Using two dimensional sectional distributions to infer three dimensional volumetric distributions - Validation using tomography

The critical process parameter for mineral separation is the degree of mineral liberation achieved by comminution. The degree of liberation provides an upper limit of efficiency for any physical separation process. The standard approach to measuring mineral liberation uses mineralogical analysis based two-dimensional sections of particles which may be acquired using a scanning electron microscope and back-scatter electron analysis or from an analysis of an image acquired using an optical microscope. Over the last 100 years, mathematical techniques have been developed to use this two dimensional information to infer three-dimensional information about the particles. For mineral processing, a particle that contains more than one mineral (a composite particle) may appear to be liberated (contain only one mineral) when analysed using only its revealed particle section. The mathematical techniques used to interpret three-dimensional information belong, to a branch of mathematics called stereology. However methods to obtain the full mineral liberation distribution of particles from particle sections are relatively new. To verify these adjustment methods, we require an experimental method which can accurately measure both sectional and three dimensional properties. Micro Cone Beam Tomography provides such a method for suitable particles and hence, provides a way to validate methods used to convert two-dimensional measurements to three dimensional estimates. For this study ore particles from a well-characterised sample were subjected to conventional mineralogical analysis (using particle sections) to estimate three-dimensional properties of the particles. A subset of these particles was analysed using a micro-cone beam tomograph. This paper presents a comparison of the three-dimensional properties predicted from measured two-dimensional sections with the measured three-dimensional properties.

Quantum computation as geometry

Quantum computers hold great promise for solving interesting computational problems, but it remains a challenge to find efficient quantum circuits that can perform these complicated tasks. Here we show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms or to prove limitations on the power of quantum computers.

Visual-auditory integration during speech imitation in autism

Children with autistic spectrum disorder (ASD) may have poor audio-visual integration, possibly reflecting dysfunctional 'mirror neuron' systems which have been hypothesised to be at the core of the condition. In the present study, a computer program, utilizing speech synthesizer software and a 'virtual' head (Baldi), delivered speech stimuli for identification in auditory, visual or bimodal conditions. Children with ASD were poorer than controls at recognizing stimuli in the unimodal conditions, but once performance on this measure was controlled for, no group difference was found in the bimodal condition. A group of participants with ASD were also trained to develop their speech-reading ability. Training improved visual accuracy and this also improved the children's ability to utilize visual information in their processing of speech. Overall results were compared to predictions from mathematical models based on integration and non-integration, and were most consistent with the integration model. We conclude that, whilst they are less accurate in recognizing stimuli in the unimodal condition, children with ASD show normal integration of visual and auditory speech stimuli. Given that training in recognition of visual speech was effective, children with ASD may benefit from multi-modal approaches in imitative therapy and language training. (C) 2004 Elsevier Ltd. All rights reserved.

Mathematical Morphology: Star/Galaxy Differentiation & Galaxy Morphology Classication

We present an application of Mathematical Morphology (MM) for the classification of astronomical objects, both for star/galaxy differentiation and galaxy morphology classification. We demonstrate that, for CCD images, 99.3 +/- 3.8% of galaxies can be separated from stars using MM, with 19.4 +/- 7.9% of the stars being misclassified. We demonstrate that, for photographic plate images, the number of galaxies correctly separated from the stars can be increased using our MM diffraction spike tool, which allows 51.0 +/- 6.0% of the high-brightness galaxies that are inseparable in current techniques to be correctly classified, with only 1.4 +/- 0.5% of the high-brightness stars contaminating the population. We demonstrate that elliptical (E) and late-type spiral (Sc-Sd) galaxies can be classified using MM with an accuracy of 91.4 +/- 7.8%. It is a method involving fewer 'free parameters' than current techniques, especially automated machine learning algorithms. The limitation of MM galaxy morphology classification based on seeing and distance is also presented. We examine various star/galaxy differentiation and galaxy morphology classification techniques commonly used today, and show that our MM techniques compare very favourably.

Robustness of mathematical models for biological systems

The robustness of mathematical models for biological systems is studied by sensitivity analysis and stochastic simulations. Using a neural network model with three genes as the test problem, we study robustness properties of synthesis and degradation processes. For single parameter robustness, sensitivity analysis techniques are applied for studying parameter variations and stochastic simulations are used for investigating the impact of external noise. Results of sensitivity analysis are consistent with those obtained by stochastic simulations. Stochastic models with external noise can be used for studying the robustness not only to external noise but also to parameter variations. For external noise we also use stochastic models to study the robustness of the function of each gene and that of the system.

Understanding technology integration in secondary mathematics: Theorising the role of the teacher

Previous research on computers and graphics calculators in mathematics education has examined effects on curriculum content and students’ mathematical achievement and attitudes while less attention has been given to the relationship between technology use and issues of pedagogy, in particular the impact on teachers’ professional learning in specific classroom and school environments. This observation is critical in the current context of educational policy making, where it is assumed – often incorrectly – that supplying schools with hardware and software will increase teachers’ use of technology and encourage more innovative teaching approaches. This paper reports on a research program that aimed to develop better understanding of how and under what conditions Australian secondary school mathematics teachers learn to effectively integrate technology into their practice. The research adapted Valsiner’s concepts of the Zone of Proximal Development, Zone of Free Movement and Zone of Promoted Action to devise a theoretical framework for analysing relationships between factors influencing teachers’ use of technology in mathematics classrooms. This paper illustrates how the framework may be used by analysing case studies of a novice teacher and an experienced teacher in different school settings.