On an extremal problem for poset dimension

Let $f(n)$ be the largest integer such that every poset on $n$ elements has a $2$-dimensional subposet on $f(n)$ elements. What is the asymptotics of $f(n)$? It is easy to see that $f(n)\geqslant n^{1/2}$. We improve the best known upper bound and show $f(n)=\mathcal{O}(n^{2/3})$. For higher dimensions, we show $f_d(n)=\mathcal{O}\left(n^\frac{d}{d+1}\right)$, where $f_d(n)$ is the largest integer such that every poset on $n$ elements has a $d$-dimensional subposet on $f_d(n)$ elements.Comment: removed proof of Theorem 3 duplicating previous work; fixed typos and reference

Linear Extensions and Comparable Pairs in Partial Orders

We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also show that a random interval partial order on $n$ elements has close to a third of the pairs comparable with high probability, and the number of linear extensions is $n! \, 2^{-\Theta(n)}$ with high probability

Rough Sets Determined by Quasiorders

In this paper, the ordered set of rough sets determined by a quasiorder relation $R$ is investigated. We prove that this ordered set is a complete, completely distributive lattice. We show that on this lattice can be defined three different kinds of complementation operations, and we describe its completely join-irreducible elements. We also characterize the case in which this lattice is a Stone lattice. Our results generalize some results of J. Pomykala and J. A. Pomykala (1988) and M. Gehrke and E. Walker (1992) in case $R$ is an equivalence.Comment: 18 pages, major revisio

Zonal image analysis of tumour vascular perfusion, hypoxia, and necrosis

A number of laboratories are utilising both hypoxia and perfusion markers to spatially quantify tumour oxygenation and vascular distributions, and scientists are increasingly turning to automated image analysis methods to quantify such interrelationships. In these studies, the presence of regions of necrosis in the immunohistochemical sections remains a potentially significant source of error. In the present work, frozen MCa-4 mammary tumour sections were used to obtain a series of corresponding image montages. Total vessels were identified using CD31 staining, perfused vessels by DiOC7 staining, hypoxia by EF5/Cy3 uptake, and necrosis by haematoxylin and eosin staining. Our goal was to utilise image analysis techniques to spatially quantitate hypoxic marker binding as a function of distance from the nearest blood vessel. Several refinements to previous imaging methods are described: (1) hypoxia marker images are quantified in terms of their intensity levels, thus providing an analysis of the gradients in hypoxia with increasing distances from blood vessels, (2) zonal imaging masks are derived, which permit spatial sampling of images at precisely defined distances from blood vessels, as well as the omission of necrotic artifacts, (3) thresholding techniques are applied to omit holes in the tissue sections, and (4) distance mapping is utilised to define vascular spacing

Effect on skin hydration of using baby wipes to clean the napkin area of newborn babies: assessor-blinded randomised controlled equivalence trial

Background Some national guidelines recommend the use of water alone for napkin cleansing. Yet, there is a readiness, amongst many parents, to use baby wipes. Evidence from randomised controlled trials, of the effect of baby wipes on newborn skin integrity is lacking. We conducted a study to examine the hypothesis that the use of a specifically formulated cleansing wipe on the napkin area of newborn infants (<1 month) has an equivalent effect on skin hydration when compared with using cotton wool and water (usual care). Methods A prospective, assessor-blinded, randomised controlled equivalence trial was conducted during 2010. Healthy, term babies (n = 280), recruited within 48 hours of birth, were randomly assigned to have their napkin area cleansed with an alcohol-free baby wipe (140 babies) or cotton wool and water (140 babies). Primary outcome was change in hydration from within 48 hours of birth to 4 weeks post-birth. Secondary outcomes comprised changes in trans-epidermal water loss, skin surface pH and erythema, presence of microbial skin contaminants/irritants at 4 weeks and napkin dermatitis reported by midwife at 4 weeks and mother during the 4 weeks. Results Complete hydration data were obtained for 254 (90.7 %) babies. Wipes were shown to be equivalent to water and cotton wool in terms of skin hydration (intention-to-treat analysis: wipes 65.4 (SD 12.4) vs. water 63.5 (14.2), p = 0.47, 95 % CI -2.5 to 4.2; per protocol analysis: wipes 64.6 (12.4) vs. water 63.6 (14.3), p = 0.53, 95 % CI -2.4 to 4.2). No significant differences were found in the secondary outcomes, except for maternal-reported napkin dermatitis, which was higher in the water group (p = 0.025 for complete responses). Conclusions Baby wipes had an equivalent effect on skin hydration when compared with cotton wool and water. We found no evidence of any adverse effects of using these wipes. These findings offer reassurance to parents who choose to use baby wipes and to health professionals who support their use. Trial registration Current Controlled Trials ISRCTN8620701

The impact of viral mutations on recognition by SARS-CoV-2 specific T cells.

