Thinplate Splines on the Sphere

In this paper we give explicit closed forms for the semi-reproducing kernels associated with thinplate spline interpolation on the sphere. Polyharmonic or thinplate splines for ${\mathbb R}^d$ were introduced by Duchon and have become a widely used tool in myriad applications. The analogues for ${\mathbb S}^{d-1}$ are the thin plate splines for the sphere. The topic was first discussed by Wahba in the early 1980's, for the ${\mathbb S}^2$ case. Wahba presented the associated semi-reproducing kernels as infinite series. These semi-reproducing kernels play a central role in expressions for the solution of the associated spline interpolation and smoothing problems. The main aims of the current paper are to give a recurrence for the semi-reproducing kernels, and also to use the recurrence to obtain explicit closed form expressions for many of these kernels. The closed form expressions will in many cases be significantly faster to evaluate than the series expansions. This will enhance the practicality of using these thinplate splines for the sphere in computations

One-Step Recurrences for Stationary Random Fields on the Sphere

Recurrences for positive definite functions in terms of the space dimension have been used in several fields of applications. Such recurrences typically relate to properties of the system of special functions characterizing the geometry of the underlying space. In the case of the sphere ${\mathbb S}^{d-1} \subset {\mathbb R}^d$ the (strict) positive definiteness of the zonal function $f(\cos \theta)$ is determined by the signs of the coefficients in the expansion of $f$ in terms of the Gegenbauer polynomials $\{C^\lambda_n\}$, with $\lambda=(d-2)/2$. Recent results show that classical differentiation and integration applied to $f$ have positive definiteness preserving properties in this context. However, in these results the space dimension changes in steps of two. This paper develops operators for zonal functions on the sphere which preserve (strict) positive definiteness while moving up and down in the ladder of dimensions by steps of one. These fractional operators are constructed to act appropriately on the Gegenbauer polynomials $\{C^\lambda_n\}$

Localized bases for kernel spaces on the unit sphere

Approximation/interpolation from spaces of positive definite or conditionally positive definite kernels is an increasingly popular tool for the analysis and synthesis of scattered data, and is central to many meshless methods. For a set of $N$ scattered sites, the standard basis for such a space utilizes $N$ \emph{globally} supported kernels; computing with it is prohibitively expensive for large $N$. Easily computable, well-localized bases, with "small-footprint" basis elements - i.e., elements using only a small number of kernels -- have been unavailable. Working on \sphere, with focus on the restricted surface spline kernels (e.g. the thin-plate splines restricted to the sphere), we construct easily computable, spatially well-localized, small-footprint, robust bases for the associated kernel spaces. Our theory predicts that each element of the local basis is constructed by using a combination of only $\mathcal{O}((\log N)^2)$ kernels, which makes the construction computationally cheap. We prove that the new basis is $L_p$ stable and satisfies polynomial decay estimates that are stationary with respect to the density of the data sites, and we present a quasi-interpolation scheme that provides optimal $L_p$ approximation orders. Although our focus is on $\mathbb{S}^2$, much of the theory applies to other manifolds - $\mathbb{S}^d$, the rotation group, and so on. Finally, we construct algorithms to implement these schemes and use them to conduct numerical experiments, which validate our theory for interpolation problems on $\mathbb{S}^2$ involving over one hundred fifty thousand data sites.Comment: This article supersedes arXiv:1111.1013 "Better bases for kernel spaces," which proved existence of better bases for various kernel spaces. This article treats a smaller class of kernels, but presents an algorithm for constructing better bases and demonstrates its effectiveness with more elaborate examples. A quasi-interpolation scheme is introduced that provides optimal linear convergence rate

Easyfig: a genome comparison visualizer

Summary: Easyfig is a Python application for creating linear comparison figures of multiple genomic loci with an easy-to-use graphical user interface. BLAST comparisons between multiple genomic regions, ranging from single genes to whole prokaryote chromosomes, can be generated, visualized and interactively coloured, enabling a rapid transition between analysis and the preparation of publication quality figures

Performance of externally validated enhanced computer-aided versions of the National Early Warning Score in predicting mortality following an emergency admission to hospital in England: a cross-sectional study

