This paper is concerned with developing low variance simulation estimators of probabilities related to the sum of Bernoulli random variables. It shows how to utilize an identity used in the Chen-Stein approach to bounding Poisson approximations to obtain low variance estimators. Applications and numerical examples in such areas as pattern occurrences, generalized coupon collecting, system reliability, and multivariate normals are presented. We also consider the problem of estimating the probability that a positive linear combination of Bernoulli random variables is greater than some specified value, and present a simulation estimator that is always less than the Markov inequality bound on that probability.

Sex and gender are important factors that impact cardiometabolic traits. Men have lower life expectancy and higher prevalence of fatal chronic conditions at younger age. Lifestyle risk profiles in young men have been rarely studied in the context of cardiometabolic health. This review aimed to summarise the evidence regarding the patterns of dietary-lifestyle behaviours in a population of young men (age <40years) and their associations with cardiometabolic health. Overall, unfavourable clusters of health behaviours are more prominent in men, when compared to women and more prevalent in younger adults, when compared to older age groups. Early signs of cardiometabolic health abnormalities have been reported among men with higher adherence to patterns which consistently shared poor dietary habits as a common denominator, combined with stimulant use, inadequate sleep or insufficient physical activity. In the majority of studies, dietary assessment was limited to the investigation of one or two behaviours, most frequently fruit and vegetable intake. Since young men may engage in a mixture of explicit behaviours, the examination of a singular dietary habit may not represent the overall diet quality. To conclude, the data regarding the synergistic effects of a broad spectrum of dietary and lifestyle behaviours in the context of cardiometabolic health remain scarce in this population. The inclusion of a broader range of dietary and lifestyle variables into the multicomponent pattern analysis might have a greater potential in explaining the association with cardiometabolic health. Defining behavioural clusters can help to develop interventions, tailored to the specific needs of the targeted group.

Growing evidence has emerged about the role of dietary patterns and components in heart failure (HF) incidence and severity. The objective here is to provide a comprehensive summary of the current evidence regarding dietary patterns/components and HF. A comprehensive search of online databases was conducted using multiple relevant keywords to identify relevant human studies. The Dietary Approaches to Stop Hypertension (DASH) and Mediterranean diets have consistently been associated with decreased HF incidence and severity. Regarding specific dietary components, fruit, vegetables, legumes and whole grains appear beneficial. Current evidence suggests that red/processed meats, eggs and refined carbohydrates are harmful, while fish, dairy products and poultry remain controversial. However, there is a notable lack of human intervention trials. The existing but limited observational and interventional evidence from human studies suggests that a plant-based dietary pattern high in antioxidants, micronutrients, nitrate and fibre but low in saturated/trans-fat and Na may decrease HF incidence/severity. Potential mechanisms include decreased oxidative stress, homocysteine and inflammation but higher antioxidant defence and NO bioavailability and gut microbiome modulation. Randomised, controlled trials are urgently required.

Adam Smith has long been celebrated as a polymath, and his wide interests in and contributions to each of the discrete component fields of PPE have long been appreciated. Yet Smith deserves the attention of practitioners of PPE today not simply for his substantive insights, but for the ways in which his inquiries into these different fields were connected. Smith’s inquiry was distinguished by a synthetic approach to knowledge generation, and specifically to generating knowledge with applications exportable to other fields. Further, Smith’s investigations of various areas of study led him to recognize patterns in and across these fields, and his sensitivity to such patterns helped guide his inquiry and render it a connected enterprise. This paper examines several of Smith’s discrete inquiries in the history of astronomy, language, moral philosophy, and political economy, to show how he employed the techniques of pattern detection that he practiced in each of these inquiries to the task of generating new insights into new fields of inquiry. In so doing, Smith not only distinguished himself as an early practitioner of what we today identify with PPE, but he also provides a useful point of reference for those doing PPE today.

