The differential recognition of children’s cultural practices in middle primary literacy classrooms

This paper argues that teachers’ recognition of children’s cultural practices is an important positive step in helping socio-economically disadvantaged children engage with school literacies. Based on twenty-one longitudinal case studies of children’s literacy development over a three-year period, the authors demonstrate that when children’s knowledges and practices assembled in home and community spheres are treated as valuable material for school learning, children are more likely to invest in the work of acquiring school literacies. However they show also that whilst some children benefit greatly from being allowed to draw on their knowledge of popular culture, sports and the outdoors, other children’s interests may be ignored or excluded. Some differences in teachers’ valuing of home and community cultures appeared to relate to gender dimensions.

Analyzing real-time video microscopy : the dynamics and geometry of vesicles and tubules in endocytosis

With the advent of live cell imaging microscopy, new types of mathematical analyses and measurements are possible. Many of the real-time movies of cellular processes are visually very compelling, but elementary analysis of changes over time of quantities such as surface area and volume often show that there is more to the data than meets the eye. This unit outlines a geometric modeling methodology and applies it to tubulation of vesicles during endocytosis. Using these principles, it has been possible to build better qualitative and quantitative understandings of the systems observed, as well as to make predictions about quantities such as ligand or solute concentration, vesicle pH, and membrane trafficked. The purpose is to outline a methodology for analyzing real-time movies that has led to a greater appreciation of the changes that are occurring during the time frame of the real-time video microscopy and how additional quantitative measurements allow for further hypotheses to be generated and tested.

Supplement : Efficient weak second-order stochastic Runge-Kutta methods for non-commutative Stratonvich stochastic differential equations

This paper gives a modification of a class of stochastic Runge–Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

Pattern recognition using invariants defined from higher order spectra - one-dimensional inputs

A new approach to pattern recognition using invariant parameters based on higher order spectra is presented. In particular, invariant parameters derived from the bispectrum are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale and amplification invariant, as well. A minimal set of these invariants is selected as the feature vector for pattern classification, and a minimum distance classifier using a statistical distance measure is used to classify test patterns. The classification technique is shown to distinguish two similar, but different bolts given their one-dimensional profiles. Pattern recognition using higher order spectral invariants is fast, suited for parallel implementation, and has high immunity to additive Gaussian noise. Simulation results show very high classification accuracy, even for low signal-to-noise ratios.

An infinite-horizon robust filter for uncertain hidden Markov Models with conditional relative entropy constraints

We consider a robust filtering problem for uncertain discrete-time, homogeneous, first-order, finite-state hidden Markov models (HMMs). The class of uncertain HMMs considered is described by a conditional relative entropy constraint on measures perturbed from a nominal regular conditional probability distribution given the previous posterior state distribution and the latest measurement. Under this class of perturbations, a robust infinite horizon filtering problem is first formulated as a constrained optimization problem before being transformed via variational results into an unconstrained optimization problem; the latter can be elegantly solved using a risk-sensitive information-state based filtering.

Practical improvements to simultaneous computation of multi-view geometry and radial lens distortion

This paper discusses practical issues related to the use of the division model for lens distortion in multi-view geometry computation. A data normalisation strategy is presented, which has been absent from previous discussions on the topic. The convergence properties of the Rectangular Quadric Eigenvalue Problem solution for computing division model distortion are examined. It is shown that the existing method can require more than 1000 iterations when dealing with severe distortion. A method is presented for accelerating convergence to less than 10 iterations for any amount of distortion. The new method is shown to produce equivalent or better results than the existing method with up to two orders of magnitude reduction in iterations. Through detailed simulation it is found that the number of data points used to compute geometry and lens distortion has a strong influence on convergence speed and solution accuracy. It is recommended that more than the minimal number of data points be used when computing geometry using a robust estimator such as RANSAC. Adding two to four extra samples improves the convergence rate and accuracy sufficiently to compensate for the increased number of samples required by the RANSAC process.

Velocity-jump models with crowding effects

Velocity jump processes are discrete random walk models that have many applications including the study of biological and ecological collective motion. In particular, velocity jump models are often used to represent a type of persistent motion, known as a “run and tumble”, which is exhibited by some isolated bacteria cells. All previous velocity jump processes are non-interacting, which means that crowding effects and agent-to-agent interactions are neglected. By neglecting these agent-to-agent interactions, traditional velocity jump models are only applicable to very dilute systems. Our work is motivated by the fact that many applications in cell biology, such as wound healing, cancer invasion and development, often involve tissues that are densely packed with cells where cell-to-cell contact and crowding effects can be important. To describe these kinds of high cell density problems using a velocity jump process we introduce three different classes of crowding interactions into a one-dimensional model. Simulation data and averaging arguments lead to a suite of continuum descriptions of the interacting velocity jump processes. We show that the resulting systems of hyperbolic partial differential equations predict the mean behavior of the stochastic simulations very well.

