Signatures of hermitian forms and the Knebusch Trace Formula

Signatures of quadratic forms have been generalized to hermitian forms over algebras with involution. In the literature this is done via Morita theory, which causes sign ambiguities in certain cases. In this paper, a hermitian version of the Knebusch Trace Formula is established and used as a main tool to resolve these ambiguities. The last page is an erratum for the published version. We inadvertently (I) gave an incorrect definition of adjoint involutions; (II) omitted dealing with the case $(H\times H, \widehat{\phantom{m}}\,)$. As $W(H\times H, \widehat{\phantom{m}}\,)= W(R\times R, \widehat{\phantom{m}}\,)=0$, the omission does not affect our reasoning or our results. For the sake of completeness we point out where some small changes should be made in the published version.Comment: This is the final version before publication. The last page is an updated erratum for the published versio

Identification and Functional Clustering of Genes Regulating Muscle Protein Degradation from amongst the Known C. elegans Muscle Mutants

Loss of muscle mass via protein degradation is an important clinical problem but we know little of how muscle protein degradation is regulated genetically. To gain insight our labs developed C. elegans into a model for understanding the regulation of muscle protein degradation. Past studies uncovered novel functional roles for genes affecting muscle and/or involved in signalling in other cells or tissues. Here we examine most of the genes previously identified as the sites of mutations affecting muscle for novel roles in regulating degradation. We evaluate genomic (RNAi knockdown) approaches and combine them with our established genetic (mutant) and pharmacologic (drugs) approaches to examine these 159 genes. We find that RNAi usually recapitulates both organismal and sub-cellular mutant phenotypes but RNAi, unlike mutants, can frequently be used acutely to study gene function solely in differentiated muscle. In the majority of cases where RNAi does not produce organismal level phenotypes, sub-cellular defects can be detected; disrupted proteostasis is most commonly observed. We identify 48 genes in which mutation or RNAi knockdown causes excessive protein degradation; myofibrillar and/or mitochondrial morphologies are also disrupted in 19 of these 48 cases. These 48 genes appear to act via at least three sub-networks to control bulk degradation of protein in muscle cytosol. Attachment to the extracellular matrix regulates degradation via unidentified proteases and affects myofibrillar and mitochondrial morphology. Growth factor imbalance and calcium overload promote lysosome based degradation whereas calcium deficit promotes proteasome based degradation, in both cases myofibrillar and mitochondrial morphologies are largely unaffected. Our results provide a framework for effectively using RNAi to identify and functionally cluster novel regulators of degradation. This clustering allows prioritization of candidate genes/pathways for future mechanistic studies

The population of propellers in Saturn's A Ring

We present an extensive data set of ~150 localized features from Cassini images of Saturn's Ring A, a third of which are demonstrated to be persistent by their appearance in multiple images, and half of which are resolved well enough to reveal a characteristic "propeller" shape. We interpret these features as the signatures of small moonlets embedded within the ring, with diameters between 40 and 500 meters. The lack of significant brightening at high phase angle indicates that they are likely composed primarily of macroscopic particles, rather than dust. With the exception of two features found exterior to the Encke Gap, these objects are concentrated entirely within three narrow (~1000 km) bands in the mid-A Ring that happen to be free from local disturbances from strong density waves. However, other nearby regions are similarly free of major disturbances but contain no propellers. It is unclear whether these bands are due to specific events in which a parent body or bodies broke up into the current moonlets, or whether a larger initial moonlet population has been sculpted into bands by other ring processes.Comment: 31 pages, 10 figures; Accepted at A

Functional diversity of microbial ecologies estimated from ancient human coprolites and dental calculus

