Two novel numerical methods for solving the two-dimensional fractional Fitzhugh-Nagumo-monodomain model

Fractional mathematical models represent a new approach to modelling complex spatial problems in which there is heterogeneity at many spatial and temporal scales. In this paper, a two-dimensional fractional Fitzhugh-Nagumo-monodomain model with zero Dirichlet boundary conditions is considered. The model consists of a coupled space fractional diffusion equation (SFDE) and an ordinary differential equation. For the SFDE, we first consider the numerical solution of the Riesz fractional nonlinear reaction-diffusion model and compare it to the solution of a fractional in space nonlinear reaction-diffusion model. We present two novel numerical methods for the two-dimensional fractional Fitzhugh-Nagumo-monodomain model using the shifted Grunwald-Letnikov method and the matrix transform method, respectively. Finally, some numerical examples are given to exhibit the consistency of our computational solution methodologies. The numerical results demonstrate the effectiveness of the methods.

The use of a Riesz fractional differential-based approach for texture enhancement in image processing

Abstract: Texture enhancement is an important component of image processing, with extensive application in science and engineering. The quality of medical images, quantified using the texture of the images, plays a significant role in the routine diagnosis performed by medical practitioners. Previously, image texture enhancement was performed using classical integral order differential mask operators. Recently, first order fractional differential operators were implemented to enhance images. Experiments conclude that the use of the fractional differential not only maintains the low frequency contour features in the smooth areas of the image, but also nonlinearly enhances edges and textures corresponding to high-frequency image components. However, whilst these methods perform well in particular cases, they are not routinely useful across all applications. To this end, we applied the second order Riesz fractional differential operator to improve upon existing approaches of texture enhancement. Compared with the classical integral order differential mask operators and other fractional differential operators, our new algorithms provide higher signal to noise values, which leads to superior image quality.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative

Rayleigh–Stokes problems have in recent years received much attention due to their importance in physics. In this article, we focus on the variable-order Rayleigh–Stokes problem for a heated generalized second grade fluid with fractional derivative. Implicit and explicit numerical methods are developed to solve the problem. The convergence, stability of the numerical methods and solvability of the implicit numerical method are discussed via Fourier analysis. Moreover, a numerical example is given and the results support the effectiveness of the theoretical analysis.

Robust aerodynamic design optimisation of morphing aerofoil/wing using distributed moga

In this paper, the shape design optimisation using morphing aerofoil/wing techniques, namely the leading and/or trailing edge deformation of a natural laminar flow RAE 5243 aerofoil is investigated to reduce transonic drag without taking into account of the piezo actuator mechanism. Two applications using a Multi-Objective Genetic Algorithm (MOGA)coupled with Euler and boundary analyser (MSES) are considered: the first example minimises the total drag with a lift constraint by optimising both the trailing edge actuator position and trailing edge deformation angle at a constant transonic Mach number (M! = 0.75)and boundary layer transition position (xtr = 45%c). The second example consists of finding reliable designs that produce lower mean total drag (μCd) and drag sensitivity ("Cd) at different uncertainty flight conditions based on statistical information. Numerical results illustrate how the solution quality in terms of mean drag and its sensitivity can be improved using MOGA software coupled with a robust design approach taking account of uncertainties (lift and boundary transition positions) and also how transonic flow over aerofoil/wing can be controlled to the best advantage using morphing techniques.

Embedding graphic organisers in the teaching and learning of family and consumer sciences (home economics) in Kuwait

Educational reforms currently being enacted in Kuwaiti Family and Consumer Sciences (FCS) in response to contemporary demands for increased student-centred teaching and learning are challenging for FCS teachers due to their limited experience with student-centred learning tools such as Graphic Organisers (GOs). To adopt these reforms, Kuwaiti teachers require a better understanding of and competency in promoting cognitive learning processes that will maximise student-centred learning approaches. This study followed the experiences of four Grade 6 FCS Kuwaiti teachers as they undertook a Professional Development (PD) program specifically designed to advance their understanding of the use of GOs and then as they implemented what they had learned in their Grade 6 FCS classroom. The PD program developed for this study was informed by Nasseh.s competency PD model as well as Piaget and Ausubel.s cognitive theories. This model enabled an assessment and evaluation of the development of the teachers. competencies as an outcome of the PD program in terms of the adoption of GOs, in particular, and their capacity to use GOs to engage students in personalised, in-depth, learning through critical thinking and understanding. The research revealed that the PD program was influential in reforming the teachers. learning, understanding of and competency in, cognitive and visual theories of learning, so that they facilitated student-centred teaching and learning processes that enabled students to adopt and adapt GOs in constructivist learning. The implementation of five GOs - Flow Chart, Concept Maps, K-W-L Chart, Fishbone Diagram and Venn Diagram - as learning tools in classrooms was investigated to find if changes in pedagogical approach for supporting conceptual learning through cognitive information processing would reduce the cognitive work load of students and produce better learning approaches. The study as evidenced by the participant teachers. responses and classroom observations, showed a marked increase in student interest, participation, critical thought, problem solving skills, as a result of using GOs, compared to using traditional teaching and learning methods. A theoretical model was developed from the study based on the premise that teachers. knowledge of the subject, pedagogy and student learning precede the implementation of student-centred learning reform, that it plays an important role in the implementation of student-centred learning and that it brings about a change in teaching practice. The model affirmed that observed change in teaching-practice included aspects of teachers. beliefs, as well as confidence and effect on workplace and on student learning, including engagement, understanding, critical thinking and problem solving. The model assumed that change in teaching practice is inseparable from teachers. lifelong PD needs related to knowledge, understanding, skills and competency. These findings produced a set of preliminary guidelines for establishing student-centred constructivist strategies in Kuwaiti education while retaining Kuwait.s cultural uniqueness.

