Geometric Theory of the Recursion Operators for the Generalized Zakharov-Shabat System in Pole Gauge on the Algebra sl(n,C)

We consider the recursion operator approach to the soliton equations related to the generalized Zakharov-Shabat system on the algebra sl(n,C) in pole gauge both in the general position and in the presence of reductions. We present the recursion operators and discuss their geometric meaning as conjugate to Nijenhuis tensors for a Poisson-Nijenhuis structure defined on the manifold of potentials

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

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

The Generalised Zakharov-Shabat System and the Gauge Group Action

The generalized Zakharov-Shabat systems with complex-valued non-regular Cartan elements and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their gauge equivalent are studied. This study includes: the properties of fundamental analytical solutions (FAS) for the gauge-equivalent to CBC systems and the minimal set of scattering data; the description of the class of nonlinear evolutionary equations, solvable by the inverse scattering method, and the recursion operator, related to such systems; the hierarchies of Hamiltonian structures. The results are illustrated on the example of the multi-component nonlinear Schrodinger (MNLS) equations and the corresponding gauge-equivalent multi-component Heisenberg ferromagnetic (MHF) type models, related to so(5;C) algebra.Comment: 17 pages, 1 figure, LaTeX. arXiv admin note: substantial text overlap with arXiv:0710.330