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John McKay's remarkable insights unveiled a connection between the 'double covers' of the groups of regular polyhedra, known since ancient Greek times, and the exceptional Lie algebras, recognized since the late nineteenth century. The correspondence involves certain diagrams, the ADE diagrams, which can be interpreted in different ways: as quivers associated with the groups, and Dynkin diagrams of root systems of Lie algebras. The ADE diagrams arise in many areas of mathematics, including topics in relativity and string theory, spectral theory of graphs and cluster algebras. Accessible to students, this book explains these connections with exercises and examples throughout. An excellent introduction for students and researchers wishing to learn more about this unifying principle of mathematics.
The journey through the wilderness ends with the people of Israel in the land of promise, but it is fraught with snares and temptations in the turbulent books of Joshua and Judges.
We compute primes $p \equiv 5 \bmod 8$ up to $10^{11}$ for which the Pellian equation $x^2-py^2=-4$ has no solutions in odd integers; these are the members of sequence A130229 in the Online Encyclopedia of Integer Sequences. We find that the number of such primes $p\leqslant x$ is well approximated by
To investigate the concordance between Australian government guidelines for classifying the healthiness of foods across various public settings.
Design:
Commonly available products in Australian food service settings across 8 food categories were classified according to each of the 17 Australian state and territory food classification guidelines applying to public schools, workplaces, and healthcare settings. Product nutrition information was retrieved from online sources. The level of concordance between each pair of guidelines was determined by the proportion of products rated at the same level of healthiness.
Setting:
Australia
Participants:
No human participants.
Results:
Approximately half (56%) of the 967 food and drink products assessed were classified as the same level of healthiness across all 15 ‘traffic light’-based systems. Within each setting type (e.g., schools), pairwise concordance in product classifications between guidelines ranged from 74% to 100%. ‘Vegetables’ (100%) and ‘sweet snacks and desserts’ (78%) had the highest concordance across guidelines while ‘cold ready-to-eat foods’ (0%) and ‘savoury snacks’ (23%) had the lowest concordance. In addition to differences in classification criteria, discrepancies between guidelines arose from different approaches to grouping of products. The largest proportion of discrepancies (58%) were attributed to whether products were classified as ‘Red’ (least healthy) or ‘Amber’ (moderately healthy).
Conclusions:
Results indicate only moderate concordance between all guidelines. National coordination to create evidence-based consistency between guidelines would help provide clarity for food businesses, which are often national, on how to better support community health through product development and reformulation.
This article critically examines the law concerning dismissal on grounds of redundancy as it applies to the Australian Public Service (‘APS’). Such an examination is timely, given the newly elected Coalition government's stated intention to reduce the APS by 12 000 employees through natural attrition.
The article argues that a reduction of 12 000 employees through natural attrition alone is unlikely, and that redundancies are almost inevitable. Against this backdrop, the article considers recent legislative developments concerning dismissal on grounds of redundancy. Its focus is the genuine redundancy exclusion contained in s 389 of the Fair Work Act 2009 (Cth) (‘FW Act’) and its application to APS employment. The genuine redundancy exclusion precludes unfair dismissal claims if the redundancy is genuine, the employer complies with any consultation obligations in a modern award or enterprise agreement and it would not have been reasonable in all the circumstances to redeploy the affected employee within the employer's enterprise or that of an associated entity.
The article argues that, prior to the FW Act, redundancy obligations were predominantly dealt with in collective agreements, and did not require consultations or redeployment of redundant employees beyond the individual agency. However the FW Act fundamentally changed the law in this area. The article contends that a failure to comply with consultation obligations in an agency enterprise agreement will increase the prospects of a dismissal being found to be unfair. In the APS this is problematic, given the convoluted nature of many consultation clauses in enterprise agreements. The article also argues that the redeployment obligations in s 389(2) are extremely broad and, contrary to past practice under the Public Service Act 1999 (Cth) (‘PS Act’), encompass redeployment across the APS. The obligation to redeploy across the APS creates tensions in the law between the provisions of the FW Act and the devolution of managerial powers under the PS Act.
The inclusion problem for theories of gender arises when those theories inappropriately fail to include certain individuals in the gender categories to which they ought to belong. The inclusion problem affects both of the most influential traditions in feminist theorizing about gender: social-position accounts and identity accounts. I argue that the inclusion problem can be solved by adopting a structured theory of gender, which incorporates aspects of both social-position accounts and identity accounts. According to the theory I favor, an individual’s gender is determined by their gender identity if they have one; otherwise, it is determined by their social position. My structured theory of gender offers a more direct solution to the gender inclusion problem than alternatives recently advocated by Barnes (2020), Jenkins (2023), and others. It also points the way to a simple solution to inclusion problems that arise at the level of gendered language.
