High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

In this paper, a class of unconditionally stable difference schemes based on the Pad´e approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original dfferential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretise the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Pad´e approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.

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.

Maximum principle and numerical method for the multi-term time–space Riesz–Caputo fractional differential equations

The maximum principle for the space and time–space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time–space Riesz–Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor–corrector method combining the L1 and L2 discrete schemes, we present a numerical method for the specified equation. Two examples are given to illustrate the obtained results.

High-performance computing for data analytics

One of the main challenges in data analytics is that discovering structures and patterns in complex datasets is a computer-intensive task. Recent advances in high-performance computing provide part of the solution. Multicore systems are now more affordable and more accessible. In this paper, we investigate how this can be used to develop more advanced methods for data analytics. We focus on two specific areas: model-driven analysis and data mining using optimisation techniques.

Efficiency of parallelisation of genetic algorithms in the data analysis context

Most real-life data analysis problems are difficult to solve using exact methods, due to the size of the datasets and the nature of the underlying mechanisms of the system under investigation. As datasets grow even larger, finding the balance between the quality of the approximation and the computing time of the heuristic becomes non-trivial. One solution is to consider parallel methods, and to use the increased computational power to perform a deeper exploration of the solution space in a similar time. It is, however, difficult to estimate a priori whether parallelisation will provide the expected improvement. In this paper we consider a well-known method, genetic algorithms, and evaluate on two distinct problem types the behaviour of the classic and parallel implementations.

Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

In this paper, we consider a two-sided space-fractional diffusion equation with variable coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new fractional finite volume method for the two-sided space-fractional diffusion equation and derive the implicit scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the implicit fractional finite volume method and conclude that the method is unconditionally stable and convergent. Finally, some numerical examples are given to show the effectiveness of the new numerical method, and the results are in excellent agreement with theoretical analysis.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

An architecture for trustworthy open data services

This paper addresses the development of trust in the use of Open Data through incorporation of appropriate authentication and integrity parameters for use by end user Open Data application developers in an architecture for trustworthy Open Data Services. The advantages of this architecture scheme is that it is far more scalable, not another certificate-based hierarchy that has problems with certificate revocation management. With the use of a Public File, if the key is compromised: it is a simple matter of the single responsible entity replacing the key pair with a new one and re-performing the data file signing process. Under this proposed architecture, the the Open Data environment does not interfere with the internal security schemes that might be employed by the entity. However, this architecture incorporates, when needed, parameters from the entity, e.g. person who authorized publishing as Open Data, at the time that datasets are created/added.

Data replication and extension: A commentary

Honig and Samuelsson (2014) and Delmar (2015) recently had an exchange in this journal related to a replication-and-extension attempt of two papers which originally arrived at different conclusions based on the same data set. This commentary provides further clarification on the issues and links the debate to broader issues scholarly culture and practices in entrepreneurship research.

Machine learning approaches to analysing textual injury surveillance data: A systematic review

Objective To synthesise recent research on the use of machine learning approaches to mining textual injury surveillance data. Design Systematic review. Data sources The electronic databases which were searched included PubMed, Cinahl, Medline, Google Scholar, and Proquest. The bibliography of all relevant articles was examined and associated articles were identified using a snowballing technique. Selection criteria For inclusion, articles were required to meet the following criteria: (a) used a health-related database, (b) focused on injury-related cases, AND used machine learning approaches to analyse textual data. Methods The papers identified through the search were screened resulting in 16 papers selected for review. Articles were reviewed to describe the databases and methodology used, the strength and limitations of different techniques, and quality assurance approaches used. Due to heterogeneity between studies meta-analysis was not performed. Results Occupational injuries were the focus of half of the machine learning studies and the most common methods described were Bayesian probability or Bayesian network based methods to either predict injury categories or extract common injury scenarios. Models were evaluated through either comparison with gold standard data or content expert evaluation or statistical measures of quality. Machine learning was found to provide high precision and accuracy when predicting a small number of categories, was valuable for visualisation of injury patterns and prediction of future outcomes. However, difficulties related to generalizability, source data quality, complexity of models and integration of content and technical knowledge were discussed. Conclusions The use of narrative text for injury surveillance has grown in popularity, complexity and quality over recent years. With advances in data mining techniques, increased capacity for analysis of large databases, and involvement of computer scientists in the injury prevention field, along with more comprehensive use and description of quality assurance methods in text mining approaches, it is likely that we will see a continued growth and advancement in knowledge of text mining in the injury field.

Sharing of clinical data in a maternity setting: How do paper hand-held records and electronic health records compare for completeness?

Background Historically, the paper hand-held record (PHR) has been used for sharing information between hospital clinicians, general practitioners and pregnant women in a maternity shared-care environment. Recently in alignment with a National e-health agenda, an electronic health record (EHR) was introduced at an Australian tertiary maternity service to replace the PHR for collection and transfer of data. The aim of this study was to examine and compare the completeness of clinical data collected in a PHR and an EHR. Methods We undertook a comparative cohort design study to determine differences in completeness between data collected from maternity records in two phases. Phase 1 data were collected from the PHR and Phase 2 data from the EHR. Records were compared for completeness of best practice variables collected The primary outcome was the presence of best practice variables and the secondary outcomes were the differences in individual variables between the records. Results Ninety-four percent of paper medical charts were available in Phase 1 and 100% of records from an obstetric database in Phase 2. No PHR or EHR had a complete dataset of best practice variables. The variables with significant improvement in completeness of data documented in the EHR, compared with the PHR, were urine culture, glucose tolerance test, nuchal screening, morphology scans, folic acid advice, tobacco smoking, illicit drug assessment and domestic violence assessment (p = 0.001). Additionally the documentation of immunisations (pertussis, hepatitis B, varicella, fluvax) were markedly improved in the EHR (p = 0.001). The variables of blood pressure, proteinuria, blood group, antibody, rubella and syphilis status, showed no significant differences in completeness of recording. Conclusion This is the first paper to report on the comparison of clinical data collected on a PHR and EHR in a maternity shared-care setting. The use of an EHR demonstrated significant improvements to the collection of best practice variables. Additionally, the data in an EHR were more available to relevant clinical staff with the appropriate log-in and more easily retrieved than from the PHR. This study contributes to an under-researched area of determining data quality collected in patient records.

Developing and evaluating approaches for utilising injury data to support product safety initiatives

With increasing concern about consumer product-related injuries in Australia, product safety regulators need evidence-based research to understand risks and patterns to inform their decision making. This study analysed paediatric injury data to identify and quantify product-related injuries in children to inform product safety prioritisation. This study provides information on novel techniques for interrogating health data to identify trends and patterns in product-related injuries to inform strategic directions in this growing area of concern.

Interpretation of morphological data to inform design Bridge to Bridge: Ridge to Ridge urban design workshop

The importance of design practice informed by urban morphology has led to intensification in interest, signalled by the formation of the ISUF Research and Practice Task Force and voiced through several recent academic publications cognisant of this current debate, this paper reports on a recent urban design workshop at which morphology was set as one of the key themes. Initially planned to be programmed as a augmented concurrent event to the 2013 20th ISUF conference held in Brisbane, the two day Bridge to Bridge: Ridge to Ridge urban design workshop nevertheless took place the following month, and involved over one hundred design professionals and academics. The workshop sought to develop several key urban design principles and recommendations addressing a major government development proposal sited in the most important heritage precinct of the city. The paper will focus specifically on one of the nine groups, in which the design proposal was purposefully guided by morphological input. The discussion will examine the design outcomes and illicit review and feedback from participants, shedding critical light on the issues that arise from such a design approach.