A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

A cellular automata model to investigate immune cell–tumor cell interactions in growing tumors in two spatial dimensions

We develop a hybrid cellular automata model to describe the effect of the immune system and chemokines on a growing tumor. The hybrid cellular automata model consists of partial differential equations to model chemokine concentrations, and discrete cellular automata to model cell–cell interactions and changes. The computational implementation overlays these two components on the same spatial region. We present representative simulations of the model and show that increasing the number of immature dendritic cells (DCs) in the domain causes a decrease in the number of tumor cells. This result strongly supports the hypothesis that DCs can be used as a cancer treatment. Furthermore, we also use the hybrid cellular automata model to investigate the growth of a tumor in a number of computational “cancer patients.” Using these virtual patients, the model can explain that increasing the number of DCs in the domain causes longer “survival.” Not surprisingly, the model also reflects the fact that the parameter related to tumor division rate plays an important role in tumor metastasis.

A humanized tissue-engineered in vivo model to dissect interactions between human prostate cancer cells and human bone

Currently used xenograft models for prostate cancer bone metastasis lack the adequate tissue composition necessary to study the interactions between human prostate cancer cells and the human bone microenvironment. We introduce a tissue engineering approach to explore the interactions between human tumor cells and a humanized bone microenvironment. Scaffolds, seeded with human primary osteoblasts in conjunction with BMP7, were implanted into immunodeficient mice to form humanized tissue engineered bone constructs (hTEBCs) which consequently resulted in the generation of highly vascularized and viable humanized bone. At 12 weeks, PC3 and LNCaP cells were injected into the hTEBCs. Seven weeks later the mice were euthanized. Micro-CT, histology, TRAP, PTHrP and osteocalcin staining results reflected the different characteristics of the two cell lines regarding their phenotypic growth pattern within bone. Microvessel density, as assessed by vWF staining, showed that tumor vessel density was significantly higher in LNCaP injected hTEBC implants than in those injected with PC3 cells (p\0.001). Interestingly, PC3 cells showed morphological features of epithelial and mesenchymal phenotypes suggesting a cellular plasticity within this microenvironment. Taken together, a highly reproducible humanized model was established which is successful in generating LNCaP and PC3 tumors within a complex humanized bone microenvironment. This model simulates the conditions seen clinically more closely than any other model described in the literature to date and hence represents a powerful experimental platform that can be used in future work to investigate specific biological questions relevant to bone metastasis.

Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

Defining a 3-dimensional (3D) in vitro model to study immune cell and renal cell interactions

This study aimed to develop a 3-Dimensional (D) hydrogel system for the co-culture of autologous human renal and immune cells. Previous studies have shown that human renal epithelial cells are able to modulate autologous immune cell responses. However, these studies were undertaken in a standard 2D culture system. The 3D model was developed to re-capitulate these observations within a more physiological relevant in vivo like environment.

Nonlinear analysis for the pre- and post-yield behaviour of a hybrid structure by a higher-order element with the refined plastic hinge approach

Efficient and accurate geometric and material nonlinear analysis of the structures under ultimate loads is a backbone to the success of integrated analysis and design, performance-based design approach and progressive collapse analysis. This paper presents the advanced computational technique of a higher-order element formulation with the refined plastic hinge approach which can evaluate the concrete and steel-concrete structure prone to the nonlinear material effects (i.e. gradual yielding, full plasticity, strain-hardening effect when subjected to the interaction between axial and bending actions, and load redistribution) as well as the nonlinear geometric effects (i.e. second-order P-d effect and P-D effect, its associate strength and stiffness degradation). Further, this paper also presents the cross-section analysis useful to formulate the refined plastic hinge approach.

