Continuous and discrete Clebsch variational principles

The Clebsch method provides a unifying approach for deriving variational principles for continuous and discrete dynamical systems where elements of a vector space are used to control dynamics on the cotangent bundle of a Lie group \emph{via} a velocity map. This paper proves a reduction theorem which states that the canonical variables on the Lie group can be eliminated, if and only if the velocity map is a Lie algebra action, thereby producing the Euler-Poincar\'e (EP) equation for the vector space variables. In this case, the map from the canonical variables on the Lie group to the vector space is the standard momentum map defined using the diamond operator. We apply the Clebsch method in examples of the rotating rigid body and the incompressible Euler equations. Along the way, we explain how singular solutions of the EP equation for the diffeomorphism group (EPDiff) arise as momentum maps in the Clebsch approach. In the case of finite dimensional Lie groups, the Clebsch variational principle is discretised to produce a variational integrator for the dynamical system. We obtain a discrete map from which the variables on the cotangent bundle of a Lie group may be eliminated to produce a discrete EP equation for elements of the vector space. We give an integrator for the rotating rigid body as an example. We also briefly discuss how to discretise infinite-dimensional Clebsch systems, so as to produce conservative numerical methods for fluid dynamics

Arthroscopic Anterior Shoulder Stabilization With Incorporation of a Comminuted Bony Bankart Lesion.

Bony Bankart lesions are a common finding in patients with anterior glenohumeral dislocation. Although there are no defined guidelines, small bony Bankart fractures are typically treated arthroscopically with suture anchors. The 2 main techniques used are double- and single-row suture anchor stabilization, with debate over superiority. Biomechanical studies have shown improved reduction and stabilization with the double-row over the single-row suture anchor technique; however, this has not been reported for small or comminuted bony fragments. Both techniques have shown promising preliminary clinical outcomes. In this Technical Note, we describe our preferred technique for arthroscopic instability repair using a single-row all-suture anchor method with the incorporation of a comminuted bony Bankart fragment in the lateral decubitus position

Un-reduction

This paper provides a full geometric development of a new technique called un-reduction, for dealing with dynamics and optimal control problems posed on spaces that are unwieldy for numerical implementation. The technique, which was originally concieved for an application to image dynamics, uses Lagrangian reduction by symmetry in reverse. A deeper understanding of un-reduction leads to new developments in image matching which serve to illustrate the mathematical power of the technique.Comment: 25 pages, revised versio

Listeriolysin S, a Novel Peptide Haemolysin Associated with a Subset of Lineage I Listeria monocytogenes

peer-reviewedStreptolysin S (SLS) is a bacteriocin-like haemolytic and cytotoxic virulence factor that plays a key role in the virulence of Group A Streptococcus (GAS), the causative agent of pharyngitis, impetigo, necrotizing fasciitis and streptococcal toxic shock syndrome. Although it has long been thought that SLS and related peptides are produced by GAS and related streptococci only, there is evidence to suggest that a number of the most notorious Gram-positive pathogenic bacteria, including Listeria monocytogenes, Clostridium botulinum and Staphylococcus aureus, produce related peptides. The distribution of the L. monocytogenes cluster is particularly noteworthy in that it is found exclusively among a subset of lineage I strains; i.e., those responsible for the majority of outbreaks of listeriosis. Expression of these genes results in the production of a haemolytic and cytotoxic factor, designated Listeriolysin S, which contributes to virulence of the pathogen as assessed by murine- and human polymorphonuclear neutrophil–based studies. Thus, in the process of establishing the existence of an extended family of SLS-like modified virulence peptides (MVPs), the genetic basis for the enhanced virulence of a proportion of lineage I L. monocytogenes may have been revealed.Work is funded by the Irish Government under the National Development Plan, through a Science Foundation Ireland Investigator award to CH, PR and PC (06/IN.1/B98)

Characteristics of Gamma-Ray Loud Blazars in the VLBA Imaging and Polarimetry Survey

