On the nonlinear Brascamp-Lieb inequality

We prove a nonlinear variant of the general Brascamp-Lieb inequality. Instances of this inequality are quite prevalent in analysis, and we illustrate this with substantial applications in harmonic analysis and partial differential equations. Our proof consists of running an efficient, or "tight", induction on scales argument, which uses the existence of gaussian near-extremisers to the underlying linear Brascamp-Lieb inequality (Lieb's theorem) in a fundamental way. A key ingredient is an effective version of Lieb's theorem, which we establish via a careful analysis of near-minimisers of weighted sums of exponential functions.Comment: 29 pages. This article subsumes the results of arXiv:1801.05214. To appear in the Duke Mathematical Journa

Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence

We employ simulations of supersonic super-Alfvenic turbulence decay as a benchmark test problem to assess and compare the performance of nine astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss convergence of various characteristics for the turbulence decay test and impacts of various components of numerical schemes on the accuracy of solutions. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the magnetic field using the constrained transport method, and using little to no explicit artificial viscosity. Codes which fall short in one or more of these areas are still useful, but they must compensate higher numerical dissipation with higher numerical resolution. This paper is the largest, most comprehensive MHD code comparison on an application-like test problem to date. We hope this work will help developers improve their numerical algorithms while helping users to make informed choices in picking optimal applications for their specific astrophysical problems.Comment: 17 pages, 5 color figures, revised version to appear in ApJ, 735, July 201

Predicting the Effects of Supplemental EPA and DHA on the Omega-3 Index

Background: Supplemental long-chain omega-3 (n–3) fatty acids (EPA and DHA) raise erythrocyte EPA + DHA [omega-3 index (O3I)] concentrations, but the magnitude or variability of this effect is unclear. Objective: The purpose of this study was to model the effects of supplemental EPA + DHA on the O3I. Methods: Deidentified data from 1422 individuals from 14 published n–3 intervention trials were included. Variables considered included dose, baseline O3I, sex, age, weight, height, chemical form [ethyl ester (EE) compared with triglyceride (TG)], and duration of treatment. The O3I was measured by the same method in all included studies. Variables were selected by stepwise regression using the Bayesian information criterion. Results: Individuals supplemented with EPA + DHA (n = 846) took a mean ± SD of 1983 ± 1297 mg/d, and the placebo controls (n = 576) took none. The mean duration of supplementation was 13.6 ± 6.0 wk. The O3I increased from 4.9% ± 1.7% to 8.1% ± 2.7% in the supplemented individuals ( P \u3c 0.0001). The final model included dose, baseline O3I, and chemical formulation type (EE or TG), and these explained 62% of the variance in response (P \u3c 0.0001). The model predicted that the final O3I (and 95% CI) for a population like this, with a baseline concentration of 4.9%, given 850 mg/d of EPA + DHA EE would be ∼6.5% (95% CI: 6.3%, 6.7%). Gram for gram, TG-based supplements increased the O3I by about 1 percentage point more than EE products. Conclusions: Of the factors tested, only baseline O3I, dose, and chemical formulation were significant predictors of O3I response to supplementation. The model developed here can be used by researchers to help estimate the O3I response to a given EPA + DHA dose and chemical form

Efferent Control of the Electrical and Mechanical Properties of Hair Cells in the Bullfrog's Sacculus

Background: Hair cells in the auditory, vestibular, and lateral-line systems respond to mechanical stimulation and transmit information to afferent nerve fibers. The sensitivity of mechanoelectrical transduction is modulated by the efferent pathway, whose activity usually reduces the responsiveness of hair cells. The basis of this effect remains unknown. Methodology and Principal Findings: We employed immunocytological, electrophysiological, and micromechanical approaches to characterize the anatomy of efferent innervation and the effect of efferent activity on the electrical and mechanical properties of hair cells in the bullfrog’s sacculus. We found that efferent fibers form extensive synaptic terminals on all macular and extramacular hair cells. Macular hair cells expressing the Ca 2+-buffering protein calretinin contain half as many synaptic ribbons and are innervated by twice as many efferent terminals as calretinin-negative hair cells. Efferent activity elicits inhibitory postsynaptic potentials in hair cells and thus inhibits their electrical resonance. In hair cells that exhibit spiking activity, efferent stimulation suppresses the generation of action potentials. Finally, efferent activity triggers a displacement of the hair bundle’s resting position. Conclusions and Significance: The hair cells of the bullfrog’s sacculus receive a rich efferent innervation with the heaviest projection to calretinin-containing cells. Stimulation of efferent axons desensitizes the hair cells and suppresses their spiking activity. Although efferent activation influences mechanoelectrical transduction, the mechanical effects on hair bundles ar

