Dimensionally Dependent Tensor Identities by Double Antisymmetrisation

Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p >= n$. We generalise Lovelock's results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrising over n+1 indices, we establish a very general 'master' identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity; in particular we give direct application to Maxwell, Lanczos, Ricci, Bel and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner.Comment: 17 pages, 2 figure

Reconstruction of eolian bed forms and paleocurrents from cross-bedded strata at Victoria Crater, Meridiani Planum, Mars

Outcrop exposures imaged by the Opportunity rover at Victoria Crater, a 750 m diameter crater in Meridiani Planum, are used to delineate sedimentary structures and further develop a dune-interdune depositional model for the region. The stratigraphy at Victoria Crater, observed during Opportunity's partial traverse of its rim, includes the best examples of meter-scale eolian cross bedding observed on Mars to date. The Cape St. Mary promontory, located at the southern end of the rim traverse, is characterized by meter-scale sets of trough cross bedding, suggesting northward migrating sinuous-crested bed forms. Cape St. Vincent, which is located at the opposite end of the traverse, shows tabular-planar stratification indicative of climbing bed forms with meter- to decameter-scale dune heights migrating southward. Promontories located between Cape St. Mary and Cape St. Vincent contain superposed stratigraphic units with northward and southward dipping beds separated by outcrop-scale bounding surfaces. These bounding surfaces are interpreted to be either reactivation and/or superposition surfaces in a complex erg sea. Any depositional model used to explain the bedding must conform to reversing northward and southward paleomigration directions and include multiple scales of bed forms. In addition to stratified outcrop, a bright diagenetic band is observed to overprint bedding and to lie on an equipotential parallel to the preimpact surface. Meter-scale cross bedding at Victoria Crater is similar to terrestrial eolian deposits and is interpreted as a dry dune field, comparable to Jurassic age eolian deposits in the western United States

Healthy shopper? Blood pressure testing in a shopping centre Pop-Up in England

Background: Improving detection of elevated blood pressure (BP) remains a public health need. We present results from a Pop-Up health check stationed in shopping centres in England. We hypothesise the rate of case detection is related to measurable ‘unhealthiness’ of the shopping centres. Methods: A Pop-Up health check was sited in four and three shopping centres sampled from the top ten unhealthiest and top 15 healthiest shopping regions respectively, following a report ranking towns/cities based on their unhealthy and healthy retail outlets. On one day in each shopping centre, people were approached and consented to BP testing. Outcome measure was people flagged with BP ≥ 140/90 mmHg (cases). Results: We detected 45 (22.6%) and 20 (13.1%) cases from testing 199 and 152 adults in the unhealthy and healthy locations respectively (relative risk 1.72; 95% confidence interval: 1.06 to 2.78). A measure of unhealthy retail outlets (e.g. fast-food outlets) within each shopping centre was associated with detection rate (R2 = 0.61; p = 0.04). Conclusion: An association exists between cases of suspect hypertension found in a health check Pop-Up and measured ‘unhealthiness’ of the shopping centre site. Results hint at strategies for public testing of BP, potentially in the context of reducing health inequalities

Formation of primordial black holes from non-Gaussian perturbations produced in a waterfall transition

We consider the process of primordial black hole (PBH) formation originated from primordial curvature perturbations produced during waterfall transition (with tachyonic instability), at the end of hybrid inflation. It is known that in such inflation models, rather large values of curvature perturbation amplitudes can be reached, which can potentially cause a significant PBH production in the early Universe. The probability distributions of density perturbation amplitudes in this case can be strongly non-Gaussian, which requires a special treatment. We calculated PBH abundances and PBH mass spectra for the model, and analyzed their dependence on model parameters. We obtained the constraints on the parameters of the inflationary potential, using the available limits on $\beta_{PBH}$.Comment: v2: 11 pages, 4 figures. Several comments and references added. Version accepted by Phys. Rev.

Feeling the pressure: a cross-sectional study exploring feasibility of a healthcare Pop-Up for intraocular pressure measurements in shopping centres in England

OBJECTIVES: To test the hypothesis that a shopping centre Pop-Up health check combining an intraocular pressure (IOP) check with a general health check (blood pressure (BP)) is more readily accepted by the general public than an IOP check only. We investigate public awareness of IOP compared with BP and the feasibility of measuring IOP in large numbers in a Pop-Up. DESIGN: A cross-sectional study using a tailor-made healthcare Pop-Up. SETTING: The 'Feeling the Pressure' Pop-Up was sited in eight regionally-different shopping centres in England. PARTICIPANTS: Adult members of the public in shopping centres. METHODS: On one day we measured IOP only and on another measured BP and IOP. IOP was measured by Icare IC100 tonometer (Helsinki, Finland). Potential participants were asked about their awareness of IOP and BP and when they last visited their optometrist. RESULTS: More people attended the combined BP + IOP days (461; 60%; 95% CI 56% to 64%) than IOP-only days (307; 40%, 95% CI 37% to 43%) over 16 days of testing. We recorded IOP in 652 participants (median (IQR) age and IOP of 54 (42 to 68) years and 13 (11 to 15) mm Hg, respectively). Fewer people reported awareness about IOP (19%, 95% CI 16% to 23%) compared with BP (71%, 95% CI 66% to 75%). Of 768 participants, 60 (8%) reported no previous optometric eye examination and 185 (24%) reported >2 years since their most recent examination. CONCLUSIONS: Measuring IOP in large numbers of the public via a shopping centre Pop-Up is feasible. Public engagement was greater when a BP check was offered alongside an IOP check, suggesting unfamiliar health checks can be promoted by aligning them with a more familiar check. Our findings hint at strategies for public health schemes that engage the public with their eye health