An experimental and computational investigation of performance of Green Gully for reusing stormwater

A new stormwater quality improvement device (SQID) called ‘Green Gully’ has been designed and developed in this study with an aim to re-using stormwater for irrigating plants and trees. The main purpose of the Green Gully is to collect road runoff/stormwater, make it suitable for irrigation and provide an automated network system for watering roadside plants and irrigational areas. This paper presents the design and development of Green Gully along with experimental and computational investigations of the performance of Green Gully. Performance (in the form of efficiency, i.e. the percentage of water flow through the gully grate) was experimentally determined using a gully model in the laboratory first, then a three dimensional numerical model was developed and simulated to predict the efficiency of Green Gully as a function of flow rate. Computational Fluid Dynamics (CFD) code FLUENT was used for the simulation. GAMBIT was used for geometry creation and mesh generation. Experimental and simulation results are discussed and compared in this paper. The predicted efficiency was compared with the laboratory measured efficiency. It was found that the simulated results are in good agreement with the experimental results.

Protection of microgrids using differential relays

A microgrid provides economical and reliable power to customers by integrating distributed resources more effectively. Islanded operation enables a continuous power supply for loads during a major grid disturbance. Reliability of a microgrid can be further increased by forming a mesh configuration. However, the protection of mesh microgrids is a challenging task. In this paper, protection schemes are discussed using current differential protection of a microgrid. The protection challenges associated with bi-directional power flow, meshed configuration, changing fault current level due to intermittent nature of DGs and reduced fault current level in an islanded mode are considered in proposing the protection solutions. Relay setting criterion and current transformer (CT) selection guidelines are also discussed. The results are verified using MATLAB calculations and PSCAD simulations.

Effect of geometry on the melting rates of iron rods burning in high pressure oxygen

The effect of sample geometry on the melting rates of burning iron rods was assessed. Promoted-ignition tests were conducted with rods having cylindrical, rectangular, and triangular cross-sectional shapes over a range of cross-sectional areas. The regression rate of the melting interface (RRMI) was assessed using a statistical approach which enabled the quantification of confidence levels for the observed differences in RRMI. Statistically significant differences in RRMI were observed for rods with the same cross-sectional area but different cross-sectional shape. The magnitude of the proportional difference in RRMI increased with the cross-sectional area. Triangular rods had the highest RRMI, followed by rectangular rods, and then cylindrical rods. The dependence of RRMI on rod shape is shown to relate to the action of molten metal at corners. The corners of the rectangular and triangular rods melted faster than the faces due to their locally higher surface area to volume ratios. This phenomenon altered the attachment geometry between liquid and solid phases, increasing the surface area available for heat transfer, causing faster melting. Findings relating to the application of standard flammability test results in industrial situations are also presented.

Facilitating growth in prospective teachers’ knowledge : teaching geometry in primary schools

This paper reports on a study that focused on growth of understanding about teaching geometry by a group of prospective teachers engaged in lesson plan study within a computer-supported collaborative learning (CSCL) environment. Participation in the activity was found to facilitate considerable growth in the participants’ pedagogical-content knowledge (PCK). Factors that influenced growth in PCK included the nature of the lesson planning task, the cognitive scaffolds inserted into the CSCL virtual space, the meta-language scaffolds provided to the participants, and the provision of both private and public discourse spaces. The paper concludes with recommendations for enhancing effective knowledge-building discourse about mathematics PCK within prospective teacher education CSCL environments.

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

The RatSLAM project : robot spatial navigation

Rats are superior to the most advanced robots when it comes to creating and exploiting spatial representations. A wild rat can have a foraging range of hundreds of meters, possibly kilometers, and yet the rodent can unerringly return to its home after each foraging mission, and return to profitable foraging locations at a later date (Davis, et al., 1948). The rat runs through undergrowth and pipes with few distal landmarks, along paths where the visual, textural, and olfactory appearance constantly change (Hardy and Taylor, 1980; Recht, 1988). Despite these challenges the rat builds, maintains, and exploits internal representations of large areas of the real world throughout its two to three year lifetime. While algorithms exist that allow robots to build maps, the questions of how to maintain those maps and how to handle change in appearance over time remain open. The robotic approach to map building has been dominated by algorithms that optimise the geometry of the map based on measurements of distances to features. In a robotic approach, measurements of distance to features are taken with range-measuring devices such as laser range finders or ultrasound sensors, and in some cases estimates of depth from visual information. The features are incorporated into the map based on previous readings of other features in view and estimates of self-motion. The algorithms explicitly model the uncertainty in measurements of range and the measurement of self-motion, and use probability theory to find optimal solutions for the geometric configuration of the map features (Dissanayake, et al., 2001; Thrun and Leonard, 2008). Some of the results from the application of these algorithms have been impressive, ranging from three-dimensional maps of large urban strucutures (Thrun and Montemerlo, 2006) to natural environments (Montemerlo, et al., 2003).

Effective shear modulus approach for two dimensional solids and plate bending problems by meshless point collocation method

For the analysis of material nonlinearity, an effective shear modulus approach based on the strain control method is proposed in this paper by using point collocation method. Hencky’s total deformation theory is used to evaluate the effective shear modulus, Young’s modulus and Poisson’s ratio, which are treated as spatial field variables. These effective properties are obtained by the strain controlled projection method in an iterative manner. To evaluate the second order derivatives of shape function at the field point, the radial basis function (RBF) in the local support domain is used. Several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method and comparisons have been made with analytical solutions and the finite element method (ABAQUS).