Human microbiome studies are increasingly incorporating macroecological approaches, such as community assembly, network analysis and functional redundancy to more fully characterize the microbiome. Such analyses have not been applied to ancient human microbiomes, preventing insights into human microbiome evolution. We address this issue by analysing published ancient microbiome datasets: coprolites from Rio Zape (n = 7; 700 CE Mexico) and historic dental calculus (n = 44; 1770-1855 CE, UK), as well as two novel dental calculus datasets: Maya (n = 7; 170 BCE-885 CE, Belize) and Nuragic Sardinians (n = 11; 1400-850 BCE, Italy). Periodontitis-associated bacteria (Treponema denticola, Fusobacterium nucleatum and Eubacterium saphenum) were identified as keystone taxa in the dental calculus datasets. Coprolite keystone taxa included known short-chain fatty acid producers (Eubacterium biforme, Phascolarctobacterium succinatutens) and potentially disease-associated bacteria (Escherichia, Brachyspira). Overlap in ecological profiles between ancient and modern microbiomes was indicated by similarity in functional response diversity profiles between contemporary hunter-gatherers and ancient coprolites, as well as parallels between ancient Maya, historic UK, and modern Spanish dental calculus; however, the ancient Nuragic dental calculus shows a distinct ecological structure. We detected key ecological signatures from ancient microbiome data, paving the way to expand understanding of human microbiome evolution. This article is part of the theme issue 'Insights into health and disease from ancient biomolecules'

On post-Lie algebras, Lie--Butcher series and moving frames

Pre-Lie (or Vinberg) algebras arise from flat and torsion-free connections on differential manifolds. They have been studied extensively in recent years, both from algebraic operadic points of view and through numerous applications in numerical analysis, control theory, stochastic differential equations and renormalization. Butcher series are formal power series founded on pre-Lie algebras, used in numerical analysis to study geometric properties of flows on euclidean spaces. Motivated by the analysis of flows on manifolds and homogeneous spaces, we investigate algebras arising from flat connections with constant torsion, leading to the definition of post-Lie algebras, a generalization of pre-Lie algebras. Whereas pre-Lie algebras are intimately associated with euclidean geometry, post-Lie algebras occur naturally in the differential geometry of homogeneous spaces, and are also closely related to Cartan's method of moving frames. Lie--Butcher series combine Butcher series with Lie series and are used to analyze flows on manifolds. In this paper we show that Lie--Butcher series are founded on post-Lie algebras. The functorial relations between post-Lie algebras and their enveloping algebras, called D-algebras, are explored. Furthermore, we develop new formulas for computations in free post-Lie algebras and D-algebras, based on recursions in a magma, and we show that Lie--Butcher series are related to invariants of curves described by moving frames.Comment: added discussion of post-Lie algebroid

Eliminating Ditransitives

Abstract. We discuss how higher arity verbs such as give or promise can be treated in an algebraic framework that admits only unary and binary relations and does not rely on event variables

Photoswitchable diacylglycerols enable optical control of protein kinase C.

Increased levels of the second messenger lipid diacylglycerol (DAG) induce downstream signaling events including the translocation of C1-domain-containing proteins toward the plasma membrane. Here, we introduce three light-sensitive DAGs, termed PhoDAGs, which feature a photoswitchable acyl chain. The PhoDAGs are inactive in the dark and promote the translocation of proteins that feature C1 domains toward the plasma membrane upon a flash of UV-A light. This effect is quickly reversed after the termination of photostimulation or by irradiation with blue light, permitting the generation of oscillation patterns. Both protein kinase C and Munc13 can thus be put under optical control. PhoDAGs control vesicle release in excitable cells, such as mouse pancreatic islets and hippocampal neurons, and modulate synaptic transmission in Caenorhabditis elegans. As such, the PhoDAGs afford an unprecedented degree of spatiotemporal control and are broadly applicable tools to study DAG signaling

Developing serious games for cultural heritage: a state-of-the-art review

Although the widespread use of gaming for leisure purposes has been well documented, the use of games to support cultural heritage purposes, such as historical teaching and learning, or for enhancing museum visits, has been less well considered. The state-of-the-art in serious game technology is identical to that of the state-of-the-art in entertainment games technology. As a result, the field of serious heritage games concerns itself with recent advances in computer games, real-time computer graphics, virtual and augmented reality and artificial intelligence. On the other hand, the main strengths of serious gaming applications may be generalised as being in the areas of communication, visual expression of information, collaboration mechanisms, interactivity and entertainment. In this report, we will focus on the state-of-the-art with respect to the theories, methods and technologies used in serious heritage games. We provide an overview of existing literature of relevance to the domain, discuss the strengths and weaknesses of the described methods and point out unsolved problems and challenges. In addition, several case studies illustrating the application of methods and technologies used in cultural heritage are presented