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.

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.

Multi-layered model of individual HIV infection progression and mechanisms of phenotypical expression

Cite as: Perrin, Dimitri (2008) Multi-layered model of individual HIV infection progression and mechanisms of phenotypical expression. PhD thesis, Dublin City University.

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.

Numerical simulation of anomalous infiltration in porous media

Nonlinear time-fractional diffusion equations have been used to describe the liquid infiltration for both subdiffusion and superdiffusion in porous media. In this paper, some problems of anomalous infiltration with a variable-order timefractional derivative in porous media are considered. The time-fractional Boussinesq equation is also considered. Two computationally efficient implicit numerical schemes for the diffusion and wave-diffusion equations are proposed. Numerical examples are provided to show that the numerical methods are computationally efficient.

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 investigation of the effect of some stable nitroxide antioxidants in prostate cancer cells

The risk of prostate cancer and disease progression may potentially be increased by oxidative stress. This project examined the stability of nitroxide antioxidants and their effects on cell growth, survival and gene regulation in prostate cancer cells. The novel nitroxide, CTMIO, synthesised here at QUT, was found to have minimal toxicity and modulated the expression of a subset of oxidative stress and antioxidant-related genes distinct from those regulated by a related derivative. This study has provided a step forward in our understanding of the mechanism of action of nitroxides within cells.

Wearable technology: The next frontier?

The ways in which technology mediates daily activities is shifting rapidly. Global trends point toward the uptake of ambient and interactive media to create radical new ways of working, interacting and socialising. Tech giants such as Google and Apple are banking on the success of this emerging market by investing in new future focused consumer products such as Google Glass and the Apple Watch. The potential implications of ubiquitous technological interactions via tangible and ambient media have never been more real or more accessible.

Structure evolution characterization of Anyang anthracites via H2O2 oxidization and HF acidification

The structural characteristics of the raw coal (AY), the H2O2 oxidized coals (AY–H2O2) and the HF acidized AY–H2O2 (AY–H2O2–HF) were investigated by SEM, X-ray diffraction, Raman and FTIR spectroscopy. The results indicate that the derivative coals show an obvious increase in the aromaticity, crystalline carbon content and hydroxyl content, especially the AY–H2O2–HF. The stacking layer number of crystalline carbon decreases and the aspect ratio (La/Lc) remarkably increases for AY–H2O2 and AY–H2O2–HF. The crystalline layers become much thinner. The particle size of AY–H2O2–HF in width significantly decreases from 1 μm to less than 100 nm. The combination of H2O2 oxidization and HF acidification is effective to reduce the size of the aromatic layers and to increase the reactivity of derivative coals. The process can help us obtain the superfine crystalline carbon materials like graphite structure.

Structural characterization of hydrogen peroxide‐oxidized anthracites by X-ray diffraction, Fourier transform infrared spectroscopy, and Raman spectra

The structural characteristics of raw coal and hydrogen peroxide (H2O2)-oxidized coals were investigated using scanning electron microscopy, X-ray diffraction (XRD), Raman spectra, and Fourier transform infrared (FT-IR) spectroscopy. The results indicate that the derivative coals oxidized by H2O2 are improved noticeably in aromaticity and show an increase first and then a decrease up to the highest aromaticity at 24 h. The stacking layer number of crystalline carbon decreases and the aspect ratio (width versus stacking height) increases with an increase in oxidation time. The content of crystalline carbon shows the same change tendency as the aromaticity measured by XRD. The hydroxyl bands of oxidized coals become much stronger due to an increase in soluble fatty acids and alcohols as a result of the oxidation of the aromatic and aliphatic C‐H bonds. In addition, the derivative coals display a decrease first and then an increase in the intensity of aliphatic C‐H bond and present a diametrically opposite tendency in the aromatic C‐H bonds with an increase in oxidation time. There is good agreement with the changes of aromaticity and crystalline carbon content as measured by XRD and Raman spectra. The particle size of oxidized coals (<200 nm in width) shows a significant decrease compared with that of raw coal (1 μm). This study reveals that the optimal oxidation time is ∼24 h for improving the aromaticity and crystalline carbon content of H2O2-oxidized coals. This process can help us obtain superfine crystalline carbon materials similar to graphite in structure.

Using decision trees to understand structure in missing data

Objectives Demonstrate the application of decision trees – classification and regression trees (CARTs), and their cousins, boosted regression trees (BRTs) – to understand structure in missing data. Setting Data taken from employees at three different industry sites in Australia. Participants 7915 observations were included. Materials and Methods The approach was evaluated using an occupational health dataset comprising results of questionnaires, medical tests, and environmental monitoring. Statistical methods included standard statistical tests and the ‘rpart’ and ‘gbm’ packages for CART and BRT analyses, respectively, from the statistical software ‘R’. A simulation study was conducted to explore the capability of decision tree models in describing data with missingness artificially introduced. Results CART and BRT models were effective in highlighting a missingness structure in the data, related to the Type of data (medical or environmental), the site in which it was collected, the number of visits and the presence of extreme values. The simulation study revealed that CART models were able to identify variables and values responsible for inducing missingness. There was greater variation in variable importance for unstructured compared to structured missingness. Discussion Both CART and BRT models were effective in describing structural missingness in data. CART models may be preferred over BRT models for exploratory analysis of missing data, and selecting variables important for predicting missingness. BRT models can show how values of other variables influence missingness, which may prove useful for researchers. Conclusion Researchers are encouraged to use CART and BRT models to explore and understand missing data.

