (FFM) from selected anthropometric dimensions and bioelectrical impedance measures of resistance (R) and reactance (Xc) for use in the NHLBI Growth and Heath Study. Using dual-energy X-ray absorptiometry measures of body composition as the dependent variable and field measures of body composition by anthropometry and bioelectrical impedance as the explanatory variables, ethnic-specific prediction equations were developed on a sample of girls representing a wide range of ages and BMI. The equations were cross-validated using (1) the Prediction of Sum of Squares (PRESS) statistic and (2) an independent sample of 20 girls of each race from a study conducted at the National Institute of Child Health and Human Development (NICHD). Subjects were 65 White and 61 Black girls 6-17 years of age. The best race-specific equations for FFM each explained 99% and 97% of the variance in the White and Black girls, respectively. Root mean square errors (RMSE) ranged from 1.14 to 1.95 kg. The equation for Black girls used Stature2/Resistance (R), weight, and reactance (Xc) as predictor variables; the equation for White girls used Stature2/R, weight, and triceps skinfold thickness. The results indicate that (1) equations to predict FFM in girls should be ethnic-specific and that (2) accurate values for TBF and %BF can be calculated from the predicted FFM

Psychometric properties of a new questionnaire to assess eating in the absence of hunger in children and adolescents

Background: Eating in the absence of hunger (EAH), studied in the context of laboratory paradigms, has been associated with obesity and is predictive of excess weight gain in children. However, no easily administered questionnaire exists to assess for EAH in children. Objective: We developed an Eating in the Absence of Hunger Questionnaire to be administered to children and adolescents (EAH-C) and examined psychometric properties of the measure. Design: Two-hundred and twenty-six obese (BMI ≥ 95th percentile for age and sex, n = 73) and non-obese (BMI \u3c 95th percentile, n = 153) youth (mean age ± S.D., 14.4 ± 2.5 y) completed the EAH-C and measures of loss of control and emotional eating, and general psychopathology. Temporal stability was assessed in a subset of participants. Results: Factor analysis generated three subscales for the EAH-C: Negative Affect, External Eating, and Fatigue/Boredom. Internal consistency for all subscales was established (Cronbach’s alphas: 0.80–0.88). The EAH-C subscales had good convergent validity with emotional eating and loss of control episodes ( p’s \u3c 0.01). Obese children reported higher Negative Affect subscale scores than non-obese children ( p ≤ 0.05). All three subscales were positively correlated with measures of general psychopathology. Intra-class correlation coefficients revealed temporal stability for all subscales (ranging from 0.65 to 0.70, p’s \u3c 0.01). We conclude that the EAH-C had internally consistent subscales with good convergent validity and temporal stability, but may have limited discriminant validity. Further investigations examining the EAH-C in relation to laboratory feeding studies are required to determine whether reported EAH is related to actual energy intake or to the development of excess weight gain

Fast Two-Robot Disk Evacuation with Wireless Communication

In the fast evacuation problem, we study the path planning problem for two robots who want to minimize the worst-case evacuation time on the unit disk. The robots are initially placed at the center of the disk. In order to evacuate, they need to reach an unknown point, the exit, on the boundary of the disk. Once one of the robots finds the exit, it will instantaneously notify the other agent, who will make a beeline to it. The problem has been studied for robots with the same speed~\cite{s1}. We study a more general case where one robot has speed $1$ and the other has speed $s \geq 1$. We provide optimal evacuation strategies in the case that $s \geq c_{2.75} \approx 2.75$ by showing matching upper and lower bounds on the worst-case evacuation time. For $1\leq s < c_{2.75}$, we show (non-matching) upper and lower bounds on the evacuation time with a ratio less than $1.22$. Moreover, we demonstrate that a generalization of the two-robot search strategy from~\cite{s1} is outperformed by our proposed strategies for any $s \geq c_{1.71} \approx 1.71$.Comment: 18 pages, 10 figure

Impact of age and race on outcomes of a program to prevent excess weight gain and disordered eating in adolescent girls

Interpersonal psychotherapy (IPT) prevents weight gain and reduces loss-of-control (LOC)-eating in adults. However, IPT was not superior to health-education (HE) for preventing excess weight gain and reducing LOC-eating over 1-year in adolescent girls at risk for excess weight gain and eating disorders. Limited data suggest that older and non-White youth may be especially responsive to IPT. In secondary analyses, we examined if age or race moderated weight and LOC-eating outcomes. The 113 participants (12–17 years; 56.6% White) from the original trial were re-contacted 3 years later for assessment. At baseline and follow-up visits through 3 years, we assessed BMI, adiposity by dual energy X-ray absorptiometry, and LOC-eating presence. In linear mixed models, baseline age moderated 3-year BMI outcome; older girls in IPT had the lowest 3-year BMI gain compared to younger girls in IPT and all girls in HE, p = 0.04. A similar pattern was observed for adiposity. Race moderated 3-year LOC-eating; non-White girls in IPT were most likely to abstain from LOC-eating at 3 years compared to all other girls, p = 0.04. This hypothesis-generating analysis suggests future studies should determine if IPT is especially efficacious at reducing LOC-eating in older, non-White adolescents