D-colorable digraphs with large girth

In 1959 Paul Erdos (Graph theory and probability, Canad. J. Math. 11 (1959), 34-38) famously proved, nonconstructively, that there exist graphs that have both arbitrarily large girth and arbitrarily large chromatic number. This result, along with its proof, has had a number of descendants (D. Bokal, G. Fijavz, M. Juvan, P.M. Kayll and B. Mohar, The circular chromatic number of a digraph, J. Graph Theory 46 (2004), 227-240; B. Bollobas and N. Sauer, Uniquely colourable graphs with large girth, Canad. J. Math. 28 (1976), 1340-1344; J. Nesetril and X. Zhu, On sparse graphs with given colorings and homomorphisms, J. Combin. Theory Ser. B 90 (2004), 161-172; X. Zhu, Uniquely H-colorable graphs with large girth, J. Graph Theory 23 (1996), 33-41) that have extended and generalized the result while strengthening the techniques used to achieve it. We follow the lead of Xuding Zhu (op. cit.) who proved that, for a suitable graph H, there exist graphs of arbitrarily large girth that are uniquely H-colorable. We establish an analogue of Zhu\u27s results in a digraph setting. Let C and D be digraphs. A mapping f:V(D)&rarr V(C) is a C-coloring if for every arc uv of D, either f(u)f(v) is an arc of C or f(u)=f(v), and the preimage of every vertex of C induces an acyclic subdigraph in D. We say that D is C-colorable if it admits a C-coloring and that D is uniquely C-colorable if it is surjectively C-colorable and any two C-colorings of D differ by an automorphism of C. We prove that if D is a digraph that is not C-colorable, then there exist graphs of arbitrarily large girth that are D-colorable but not C-colorable. Moreover, for every digraph D that is uniquely D-colorable, there exists a uniquely D-colorable digraph of arbitrarily large girth

Uniquely D-colourable digraphs with large girth

Let C and D be digraphs. A mapping $f:V(D)\to V(C)$ is a C-colouring if for every arc $uv$ of D, either $f(u)f(v)$ is an arc of C or $f(u)=f(v)$, and the preimage of every vertex of C induces an acyclic subdigraph in D. We say that D is C-colourable if it admits a C-colouring and that D is uniquely C-colourable if it is surjectively C-colourable and any two C-colourings of D differ by an automorphism of C. We prove that if a digraph D is not C-colourable, then there exist digraphs of arbitrarily large girth that are D-colourable but not C-colourable. Moreover, for every digraph D that is uniquely D-colourable, there exists a uniquely D-colourable digraph of arbitrarily large girth. In particular, this implies that for every rational number $r\geq 1$, there are uniquely circularly r-colourable digraphs with arbitrarily large girth.Comment: 21 pages, 0 figures To be published in Canadian Journal of Mathematic

Nitrogen plasma surface modification enhances cellular compatibility of aluminosilicate glass

The effect of Active Screen Plasma Nitriding (ASPN) treatment on the surface-cellular compatibility of an inert aluminosilicate glass surface has been investigated. ASPN is a novel surface engineering technique, the main advantage of which is the capacity to treat homogeneously all kind of materials surfaces of any shape. A conventional direct current nitriding unit has been used together with an active screen experimental arrangement. The material that was treated was an ionomer glass of the composition 4.5SiO2-3Al2O3-1.5P2O5-3CaO-2CaF2. The modified glass surface showed increased hardness and elastic modulus, decreased surface roughness. The incorporation of nitrogen-containing groups was confirmed using X-ray photoelectron spectroscopy. The modified surface favoured attachment and proliferation of NIH 3T3 fibroblasts

ARTP statement on pulmonary function testing 2020.

The Association for Respiratory Technology & Physiology (ARTP) last produced a statement on the performance of lung function testing in 1994. At that time the focus was on a practical statement for people working in lung function laboratories. Since that time there have been many technological advances and alterations to best practice in the measurement and interpretation of lung function assessments. In light of these advances an update was warranted. ARTP, therefore, have provided within this document, where available, the most up-to-date and evidence-based recommendations for the most common lung function assessments performed in laboratories across the UK. These recommendations set out the requirements and considerations that need to be made in terms of environmental and patient factors that may influence both the performance and interpretation of lung function tests. They also incorporate procedures to ensure quality assured diagnostic investigations that include those associated with equipment, the healthcare professional conducting the assessments and the results achieved by the subject. Each section aims to outline the common parameters provided for each investigation, a brief principle behind the measurements (where applicable), and suggested acceptability and reproducibility criteria

Nonacid reflux episodes reaching the pharynx are important factors associated with cough

