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

Expression of recombinant multi-coloured fluorescent antibodies in gor -/trxB- E. coli cytoplasm

<p>Abstract</p> <p>Background</p> <p>Antibody-fluorophore conjugates are invaluable reagents used in contemporary molecular cell biology for imaging, cell sorting and tracking intracellular events. However they suffer in some cases from batch to batch variation, partial loss of binding and susceptibility to photo-bleaching. In theory, these issues can all be addressed by using recombinant antibody fused directly to genetically encoded fluorescent reporters. However, single-chain fragment variable domains linked by long flexible linkers are themselves prone to disassociation and aggregation, and in some cases with isoelectric points incompatible with use in physiologically relevant milieu. Here we describe a general approach that permits fully functional intracellular production of a range of coloured fluorescent recombinant antibodies with optimally orientated V_H/V_Linterfaces and isoelectric points compatible for use in physiological solutions at pH 7.4 with a binding site to fluorophore stoichiometry of 1:1.</p> <p>Results</p> <p>Here we report the design, assembly, intracellular bacterial production and purification of a panel of novel antibody fluorescent protein fusion constructs. The insertion of monomeric fluorescent protein derived from either <it>Discosoma </it>or <it>Aequorea </it>in-between the variable regions of anti-p185^HER2-ECDantibody 4D5-8 resulted in optimal V_H/V_Linterface interactions to create soluble coloured antibodies each with a single binding site, with isoelectric points of 6.5- 6. The fluorescent antibodies used in cell staining studies with SK-BR-3 cells retained the fluorophore properties and antibody specificity functions, whereas the conventional 4D5-8 single chain antibody with a (Gly₄Ser)₃linker precipitated at physiological pH 7.4.</p> <p>Conclusions</p> <p>This modular monomeric recombinant fluorescent antibody platform may be used to create a range of recombinant coloured antibody molecules for quantitative <it>in situ, in vivo </it>and <it>ex vivo </it>imaging, cell sorting and cell trafficking studies. Assembling the single chain antibody with monomeric fluorescent protein linker facilitates optimal variable domain pairing and alters the isoelectric point of the recombinant 4D5-8 protein conferring solubility at physiological pH 7.4. The efficient intracellular expression of these functional molecules opens up the possibility of developing an alternative approach for tagging intracellular targets with fluorescent proteins for a range of molecular cell biology imaging studies.</p

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

Harnessing cd8⁺cd28⁻ regulatory t cells as a tool to treat autoimmune disease

T regulatory cell therapy presents a novel therapeutic strategy for patients with autoimmune diseases or who are undergoing transplantation. At present, the CD4+ Treg population has been extensively characterized, as a result of defined phenotypic and functional readouts. In this review article, we discuss the development and biology of CD8+ Tregs and their role in murine and human disease indications. A subset of CD8+ Tregs that lack the surface expression of CD28 (CD8+CD28− Treg) has proved efficacious in preclinical models. CD8+CD28− Tregs are present in healthy individuals, but their impaired functionality in disease renders them less effective in mediating immunosuppression. We primarily focus on harnessing CD8+ Treg cell therapy in the clinic to support current treatment for patients with autoimmune or inflammatory conditions