Quartet compatibility and the quartet graph

A collection P of leaf-labelled trees is compatible if there exists a single leaf-labelled tree that displays each of the trees in P. Despite its difficulty, determining the compatibility of P is a fundamental task in evolutionary biology. Attractive characterizations in terms of chordal graphs have been previously given for this problem as well as for the problems of (i) determining if there is a unique tree that displays each of the trees in P, that is 'P is definitive and (ii) determining if there is a tree that displays P and has the property that every other tree that displays P is a refinement of it, that is 'P identifies a leaf-labelled tree. In this paper, we describe new characterizations of each of these problems in terms of edge colourings. Furthermore, for an arbitrary leaf-labelled tree 'T, we also determine the minimum number of 'quartets' required to identify 'T, thus correcting a previously published result

The comparative clinical course of pregnant and non-pregnant women hospitalised with influenza A(H1N1)pdm09 infection

Introduction: The Influenza Clinical Information Network (FLU-CIN) was established to gather detailed clinical and epidemiological information about patients with laboratory confirmed A(H1N1)pdm09 infection in UK hospitals. This report focuses on the clinical course and outcomes of infection in pregnancy.Methods: A standardised data extraction form was used to obtain detailed clinical information from hospital case notes and electronic records, for patients with PCR-confirmed A(H1N1)pdm09 infection admitted to 13 sentinel hospitals in five clinical 'hubs' and a further 62 non-sentinel hospitals, between 11th May 2009 and 31st January 2010.Outcomes were compared for pregnant and non-pregnant women aged 15-44 years, using univariate and multivariable techniques.Results: Of the 395 women aged 15-44 years, 82 (21%) were pregnant; 73 (89%) in the second or third trimester. Pregnant women were significantly less likely to exhibit severe respiratory distress at initial assessment (OR?=?0.49 (95% CI: 0.30-0.82)), require supplemental oxygen on admission (OR?=?0.40 (95% CI: 0.20-0.80)), or have underlying co-morbidities (p-trend <0.001). However, they were equally likely to be admitted to high dependency (Level 2) or intensive care (Level 3) and/or to die, after adjustment for potential confounders (adj. OR?=?0.93 (95% CI: 0.46-1.92). Of 11 pregnant women needing Level 2/3 care, 10 required mechanical ventilation and three died.Conclusions: Since the expected prevalence of pregnancy in the source population was 6%, our data suggest that pregnancy greatly increased the likelihood of hospital admission with A(H1N1)pdm09. Pregnant women were less likely than non-pregnant women to have respiratory distress on admission, but severe outcomes were equally likely in both groups

Neighborhoods of trees in circular orderings

In phylogenetics, a common strategy used to construct an evolutionary tree for a set of species X is to search in the space of all such trees for one that optimizes some given score function (such as the minimum evolution, parsimony or likelihood score). As this can be computationally intensive, it was recently proposed to restrict such searches to the set of all those trees that are compatible with some circular ordering of the set X. To inform the design of efficient algorithms to perform such searches, it is therefore of interest to find bounds for the number of trees compatible with a fixed ordering in the neighborhood of a tree that is determined by certain tree operations commonly used to search for trees: the nearest neighbor interchange (nni), the subtree prune and regraft (spr) and the tree bisection and reconnection (tbr) operations. We show that the size of such a neighborhood of a binary tree associated with the nni operation is independent of the tree’s topology, but that this is not the case for the spr and tbr operations. We also give tight upper and lower bounds for the size of the neighborhood of a binary tree for the spr and tbr operations and characterize those trees for which these bounds are attained

The relationship between workers' self-reported changes in health and their attitudes towards a workplace intervention: lessons from smoke-free legislation across the UK hospitality industry

Background: The evaluation of smoke-free legislation (SFL) in the UK examined the impacts on exposure to second-hand smoke, workers’ attitudes and changes in respiratory health. Studies that investigate changes in the health of groups of people often use self-reported symptoms. Due to the subjective nature it is of interest to determine whether workers’ attitudes towards the change in their working conditions may be linked to the change in health they report. Methods: Bar workers were recruited before the introduction of the SFL in Scotland and England with the aim of investigating their changes to health, attitudes and exposure as a result of the SFL. They were asked about their attitudes towards SFL and the presence of respiratory and sensory symptoms both before SFL and one year later. Here we examine the possibility of a relationship between initial attitudes and changes in reported symptoms, through the use of regression analyses. Results: There was no difference in the initial attitudes towards SFL between those working in Scotland and England. Bar workers who were educated to a higher level tended to be more positive towards SFL. Attitude towards SFL was not found to be related to change in reported symptoms for bar workers in England (Respiratory, p = 0.755; Sensory, p = 0.910). In Scotland there was suggestion of a relationship with reporting of respiratory symptoms (p = 0.042), where those who were initially more negative to SFL experienced a greater improvement in self-reported health. Conclusions: There was no evidence that workers who were more positive towards SFL reported greater improvements in respiratory and sensory symptoms. This may not be the case in all interventions and we recommend examining subjects’ attitudes towards the proposed intervention when evaluating possible health benefits using self-reported methods. Keywords: ‘Self-Reported Health’, Attitudes, ‘Workplace Intervention’, ‘Public Health Intervention

