Modelling as a vehicle for philosophical inquiry in the mathematics curriculum

Philosophical inquiry in the teaching and learning of mathematics has received continued, albeit limited, attention over many years (e.g., Daniel, 2000; English, 1994; Lafortune, Daniel, Fallascio, & Schleider, 2000; Kennedy, 2012a). The rich contributions these communities can offer school mathematics, however, have not received the deserved recognition, especially from the mathematics education community. This is a perplexing situation given the close relationship between the two disciplines and their shared values for empowering students to solve a range of challenging problems, often unanticipated, and often requiring broadened reasoning. In this article, I first present my understanding of philosophical inquiry as it pertains to the mathematics classroom, taking into consideration the significant work that has been undertaken on socio-political contexts in mathematics education (e.g., Skovsmose & Greer, 2012). I then consider one approach to advancing philosophical inquiry in the mathematics classroom, namely, through modelling activities that require interpretation, questioning, and multiple approaches to solution. The design of these problem activities, set within life-based contexts, provides an ideal vehicle for stimulating philosophical inquiry.

Analysis of interrelationships between critical waste factors in office building retrofit projects using interpretive structural modelling

The number of office building retrofit projects is increasing. These projects are characterised by processes which have a close relationship with waste generation and therefore demand a high level of waste management. In a preliminary study reported separately, we identified seven critical factors of on-site waste generation in office building retrofit projects. Through semi-structured interviews and Interpretive Structural Modelling, this research further investigated the interrelationships among these critical waste factors, to identify each factor’s level of influence on waste generation and propose effective solutions for waste minimization. “Organizational commitment” was identified as the fundamental issue for waste generation in the ISM system. Factors related to plan, design and construction processes were found to be located in the middle levels of the ISM model but still had significant impacts on the system as a whole. Based on the interview findings and ISM analysis results, some practical solutions were proposed for waste minimization in building retrofit projects: (1) reusable and adaptable fit-out design; (2) a system for as-built drawings and building information; (3) integrated planning for retrofitting work process and waste management; and (4) waste benchmarking development for retrofit projects. This research will provide a better understanding of waste issues associated with building retrofit projects and facilitate enhanced waste minimization.

Local inter-session variability modelling for object classification

Object classification is plagued by the issue of session variation. Session variation describes any variation that makes one instance of an object look different to another, for instance due to pose or illumination variation. Recent work in the challenging task of face verification has shown that session variability modelling provides a mechanism to overcome some of these limitations. However, for computer vision purposes, it has only been applied in the limited setting of face verification. In this paper we propose a local region based intersession variability (ISV) modelling approach, and apply it to challenging real-world data. We propose a region based session variability modelling approach so that local session variations can be modelled, termed Local ISV. We then demonstrate the efficacy of this technique on a challenging real-world fish image database which includes images taken underwater, providing significant real-world session variations. This Local ISV approach provides a relative performance improvement of, on average, 23% on the challenging MOBIO, Multi-PIE and SCface face databases. It also provides a relative performance improvement of 35% on our challenging fish image dataset.

Process modelling and simulation of tissue damage during mechanical peeling of pumpkin as a tough skinned vegetable

Food waste is a current challenge that both developing and developed countries face. This project applied a novel combination of available methods in Mechanical, agricultural and food engineering to address these challenges. A systematic approach was devised to investigate possibilities of reducing food waste and increasing the efficiency of industry by applying engineering concepts and theories including experimental, mathematical and computational modelling methods. This study highlights the impact of comprehensive understanding of agricultural and food material response to the mechanical operations and its direct relation to the volume of food wasted globally.

Reluctantly virtual : modelling copyright industry dynamics

During the evolution of the music industry, developments in the media environment have required music firms to adapt in order to survive. Changes in broadcast radio programming during the 1950s; the Compact Cassette during the 1970s; and the deregulation of media ownership during the 1990s are all examples of changes which have heavily affected the music industry. This study explores similar contemporary dynamics, examines how decision makers in the music industry perceive and make sense of the developments, and reveals how they revise their business strategies, based on their mental models of the media environment. A qualitative system dynamics model is developed in order to support the reasoning brought forward by the study. The model is empirically grounded, but is also based on previous music industry research and a theoretical platform constituted by concepts from evolutionary economics and sociology of culture. The empirical data primarily consist of 36 personal interviews with decision makers in the American, British and Swedish music industrial ecosystems. The study argues that the model which is proposed, more effectively explains contemporary music industry dynamics than music industry models presented by previous research initiatives. Supported by the model, the study is able to show how “new” media outlets make old music business models obsolete and challenge the industry’s traditional power structures. It is no longer possible to expose music at one outlet (usually broadcast radio) in the hope that it will lead to sales of the same music at another (e.g. a compact disc). The study shows that many music industry decision makers still have not embraced the new logic, and have not yet challenged their traditional mental models of the media environment. Rather, they remain focused on preserving the pivotal role held by the CD and other physical distribution technologies. Further, the study shows that while many music firms remain attached to the old models, other firms, primarily music publishers, have accepted the transformation, and have reluctantly recognised the realities of a virtualised environment.

