Effective employment-based training models for childcare workers

Childcare workers play a significant role in the learning and development of children in their care. This has major implications for the training of workers. Under new reforms of the childcare industry the Australian government now requires all workers to obtain qualifications from a vocational education and training provider (eg. Technical and Further Education) or university. Effective models of employment-based training are critical to provide training to highly competent workers. This paper presents findings from a study that examined current and emerging models of employment-based training in the childcare sector, particularly at the Diploma level. Semi-structured interviews were conducted with a sample of 16 participants who represented childcare directors, employers, and workers located in childcare services in urban, regional and remote locations in the State of Queensland. The study proposes a ‘best-fit’ employment-based training approach that is characterised by a compendium of five models instead of a ‘one size fits all’. Issues with successful implementation of the EBT models are also discussed

Mathematical models for describing the shape of the in vitro unstretched human crystalline lens

We developed orthogonal least-squares techniques for fitting crystalline lens shapes, and used the bootstrap method to determine uncertainties associated with the estimated vertex radii of curvature and asphericities of five different models. Three existing models were investigated including one that uses two separate conics for the anterior and posterior surfaces, and two whole lens models based on a modulated hyperbolic cosine function and on a generalized conic function. Two new models were proposed including one that uses two interdependent conics and a polynomial based whole lens model. The models were used to describe the in vitro shape for a data set of twenty human lenses with ages 7–82 years. The two-conic-surface model (7 mm zone diameter) and the interdependent surfaces model had significantly lower merit functions than the other three models for the data set, indicating that most likely they can describe human lens shape over a wide age range better than the other models (although with the two-conic-surfaces model being unable to describe the lens equatorial region). Considerable differences were found between some models regarding estimates of radii of curvature and surface asphericities. The hyperbolic cosine model and the new polynomial based whole lens model had the best precision in determining the radii of curvature and surface asphericities across the five considered models. Most models found significant increase in anterior, but not posterior, radius of curvature with age. Most models found a wide scatter of asphericities, but with the asphericities usually being positive and not significantly related to age. As the interdependent surfaces model had lower merit function than three whole lens models, there is further scope to develop an accurate model of the complete shape of human lenses of all ages. The results highlight the continued difficulty in selecting an appropriate model for the crystalline lens shape.

Models of supervision : from theory to practice

This chapter will address psychodynamic, cognitive-behavioural, and developmental models in supervision by initially considering the historical underpinnings of each and then examining in turn some of the key processes that are evident in the supervisory relationships. Case studies are included where appropriate to highlight the application of theory to practice and several processes are fully elaborated over all models to enable a contemporary view of style and substance in the supervision context.

The effect of language models on phonetic decoding for spoken term detection

Spoken term detection (STD) popularly involves performing word or sub-word level speech recognition and indexing the result. This work challenges the assumption that improved speech recognition accuracy implies better indexing for STD. Using an index derived from phone lattices, this paper examines the effect of language model selection on the relationship between phone recognition accuracy and STD accuracy. Results suggest that language models usually improve phone recognition accuracy but their inclusion does not always translate to improved STD accuracy. The findings suggest that using phone recognition accuracy to measure the quality of an STD index can be problematic, and highlight the need for an alternative that is more closely aligned with the goals of the specific detection task.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

Numerical method and analytical technique of the modified anomalous subdiffusion equation with a nonlinear source term

In this paper, we consider a modified anomalous subdiffusion equation with a nonlinear source term for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. A new implicit difference method is constructed. The stability and convergence are discussed using a new energy method. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis

Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.

Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation

Anomalous dynamics in complex systems have gained much interest in recent years. In this paper, a two-dimensional anomalous subdiffusion equation (2D-ASDE) is considered. Two numerical methods for solving the 2D-ASDE are presented. Their stability, convergence and solvability are discussed. A new multivariate extrapolation is introduced to improve the accuracy. Finally, numerical examples are given to demonstrate the effectiveness of the schemes and confirm the theoretical analysis.

Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

Assessing information systems success models : empirical comparison (Research in Progress)

Information System (IS) success may be the most arguable and important dependent variable in the IS field. The purpose of the present study is to address IS success by empirically assess and compare DeLone and McLean’s (1992) and Gable’s et al. (2008) models of IS success in Australian Universities context. The two models have some commonalities and several important distinctions. Both models integrate and interrelate multiple dimensions of IS success. Hence, it would be useful to compare the models to see which is superior; as it is not clear how IS researchers should respond to this controversy.

Development of a computer simulation tool for application in adolescent spinal deformity surgery

Scoliosis is a three-dimensional spinal deformity which requires surgical correction in progressive cases. In order to optimize correction and avoid complications following scoliosis surgery, patient-specific finite element models (FEM) are being developed and validated by our group. In this paper, the modeling methodology is described and two clinically relevant load cases are simulated for a single patient. Firstly, a pre-operative patient flexibility assessment, the fulcrum bending radiograph, is simulated to assess the model's ability to represent spine flexibility. Secondly, intra-operative forces during single rod anterior correction are simulated. Clinically, the patient had an initial Cobb angle of 44 degrees, which reduced to 26 degrees during fulcrum bending. Surgically, the coronal deformity corrected to 14 degrees. The simulated initial Cobb angle was 40 degrees, which reduced to 23 degrees following the fulcrum bending load case. The simulated surgical procedure corrected the coronal deformity to 14 degrees. The computed results for the patient-specific FEM are within the accepted clinical Cobb measuring error of 5 degrees, suggested that this modeling methodology is capable of capturing the biomechanical behaviour of a scoliotic human spine during anterior corrective surgery.

Simplified numerical models of LiteSteel Beam floor joists with Web openings for the prediction of section moment capacities

This paper is aimed at investigating the effect of web openings on the plastic bending behaviour and section moment capacity of a new cold-formed steel beam known as LiteSteel beam (LSB) using numerical modelling. Different LSB sections with varying circular hole diameter and spacing were considered. A simplified but appropriate numerical modelling technique was developed for the modelling of monosymmetric sections such as LSBs subject to bending, and was used to simulate a series of section moment capacity tests of LSB flexural members with web openings. The buckling and ultimate strength behaviour was investigated in detail and the modeling technique was further improved through a comparison of numerical and experimental results. This paper describes the simplified finite element modeling technique used in this study that includes all the significant behavioural effects affecting the plastic bending behaviour and section moment capacity of LSB sections with web holes. Numerical and test results and associated findings are also presented.