Multiple Luminaire Identification in Airborne Images of Airport’s Approach Lighting Using Mathematical Morphology With Variable Length Structuring Element

The increasing demand for fast air transportation around the clock
has increased the number of night flights in civil aviation over
the past few decades. In night aviation, to land an aircraft, a
pilot needs to be able to identify an airport. The approach
lighting system (ALS) at an airport is used to provide
identification and guidance to pilots from a distance. ALS
consists of more than $100$ luminaires which are installed in a
defined pattern following strict guidelines by the International
Civil Aviation Organization (ICAO). ICAO also has strict
regulations for maintaining the performance level of the
luminaires. However, once installed, to date there is no automated
technique by which to monitor the performance of the lighting. We
suggest using images of the lighting pattern captured using a camera
placed inside an aircraft. Based on the information contained
within these images, the performance of the luminaires has to be
evaluated which requires identification of over $100$ luminaires
within the pattern of ALS image. This research proposes analysis
of the pattern using morphology filters which use a variable
length structuring element (VLSE). The dimension of the VLSE changes
continuously within an image and varies for different images.
A novel
technique for automatic determination of the VLSE is proposed and
it allows successful identification of the luminaires from the
image data as verified through the use of simulated and real data.

2DRMP-G: Migrating a large-scale numerical mathematical application to a grid environment

We report on the migration of a traditional, single architecture application to a grid application using heterogeneous resources. We focus on the use of the UK e-Science Level 2 grid (UKL2G) which provides a heterogeneous collection of resources distributed within the UK. We discuss the solution architecture, the performance of our application, its future development as a grid-based application and comment on the lessons we have learned in using a grid infrastructure for large-scale numerical problems.

A longitudinal analysis of estimation, counting skills, and mathematical ability across the first school year

In response to claims that the quality (and in particular linearity) of children's mental representation of number acts as a constraint on number development, we carried out a longitudinal assessment of the relationships between number line estimation, counting, and mathematical abilities. Ninety-nine 5-year-olds were tested on 4 occasions at 3 monthly intervals. Correlations between the 3 types of ability were evident, but while the quality of children's estimations changed over time and performance on the mathematical tasks improved over the same period, changes in one were not associated with changes in the other. In contrast to the earlier claims that the linearity of number representation is potentially a unique contributor to children's mathematical development, the data suggest that this variable is not significantly privileged in its impact over and above simple procedural number skills. We propose that both early arithmetic success and estimating skill are bound closely to developments in counting ability.

Mathematical Modelling of a Reciprocating Piston Expander

Modern internal combustion (IC) engines reject around two thirds of the energy provided by the fuel as low-grade waste heat. Capturing a portion of this waste heat energy and transforming it into a more useful form of energy could result in a significant reduction in fuel consumption. By using the low-grade heat, an organic Rankine cycle (ORC) can produce mechanical work from a pressurised organic fluid with the use of an expander.
Ideal gas assumptions are shown to produce significant errors in expander performance predictions when using an organic fluid. This paper details the mathematical modelling technique used to accurately model the thermodynamic processes for both ideal and non-ideal fluids within the reciprocating expander. A comparison between the two methods illustrates the extent of the errors when modelling a reciprocating piston expander. Use of the ideal gas assumptions are shown to produce an error of 55% in the prediction of power produced by the expander when operating on refrigerant R134a.

Communicating musical knowledge through gesture: Piano teachers’ gestural behaviours across different levels of student proficiency

Teachers’ communication of musical knowledge through physical gesture represents a valuable pedagogical field in need of investigation. This exploratory case study compares the gestural behaviour of three piano teachers while giving individual lessons to students who differed according to piano proficiency levels. The data was collected by video recordings of one-to-one piano lessons and gestures were categorized using two gesture classifications: the spontaneous co-verbal gesture classification (McNeill, 1992; 2005) and spontaneous co-musical gesture classification (Simones, Schroeder & Rodger, 2013). Poisson regression analysis and qualitative observation suggest a relationship between teachers’ didactic intentions and the types of gesture they produced while teaching, as shown by differences in gestural category frequency between teaching students of higher and lower levels of proficiency. Such reported agreement between teachers’ gestural approach in relation to student proficiency levels indicates a teachers’ gestural scaffolding approach whereby teachers adapted gestural communicative channels to suit students’ specific conceptual skill levels.

