Bourgain-Brezis-Mironescu Convergence via Triebel-Lizorkin Spaces

We study a convergence result of Bourgain--Brezis--Mironescu (BBM) using Triebel-Lizorkin spaces. It is well known that as spaces $W^{s,p} = F^{s}_{p,p}$, and $H^{1,p} = F^{1}_{p,2}$. When $s\to 1$, the $F^{s}_{p,p}$ norm becomes the $F^{1}_{p,p}$ norm but BBM showed that the $W^{s,p}$ norm becomes the $H^{1,p} = F^{1}_{p,2}$ norm. Naively, for $p \neq 2$ this seems like a contradiction, but we resolve this by providing embeddings of $W^{s,p}$ into $F^{s}_{p,q}$ for $q \in \{p,2\}$ with sharp constants with respect to $s \in (0,1)$. As a consequence we obtain an $\mathbb{R}^N$-version of the BBM-result, and obtain several more embedding and convergence theorems of BBM-type that to the best of our knowledge are unknown.Comment: changes in presentation, new reference

Decision-making on intra-household allocation of bed nets in Uganda: do households prioritize the most vulnerable members?

Abstract Background Access to insecticide-treated bed nets has increased substantially in recent years, but ownership and use remain well below 100% in many malaria endemic areas. Understanding decision-making around net allocation in households with too few nets is essential to ensuring protection of the most vulnerable. This study explores household net allocation preferences and practices across four districts in Uganda. Methods Data collection consisted of eight focus group discussions, twelve in-depth interviews, and a structured questionnaire to inventory 107 sleeping spaces in 28 households. Results In focus group discussions and in-depth interviews, participants almost unanimously stated that pregnant women, infants, and young children should be prioritized when allocating nets. However, sleeping space surveys reveal that heads of household sometimes receive priority over children less than five years of age when households have too few nets to cover all members. Conclusions When asked directly, most net owners highlight the importance of allocating nets to the most biologically vulnerable household members. This is consistent with malaria behaviour change and health education messages. In actual allocation, however, factors other than biological vulnerability may influence who does and does not receive a net.http://deepblue.lib.umich.edu/bitstream/2027.42/109479/1/12936_2014_Article_3219.pd

Optimizing static thermodynamic models of transcriptional regulation

Motivation: Modeling transcriptional regulation using thermo-dynamic modeling approaches has become increasingly relevant as a way to gain a detailed understanding of transcriptional regulation. Thermodynamic models are able to model the interactions between transcription factors (TFs) and DNA that lead to a specific transcriptional output of the target gene. Such models can be ‘trained’ by fitting their free parameters to data on the transcription rate of a gene and the concentrations of its regulating factors. However, the parameter fitting process is computationally very expensive and this limits the number of alternative types of model that can be explored

Energy Dose-Response in Selective Laser Trabeculoplasty: A Review

PRCIS: A literature review of SLT energy dose response found no definitive relationship between IOP reduction with respect to total or pulse energy, race, pigmentation, or application pattern. PURPOSE: Selective laser trabeculoplasty (SLT) is a safe and effective treatment for lowering intraocular pressure (IOP). While evidence is mounting for the advantage of its use as a first-line treatment for IOP reduction, the SLT procedures in use vary widely. The purpose of this literature review was to investigate if there were any relationships between SLT energy and efficacy for lowering IOP in the published literature. METHODS: A literature review was undertaken that included studies in which energy levels required for successful SLT treatment were investigated: in general, with respect to angle pigmentation, race or ethnicity, and treatment arc extent. RESULTS: There was no indication that higher (or lower) energy used in the treatment leads to greater (or less) IOP reduction. Similar results were obtained regarding level of trabecular meshwork (TM) pigmentation. Race was not found to be associated with altered dose response in SLT. There were indications that treating the full 360 degrees, as opposed to smaller arcs, could be beneficial for more IOP reduction. IOP reduction from SLT was found to be similar to that provided by topical medications. CONCLUSIONS: The optimal energy level of SLT needed for IOP reduction has not yet been definitively established, with all reported pulse energies resulting in similar IOP reduction. Furthermore, similar lack of conclusive findings exists regarding optimal SLT energy dosage for use in different races and degrees of TM pigmentation. This parameter, as well as each of the above-mentioned factors, requires further research

Monitoring of Superparamagnetic Particle Sizes in the Langevin Law Regime

peer reviewedIn this work, aqueous solutions of magnetite nanoparticles (NPs) are studied. Magnetite NPs are very useful in biomedicine for magnetic resonance imaging (MRI), for drug delivery therapy, and also for hyperthermia. In order to predict the NP efficiency in these applications, it is crucial to accurately characterize their size distribution and their magnetization. Magnetometry, through the dependence of NP magnetization on the magnetic induction (MB curve), can provide interesting information on these physical properties. In this work, the extraction of the NP size distribution and magnetization from experimental MB curves of aqueous solutions of magnetite NPs is discussed. The results are compared to TEM and XRD characterizations. It is shown that an expression taking into account the size distribution better fits the results than the commonly used simple Langevin function. The size distributions obtained by magnetometry seem comparable to those obtained by TEM measurements. However, a closer look at the results shows some nonnegligible discrepancies: the size distributions obtained by magnetometry vary with the temperature and are closer to the TEM ones at room temperature. Our study suggests that it could be explained by the nonnegligible anisotropy energy of the NPs at low temperature and the lack of NP Brownian rotation below the freezing point of water. This demonstrates that care must be taken when interpreting the results obtained by magnetometry of magnetite NPs: only the size and size distribution obtained at room temperature should be used

