Centrifiers and ring commutativity

A result of Herstein says in particular that if there exists n > 1 such that xᵑ − x ∈ Z(R) for all x in a ring R then R is commutative. We give an elementary proof of this fact for certain values of n, based on the theory of centrifiers which we develop. For n = 5; 7, we also give an elementary proof of the commutativity of rings R such that xᵑ + x ∈ Z(R) for all x ∈ R

Is there any Evidence for Regional Atmospheric 14C Offsets in the Southern Hemisphere?

Center for Accelerator Mass Spectrometry (CAMS) Tasmanian huon pine (Lagarostrobos franklinii) decadal measurements for the interval AD 745–855 suggest a mean interhemispheric radiocarbon offset (20 ± 5 yr), which is considerably lower than the previously reported mean interhemispheric offset for the last 2 millennia (44 ± 17 yr). However, comparable University of Waikato (Wk) New Zealand kauri (Agathis australis) measurements show significantly higher values (56 ± 6 yr), suggesting the possibility of a temporary geographic (intrahemispheric) offset between Tasmania, Australia, and Northland, New Zealand, during at least 1 common time interval. Here, we report 9 new Wk Tasmanian huon pine measurements from the decades showing the largest huon/kauri difference. We show statistically indistinguishable Wk huon and Wk kauri 14C ages, thus dispelling the suggestion of a 14C geographic offset between Tasmania and Northland

Using commercial and recreational fisher knowledge to reconstruct historical catch rates for Queensland snapper (Chrysophrys auratus), Spanish mackerel (Scomberomorus commerson) and coral trout (Plectropomus spp.): long-term data for incorporation into future stock assessments

[Excerpt] This project was funded by the Fisheries Research and Development Corporation (project number 2013-018). The Great Barrier Reef Marine Park Authority also provided funding for the Coral Trout component of the research. We wish to thank both funders for their support. We thank staff at the FRDC, members of the Queensland FRAB, the Queensland Government Department for Agriculture and Fisheries, and the Great Barrier Reef Marine Park Authority, who provided invaluable advice throughout the project

Ptolemaic spaces and CAT (0)

We consider Ptolemy’s inequality in a metric space setting. It is not hard to see that CAT(0) spaces satisfy this inequality. Although the converse is not true in full generality, we show that if our Ptolemaic space is either a Riemannian or Finsler manifold, then it must also be CAT(0). Ptolemy’s inequality is closely related to inversions of metric spaces. We exploit this link to establish a new characterization of Euclidean space amongst all Riemannian manifolds

On Ptolemaic metric simplicial complexes

We show that under certain mild conditions, a metric simplicial complex which satisfies the Ptolemy inequality is a CAT(0) space. Ptolemy’s inequality is closely related to inversions of metric spaces. For a large class of metric simplicial complexes, we characterize those which are isometric to Euclidean space in terms of metric inversions

Signs Workshop: the importance of natural gestures in the promotion of early communication skills of children with developmental disabilities

This article emphasises the importance of natural gestures and describes the framework and the development process of the “Signs Workshop” CD-ROM, which is a multimedia application for the promotion of early communication skills of children with developmental disabilities. Signs Workshop CD-ROM was created in the scope of Down’s Comm Project, which was financed by the Calouste Gulbenkian Foundation, and is the result of a partnership between UNICA (Communication and Arts Research Unit of the University of Aveiro) and the Portuguese Down Syndrome Association (APPT21/Differences)

Improving outcomes for older people in the emergency department : a review of reviews