We identify amino acid variants within dominant SARS-CoV-2 T cell epitopes by interrogating global sequence data. Several variants within nucleocapsid and ORF3a epitopes have arisen independently in multiple lineages and result in loss of recognition by epitope-specific T cells assessed by IFN-γ and cytotoxic killing assays. Complete loss of T cell responsiveness was seen due to Q213K in the A∗01:01-restricted CD8+ ORF3a epitope FTSDYYQLY207-215; due to P13L, P13S, and P13T in the B∗27:05-restricted CD8+ nucleocapsid epitope QRNAPRITF9-17; and due to T362I and P365S in the A∗03:01/A∗11:01-restricted CD8+ nucleocapsid epitope KTFPPTEPK361-369. CD8+ T cell lines unable to recognize variant epitopes have diverse T cell receptor repertoires. These data demonstrate the potential for T cell evasion and highlight the need for ongoing surveillance for variants capable of escaping T cell as well as humoral immunity.This work is supported by the UK Medical Research Council (MRC); Chinese Academy of Medical Sciences(CAMS) Innovation Fund for Medical Sciences (CIFMS), China; National Institute for Health Research (NIHR)Oxford Biomedical Research Centre, and UK Researchand Innovation (UKRI)/NIHR through the UK Coro-navirus Immunology Consortium (UK-CIC). Sequencing of SARS-CoV-2 samples and collation of data wasundertaken by the COG-UK CONSORTIUM. COG-UK is supported by funding from the Medical ResearchCouncil (MRC) part of UK Research & Innovation (UKRI),the National Institute of Health Research (NIHR),and Genome Research Limited, operating as the Wellcome Sanger Institute. T.I.d.S. is supported by a Well-come Trust Intermediate Clinical Fellowship (110058/Z/15/Z). L.T. is supported by the Wellcome Trust(grant number 205228/Z/16/Z) and by theUniversity of Liverpool Centre for Excellence in Infectious DiseaseResearch (CEIDR). S.D. is funded by an NIHR GlobalResearch Professorship (NIHR300791). L.T. and S.C.M.are also supported by the U.S. Food and Drug Administration Medical Countermeasures Initiative contract75F40120C00085 and the National Institute for Health Research Health Protection Research Unit (HPRU) inEmerging and Zoonotic Infections (NIHR200907) at University of Liverpool inpartnership with Public HealthEngland (PHE), in collaboration with Liverpool School of Tropical Medicine and the University of Oxford.L.T. is based at the University of Liverpool. M.D.P. is funded by the NIHR Sheffield Biomedical ResearchCentre (BRC – IS-BRC-1215-20017). ISARIC4C is supported by the MRC (grant no MC_PC_19059). J.C.K.is a Wellcome Investigator (WT204969/Z/16/Z) and supported by NIHR Oxford Biomedical Research Centreand CIFMS. The views expressed are those of the authors and not necessarily those of the NIHR or MRC

Controlled intermittent shortening contractions of a muscle-tendon complex: muscle fibre damage and effects on force transmission from a single head of rat EDL

This study was performed to examine effects of prolonged (3 h) intermittent shortening (amplitude 2 mm) contractions (muscles were excited maximally) of head III of rat extensor digitorum longus muscle (EDL III) on indices of muscle damage and on force transmission within the intact anterior crural compartment. Three hours after the EDL III exercise, muscle fibre damage, as assessed by immunohistochemical staining of structural proteins (i.e. dystrophin, desmin, titin, laminin-2), was found in EDL, tibialis anterior (TA) and extensor hallucis longus (EHL) muscles. The damaged muscle fibres were not uniformly distributed throughout the muscle cross-sections, but were located predominantly near the interface of TA and EDL muscles as well as near intra- and extramuscular neurovascular tracts. In addition, changes were observed in desmin, muscle ankyrin repeat protein 1, and muscle LIM protein gene expression: significantly (P < 0.01) higher (1.3, 45.5 and 2.3-fold, respectively) transcript levels compared to the contralateral muscles. Post-EDL III exercise, length-distal force characteristics of EDL III were altered significantly (P < 0.05): at high EDL III lengths, active forces decreased and the length range between active slack length and optimum length increased. For all EDL III lengths tested, proximal passive and active force of EDL decreased. The slope of the EDL III length-TA + EHL force curve decreased, which indicates a decrease of the degree of intermuscular interaction between EDL III and TA + EHL. It is concluded that prolonged intermittent shortening contractions of a single head of multi-tendoned EDL muscle results in structural damage to muscle fibres as well as altered force transmission within the compartment. A possible role of myofascial force transmission is discussed. © Springer 2005