Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Mesoporous bioactive glass scaffolds for efficient delivery of vascular endothelial growth factor

In this article, we, for the first time, investigated mesoporous bioactive glass scaffolds for the delivery of vascular endothelial growth factor. We have found that mesoporous bioactive glass scaffolds have significantly higher loading efficiency and more sustained release of vascular endothelial growth factor than non-mesoporous bioactive glass scaffolds. In addition, vascular endothelial growth factor delivery from mesoporous bioactive glass scaffolds has improved the viability of endothelial cells. The study has suggested that mesopore structures in mesoporous bioactive glass scaffolds play an important role in improving the loading efficiency, decreasing the burst release, and maintaining the bioactivity of vascular endothelial growth factor, indicating that mesoporous bioactive glass scaffolds are an excellent carrier of vascular endothelial growth factor for potential bone tissue engineering applications.

The cementogenic differentiation of periodontal ligament cells via the activation of Wnt/β-catenin signalling pathway by Li+ ions released from bioactive scaffolds

Lithium (Li) has been widely used as a long-term mood stabilizer in the treatment of bipolar and depressive disorders. Li+ ions are thought to enhance the remyelination of peripheral nerves and also stimulate the proliferation of neural progenitor cells and retinoblastoma cells via activation of the Wnt/β-catenin signalling pathway. Until now there have been no studies reporting the biological effects of released Li+ in bioactive scaffolds on cemetogenesis in periodontal tissue engineering applications. In this study, we incorporated parts of Li+ ions into the mesoporous bioactive glass (MBG) scaffolds and showed that this approach yielded scaffolds with a favourable composition, microstructure and mesopore properties for cell attachment, proliferation, and cementogenic differentiation of human periodontal ligament-derived cells (hPDLCs). We went on to investigate the biological effects of Li+ ions themselves on cell proliferation and cementogenic differentiation. The results showed that 5% Li+ ions incorporated into MBG scaffolds enhanced the proliferation and cementogenic differentiation of hPDLCs on scaffolds, most likely via activation of Wnt/β-catenin signalling pathway. Further study demonstrated that Li+ ions by themselves significantly enhanced the proliferation, differentiation and cementogenic gene expression of PDLCs. Our results indicate that incorporation of Li+ ions into bioactive scaffolds is a viable means of enhancing the Wnt canonical signalling pathway to stimulate cementogenic differentiation of PDLCs.

Multi-method, multi-theoretical, multi-level research in the learning sciences

We examine methodologies and methods that apply to multi-level research in the learning sciences. In so doing we describe how multiple theoretical frameworks informs the use of different methods that apply to social levels involving space-time relationships that are not accessible consciously as social life is enacted. Most of the methods involve analyses of video and audio files. Within a framework of interpretive research we present a methodology of event-oriented social science, which employs video ethnography, narrative, conversation analysis, prosody analysis, and facial expression analysis. We illustrate multi-method research in an examination of the role of emotions in teaching and learning. Conversation and prosody analyses augment facial expression analysis and ethnography. We conclude with an exploration of ways in which multi-level studies can be complemented with neural level analyses.

An innovative approach to the assessment of nutrient intake in adults with type 2 diabetes : the development, trial and evaluation of a mobile phone photo/voice dietary record