Background: There has been a recognised trend of increasing use of emergency and urgent care and emergency departments (EDs) by older people, which is marked by a substantial evidence base reporting interventions for this population and guidance from key organisations. Despite this, outcomes for this population remain suboptimal. A plethora of reviews in this area provides challenges for clinicians and commissioners in determining which interventions and models of care best meet people’s needs. The aim of this review was to identify effective ED interventions which have been reported for older people, and to provide a clear summary of the myriad reviews and numerous intervention types in this area. Methods: A review of reviews, reporting interventions for older people, either initiated or wholly delivered within the ED. Results: A total of 15 review articles describing 83 primary studies met our content and reporting standards criteria. The majority (n=13) were systematic reviews (four using meta-analysis.) Across the reviews, 26 different outcomes were reported with inconsistency. Follow-up duration varied within and across the reviews. Based on how authors had reported results, evidence clusters were developed: (1) staff-focused reviews, (2) discharge intervention reviews, (3) population-focused reviews and (4) intervention component reviews. Conclusions: The evidence base describing interventions is weak due to inconsistent reporting, differing emphasis placed on the key characteristics of primary studies (staff, location and outcome) by review authors and varying quality of reviews. No individual interventions have been found to be more promising, but interventions initiated in the ED and continued into other settings have tended to result in more favourable patient and health service outcomes. Despite many interventions reported within the reviews being holistic and patient focused, outcomes measured were largely service focused. PROSPERO registration number: PROSPERO CRD42018111461

Stock assessment of Australian east coast Spanish mackerel : Predictions of stock status and reference points

The stock assessment describes Australia’s east coast Spanish mackerel fishery operating in ocean waters between Cape York Peninsula and northern New South Wales. The species are a large offshore pelagic fish that can live for up to 26 years and weigh in excess of 30 kg. Spanish mackerel reach maturity above the minimum legal size of 75 cm at between two and four years of age. The stock assessment was conducted at the whole stock level and included commercial, charter, recreational and research data from both New South Wales and Queensland. The data included estimates of Spanish mackerel harvest from logbook systems and recreational fishing surveys, catch rates from commercial logbooks and historical surveys of long term commercial fishers, and annual fish age-length compositions. The fishery for east coast Spanish mackerel commenced in the early 1900s. Annual east coast harvests taken by commercial, charter and recreational fishing steadily built to peak at 1000–1300 tonnes (t) per year during the 1970s and 1000–1150 t per year between 1998 and 2003. The estimated annual Spanish mackerel harvest since 2005 reduced to 500–760 t per year. Most fishers harvest Spanish mackerel using line-fishing techniques. Net fishing for Spanish mackerel is illegal. In recent years about 47 per cent, 6 per cent and 47 per cent of annual Spanish mackerel harvests were taken respectively by commercial, charter and recreational fishing across all east coast waters. Population modelling of the data estimated that Spanish mackerel population size in 2016 was between 30–50 per cent of original biomass estimated at the start of the fishery in 1911 (best estimate around 40 per cent biomass). Estimates of recommended sustainable annual harvest of Spanish mackerel for all fishing sectors and east-coast waters ranged between 400 and 800 t. There is presently substantial unfished commercial quota. The current Queensland total allowable commercial catch quota is 574.6 t. If this were to be largely utilised, together with current or increased charter, recreational and New South Wales commercial harvests, then the biomass of the Spanish mackerel population may decline. Such high harvests would result in overfishing and reduce average catch rates longer-term. The results suggested annual harvests of around 550 t (across all sectors) will build the biomass towards the 60 per cent level, consistent with the 2027 biomass targets set in the Queensland Government’s Sustainable Fisheries Strategy. If there is a desire to operate the fishery closer towards 60 per cent biomass for better economic yield and quality of fishing (higher catch rates), then fishing pressure will need to reduce for a period of time to build the fish population to a higher biomass

A Bayesian approach to the g-formula

Epidemiologists often wish to estimate quantities that are easy to communicate and correspond to the results of realistic public health interventions. Methods from causal inference can answer these questions. We adopt the language of potential outcomes under Rubin’s original Bayesian framework and show that the parametric g-formula is easily amenable to a Bayesian approach. We show that the frequentist properties of the Bayesian g-formula suggest it improves the accuracy of estimates of causal effects in small samples or when data are sparse. We demonstrate an approach to estimate the effect of environmental tobacco smoke on body mass index among children aged 4–9 years who were enrolled in a longitudinal birth cohort in New York, USA. We provide an algorithm and supply SAS and Stan code that can be adopted to implement this computational approach more generally

Harnack inequality and regularity for degenerate quasilinear elliptic equations

We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,\alpha}$ local estimates for solutions of a degenerate equation in non divergence form