A positivity result in the theory of Macdonald polynomials

We outline here a proof that a certain rational function Cn(q, t), which has come to be known as the “q, t-Catalan,” is in fact a polynomial with positive integer coefficients. This has been an open problem since 1994. Because Cn(q, t) evaluates to the Catalan number at t = q = 1, it has also been an open problem to find a pair of statistics a, b on the collection

Visual constraints in foraging bumblebees: Flower size and color affect search time and flight behavior

In optimal foraging theory, search time is a key variable defining the value of a prey type. But the sensory-perceptual processes that constrain the search for food have rarely been considered. Here we evaluate the flight behavior of bumblebees (Bombus terrestris) searching for artificial flowers of various sizes and colors. When flowers were large, search times correlated well with the color contrast of the targets with their green foliage-type background, as predicted by a model of color opponent coding using inputs from the bees' UV, blue, and green receptors. Targets that made poor color contrast with their backdrop, such as white, UV-reflecting ones, or red flowers, took longest to detect, even though brightness contrast with the background was pronounced. When searching for small targets, bees changed their strategy in several ways. They flew significantly slower and closer to the ground, so increasing the minimum detectable area subtended by an object on the ground. In addition, they used a different neuronal channel for flower detection. Instead of color contrast, they used only the green receptor signal for detection. We relate these findings to temporal and spatial limitations of different neuronal channels involved in stimulus detection and recognition. Thus, foraging speed may not be limited only by factors such as prey density, flight energetics, and scramble competition. Our results show that understanding the behavioral ecology of foraging can substantially gain from knowledge about mechanisms of visual information processing.

Positive selection and rates of evolution in immunodeficiency viruses from humans and chimpanzees.

Evolutionary theory predicts the recent spread of primate immunodeficiency viruses (PIVs) to new human populations to be accompanied by positive selection in response to new host environments and/or by random genetic drift. I assess evidence for positive selection in human and chimpanzee PIVs type I (PIV1s), using ratios of synonymous to nonsynonymous nucleotide change based on branch lengths and outgroup rooting. Ratios are smaller for PIV1s from humans than for PIV1 from a chimpanzee for the pol, gag, and env glycoprotein 120 (gp120) regions, indicating greater effects of positive selection in PIV1s from humans. Parsimony-based relative rate tests for amino acid changes showed significant differences between PIV1s from humans and chimpanzees in 18 of 48 pairwise comparisons, with all 18 showing faster rates of change in PIV1s from humans. This study indicates that in some instances, the recent evolution of human PIV1s follows a speciational pattern, in which increased diversification of taxa is correlated with greater amounts of character change appearing and being maintained through time. This extends the generality of the speciational pattern to a group of organisms (viruses) having the fastest known rates of anagenetic change for nucleotide characters and indicates that comprehensive understanding of PIV1 evolution requires consideration of both anagenetic change within viral lineages and the relative historical success of different viral clades. Phylogenetic analyses show that neither PIV1s infecting humans nor those infecting chimpanzees represent monophyletic groups and suggest multiple host-species shifts for PIV1s.

Corticotropin-releasing factor-binding protein ligand inhibitor blunts excessive weight gain in genetically obese Zucker rats and rats during nicotine withdrawal

Elevation of the neuropeptide corticotropin-releasing factor (CRF) in the brain is associated with a reduction of food intake and body weight gain in normal and obese animals. A protein that binds CRF and the related peptide, urocortin, with high affinity, CRF-binding protein (CRF-BP), may play a role in energy homeostasis by inactivating members of this peptide family in ingestive and metabolic regulatory brain regions. Intracerebroventricular administration in rats of the high-affinity CRF-BP ligand inhibitor, rat/human CRF (6-33), which dissociates CRF or urocortin from CRF-BP and increases endogenous brain levels of “free” CRF or urocortin significantly blunted exaggerated weight gain in Zucker obese subjects and in animals withdrawn from chronic nicotine. Chronic administration of CRF suppressed weight gain nonselectively by 60% in both Zucker obese and lean control rats, whereas CRF-BP ligand inhibitor treatment significantly reduced weight gain in obese subjects, without altering weight gain in lean control subjects. Nicotine abstinent subjects, but not nicotine-naive controls, experienced a 35% appetite suppression and a 25% weight gain reduction following acute and chronic administration, respectively, of CRF-BP ligand inhibitor. In marked contrast to the effects of a CRF-receptor agonist, the CRF-BP ligand inhibitor did not stimulate adrenocorticotropic hormone secretion or elevate heart rate and blood pressure. These results provide support for the hypothesis that the CRF-BP may function within the brain to limit selected actions of CRF and/or urocortin. Furthermore, CRF-BP may represent a novel and functionally selective target for the symptomatic treatment of excessive weight gain associated with obesity of multiple etiology.