Notes on the mathematical basis of the UK Non-Native Organism Risk Assessment Scheme

Two papers published in peer-reviewed journals (Holt, 2006; Holt et al., 2006) describe the mathematical basis of the UK Non-Native Organism Risk Assessment Scheme2. The current risk assessment methodology (specifically including the proposed scoring system and the categorization of responses) has also been peer reviewed in a report by RPS Group Ltd, available on the website of the GB Non-Native Species Secretariat3. In the notes that follow, some previously unreported problems with the mathematical analysis on which the Scheme is based are outlinedRisk and Uncertainty,

Solar sailing

An introduction to solar sailing is presented. The physical principles are briefly reviewed along with an introduction to the historical context of solar sailing. Potential solar sail configurations are briefly introduced, while placing these in the context of the current hardware development programmes. Following the introduction to solar sailing we progress onto a discussion of solar sail orbital dynamics in a planet-centred environment. The development of solar sail trajectory generation is presented, from Earth escape trajectories through to lunar fly-by trajectories and more accurate Earth escape methods. Much of this work relies on assumptions to generate near-optimal solutions rather than true globally optimal solutions, which are computationally difficult to determine for multiple revolution trajectories. Many of these traditional planet-centred solar sail applications, such as Earth escape, also require rapid attitude slew manoeuvres to achieve. This first lecture is based on theory development and application with a view towards future missions, such as planetary sample return

Small-body encounters using solar sail propulsion

Cometary Rendezvous and Flybys have large V requirements, which impose almost unattainable, and sometimes prohibitive, demands on the propellant budget of conventional, chemical propulsion. Ion Propulsion is a viable alternative, but as the number and difficulty of target objectives increases then the potential of this technology becomes rapidly less attractive. Solar sails exhibit an extremely high effective specific impulse over long mission durations. No propellant is required so that large changes in V could be realised without necessitating the introduction of complex gravity assists, which prolong mission duration and restrict launch opportunities. The endurance of the structures and materials are thus the only limiting factors dictating the number and range of bodies with which the solar-sail propelled vehicle can encounter throughout its lifetime. In this paper we have analysed a number of high-energy, small-body mission scenarios using a parameterised approach to sail control representation. The sail cone and clock angle histories were characterised by linear interpolation across a set of discrete nodes. The optimal control problem was thus transcribed to a Non-Linear Programming problem to select the optimal controls at the nodes that minimised the transfer time while enforcing the cartesian end-point boundary constraints (6 states for rendezvous, 3 for flypast). The Fortran77 optimisation package NPSOL 5.0 was used for this purpose with the variational equations of motion formulated in modified equinoctial orbital elements and integrated using a variable-order, adaptive step-size Adams-Moulton-Bashforth method. We present optimal rendezvous trajectories to Short-Period Comets such as 46P/Wirtanen in 484 days with a sail characteristic acceleration of 1.9 mms-2, and with 2P/Encke in 574 days with a characteristic acceleration of 1.0 mms-2. An analysis using high-performance sails has been conducted to permit fast flyby intercepts of newly discovered Long Period Comets (LPCs). Previous examples adopted were C/1995 O1/Hale- Bopp, C/1995 Y1/Hyakutake, C/1999 T1/McNaught-Hartley, C/1999 F1/Catalina, C/1999 N2/Lynn and C/1999 H1/Lee, to demonstrate the feasibility of a late launch to quickly intercept a new LPC using a solar sail. Since the time between discovery of a new LPC such as Hale-Bopp and perihelion passage was less then 2 years, this then leaves a very short time-span for orbit determination, preparation, planning and operational phases. Preliminary mission analysis shows that a Hale-Bopp perihelion flypast could have been achieved, with a sail characteristic acceleration of 5.0 mms-2, by launching just 209 days before comet perihelion passage. With a characteristic acceleration of 2.0 mms-2 Hale-Bopp could also have been intercepted at its descending node by launching 270 days before nodal descent. The sail could then have returned to rendezvous with the Earth 261 days later, giving a minimum total mission turn-around time of 531 days. An alternative, dual flyby scenario has been investigated, to continue on to C/1997 D1/Mueller, after which solar system escape was reached and arrival at Heliopause would occur in 12 years. Solar Electric Propulsion has been adopted as the primary propulsion system for the DAWN dual asteroid rendezvous mission scheduled for launch in 2006. The objective of this mission is to rendezvous with inner main-belt asteroids, Vesta and Ceres. We have also investigated solar sail adaptation to this mission, for the same launch date and 11 month orbiter stay-times. We have extended the mission objectives to two further asteroids, Lucina and Lutetia, with the aim of demonstrating a Mainbelt Asteroid Survey scenario

