Parameter estimation for a phenomenological model of the cardiac action potential

The action potential (ap) of a cardiac cell is made up of a complex balance of ionic currents which flow across the cell membrane in response to electrical excitation of the cell. Biophysically detailed mathematical models of the ap have grown larger in terms of the variables and parameters required to model new findings in subcellular ionic mechanisms. The fitting of parameters to such models has seen a large degree of parameter and module re-use from earlier models. An alternative method for modelling electrically exciteable cardiac tissue is a phenomenological model, which reconstructs tissue level ap wave behaviour without subcellular details. A new parameter estimation technique to fit the morphology of the ap in a four variable phenomenological model is presented. An approximation of a nonlinear ordinary differential equation model is established that corresponds to the given phenomenological model of the cardiac ap. The parameter estimation problem is converted into a minimisation problem for the unknown parameters. A modified hybrid Nelder–Mead simplex search and particle swarm optimization is then used to solve the minimisation problem for the unknown parameters. The successful fitting of data generated from a well known biophysically detailed model is demonstrated. A successful fit to an experimental ap recording that contains both noise and experimental artefacts is also produced. The parameter estimation method’s ability to fit a complex morphology to a model with substantially more parameters than previously used is established.

On the contemporary position of the Indigenous peoples of Australia

This paper highlights the contemporary disadvantaged position of Indigenous peoples of Australia.∗ It discusses a number of data quality issues on Indigenous data, before examining Indigenous disadvantage across five key areas: (1) education; (2) employment; (3) housing and living conditions; (4) health and wellbeing; and (5) crime and justice. Given the call for all governments to implement a framework to overcome Indigenous disadvantage, we recommend that future research begin with an investigation of non-Indigenous attitudes towards, and knowledge of, the position of Indigenous peoples in Australia. This is essential towards developing an understanding of the general public’s current perceptions of Indigenous peoples’ position in Australia, particularly where the development of policies pertaining to Indigenous peoples requires cooperative action and the support of the broader Australian population.

Stochastic analysis of the VEGF receptor response curve

Recently, an analysis of the response curve of the vascular endothelial growth factor (VEGF) receptor and its application to cancer therapy was described in [T. Alarcón, and K. Page, J. R. Soc. Lond. Interface 4, 283–304 (2007)]. The analysis is significantly extended here by demonstrating that an alternative computational strategy, namely the Krylov FSP algorithm for the direct solution of the chemical master equation, is feasible for the study of the receptor model. The new method allows us to further investigate the hypothesis of symmetry in the stochastic fluctuations of the response. Also, by augmenting the original model with a single reversible reaction we formulate a plausible mechanism capable of realizing a bimodal response, which is reported experimentally but which is not exhibited by the original model. The significance of these findings for mechanisms of tumour resistance to antiangiogenic therapy is discussed.

An analytical and experimental study of the vibration response of a clamped ribbed plate

An analytical solution is presented in this paper for the vibration response of a ribbed plate clamped on all its boundary edges by employing a travelling wave solution. A clamped ribbed plate test rig is also assembled in this study for the experimental investigation of the ribbed plate response and to provide verification results to the analytical solution. The dynamic characteristics and mode shapes of the ribbed plate are measured and compared to those obtained from the analytical solution and from finite element analysis (FEA). General good agreements are found between the results. Discrepancies between the computational and experimental results at low and high frequencies are also discussed. Explanations are offered in the study to disclose the mechanism causing the discrepancies. The dependency of the dynamic response of the ribbed plate on the distance between the excitation force and the rib is also investigated experimentally. It confirms the findings disclosed in a previous analytical study [T. R. Lin and J. Pan, A closed form solution for the dynamic response of finite ribbed plates. Journal of the Acoustical Society of America 119 (2006) 917-925] that the vibration response of a clamped ribbed plate due to a point force excitation is controlled by the plate stiffness when the source is more than a quarter plate bending wavelength away from the rib and from the plate boundary. The response is largely affected by the rib stiffness when the source location is less than a quarter bending wavelength away from the rib.

Active regulation of the epidermal calcium profile

A distinct calcium profile is strongly implicated in regulating the multi-layered structure of the epidermis. However, the mechanisms that govern the regulation of this calcium profile are currently unclear. It clearly depends on the relatively impermeable barrier of the stratum corneum (passive regulation) but may also depend on calcium exchanges between keratinocytes and extracellular fluid (active regulation). Using a mathematical model that treats the viable sublayers of unwounded human and murine epidermis as porous media and assumes that their calcium profiles are passively regulated, we demonstrate that these profiles are also actively regulated. To obtain this result, we found that diffusion governs extracellular calcium motion in the viable epidermis and hence intracellular calcium is the main source of the epidermal calcium profile. Then, by comparison with experimental calcium profiles and combination with a hypothesised cell velocity distribution in the viable epidermis, we found that the net influx of calcium ions into keratinocytes from extracellular fluid may be constant and positive throughout the stratum basale and stratum spinosum, and that there is a net outflux of these ions in the stratum granulosum. Hence the calcium exchange between keratinocytes and extracellular fluid differs distinctly between the stratum granulosum and the underlying sublayers, and these differences actively regulate the epidermal calcium profile. Our results also indicate that plasma membrane dysfunction may be an early event during keratinocyte disintegration in the stratum granulosum.

