Random Convex Hulls and Extreme Value Statistics

In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting

Search for Neutrinoless Double- β Decay with the Complete EXO-200 Dataset

A search for neutrinoless double-β decay (0νββ) in Xe136 is performed with the full EXO-200 dataset using a deep neural network to discriminate between 0νββ and background events. Relative to previous analyses, the signal detection efficiency has been raised from 80.8% to 96.4±3.0%, and the energy resolution of the detector at the Q value of Xe136 0νββ has been improved from σ/E=1.23% to 1.15±0.02% with the upgraded detector. Accounting for the new data, the median 90% confidence level 0νββ half-life sensitivity for this analysis is 5.0×1025 yr with a total Xe136 exposure of 234.1 kg yr. No statistically significant evidence for 0νββ is observed, leading to a lower limit on the 0νββ half-life of 3.5×1025 yr at the 90% confidence level

Search for Neutrinoless Double-Beta Decay with the Upgraded EXO-200 Detector

Results from a search for neutrinoless double-beta decay (0νββ) of Xe136 are presented using the first year of data taken with the upgraded EXO-200 detector. Relative to previous searches by EXO-200, the energy resolution of the

Dimethyl fumarate in patients admitted to hospital with COVID-19 (RECOVERY): a randomised, controlled, open-label, platform trial

Dimethyl fumarate (DMF) inhibits inflammasome-mediated inflammation and has been proposed as a treatment for patients hospitalised with COVID-19. This randomised, controlled, open-label platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]), is assessing multiple treatments in patients hospitalised for COVID-19 (NCT04381936, ISRCTN50189673). In this assessment of DMF performed at 27 UK hospitals, adults were randomly allocated (1:1) to either usual standard of care alone or usual standard of care plus DMF. The primary outcome was clinical status on day 5 measured on a seven-point ordinal scale. Secondary outcomes were time to sustained improvement in clinical status, time to discharge, day 5 peripheral blood oxygenation, day 5 C-reactive protein, and improvement in day 10 clinical status. Between 2 March 2021 and 18 November 2021, 713 patients were enroled in the DMF evaluation, of whom 356 were randomly allocated to receive usual care plus DMF, and 357 to usual care alone. 95% of patients received corticosteroids as part of routine care. There was no evidence of a beneficial effect of DMF on clinical status at day 5 (common odds ratio of unfavourable outcome 1.12; 95% CI 0.86-1.47; p = 0.40). There was no significant effect of DMF on any secondary outcome

Colonic bacterial proteases to IgA1 and sIgA in patients with ulcerative colitis.

The colonic faecal and mucosal associated bacterial populations of five patients with ulcerative colitis and four control patients were studied in detail to assess their ability to produce IgA1-proteases. A total of 330 bacterial strains were isolated from the patients with ulcerative colitis and IgA1-protease activity was unable to be reliably shown in any. It is therefore unlikely that such enzyme production by colonic bacteria plays a significant role in the pathogenesis of ulcerative colitis

Further delineation of phenotypic spectrum of SCN2A-related disorder

SCN2A-related disorders include intellectual disability, autism spectrum disorder, seizures, episodic ataxia, and schizophrenia. In this study, the phenotype–genotype association in SCN2A-related disorders was further delineated by collecting detailed clinical and molecular characteristics. Using previously proposed genotype–phenotype hypotheses based on variant function and position, the potential of phenotype prediction from the variants found was examined. Patients were identified through the Deciphering Developmental Disorders study and gene matching strategies. Phenotypic information and variant interpretation evidence were collated. Seventeen previously unreported patients and five patients who had been previously reported (but with minimal phenotypic and segregation data) were included (10 males, 12 females; median age 10.5 years). All patients had developmental delays and the majority had intellectual disabilities. Seizures were reported in 15 of 22 (68.2%), four of 22 (18.2%) had autism spectrum disorder and no patients were reported with episodic ataxia. The majority of variants were de novo. One family had presumed gonadal mosaicism. The correlation of the use of sodium channel-blocking antiepileptic drugs with phenotype or genotype was variable. These data suggest that variant type and position alone can provide some predictive information about the phenotype in a proportion of cases, but more precise assessment of variant function is needed for meaningful phenotype prediction