In 2009, Australia experienced a record ‘high’ of 36 487 personal insolvencies. The magnitude of this figure, which represents all bankruptcies, debt agreements, and personal insolvency agreements in that financial year, is augmented when placed in the context of the 300 per cent increase seen in the number of Australian personal insolvencies between 1990 and 2009. This growth far exceeded the 28 per cent increase in the Australian population during that period. It is indisputable that personal insolvency is affecting a growing number of Australians.
In Breavington v Godleman, Deane J stated: Basic to the jurisprudence of this country is the notion that the courts apply, as distinct from make, the law, that is to say, that the law operates contemporaneously to regulate lawfulness and consequences of conduct independently of judicial proceedings. In that context, it would be to substitute the bedlam of a Babel for an ordered system of law to recognise the right of each of the country's court systems, notwithstanding the place of this Court inall of them, to speak at the same time but in conflicting terms about the lawfulness, consequences or attributes of a particular act or thing in a particular place at a particular time.
Syncope is common among pediatric patients and is rarely pathologic. The mechanisms for symptoms during exercise are less well understood than the resting mechanisms. Additionally, inert gas rebreathing analysis, a non-invasive examination of haemodynamics including cardiac output, has not previously been studied in youth with neurocardiogenic syncope.
Methods:
This was a retrospective (2017–2023), single-center cohort study in pediatric patients ≤ 21 years with prior peri-exertional syncope evaluated with echocardiography and cardiopulmonary exercise testing with inert gas rebreathing analysis performed on the same day. Patients with and without symptoms during or immediately following exercise were noted.
Results:
Of the 101 patients (15.2 ± 2.3 years; 31% male), there were 22 patients with symptoms during exercise testing or recovery. Resting echocardiography stroke volume correlated with resting (r = 0.53, p < 0.0001) and peak stroke volume (r = 0.32, p = 0.009) by inert gas rebreathing and with peak oxygen pulse (r = 0.61, p < 0.0001). Patients with syncopal symptoms peri-exercise had lower left ventricular end-diastolic volume (Z-score –1.2 ± 1.3 vs. –0.36 ± 1.3, p = 0.01) and end-systolic volume (Z-score –1.0 ± 1.4 vs. −0.1 ± 1.1, p = 0.001) by echocardiography, lower percent predicted peak oxygen pulse during exercise (95.5 ± 14.0 vs. 104.6 ± 18.5%, p = 0.04), and slower post-exercise heart rate recovery (31.0 ± 12.7 vs. 37.8 ± 13.2 bpm, p = 0.03).
Discussion:
Among youth with a history of peri-exertional syncope, those who become syncopal with exercise testing have lower left ventricular volumes at rest, decreased peak oxygen pulse, and slower heart rate recovery after exercise than those who remain asymptomatic. Peak oxygen pulse and resting stroke volume on inert gas rebreathing are associated with stroke volume on echocardiogram.
Patients with hematological malignancies are at high risk of infections due to both the disease and the associated treatments. The use of immunoglobulin (Ig) to prevent infections is increasing in this population, but its cost effectiveness is unknown. This trial-based economic evaluation aimed to compare the cost effectiveness of prophylactic Ig with prophylactic antibiotics in patients with hematological malignancies.
Methods
The economic evaluation used individual patient data from the RATIONAL feasibility trial, which randomly assigned 63 adults with chronic lymphocytic leukemia, multiple myeloma, or lymphoma to prophylactic Ig or prophylactic antibiotics. The following two analyses were conducted to estimate the cost effectiveness of the two treatments over the 12-month trial period from the perspective of the Australian health system:
(i) a cost-utility analysis (CUA) to assess the incremental cost per quality-adjusted life-year (QALY) gained using data collected with the EuroQol 5D-5L questionnaire; and
(ii) a cost-effectiveness analysis (CEA) to assess the incremental cost per serious infection prevented (grade ≥3) and per infection prevented (any grade).
Results
The total cost per patient was significantly higher in the Ig arm than in the antibiotic arm (difference AUD29,140 [USD19,000]). There were non-significant differences in health outcomes between the treatment arms: patients treated with Ig had fewer QALYs (difference −0.072) and serious infections (difference −0.26) than those given antibiotics, but more overall infections (difference 0.76). The incremental cost-effectiveness from the CUA indicated that Ig was more costly than antibiotics and associated with fewer QALYs. In the CEA, Ig costed an additional AUD111,262 (USD73,000) per serious infection prevented, but it was more costly than antibiotics and associated with more infections when all infections were included.
