A PTAS for Bounded-Capacity Vehicle Routing in Planar Graphs

The Capacitated Vehicle Routing problem is to find a minimum-cost set of tours that collectively cover clients in a graph, such that each tour starts and ends at a specified depot and is subject to a capacity bound on the number of clients it can serve. In this paper, we present a polynomial-time approximation scheme (PTAS) for instances in which the input graph is planar and the capacity is bounded. Previously, only a quasipolynomial-time approximation scheme was known for these instances. To obtain this result, we show how to embed planar graphs into bounded-treewidth graphs while preserving, in expectation, the client-to-client distances up to a small additive error proportional to client distances to the depot

Hedonic and incentive signals for body weight control

Here we review the emerging neurobiological understanding of the role of the brain’s reward system in the regulation of body weight in health and in disease. Common obesity is characterized by the over-consumption of palatable/rewarding foods, reflecting an imbalance in the relative importance of hedonic versus homeostatic signals. The popular ‘incentive salience theory’ of food reward recognises not only a hedonic/pleasure component (‘liking’) but also an incentive motivation component (‘wanting’ or ‘reward-seeking’). Central to the neurobiology of the reward mechanism is the mesoaccumbal dopamine system that confers incentive motivation not only for natural rewards such as food but also by artificial rewards (eg. addictive drugs). Indeed, this mesoaccumbal dopamine system receives and integrates information about the incentive (rewarding) value of foods with information about metabolic status. Problematic over-eating likely reflects a changing balance in the control exerted by hypothalamic versus reward circuits and/or it could reflect an allostatic shift in the hedonic set point for food reward. Certainly, for obesity to prevail, metabolic satiety signals such as leptin and insulin fail to regain control of appetitive brain networks, including those involved in food reward. On the other hand, metabolic control could reflect increased signalling by the stomach-derived orexigenic hormone, ghrelin. We have shown that ghrelin activates the mesoaccumbal dopamine system and that central ghrelin signalling is required for reward from both chemical drugs (eg alcohol) and also from palatable food. Future therapies for problematic over-eating and obesity may include drugs that interfere with incentive motivation, such as ghrelin antagonists

New genetic loci link adipose and insulin biology to body fat distribution.

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10(-8)). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms