Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Connecting across continents : collaborative learning in a Web 2.0 world

Purpose – The article aims to review a university course, offered to students in both Australia and Germany, to encourage them to learn about designing, implementing, marketing and evaluating information programs and services in order to build active and engaged communities. The concepts and processes of Web 2.0 technologies come together in the learning activities, with students establishing their own personal learning networks (PLNs). Design/methodology/approach – The case study examines the principles of learning and teaching that underpin the course and presents the students' own experiences of the challenges they faced as they explored the interactive, participative and collaborative dimensions of the web. Findings – The online format of the course and the philosophy of learning through play provided students with a safe and supportive environment for them to move outside of their comfort zones, to be creative, to experiment and to develop their professional personas. Reflection on learning was a key component that stressed the value of reflective practice in assisting library and information science (LIS) professionals to adapt confidently to the rapidly changing work environment. Originality/value – This study provides insights into the opportunities for LIS courses to work across geographical boundaries, to allow students to critically appraise library practice in different contexts and to become active participants in wider professional networks.

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 approximation for a variable-order nonlinear reaction–subdiffusion equation

Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.

The knock-on from the knock-off : recent shifts within Australian mass market fashion design practice

Australia's mass market fashion labels have traditionally benefitted from their peripheral location to the world's fashion centres. Operating a season behind, Australian mass market designers and buyers were well-placed to watch trends play out overseas before testing them in the Australian marketplace. For this reason, often a designer's role was to source and oversee the manufacture of 'knock-offs', or close copies of northern hemisphere mass market garments. Both Weller and Walsh have commented on this practice.12 The knock-on effect from this continues to be a cautious, derivative fashion sensibility within Australian mass market fashion design, where any new trend or product is first tested and proved overseas months earlier. However, there is evidence that this is changing. The rapid online dissemination of global fashion trends, coupled with the Australian consumer’s willingness to shop online, has meant that the ‘knock-off’ is less viable. For this reason, a number of mass market companies are moving away from the practice of direct sourcing and are developing product in-house under a northern hemisphere model. This shift is also witnessed in the trend for mass market companies to develop collections in partnership with independent Australian designers. This paper explores the current and potential effects of these shifts within Australian mass market design practice, and discusses how they may impact on both consumers and on the wider culture of Australian fashion.

A Flight control scheme to improve position tracking performance of rotary-wing UASs

This paper outlines an innovative and feasible flight control scheme for a rotary-wing unmanned aerial system (RUAS) with guaranteed safety and reliable flight quality in a gusty environment. The proposed control methodology aims to increase gust-attenuation capability of a RUAS to ensure improved flight performance when strong gusts occur. Based on the design of an effective estimator, an altitude controller is firstly constructed to synchronously compensate for fluctuations of the main rotor thrust which might lead to crashes in a gusty environment. Afterwards, a nonlinear state feedback controller is proposed to stabilize horizontal positions of the RUAS with gust-attenuation property. Performance of the proposed control framework is evaluated using parameters of a Vario XLC helicopter and high-fidelity simulations show that the proposed controllers can effectively reduce side-effect of gusts and demonstrate performance improvement when compared with the proportional-integral-derivative (PID) controllers.

A neural-network based flight controller for UASs

This paper presents a nonlinear gust-attenuation controller based on constrained neural-network (NN) theory. The controller aims to achieve sufficient stability and handling quality for a fixed-wing unmanned aerial system (UAS) in a gusty environment when control inputs are subjected to constraints. Constraints in inputs emulate situations where aircraft actuators fail requiring the aircraft to be operated with fail-safe capability. The proposed controller enables gust-attenuation property and stabilizes the aircraft dynamics in a gusty environment. The proposed flight controller is obtained by solving the Hamilton-Jacobi-Isaacs (HJI) equations based on an policy iteration (PI) approach. Performance of the controller is evaluated using a high-fidelity six degree-of-freedom Shadow UAS model. Simulations show that our controller demonstrates great performance improvement in a gusty environment, especially in angle-of-attack (AOA), pitch and pitch rate. Comparative studies are conducted with the proportional-integral-derivative (PID) controllers, justifying the efficiency of our controller and verifying its suitability for integration into the design of flight control systems for forced landing of UASs.