Nutrition interventions in the form of both self-management education and individualised diet therapy are considered essential for the long-term management of type 2 diabetes mellitus (T2DM). The measurement of diet is essential to inform, support and evaluate nutrition interventions in the management of T2DM. Barriers inherent within health care settings and systems limit ongoing access to personnel and resources, while traditional prospective methods of assessing diet are burdensome for the individual and often result in changes in typical intake to facilitate recording. This thesis investigated the inclusion of information and communication technologies (ICT) to overcome limitations to current approaches in the nutritional management of T2DM, in particular the development, trial and evaluation of the Nutricam dietary assessment method (NuDAM) consisting of a mobile phone photo/voice application to assess nutrient intake in a free-living environment with older adults with T2DM. Study 1: Effectiveness of an automated telephone system in promoting change in dietary intake among adults with T2DM The effectiveness of an automated telephone system, Telephone-Linked Care (TLC) Diabetes, designed to deliver self-management education was evaluated in terms of promoting dietary change in adults with T2DM and sub-optimal glycaemic control. In this secondary data analysis independent of the larger randomised controlled trial, complete data was available for 95 adults (59 male; mean age(±SD)=56.8±8.1 years; mean(±SD)BMI=34.2±7.0kg/m2). The treatment effect showed a reduction in total fat of 1.4% and saturated fat of 0.9% energy intake, body weight of 0.7 kg and waist circumference of 2.0 cm. In addition, a significant increase in the nutrition self-efficacy score of 1.3 (p<0.05) was observed in the TLC group compared to the control group. The modest trends observed in this study indicate that the TLC Diabetes system does support the adoption of positive nutrition behaviours as a result of diabetes self-management education, however caution must be applied in the interpretation of results due to the inherent limitations of the dietary assessment method used. The decision to use a close-list FFQ with known bias may have influenced the accuracy of reporting dietary intake in this instance. This study provided an example of the methodological challenges experienced with measuring changes in absolute diet using a FFQ, and reaffirmed the need for novel prospective assessment methods capable of capturing natural variance in usual intakes. Study 2: The development and trial of NuDAM recording protocol The feasibility of the Nutricam mobile phone photo/voice dietary record was evaluated in 10 adults with T2DM (6 Male; age=64.7±3.8 years; BMI=33.9±7.0 kg/m2). Intake was recorded over a 3-day period using both Nutricam and a written estimated food record (EFR). Compared to the EFR, the Nutricam device was found to be acceptable among subjects, however, energy intake was under-recorded using Nutricam (-0.6±0.8 MJ/day; p<0.05). Beverages and snacks were the items most frequently not recorded using Nutricam; however forgotten meals contributed to the greatest difference in energy intake between records. In addition, the quality of dietary data recorded using Nutricam was unacceptable for just under one-third of entries. It was concluded that an additional mechanism was necessary to complement dietary information collected via Nutricam. Modifications to the method were made to allow for clarification of Nutricam entries and probing forgotten foods during a brief phone call to the subject the following morning. The revised recording protocol was evaluated in Study 4. Study 3: The development and trial of the NuDAM analysis protocol Part A explored the effect of the type of portion size estimation aid (PSEA) on the error associated with quantifying four portions of 15 single foods items contained in photographs. Seventeen dietetic students (1 male; age=24.7±9.1 years; BMI=21.1±1.9 kg/m2) estimated all food portions on two occasions: without aids and with aids (food models or reference food photographs). Overall, the use of a PSEA significantly reduced mean (±SD) group error between estimates compared to no aid (-2.5±11.5% vs. 19.0±28.8%; p<0.05). The type of PSEA (i.e. food models vs. reference food photograph) did not have a notable effect on the group estimation error (-6.7±14.9% vs. 1.4±5.9%, respectively; p=0.321). This exploratory study provided evidence that the use of aids in general, rather than the type, was more effective in reducing estimation error. Findings guided the development of the Dietary Estimation and Assessment Tool (DEAT) for use in the analysis of the Nutricam dietary record. Part B evaluated the effect of the DEAT on the error associated with the quantification of two 3-day Nutricam dietary records in a sample of 29 dietetic students (2 males; age=23.3±5.1 years; BMI=20.6±1.9 kg/m2). Subjects were randomised into two groups: Group A and Group B. For Record 1, the use of the DEAT (Group A) resulted in a smaller error compared to estimations made without the tool (Group B) (17.7±15.8%/day vs. 34.0±22.6%/day, p=0.331; respectively). In comparison, all subjects used the DEAT to estimate Record 2, with resultant error similar between Group A and B (21.2±19.2%/day vs. 25.8±13.6%/day; p=0.377 respectively). In general, the moderate estimation error associated with quantifying food items did not translate into clinically significant differences in the nutrient profile of the Nutricam dietary records, only amorphous foods were notably over-estimated in energy content without the use of the DEAT (57kJ/day vs. 274kJ/day; p<0.001). A large proportion (89.6%) of the group found the DEAT helpful when quantifying food items contained in the Nutricam dietary records. The use of the DEAT reduced quantification error, minimising any potential effect on the estimation of energy and macronutrient intake. Study 4: Evaluation of the NuDAM The accuracy and inter-rater reliability of the NuDAM to assess energy and macronutrient intake was evaluated in a sample of 10 adults (6 males; age=61.2±6.9 years; BMI=31.0±4.5 kg/m2). Intake recorded using both the NuDAM and a weighed food record (WFR) was coded by three dietitians and compared with an objective measure of total energy expenditure (TEE) obtained using the doubly labelled water technique. At the group level, energy intake (EI) was under-reported to a similar extent using both methods, with the ratio of EI:TEE was 0.76±0.20 for the NuDAM and 0.76±0.17 for the WFR. At the individual level, four subjects reported implausible levels of energy intake using the WFR method, compared to three using the NuDAM. Overall, moderate to high correlation coefficients (r=0.57-0.85) were found across energy and macronutrients except fat (r=0.24) between the two dietary measures. High agreement was observed between dietitians for estimates of energy and macronutrient derived for both the NuDAM (ICC=0.77-0.99; p<0.001) and WFR (ICC=0.82-0.99; p<0.001). All subjects preferred using the NuDAM over the WFR to record intake and were willing to use the novel method again over longer recording periods. This research program explored two novel approaches which utilised distinct technologies to aid in the nutritional management of adults with T2DM. In particular, this thesis makes a significant contribution to the evidence base surrounding the use of PhRs through the development, trial and evaluation of a novel mobile phone photo/voice dietary record. The NuDAM is an extremely promising advancement in the nutritional management of individuals with diabetes and other chronic conditions. Future applications lie in integrating the NuDAM with other technologies to facilitate practice across the remaining stages of the nutrition care process.