The impact of nonlinear pedagogy on physical education teacher education students’ intrinsic motivation

Background: Providing motivationally supportive physical education experiences for learners is crucial since empirical evidence in sport and physical education research has associated intrinsic motivation with positive educational outcomes. Self-determination theory (SDT) provides a valuable framework for examining motivationally supportive physical education experiences through satisfaction of three basic psychological needs: autonomy, competence and relatedness. However, the capacity of the prescriptive teaching philosophy of the dominant traditional physical education teaching approach to effectively satisfy the psychological needs of students to engage in physical education has been questioned. The constraints-led approach (CLA) has been proposed as a viable alternative teaching approach that can effectively support students’ self-motivated engagement in physical education. Purpose: We sought to investigate whether adopting the learning design and delivery of the CLA, guided by key pedagogical principles of nonlinear pedagogy (NLP), would address basic psychological needs of learners, resulting in higher self-reported levels of intrinsic motivation. The claim was investigated using action research. The teacher/researcher delivered two lessons aimed at developing hurdling skills: one taught using the CLA and the other using the traditional approach. Participants and Setting: The main participant for this study was the primary researcher and lead author who is a PETE educator, with extensive physical education teaching experience. A sample of 54 pre-service PETE students undertaking a compulsory second year practical unit at an Australian university was recruited for the study, consisting of an equal number of volunteers from each of two practical classes. A repeated measures experimental design was adopted, with both practical class groups experiencing both teaching approaches in a counterbalanced order. Data collection and analysis: Immediately after participation in each lesson, participants completed a questionnaire consisting of 22 items chosen from validated motivation measures of basic psychological needs and indices of intrinsic motivation, enjoyment and effort. All questionnaire responses were indicated on a 7-point Likert scale. A two-tailed, paired-samples t-test was used to compare the groups’ motivation subscale mean scores for each teaching approach. The size of the effect for each group was calculated using Cohen’s d. To determine whether any significant differences between the subscale mean scores of the two groups was due to an order effect, a two-tailed, independent samples t test was used. Findings: Participants’ reported substantially higher levels of self-determination and intrinsic motivation during the CLA hurdles lesson compared to during the traditional hurdles lesson. Both groups reported significantly higher motivation subscale mean scores for competence, relatedness, autonomy, enjoyment and effort after experiencing the CLA than mean scores reported after experiencing the traditional approach. This significant difference was evident regardless of the order that each teaching approach was experienced. Conclusion: The theoretically based pedagogical principles of NLP that inform learning design and delivery of the CLA may provide teachers and coaches with tools to develop more functional pedagogical climates, which result in students exhibiting more intrinsically motivated behaviours during learning.

Somewhere between haste and delay... Investigating the interactions of road users and pedestrians in a dynamic rail level crossing environment

There are currently 23,500 level crossings in Australia, broadly divided into one of two categories: active level crossings which are fully automatic and have boom barriers, alarm bells, flashing lights, and pedestrian gates; and passive level crossings, which are not automatic and aim to control road and pedestrianised walkways solely with stop and give way signs. Active level crossings are considered to be the gold standard for transport ergonomics when grade separation (i.e. constructing an over- or underpass) is not viable. In Australia, the current strategy is to annually upgrade passive level crossings with active controls but active crossings are also associated with traffic congestion, largely as a result of extended closure times. The percentage of time level crossings are closed to road vehicles during peak periods increases with the rise in the frequency of train services. The popular perception appears to be that once a level crossing is upgraded, one is free to wipe their hands and consider the job done. However, there may also be environments where active protection is not enough, but where the setting may not justify the capital costs of grade separation. Indeed, the associated congestion and traffic delay could compromise safety by contributing to the risk taking behaviour by motorists and pedestrians. In these environments it is important to understand what human factor issues are present and ask the question of whether a one size fits all solution is indeed the most ergonomically sound solution for today’s transport needs.

Investigation of the binding interactions between insulin and its receptor

This project investigated the interactions between insulin and its receptor. A combination of computational and experimental investigations resulted in the identification of four residues in non-canonical sites that, when mutated, had detrimental effects on insulin binding. An increased understanding of the binding mechanism will aid future research into diseases involving the insulin receptor and its relatives and could potentially lead to new therapeutic avenues to combat these health related issues.

