Fixed-point spectrum for group actions by affine isometries on Lp-spaces

The fixed-point spectrum of a locally compact second countable group G on lp is defined to be the set of real numbers p such that every action by affine isometries of G on lp admits a fixed-point. We show that this set is either empty, or is equal to a set of one of the following forms : [1,\pc[, [1,\pc[\{2} for some \pc<\infty or \pc=\infty, or [1,\pc], [1,\pc]\{2} for some pc<infty. This answers a question closely related to a conjecture of C. Drutu which asserts that the fixed-point spectrum is connected for isometric actions on Lp(0,1). We also study the topological properties of the fixed-point spectrum on Lp(X,\mu) for general measure spaces (X,\mu), and show partial results toward the conjecture for actions on Lp(0,1). In particular, we prove that the spectrum F_{L^{\infty}(X,\mu)(G,\pi) of actions with linear part \pi is either empty, or an interval of the form [1,\pc] or [1,\infty[, whenever \pi is an orthogonal representation associated to a measure-preserving ergodic action on a finite measure space (X,\mu).Comment: 25 page

The Effect of Density-Dependent Phase on the Locust Gut Bacterial Composition

The desert locust demonstrates density-dependent phase polyphenism: For extended periods it appears in a non-aggregating, non-migrating phenotype, known as the solitary phase. When circumstances change, solitary individuals may aggregate and transform to the gregarious phenotype, which have a strong propensity for generating large swarms. Previous reports have suggested a role for gut-bacteria derived volatiles in the swarming phenomenon, and suggested that locusts are capable of manipulating their gut microbiome according to their density-dependent phases. Here, we directly tested this hypothesis for the first time. Using locusts of both phases from well-controlled laboratory cultures as well as gregarious field-collected individuals; and high-throughput sequencing. We characterized the hindgut bacterial community composition in the two phases of the desert locust. Our findings demonstrate that laboratory-reared gregarious and solitary locusts maintain a stable core of Enterobacter. However, while different generations of gregarious locust experience shifts in their Enterobacter’s relative abundance; the solitary locusts maintain a stable gut microbiome, highly similar to that of the field-collected locusts. Tentative phase differences in wild populations’ microbiome may thus be an indirect effect of environmental or other factors that push the swarming individuals to homogenous gut bacteria. We therefore conclude that there are phase-related differences in the population dynamics of the locust hindgut bacterial composition, but there is no intrinsic density-dependent mechanism directly affecting the gut microbiome

Locust Bacterial Symbionts: An Update

As one of the world&rsquo;s most infamous agricultural pests, locusts have been subjected to many in-depth studies. Their ability at one end of their behavioral spectrum to live as solitary individuals under specific conditions, and at the other end of the spectrum to form swarms of biblical scale, has placed them at the focus of vast research efforts. One important aspect of locust ecology is that of their interactions with the bacteria that reside in and on them. Although this aspect of locust ecology has been little studied relative to the mainstream locust research, these bacteria have been shown both to affect locust immunity and to participate in maintaining swarm integrity through the secretion of attractant volatiles. The interaction between locusts and their bacteria seems, however, to be bi-directional, with the bacteria themselves, as recently shown, being influenced by their host&rsquo;s swarming tendencies. This seems to be a consequence of the bacterial composition in the locust&rsquo;s gut, reproductive organs, and integument undergoing change with the change in their host&rsquo;s behavior. In this review we describe the current state of knowledge of the locust&ndash;bacteria interactions (data exists mainly for the desert and the migratory locusts), as well as highlighting some newly-gained understanding; and offer perspectives for future research

Incidental colorectal computed tomography abnormalities: Would you send every patient for a colonoscopy?

BACKGROUND: The clinical significance of colorectal wall thickening (CRWT) in patients undergoing abdominal computed tomography (CT) has not yet been definitively established