Introduction: Traumatic brain injury (TBI) is a leading cause of death and disability in Nova Scotia. TBI occurs in approximately 50% of major trauma seen annually in the province. The purpose of this study was to describe the characteristics and patterns of major TBI seen in Nova Scotia over a 12-year period. Methods: This was a retrospective case series. Data were obtained from the Nova Scotia Trauma Registry for all patients presenting with major TBI (abbreviated injury score [AIS] head ≥3) between 2002 and 2013. Injury rates were calculated on the basis of 100,000 population (all ages) using population estimates from Statistics Canada. Results: Overall, 4152 major TBI patients were seen in Nova Scotia hospitals during the study period. Mean age of TBI patients was 51±25 years; 73% were male. The majority of injuries were the result of blunt trauma (93%), with relatively few major TBIs resulting from penetrating trauma (7%). The most common mechanisms of injury were falls (44%) and motor vehicle crashes (27%). Analysis of census-based subpopulations of the province showed that injury rates varied significantly among counties (from 25 to 63 per 100,000 population). We observed an increase in the number of major TBI patients over twelve years. Conclusion: Our findings suggest significant regional variation in major TBI rates in Nova Scotia. There are ongoing needs for prevention and intervention efforts that focus on unintentional falls and motor vehicle crashes, especially in older adults. These results also suggest that geographically targeted efforts may be warranted.

Specific dietary patterns are associated with the risk of chronic disease. An in-depth understanding more reflective of lifestyle would be possible when assessing the synergistic effects of both diet and physical activity in pattern analysis. In the present study, we examined the biochemical markers of dysglycaemia and cardiometabolic risk in relation to lifestyle patterns using principal component analysis (PCA). Urban women (n 2800) aged 30–45 years were screened for dysglycaemia using cluster sampling from the Colombo Municipal Council area. All the 272 dysglycaemic women detected through screening and 345 randomly selected normoglycaemic women were enrolled. The International Physical Activity Questionnaire and a quantitative FFQ were used to assess physical activity and diet, respectively. Anthropometric measurements, bioelectrical impedance analysis and biochemical estimations were carried out. Lifestyle patterns were identified based on dietary and physical activity data using exploratory factor analysis. PCA was used for the extraction of factors. A total of three lifestyle patterns were identified. Women who were predominantly physically inactive and consumed snacks and dairy products had the greatest cardiometabolic risk, with a higher likelihood of having unfavourable obesity indices (increased waist circumference, fat mass percentage and BMI and decreased fat-free mass percentage), glycaemic indices (increased glycosylated Hb (HbA1c) and fasting blood sugar concentrations) and lipid profile (increased total cholesterol/TAG and decreased HDL-cholesterol concentrations) and increased high-sensitivity C-reactive protein concentrations. For the first time, we report lifestyle patterns and demonstrate the synergistic effects of physical activity/inactivity and diet and their relative association with cardiometabolic risk in urban women. Lifestyle pattern analysis greatly increases our understanding of high-risk behaviours occurring within real-life complexities.

Pattern avoidance is an important topic in combinatorics on words which dates back to the beginning of the twentieth century when Thue constructed an infinite word over a ternary alphabet that avoids squares, i.e., a word with no two adjacent identical factors. This result finds applications in various algebraic contexts where more general patterns than squares are considered. On the other hand, Erdős raised the question as to whether there exists an infinite word that avoids abelian squares, i.e., a word with no two adjacent factors being permutations of one another. Although this question was answered affirmately years later, knowledge of abelian pattern avoidance is rather limited. Recently, (abelian) pattern avoidance was initiated in the more general framework of partial words, which allow for undefined positions called holes. In this paper, we show that any pattern p with n> 3 distinct variables of length at least 2n is abelian avoidable by a partial word with infinitely many holes, the bound on the length of p being tight. We complete the classification of all the binary and ternary patterns with respect to non-trivial abelian avoidability, in which no variable can be substituted by only one hole. We also investigate the abelian avoidability indices of the binary and ternary patterns.

The use of criminal-law powers to respond to people with HIV who place others at risk of HIV infection has emerged as a focal point of AIDS advocacy at global, national, and local levels. In the Canadian context, reform efforts that address the criminalization of HIV non-disclosure have been hampered by the absence of data on the contours, scale, and outcomes of criminalization. This article responds to that gap in knowledge with the first comprehensive analysis of the temporal trends, demographic patterns, and aggregate outcomes of Canadian criminal cases of HIV non-disclosure. The authors draw on insights into the role that rendering social phenomena in numerical terms plays for the governance of social life in order to make criminalization “visible” in ways that might contribute to activist responses. The article examines temporal trends, demographic patterns, and outcomes separately. In each instance, the pattern or trend identified is described, potential explanations for findings are offered, and an account is given of how the data have informed efforts to reform criminal law. Particular attention is paid to the following key findings: a sharp increase in criminal cases that began in 2004; the large proportion of recent criminal cases involving defendants who are heterosexual Black, African, and Caribbean men; and the high proportion of criminal cases resulting in conviction. The article closes with suggestions for future research.