Conclusions
These results indicate that, on average, Ig prophylactic treatment may not be cost effective compared with prophylactic antibiotics for the group of patients with hematological malignancies recruited to the RATIONAL feasibility trial. Further research is needed to confirm these findings in a larger population and over the longer term.
There are ethnic differences, including differences related to indigeneity, in the incidence of first episode psychosis (FEP) and pathways into care, but research on ethnic disparities in outcomes following FEP is limited.
Aims
In this study we examined social and health outcomes following FEP diagnosis for a cohort of Māori (Indigenous people of New Zealand) and non-Māori (non-Indigenous) young people. We have focused on understanding the opportunities for better outcomes for Māori by examining the relative advantage of non-Māori with FEP.
Method
Statistics New Zealand's Integrated Data Infrastructure was accessed to describe mental health and social service interactions and outcomes for a retrospective FEP cohort comprising 918 young Māori and 1275 non-Māori aged 13 to 25 at diagnosis. Logistic regression models were used to examine whether social outcomes including employment, benefit receipt, education and justice involvement in year 5 differed by indigeneity.
Results
Non-Māori young people were more likely than Māori to have positive outcomes in the fifth year after FEP diagnosis, including higher levels of employment and income, and lower rates of benefit receipt and criminal justice system involvement. These patterns were seen across diagnostic groups, and for both those receiving ongoing mental healthcare and those who were not.
Conclusions
Non-Māori experience relative advantage in outcomes 5 years after FEP diagnosis. Indigenous-based social disparities following FEP urgently require a response from the health, education, employment, justice and political systems to avoid perpetuating these inequities, alongside efforts to address the disadvantages faced by all young people with FEP.
To understand the characteristics of food environments in the Pacific region, and the broader economic, policy and sociocultural surroundings that influence food choices and interventions to improve food environments for Pacific communities.
Design:
Systematic searches were conducted for articles related to food environments or factors influencing food choices from 1993 to 2024 in five academic databases, Google, Google Scholar and relevant organisations’ websites. Studies were included if they meet the eligibility criteria. Two authors independently reviewed the title and abstract of identified articles. Full-text screening was conducted before data were extracted from eligible studies. A narrative analysis was informed by an existing food environments framework.
Setting:
Pacific Island countries or territories that are a member of the Pacific Community (SPC).
Participants:
Not applicable.
Results:
From the sixty-six included studies (of 2520 records screened), it was clear that food environments in the Pacific region are characterised by high availability and promotion of ultra-processed unhealthy foods. These foods were reported to be cheaper than healthier alternatives and have poor nutritional labelling. Food trade and investment, together with sociocultural and political factors, were found to contribute to unhealthy food choices. Policy interventions have been implemented to address food environments; however, the development and implementation of food environment policies could be strengthened through stronger leadership, effective multisectoral collaboration and clear lines of responsibility.
Conclusions:
Interventions focused on improving physical, economic, policy and sociocultural influences on food choices should be prioritised in the Pacific region to improve the food environment and mitigate barriers to healthy eating.
Logwood, a dyestuff extracted from its namesake tree native to the Yucatán Peninsula, was a commodity valued in the textile centres of early modern Europe. The trade in logwood began as an extractive endeavour attempted by merchants and former pirates on the margins of Spanish colonial authority, but by the late eighteenth century it had expanded to become a wide-reaching activity with connections to broader trends on both sides of the Atlantic. In the New World, the trade's growth fuelled Anglo-Spanish imperial rivalries and led to the introduction of slave labour to harvest dwindling logwood stands. The ecological consequences of human exchange also spread logwood's range to Caribbean islands, turning a frontier trade into a domesticated plantation industry. In the Old World, logwood was a versatile dye source that contributed to a range of hues. Initial regulations to protect consumers eased as dyers improved the quality of logwood dyes. The logwood trade expanded global textile supply chains and brought innovation to Europe's proto-industrial textile industry. It gave the continent's dyers new ways to meet consumer demand and spurred the development of mechanical methods to expedite refining.
Previous research has examined whether voters will punish candidates who engage in sexual harassment in national-level elections, revealing partisanship as a strong predictor of electoral punishment. Using original survey data, we evaluate whether the public supports a broader range of sanctions (e.g. apologies, training, and removal from office) that legislatures can impose upon politicians who perpetrate sexual harassment in Canada’s municipalities, a non-partisan context. In the absence of partisan-based motivated reasoning, we find that women are more likely than men to support the removal from office of a councillor who engages in sexual harassment. Respondents who do not believe that sexism is a problem and are skeptical about claims of gender-based violence are also less likely to support punishment in these cases. These findings have relevance for democratic institutions, revealing that sanctions imposed on politicians who perpetrate sexual harassment can help maintain political accountability and restore public trust.