YesOBJECTIVES: In the English National Health Service, the patient's vital signs are monitored and summarised into a National Early Warning Score (NEWS) to support clinical decision making, but it does not provide an estimate of the patient's risk of death. We examine the extent to which the accuracy of NEWS for predicting mortality could be improved by enhanced computer versions of NEWS (cNEWS). DESIGN: Logistic regression model development and external validation study. SETTING: Two acute hospitals (YH-York Hospital for model development; NH-Northern Lincolnshire and Goole Hospital for external model validation). PARTICIPANTS: Adult (≥16 years) medical admissions discharged over a 24-month period with electronic NEWS (eNEWS) recorded on admission are used to predict mortality at four time points (in-hospital, 24 hours, 48 hours and 72 hours) using the first electronically recorded NEWS (model M0) versus a cNEWS model which included age+sex (model M1) +subcomponents of NEWS (including diastolic blood pressure) (model M2). RESULTS: The risk of dying in-hospital following emergency medical admission was 5.8% (YH: 2080/35 807) and 5.4% (NH: 1900/35 161). The c-statistics for model M2 in YH for predicting mortality (in-hospital=0.82, 24 hours=0.91, 48 hours=0.88 and 72 hours=0.88) was higher than model M0 (in-hospital=0.74, 24 hours=0.89, 48 hours=0.86 and 72 hours=0.85) with higher Positive Predictive Value (PPVs) for in-hospital mortality (M2 19.3% and M0 16.6%). Similar findings were seen in NH. Model M2 performed better than M0 in almost all major disease subgroups. CONCLUSIONS: An externally validated enhanced computer-aided NEWS model (cNEWS) incrementally improves on the performance of a NEWS only model. Since cNEWS places no additional data collection burden on clinicians and is readily automated, it may now be carefully introduced and evaluated to determine if it can improve care in hospitals that have eNEWS systems.This research was supported by the Health Foundation. The Health Foundation is an independent charity working to improve the quality of healthcare in the UK. This research was also supported by the National Institute for Health Research (NIHR) Yorkshire and Humberside Patient Safety Translational Research Centre (YHPSTRC)

The inclusion of delirium in version 2 of the National Early Warning Score will substantially increase the alerts for escalating levels of care: findings from a retrospective database study of emergency medical admissions in two hospitals

YesBackground The National Early Warning Score (NEWS) is being replaced with NEWS2 which adds 3 points for new confusion or delirium. We estimated the impact of adding delirium on the number of medium/high level alerts that are triggers to escalate care. Methods Analysis of emergency medical admissions in two acute hospitals (York Hospital (YH) and Northern Lincolnshire and Goole NHS Foundation Trust hospitals (NH)) in England. Twenty per cent were randomly assigned to have delirium. Results The number of emergency admissions (YH: 35584; NH: 35795), mortality (YH: 5.7%; NH: 5.5%), index NEWS (YH: 2.5; NH: 2.1) and numbers of NEWS recorded (YH: 879193; NH: 884072) were similar in each hospital. The mean number of patients with medium level alerts per day increased from 55.3 (NEWS) to 69.5 (NEWS2), a 25.7% increase in YH and 64.1 (NEWS) to 77.4 (NEWS2), a 20.7% increase in NH. The mean number of patients with high level alerts per day increased from 27.3 (NEWS) to 34.4 (NEWS2), a 26.0% increase in YH and 29.9 (NEWS) to 37.7 (NEWS2), a 26.1% increase in NH. Conclusions The addition of delirium in NEWS2 will have a substantial increase in medium and high level alerts in hospitalised emergency medical patients. Rigorous evaluation of NEWS2 is required before widespread implementation because the extent to which staff can cope with this increase without adverse consequences remains unknown

The co-transcriptome of uropathogenic Escherichia coli-infected mouse macrophages reveals new insights into host-pathogen interactions

