We prove a number of results related to a problem of Po-Shen Loh [9], which is equivalent to a problem in Ramsey theory. Let a = (a1, a2, a3) and b = (b1, b2, b3) be two triples of integers. Define a to be 2-less than b if ai < bi for at least two values of i, and define a sequence a1, …, am of triples to be 2-increasing if ar is 2-less than as whenever r < s. Loh asks how long a 2-increasing sequence can be if all the triples take values in {1, 2, …, n}, and gives a log* improvement over the trivial upper bound of n2 by using the triangle removal lemma. In the other direction, a simple construction gives a lower bound of n3/2. We look at this problem and a collection of generalizations, improving some of the known bounds, pointing out connections to other well-known problems in extremal combinatorics, and asking a number of further questions.

A study on ${Re} =2000$ and 4000 vortex rings colliding with V-walls with included angles of $\theta =30^{\circ }$ to 120 $^{\circ }$ has been conducted. Along the valley plane, higher Reynolds numbers and/or included angles of $\theta \leqslant 60^{\circ }$ lead to secondary/tertiary vortex-ring cores leapfrogging past the primary vortex-ring cores. The boundary layers upstream of the latter separate and the secondary/tertiary vortex-ring cores pair up with these wall-separated vortices to form small daisy-chained vortex dipoles. Along the orthogonal plane, primary vortex-ring cores grow bulbous and incoherent after collisions, especially as the included angle reduces. Secondary and tertiary vortex-ring core formations along this plane also lag those along the valley plane, indicating that they form by propagating from the wall surfaces to the orthogonal plane as the primary vortex ring gradually comes into contact with the entire V-wall. Circulation results show significant variations between the valley and orthogonal plane, and reinforce the notion that the collision behaviour for $\theta \leqslant 60^{\circ }$ is distinctively different from those at larger included angles. Vortex-core trajectories are compared to those for inclined-wall collisions, and secondary vortex-ring cores are found to initiate earlier for the V-walls, postulated to be a result of the opposing circumferential flows caused by the simultaneous collisions of both primary vortex-ring cores with the V-wall surfaces. These circumferential flows produce a bi-helical flow mode (Lim, Exp. Fluids, vol. 7, issue 7, 1989, pp. 453–463) that sees higher vortex compression levels along the orthogonal plane, which limit vortex stretching along the wall surfaces and produce secondary vortex rings earlier. Lastly, vortex structures and behaviour of the present collisions are compared to those associated with flat/inclined walls and round-cylinder-based collisions for a more systematic understanding of their differences.

There is a need for accurate, inexpensive and field-friendly methods to assess body composition in children. Bioelectrical impedance analysis (BIA) is a promising approach; however, there have been limited validation and use among young children in resource-poor settings. We aim to develop and validate population-specific prediction equations for estimating total fat mass (FM), fat free-mass (FFM) and percentage body fat (PBF) in Vietnamese children (4–7 years) using reactance and resistance from BIA, anthropometric variables and demographic information. We conducted a cross-sectional survey of 120 children. Body composition was measured using dual-energy X-ray absorptiometry (DXA), BIA and anthropometry. To develop prediction equations, we split all data into development (70 %) and validation datasets (30 %). The model performance was evaluated using predicted residual error sum of squares, root mean squared error (RMSE), mean absolute error (MAE) and R2. We identified a top performing model with the least number of parameters (age, sex, weight and resistance index or resistance and height), low RMSE (FM 0·70, FFM 0·74, PBF 3·10), low MAE (FM 0·55, FFM 0·62, PBF 2·49), high R2 (FM 0·95, FFM 0·92, PBF 0·82) and the least difference between predicted values and actual values from DXA (FM 0·03 kg or 0·01 sd, FFM 0·06 kg or 0·02 sd, PBF 0·27 % or 0·04 sd). In conclusion, we developed the first valid and highly predictive equations to estimate FM, FFM and PBF in Vietnamese children using BIA. These findings have important implications for future research on the double burden of disease and risks associated with overweight and obesity in young children.

