Edge Partitions of Optimal 22-plane and 33-plane Graphs

A topological graph is a graph drawn in the plane. A topological graph is $k$-plane, $k>0$, if each edge is crossed at most $k$ times. We study the problem of partitioning the edges of a $k$-plane graph such that each partite set forms a graph with a simpler structure. While this problem has been studied for $k=1$, we focus on optimal $2$-plane and $3$-plane graphs, which are $2$-plane and $3$-plane graphs with maximum density. We prove the following results. (i) It is not possible to partition the edges of a simple optimal $2$-plane graph into a $1$-plane graph and a forest, while (ii) an edge partition formed by a $1$-plane graph and two plane forests always exists and can be computed in linear time. (iii) We describe efficient algorithms to partition the edges of a simple optimal $2$-plane graph into a $1$-plane graph and a plane graph with maximum vertex degree $12$, or with maximum vertex degree $8$ if the optimal $2$-plane graph is such that its crossing-free edges form a graph with no separating triangles. (iv) We exhibit an infinite family of simple optimal $2$-plane graphs such that in any edge partition composed of a $1$-plane graph and a plane graph, the plane graph has maximum vertex degree at least $6$ and the $1$-plane graph has maximum vertex degree at least $12$. (v) We show that every optimal $3$-plane graph whose crossing-free edges form a biconnected graph can be decomposed, in linear time, into a $2$-plane graph and two plane forests

MOSFiT: Modular open source fitter for transients

Much of the progress made in time-domain astronomy is accomplished by relating observational multi-wavelength time series data to models derived from our understanding of physical laws. This goal is typically accomplished by dividing the task in two: collecting data (observing), and constructing models to represent that data (theorizing). Owing to the natural tendency for specialization, a disconnect can develop between the best available theories and the best available data, potentially delaying advances in our understanding new classes of transients. We introduce MOSFiT: the Modular Open-Source Fitter for Transients, a Python-based package that downloads transient datasets from open online catalogs (e.g., the Open Supernova Catalog), generates Monte Carlo ensembles of semi-analytical light curve fits to those datasets and their associated Bayesian parameter posteriors, and optionally delivers the fitting results back to those same catalogs to make them available to the rest of the community. MOSFiT is designed to help bridge the gap between observations and theory in time-domain astronomy; in addition to making the application of existing models and creation of new models as simple as possible, MOSFiT yields statistically robust predictions for transient characteristics, with a standard output format that includes all the setup information necessary to reproduce a given result. As large-scale surveys such as LSST discover entirely new classes of transients, tools such as MOSFiT will be critical for enabling rapid comparison of models against data in statistically consistent, reproducible, and scientifically beneficial ways

Foot health education for people with rheumatoid arthritis : the practitioner's perspective

Background: Patient education is considered to be a key role for podiatrists in the management of patients with rheumatoid arthritis (RA). Patient education has undoubtedly led to improved clinical outcomes, however no attempts have been made to optimise its content or delivery to maximise benefits within the context of the foot affected by rheumatoid arthritis. The aim of this study was to identify the nature and content of podiatrists' foot health education for people with RA. Any potential barriers to its provision were also explored. Methods: A focus group was conducted. The audio dialogue was recorded digitally, transcribed verbatim and analysed using a structured, thematic approach. The full transcription was verified by the focus group as an accurate account of what was said. The thematic analysis framework was verified by members of the research team to ensure validity of the data. Results: Twelve members (all female) of the north west Podiatry Clinical Effectiveness Group for Rheumatology participated. Six overarching themes emerged: (i) the essence of patient education; (ii) the content; (iii) patient-centred approach to content and timing; (iv) barriers to provision; (v) the therapeutic relationship; and (vi) tools of the trade. Conclusion: The study identified aspects of patient education that this group of podiatrists consider most important in relation to its: content, timing, delivery and barriers to its provision. General disease and foot health information in relation to RA together with a potential prognosis for foot health, the role of the podiatrist in management of foot health, and appropriate self-management strategies were considered to be key aspects of content, delivered according to the needs of the individual. Barriers to foot health education provision, including financial constraints and difficulties in establishing effective therapeutic relationships, were viewed as factors that strongly influenced foot health education provision. These data will contribute to the development of a patient-centred, negotiated approach to the provision of foot health education for people with RA

Daily emollient during infancy for prevention of eczema: the BEEP randomised controlled trial.