Mathematics background of engineering students in Northern Ireland and Finland

The Organisation for Economic Co-operation and Development investigated numeracy proficiency among adults of working age in 23 countries across the world. Finland had the highest mean numeracy proficiency for people in the 16 – 24 age group while Northern Ireland’s score was below the mean for all the countries. An international collaboration has been undertaken to investigate the prevalence of mathematics within the secondary education systems in Northern Ireland and Finland, to highlight particular issues associated with transition into university and consider whether aspects of the Finnish experience are applicable elsewhere. In both Northern Ireland and Finland, at age 16, about half of school students continue into upper secondary level following their compulsory education. The upper secondary curriculum in Northern Ireland involves a focus on three subjects while Finnish students study a very wide range of subjects with about two-thirds of the courses being compulsory. The number of compulsory courses in maths is proportionally large; this means that all upper secondary pupils in Finland (about 55% of the population) follow a curriculum which has a formal maths content of 8%, at the very minimum. In contrast, recent data have indicated that only about 13% of Northern Ireland school leavers studied mathematics in upper secondary school. The compulsory courses of the advanced maths syllabus in Finland are largely composed of pure maths with a small amount of statistics but no mechanics. They lack some topics (for example, in advanced calculus and numerical methods for integration) which are core in Northern Ireland. This is not surprising given the much broader curriculum within upper secondary education in Finland. In both countries, there is a wide variation in the mathematical skills of school leavers. However, given the prevalence of maths within upper secondary education in Finland, it is to be expected that young adults in that country demonstrate high numeracy proficiency.

Derivation of scientific software from mathematical specifications

Often the modification and enhancement of large scientific software systems are severely hampered because many components of the system are written in an implementation dependent fashion, they are inadequately documented, and their functionalities are not precisely known. In this paper we consider how mathematics may be employed to alleviate some of these problems. In particular, we illustrate how the formal specification notation VDM-SL is being used to specify precisely abstract data types for use in the development of scientific software.

Mathematical anxiety is linked to reduced cognitive reflection: A potential road from discomfort in the mathematics classroom to susceptibility to biases

Background
When asked to solve mathematical problems, some people experience anxiety and threat, which can lead to impaired mathematical performance (Curr Dir Psychol Sci 11:181–185, 2002). The present studies investigated the link between mathematical anxiety and performance on the cognitive reflection test (CRT; J Econ Perspect 19:25–42, 2005). The CRT is a measure of a person’s ability to resist intuitive response tendencies, and it correlates strongly with important real-life outcomes, such as time preferences, risk-taking, and rational thinking.

Methods
In Experiments 1 and 2 the relationships between maths anxiety, mathematical knowledge/mathematical achievement, test anxiety and cognitive reflection were analysed using mediation analyses. Experiment 3 included a manipulation of working memory load. The effects of anxiety and working memory load were analysed using ANOVAs.

Results
Our experiments with university students (Experiments 1 and 3) and secondary school students (Experiment 2) demonstrated that mathematical anxiety was a significant predictor of cognitive reflection, even after controlling for the effects of general mathematical knowledge (in Experiment 1), school mathematical achievement (in Experiment 2) and test anxiety (in Experiments 1–3). Furthermore, Experiment 3 showed that mathematical anxiety and burdening working memory resources with a secondary task had similar effects on cognitive reflection.

Conclusions
Given earlier findings that showed a close link between cognitive reflection, unbiased decisions and rationality, our results suggest that mathematical anxiety might be negatively related to individuals’ ability to make advantageous choices and good decisions.

The Equiprobability Bias from a Mathematical and Psychological Perspective

The equiprobability bias (EB) is a tendency to believe that every process in which randomness is involved corresponds to a fair distribution, with equal probabilities for any possible outcome. The EB is known to affect both children and adults, and to increase with probability education. Because it results in probability errors resistant to pedagogical interventions, it has been described as a deep misconception about randomness: the erroneous belief that randomness implies uniformity. In the present paper, we show that the EB is actually not the result of a conceptual error about the definition of randomness. On the contrary, the mathematical theory of randomness does imply uniformity. However, the EB is still a bias, because people tend to assume uniformity even in the case of events that are not random. The pervasiveness of the EB reveals a paradox: The combination of random processes is not necessarily random. The link between the EB and this paradox is discussed, and suggestions are made regarding educational design to overcome difficulties encountered by students as a consequence of the EB.

Mathematical modelling of quantum yield enhancements of methyl orange photooxidation in aqueous TiO2 suspensions under controlled periodic UV LED illumination

Quantum yields of the photocatalytic degradation of methyl orange under controlled periodic illumination (CPI) have been modelled using existing models. A modified Langmuir-Hinshelwood (L-H) rate equation was used to predict the degradation reaction rates of methyl orange at various duty cycles and a simple photocatalytic model was applied in modelling quantum yield enhancement of the photocatalytic process due to the CPI effect. A good agreement between the modelled and experimental data was observed for quantum yield modelling. The modified L-H model, however, did not accurately predict the photocatalytic decomposition of the dye under periodic illumination.