Introduction: Rapid diagnostic algorithms using high-sensitivity cardiac troponin can rapidly diagnose or exclude acute myocardial infarction (MI). However, multiple algorithms have been proposed and it is unclear if some outperform others. The objective of this study was to prospectively compare the diagnostic performance of 1- and 2-hour algorithms in clinical practice in a Canadian population. Methods: Emergency department patients with chest pain had high-sensitivity cardiac troponin-T (hs-cTnT) collected on presentation and 1- and 2-hours later at a single academic tertiary hospital and regional percutaneous coronary intervention site over a 2-year period. The primary outcome was index MI, the secondary outcome was 30-day major adverse cardiac events (MACE). All outcomes were 2 physician adjudicated. Results: We enrolled 1,167 patients with hs-cTnT collected on ED presentation. Of these, 350 had a valid 1-hour and 550 had a 2-hour hs-cTnT sample. Index MI prevalence was ~11%. Sensitivity of the 1- and 2-hour algorithms for index MI was 97.3% (95% CI 85.8-99.9%) and 100% (95% CI 91.6-100%) and for 30-day MACE was 80.9% (95% CI 66.7-90.9%) and 83.3% (95% CI 73.2-90.8%), respectively. The 1-hour algorithm was 96.3% specific for index MI (95% CI 93.8-98.2%) whereas specificity for the 2-hour algorithm was 97.9% (95% CI 96.3-100%). Both algorithms classified about one-quarter of patients in an indeterminate observational zone with an ~11% MI prevalence. Conclusion: Both the 1- and 2-hour algorithms were highly sensitive and specific for MI, but were less sensitive for 30-day MACE. However, the 2-hour algorithm trended toward better performance, likely because its larger delta cutoffs reduce the risk of misclassification owing to analytic variability. These findings suggest algorithms using larger delta cutoffs may provide a greater margin of safety. Further comparative evaluation of rapid diagnostic algorithms using different cutoffs and characterization of patients in the observational zone is warranted.

Introduction: Very low high-sensitivity troponin-T (hs-cTnT) concentrations on presentation can rule out acute myocardial infarction (AMI), but the ability to identify patients at low risk of 30-day major adverse cardiac events (MACE) is less clear. This study examines the sensitivity of low concentrations of hs-cTnT on presentation to rule out 30-day MACE. Methods: This prospective cohort study enrolled emergency department chest pain patients with non-ischemic ECGs who underwent AMI rule-out with an hs-cTnT assay. The primary outcome was 30-day MACE; secondary outcomes were individual MACE components. Because guidelines recommend using a single hs-cTnT strategy only for patients with more than 3-hours since symptom onset, a subgroup analysis was performed for this population. Outcomes were adjudicated based on review of medical records and telephone follow-up. Results: Of 1,167 patients enrolled, 125 (10.7%) experienced 30-day MACE and 97 (8.3%) suffered AMI on the index visit. More than one-third (35.6%) had presenting hs-cTnT concentrations below the limit of detection (5ng/L), which was 94.4% (95%CI 88.8-97.7%) sensitive for 30-day MACE and 99.0% (95%CI 94.5-100%) sensitive for index AMI. Of 292 (25.0%) patients with hs-cTnT < 5ng/L and at least 3-hours since symptom onset, only 3 experienced 30-day MACE (sensitivity 97.6%, 95%CI 93.2-100%) and none suffered AMI within 30-days (sensitivity 100%, 95%CI 96.3-100%). Conclusion: Among patients with non-ischemic ECGs and >3-hours since symptom onset, low hs-cTnT concentrations on presentation confer a very low risk of 30-day MACE. In the absence of a high risk clinical presentation, further risk stratification is likely to be low yield.

