A well-separated pairs decomposition algorithm for k-d trees implemented on multi-core architectures

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Variations of k-d trees represent a fundamental data structure used in Computational Geometry with numerous applications in science. For example particle track tting in the software of the LHC experiments, and in simulations of N-body systems in the study of dynamics of interacting galaxies, particle beam physics, and molecular dynamics in biochemistry. The many-body tree methods devised by Barnes and Hutt in the 1980s and the Fast Multipole Method introduced in 1987 by Greengard and Rokhlin use variants of k-d trees to reduce the computation time upper bounds to O(n log n) and even O(n) from O(n2). We present an algorithm that uses the principle of well-separated pairs decomposition to always produce compressed trees in O(n log n) work. We present and evaluate parallel implementations for the algorithm that can take advantage of multi-core architectures.The Science and Technology Facilities Council, UK

Efficacy and safety of statin treatment for cardiovascular disease: a network meta-analysis of 170 255 patients from 76 randomized trials

Background: Statins represent the largest selling class of cardiovascular drug in the world. Previous randomized trials (RCTs) have demonstrated important clinical benefits with statin therapy. Aim: We combined evidence from all RCTs comparing a statin with placebo or usual care among patients with and without prior coronary heart disease (CHD) to determine clinical outcomes. Design: We searched independently, in duplicate, 12 electronic databases (from inception to August 2010), including full text journal content databases, to identify all statin versus inert control RCTs. We included RCTs of any statin versus any non-drug control in any populations. We abstracted data in duplicate on reported major clinical events and adverse events. We performed a random-effects meta-analysis and meta-regression. We performed a mixed treatment comparison using Bayesian methods. Results: We included a total of 76 RCTs involving 170 255 participants. There were a total of 14 878 deaths. Statin therapy reduced all-cause mortality, Relative Risk (RR) 0.90 [95% confidence interval (CI) 0.86-0.94, P ≤ 0.0001, I 2 = 17%]; cardiovascular disease (CVD) mortality (RR 0.80, 95% CI 0.74-0.87, P < 0.0001, I 2 = 27%); fatal myocardial infarction (MI) (RR 0.82, 95% CI 0.75-0.91, P < 0.0001, I 2 = 21%); non-fatal MI (RR 0.74, 95% CI 0.67-0.81, P ≤ 0.001, I 2 = 45%); revascularization (RR 0.76, 95% CI 0.70-0.81, P ≤ 0.0001); and a composite of fatal and non-fatal strokes (0.86, 95% CI 0.78-0.95, P = 0.004, I 2 = 41%). Adverse events were generally mild, but 17 RCTs reported on increased risk of development of incident diabetes [Odds Ratio (OR) 1.09; 95% CI 1.02-1.17, P = 0.001, I 2 = 11%]. Studies did not yield important differences across populations. We did not find any differing treatment effects between statins. Discussion: Statin therapies offer clear benefits across broad populations. As generic formulations become more available efforts to expand access should be a priorit

What guidance are researchers given on how to present network meta-analyses to end-users such as policymakers and clinicians? A systematic review

© 2014 Sullivan et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Introduction: Network meta-analyses (NMAs) are complex methodological approaches that may be challenging for non-technical end-users, such as policymakers and clinicians, to understand. Consideration should be given to identifying optimal approaches to presenting NMAs that help clarify analyses. It is unclear what guidance researchers currently have on how to present and tailor NMAs to different end-users. Methods: A systematic review of NMA guidelines was conducted to identify guidance on how to present NMAs. Electronic databases and supplementary sources were searched for NMA guidelines. Presentation format details related to sample formats, target audiences, data sources, analysis methods and results were extracted and frequencies tabulated. Guideline quality was assessed following criteria developed for clinical practice guidelines. Results: Seven guidelines were included. Current guidelines focus on how to conduct NMAs but provide limited guidance to researchers on how to best present analyses to different end-users. None of the guidelines provided reporting templates. Few guidelines provided advice on tailoring presentations to different end-users, such as policymakers. Available guidance on presentation formats focused on evidence networks, characteristics of individual trials, comparisons between direct and indirect estimates and assumptions of heterogeneity and/or inconsistency. Some guidelines also provided examples of figures and tables that could be used to present information. Conclusions: Limited guidance exists for researchers on how best to present NMAs in an accessible format, especially for non-technical end-users such as policymakers and clinicians. NMA guidelines may require further integration with end-users' needs, when NMAs are used to support healthcare policy and practice decisions. Developing presentation formats that enhance understanding and accessibility of NMAs could also enhance the transparency and legitimacy of decisions informed by NMAs.The Canadian Institute of Health Research (CIHR) Drug Safety and Effectiveness Network (Funding reference number – 116573)

