Forced gradings and the Humphreys-Verma conjecture

Let $G$ be a semisimple, simply connected algebraic group defined and split over a prime field ${\mathbb F}_p$ of positive characteristic. For a positive integer $r$, let $G_r$ be the $r$th Frobenius kernel of $G$. Let $Q$ be a projective indecomposable (rational) $G_r$-module. The well-known Humprheys-Verma conjecture (cf. \cite{Ballard}) asserts that the $G_r$-action on $Q$ lifts to an rational action of $G$ on $Q$. For $p\geq 2h-2$ (where $h$ is the Coxeter number of $G$), this conjecture was proved by Jantzen in 1980, improving on early work of Ballard. However, it remains open for general characteristics. In this paper, the authors establish several graded analogues of the Humphreys-Verma conjecture, valid for all $p$. The most general of our results, proved in full here, was announced (without proof) in an earlier paper. Another result relates the Humphreys-Verma conjecture to earlier work of Alperin, Collins, and Sibley on finite group representation theory. A key idea in all formulations involves the notion of a forced grading. The latter goes back, in particular, to the recent work of the authors, relating graded structures and $p$-filtrations. The authors anticipate that the Humphreys-Verma conjecture results here will lead to extensions to smaller characteristics of these earlier papers

The Pleiotropic Effects of Beneficial Mutations of Adapted Escherichia coli Populations

Mutations that improve fitness in one environment can often be beneficial, deleterious, or neutral in alternative environments. When a single mutation effects fitness in multiple environments, it is said to be a pleiotropic, which can have important consequences for niche specialization, niche expansion, speciation, and even extinction in the face of environmental change. While previous studies have revealed that pleiotropy is nearly universal, the role of adaptive history in the spectrum of pleiotropic effects has yet to undergo detailed experimental observation. Using experimental evolution we gathered beneficial mutations in a previously adapted strain of Escherichia coli growing in the same common substrate over hundreds of generations. We then tested the effects of these mutations in multiple alternative environments and compared their fitness to the ancestor. We found that the magnitude of the effects correlates positively with the similarity of resources to glucose, indicating that selective history has an influence in the distribution of beneficial mutations. These findings broaden our understanding of the effects of history on pleiotropy, and may provide answers into how evolution in a constant environment influences ecological niche formation and constraint

Arkansas Bulletin of Water Research - Issue 2018

The Arkansas Bulletin of Water Research is a publication of the Arkansas Water Resources Center (AWRC). This bulletin is produced in an effort to share water research relevant to Arkansas water stakeholders in an easily searchable and aesthetically engaging way. This is the second publication of the bulletin and will be published annually. The submission of a paper to this bulletin is appropriate for topics at all related to water resources, by anyone conducting water research or investigations. This includes but is not limited to university researchers, consulting firms, watershed groups, and other agencies. Prospective authors should read the “Introduction to the Arkanasas Bulletin of Water Research” contained within this publication and should refer to the AWRC website for additional infromation. https://arkansas-water-center.uark.edu