BACKGROUND: Gastroesophageal reflux is implicated in the pathogenesis of asthma and chronic cough. To date most studies have focused on acid reflux measured by pH below the upper esophageal sphincter (UES). The aim of this study was to assess the relationship between cough and reflux through the UES into the pharynx. METHODS: Thirty-seven patients with asthma (19) and chronic cough (18) were recruited from the respiratory clinic. Reflux was monitored using a combined multichannel intraluminal impedance and pH probe by detecting (1) bolus reflux episodes within the esophagus and in the pharynx and (2) acidic reflux episodes within the esophagus and in the pharynx. All acid suppressive therapy was stopped for at least 7 days before the study. Demonstration of cough being linked to reflux was achieved using the symptom association probability (SAP). This was calculated using a 2-minute association window between symptoms and bolus entry into the esophagus. SAP was considered positive if >95%. RESULTS: A positive SAP for cough was noted in 7/26 patients reporting symptoms on the day of monitoring. Compared with SAP-negative patients, SAP-positive patients had both a greater number [median (interquartile range), 5(2 to 8) vs. 2(0 to 4), P<0.05] and a higher proportion of reflux episodes crossing the UES into the pharynx [25%(14% to 28%) vs. 7% (2% to 14%), P<0.02]. There was no difference in the number of reflux episodes or acid exposure time in the distal esophagus between SAP-positive and SAP-negative patients. Only 1% to 2% of episodes were detected by the pharyngeal pH sensor. CONCLUSIONS: Impedance detected pharyngeal reflux episodes are important factors in symptom production in cough patients

Pilot study of bevacizumab in combination with docetaxel and cyclophosphamide as adjuvant treatment for patients with early stage HER-2 negative breast cancer, including analysis of candidate circulating markers of cardiac toxicity: ICORG 08–10 trial.

Background: Combining bevacizumab and chemotherapy produced superior response rates compared with chemotherapy alone in metastatic breast cancer. As bevacizumab may cause hypertension (HTN) and increase the risk of cardiac failure, we performed a pilot study to evaluate the feasibility and toxicity of a non-anthracycline-containing combination of docetaxel with cyclophosphamide and bevacizumab in early stage breast cancer patients.Methods: Treatment consisted of four 3-weekly cycles of docetaxel and cyclophosphamide (75/600 mg/m2). Bevacizumab was administered 15 mg/kg intravenously on day 1, and then every 3 weeks to a total of 18 cycles of treatment. Serum biomarker concentrations of vascular endothelial growth factor (VEGF), cardiac troponin-I (cTnI), myeloperoxidase (MPO), and placental growth factor (PlGF) were quantified using enzyme-linked immunosorbent assay (ELISA) in 62 patients at baseline and whilst on treatment to determine their utility as biomarkers of cardiotoxicity, indicated by left ventricular ejection fraction (LVEF).Results: A total of 106 patients were accrued in nine sites. Median follow up was 65 months (1-72 months). Seventeen protocol-defined relapse events were observed, accounting for an overall disease-free survival (DFS) rate of 84%. The DFS rates for hormone receptor positive (HR+) and triple-negative (TN) patients were 95% versus 43%, respectively. The median time to relapse was 25 (12-54) months in TN patients versus 38 (22-71) months in HR+ patients. There have been 13 deaths related to breast cancer . The overall survival (OS) rate was 88%. The 5-year OS rate in HR+ versus TN was 95% versus 57%. None of the measured biomarkers predicted the development of cardiotoxicity.Conclusions: We observed a low relapse rate in node-positive, HR+ patients; however, results in TN breast cancer were less encouraging. Given the negative results of three large phase III trials, it is unlikely that this approach will be investigated further.Trial registration: ClinicalTrials.gov Identifier: NCT00911716.</p

Weight-bearing in ankle fractures: An audit of UK practice.

INTRODUCTION: The purpose of this national study was to audit the weight-bearing practice of orthopaedic services in the National Health Service (NHS) in the treatment of operatively and non-operatively treated ankle fractures. METHODS: A multicentre prospective two-week audit of all adult ankle fractures was conducted between July 3rd 2017 and July 17th 2017. Fractures were classified using the AO/OTA classification. Fractures fixed with syndesmosis screws or unstable fractures (>1 malleolus fractured or talar shift present) treated conservatively were excluded. No outcome data were collected. In line with NICE (The National Institute for Health and Care Excellence) criteria, "early" weight-bearing was defined as unrestricted weight-bearing on the affected leg within 3 weeks of injury or surgery and "delayed" weight-bearing as unrestricted weight-bearing permitted after 3 weeks. RESULTS: 251 collaborators from 81 NHS hospitals collected data: 531 patients were managed non-operatively and 276 operatively. The mean age was 52.6 years and 50.5 respectively. 81% of non-operatively managed patients were instructed for early weight-bearing as recommended by NICE. In contrast, only 21% of operatively managed patients were instructed for early weight-bearing. DISCUSSION: The majority of patients with uni-malleolar ankle fractures which are managed non-operatively are treated in accordance with NICE guidance. There is notable variability amongst and within NHS hospitals in the weight-bearing instructions given to patients with operatively managed ankle fractures. CONCLUSION: This study demonstrates community equipoise and suggests that the randomized study to determine the most effective strategy for postoperative weight-bearing in ankle fractures described in the NICE research recommendation is feasible

Open data from the first and second observing runs of Advanced LIGO and Advanced Virgo

Advanced LIGO and Advanced Virgo are monitoring the sky and collecting gravitational-wave strain data with sufficient sensitivity to detect signals routinely. In this paper we describe the data recorded by these instruments during their first and second observing runs. The main data products are gravitational-wave strain time series sampled at 16384 Hz. The datasets that include this strain measurement can be freely accessed through the Gravitational Wave Open Science Center at http://gw-openscience.org, together with data-quality information essential for the analysis of LIGO and Virgo data, documentation, tutorials, and supporting software