Geometric Interpretation of the Mixed Invariants of the Riemann Spinor

Mixed invariants are used to classify the Riemann spinor in the case of Einstein-Maxwell fields and perfect fluids. In the Einstein-Maxwell case these mixed invariants provide information as to the relative orientation of the gravitational and electromagnetic principal null directions. Consideration of the perfect fluid case leads to some results about the behaviour of the Bel-Robinson tensor regarded as a quartic form on unit timelike vectors.Comment: 31 pages, AMS-LaTe

Generalized Buneman pruning for inferring the most parsimonious multi-state phylogeny

Accurate reconstruction of phylogenies remains a key challenge in evolutionary biology. Most biologically plausible formulations of the problem are formally NP-hard, with no known efficient solution. The standard in practice are fast heuristic methods that are empirically known to work very well in general, but can yield results arbitrarily far from optimal. Practical exact methods, which yield exponential worst-case running times but generally much better times in practice, provide an important alternative. We report progress in this direction by introducing a provably optimal method for the weighted multi-state maximum parsimony phylogeny problem. The method is based on generalizing the notion of the Buneman graph, a construction key to efficient exact methods for binary sequences, so as to apply to sequences with arbitrary finite numbers of states with arbitrary state transition weights. We implement an integer linear programming (ILP) method for the multi-state problem using this generalized Buneman graph and demonstrate that the resulting method is able to solve data sets that are intractable by prior exact methods in run times comparable with popular heuristics. Our work provides the first method for provably optimal maximum parsimony phylogeny inference that is practical for multi-state data sets of more than a few characters.Comment: 15 page

Impact of Scottish smoke-free legislation on smoking quit attempts and prevalence

<p><b>Objectives:</b> In Scotland, legislation was implemented in March 2006 prohibiting smoking in all wholly or partially enclosed public spaces. We investigated the impact on attempts to quit smoking and smoking prevalence.</p> <p><b>Methods:</b> We performed time series models using Box-Jenkins autoregressive integrated moving averages (ARIMA) on monthly data on the gross ingredient cost of all nicotine replacement therapy (NRT) prescribed in Scotland in 2003–2009, and quarterly data on self-reported smoking prevalence between January 1999 and September 2010 from the Scottish Household Survey.</p> <p><b>Results:</b> NRT prescription costs were significantly higher than expected over the three months prior to implementation of the legislation. Prescription costs peaked at £1.3 million in March 2006; £292,005.9 (95% CI £260,402.3, £323,609, p<0.001) higher than the monthly norm. Following implementation of the legislation, costs fell exponentially by around 26% per month (95% CI 17%, 35%, p<0.001). Twelve months following implementation, the costs were not significantly different to monthly norms. Smoking prevalence fell by 8.0% overall, from 31.3% in January 1999 to 23.7% in July–September 2010. In the quarter prior to implementation of the legislation, smoking prevalence fell by 1.7% (95% CI 2.4%, 1.0%, p<0.001) more than expected from the underlying trend.</p> <p><b>Conclusions:</b> Quit attempts increased in the three months leading up to Scotland's smoke-free legislation, resulting in a fall in smoking prevalence. However, neither has been sustained suggesting the need for additional tobacco control measures and ongoing support.</p&gt

A Note on Encodings of Phylogenetic Networks of Bounded Level

Driven by the need for better models that allow one to shed light into the question how life's diversity has evolved, phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees, such networks canonically induce collections of phylogenetic trees, clusters, and triplets, respectively. Thus it is not surprising that many network approaches aim to reconstruct a phylogenetic network from such collections. Related to the well-studied perfect phylogeny problem, the following question is of fundamental importance in this context: When does one of the above collections encode (i.e. uniquely describe) the network that induces it? In this note, we present a complete answer to this question for the special case of a level-1 (phylogenetic) network by characterizing those level-1 networks for which an encoding in terms of one (or equivalently all) of the above collections exists. Given that this type of network forms the first layer of the rich hierarchy of level-k networks, k a non-negative integer, it is natural to wonder whether our arguments could be extended to members of that hierarchy for higher values for k. By giving examples, we show that this is not the case