BACKGROUND: Skin barrier dysfunction precedes eczema development. We tested whether daily use of emollient in the first year could prevent eczema in high-risk children. METHODS: We did a multicentre, pragmatic, parallel-group, randomised controlled trial in 12 hospitals and four primary care sites across the UK. Families were approached via antenatal or postnatal services for recruitment of term infants (at least 37 weeks' gestation) at high risk of developing eczema (ie, at least one first-degree relative with parent-reported eczema, allergic rhinitis, or asthma, diagnosed by a doctor). Term newborns with a family history of atopic disease were randomly assigned (1:1) to application of emollient daily (either Diprobase cream or DoubleBase gel) for the first year plus standard skin-care advice (emollient group) or standard skin-care advice only (control group). The randomisation schedule was created using computer-generated code (stratified by recruiting centre and number of first-degree relatives with atopic disease) and participants were assigned to groups using an internet-based randomisation system. The primary outcome was eczema at age 2 years (defined by UK working party criteria) with analysis as randomised regardless of adherence to allocation for participants with outcome data collected, and adjusting for stratification variables. This trial is registered with ISRCTN, ISRCTN21528841. Data collection for long-term follow-up is ongoing, but the trial is closed to recruitment. FINDINGS: 1394 newborns were randomly assigned to study groups between Nov 19, 2014, and Nov 18, 2016; 693 were assigned to the emollient group and 701 to the control group. Adherence in the emollient group was 88% (466 of 532) at 3 months, 82% (427 of 519) at 6 months, and 74% (375 of 506) at 12 months in those with complete questionnaire data. At age 2 years, eczema was present in 139 (23%) of 598 infants with outcome data collected in the emollient group and 150 (25%) of 612 infants in the control group (adjusted relative risk 0·95 [95% CI 0·78 to 1·16], p=0·61; adjusted risk difference -1·2% [-5·9 to 3·6]). Other eczema definitions supported the results of the primary analysis. Mean number of skin infections per child in year 1 was 0·23 (SD 0·68) in the emollient group versus 0·15 (0·46) in the control group; adjusted incidence rate ratio 1·55 (95% CI 1·15 to 2·09). INTERPRETATION: We found no evidence that daily emollient during the first year of life prevents eczema in high-risk children and some evidence to suggest an increased risk of skin infections. Our study shows that families with eczema, asthma, or allergic rhinitis should not use daily emollients to try and prevent eczema in their newborn. FUNDING: National Institute for Health Research Health Technology Assessment

Daily emollient during infancy for prevention of eczema: the BEEP randomised controlled trial.

BACKGROUND: Skin barrier dysfunction precedes eczema development. We tested whether daily use of emollient in the first year could prevent eczema in high-risk children. METHODS: We did a multicentre, pragmatic, parallel-group, randomised controlled trial in 12 hospitals and four primary care sites across the UK. Families were approached via antenatal or postnatal services for recruitment of term infants (at least 37 weeks' gestation) at high risk of developing eczema (ie, at least one first-degree relative with parent-reported eczema, allergic rhinitis, or asthma, diagnosed by a doctor). Term newborns with a family history of atopic disease were randomly assigned (1:1) to application of emollient daily (either Diprobase cream or DoubleBase gel) for the first year plus standard skin-care advice (emollient group) or standard skin-care advice only (control group). The randomisation schedule was created using computer-generated code (stratified by recruiting centre and number of first-degree relatives with atopic disease) and participants were assigned to groups using an internet-based randomisation system. The primary outcome was eczema at age 2 years (defined by UK working party criteria) with analysis as randomised regardless of adherence to allocation for participants with outcome data collected, and adjusting for stratification variables. This trial is registered with ISRCTN, ISRCTN21528841. Data collection for long-term follow-up is ongoing, but the trial is closed to recruitment. FINDINGS: 1394 newborns were randomly assigned to study groups between Nov 19, 2014, and Nov 18, 2016; 693 were assigned to the emollient group and 701 to the control group. Adherence in the emollient group was 88% (466 of 532) at 3 months, 82% (427 of 519) at 6 months, and 74% (375 of 506) at 12 months in those with complete questionnaire data. At age 2 years, eczema was present in 139 (23%) of 598 infants with outcome data collected in the emollient group and 150 (25%) of 612 infants in the control group (adjusted relative risk 0·95 [95% CI 0·78 to 1·16], p=0·61; adjusted risk difference -1·2% [-5·9 to 3·6]). Other eczema definitions supported the results of the primary analysis. Mean number of skin infections per child in year 1 was 0·23 (SD 0·68) in the emollient group versus 0·15 (0·46) in the control group; adjusted incidence rate ratio 1·55 (95% CI 1·15 to 2·09). INTERPRETATION: We found no evidence that daily emollient during the first year of life prevents eczema in high-risk children and some evidence to suggest an increased risk of skin infections. Our study shows that families with eczema, asthma, or allergic rhinitis should not use daily emollients to try and prevent eczema in their newborn. FUNDING: National Institute for Health Research Health Technology Assessment