Middle school social sciences : exploring teachers’ conceptions of essential knowledge

This study examines teachers’ conceptions of essential knowledge in the humanities and social sciences, commonly referred to as "social education", in the middle years of schooling. Social education has long been a highly contested area of the curriculum in Australia. In Queensland, social education comprises the integrated learning area of Studies of Society and Environment (SOSE). However, the new Australian Curriculum marks a return to discipline-based study of history and geography. This phenomenographic study addresses a perceived lack of understanding in the current research literature in Australia of the nature of middle school teachers’ professional knowledge for teaching the social sciences. Teachers are conceptualised in this study as curriculum makers in the classroom and, as such, their conceptions of essential knowledge are significant. Shulman’s (1986, 1987) theory of teachers’ knowledge forms the theoretical foundation of the study, which is contextualised in Federal and State education policies and the literature on the middle phase of schooling. Transcripts of interviews conducted with a group of thirty-one Queensland middle school teachers of SOSE were subjected to phenomenographic analysis, revealing seven qualitatively different categories of description. Essential aspects of knowledge for social education emerging from the study were: (1) discipline-based knowledge; (2) curriculum knowledge; (3) knowledge derived from teaching experience; (4) knowledge of middle years learners; (5) knowledge of integration; (6) knowledge of current affairs; and (7) knowledge invested in teacher identity. The three dimensions of variation that linked and differentiated the categories were: (1) content; (2) inquiry learning; and (3) teacher autonomy. These findings are presented as an outcome space where the categories are grouped as knowledge of the learning area, knowledge of contexts and knowledge of self as teacher. The results of the study suggest that social education teachers’ identity and knowledge of self are critical aspects of their knowledge as curriculum makers. The results illustrate that the professional and personal domains intersect, extending Shulman’s (1986, 1987) original theorisation of teachers’ knowledge into the personal arena. Further, middle years teachers’ conceptions of essential knowledge reveal a practice-based theorisation of knowledge for social education that fits the goals of middle schooling. The research concludes that attention to teacher identity in teacher education and in-service professional development has considerable potential to grow teachers’ knowledge in the social sciences and enhance their capacity for school-based curriculum leadership.