There is strong evidence that foods containing dietary fibre protect against colorectal cancer, resulting at least in part from its anti-proliferative properties. This study aimed to investigate the effects of supplementation with two non-digestible carbohydrates, resistant starch (RS) and polydextrose (PD), on crypt cell proliferative state (CCPS) in the macroscopically normal rectal mucosa of healthy individuals. We also investigated relationships between expression of regulators of apoptosis and of the cell cycle on markers of CCPS. Seventy-five healthy participants were supplemented with RS and/or PD or placebo for 50 d in a 2 × 2 factorial design in a randomised, double-blind, placebo-controlled trial (the Dietary Intervention, Stem cells and Colorectal Cancer (DISC) Study). CCPS was assessed, and the expression of regulators of the cell cycle and of apoptosis was measured by quantitative PCR in rectal mucosal biopsies. SCFA concentrations were quantified in faecal samples collected pre- and post-intervention. Supplementation with RS increased the total number of mitotic cells within the crypt by 60 % (P = 0·001) compared with placebo. This effect was limited to older participants (aged ≥50 years). No other differences were observed for the treatments with PD or RS as compared with their respective controls. PD did not influence any of the measured variables. RS, however, increased cell proliferation in the crypts of the macroscopically-normal rectum of older adults. Our findings suggest that the effects of RS on CCPS are not only dose, type of RS and health status-specific but are also influenced by age.

Recent technological advances have led to unprecedented amounts of generated data that originate from the Web, sensor networks, and social media. Analytics in terms of defeasible reasoning – for example, for decision making – could provide richer knowledge of the underlying domain. Traditionally, defeasible reasoning has focused on complex knowledge structures over small to medium amounts of data, but recent research efforts have attempted to parallelize the reasoning process over theories with large numbers of facts. Such work has shown that traditional defeasible logics come with overheads that limit scalability. In this work, we design a new logic for defeasible reasoning, thus ensuring scalability by design. We establish several properties of the logic, including its relation to existing defeasible logics. Our experimental results indicate that our approach is indeed scalable and defeasible reasoning can be applied to billions of facts.

Bottom-heated convection in rotating spherical shells provides a simple analogue for many astrophysical and geophysical fluid systems. We construct a database of 74 three-dimensional numerical convection models to investigate the scaling behaviour of seven diagnostics over a range of Ekman $(10^{-6}\leqslant E\leqslant 10^{-3})$ and Rayleigh $(15\leqslant \widetilde{Ra}\leqslant 18\,000)$ numbers while using a Prandtl number of unity. Our configuration is chosen to model Earth’s core as defined by the fixed flux thermal boundary conditions, radius ratio $r_{i}/r_{o}$ of $0.35$ and a gravity profile that varies linearly with radius. The quantities of interest are the viscous and thermal boundary layer thickness, mean temperature gradient, mean interior temperature, Nusselt number, horizontal flow length scale, and Reynolds number. We find four parameter regimes characterised by different scaling behaviour. For $E\leqslant 10^{-4}$ and low $Ra$ the weakly nonlinear regime is characterised by a balance between viscous, Archimedean and Coriolis forces and the heat transfer is described by weakly nonlinear theory. At low $E$ and moderate $Ra$ , the rapidly rotating regime sees inertia take over from viscosity in the global force balance. In this regime the heat transfer scaling has increasing exponent with decreasing Ekman number and shows no saturation to the diffusion free $Ra^{3/2}E^{2}$ scaling. At high $Ra$ and all $E$ the importance of the Coriolis force gradually decreases and all diagnostics continually change in the transitional regime before approaching the scaling behaviour of non-rotating convection.

We describe the delivery of real-time feedback on hand hygiene compliance between healthcare personnel over a 3-year time period via a crowdsourcing web-based application. Feedback delivery as a metric can be used to examine and improve a culture of safety within a healthcare setting.