On the binormal predictive receiver operating characteristic curve for the joint assessment of positive and negative predictive values

The predictive receiver operating characteristic (PROC) curve is a diagrammatic format with application in the statistical evaluation of probabilistic disease forecasts. The PROC curve differs from the more well-known receiver operating characteristic (ROC) curve in that it provides a basis for evaluation using metrics defined conditionally on the outcome of the forecast rather than metrics defined conditionally on the actual disease status. Starting from the binormal ROC curve formulation, an overview of some previously published binormal PROC curves is presented in order to place the PROC curve in the context of other methods used in statistical evaluation of probabilistic disease forecasts based on the analysis of predictive values; in particular, the index of separation (PSEP) and the leaf plot. An information theoretic perspective on evaluation is also outlined. Five straightforward recommendations are made with a view to aiding understanding and interpretation of the sometimes-complex patterns generated by PROC curve analysis. The PROC curve and related analyses augment the perspective provided by traditional ROC curve analysis. Here, the binormal ROC model provides the exemplar for investigation of the PROC curve, but potential application extends to analysis based on other distributional models as well as to empirical analysis

QT prolongation in patients treated for drug-resistant tuberculosis

Introduction STREAM (Standardised Treatment Regimen of Anti-TB Drugs for Patients with MDRTB) Stage 1 demonstrated non-inferior efficacy of a Short regimen for rifampicin-resistant TB compared to the WHO-recommended Long regimen. Cardiac safety of participants was a concern due to the composition of the Short (study) regimen. It was unclear how many patients would be affected, who would be affected, the best monitoring strategy and how to identify those at risk of developing QT prolongation. Methods An analysis of new data created from STREAM Stage 1 ECGs was performed to investigate cardiac safety. In total, 424 participants (282 Short: 142 Long) were randomised. Data were analysed to identify risk factors for clinically relevant QT prolongation (QT/QTcF ≥500ms), how it evolved over time, whether a monitoring strategy could be refined, if machine readings were reliable and whether differences between groups for T-wave morphology abnormalities existed. Results The risk of developing QT or QTcF prolongation ≥500ms was higher for participants on the Short regimen (11%) vs the Long regimen (5%) (HR 95% CI: 2.31 (1.02-5.26)), p=0.0470. QT/QTcF prolongation ≥500ms was more frequent in patients from Mongolia (10/22 45.5%) compared with 3.5-11.9% at other sites, as well as those with higher baseline values (QTcF ≥400ms; OR 5.99, 95% CI 2.04-17.62). Compared with manual readings, machine readings overestimated the QT interval by a mean of 22.5ms. Nearly half (90/200) of ECGs reviewed had T-wave morphology abnormalities by 3 months or more of treatment. Conclusion Though a sizeable number developed clinically relevant QT prolongation, the Short regimen in STREAM Stage 1 was safe and tolerated by most participants. This thesis has shown who was at greater risk, how they were managed and how early ECG readings can identify them for more targeted monitoring. This will inform clinicians and policy makers involved in rifampicin resistant tuberculosis (RR-TB) treatment programmes

A study into annotation ranking metrics in geo-tagged image corpora

Community contributed datasets are becoming increasingly common in automated image annotation systems. One important issue with community image data is that there is no guarantee that the associated metadata is relevant. A method is required that can accurately rank the semantic relevance of community annotations. This should enable the extracting of relevant subsets from potentially noisy collections of these annotations. Having relevant, non heterogeneous tags assigned to images should improve community image retrieval systems, such as Flickr, which are based on text retrieval methods. In the literature, the current state of the art approach to ranking the semantic relevance of Flickr tags is based on the widely used tf-idf metric. In the case of datasets containing landmark images, however, this metric is inefficient due to the high frequency of common landmark tags within the data set and can be improved upon. In this paper, we present a landmark recognition framework, that provides end-to-end automated recognition and annotation. In our study into automated annotation, we evaluate 5 alternate approaches to tf-idf to rank tag relevance in community contributed landmark image corpora. We carry out a thorough evaluation of each of these ranking metrics and results of this evaluation demonstrate that four of these proposed techniques outperform the current commonly-used tf-idf approach for this task

Visual and geographical data fusion to classify landmarks in geo-tagged images

High level semantic image recognition and classification is a challenging task and currently is a very active research domain. Computers struggle with the high level task of identifying objects and scenes within digital images accurately in unconstrained environments. In this paper, we present experiments that aim to overcome the limitations of computer vision algorithms by combining them with novel contextual based features to describe geo-tagged imagery. We adopt a machine learning based algorithm with the aim of classifying classes of geographical landmarks within digital images. We use community contributed image sets downloaded from Flickr and provide a thorough investigation, the results of which are presented in an evaluation section