PLDA based speaker recognition on short utterances

This paper investigates the effects of limited speech data in the context of speaker verification using a probabilistic linear discriminant analysis (PLDA) approach. Being able to reduce the length of required speech data is important to the development of automatic speaker verification system in real world applications. When sufficient speech is available, previous research has shown that heavy-tailed PLDA (HTPLDA) modeling of speakers in the i-vector space provides state-of-the-art performance, however, the robustness of HTPLDA to the limited speech resources in development, enrolment and verification is an important issue that has not yet been investigated. In this paper, we analyze the speaker verification performance with regards to the duration of utterances used for both speaker evaluation (enrolment and verification) and score normalization and PLDA modeling during development. Two different approaches to total-variability representation are analyzed within the PLDA approach to show improved performance in short-utterance mismatched evaluation conditions and conditions for which insufficient speech resources are available for adequate system development. The results presented within this paper using the NIST 2008 Speaker Recognition Evaluation dataset suggest that the HTPLDA system can continue to achieve better performance than Gaussian PLDA (GPLDA) as evaluation utterance lengths are decreased. We also highlight the importance of matching durations for score normalization and PLDA modeling to the expected evaluation conditions. Finally, we found that a pooled total-variability approach to PLDA modeling can achieve better performance than the traditional concatenated total-variability approach for short utterances in mismatched evaluation conditions and conditions for which insufficient speech resources are available for adequate system development.

PLDA based speaker verification with weighted LDA techniques

This paper investigates the use of the dimensionality-reduction techniques weighted linear discriminant analysis (WLDA), and weighted median fisher discriminant analysis (WMFD), before probabilistic linear discriminant analysis (PLDA) modeling for the purpose of improving speaker verification performance in the presence of high inter-session variability. Recently it was shown that WLDA techniques can provide improvement over traditional linear discriminant analysis (LDA) for channel compensation in i-vector based speaker verification systems. We show in this paper that the speaker discriminative information that is available in the distance between pair of speakers clustered in the development i-vector space can also be exploited in heavy-tailed PLDA modeling by using the weighted discriminant approaches prior to PLDA modeling. Based upon the results presented within this paper using the NIST 2008 Speaker Recognition Evaluation dataset, we believe that WLDA and WMFD projections before PLDA modeling can provide an improved approach when compared to uncompensated PLDA modeling for i-vector based speaker verification systems.

In vitro breeding strategies in the development of Australian native plants

Plant tissue culture is a technique that exploits the ability of many plant cells to revert to a meristematic state. Although originally developed for botanical research, plant tissue culture has now evolved into important commercial practices and has become a significant research tool in agriculture, horticulture and in many other areas of plant sciences. Plant tissue culture is the sterile culture of plant cells, tissues, or organs under aseptic conditions leading to cell multiplication or regeneration or organs and whole plants. The steps required to develop reliable systems for plant regeneration and their application in plant biotechnology are reviewed in countless books. Some of the major landmarks in the evolution of in vitro techniques are summarised in Table 5.1. In this chapter the current applications of this technology to agriculture, horticulture, forestry and plant breeding are briefly described with specific examples from Australian plants when applicable.