Representations of an integer by some quaternary and octonary quadratic forms

In this paper we consider certain quaternary quadratic forms and octonary quadratic forms and by using the theory of modular forms, we find formulae for the number of representations of a positive integer by these quadratic forms.Comment: 20 pages, 4 tables. arXiv admin note: text overlap with arXiv:1607.0380

How to use the HOME Core Outcome Set for atopic dermatitis trials - a users' guide

The Harmonizing Outcome Measures for Eczema (HOME) initiative has agreed upon the core outcome set for use in atopic dermatitis (AD) clinical trials, but additional guidance is needed to maximise uptake of the core set. This article provides answers to some of the commonly asked questions about using the HOME core outcome set. It also provides data to aid interpretation of trial results and to support sample size calculations for future trials. By encouraging adoption of the core outcome set and facilitating consistent reporting of outcome data, we hope that results of eczema trials will be more comprehensive and readily combined in meta-analyses and patient care will be improved

Attenuating Effect of Vigorous Physical Activity on the Risk for Inherited Obesity: A Study of 47,691 Runners

Objective: Physical activity has been shown to attenuate the effect of the FTO polymorphism on body weight, and the heritability of body weight in twin and in family studies. The dose-response relationship between activity and the risk for inherited obesity is not well known, particularly for higher doses of vigorous exercise. Such information is needed to best prescribe an exercise dose for obesity prevention in those at risk due to their family history. Design: We therefore analyzed self-reported usual running distance, body mass index (BMI), waist circumference, and mother’s and father’s adiposity (1 = lean, 2 = normal, 3 = overweight, and 4 = very overweight) from survey data collected on 33,480 male and 14,211 female runners. Age-, education-, and alcohol-adjusted regression analyses were used to estimate the contribution of parental adiposities to the BMI and waist circumferences in runners who ran an average of,3, 3–6, 6–9, $9 km/day. Results: BMI and waist circumferences of runners who ran,3 km/day were significantly related to their parents adiposity (P,10 215 and P,10 211, respectively). These relationships (i.e., kg/m 2 or cm per increment in parental adiposity) diminished significantly with increasing running distance for both BMI (inheritance6exercise interaction, males: P,10 210; females: P,10 25) and waist circumference (inheritance6exercise interaction, males: P,10 29; females: P = 0.004). Compared to,3 km/day, the parental contribution to runners who averaged$9 km/day was diminished by 48 % for male BMI, 58 % for female BMI, 55 % for male waist circumference, and 58 % for female waist circumference. These results could not b

Quantile-Specific Penetrance of Genes Affecting Lipoproteins, Adiposity and Height

Quantile-dependent penetrance is proposed to occur when the phenotypic expression of a SNP depends upon the population percentile of the phenotype. To illustrate the phenomenon, quantiles of height, body mass index (BMI), and plasma lipids and lipoproteins were compared to genetic risk scores (GRS) derived from single nucleotide polymorphisms (SNP)s having established genome-wide significance: 180 SNPs for height, 32 for BMI, 37 for low-density lipoprotein (LDL)-cholesterol, 47 for high-density lipoprotein (HDL)-cholesterol, 52 for total cholesterol, and 31 for triglycerides in 1930 subjects. Both phenotypes and GRSs were adjusted for sex, age, study, and smoking status. Quantile regression showed that the slope of the genotype-phenotype relationships increased with the percentile of BMI (P = 0.002), LDL-cholesterol (P = 3×10−8), HDL-cholesterol (P = 5×10−6), total cholesterol (P = 2.5×10−6), and triglyceride distribution (P = 7.5×10−6), but not height (P = 0.09). Compared to a GRS's phenotypic effect at the 10th population percentile, its effect at the 90th percentile was 4.2-fold greater for BMI, 4.9-fold greater for LDL-cholesterol, 1.9-fold greater for HDL-cholesterol, 3.1-fold greater for total cholesterol, and 3.3-fold greater for triglycerides. Moreover, the effect of the rs1558902 (FTO) risk allele was 6.7-fold greater at the 90th than the 10th percentile of the BMI distribution, and that of the rs3764261 (CETP) risk allele was 2.4-fold greater at the 90th than the 10th percentile of the HDL-cholesterol distribution. Conceptually, it maybe useful to distinguish environmental effects on the phenotype that in turn alters a gene's phenotypic expression (quantile-dependent penetrance) from environmental effects affecting the gene's phenotypic expression directly (gene-environment interaction)