Stigmergy within web modelling languages : positive feedback mechanisms

Stigmergy is a biological term originally used when discussing insect or swarm behaviour, and describes a model supporting environment-based communication separating artefacts from agents. This phenomenon is demonstrated in the behavior of ants and their food foraging supported by pheromone trails, or similarly termites and their termite nest building process. What is interesting with this mechanism is that highly organized societies are formed without an apparent central management function. We see design features in Web sites that mimic stigmergic mechanisms as part of the User Interface and we have created generalizations of these patterns. Software development and Web site development techniques have evolved significantly over the past 20 years. Recent progress in this area proposes languages to model web applications to facilitate the nuances specific to these developments. These modeling languages provide a suitable framework for building reusable components encapsulating our design patterns of stigmergy. We hypothesize that incorporating stigmergy as a separate feature of a site’s primary function will ultimately lead to enhanced user coordination.

A hybrid association rule mining approach for characterizing network traffic behaviour

Understanding network traffic behaviour is crucial for managing and securing computer networks. One important technique is to mine frequent patterns or association rules from analysed traffic data. On the one hand, association rule mining usually generates a huge number of patterns and rules, many of them meaningless or user-unwanted; on the other hand, association rule mining can miss some necessary knowledge if it does not consider the hierarchy relationships in the network traffic data. Aiming to address such issues, this paper proposes a hybrid association rule mining method for characterizing network traffic behaviour. Rather than frequent patterns, the proposed method generates non-similar closed frequent patterns from network traffic data, which can significantly reduce the number of patterns. This method also proposes to derive new attributes from the original data to discover novel knowledge according to hierarchy relationships in network traffic data and user interests. Experiments performed on real network traffic data show that the proposed method is promising and can be used in real applications. Copyright2013 John Wiley & Sons, Ltd.

Comment on "Local accumulation times for source, diffusion, and degradation models in two and three dimensions" [J. Chem. Phys. 138, 104121 (2013)]

In a recent paper, Gordon, Muratov, and Shvartsman studied a partial differential equation (PDE) model describing radially symmetric diffusion and degradation in two and three dimensions. They paid particular attention to the local accumulation time (LAT), also known in the literature as the mean action time, which is a spatially dependent timescale that can be used to provide an estimate of the time required for the transient solution to effectively reach steady state. They presented exact results for three-dimensional applications and gave approximate results for the two-dimensional analogue. Here we make two generalizations of Gordon, Muratov, and Shvartsman’s work: (i) we present an exact expression for the LAT in any dimension and (ii) we present an exact expression for the variance of the distribution. The variance provides useful information regarding the spread about the mean that is not captured by the LAT. We conclude by describing further extensions of the model that were not considered by Gordon,Muratov, and Shvartsman. We have found that exact expressions for the LAT can also be derived for these important extensions...

Proceedings of the Fourth Australasian Workshop on Health Informatics and Knowledge Management [Volume 120]

We are pleased to present the papers from the Australasian Health Informatics and Knowledge Management (HIKM) conference stream held on 20 January 2011 in Perth as a session of the Australasian Computer Science Week (ASCW) 2011. Formerly HIKM was named Health Data and Knowledge Management, however the inclusion of the health informatics term is timely given the current health reform. The submissions to HIKM 2011 demonstrated that Australasian researchers lead with many research and development innovations coming to fruition. Some of these innovations can be seen here, and we believe further recognition will accomplish by continuation to HIKM in the future. The HIKM conference is a review of health informatics related research, development and education opportunities. The conference papers were written to communicate with other researchers and share research findings, capturing each and every aspect of the health informatics field. They are namely: conceptual models and architectures, privacy and quality of health data, health workflow management patient journey analysis, health information retrieval, analysis and visualisation, data integration/linking, systems for integrated or coordinated care, electronic health records (EHRs) and personally controlled electronic health records (PCEHRs), health data ontologies, and standardisation in health data and clinical applications.