Simple rules to contain an invasive species with a complex life cycle and high dispersal capacity

Designing practical rules for controlling invasive species is a challenging task for managers, particularly when species are long-lived, have complex life cycles and high dispersal capacities. Previous findings derived from plant matrix population analyses suggest that effective control of long-lived invaders may be achieved by focusing on killing adult plants. However, the cost-effectiveness of managing different life stages has not been evaluated. We illustrate the benefits of integrating matrix population models with decision theory to undertake this evaluation, using empirical data from the largest infestation of mesquite (Leguminosae: Prosopis spp) within Australia. We include in our model the mesquite life cycle, different dispersal rates and control actions that target individuals at different life stages with varying costs, depending on the intensity of control effort. We then use stochastic dynamic programming to derive cost-effective control strategies that minimize the cost of controlling the core infestation locally below a density threshold and the future cost of control arising from infestation of adjacent areas via seed dispersal. Through sensitivity analysis, we show that four robust management rules guide the allocation of resources between mesquite life stages for this infestation: (i) When there is no seed dispersal, no action is required until density of adults exceeds the control threshold and then only control of adults is needed; (ii) when there is seed dispersal, control strategy is dependent on knowledge of the density of adults and large juveniles (LJ) and broad categories of dispersal rates only; (iii) if density of adults is higher than density of LJ, controlling adults is most cost-effective; (iv) alternatively, if density of LJ is equal or higher than density of adults, management efforts should be spread between adults, large and to a lesser extent small juveniles, but never saplings. Synthesis and applications.In this study, we show that simple rules can be found for managing invasive plants with complex life cycles and high dispersal rates when population models are combined with decision theory. In the case of our mesquite population, focussing effort on controlling adults is not always the most cost-effective way to meet our management objective.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

Group dynamics and software engineering

This paper reports on an experiment that was conducted to determine the extent to which group dynamics impacts on the effectiveness of software development teams. The experiment was conducted on software engineering project students at the Queensland University of Technology (QUT).

A new implicit numerical method for the space and time fractional Bloch-Torrey equation

In recent years, it has been found that many phenomena in engineering, physics, chemistry and other sciences can be described very successfully by models using mathematical tools from fractional calculus. Recently, noted a new space and time fractional Bloch-Torrey equation (ST-FBTE) has been proposed (see Magin et al. (2008)), and successfully applied to analyse diffusion images of human brain tissues to provide new insights for further investigations of tissue structures. In this paper, we consider the ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we propose a new effective implicit numerical method (INM) for the STFBTE whereby we discretize the Riesz fractional derivative using a fractional centered difference. Secondly, we prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent, and the order of convergence of the implicit numerical method is ( T2 - α + h2 x + h2 y + h2 z ). Finally, some numerical results are presented to support our theoretical analysis.

Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media

Percolation flow problems are discussed in many research fields, such as seepage hydraulics, groundwater hydraulics, groundwater dynamics and fluid dynamics in porous media. Many physical processes appear to exhibit fractional-order behavior that may vary with time, or space, or space and time. The theory of pseudodifferential operators and equations has been used to deal with this situation. In this paper we use a fractional Darcys law with variable order Riemann-Liouville fractional derivatives, this leads to a new variable-order fractional percolation equation. In this paper, a new two-dimensional variable-order fractional percolation equation is considered. A new implicit numerical method and an alternating direct method for the two-dimensional variable-order fractional model is proposed. Consistency, stability and convergence of the implicit finite difference method are established. Finally, some numerical examples are given. The numerical results demonstrate the effectiveness of the methods. This technique can be used to simulate a three-dimensional variable-order fractional percolation equation.

The Galerkin finite element approximation of the fractional cable equation

The cable equation is one of the most fundamental equations for modeling neuronal dynamics. Cable equations with a fractional order temporal derivative have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper, the fractional cable equation involving two integro-differential operators is considered. The Galerkin finite element approximations of the fractional cable equation are proposed. The main contribution of this work is outlined as follow: • A semi-discrete finite difference approximation in time is proposed. We prove that the scheme is unconditionally stable, and the numerical solution converges to the exact solution with order O(Δt). • A semi-discrete difference scheme for improving the order of convergence for solving the fractional cable equation is proposed, and the numerical solution converges to the exact solution with order O((Δt)2). • Based on the above semi-discrete difference approximations, Galerkin finite element approximations in space for a full discretization are also investigated. • Finally, some numerical results are given to demonstrate the theoretical analysis.