Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems

We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on the mean curvature of the hypersurface. Using these results, we give a new proof of Hawking's singularity theorem.Comment: 15 pages, LaTe

Cohort Profile:Health and Wellbeing of People with Intellectual Disability in New South Wales, Australia – A data linkage cohort

Purpose People with intellectual disability (ID) experience high rates of physical and mental health problems, while access to appropriate healthcare is often poor. This cohort was established to develop an epidemiological profile related to the health, health service use, disability services, mortality and corrective services records of people with ID. Participants The cohort contains 92 542 people with ID (40% females) with a median age of 23 years (IQR: 12–43 years) and 2 004 475 people with a neuropsychiatric or developmental disorder diagnosis (50% females) with a median age of 51 years (IQR: 29–73 years) from New South Wales, Australia. The whole sample contains records for 2 097 017 individuals with most data sets spanning financial years 1 July 2001 to 30 June 2016. A wide range of data from linked population data sets are included in the areas of disability, health, corrective services and targeted specialist support services in public schools, Public Guardian and Ombudsman services. Findings to date This study includes one of the largest cohorts of people with ID internationally. Our data have shown that the presence of ID is significantly associated with emergency department presentations and psychiatric readmissions after the first psychiatric admission based on a subcohort of people with a psychiatric admission. Adults with ID experience premature mortality and over-representation of potentially avoidable deaths compared with the general population. Future plans Within the health service system, we will examine different components, that is, inpatient, emergency adult services, children and younger people services and costs associated with healthcare as well as mortality, cause and predictors of death. The neuropsychiatric and developmental disorders comparison cohort allows comparisons of the physical health, mental health and service use profiles of people with ID and those with other neuropsychiatric disorders

On the growth of nonuniform lattices in pinched negatively curved manifolds

We study the relation between the exponential growth rate of volume in a pinched negatively curved manifold and the critical exponent of its lattices. These objects have a long and interesting story and are closely related to the geometry and the dynamical properties of the geodesic flow of the manifold

Brownian bridges to submanifolds

We introduce and study Brownian bridges to submanifolds. Our method involves proving a general formula for the integral over a submanifold of the minimal heat kernel on a complete Riemannian manifold. We use the formula to derive lower bounds, an asymptotic relation and derivative estimates. We also see a connection to hypersurface local time. This work is motivated by the desire to extend the analysis of path and loop spaces to measures on paths which terminate on a submanifold

Low threshold particle arrays

While atmospheric Cherenkov telescopes have a small field of view and a small duty fraction, arrays of particle detectors on ground have a 1\,sr field of view and a 100% duty fraction. On the other hand, particle detector arrays have a much higher energy threshold and an inferior hadron rejection as compared to Cherenkov telescopes. Low threshold particle detector arrays would have potential advantages over Cherenkov telescopes in the search for episodic or unexpected sources of gamma rays in the multi-TeV energy range. Ways to improve the threshold and hadron rejection of arrays are shown, based on existing technology for the timing method (with scintillator or water Cherenkov counters) and the tracking method (with tracking detectors). The performance that could be achieved is shown by examples for both methods. At mountain altitude (about 4000 m or above) an energy threshold close to 1\,TeV could be achieved. For any significant reduction of the hadronic background by selecting muon-poor showers a muon detection area of at least 1000 m^2 is required, even for a compact array

Implications for post critical illness trial design: sub-phenotyping trajectories of functional recovery among sepsis survivors.

This is a post-peer-review, pre-copyedit version of an article published in Critical Care. The final authenticated version is available online at: https://doi.org/10.1186/s13054-020-03275-wBACKGROUND: Patients who survive critical illness suffer from a significant physical disability. The impact of rehabilitation strategies on health-related quality of life is inconsistent, with population heterogeneity cited as one potential confounder. This secondary analysis aimed to (1) examine trajectories of functional recovery in critically ill patients to delineate sub-phenotypes and (2) to assess differences between these cohorts in both clinical characteristics and clinimetric properties of physical function assessment tools. METHODS: Two hundred ninety-one adult sepsis survivors were followed-up for 24 months by telephone interviews. Physical function was assessed using the Physical Component Score (PCS) of the Short Form-36 Questionnaire (SF-36) and Activities of Daily Living and the Extra Short Musculoskeletal Function Assessment (XSFMA-F/B). Longitudinal trajectories were clustered by factor analysis. Logistical regression analyses were applied to patient characteristics potentially determining cluster allocation. Responsiveness, floor and ceiling effects and concurrent validity were assessed within clusters. RESULTS: One hundred fifty-nine patients completed 24 months of follow-up, presenting overall low PCS scores. Two distinct sub-cohorts were identified, exhibiting complete recovery or persistent impairment. A third sub-cohort could not be classified into either trajectory. Age, education level and number of co-morbidities were independent determinants of poor recovery (AUROC 0.743 ((95%CI 0.659-0.826), p < 0.001). Those with complete recovery trajectories demonstrated high levels of ceiling effects in physical function (PF) (15%), role physical (RP) (45%) and body pain (BP) (57%) domains of the SF-36. Those with persistent impairment demonstrated high levels of floor effects in the same domains: PF (21%), RP (71%) and BP (12%). The PF domain demonstrated high responsiveness between ICU discharge and at 6 months and was predictive of a persistent impairment trajectory (AUROC 0.859 (95%CI 0.804-0.914), p < 0.001). CONCLUSIONS: Within sepsis survivors, two distinct recovery trajectories of physical recovery were demonstrated. Older patients with more co-morbidities and lower educational achievements were more likely to have a persistent physical impairment trajectory. In regard to trajectory prediction, the PF score of the SF-36 was more responsive than the PCS and could be considered for primary outcomes. Future trials should consider adaptive trial designs that can deal with non-responders or sub-cohort specific outcome measures more effectively

The effectiveness of public health interventions to reduce the health impact of climate change:a systematic review of systematic reviews

Climate change is likely to be one of the most important threats to public health in the coming years. Yet despite the large number of papers considering the health impact of climate change, few have considered what public health interventions may be of most value in reducing the disease burden. We aimed to evaluate the effectiveness of public health interventions to reduce the disease burden of high priority climate sensitive diseases

A Cryogenic Silicon Interferometer for Gravitational-wave Detection

The detection of gravitational waves from compact binary mergers by LIGO has opened the era of gravitational wave astronomy, revealing a previously hidden side of the cosmos. To maximize the reach of the existing LIGO observatory facilities, we have designed a new instrument that will have 5 times the range of Advanced LIGO, or greater than 100 times the event rate. Observations with this new instrument will make possible dramatic steps toward understanding the physics of the nearby universe, as well as observing the universe out to cosmological distances by the detection of binary black hole coalescences. This article presents the instrument design and a quantitative analysis of the anticipated noise floor