Information accountability and usability : are there any connections?

Availability of health information is rapidly increasing and the expansion and proliferation of health information is inevitable. The Electronic Healthcare Record, Electronic Medical Record and Personal Health Record are at the core of this trend and are required for appropriate and practicable exchange and sharing of health information. However, it is becoming increasingly recognized that it is essential to preserve patient privacy and information security when utilising sensitive information for clinical, management and administrative processes. Furthermore, the usability of emerging healthcare applications is also becoming a growing concern. This paper proposes a novel approach for integrating consideration of information accountability with a perspective from usability engineering that can be applied when developing healthcare information technology applications. A social networking user case in the healthcare information exchange will be presented in the context of our approach.

A performance test of query operation on encrypted database

Database security techniques are available widely. Among those techniques, the encryption method is a well-certified and established technology for protecting sensitive data. However, once encrypted, the data can no longer be easily queried. The performance of the database depends on how to encrypt the sensitive data, and an approach for searching and retrieval efficiencies that are implemented. In this paper we analyze the database queries and the data properties and propose a suitable mechanism to query the encrypted database. We proposed and analyzed the new database encryption algorithm using the Bloom Filter with the bucket index method. Finally, we demonstrated the superiority of the proposed algorithm through several experiments that should be useful for database encryption related research and application activities.

Synchronised integrated online e-health profiles

Web-based social networking applications have become increasingly important in recent years. The current applications in the healthcare sphere can support the health management, but to date there is no patient-controlled integrator. This paper proposes a platform called Multiple Profile Manager (MPM) that enables a user to create and manage an integrated profile that can be shared across numerous social network sites. Moreover, it is able to facilitate the collection of personal healthcare data, which makes a contribution to the development of public health informatics. Here we want to illustrate how patients and physicians can be benefited from enabling the platform for online social network sites. The MPM simplifies the management of patients' profiles and allows health professionals to obtain a more complete picture of the patients' background so that they can provide better health care. To do so, we demonstrate a prototype of the platform and describe its protocol specification, which is an XMPP (Extensible Messaging and Presence Protocol) [1] extension, for sharing and synchronising profile data (vCard²) between different social networks.

Fractional models for the migration of biological cells in complex spatial domains

Travelling wave phenomena are observed in many biological applications. Mathematical theory of standard reaction-diffusion problems shows that simple partial differential equations exhibit travelling wave solutions with constant wavespeed and such models are used to describe, for example, waves of chemical concentrations, electrical signals, cell migration, waves of epidemics and population dynamics. However, as in the study of cell motion in complex spatial geometries, experimental data are often not consistent with constant wavespeed. Non-local spatial models have successfully been used to model anomalous diffusion and spatial heterogeneity in different physical contexts. In this paper, we develop a fractional model based on the Fisher-Kolmogoroff equation and analyse it for its wavespeed properties, attempting to relate the numerical results obtained from our simulations to experimental data describing enteric neural crest-derived cells migrating along the intact gut of mouse embryos. The model proposed essentially combines fractional and standard diffusion in different regions of the spatial domain and qualitatively reproduces the behaviour of neural crest-derived cells observed in the caecum and the hindgut of mouse embryos during in vivo experiments.

Role of charge in destabilizing AlH4 and BH4 complex anions for hydrogen storage applications : Ab initio density functional calculations

NaAlH4 and LiBH4 are potential candidate materials for mobile hydrogen storage applications, yet they have the drawback of being highly stable and desorbing hydrogen only at elevated temperatures. In this letter, ab initio density functional theory calculations reveal how the stabilities of the AlH4 and BH4 complex anions will be affected by reducing net anionic charge. Tetrahedral AlH4 and BH4 complexes are found to be distorted with the decrease of negative charge. One H-H distance becomes smaller and the charge density will overlap between them at a small anion charge. The activation energies to release of H2 from AlH4 and BH4 complexes are thus greatly decreased. We demonstrate that point defects such as neutral Na vacancies or substitution of a Na atom with Ti on the NaAlH4(001) surface can potentially cause strong distortion of neighboring AlH4 complexes and even induce spontaneous dehydrogenation. Our results help to rationalize the conjecture that the suppression of charge transfer to AlH4 and BH4 anion as a consequence of surface defects should be very effective for improving the recycling performance of H2 in NaAlH4 and LiBH4. The understanding gained here will aid in the rational design and development of hydrogen storage materials based on these two systems.