We present some results from the DRAGON simulations, a set of four direct N-body simulations of globular clusters (GCs) with a million stars and five percent initial (primordial) binaries. These simulations were undertaken with the NBODY6++GPU code, which allowed us to follow dynamical and stellar evolution of individual stars and binaries, formation and evolution of white dwarfs, neutron stars, and black holes, and the effect of a galactic tidal field. The simulations are the largest existing models of a realistic globular cluster over its full lifetime of 12 billion years. In particular we will show here an investigation of the population of binaries including compact objects (such as white dwarfs - cataclysmic variables and merging black hole binaries in the model as counterparts of LIGO/Virgo sources); their distribution in the cluster and evolution with time.

A piezoelectric biomedical microelectromechanical system (bioMEMS) cantilever device was designed and fabricated to act as either a sensing element for muscle tissue contraction or as an actuator to apply mechanical force to cells. The sensing ability of the piezoelectric cantilevers was shown by monitoring the electrical signal generated from the piezoelectric aluminum nitride in response to the contraction of iPSC-derived cardiomyocytes cultured on the piezoelectric cantilevers. Actuation was demonstrated by applying electrical pulses to the piezoelectric cantilever and observing bending via an optical detection method. This piezoelectric cantilever device was designed to be incorporated into body-on-a-chip systems.

Despite trends towards greater LGBTQ (lesbian, gay, bisexual, transgender, and queer) rights in industrialized democracies, the rights of sexual minorities have become increasingly politicized and restricted throughout Africa. Recognizing religion's central role in shaping attitudes toward gays and lesbians, we hypothesize that local religious diversity could expose individuals to alternative religious perspectives, engender tolerance toward marginalized communities, and therefore dislodge dogmatic beliefs about social issues. Employing cross-national Afrobarometer survey data from 33 countries with an index of district-level religious concentration, we find that respondents living in religiously pluralistic communities are 4–5 points more likely to express tolerance of homosexual neighbors (50% increase) compared to those in homogeneous locales. This effect is not driven by outlier countries, the existence of specific religious affiliations within diverse communities, respondents' religiosity, or other observable and latent factors at the country, sub-national, district, and individual level. Further robustness checks address potential threats to validity. We conclude that religious diversity can foster inclusion of sexual minorities in Africa.

Discrete episodes of overconsumption may induce a positive energy balance and impair metabolic control. However, the effects of an ecologically relevant, single day of balanced macronutrient overfeeding are unknown. Twelve healthy men (of age 22 (sd 2) years, BMI 26·1 (sd 4·2) kg/m2) completed two 28 h, single-blind experimental trials. In a counterbalanced repeated measures design, participants either consumed their calculated daily energy requirements (energy balance trial (EB): 10 755 (sd 593) kJ) or were overfed by 50 % (overfeed trial (OF): 16 132 (sd 889) kJ) under laboratory supervision. Participants returned to the laboratory the next day, after an overnight fast, to complete a mixed-meal tolerance test (MTT). Appetite was not different between trials during day 1 (P>0·211) or during the MTT in the fasted or postprandial state (P>0·507). Accordingly, plasma acylated ghrelin, total glucagon-like peptide-1 and total peptide YY concentrations did not differ between trials during the MTT (all P>0·335). Ad libitum energy intake, assessed upon completion of the MTT, did not differ between trials (EB 6081 (sd 2260) kJ; OF 6182 (sd 1960) kJ; P=0·781). Plasma glucose and insulin concentrations were not different between trials (P>0·715). Fasted NEFA concentrations were lower in OF compared with EB (P=0·005), and TAG concentrations increased to a greater extent on OF than on EB during the MTT (P=0·009). The absence of compensatory changes in appetite-related variables after 1 d of mixed macronutrient overfeeding highlights the limited physiological response to defend against excess energy intake. This supports the concept that repeated discrete episodes of overconsumption may promote weight gain, while elevations in postprandial lipaemia may increase CVD risk.