© 2014 The Authors. Cellular Microbiology published by John Wiley & Sons Ltd. Urinary tract infections (UTI) are among the most common infections in humans. Uropathogenic Escherichia coli (UPEC) can invade and replicate within bladder epithelial cells, and some UPEC strains can also survive within macrophages. To understand the UPEC transcriptional programme associated with intramacrophage survival, we performed host-pathogen co-transcriptome analyses using RNA sequencing. Mouse bone marrow-derived macrophages (BMMs) were challenged over a 24h time course with two UPEC reference strains that possess contrasting intramacrophage phenotypes: UTI89, which survives in BMMs, and 83972, which is killed by BMMs. Neither of these strains caused significant BMM cell death at the low multiplicity of infection that was used in this study. We developed an effective computational framework that simultaneously separated, annotated and quantified the mammalian and bacterial transcriptomes. Bone marrow-derived macrophages responded to the two UPEC strains with a broadly similar gene expression programme. In contrast, the transcriptional responses of the UPEC strains diverged markedly from each other. We identified UTI89 genes up-regulated at 24h post-infection, and hypothesized that some may contribute to intramacrophage survival. Indeed, we showed that deletion of one such gene (pspA) significantly reduced UTI89 survival within BMMs. Our study provides a technological framework for simultaneously capturing global changes at the transcriptional level in co-cultures, and has generated new insights into the mechanisms that UPEC use to persist within the intramacrophage environment

Predictive accuracy of enhanced versions of the on-admission National Early Warning Score in estimating the risk of COVID-19 for unplanned admission to hospital: a retrospective development and validation study

YesThe novel coronavirus SARS-19 produces 'COVID-19' in patients with symptoms. COVID-19 patients admitted to the hospital require early assessment and care including isolation. The National Early Warning Score (NEWS) and its updated version NEWS2 is a simple physiological scoring system used in hospitals, which may be useful in the early identification of COVID-19 patients. We investigate the performance of multiple enhanced NEWS2 models in predicting the risk of COVID-19. Our cohort included unplanned adult medical admissions discharged over 3 months (11 March 2020 to 13 June 2020 ) from two hospitals (YH for model development; SH for external model validation). We used logistic regression to build multiple prediction models for the risk of COVID-19 using the first electronically recorded NEWS2 within ± 24 hours of admission. Model M0' included NEWS2; model M1' included NEWS2 + age + sex, and model M2' extends model M1' with subcomponents of NEWS2 (including diastolic blood pressure + oxygen flow rate + oxygen scale). Model performance was evaluated according to discrimination (c statistic), calibration (graphically), and clinical usefulness at NEWS2 ≥ 5. The prevalence of COVID-19 was higher in SH (11.0 %=277/2520) than YH (8.7 %=343/3924) with a higher first NEWS2 scores ( SH 3.2 vs YH 2.8) but similar in-hospital mortality (SH 8.4 % vs YH 8.2 %). The c-statistics for predicting the risk of COVID-19 for models M0',M1',M2' in the development dataset were: M0': 0.71 (95 %CI 0.68-0.74); M1': 0.67 (95 %CI 0.64-0.70) and M2': 0.78 (95 %CI 0.75-0.80)). For the validation datasets the c-statistics were: M0' 0.65 (95 %CI 0.61-0.68); M1': 0.67 (95 %CI 0.64-0.70) and M2': 0.72 (95 %CI 0.69-0.75) ). The calibration slope was similar across all models but Model M2' had the highest sensitivity (M0' 44 % (95 %CI 38-50 %); M1' 53 % (95 %CI 47-59 %) and M2': 57 % (95 %CI 51-63 %)) and specificity (M0' 75 % (95 %CI 73-77 %); M1' 72 % (95 %CI 70-74 %) and M2': 76 % (95 %CI 74-78 %)) for the validation dataset at NEWS2 ≥ 5. Model M2' appears to be reasonably accurate for predicting the risk of COVID-19. It may be clinically useful as an early warning system at the time of admission especially to triage large numbers of unplanned hospital admissions.The Health Foundation (Award No 7380) and the National Institute for Health Research (NIHR) Yorkshire and Humber Patient Safety Translational Research Centre (NIHR Yorkshire and Humber PSTRC) (Award No PSTRC-2016-006)Research Development Fund Publication Prize Award winner, Aug 2021