Faster than light motion does not imply time travel

Seeing the many examples in the literature of causality violations based on faster-than-light (FTL) signals one naturally thinks that FTL motion leads inevitably to the possibility of time travel. We show that this logical inference is invalid by demonstrating a model, based on (3+1)-dimensional Minkowski spacetime, in which FTL motion is permitted (in every direction without any limitation on speed) yet which does not admit time travel. Moreover, the Principle of Relativity is true in this model in the sense that all observers are equivalent. In short, FTL motion does not imply time travel after all

Meta-analysis of antibiotics versus appendicectomy for non-perforated acute appendicitis

Background: For more than a century, appendicectomy has been the treatment of choice for appendicitis. Recent trials have challenged this view. This study assessed the benefits and harms of antibiotic therapy compared with appendicectomy in patients with non-perforated appendicitis. Methods: A comprehensive search was conducted for randomized trials comparing antibiotic therapy with appendicectomy in patients with non-perforated appendicitis. Key outcomes were analysed using random-effects meta-analysis, and the quality of evidence was assessed using the Grading of Recommendations Assessment, Development and Evaluation (GRADE) approach. Results: Five studies including 1116 patients reported major complications in 25 (4.9 per cent) of 510 patients in the antibiotic and 41 (8.4 per cent) of 489 in the appendicectomy group: risk difference -2.6 (95 per cent c.i. -6.3 to 1.1) per cent (low-quality evidence). Minor complications occurred in 11 (2.2 per cent) of 510 and 61 (12.5 per cent) of 489 patients respectively: risk difference -7.2 (-18.1 to 3.8) per cent (very low-quality evidence). Of 550 patients in the antibiotic group, 47 underwent appendicectomy within 1 month: pooled estimate 8.2 (95 per cent c.i. 5.2 to 11.8) per cent (high-quality evidence). Within 1 year, appendicitis recurred in 114 of 510 patients in the antibiotic group: pooled estimate 22.6 (15.6 to 30.4) per cent (high-quality evidence). For every 100 patients with non-perforated appendicitis, initial antibiotic therapy compared with prompt appendicectomy may result in 92 fewer patients receiving surgery within the first month, and 23 more experiencing recurrent appendicitis within the first year. Conclusion: The choice of medical versus surgical management in patients with clearly uncomplicated appendicitis is value-and preference-dependent, suggesting a change in practice towards shared decision-making is necessary.Peer reviewe

The asymptotic behaviour of a distributive sorting method

In the distributive sorting method of Dobosiewicz, both the interval between the minimum and the median of the numbers to be sorted and the interval between the median and the maximum are partitioned inton/2 subintervals of equal length; the procedure is then applied recursively on each subinterval containing more than three numbers. We refine and extend previous analyses of this method, e.g., by establishing its asymptotic linear behaviour under various probabilistic assumptions

Preconditioning 2D integer data for fast convex hull computations

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ? n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ? n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ? n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved

Improving corporate governance in state-owned corporations in China: which way forward?

This article discusses corporate governance in China. It outlines the basic agency problem in Chinese listed companies and questions the effectiveness of the current mechanisms employed to improve their standards of governance. Importantly, it considers alternative means through which corporate practice in China can be brought into line with international expectations and stresses the urgency with which this task must be tackled. It concludes that regulators in China must construct a corporate governance model which is compatible with its domestic setting and not rush to adopt governance initiatives modelled on those in cultures which are fundamentally different in the hope of also reproducing their success

The convex hull for a random acceleration process in two dimensions

We compute exactly the mean perimeter and the mean area of the convex hull of a random acceleration process of duration T in two dimensions. We use an exact mapping that relates, via Cauchy's formulae, the computation of the perimeter and the area of the convex hull of an arbitrary two dimensional stochastic process [x(t); y(t)] to the computation of the extreme value statistics of the associated one dimensional component process x(t). The latter can be computed exactly for the one dimensional random acceleration process even though the process in non-Markovian. Physically, our results are relevant in describing theaverage shape of a semi-flexible ideal polymer chain in two dimensions.Comment: 17 pages, 7 figures, accepeted in Journal of Physics A: Mathematical and Theoretica