Similar dissection of sets

In 1994, Martin Gardner stated a set of questions concerning the dissection of a square or an equilateral triangle in three similar parts. Meanwhile, Gardner's questions have been generalized and some of them are already solved. In the present paper, we solve more of his questions and treat them in a much more general context. Let $D\subset \mathbb{R}^d$ be a given set and let $f_1,...,f_k$ be injective continuous mappings. Does there exist a set $X$ such that $D = X \cup f_1(X) \cup ... \cup f_k(X)$ is satisfied with a non-overlapping union? We prove that such a set $X$ exists for certain choices of $D$ and $\{f_1,...,f_k\}$. The solutions $X$ often turn out to be attractors of iterated function systems with condensation in the sense of Barnsley. Coming back to Gardner's setting, we use our theory to prove that an equilateral triangle can be dissected in three similar copies whose areas have ratio $1:1:a$ for $a \ge (3+\sqrt{5})/2$

Gender-specific effects of COVID-19 lockdowns on scientific publishing productivity: Impact and resilience

Available online 3 February 2023Rationale: The SARS-CoV2 pandemic led to drastic social restrictions globally. Early data suggest that women in science have been more adversely affected by these lockdowns than men, with relatively fewer scientific articles authored by women. However, these observations test broad populations with many potential causes of disparity. Australia presents a natural experimental condition where several states of similar demographics and disease impact had differing approaches in their social isolation strategies. The state of Victoria experienced 280 days of lockdowns from 2020 to 2021, whereas the comparable state of New South Wales experienced 107 days, most of these in 2021, and other states even fewer restrictions. Objective and methods: To assess how the gender balance changed in Australian biomedical publishing with the lockdowns, we created a custom workflow to analyse PubMed data from more than 120,000 published articles submitted in 2019–2021 from Australian authors. Results: Broadly, Australian women have been incredibly resilient to the challenges faced by the lockdowns. There was an increase in the number of published articles submitted in 2020 that was equally due to women as men, including from Victoria. On the other hand, articles specifically addressing COVID-19 were significantly less likely to be authored by women than those on other topics, a finding not likely due to particular gender imbalance in virology or viral epidemiology, since publications on HIV followed similar patterns to previous years. By 2021, this imbalance had reversed, with more COVID-19-related papers authored by women than men. Conclusions: These data suggest women from Victoria were less able to rapidly transition to new research early in the pandemic but had accommodated to the new conditions by 2021. This work indicates we need strategies to support women in science as the pandemic continues and to continue to monitor the situation for its impact on vulnerable groups.M. Ryan, J. Tuke, M.R. Hutchinson, S.J. Spence

Comparison of case note review methods for evaluating quality and safety in health care

Objectives: To determine which of two methods of case note review – holistic (implicit) and criterion-based (explicit) – provides the most useful and reliable information for quality and safety of care, and the level of agreement within and between groups of health-care professionals when they use the two methods to review the same record. To explore the process–outcome relationship between holistic and criterion-based quality-of-care measures and hospital-level outcome indicators. © 2010 Crown Copyrigh

Complex differences in infection rates between ethnic groups in Scotland: a retrospective, national census-linked cohort study of 1.65 million cases

Background Ethnicity can influence susceptibility to infection, as COVID-19 has shown. Few countries have systematically investigated ethnic variations in infection. Methods We linked the Scotland 2001 Census, including ethnic group, to national databases of hospitalizations/deaths and serological diagnoses of bloodborne viruses for 2001–2013. We calculated age-adjusted rate ratios (RRs) in 12 ethnic groups for all infections combined, 15 infection categories, and human immunodeficiency virus (HIV), hepatitis B (HBV) and hepatitis C (HCV) viruses. Results We analysed over 1.65 million infection-related hospitalisations/deaths. Compared with White Scottish, RRs for all infections combined were 0.8 or lower for Other White British, Other White and Chinese males and females, and 1.2–1.4 for Pakistani and African males and females. Adjustment for socioeconomic status or birthplace had little effect. RRs for specific infection categories followed similar patterns with striking exceptions. For HIV, RRs were 136 in African females and 14 in males; for HBV, 125 in Chinese females and 59 in males, 55 in African females and 24 in males; and for HCV, 2.3–3.1 in Pakistanis and Africans. Conclusions Ethnic differences were found in overall rates and many infection categories, suggesting multiple causative pathways. We recommend census linkage as a powerful method for studying the disproportionate impact of COVID-19

Evaluation of a general practice based Hepatitis C virus screening intervention

In 2003 an estimated 37,500 of Scotland's population was chronically infected with HCV; 44% were undiagnosed former injecting drug users (IDU) - a priority group for arrival therapy. Aims to evaluate a hepatitis C virus (HCV) screening intervention. Outcomes measures among two similar general practice populations in an area of high HCV and drug use prevalence, one of which was exposed to an HCV screening intervention, were compared. Thirty to fifty four year old attendees of the intervention practice were opportunistically offered testing and counselling, where clinically appropriate, (November 2003 - April 2004). Outcomes: HCV test uptake, case detection, referral and treatment administration rates. Of 584 eligible attendees, 421 (72%) were offered and 117 (28%) accepted testing in the intervention practice; no testing was undertaken in the comparison practice. Prevalences of HCV antibody were 13% (15/117), 75% (3/4) and 91% (10/11) among all tested persons, current IDUs and former IDUs respectively. For 4/15 (27%) evidence of binge drinking following the receipt of their positive result, was available. Of the 11 referred to specialist care because they were HCV RNA positive, nine attended at least one appointment. Two received treatment: one had achieved a sustained viral response as of February 2008. While non targeted HCV screening in the general practice setting can detect infected former IDU, the low diagnostic yield among non IDUs limited the effectiveness of the intervention. A more targeted approach for identifying former IDUs is recommended. Additionally, the low uptake of treatment among chronically infected persons four years after diagnosis demonstrates the difficulties in clinically managing such individuals. Strategies, including support for those with a history of problem alcohol use, to improve treatment uptake are required