Holonomy algebras of pseudo-quaternionic-K\"ahlerian manifolds of signature (4,4)(4,4)

Possible holonomy algebras of pseudo-quaternionic-K\"ahlerian manifolds of signature $(4,4)$ are classified. Using this, a new proof of the classification of simply connected pseudo-quaternionic-K\"ahlerian symmetric spaces of signature $(4,4)$ is obtained.Comment: 16 page

(M-theory-)Killing spinors on symmetric spaces

We show how the theory of invariant principal bundle connections for reductive homogeneous spaces can be applied to determine the holonomy of generalised Killing spinor covariant derivatives of the form $D= \nabla + \Omega$ in a purely algebraic and algorithmic way, where $\Omega : TM \rightarrow \Lambda^*(TM)$ is a left-invariant homomorphism. Specialising this to the case of symmetric M-theory backgrounds (i.e. $(M,g,F)$ with $(M,g)$ a symmetric space and $F$ an invariant closed 4-form), we derive several criteria for such a background to preserve some supersymmetry and consequently find all supersymmetric symmetric M-theory backgrounds.Comment: Updated abstract for clarity. Added missing geometries to section 6. Main result stand

Health economic burden that wounds impose on the National Health Service in the UK

OBJECTIVE: To estimate the prevalence of wounds managed by the UK's National Health Service (NHS) in 2012/2013 and the annual levels of healthcare resource use attributable to their management and corresponding costs. METHODS: This was a retrospective cohort analysis of the records of patients in The Health Improvement Network (THIN) Database. Records of 1000 adult patients who had a wound in 2012/2013 (cases) were randomly selected and matched with 1000 patients with no history of a wound (controls). Patients' characteristics, wound-related health outcomes and all healthcare resource use were quantified and the total NHS cost of patient management was estimated at 2013/2014 prices. RESULTS: Patients' mean age was 69.0 years and 45% were male. 76% of patients presented with a new wound in the study year and 61% of wounds healed during the study year. Nutritional deficiency (OR 0.53; p<0.001) and diabetes (OR 0.65; p<0.001) were independent risk factors for non-healing. There were an estimated 2.2 million wounds managed by the NHS in 2012/2013. Annual levels of resource use attributable to managing these wounds and associated comorbidities included 18.6 million practice nurse visits, 10.9 million community nurse visits, 7.7 million GP visits and 3.4 million hospital outpatient visits. The annual NHS cost of managing these wounds and associated comorbidities was pound5.3 billion. This was reduced to between pound5.1 and pound4.5 billion after adjusting for comorbidities. CONCLUSIONS: Real world evidence highlights wound management is predominantly a nurse-led discipline. Approximately 30% of wounds lacked a differential diagnosis, indicative of practical difficulties experienced by non-specialist clinicians. Wounds impose a substantial health economic burden on the UK's NHS, comparable to that of managing obesity ( pound5.0 billion). Clinical and economic benefits could accrue from improved systems of care and an increased awareness of the impact that wounds impose on patients and the NHS.Ye

On the characteristic connection of gwistor space

We give a brief presentation of gwistor space, which is a new concept from G_2 geometry. Then we compute the characteristic torsion T^c of the gwistor space of an oriented Riemannian 4-manifold with constant sectional curvature k and deduce the condition under which T^c is \nabla^c-parallel; this allows for the classification of the G_2 structure with torsion and the characteristic holonomy according to known references. The case with the Einstein base manifold is envisaged.Comment: Many changes since first version, including title; Central European Journal of Mathematics, 201

Domiciliary transcutaneous electrical stimulation in patients with obstructive sleep apnoea and limited adherence to continuous positive airway pressure therapy: a single-centre, open-label, randomised, controlled phase III trial

