Interpreting A-level Mathematics grades – as easy as A, B, C?

Many concerns have been expressed that students’ basic mathematical skills have deteriorated during the 1990s and there has been disquiet that current A-level grading does not distinguish adequately between the more able students. This study reports the author’s experiences of teaching maths to large classes of first-year engineering students and aims to enhance understanding of levels of mathematical competence in more recent years. Over the last four years, the classes have consisted of a very large proportion of highly qualified students – about 91% of them had at least grade B in A-level Mathematics. With a small group of students having followed a non-traditional route to university (no A-level maths) and another group having benefitted through taking A-level Further Mathematics at school, the classes have contained a very wide range of mathematical backgrounds. Despite the introductory maths course at university involving mainly repetition of A-level material, students’ marks were spread over a very wide range – for example, A-level Mathematics grade B students have scored across the range 16 – 97%. Analytical integration is the topic which produced the largest variation in performance across the class but, in contrast, the A-level students generally performed well in differentiation. Initial analysis suggests some stability in recent years in the mathematical proficiency of students with a particular A-level Mathematics grade. Allowing choice of applied maths modules as part of the A-level maths qualification increases the variety of students’ mathematical backgrounds and their selection from mechanics, statistics or decision maths is not clear from the final qualification.

Four steps to interpreting arterial blood gases

This article examines acid-base balance and the interpretation of arterial blood gases (ABG). The
article begins with a brief revision of related physiology, followed by a description of the primary
disorders associated with acid-base imbalance. The normal ranges and the significance of
abnormal ABG results are explored. The article concludes by providing an easy to follow four-step
guide to ABG interpretation with practice examples presented in the CPD task section.

Interpreting pedestrian behaviour by visualising and clustering movement data

Recent technological advances have increased the quantity of movement data being recorded. While valuable knowledge can be gained by analysing such data, its sheer volume creates challenges. Geovisual analytics, which helps the human cognition process by using tools to reason about data, offers powerful techniques to resolve these challenges. This paper introduces such a geovisual analytics environment for exploring movement trajectories, which provides visualisation interfaces, based on the classic space-time cube. Additionally, a new approach, using the mathematical description of motion within a space-time cube, is used to determine the similarity of trajectories and forms the basis for clustering them. These techniques were used to analyse pedestrian movement. The results reveal interesting and useful spatiotemporal patterns and clusters of pedestrians exhibiting similar behaviour.

Finding the Most Descriptive Substructures in Graphs with Discrete and Numeric Labels

Many graph datasets are labelled with discrete and numeric attributes. Most frequent substructure discovery algorithms ignore numeric attributes; in this paper we show how they can be used to improve search performance and discrimination. Our thesis is that the most descriptive substructures are those which are normative both in terms of their structure and in terms of their numeric values. We explore the relationship between graph structure and the distribution of attribute values and propose an outlier-detection step, which is used as a constraint during substructure discovery. By pruning anomalous vertices and edges, more weight is given to the most descriptive substructures. Our method is applicable to multi-dimensional numeric attributes; we outline how it can be extended for high-dimensional data. We support our findings with experiments on transaction graphs and single large graphs from the domains of physical building security and digital forensics, measuring the effect on runtime, memory requirements and coverage of discovered patterns, relative to the unconstrained approach.

AGWAN: A Generative Model for Labelled, Weighted Graphs

Real-world graphs or networks tend to exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Much effort has been directed into creating realistic and tractable models for unlabelled graphs, which has yielded insights into graph structure and evolution. Recently, attention has moved to creating models for labelled graphs: many real-world graphs are labelled with both discrete and numeric attributes. In this paper, we presentAgwan (Attribute Graphs: Weighted and Numeric), a generative model for random graphs with discrete labels and weighted edges. The model is easily generalised to edges labelled with an arbitrary number of numeric attributes. We include algorithms for fitting the parameters of the Agwanmodel to real-world graphs and for generating random graphs from the model. Using real-world directed and undirected graphs as input, we compare our approach to state-of-the-art random labelled graph generators and draw conclusions about the contribution of discrete vertex labels and edge weights to graph structure.

Using postal questionnaires to evaluate physical activity and diet behaviour change: case study exploring implications of valid responder characteristics in interpreting intervention outcomes.

Background: Patient reported outcome measures (PROMs) are used to evaluate lifestyle interventions but littleis known about differences between patients returning valid and invalid responses, or of potential for bias inevaluations. We aimed to examine the characteristics of patients who returned valid responses to lifestylequestionnaires compared to those whose responses were invalid for evaluating lifestyle change. 
Methods: We conducted a secondary data analysis from the SPHERE Study, a trial of an intervention to improveoutcomes for patients with coronary heart disease in primary care. Postal questionnaires were used to assessphysical activity (Godin) and diet (DINE) among study participants at baseline and 18 month follow-up. Three binaryresponse variables were generated for analysis: (1) valid Godin score; (2) valid DINE Fibre score; and (3) validDINE Total Fat score. Multivariate analysis comprised generalised estimating equation regression to examine theassociation of patients’ characteristics with their return of valid responses at both timepoints. 
Results: Overall, 92.1% of participants (832/903) returned questionnaires at both baseline and 18 months. Relativelyfewer valid Godin scores were returned by those who left school aged <15 years (36.5%) than aged 18 and over(50.5%), manual workers (39.5%) than non-manual (49.5%) and those with an elevated cholesterol (>5 mmol)(34.7%) than those with a lower cholesterol (44.4%) but multivariate analysis identified that only school leaving age(p = 0.047) was of statistical significance.Relatively fewer valid DINE scores were returned by manual than non-manual workers (fibre: 80.8% v 86.8%;fat: 71.2% v 80.0%), smokers (fibre: 72.6% v 84.7%; fat: 67.5% v 76.9%), patients with diabetes (fibre: 75.9% v 82.9%;fat: 66.9% v 75.8%) and those with cholesterol >5 mmol (fat: 68.2% v 76.2%) but multivariate analysis showedstatistical significance only for smoking (fibre: p = 0.013; fat: p = 0.045), diabetes (fibre: p = 0.039; fat: p = 0.047), andcholesterol (fat: p = 0.039). 
Conclusions: Our findings illustrate the importance of detailed reporting of research methods, with clearinformation about response rates, respondents and valid outcome data. Outcome measures which are relevant to astudy population should be chosen carefully. The impact of methods of outcome measurement and valid responserates in evaluating healthcare requires further study.

Interpreting signals from astrophysical transient experiments

Time domain astronomy has come of age with astronomers now able to monitor the sky at high cadence both across the electromagnetic spectrum and using neutrinos and gravitational waves. The advent of new observing facilities permits new science, but the ever increasing throughput of facilities demands efficient communication of coincident detections and better subsequent coordination among the scientific community so as to turn detections into scientific discoveries. To discuss the revolution occurring in our ability to monitor the Universe and the challenges it brings, on 2012 April 25-26 a group of scientists from observational and theoretical teams studying transients met with representatives of the major international transient observing facilities at the Kavli Royal Society International Centre, UK. This immediately followed the Royal Society Discussion meeting "New windows on transients across the Universe" held in London. Here we present a summary of the Kavli meeting at which the participants discussed the science goals common to the transient astronomy community and analysed how to better meet the challenges ahead as ever more powerful observational facilities come on stream.

Generating Realistic Labelled, Weighted Random Graphs

Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs) with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI) approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs). Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.