The radio properties of blazars detected by the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope have been observed as part of the VLBA Imaging and Polarimetry Survey (VIPS). This large, flux-limited sample of active galactic nuclei (AGN) provides insights into the mechanism that produces strong gamma-ray emission. At lower flux levels, radio flux density does not directly correlate with gamma-ray flux. We find that the LAT-detected BL Lacs tend to be similar to the non-LAT BL Lacs, but that the LAT-detected FSRQs are often significantly different from the non-LAT FSRQs. The differences between the gamma-ray loud and quiet FSRQs can be explained by Doppler boosting; these objects appear to require larger Doppler factors than those of the BL Lacs. It is possible that the gamma-ray loud FSRQs are fundamentally different from the gamma-ray quiet FSRQs. Strong polarization at the base of the jet appears to be a signature for gamma-ray loud AGN.Comment: 32 pages, 9 figures, accepted by Ap

Impact of Environmental Factors on Bacteriocin Promoter Activity in Gut-Derived Lactobacillus salivarius

peer-reviewedBacteriocin production is regarded as a desirable probiotic trait that aids in colonization and persistence in the gastrointestinal tract (GIT). Strains of Lactobacillus salivarius, a species associated with the GIT, are regarded as promising probiotic candidates and have a number of associated bacteriocins documented to date. These include multiple class IIb bacteriocins (salivaricin T, salivaricin P, and ABP-118) and the class IId bacteriocin bactofencin A, which show activity against medically important pathogens. However, the production of a bacteriocin in laboratory media does not ensure production under stressful environmental conditions, such as those encountered within the GIT. To allow this issue to be addressed, the promoter regions located upstream of the structural genes encoding the L. salivarius bacteriocins mentioned above were fused to a number of reporter proteins (green fluorescent protein [GFP], red fluorescent protein [RFP], and luciferase [Lux]). Of these, only transcriptional fusions to GFP generated signals of sufficient strength to enable the study of promoter activity in L. salivarius. While analysis of the class IIb bacteriocin promoter regions indicated relatively weak GFP expression, assessment of the promoter of the antistaphylococcal bacteriocin bactofencin A revealed a strong promoter that is most active in the absence of the antimicrobial peptide and is positively induced in the presence of mild environmental stresses, including simulated gastric fluid. Taken together, these data provide information on factors that influence bacteriocin production, which will assist in the development of strategies to optimize in vivo and in vitro production of these antimicrobials.This work was funded by a SFI PI award “Obesibiotics” (11/PI/1137) to PD

Besov priors for Bayesian inverse problems

We consider the inverse problem of estimating a function $u$ from noisy, possibly nonlinear, observations. We adopt a Bayesian approach to the problem. This approach has a long history for inversion, dating back to 1970, and has, over the last decade, gained importance as a practical tool. However most of the existing theory has been developed for Gaussian prior measures. Recently Lassas, Saksman and Siltanen (Inv. Prob. Imag. 2009) showed how to construct Besov prior measures, based on wavelet expansions with random coefficients, and used these prior measures to study linear inverse problems. In this paper we build on this development of Besov priors to include the case of nonlinear measurements. In doing so a key technical tool, established here, is a Fernique-like theorem for Besov measures. This theorem enables us to identify appropriate conditions on the forward solution operator which, when matched to properties of the prior Besov measure, imply the well-definedness and well-posedness of the posterior measure. We then consider the application of these results to the inverse problem of finding the diffusion coefficient of an elliptic partial differential equation, given noisy measurements of its solution.Comment: 18 page

ICP polishing of silicon for high quality optical resonators on a chip

Miniature concave hollows, made by wet etching silicon through a circular mask, can be used as mirror substrates for building optical micro-cavities on a chip. In this paper we investigate how ICP polishing improves both shape and roughness of the mirror substrates. We characterise the evolution of the surfaces during the ICP polishing using white-light optical profilometry and atomic force microscopy. A surface roughness of 1 nm is reached, which reduces to 0.5 nm after coating with a high reflectivity dielectric. With such smooth mirrors, the optical cavity finesse is now limited by the shape of the underlying mirror