A simple tool to predict admission at the time of triage

Aim To create and validate a simple clinical score to estimate the probability of admission at the time of triage. Methods This was a multicentre, retrospective, cross-sectional study of triage records for all unscheduled adult attendances in North Glasgow over 2 years. Clinical variables that had significant associations with admission on logistic regression were entered into a mixed-effects multiple logistic model. This provided weightings for the score, which was then simplified and tested on a separate validation group by receiving operator characteristic (ROC) analysis and goodness-of-fit tests. Results 215 231 presentations were used for model derivation and 107 615 for validation. Variables in the final model showing clinically and statistically significant associations with admission were: triage category, age, National Early Warning Score (NEWS), arrival by ambulance, referral source and admission within the last year. The resulting 6-variable score showed excellent admission/discharge discrimination (area under ROC curve 0.8774, 95% CI 0.8752 to 0.8796). Higher scores also predicted early returns for those who were discharged: the odds of subsequent admission within 28 days doubled for every 7-point increase (log odds=+0.0933 per point, p&#60;0.0001). Conclusions This simple, 6-variable score accurately estimates the probability of admission purely from triage information. Most patients could accurately be assigned to ‘admission likely’, ‘admission unlikely’, ‘admission very unlikely’ etc., by setting appropriate cut-offs. This could have uses in patient streaming, bed management and decision support. It also has the potential to control for demographics when comparing performance over time or between departments.</p

One-parameter groups and combinatorial physics

In this communication, we consider the normal ordering of sums of elements of the form (a*^r a a*^s), where a* and a are boson creation and annihilation operators. We discuss the integration of the associated one-parameter groups and their combinatorial by-products. In particular, we show how these groups can be realized as groups of substitutions with prefunctions.Comment: 15 pages, 23 references. Presented at the Third International Workshop on Contemporary Problems in Mathematical Physics (COPROMAPH3), Porto-Novo (Benin), November 200

Normal Order: Combinatorial Graphs

A conventional context for supersymmetric problems arises when we consider systems containing both boson and fermion operators. In this note we consider the normal ordering problem for a string of such operators. In the general case, upon which we touch briefly, this problem leads to combinatorial numbers, the so-called Rook numbers. Since we assume that the two species, bosons and fermions, commute, we subsequently restrict ourselves to consideration of a single species, single-mode boson monomials. This problem leads to elegant generalisations of well-known combinatorial numbers, specifically Bell and Stirling numbers. We explicitly give the generating functions for some classes of these numbers. In this note we concentrate on the combinatorial graph approach, showing how some important classical results of graph theory lead to transparent representations of the combinatorial numbers associated with the boson normal ordering problem.Comment: 7 pages, 15 references, 2 figures. Presented at "Progress in Supersymmetric Quantum Mechanics" (PSQM'03), Valladolid, Spain, July 200

Combinatorial algebra for second-quantized Quantum Theory

We describe an algebra G of diagrams that faithfully gives a diagrammatic representation of the structures of both the Heisenberg–Weyl algebra H – the associative algebra of the creation and annihilation operators of quantum mechanics – and U(LH), the enveloping algebra of the Heisenberg Lie algebra LH. We show explicitly how G may be endowed with the structure of a Hopf algebra, which is also mirrored in the structure of U(LH). While both H and U(LH) are images of G, the algebra G has a richer structure and therefore embodies a finer combinatorial realization of the creation–annihilation system, of which it provides a concrete model

On certain non-unique solutions of the Stieltjes moment problem

We construct explicit solutions of a number of Stieltjes moment problems based on moments of the form (2rn)! and [(rn)!]2. It is shown using criteria for uniqueness and non-uniqueness (Carleman, Krein, Berg, Pakes, Stoyanov) that for r > 1 both forms give rise to non-unique solutions. Examples of such solutions are constructed using the technique of the inverse Mellin transform supplemented by a Mellin convolution. We outline a general method of generating non-unique solutions for moment problems

Landscape genetic connectivity in a riparian foundation tree is jointly driven by climatic gradients and river networks

Fremont cottonwood (Populus fremonti) is a foundation riparian tree species that drives community structure and ecosystem processes in southwestern U.S. ecosystems. Despite its ecological importance, little is known about the ecological and environmental processes that shape its genetic diversity, structure, and landscape connectivity. Here, we combined molecular analyses of 82 populations including 1312 individual trees dispersed over the species’ geographical distribution. We reduced the data set to 40 populations and 743 individuals to eliminate admixture with a sibling species, and used multivariate restricted optimization and reciprocal causal modeling to evaluate the effects of river network connectivity and climatic gradients on gene flow. Our results confirmed the following: First, gene flow of Fremont cottonwood is jointly controlled by the connectivity of the river network and gradients of seasonal precipitation. Second, gene flow is facilitated by mid-sized to large rivers, and is resisted by small streams and terrestrial uplands, with resistance to gene flow decreasing with river size. Third, genetic differentiation increases with cumulative differences in winter and spring precipitation. Our results suggest that ongoing fragmentation of riparian habitats will lead to a loss of landscape-level genetic connectivity, leading to increased inbreeding and the concomitant loss of genetic diversity in a foundation species. These genetic effects will cascade to a much larger community of organisms, some of which are threatened and endangered

Effect of Air Injection on Nucleation Rates: An Approach from Induction Time Statistics

From disruption of the supersaturated solution to improved mass transfer in the crystallizing suspension, the introduction of a moving gas phase in a crystallizer could lead to improved rates of nucleation and crystal growth. In this work, saturated air has been injected to batch crystallizers to study the effects on formation of the first crystal and subsequent turbidity buildup. To account for the typically large sample-to-sample variation, nucleation rates were evaluated for a large number of replicates using probability distributions of induction times. The slope and the intercept of the distributions were studied independently, allowing the simultaneous determination of the mean induction time and a certain detection delay related to the rate of crystal growth after formation of the first nucleus. When saturated air was injected in aqueous glycine solutions, the average detection delay was reduced from 69 to 13 min, and the mean induction time decreased from 128 to 36 min. The effect on aqueous solutions of l-arginine was less apparent, with a detection delay reduction from 15 to 3 min, and no significant changes on the rate of primary nucleation. These results demonstrate the potential of this technique for reduction in nucleation induction time and improved mass deposition rates in crystallization operations