Untangling Source-To-Sink Geochemical Signals in a ~3.5 Ga Martian Lake: Sedimentology and Geochemistry of the Murray Formation

Sedimentary rocks are historical archives of planetary surface processes; their grains, textures, and chemistry integrate the effects of source terrains, paleoclimatic conditions, weathering and transport processes, authigenic mineral precipitation, and diagenesis, which records groundwater chemistry through time. Source to Sink basin analysis seeks to constrain the influence of each of these different signals through sedimentary and geochemical analyses. Here, we use Mars Science Laboratory (MSL) Curiosity rover images and geochemical and mineralogical data from a traverse across a portion of the Murray formationthe lowermost unit exposed in the Gale crater central moundto begin to constrain the aspects of the source to sink system that formed this Martian mudstone between 3.7 and 3.2 Ga

Characterization of the nitrogen split interstitial defect in wurtzite aluminum nitride using density functional theory

We carried out Heyd-Scuseria-Ernzerhof hybrid density functional theory plane wave supercell calculations in wurtzite aluminum nitride in order to characterize the geometry, formation energies, transition levels and hyperfine tensors of the nitrogen split interstitial defect. The calculated hyperfine tensors may provide useful fingerprint of this defect for electron paramagnetic resonance measurement.Comment: 5 pages, 3 figure

Socially-mediated arousal and contagion within domestic chick broods

Emotional contagion – an underpinning valenced feature of empathy – is made up of simpler, potentially dissociable social processes which can include socially-mediated arousal and behavioural/physiological contagion. Previous studies of emotional contagion have often conflated these processes rather than examining their independent contribution to empathic response. We measured socially-mediated arousal and contagion in 9-week old domestic chicks (n = 19 broods), who were unrelated but raised together from hatching. Pairs of observer chicks were exposed to two conditions in a counterbalanced order: air puff to conspecifics (AP) (during which an air puff was applied to three conspecifics at 30 s intervals) and control with noise of air puff (C) (during which the air puff was directed away from the apparatus at 30 s intervals). Behaviour and surface eye temperature of subjects and observers were measured throughout a 10-min pre-treatment and 10-min treatment period. Subjects and observers responded to AP with increased freezing, and reduced preening and ground pecking. Subjects and observers also showed reduced surface eye temperature - indicative of stress-induced hyperthermia. Subject-Observer behaviour was highly correlated within broods during both C and AP conditions, but with higher overall synchrony during AP. We demonstrate the co-occurrence of socially-mediated behavioural and physiological arousal and contagion; component features of emotional contagion

Scientific research on animal biodiversity is systematically biased towards vertebrates and temperate regions.

Over the last 25 years, research on biodiversity has expanded dramatically, fuelled by increasing threats to the natural world. However, the number of published studies is heavily weighted towards certain taxa, perhaps influencing conservation awareness of and funding for less-popular groups. Few studies have systematically quantified these biases, although information on this topic is important for informing future research and conservation priorities. We investigated: i) which animal taxa are being studied; ii) if any taxonomic biases are the same in temperate and tropical regions; iii) whether the taxon studied is named in the title of papers on biodiversity, perhaps reflecting a perception of what biodiversity is; iv) the geographical distribution of biodiversity research, compared with the distribution of biodiversity and threatened species; and v) the geographical distribution of authors' countries of origin. To do this, we used the search engine Web of Science to systematically sample a subset of the published literature with 'biodiversity' in the title. In total 526 research papers were screened-5% of all papers in Web of Science with biodiversity in the title. For each paper, details on taxonomic group, title phrasing, number of citations, study location, and author locations were recorded. Compared to the proportions of described species, we identified a considerable taxonomic weighting towards vertebrates and an under-representation of invertebrates (particularly arachnids and insects) in the published literature. This discrepancy is more pronounced in highly cited papers, and in tropical regions, with only 43% of biodiversity research in the tropics including invertebrates. Furthermore, while papers on vertebrate taxa typically did not specify the taxonomic group in the title, the converse was true for invertebrate papers. Biodiversity research is also biased geographically: studies are more frequently carried out in developed countries with larger economies, and for a given level of species or threatened species, tropical countries were understudied relative to temperate countries. Finally, biodiversity research is disproportionately authored by researchers from wealthier countries, with studies less likely to be carried out by scientists in lower-GDP nations. Our results highlight the need for a more systematic and directed evaluation of biodiversity studies, perhaps informing more targeted research towards those areas and taxa most depauperate in research. Only by doing so can we ensure that biodiversity research yields results that are relevant and applicable to all regions and that the information necessary for the conservation of threatened species is available to conservation practitioners