Rationally designed immunogens enable immune focusing following SARS-CoV-2 spike imprinting

Eliciting antibodies to surface-exposed viral glycoproteins can generate protective responses that control and prevent future infections. Targeting conserved sites may reduce the likelihood of viral escape and limit the spread of related viruses with pandemic potential. Here we leverage rational immunogen design to focus humoral responses on conserved epitopes. Using glycan engineering and epitope scaffolding in boosting immunogens, we focus murine serum antibody responses to conserved receptor binding motif (RBM) and receptor binding domain (RBD) epitopes following severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike imprinting. Although all engineered immunogens elicit a robust SARS-CoV-2-neutralizing serum response, RBM-focusing immunogens exhibit increased potency against related sarbecoviruses, SARS-CoV, WIV1-CoV, RaTG13-CoV, and SHC014-CoV; structural characterization of representative antibodies defines a conserved epitope. RBM-focused sera confer protection against SARS-CoV-2 challenge. Thus, RBM focusing is a promising strategy to elicit breadth across emerging sarbecoviruses without compromising SARS-CoV-2 protection. These engineering strategies are adaptable to other viral glycoproteins for targeting conserved epitopes

Anodic oxidation of dithiane carboxylic acids: a rapid and mild 2 way to access functionalized orthoesters

A new electrochemical methodology has been developed for the preparation of a wide variety of functionalized orthoesters under mild and green conditions from easily accessible dithiane derivatives. The new methodology also offers an unprecedented way to access tri(fluorinated) orthoesters, a class of compound that has never been studied before. This provides the community with a rapid and general method to prepare libraries of functionalized orthoesters from simple and readily available starting materials

Analysis of spatial and temporal patterns of on-road NO2 concentrations in Hong Kong

In this paper we present an investigation of the spatial and temporal variability of street-level concentrations of NO2 in Hong Kong as an example of a densely populated megacity with heavy traffic. For the study we use a combination of open-path remote sensing and in situ measurement techniques that allows us to separate temporal changes and spatial patterns and analyse them separately. Two measurement campaigns have been conducted, one in December 2010 and one in March 2017. Each campaign lasted for a week which allowed us to examine diurnal cycles, weekly patterns as well as spatially resolved long-term changes. We combined a long-path differential optical absorption spectroscopy (DOAS) instrument with a cavity-enhanced DOAS and applied several normalizations to the data sets in order to make the different measurement routes comparable. For the analysis of long-term changes we used the entire unfiltered data set and for the comparison of spatial patterns we filtered out the accumulation of NO2 when stopping at traffic lights for focusing on the changes of NO2 spatial distribution instead of comparing traffic flow patterns. For the generation of composite maps the diurnal cycle has been normalized by scaling the mobile data with coinciding citywide path-averaged measurement results. An overall descending trend from 2010 to 2017 could be observed, consistent with the observations of the Ozone Monitoring Instrument (OMI) and the Environment Protection Department (EPD) air quality monitoring network data. However, long-term difference maps show pronounced spatial structures with some areas, e.g. around subway stations, revealing an increasing trend. We could also show that the weekend effect, which for the most part of Hong Kong shows reduced NO2 concentrations on Sundays and to a lesser degree on Saturdays, is reversed around shopping malls. Our study shows that spatial differences have to be considered when discussing citywide trends and can be used to put local point measurements into perspective. The resulting data set provides a better insight into on-road NO2 characteristics in Hong Kong, which helps to identify heavily polluted areas and represents a useful database for urban planning and the design of pollution control measures

Author response

In eukaryotes, exposure to hypertonic conditions activates a MAPK (Hog1 in Saccharomyces cerevisiae and ortholog p38 in human cells). In yeast, intracellular glycerol accumulates to counterbalance the high external osmolarity. To prevent glycerol efflux, Hog1 action impedes the function of the aquaglyceroporin Fps1, in part, by displacing channel co-activators (Rgc1/2). However, Fps1 closes upon hyperosmotic shock even in hog1∆ cells, indicating another mechanism to prevent Fps1-mediated glycerol efflux. In our prior proteome-wide screen, Fps1 was identified as a target of TORC2-dependent protein kinase Ypk1 (Muir et al., 2014). We show here that Fps1 is an authentic Ypk1 substrate and that the open channel state of Fps1 requires phosphorylation by Ypk1. Moreover, hyperosmotic conditions block TORC2-dependent Ypk1-mediated Fps1 phosphorylation, causing channel closure, glycerol accumulation, and enhanced survival under hyperosmotic stress. These events are all Hog1-independent. Our findings define the underlying molecular basis of a new mechanism for responding to hypertonic conditions. DOI: http://dx.doi.org/10.7554/eLife.09336.00