Numerical modelling of load bearing light gauge steel frame wall systems exposed to realistic design fires

Fire safety has become an important part in structural design due to the ever increasing loss of properties and lives during fires. Conventionally the fire rating of load bearing wall systems made of Light gauge Steel Frames (LSF) is determined using fire tests based on the standard time-temperature curve in ISO834 [1]. However, modern commercial and residential buildings make use of thermoplastic materials, which mean considerably high fuel loads. Hence a detailed fire research study into the fire performance of LSF walls was undertaken using realistic design fire curves developed based on Eurocode parametric [2] and Barnett’s BFD [3] curves using both full scale fire tests and numerical studies. It included LSF walls without cavity insulation, and the recently developed externally insulated composite panel system. This paper presents the details of finite element models developed to simulate the full scale fire tests of LSF wall panels under realistic design fires. Finite element models of LSF walls exposed to realistic design fires were developed, and analysed under both transient and steady state fire conditions using the measured stud time-temperature curves. Transient state analyses were performed to simulate fire test conditions while steady state analyses were performed to obtain the load ratio versus time and failure temperature curves of LSF walls. Details of the developed finite element models and the results including the axial deformation and lateral deflection versus time curves, and the stud failure modes and times are presented in this paper. Comparison with fire test results demonstrate the ability of developed finite element models to predict the performance and fire resistance ratings of LSF walls under realistic design fires.

A multiscale road map of cancer spheroids : incorporating experimental and mathematical modelling to understand cancer progression

Computational models represent a highly suitable framework, not only for testing biological hypotheses and generating new ones but also for optimising experimental strategies. As one surveys the literature devoted to cancer modelling, it is obvious that immense progress has been made in applying simulation techniques to the study of cancer biology, although the full impact has yet to be realised. For example, there are excellent models to describe cancer incidence rates or factors for early disease detection, but these predictions are unable to explain the functional and molecular changes that are associated with tumour progression. In addition, it is crucial that interactions between mechanical effects, and intracellular and intercellular signalling are incorporated in order to understand cancer growth, its interaction with the extracellular microenvironment and invasion of secondary sites. There is a compelling need to tailor new, physiologically relevant in silico models that are specialised for particular types of cancer, such as ovarian cancer owing to its unique route of metastasis, which are capable of investigating anti-cancer therapies, and generating both qualitative and quantitative predictions. This Commentary will focus on how computational simulation approaches can advance our understanding of ovarian cancer progression and treatment, in particular, with the help of multicellular cancer spheroids, and thus, can inform biological hypothesis and experimental design.

A Bayesian regression approach to assess uncertainty in pollutant wash-off modelling

Due to knowledge gaps in relation to urban stormwater quality processes, an in-depth understanding of model uncertainty can enhance decision making. Uncertainty in stormwater quality models can originate from a range of sources such as the complexity of urban rainfall-runoff-stormwater pollutant processes and the paucity of observed data. Unfortunately, studies relating to epistemic uncertainty, which arises from the simplification of reality are limited and often deemed mostly unquantifiable. This paper presents a statistical modelling framework for ascertaining epistemic uncertainty associated with pollutant wash-off under a regression modelling paradigm using Ordinary Least Squares Regression (OLSR) and Weighted Least Squares Regression (WLSR) methods with a Bayesian/Gibbs sampling statistical approach. The study results confirmed that WLSR assuming probability distributed data provides more realistic uncertainty estimates of the observed and predicted wash-off values compared to OLSR modelling. It was also noted that the Bayesian/Gibbs sampling approach is superior compared to the most commonly adopted classical statistical and deterministic approaches commonly used in water quality modelling. The study outcomes confirmed that the predication error associated with wash-off replication is relatively higher due to limited data availability. The uncertainty analysis also highlighted the variability of the wash-off modelling coefficient k as a function of complex physical processes, which is primarily influenced by surface characteristics and rainfall intensity.

Representations for evolutionary design modelling

This research looked at using the metaphor of biological evolution as a way of solving architectural design problems. Drawing from fields such as language grammars, algorithms and cellular biology, this thesis looked at ways of encoding design information for processing. The aim of this work is to help in the building of software that support the architectural design process and allow designers to examine more variations.

