A numerical method for the fractional Fitzhugh–Nagumo monodomain model

A fractional FitzHugh–Nagumo monodomain model with zero Dirichlet boundary conditions is presented, generalising the standard monodomain model that describes the propagation of the electrical potential in heterogeneous cardiac tissue. The model consists of a coupled fractional Riesz space nonlinear reaction-diffusion model and a system of ordinary differential equations, describing the ionic fluxes as a function of the membrane potential. We solve this model by decoupling the space-fractional partial differential equation and the system of ordinary differential equations at each time step. Thus, this means treating the fractional Riesz space nonlinear reaction-diffusion model as if the nonlinear source term is only locally Lipschitz. The fractional Riesz space nonlinear reaction-diffusion model is solved using an implicit numerical method with the shifted Grunwald–Letnikov approximation, and the stability and convergence are discussed in detail in the context of the local Lipschitz property. Some numerical examples are given to show the consistency of our computational approach.

Global, regional, and national age–sex specifi c all-cause and cause-specifi c mortality for 240 causes of death, 1990–2013: a systematic analysis for the Global Burden of Disease Study 2013

Background Up-to-date evidence on levels and trends for age-sex-specific all-cause and cause-specific mortality is essential for the formation of global, regional, and national health policies. In the Global Burden of Disease Study 2013 (GBD 2013) we estimated yearly deaths for 188 countries between 1990, and 2013. We used the results to assess whether there is epidemiological convergence across countries. Methods We estimated age-sex-specific all-cause mortality using the GBD 2010 methods with some refinements to improve accuracy applied to an updated database of vital registration, survey, and census data. We generally estimated cause of death as in the GBD 2010. Key improvements included the addition of more recent vital registration data for 72 countries, an updated verbal autopsy literature review, two new and detailed data systems for China, and more detail for Mexico, UK, Turkey, and Russia. We improved statistical models for garbage code redistribution. We used six different modelling strategies across the 240 causes; cause of death ensemble modelling (CODEm) was the dominant strategy for causes with sufficient information. Trends for Alzheimer's disease and other dementias were informed by meta-regression of prevalence studies. For pathogen-specific causes of diarrhoea and lower respiratory infections we used a counterfactual approach. We computed two measures of convergence (inequality) across countries: the average relative difference across all pairs of countries (Gini coefficient) and the average absolute difference across countries. To summarise broad findings, we used multiple decrement life-tables to decompose probabilities of death from birth to exact age 15 years, from exact age 15 years to exact age 50 years, and from exact age 50 years to exact age 75 years, and life expectancy at birth into major causes. For all quantities reported, we computed 95% uncertainty intervals (UIs). We constrained cause-specific fractions within each age-sex-country-year group to sum to all-cause mortality based on draws from the uncertainty distributions. Findings Global life expectancy for both sexes increased from 65·3 years (UI 65·0–65·6) in 1990, to 71·5 years (UI 71·0–71·9) in 2013, while the number of deaths increased from 47·5 million (UI 46·8–48·2) to 54·9 million (UI 53·6–56·3) over the same interval. Global progress masked variation by age and sex: for children, average absolute differences between countries decreased but relative differences increased. For women aged 25–39 years and older than 75 years and for men aged 20–49 years and 65 years and older, both absolute and relative differences increased. Decomposition of global and regional life expectancy showed the prominent role of reductions in age-standardised death rates for cardiovascular diseases and cancers in high-income regions, and reductions in child deaths from diarrhoea, lower respiratory infections, and neonatal causes in low-income regions. HIV/AIDS reduced life expectancy in southern sub-Saharan Africa. For most communicable causes of death both numbers of deaths and age-standardised death rates fell whereas for most non-communicable causes, demographic shifts have increased numbers of deaths but decreased age-standardised death rates. Global deaths from injury increased by 10·7%, from 4·3 million deaths in 1990 to 4·8 million in 2013; but age-standardised rates declined over the same period by 21%. For some causes of more than 100 000 deaths per year in 2013, age-standardised death rates increased between 1990 and 2013, including HIV/AIDS, pancreatic cancer, atrial fibrillation and flutter, drug use disorders, diabetes, chronic kidney disease, and sickle-cell anaemias. Diarrhoeal diseases, lower respiratory infections, neonatal causes, and malaria are still in the top five causes of death in children younger than 5 years. The most important pathogens are rotavirus for diarrhoea and pneumococcus for lower respiratory infections. Country-specific probabilities of death over three phases of life were substantially varied between and within regions. Interpretation For most countries, the general pattern of reductions in age-sex specific mortality has been associated with a progressive shift towards a larger share of the remaining deaths caused by non-communicable disease and injuries. Assessing epidemiological convergence across countries depends on whether an absolute or relative measure of inequality is used. Nevertheless, age-standardised death rates for seven substantial causes are increasing, suggesting the potential for reversals in some countries. Important gaps exist in the empirical data for cause of death estimates for some countries; for example, no national data for India are available for the past decade.

Acoustic identification of twelve species of echolocating bat by discriminant function analysis and artificial neural networks

We recorded echolocation calls from 14 sympatric species of bat in Britain. Once digitised, one temporal and four spectral features were measured from each call. The frequency-time course of each call was approximated by fitting eight mathematical functions, and the goodness of fit, represented by the mean-squared error, was calculated. Measurements were taken using an automated process that extracted a single call from background noise and measured all variables without intervention. Two species of Rhinolophus were easily identified from call duration and spectral measurements. For the remaining 12 species, discriminant function analysis and multilayer back-propagation perceptrons were used to classify calls to species level. Analyses were carried out with and without the inclusion of curve-fitting data to evaluate its usefulness in distinguishing among species. Discriminant function analysis achieved an overall correct classification rate of 79% with curve-fitting data included, while an artificial neural network achieved 87%. The removal of curve-fitting data improved the performance of the discriminant function analysis by 2 %, while the performance of a perceptron decreased by 2 %. However, an increase in correct identification rates when curve-fitting information was included was not found for all species. The use of a hierarchical classification system, whereby calls were first classified to genus level and then to species level, had little effect on correct classification rates by discriminant function analysis but did improve rates achieved by perceptrons. This is the first published study to use artificial neural networks to classify the echolocation calls of bats to species level. Our findings are discussed in terms of recent advances in recording and analysis technologies, and are related to factors causing convergence and divergence of echolocation call design in bats.

Finite volume methods for simulating anomalous transport

In this thesis a new approach for solving a certain class of anomalous diffusion equations was developed. The theory and algorithms arising from this work will pave the way for more efficient and more accurate solutions of these equations, with applications to science, health and industry. The method of finite volumes was applied to discretise the spatial derivatives, and this was shown to outperform existing methods in several key respects. The stability and convergence of the new method were rigorously established.

Recreational needs and service performance expectations

The theoretical contribution of this study lies with its focus on subjective experiencing, that is, the emotional convergence between feeling states, and perceptions of servicescapes and holiday activities. An empirical study models the impact of recreational needs on the perceived importance of destination attributes and intentions to participate in activities. A sample of prospective tourists was asked to indicate how important they considered servicescape elements to be in their general holiday planning. They were also asked to report on their emotional state (orientation) as a proxy for their needs for recreation, and to state their intention and likely involvement with holiday activities. Results suggest that those with high recreational needs (self-reflexive and inward-looking) regard elements of tourism servicescapes as significantly more important than those without (who are outward-looking and energetic), as well as show significant variations in their inclinations to be active and explorative at destinations. Rather, those with higher recreational needs as measured by combinations of lack of energy, self-confidence, and physiological well-being look for creature comfort, coziness, and familiarity, in other words, for things they already know and have experienced before. Subjective experiencing and service performance evaluations are thereby suggested to be influenced by emotional states. These states may also impact tourists' recognition of destination uniqueness as a major component of a destination's competitive advantage that cannot easily be copied. As a consequence, it may be worth reconsidering the role of recreation in tourism service design. Turning an inwardlooking focus bent on recreation to an outward-looking one interested in discovery would enable more tourists to more fully experience the destination before they leave.