Pharmacokinetics of cimifugin in rat plasma after oral administration of the extract of Saposhnikovia divaricatae root : Determination of cimifugin by high performance liquid chromatography coupled with solid phase extraction

High performance liquid chromatography (HPLC) coupled with the solid phase extraction method was developed for determining cimifugin (a coumarin derivative; one of Saposhnikovia divaricatae's constituents) in rat plasma after oral administration of Saposhnikovia divaricatae extract (SDE), and the pharmacokinetics of cimifugin either in SDE or as a single compound was investigated. The HPLC analysis was performed on a commercially available column (4.6 mm x 200 mm, 5 pm) with the isocratic elution of solvent A (Methanol) and solvent B (Water) (A:B=60:40) and the detection wavelength was set at 250 nm. The calibration curve was linear over the range of 0.100-10.040 microg/mL. The limit of detection was 30 ng/mL. At the rat plasma concentrations of 0.402, 4.016, 10.040 microg/mL, the intra-day precision was 6.21%, 3.98%, and 2.23%; the inter-day precision was 7.59%, 4.26%, and 2.09%, respectively. The absolute recovery was 76.58%, 76.61%, and 77.67%, respectively. When the dosage of SDE was equal to the pure compound calculated by the amount of cimifugin, it was found to have two maximum peaks while the pure compound only showed one peak in the plasma concentration-time curve. The pharmacokinetic characteristics of SDE showed the superiority of the extract and the properties of traditional Chinese medicine.

A closed-form approximation for pricing temperature-based weather derivatives

This paper develops analytical distributions of temperature indices on which temperature derivatives are written. If the deviations of daily temperatures from their expected values are modelled as an Ornstein-Uhlenbeck process with timevarying variance, then the distributions of the temperature index on which the derivative is written is the sum of truncated, correlated Gaussian deviates. The key result of this paper is to provide an analytical approximation to the distribution of this sum, thus allowing the accurate computation of payoffs without the need for any simulation. A data set comprising average daily temperature spanning over a hundred years for four Australian cities is used to demonstrate the efficacy of this approach for estimating the payoffs to temperature derivatives. It is demonstrated that expected payoffs computed directly from historical records are a particularly poor approach to the problem when there are trends in underlying average daily temperature. It is shown that the proposed analytical approach is superior to historical pricing.

Pten and Ndufb8 aberrations in cervical cancer tissue

Cervical cancer is one of the world's major health issues. Despite many studies in this field, the carcinogenetic events of malignant conversion in cervical tumours have not been significantly characterised. The first aim of this project was to investigate the mutation status of the tumour suppressor gene- Phosphatase and Tension Homolog (PTEN)- in cervical cancer tissue. The second aim of this study was the analysis in the same cervical cancer tissue for aberrations in the mitochondrial electron transport chain subunit gene NDUFB8, which is localised to the same chromosomal contig as PTEN. The third aim was the evaluation of the potential therapeutic anti-cancer drug 2,4-Thiazolidinediones (TZDs) and its affect in regulating the PTEN protein in a cervical cancer cell line (HeLa). To approach the aims, paraffin-embedded cancerous cervical tissue and non-cancerous cervical tissue were obtained. DNA recovered from those tissues was then used to investigate the putative genomic changes regarding the NDUFB8 gene utilising SYBR Green I Real-Time PCR. The PTEN gene was studied via Dual-Labelled probe Real-Time PCR. To investigate the protein expression change of the PTEN protein, HeLa cells were firstly treated with different concentrations of 2,4-Thiazolidinediones and the level of PTEN protein expression was then observed utilising standard protein assays. Results indicated that there were putative copy-number changes between the cancerous cervical tissue and non-cancerous cervical tissue, with regard to the PTEN locus. This implies a potential gain of the PTEN gene in cancerous cervical tissue. With regards to normal cervical tissue versus cancerous cervical tissue no significant melting temperature differences were observed with the SYBR Green I Real-Time PCR in respect to the NDUFB8 gene. A putative up-regulation of PTEN protein was observed in TZD treated HeLa cells. © 2008 Springer Science+Business Media, LLC.

Proof of concept : A bioinformatic and serological screening method for identifying new peptide antigens for Chlamydia trachomatis related sequelae in women

This study aimed to identify new peptide antigens from Chlamydia (C.) trachomatis in a proof of concept approach which could be used to develop an epitope-based serological diagnostic for C. trachomatis related infertility in women. A bioinformatics analysis was conducted examining several immunodominant proteins from C. trachomatis to identify predicted immunoglobulin epitopes unique to C. trachomatis. A peptide array of these epitopes was screened against participant sera. The participants (all female) were categorized into the following cohorts based on their infection and gynecological history; acute (single treated infection with C. trachomatis), multiple (more than one C. trachomatis infection, all treated), sequelae (PID or tubal infertility with a history of C. trachomatis infection), and infertile (no history of C. trachomatis infection and no detected tubal damage). The bioinformatics strategy identified several promising epitopes. Participants who reacted positively in the peptide 11 ELISA were found to have an increased likelihood of being in the sequelae cohort compared to the infertile cohort with an odds ratio of 16.3 (95% c.i. 1.65 – 160), with 95% specificity and 46% sensitivity (0.19-0.74). The peptide 11 ELISA has the potential to be further developed as a screening tool for use during the early IVF work up and provides proof of concept that there may be further peptide antigens which could be identified using bioinformatics and screening approaches.