Characterization of the Modular Design of the Autolysin/Adhesin Aaa from Staphylococcus Aureus

BACKGROUND: Staphylococcus aureus is a frequent cause of serious and life-threatening infections, such as endocarditis, osteomyelitis, pneumonia, and sepsis. Its adherence to various host structures is crucial for the establishment of diseases. Adherence may be mediated by a variety of adhesins, among them the autolysin/adhesins Atl and Aaa. Aaa is composed of three N-terminal repeated sequences homologous to a lysin motif (LysM) that can confer cell wall attachment and a C-terminally located cysteine, histidine-dependent amidohydrolase/peptidase (CHAP) domain having bacteriolytic activity in many proteins. METHODOLOGY/PRINCIPAL FINDINGS: Here, we show by surface plasmon resonance that the LysM domain binds to fibrinogen, fibronectin, and vitronectin respresenting a novel adhesive function for this domain. Moreover, we demonstrated that the CHAP domain not only mediates the bacteriolytic activity, but also adherence to fibrinogen, fibronectin, and vitronectin, thus demonstrating for the first time an adhesive function for this domain. Adherence of an S. aureus aaa mutant and the complemented aaa mutant is slightly decreased and increased, respectively, to vitronectin, but not to fibrinogen and fibronectin, which might at least in part result from an increased expression of atl in the aaa mutant. Furthermore, an S. aureus atl mutant that showed enhanced adherence to fibrinogen, fibronectin, and endothelial cells also demonstrated increased aaa expression and production of Aaa. Thus, the redundant functions of Aaa and Atl might at least in part be interchangeable. Lastly, RT-PCR and zymographic analysis revealed that aaa is negatively regulated by the global virulence gene regulators agr and SarA. CONCLUSIONS/SIGNIFICANCE: We identified novel functions for two widely distributed protein domains, LysM and CHAP, i.e. the adherence to the extracellular matrix proteins fibrinogen, fibronectin, and vitronectin. The adhesive properties of Aaa might promote S. aureus colonization of host extracellular matrix and tissue, suggesting a role for Aaa in the pathogenesis of S. aureus infections

Traveler Phase 1A Joint Review

The briefing contains the preliminary findings and suggestions for improvement of methods used in development and evaluation of a multi monitor runtime assurance architecture for autonomous flight vehicles. Initial system design, implementation, verification, and flight testing has been conducted. As of yet detailed data review is incomplete, and flight testing has been limited to initial monitor force fights. Detailed monitor flight evaluations have yet to be performed

Structure Based Descriptors for the Estimation of Colloidal Interactions and Protein Aggregation Propensities

<div><p>The control of protein aggregation is an important requirement in the development of bio-pharmaceutical formulations. Here a simple protein model is proposed that was used in molecular dynamics simulations to obtain a quantitative assessment of the relative contributions of proteins’ net-charges, dipole-moments, and the size of hydrophobic or charged surface patches to their colloidal interactions. The results demonstrate that the strength of these interactions correlate with net-charge and dipole moment. Variation of both these descriptors within ranges typical for globular proteins have a comparable effect. By comparison no clear trends can be observed upon varying the size of hydrophobic or charged patches while keeping the other parameters constant. The results are discussed in the context of experimental literature data on protein aggregation. They provide a clear guide line for the development of improved algorithms for the prediction of aggregation propensities.</p> </div

Properties of pseudo proteins used in this study.

a<p>Net-charge in elementary charge units, e.</p>b<p>Dipole moment in eÅ.</p>c<p>first energy minimum in potential of mean force in kJ/mol.</p>d<p>Error bars from boot-strap analysis.</p