Using simplified peer review processes to fund research: A prospective study

Objective: To prospectively test two simplified peer review processes, estimate the agreement between the simplified and official processes, and compare the costs of peer review. Design, participants and setting: A prospective parallel study of Project Grant proposals submitted in 2013 to the National Health and Medical Research Council (NHMRC) of Australia. The official funding outcomes were compared with two simplified processes using proposals in Public Health and Basic Science. The two simplified processes were: panels of 7 reviewers who met face-to-face and reviewed only the nine-page research proposal and track record (simplified panel); and 2 reviewers who independently reviewed only the nine-page research proposal (journal panel). The official process used panels of 12 reviewers who met face-to-face and reviewed longer proposals of around 100 pages. We compared the funding outcomes of 72 proposals that were peer reviewed by the simplified and official processes. Main outcome measures: Agreement in funding outcomes; costs of peer review based on reviewers’ time and travel costs. Results: The agreement between the simplified and official panels (72%, 95% CI 61% to 82%), and the journal and official panels (74%, 62% to 83%), was just below the acceptable threshold of 75%. Using the simplified processes would save $A2.1–$A4.9 million per year in peer review costs. Conclusions: Using shorter applications and simpler peer review processes gave reasonable agreement with the more complex official process. Simplified processes save time and money that could be reallocated to actual research. Funding agencies should consider streamlining their application processes.

Intravascular device administration sets: Replacement after standard versus prolonged use in hospitalised patients--a study protocol for a randomised controlled trial (The RSVP Trial)

Introduction Vascular access devices (VADs), such as peripheral or central venous catheters, are vital across all medical and surgical specialties. To allow therapy or haemodynamic monitoring, VADs frequently require administration sets (AS) composed of infusion tubing, fluid containers, pressure-monitoring transducers and/or burettes. While VADs are replaced only when necessary, AS are routinely replaced every 3–4 days in the belief that this reduces infectious complications. Strong evidence supports AS use up to 4 days, but there is less evidence for AS use beyond 4 days. AS replacement twice weekly increases hospital costs and workload. Methods and analysis This is a pragmatic, multicentre, randomised controlled trial (RCT) of equivalence design comparing AS replacement at 4 (control) versus 7 (experimental) days. Randomisation is stratified by site and device, centrally allocated and concealed until enrolment. 6554 adult/paediatric patients with a central venous catheter, peripherally inserted central catheter or peripheral arterial catheter will be enrolled over 4 years. The primary outcome is VAD-related bloodstream infection (BSI) and secondary outcomes are VAD colonisation, AS colonisation, all-cause BSI, all-cause mortality, number of AS per patient, VAD time in situ and costs. Relative incidence rates of VAD-BSI per 100 devices and hazard rates per 1000 device days (95% CIs) will summarise the impact of 7-day relative to 4-day AS use and test equivalence. Kaplan-Meier survival curves (with log rank Mantel-Cox test) will compare VAD-BSI over time. Appropriate parametric or non-parametric techniques will be used to compare secondary end points. p Values of <0.05 will be considered significant.

Bloomsday: Copyright estates and cultural festivals

Copyright estates have been unduly empowered by the extension of the term of copyright protection in Europe, the United States, Australia and elsewhere. The Estate of the Irish novelist, James Joyce, has been particularly aggressive in policing his revived copyrights. The "keepers of the flame" have relied upon threats of legal action to discourage the production of derivative works based upon the canonical texts of the novelist. The Estate has also jealously guarded the reputation of the author by vetoing the use of his work in various scholarly productions. Most radically of all, the grandson Stephen Joyce threatened to take legal action to prevent the staging of "Rejoyce Dublin 2004", a festival celebrating the centenary of Bloomsday. In response, the Irish Parliament rushed through emergency legislation, entitled the Copyright and Related Rights (Amendment) Act 2004 (Ireland) to safeguard the celebrations. The legislation clarified that a person could place literary and artistic works on public exhibition, without breaching the copyright vested in such cultural texts. Arguably, though, the ad hoc legislation passed by the Irish Parliament is inadequate. The Estate of James Joyce remains free to exercise its suite of economic and moral rights to control the use and adaptation of works of the Irish novelist. It is contended that copyright law needs to be revised to promote the interests of libraries and other cultural institutions. Most notably, the defence of fair dealing should be expanded to allow for the transformative use of copyright works, particularly in respect of adaptations and derived works. There should be greater scope for compulsory licensing and crown acquisition of revived copyrights.

Simultaneous enhancement of brightness, efficiency, and switching in RGB organic light emitting transistors

An innovative design strategy for light emitting field effect transistors (LEFETs) to harvest higher luminance and switching is presented. The strategy uses a non-planar electrode geometry in tri-layer LEFETs for simultaneous enhancement of the key parameters of quantum efficiency, brightness, switching, and mobility across the RGB color gamut.