Class contestations and Australia’s resource boom : the emergence of the ‘cashed-up bogan’

This article examines the figure of the ‘Cashed-up Bogan’ or ‘Cub’ in Australian media from 2006 to 2009. It explains that ‘Bogan’, like that of ‘Chav’ in Britain, is a widely engaged negative descriptor for the white working-class poor. In contrast, ‘Cubs’ have economic capital. This capital, and the Cub’s emergence, is linked to Australia’s resource boom of recent decades when the need for skilled labour allowed for a highly demarcated segment of the working class to earn relatively high incomes in the mining sector and to participate in consumption. We argue that access to economic capital has provided the Cub with mobility to enter the everyday spaces of the middle class, but this has caused disruption and anxiety to middle-class hegemony. As a result, the middle class has redrawn and reinforced class-infused symbolic and cultural boundaries, whereby, despite their wealth, pernicious media representations mark Cubs as ‘other’ to the middle-class deservingness, taste and morality.

Scaling for the Prandtl number of the natural convection boundary layer of an inclined flat plate under uniform surface heat flux

An improved scaling analysis and direct numerical simulations are performed for the unsteady natural convection boundary layer adjacent to a downward facing inclined plate with uniform heat flux. The development of the thermal or viscous boundary layers may be classified into three distinct stages: a start-up stage, a transitional stage and a steady stage, which can be clearly identified in the analytical as well as the numerical results. Previous scaling shows that the existing scaling laws of the boundary layer thickness, velocity and steady state time scale for the natural convection flow on a heated plate of uniform heat flux provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings perform very well with Rayleigh number and aspect ratio dependency. In this study, a modified Prandtl number scaling is developed using a triple layer integral approach for Pr > 1. It is seen that in comparison to the direct numerical simulations, the modified scaling performs considerably better than the previous scaling.

Serious fears across cultures about the collapse of the world order

This chapter approaches resilience from an evolutionary psychology (socio-biological) perspective. It argues that the internal constitution and mental toughness of the individual will provide a core protection for life’s inevitable tests in the innumerable micro and macro environments humans find themselves. The many descriptors of the construct of resilience used in various studies are explored. Finally, the difference psychologists can make in the therapy of clients whose resilience is being tested, is examined by means of case examples.

The development of the graphics-decoding proficiency instrument

The Graphics-Decoding Proficiency (G-DP) instrument was developed as a screening test for the purpose of measuring students’ (aged 8-11 years) capacity to solve graphics-based mathematics tasks. These tasks include number lines, column graphs, maps and pie charts. The instrument was developed within a theoretical framework which highlights the various types of information graphics commonly presented to students in large-scale national and international assessments. The instrument provides researchers, classroom teachers and test designers with an assessment tool which measures students’ graphics decoding proficiency across and within five broad categories of information graphics. The instrument has implications for a number of stakeholders in an era where graphics have become an increasingly important way of representing information.

A continuum model of the growth of engineered epidermal skin substitutes

We present a porous medium model of the growth and deterioration of the viable sublayers of an epidermal skin substitute. It consists of five species: cells, intracellular and extracellular calcium, tight junctions, and a hypothesised signal chemical emanating from the stratum corneum. The model is solved numerically in Matlab using a finite difference scheme. Steady state calcium distributions are predicted that agree well with the experimental data. Our model also demonstrates epidermal skin substitute deterioration if the calcium diffusion coefficient is reduced compared to reported values in the literature.

Meeting under the “Omei” Tree in the Torres Strait Islands : networks and funds of knowledge of mathematical ideas

This paper focuses on the turning point experiences that worked to transform the researcher during a preliminary consultation process to seek permission to conduct of a small pilot project on one Torres Strait Island. The project aimed to learn from parents how they support their children in their mathematics learning. Drawing on a community research design, a consultative meeting was held with one Torres Strait Islander community to discuss the possibility of piloting a small project that focused on working with parents and children to learn about early mathematics processes. Preliminary data indicated that parents use networks in their community. It highlighted the funds of knowledge of mathematics that exist in the community and which are used to teach their children. Such knowledges are situated within a community’s unique histories, culture and the voices of the people. “Omei” tree means the Tree of Wisdom in the Island community.

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.

Prandtl number scaling of the unsteady natural convection boundary layer adjacent to a vertical flat plate for Pr > 1 subject to ramp surface heat flux

It is found in the literature that the existing scaling results for the boundary layer thickness, velocity and steady state time for the natural convection flow over an evenly heated plate provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings provide a good prediction of two other governing parameters’ dependency, the Rayleigh number and the aspect ratio. Therefore, an improved scaling analysis using a triple-layer integral approach and direct numerical simulations have been performed for the natural convection boundary layer along a semi-infinite flat plate with uniform surface heat flux. This heat flux is a ramp function of time, where the temperature gradient on the surface increases with time up to some specific time and then remains constant. The growth of the boundary layer strongly depends on the ramp time. If the ramp time is sufficiently long, the boundary layer reaches a quasi steady mode before the growth of the temperature gradient is completed. In this mode, the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the ramp time is sufficiently short, the boundary layer develops differently, but after the wall temperature gradient growth is completed, the boundary layer develops as though the startup had been instantaneous.