Mathematics and complex learning

There is unprecedented worldwide demand for mathematical solutions to complex problems. That demand has generated a further call to update mathematics education in a way that develops students’ abilities to deal with complex systems.

Improving short utterance i-vector speaker verification using utterance variance modelling and compensation techniques

This paper proposes techniques to improve the performance of i-vector based speaker verification systems when only short utterances are available. Short-length utterance i-vectors vary with speaker, session variations, and the phonetic content of the utterance. Well established methods such as linear discriminant analysis (LDA), source-normalized LDA (SN-LDA) and within-class covariance normalisation (WCCN) exist for compensating the session variation but we have identified the variability introduced by phonetic content due to utterance variation as an additional source of degradation when short-duration utterances are used. To compensate for utterance variations in short i-vector speaker verification systems using cosine similarity scoring (CSS), we have introduced a short utterance variance normalization (SUVN) technique and a short utterance variance (SUV) modelling approach at the i-vector feature level. A combination of SUVN with LDA and SN-LDA is proposed to compensate the session and utterance variations and is shown to provide improvement in performance over the traditional approach of using LDA and/or SN-LDA followed by WCCN. An alternative approach is also introduced using probabilistic linear discriminant analysis (PLDA) approach to directly model the SUV. The combination of SUVN, LDA and SN-LDA followed by SUV PLDA modelling provides an improvement over the baseline PLDA approach. We also show that for this combination of techniques, the utterance variation information needs to be artificially added to full-length i-vectors for PLDA modelling.

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.

Statistical, electrical and mathematical analysis of water treed cross-linked polyethylene cable insulation

This work examined a new method of detecting small water filled cracks in underground insulation ('water trees') using data from commecially available non-destructive testing equipment. A testing facility was constructed and a computer simulation of the insulation designed in order to test the proposed ageing factor - the degree of non-linearity. This was a large industry-backed project involving an ARC linkage grant, Ergon Energy and the University of Queensland, as well as the Queensland University of Technology.

Synergistic use of thermogravimetric and electrochemical techniques for thermodynamic study of TiOx (1.67 <= x <= 2.0) at 1573 K

A thermodynamic study of the Ti-O system at 1573 K has been conducted using a combination of thermogravimetric and emf techniques. The results indicate that the variation of oxygen potential with the nonstoichiometric parameter delta in stability domain of TiO2-delta with rutile structure can be represented by the relation, Delta mu o(2) = -6RT In delta - 711970(+/-1600) J/mol. The corresponding relation between non-stoichiometric parameter delta and partial pressure of oxygen across the whole stability range of TiO2-delta at 1573 K is delta proportional to P-O2(-1/6). It is therefore evident that the oxygen deficient behavior of nonstoichiometric TiO2-delta is dominated by the presence of doubly charged oxygen vacancies and free electrons. The high-precision measurements enabled the resolution of oxygen potential steps corresponding to the different Magneli phases (Ti-n O2n-1) up to n = 15. Beyond this value of n, the oxygen potential steps were too small to be resolved. Based on composition of the Magneli phase in equilibrium with TiO2-delta, the maximum value of n is estimated to be 28. The chemical potential of titanium was derived as a function of composition using the Gibbs-Duhem relation. Gibbs energies of formation of the Magneli phases were derived from the chemical potentials of oxygen and titanium. The values of -2441.8(+/-5.8) kJ/mol for Ti4O7 and -1775.4(+/-4.3) kJ/mol for Ti3O5 Obtained in this study refine values of -2436.2(+/-26.1) kJ/mol and-1771.3(+/-6.9) kJ/mol, respectively, given in the JANAF thermochemical tables.

Joining of dissimilar metals: issues and modelling techniques

Joining of dissimilar metals involves a number of scientific issues, the modelling of which offers unique challenges. This review discusses the complexities in different joining processes and dissimilar combinations, and the corresponding computational techniques that have the potential to address the same. Future directions in modelling at both macroscopic and microscopic scales are also suggested.

Improved parametric models and DPCM techniques for EGG data compiression

This paper presents a novel algorithm for compression of single lead Electrocardiogram (ECG) signals. The method is based on Pole-Zero modelling of the Discrete Cosine Transformed (DCT) signal. An extension is proposed to the well known Steiglitz-Hcbride algorithm, to model the higher frequency components of the input signal more accurately. This is achieved by weighting the error function minimized by the algorithm to estimate the model parameters. The data compression achieved by the parametric model is further enhanced by Differential Pulse Code Modulation (DPCM) of the model parameters. The method accomplishes a compression ratio in the range of 1:20 to 1:40, which far exceeds those achieved by most of the current methods.

Content Based Integration of Construction Site Images in Architecture, Engineering, Construction, and Facilities Management (AEC/FM) Model based Systems

This book explores the processes for retrieval, classification, and integration of construction images in AEC/FM model based systems. The author describes a combination of techniques from the areas of image and video processing, computer vision, information retrieval, statistics and content-based image and video retrieval that have been integrated into a novel method for the retrieval of related construction site image data from components of a project model. This method has been tested on available construction site images from a variety of sources like past and current building construction and transportation projects and is able to automatically classify, store, integrate and retrieve image data files in inter-organizational systems so as to allow their usage in project management related tasks. objects. Therefore, automated methods for the integration of construction images are important for construction information management. During this research, processes for retrieval, classification, and integration of construction images in AEC/FM model based systems have been explored. Specifically, a combination of techniques from the areas of image and video processing, computer vision, information retrieval, statistics and content-based image and video retrieval have been deployed in order to develop a methodology for the retrieval of related construction site image data from components of a project model. This method has been tested on available construction site images from a variety of sources like past and current building construction and transportation projects and is able to automatically classify, store, integrate and retrieve image data files in inter-organizational systems so as to allow their usage in project management related tasks.

Some issues on assessment methods and learning in mathematics and statistics

This paper looks at the application of some of the assessment methods in practice with the view to enhance students’ learning in mathematics and statistics. It explores the effective application of assessment methods and highlights the issues or problems, and ways of avoiding them, related to some of the common methods of assessing mathematical and statistical learning. Some observations made by the author on good assessment practice and useful approaches employed at his institution in designing and applying assessment methods are discussed. Successful strategies in implementing assessment methods at different levels are described.