Are road traffic crash fatality rates converging among OECD countries?

This article examines the trends of road traffic crash (RTC) fatality rates in OECD countries over the past four decades. Based on recent developments in the economic growth literature we propose and test the hypothesis that RTC fatality rates initially increase with economic development, peak, and then gradually decrease. The theory predicts that, as a result, the RTC fatality rates of different countries will tend to converge over time. Our results for the period 1961–2007 reveal no evidence of the convergence of RTC fatality rates across the OECD as a whole for that time period. Nevertheless, there is evidence of convergence among sub-groups of countries. This evidence may assist policymakers as an additional way of benchmarking their country's performance against that of its peers and to identify the next-closest peer in country sub-groups with superior road safety performance.

A semi-alternating direction method for a 2-D fractional FitzHugh–Nagumo monodomain model on an approximate irregular domain

A FitzHugh-Nagumo monodomain model has been used to describe the propagation of the electrical potential in heterogeneous cardiac tissue. In this paper, we consider a two-dimensional fractional FitzHugh-Nagumo monodomain model on an irregular domain. The model consists of a coupled Riesz space fractional nonlinear reaction-diffusion model and an ordinary differential equation, describing the ionic fluxes as a function of the membrane potential. Secondly, we use a decoupling technique and focus on solving the Riesz space fractional nonlinear reaction-diffusion model. A novel spatially second-order accurate semi-implicit alternating direction method (SIADM) for this model on an approximate irregular domain is proposed. Thirdly, stability and convergence of the SIADM are proved. Finally, some numerical examples are given to support our theoretical analysis and these numerical techniques are employed to simulate a two-dimensional fractional Fitzhugh-Nagumo model on both an approximate circular and an approximate irregular domain.

Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of $O(\tau+h^{r+1})$ in the $L^2$ norm, where $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are $O(\tau^{1.5}+h^{r+1})$. Furthermore, two improved algorithms are constrcted, they are also unconditionally stable and convergent of order $O(\tau^2+h^{r+1})$. Numerical examples are provided to verify the theoretical analysis. The comparisons between the present algorithms and the existing ones are included, which show that our numerical algorithms exhibit better performances than the known ones.

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.

Career counseling : joint contributions of contextual action theory and the systems theory framework

The influence of constructivism and the ongoing drive for convergence, both of career theories and between theory and practice, have been key drivers in the career development literature for two decades (Patton, International Handbook of Career Guidance, 2008). Both contextual action theory and systems theory are derived from the root metaphor of contextualism, which has been proffered as a worldview to assist scientists and practitioners in organizing day-to-day experiential data. This chapter identifies the theoretical contributions of the Systems Theory Framework (STF) (Patton and McMahon, Career development and systems theory: A new development, 1999, Career psychology in South Africa, 2006) and Contextual Action Theory (Young and Valach, The future of career, 2000, Journal of Vocational Behavior 64:499–514, 2004; Young et al., Career choice and development, 1996, Career choice and development, 2002), each of which has advanced thinking in theory integration and in the integration between theory and practice in the career development and counseling field. Young et al. (Career development in childhood and adolescence, 2007) noted the connections between the Patton and McMahon systems theory approach and the contextual action theory approach and these connections will be highlighted in terms of the application of these theoretical developments to practice in career counseling, with a particular focus on the commonalities between the two approaches and what counselors can learn from each of them. In particular, this chapter will discuss common conceptual understandings and practice dimensions.

Changing the game: The role of social media in overcoming old media's attention deficit toward women's sport

Social media is now an integral part of modern sports broadcasting, which combines old and new media into a redefined and multidimensional experience for fans. The popularity of social media has particular implications for professional women's sports due to this convergence, and may be utilised by organisations to address some of the issues women's sports face from a lack of traditional broadcast coverage. This article discusses Twitter activity surrounding the ANZ Championship netball competition and analyses the ways social media can help transcend the structural challenges that “old” media has placed on professional women's sports.

