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On product Schur triples in the integers
No full textSchur’s theorem states that in any k-coloring of the set of integers [n] there is a monochromatic solution to a + b = c , provided n is sufficiently large. Abbott and Wang studied the size of the largest subset of [n] such that there is a k-coloring avoiding a monochromatic a + b = c. This led to the exploration of related problems, such as the minimum number of monochromatic a + b = c in k-colorings of [n] and the probability threshold for a random subset of [n] to have a monochromatic a + b = c in any k-coloring. In this paper, we study natural generalizations of these problems to products ab = c, in deterministic, random, and randomly perturbed environments
Digital care planning in care homes for older people: perspectives of unpaid carers and care practitioners
No full textCan science diplomacy keep up with a world in crisis?
No full textA new report from the Royal Society and AAAS updates their 2010 vision of the relationship between science and diplomacy, trading optimism for realism. Matthew Adamson, Sam Robinson, Gordon Barrett and Lif Jacobsen argue that the new framework flattens the messy realities of power, politics and expertise. Rather than forging harmony, they write, science diplomacy must be seen as a way to navigate complexity
Digital storytelling as an act of academic courage
No full textResearch is often framed as a pursuit of knowledge – rigorous, methodical, and objective. Yet, beneath this structure lies a deeper question: what stories emanate from these endeavours and who are they for? Annalena Oppel proposes that a renewed engagement with storytelling, and specifically digital storytelling, presents an opportunity for research and researchers to reconnect with their original motivations and engage in collective action. However, to do so requires the courage to resist increasingly institutionalised and isolating forms of scholarship
Apprenticeship and economic growth in early modern England
No full textIn this extract from the introduction to his new book, The Market for Skill: Apprenticeship and Economic Growth in Early Modern England, Patrick Wallis explains how apprenticeship transformed England’s workforce from the 16th to 19th century, fostering human capital, innovation, urbanisation and economic growth. The Market for Skill: Apprenticeship and Economic Growth in Early Modern England. Patrick Wallis. Princeton University Press. 2025
How the Labour heartlands lost their faith in politics
No full textThe loss of the Red Wall might not be just Labour’s problem. Sacha Hilhorst writes that voters in ex-mining constituencies are not only disappointed with Labour, but with all politicians who they see as self-interested and corrupt. Reform UK, however, are set to reap the rewards of these disaffected voters
Ethnic disparities in sentencing and the perception of fairness
No full textThe publication of new guidelines on pre-sentencing reports by the Sentencing Council focussing on offenders from ethnic and faith minorities has sparked claims of “two-tier justice”. Eoin Guilfoyle, Jose Pina Sanchez and Sara Geneletti defend the intentions of the new guidelines, but argue that it’s important that they not only contribute to greater fairness in sentencing, but that they are also perceived to do so by the public
Should cohabiting siblings be offered legal protection?
No full textFamily life takes many different forms. But when it comes to the legal recognition and protection of these different forms, the law has yet to catch up. Sarah Trotter looks into the debates over the legal recognition and protection of cohabiting (adult) siblings in the UK, and extends an invitation to those who share experience in this domain to participate in her research project
A multinational cohort study of trends in survival following dementia diagnosis
No full textAbatract: Background: Information on the survival of people living with dementia over time and across systems can help policymakers understand the real-world impact of dementia on health and social care systems. This multinational cohort study examines the trends in relative mortality risk following a dementia diagnosis. Methods: A common protocol was applied to population-based data from the UK, Germany, Finland, Canada (Ontario), New Zealand, South Korea, Taiwan and Hong Kong. Individuals aged 60+ with an incident dementia diagnosis recorded between 2000 and 2018 were followed until death or the end of the study period. Cox proportional hazards regression was used to assess the association of mortality in dementia patients with the year of dementia diagnosis. Results: Data from 1,272,495 individuals, with the mean age at diagnosis ranging from 76.8 years (South Korea) to 82.9 years (Germany), show that the overall median length of survival following recorded diagnosis ranges from 2.4 years (New Zealand) to 7.9 years (South Korea). Hazard ratios (HRs) estimated from Cox proportional hazard models decline consistently over the study period in the UK, Canada, South Korea, Taiwan and Hong Kong, which accounted for 84% of all participants. For example, the HR decreases from 0.97 (95% CI: 0.92–1.02) in 2001 to 0.72 (0.65–0.79) in 2016 in comparison to year 2000 in the UK. Conclusions: This study shows a steady trend of decreasing risk of mortality in five out of eight databases, which signals the potential positive effect of dementia plans and associated policies and provides reference for future policy evaluation
Did COVID-19 vaccine enforcement work? Evidence from northwestern and northern Uganda
No full textDuring the COVID-19 pandemic, vaccination programmes were shaped by diverse approaches to enforcement. Yet, little is known about how public authority influenced modes of enforcement on the ground or their ramifications for governance and public health more broadly. This article focuses on the Ugandan mandatory COVID-19 vaccination programme in two contrasting geographical and socio-political spaces: rural Dei and peri-urban Gulu. Ethnographic and survey research demonstrated that enforcement occurred in different ways and by diverse public authorities, with ostensibly contrasting results. In Dei, self-reported vaccine uptake and coverage was 77 % and 73 % respectively; while in Gulu, it was 46 % and 23 %, and below the national target of 70 %. Public authority dynamics explain these differences. In Dei, the military co-opted official political figures and side-lined other local leaders. Anxieties about the vaccine were dismissed, and people were forcibly vaccinated against a disease which they did not perceive to be a significant problem. In Gulu, the military were barely involved. Instead, government appointees and civil servants made efforts to alleviate anxieties through news media, whilst also requiring proof of vaccination to access, or remain employed at, schools, universities, health care facilities. However, some officials undermined the strategy, including health care workers who provided false vaccination certificates. Despite the apparent success of high vaccine uptake reported in Dei, available data suggests that it is unlikely that efforts to enforce vaccination at either field site shaped the course of the COVID-19 outbreaks. Instrumentally violent enforcement ‘works’ if resistance is not possible, as it was in Dei, but may be counterproductive. Enforcement procedures at both sites provided opportunities to entrench unaccountable modes of governance and fostered mistrust of the government's intentions, thereby weakening previously established vaccine compliance procedures. A public authority lens thus foregrounds the importance of moving beyond narrow public health metrics and engaging with broader conceptions of whether enforced vaccination is effective, and if so, for whom and what purpose