Great changes have taken place in the approach of historians to the topic since the publication of East of Byzantium (1980). Instead of centre-periphery or top-down models they now see the relations between Byzantium and the east in terms of connectivity, networks and horizontal ties. This is connected with the spread of late antiquity as a concept and includes a great expansion in Syriac studies. Late antiquity now embraces the emergence of Islam and looks towards Eurasia; another challenge is posed by the rise of global history. But these developments, with the new focus on the fall of the western empire, raise major problems of identity for Byzantium itself, and indeed for western Europe.
This study investigates the use of double modals in Australian and New Zealand English using Twitter/𝕏 data. Double modals are rare grammatical constructions long believed to be limited to regional dialects in the Northern UK and the Southern US. Utilizing a geolocated corpus of over 80 million tweets, the study identifies 314 authentic double modal instances across 51 types, primarily occurring in informal tweets. Findings reveal widespread, albeit low-frequency, usage across both countries without clear geographical patterns. The results align with recent studies suggesting double modals are not confined to specific regions but are possible for most English speakers. The study also questions the traditional Scots-Irish origin theory, proposing an alternative view where the feature is a broader syntactic possibility. Future research should explore larger datasets and extend investigations to outer-circle English varieties to understand better the historical spread and syntactic nature of double modals.
To determine and compare the intraoperative durability of 4 major surgical glove brands.
Design, Setting, and Participants:
This study is a randomized open-label clinical trial in which surgical gloves from 4 manufacturers are randomized to 5 surgical subspecialty study groups: (1) orthopedic surgery, (2) neurosurgery, (3) colorectal surgery, (4) trauma or acute general surgery, and (5) cardiac and plastic surgeries. The study was divided into 10 periods, with a cross-over design, and was conducted at a tertiary care academic medical center. Participants were licensed and certified physicians, physicians-in-training, scrub nurses, or technicians working within the sterile field.
Interventions:
Participants from each study group were randomly assigned to 1 of 4 surgical glove manufacturer types and subsequently rotated through the other 3 glove brands such that each participant acted as their own control in the sequential cross-over design.
Main Outcomes and Measures:
The primary outcome was to determine and compare the intraoperative failure rate of Biogel® Sterile Surgical undergloves against sterile surgical undergloves from 3 other manufacturers, both as a combined competitor group and individually.
Results:
There were no differences between brands with respect to the primary outcome of underglove intraoperative failures. Brand 1 wearers were slightly more likely to detect glove failures when they occurred.
Conclusion:
The durability of surgical gloves intraoperatively is similar across 4 major glove manufacturers. Detection of intraoperative failures is infrequent, though specific glove characteristics may promote enhanced detection. Recognition of glove perforations intraoperatively is important in the maintenance of a maximally sterile field.
People with psychosis experience worse cardiometabolic health than the same-aged general population. In New Zealand, Indigenous Māori experiencing psychosis have greater risk of cardiometabolic and other physical health problems.
Aims
To identify a cohort of adults accessing secondary mental health and addiction services in New Zealand, with a previous psychosis diagnosis as of 1 January 2018, and compare odds of hospital admission outcomes, mortality and receipt of cardiometabolic blood screening between Māori and non-Māori in the following 2 years.
Method
Crude and adjusted logistic regression models compared odds of hospital admission outcomes, mortality and receipt of cardiometabolic blood screening (lipids and haemoglobin A1c) between Māori and non-Māori, occurring between 1 January 2018 and 31 December 2019.
Results
A cohort (N = 21 214) of Māori (n = 7274) and non-Māori (n = 13 940) was identified. Māori had higher adjusted risk of mortality (odds ratio 1.26, 95% CI 1.03–1.54), and hospital admission with diabetes (odds ratio 1.64, 95% CI 1.43–1.87), cardiovascular disease (odds ratio 1.54, 95% CI 1.25–1.88) and any physical health condition (odds ratio 1.07, 95% CI 1.00–1.15) than non-Māori. Around a third of people did not receive recommended cardiometabolic blood screening, with no difference between Māori and non-Māori after covariate adjustment.
Conclusions
Māori experiencing psychosis are more likely to die and be admitted to hospital with cardiovascular disease or diabetes than non-Māori. Because of the higher cardiometabolic risk borne by Māori, it is suggested that cardiometabolic screening shortfalls will lead to worsening physical health inequities for Māori experiencing psychosis.