Green: Exploring the aestheticized use of chroma-key techniques and technologies in two intermedial productions

Peggy Shaw’s RUFF, (USA 2013) and Queensland Theatre Company’s collaboration with Queensland University of Technology, Total Dik!, (Australia 2013) overtly and evocatively draw on an aestheticized use of the cinematic techniques and technologies of Chroma Key to reveal the tensions in their production and add layers to their performances. In doing so they offer invaluable insight where the filmic and theatrical approaches overlap. This paper draws on Eckersall, Grehan and Scheer’s New Media Dramaturgy (2014) to reposition the frame as a contribution to intermedial theatre and performance practices in light of increasing convergence between seemingly disparate discourses. In RUFF, the scenic environment replicates a chroma-key ‘studio’ which facilitates the reconstruction of memory displaced after a stroke. RUFF uses the screen and projections to recall crooners, lounge singers, movie stars, rock and roll bands, and an eclectic line of eccentric family members living inside Shaw. While the show pays tribute to those who have kept her company across decades of theatrical performance, use of non-composited chroma-key technique as a theatrical device and the work’s taciturn revelation of the production process during performance, play a central role in its exploration of the juxtaposition between its reconstructed form and content. In contrast Total Dik! uses real-time green screen compositing during performance as a scenic device. Actors manipulate scale models, refocus cameras and generate scenes within scenes in the construction of the work’s examination of an isolated Dictator. The ‘studio’ is again replicated as a site for (re)construction, only in this case Total Dik! actively seeks to reveal the process of production as the performance plays out. Building on RUFF, and other works such as By the Way, Meet Vera Stark, (2012) and Hotel Modern’s God’s Beard (2012), this work blends a convergence of mobile technologies, models, and green screen capture to explore aspects of transmedia storytelling in a theatrical environment (Jenkins, 2009, 2013). When a green screen is placed on stage, it reads at once as metaphor and challenge to the language of theatre. It becomes, or rather acts, as a ‘sign’ that alludes to the nature of the reconstructed, recomposited, manipulated and controlled. In RUFF and in Total Dik!, it is also a place where as a mode of production and subsequent reveal, it adds weight to performance. These works are informed by Auslander (1999) and Giesenkam (2007) and speak to and echo Lehmann’s Postdramatic Theatre (2006). This paper’s consideration of the integration of studio technique and live performance as a dynamic approach to multi-layered theatrical production develops our understanding of their combinatory use in a live performance environment.

Improved Kalman filter initialisation using neurofuzzy estimation

It is traditional to initialise Kalman filters and extended Kalman filters with estimates of the states calculated directly from the observed (raw) noisy inputs, but unfortunately their performance is extremely sensitive to state initialisation accuracy: good initial state estimates ensure fast convergence whereas poor estimates may give rise to slow convergence or even filter divergence. Divergence is generally due to excessive observation noise and leads to error magnitudes that quickly become unbounded (R.J. Fitzgerald, 1971). When a filter diverges, it must be re initialised but because the observations are extremely poor, re initialised states will have poor estimates. The paper proposes that if neurofuzzy estimators produce more accurate state estimates than those calculated from the observed noisy inputs (using the known state model), then neurofuzzy estimates can be used to initialise the states of Kalman and extended Kalman filters. Filters whose states have been initialised with neurofuzzy estimates should give improved performance by way of faster convergence when the filter is initialised, and when a filter is re started after divergence

Towards strongly consistent online HMM parameter estimation using one-step Kerridge inaccuracy

In this paper, we propose a novel online hidden Markov model (HMM) parameter estimator based on the new information-theoretic concept of one-step Kerridge inaccuracy (OKI). Under several regulatory conditions, we establish a convergence result (and some limited strong consistency results) for our proposed online OKI-based parameter estimator. In simulation studies, we illustrate the global convergence behaviour of our proposed estimator and provide a counter-example illustrating the local convergence of other popular HMM parameter estimators.