Background: Hypoglossal nerve stimulation (HNS) for obstructive sleep apnoea (OSA) is a novel way to manage the condition. We hypothesised that in patients with OSA and limited adherence to continuous positive airway pressure (CPAP) therapy, domiciliary transcutaneous electrical stimulation (TESLA) would control sleep apnoea and provide health benefits. Methods: We undertook a single-centre, open-label, randomised, controlled phase III trial in patients with OSA (apnoea-hypopnoea-index [AHI] 5-35 h-1), a BMI of 18.5-32 kg∗m-2, and a documented lack of adherence to CPAP therapy (<4 h∗night-1) at Guy's & St Thomas' NHS Foundation Trust (hospital), UK. Patients were randomly assigned (1:1) using minimisation (gender and OSA severity) to receive TESLA or usual care (CPAP) for at least 3 months; sleep study analysis was provided without knowledge of the assignment arm. The primary outcome was change in AHI at 3-months. The primary outcome and safety were analysed in the intention-to-treat population. Data are reported as median (interquartile range), unless otherwise explained. This trial is registered at ClinicalTrials.gov, NCT03160456. Findings: Between 6 June 2018 and 7 February 2023, 56 participants were enrolled and randomly assigned (29 patients in the intervention group and 27 in the usual care group). Patients were followed up for a median of 3.0 months (IQR 3.0; 10.0). The groups were similar in terms of age (55.8 (48.2; 66.0) vs 59.3 (47.8; 64.4) years), gender (male:female, 19:10 vs 18:9) and BMI (28.7 (26.4; 31.9) vs 28.4 (24.4; 31.9) kg∗m-2). The unadjusted group difference in the Δ AHI was -11.5 (95% CI -20.7; -2.3) h-1 (p = 0.016). Adjusted for the baseline value, the difference was Δ AHI -7.0 (-15.7; 1.8) h-1 (p = 0.12), in favour of the intervention. Minor adverse events were found in one of the participants who developed mild headaches related to the intervention. Interpretation: Domiciliary TESLA can be used safely and effectively in OSA patients with poor adherence to CPAP, with favourable impact on sleepiness and sleep fragmentation. Despite pandemic-related limitations of the amended protocol this trial provides the evidence that TESLA improves clinically meaningful outcomes over the observed follow up period, and the transcutaneous approach is likely to offer an affordable alternative for responders to electrical stimulation in clinical practice. Funding: British Lung Foundation, United Kingdom Clinical Research Collaboration-registered King's Clinical Trials Unit at King's Health Partners. Keywords: CPAP; Genioglossus; Hypoglossal nerve stimulation; Non-CPAP therapy

Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times

We prove upper bounds on angular momentum and centre of mass in terms of the Hamiltonian mass and cosmological constant for non-singular asymptotically anti-de Sitter initial data sets satisfying the dominant energy condition. We work in all space-dimensions larger than or equal to three, and allow a large class of asymptotic backgrounds, with spherical and non-spherical conformal infinities; in the latter case, a spin-structure compatibility condition is imposed. We give a large class of non-trivial examples saturating the inequality. We analyse exhaustively the borderline case in space-time dimension four: for spherical cross-sections of Scri, equality together with completeness occurs only in anti-de Sitter space-time. On the other hand, in the toroidal case, regular non-trivial initial data sets saturating the bound exist.Comment: improvements in the presentation; some statements correcte

On the maximal superalgebras of supersymmetric backgrounds

In this note we give a precise definition of the notion of a maximal superalgebra of certain types of supersymmetric supergravity backgrounds, including the Freund-Rubin backgrounds, and propose a geometric construction extending the well-known construction of its Killing superalgebra. We determine the structure of maximal Lie superalgebras and show that there is a finite number of isomorphism classes, all related via contractions from an orthosymplectic Lie superalgebra. We use the structure theory to show that maximally supersymmetric waves do not possess such a maximal superalgebra, but that the maximally supersymmetric Freund-Rubin backgrounds do. We perform the explicit geometric construction of the maximal superalgebra of AdS_4 x S^7 and find that is isomorphic to osp(1|32). We propose an algebraic construction of the maximal superalgebra of any background asymptotic to AdS_4 x S^7 and we test this proposal by computing the maximal superalgebra of the M2-brane in its two maximally supersymmetric limits, finding agreement.Comment: 17 page

The return of the four- and five-dimensional preons

We prove the existence of 3/4-BPS preons in four- and five-dimensional gauged supergravities by explicitly constructing them as smooth quotients of the AdS_4 and AdS_5 maximally supersymmetric backgrounds, respectively. This result illustrates how the spacetime topology resurrects a fraction of supersymmetry previously ruled out by the local analysis of the Killing spinor equations.Comment: 10 pages (a minor imprecision has been corrected