A nanometre-scale non-periodic structural variation in high temperature superconducting ceramics and the implications for properties

Non-periodic structural variation has been found in the high Tc cuprates, YBa2Cu3O7-x and Hg0.67Pb0.33Ba2Ca2Cu 3O8+δ, by image analysis of high resolution transmission electron microscope (HRTEM) images. We use two methods for analysis of the HRTEM images. The first method is a means for measuring the bending of lattice fringes at twin planes. The second method is a low-pass filter technique which enhances information contained by diffuse-scattered electrons and reveals what appears to be an interference effect between domains of differing lattice parameter in the top and bottom of the thin foil. We believe that these methods of image analysis could be usefully applied to the many thousands of HRTEM images that have been collected by other workers in the high temperature superconductor field. This work provides direct structural evidence for phase separation in high Tc cuprates, and gives support to recent stripes models that have been proposed to explain various angle resolved photoelectron spectroscopy and nuclear magnetic resonance data. We believe that the structural variation is a response to an opening of an electronic solubility gap where holes are not uniformly distributed in the material but are confined to metallic stripes. Optimum doping may occur as a consequence of the diffuse boundaries between stripes which arise from spinodal decomposition. Theoretical ideas about the high Tc cuprates which treat the cuprates as homogeneous may need to be modified in order to take account of this type of structural variation.

Probing second harmonic components of pH-sensitive Redox processes in a mesoporous TiO2-Nafion film electrode with Fourier-transformed large-amplitude sinusoidally modulated voltammetry

Electrochemical processes in mesoporous TiO2-Nafion thin films deposited on indium tin oxide (ITO) electrodes are inherently complex and affected by capacitance, Ohmic iR-drop, RC-time constant phenomena, and by potential and pH-dependent conductivity. In this study, large-amplitude sinusoidally modulated voltammetry (LASMV) is employed to provide access to almost purely Faradaic-based current data from second harmonic components, as well as capacitance and potential domain information from the fundamental harmonic for mesoporous TiO2-Nafion film electrodes. The LASMV response has been investigated with and without an immobilized one-electron redox system, ferrocenylmethyltrimethylammonium+. Results clearly demonstrate that the electron transfer associated with the immobilized ferrocene derivative follows two independent pathways i) electron hopping within the Nafion network and ii) conduction through the TiO2 backbone. The pH effect on the voltammetric response for the TiO2 reduction pathway (ii) can be clearly identified in the 2nd harmonic LASMV response with the diffusion controlled ferrocene response (i) acting as a pH independent reference. Application of second harmonic data derived from LASMV measurement, because of the minimal contribution from capacitance currents, may lead to reference-free pH sensing with systems like that found for ferrocene derivatives.

Bone matters in lung cancer

Background: Bone metastases are a significant and undertreated clinical problem in patients with advanced lung cancer. Design: We reviewed the incidence of bone metastases and skeletal-related events (SREs) in patients with lung cancer and examined the burden on patients' lives and on health care systems. Available therapies to improve survival and lessen the impact of SREs on quality of life (QoL) were also investigated. Results: Bone metastases are common in lung cancer; however, owing to short survival times, data on the incidences of SREs are limited. As with other cancers, the costs associated with treating SREs in lung cancer are substantial. Bisphosphonates reduce the frequency of SREs and improve measures of pain and QoL in patients with lung cancer; however, nephrotoxicity is a common complication of therapy. Denosumab, a recently approved bone-targeted therapy, is superior to zoledronic acid in increasing the time to first on-study SRE in patients with solid tumours, including lung cancer. Additional roles of bone-targeted therapies beyond the prevention of SREs are under investigation. Conclusions: With increasing awareness of the consequences of SREs, bone-targeted therapies may play a greater role in the management of patients with lung cancer, with the aim of delaying disease progression and preserving QoL. © The Author 2012. Published by Oxford University Press on behalf of the European Society for Medical Oncology.