A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

Use of phage display technology to investigate allergen-antibody interactions

Phage display is an advanced technology that can be used to characterize the interactions of antibody with antigen at the molecular level. It provides valuable data when applied to the investigation of IgE interaction with allergens. The aim of this rostrum article is to provide an explanation of the potential of phage display for increasing the understanding of allergen- IgE interaction, the discovery of diagnostic reagents, and the development of novel therapeutics for the treatment of allergic disease. The significance of initial studies that have applied phage display technology in allergy research will be highlighted. Phage display has been used to clone human IgE to timothy grass pollen allergen Phl p 5, to characterize the epitopes for murine and human antibodies to a birch pollen allergen Bet v 1, and to elucidate the epitopes of a murine mAb to the house dust mite allergen Der p 1. The technology has identified peptides that functionally mimic sites of human IgE constant domains and that were used to raise antiserum for blocking binding of IgE to the FcεRI on basophils and subsequent release of histamine. Phage display has also been used to characterize novel peanut and fungal allergens. The method has been used to increase our understanding of the molecular basis of allergen-IgE interactions and to develop clinically relevant reagents with the pharmacologic potential to block the effector phase of allergic reactions. Many advances from these early studies are likely as phage display technology evolves and allergists gain expertise in its research applications.

Analysis of complex molecular systems: The impact of multivariate analysis for resolving the interactions of small molecules with biopolymers - a review

This review is focused on the impact of chemometrics for resolving data sets collected from investigations of the interactions of small molecules with biopolymers. These samples have been analyzed with various instrumental techniques, such as fluorescence, ultraviolet–visible spectroscopy, and voltammetry. The impact of two powerful and demonstrably useful multivariate methods for resolution of complex data—multivariate curve resolution–alternating least squares (MCR–ALS) and parallel factor analysis (PARAFAC)—is highlighted through analysis of applications involving the interactions of small molecules with the biopolymers, serum albumin, and deoxyribonucleic acid. The outcomes illustrated that significant information extracted by the chemometric methods was unattainable by simple, univariate data analysis. In addition, although the techniques used to collect data were confined to ultraviolet–visible spectroscopy, fluorescence spectroscopy, circular dichroism, and voltammetry, data profiles produced by other techniques may also be processed. Topics considered including binding sites and modes, cooperative and competitive small molecule binding, kinetics, and thermodynamics of ligand binding, and the folding and unfolding of biopolymers. Applications of the MCR–ALS and PARAFAC methods reviewed were primarily published between 2008 and 2013.

Quantification of stability in an agility drill using linear and nonlinear measures of variability

This study implemented linear and nonlinear methods of measuring variability to determine differences in stability of two groups of skilled (n = 10) and unskilled (n = 10) participants performing 3m forward/backward shuttle agility drill. We also determined whether stability measures differed between the forward and backward segments of the drill. Finally, we sought to investigate whether local dynamic stability, measured using largest finite-time Lyapunov exponents, changed from distal to proximal lower extremity segments. Three-dimensional coordinates of five lower extremity markers data were recorded. Results revealed that the Lyapunov exponents were lower (P < 0.05) for skilled participants at all joint markers indicative of higher levels of local dynamic stability. Additionally, stability of motion did not differ between forward and backward segments of the drill (P > 0.05), signifying that almost the same control strategy was used in forward and backward directions by all participants, regardless of skill level. Furthermore, local dynamic stability increased from distal to proximal joints (P < 0.05) indicating that stability of proximal segments are prioritized by the neuromuscular control system. Finally, skilled participants displayed greater foot placement standard deviation values (P < 0.05), indicative of adaptation to task constraints. The results of this study provide new methods for sport scientists, coaches to characterize stability in agility drill performance.