Statistical modelling of district-level residential electricity use in NSW, Australia

Electricity network investment and asset management require accurate estimation of future demand in energy consumption within specified service areas. For this purpose, simple models are typically developed to predict future trends in electricity consumption using various methods and assumptions. This paper presents a statistical model to predict electricity consumption in the residential sector at the Census Collection District (CCD) level over the state of New South Wales, Australia, based on spatial building and household characteristics. Residential household demographic and building data from the Australian Bureau of Statistics (ABS) and actual electricity consumption data from electricity companies are merged for 74 % of the 12,000 CCDs in the state. Eighty percent of the merged dataset is randomly set aside to establish the model using regression analysis, and the remaining 20 % is used to independently test the accuracy of model prediction against actual consumption. In 90 % of the cases, the predicted consumption is shown to be within 5 kWh per dwelling per day from actual values, with an overall state accuracy of -1.15 %. Given a future scenario with a shift in climate zone and a growth in population, the model is used to identify the geographical or service areas that are most likely to have increased electricity consumption. Such geographical representation can be of great benefit when assessing alternatives to the centralised generation of energy; having such a model gives a quantifiable method to selecting the 'most' appropriate system when a review or upgrade of the network infrastructure is required.

Modelling after-the-fact leakage for key exchange

Security models for two-party authenticated key exchange (AKE) protocols have developed over time to prove the security of AKE protocols even when the adversary learns certain secret values. In this work, we address more granular leakage: partial leakage of long-term secrets of protocol principals, even after the session key is established. We introduce a generic key exchange security model, which can be instantiated allowing bounded or continuous leakage, even when the adversary learns certain ephemeral secrets or session keys. Our model is the strongest known partial-leakage-based security model for key exchange protocols. We propose a generic construction of a two-pass leakage-resilient key exchange protocol that is secure in the proposed model, by introducing a new concept: the leakage-resilient NAXOS trick. We identify a special property for public-key cryptosystems: pair generation indistinguishability, and show how to obtain the leakage-resilient NAXOS trick from a pair generation indistinguishable leakage-resilient public-key cryptosystem.

Comparative susceptibility of mosquito populations in North Queensland, Australia to oral infection with dengue virus

Dengue is the most prevalent arthropod-borne virus, with at least 40% of the world’s population at risk of infection each year. In Australia, dengue is not endemic, but viremic travelers trigger outbreaks involving hundreds of cases. We compared the susceptibility of Aedes aegypti mosquitoes from two geographically isolated populations with two strains of dengue virus serotype 2. We found, interestingly, that mosquitoes from a city with no history of dengue were more susceptible to virus than mosquitoes from an outbreak-prone region, particularly with respect to one dengue strain. These findings suggest recent evolution of population-based differences in vector competence or different historical origins. Future genomic comparisons of these populations could reveal the genetic basis of vector competence and the relative role of selection and stochastic processes in shaping their differences. Lastly, we show the novel finding of a correlation between midgut dengue titer and titer in tissues colonized after dissemination.

GPU accelerated MCMC for modelling terrorist activity

The use of graphical processing unit (GPU) parallel processing is becoming a part of mainstream statistical practice. The reliance of Bayesian statistics on Markov Chain Monte Carlo (MCMC) methods makes the applicability of parallel processing not immediately obvious. It is illustrated that there are substantial gains in improved computational time for MCMC and other methods of evaluation by computing the likelihood using GPU parallel processing. Examples use data from the Global Terrorism Database to model terrorist activity in Colombia from 2000 through 2010 and a likelihood based on the explicit convolution of two negative-binomial processes. Results show decreases in computational time by a factor of over 200. Factors influencing these improvements and guidelines for programming parallel implementations of the likelihood are discussed.

Sub-modelling for the ratchetting failure of insulated rail joints

Insulated rail joints are critical for train safety as they control electrical signalling systems; unfortunately they exhibit excessive ratchetting of the railhead near the endpost insulators. This paper reports a three-dimensional global model of these joints under wheel–rail contact pressure loading and a sub-model examining the ratchetting failures of the railhead. The sub-model employs a non-linear isotropic–kinematic elastic–plastic material model and predicts stress/strain levels in the localised railhead zone adjacent to the endpost which is placed in the air gap between the two rail ends at the insulated rail joint. The equivalent plastic strain plot is utilised to capture the progressive railhead damage adequately. Associated field and laboratory testing results of damage to the railhead material suggest that the simulation results are reasonable.

Characterising an ECG signal using statistical modelling : a feasibility study

For clinical use, in electrocardiogram (ECG) signal analysis it is important to detect not only the centre of the P wave, the QRS complex and the T wave, but also the time intervals, such as the ST segment. Much research focused entirely on qrs complex detection, via methods such as wavelet transforms, spline fitting and neural networks. However, drawbacks include the false classification of a severe noise spike as a QRS complex, possibly requiring manual editing, or the omission of information contained in other regions of the ECG signal. While some attempts were made to develop algorithms to detect additional signal characteristics, such as P and T waves, the reported success rates are subject to change from person-to-person and beat-to-beat. To address this variability we propose the use of Markov-chain Monte Carlo statistical modelling to extract the key features of an ECG signal and we report on a feasibility study to investigate the utility of the approach. The modelling approach is examined with reference to a realistic computer generated ECG signal, where details such as wave morphology and noise levels are variable.