Regularized trace on separable Banach spaces

If H is a separable Hilbert space, Gül (2008) has shown that a regularized trace formula can be computed on L² (H, [0, π]) for a second order differential operator with bounded operator-valued coefficients, where H is a separable Hilbert space. Kuelbs (1970) has shown that every separable Banach space can be continuously and densely embedded into a separable Hilbert space, while Gill (2016) has used Kuelbs result to show that the dual of a Banach space does not have a unique representation. In this paper, we use the results of Kuelbs and Gill to study the regularized trace formula on L2 (B, [0, π]), where B is an arbitrary separable Banach space.Publisher's Versio

The effect of boundary adaptivity on hexagonal ordering and bistability in circularly confined quasi hard discs

The behaviour of materials under spatial confinement is sensitively dependent on the nature of the confining boundaries. In two dimensions, confinement within a hard circular boundary inhibits the hexagonal ordering observed in bulk systems at high density. Using colloidal experiments and Monte Carlo simulations, we investigate two model systems of quasi hard discs under circularly symmetric confinement. The first system employs an adaptive circular boundary, defined experimentally using holographic optical tweezers. We show that deformation of this boundary allows, and indeed is required for, hexagonal ordering in the confined system. The second system employs a circularly symmetric optical potential to confine particles without a physical boundary. We show that, in the absence of a curved wall, near perfect hexagonal ordering is possible. We propose that the degree to which hexagonal ordering is suppressed by a curved boundary is determined by the `strictness' of that wall.Comment: 10 pages, 8 figure

High-altitude gravity waves in the Martian thermosphere observed by MAVEN/NGIMS and modeled by a gravity wave scheme

First high-altitude observations of gravity wave (GW)-induced CO$_2$ density perturbations in the Martian thermosphere retrieved from NASA's NGIMS instrument on board the MAVEN satellite are presented and interpreted using the extended GW parameterization of Yi\u{g}it et al. [2008] and the Mars Climate Database as an input. Observed relative density perturbations between 180-220 km of 20-40 % demonstrate appreciable local time, latitude, and altitude variations. Modeling for the spatiotemporal conditions of the MAVEN observations suggests that GWs can directly propagate from the lower atmosphere to the thermosphere, produce appreciable dynamical effects, and likely contribute to the observed fluctuations. Modeled effects are somewhat smaller than the observed but their highly variable nature is in qualitative agreement with observations. Possible reasons for discrepancies between modeling and measurements are discussed.Comment: Accepted for publication in Geophysical Research Letters (GRL). Special section: First Results from the MAVEN Mission to Mar

Serum Lipidomics of Bovine Paratuberculosis: Disruption of Choline-Containing Glycerophospholipids and Sphingolipids

Objectives: Bovine paratuberculosis is a devastating infection with Mycobacterium avium subspecies paratuberculosis that ultimately results in death from malnutrition. While the infection is characterized by a long (2–4 years) subclinical phase with immune activation, ultimately host defense mechanisms fail and the bacteria spread from the small intestine to other organs. Since both the gastrointestinal tract and liver are essential for the biosynthesis of structural glycerophospholipids, we investigated the circulating levels of these lipids in field infections and experimentally infected cattle. Methods: Serum lipidomics of control and M. avium subspecies paratuberculosis–infected cattle were performed utilizing high-resolution mass spectrometry. Results: In M. avium subspecies paratuberculosis–positive cattle, demonstrating clinical signs, we monitored large decreases in the levels of circulating phosphocholine-containing lipids. These included phosphatidylcholines, choline plasmalogens, and sphingomyelins. Next, we monitored the time course of these lipid alterations in experimentally infected calves and found that altered lipid levels were only detected in cattle with clinical signs of infection. Conclusions: Our data indicate that altered availability of choline-containing lipids occurs late in the disease process and is most likely a result of malnutrition and altered biosynthetic capacities of the liver and gastrointestinal tract. Alterations in the bioavailability of these critical structural lipids presumably contributes to the demise of M. avium subspecies paratuberculosis–infected cattle. In light of increasing concern that M. avium subspecies paratuberculosis may be a zoonotic bacterium that contributes to the development of Crohn’s disease and multiple sclerosis, our data also have human clinical relevance

Lipidomic Analysis of Immune Activation in Equine Leptospirosis and \u3cem\u3eLeptospira\u3c/em\u3e-Vaccinated Horses

Currently available diagnostic assays for leptospirosis cannot differentiate vaccine from infection serum antibody. Several leptospiral proteins that are upregulated during infection have been described, but their utility as a diagnostic marker is still unclear. In this study, we undertook a lipidomics approach to determine if there are any differences in the serum lipid profiles of horses naturally infected with pathogenic Leptospira spp. and horses vaccinated against a commercially available bacterin. Utilizing a high-resolution mass spectrometry serum lipidomics analytical platform, we demonstrate that cyclic phosphatidic acids, diacylglycerols, and hydroperoxide oxidation products of choline plasmalogens are elevated in the serum of naturally infected as well as vaccinated horses. Other lipids of interest were triacylglycerols that were only elevated in the serum of infected horses and sphingomyelins that were increased only in the serum of vaccinated horses. This is the first report looking at the equine serum lipidome during leptospiral infection and vaccination