Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.

Combined VEGF and PDGF treatment reduces secondary degeneration after spinal cord injury

Trauma to the spinal cord creates an initial physical injury damaging neurons, glia, and blood vessels, which then induces a prolonged inflammatory response, leading to secondary degeneration of spinal cord tissue, and further loss of neurons and glia surrounding the initial site of injury. Angiogenesis is a critical step in tissue repair, but in the injured spinal cord angiogenesis fails; blood vessels formed initially later regress. Stabilizing the angiogenic response is therefore a potential target to improve recovery after spinal cord injury (SCI). Vascular endothelial growth factor (VEGF) can initiate angiogenesis, but cannot sustain blood vessel maturation. Platelet-derived growth factor (PDGF) can promote blood vessel stability and maturation. We therefore investigated a combined application of VEGF and PDGF as treatment for traumatic spinal cord injury, with the aim to reduce secondary degeneration by promotion of angiogenesis. Immediately after hemisection of the spinal cord in the rat we delivered VEGF and PDGF and to the injury site. One and 3 months later the size of the lesion was significantly smaller in the treated group compared to controls, and there was significantly reduced gliosis surrounding the lesion. There was no significant effect of the treatment on blood vessel density, although there was a significant reduction in the numbers of macrophages/microglia surrounding the lesion, and a shift in the distribution of morphological and immunological phenotypes of these inflammatory cells. VEGF and PDGF delivered singly exacerbated secondary degeneration, increasing the size of the lesion cavity. These results demonstrate a novel therapeutic intervention for SCI, and reveal an unanticipated synergy for these growth factors whereby they modulated inflammatory processes and created a microenvironment conducive to axon preservation/sprouting.

Role of particle size and composition in metal adsorption by solids deposited on urban road surfaces

Despite common knowledge that the metal content adsorbed by fine particles is relatively higher compared to coarser particles, the reasons for this phenomenon has gained little research attention. The research study discussed in the paper investigated the variations in metal content for different particle sizes of solids associated with pollutant build-up on urban road surfaces. Data analysis confirmed that parameters favourable for metal adsorption to solids such as specific surface area, organic carbon content, effective cation exchange capacity and clay forming minerals content decrease with the increase in particle size. Furthermore, the mineralogical composition of solids was found to be the governing factor influencing the specific surface area and effective cation exchange capacity. There is high quartz content in particles >150µm compared to particles <150µm. As particle size reduces below 150µm, the clay forming minerals content increases, providing favourable physical and chemical properties that influence adsorption.

Management based on exhaled nitric oxidelevels adjusted for atopy reduces asthma exacerbations in children : A dual centre randomised controlled trial

While several randomised control trials (RCTs) have evaluated the use of fractional exhaled nitric oxide (FeNO) to improve asthma outcomes, none used FeNO cut-offs adjusted for atopy, a determinant of FeNO levels. In a dual centre RCT, we assessed whether a treatment strategy based on FeNO levels, adjusted for atopy, reduces asthma exacerbations compared with the symptoms-based management (controls). Children with asthma from hospital clinics of two hospitals were randomly allocated to receive an a-priori determined treatment hierarchy based on symptoms or FeNO levels. There was a 2-week run-in period and they were then reviewed ten times over 12-months. The primary outcome was the number of children with exacerbations over 12-months. Sixty-three children were randomised (FeNO=31, controls=32); 55 (86%) completed the study. Although we did achieve our planned sample size, significantly fewer children in the FeNO group (6 of 27) had an asthma exacerbation compared to controls (15 of 28), p=0.021; number to treat for benefit=4 (95%CI 3-24). There was no difference between groups for any secondary outcomes (quality of life, symptoms, FEV1). The final daily inhaled corticosteroids (ICS) dose was significantly (p=0.037) higher in the FeNO group (median 400µg, IQR 250-600) compared to the controls (200, IQR100-400). Taking atopy into account when using FeNO to tailor asthma medications is likely beneficial in reducing the number of children with severe exacerbations at the expense of increased ICS use. However, the strategy is unlikely beneficial for improving asthma control. A larger study is required to confirm or refute our findings.

Tracking people in 3D using position, size and shape

This paper presents a prototype tracking system for tracking people in enclosed indoor environments where there is a high rate of occlusions. The system uses a stereo camera for acquisition, and is capable of disambiguating occlusions using a combination of depth map analysis, a two step ellipse fitting people detection process, the use of motion models and Kalman filters and a novel fit metric, based on computationally simple object statistics. Testing shows that our fit metric outperforms commonly used position based metrics and histogram based metrics, resulting in more accurate tracking of people.

ERP success: Does organisation size matter?

Organisations invest enormous sums of money in acquiring Enterprise Resource Planning (ERP) systems, presumably expecting positive impacts to the organisation and its functions. Despite the optimistic motives some ERP projects have reported nil or detrimental impacts. This paper studies the proposition that the size of an organisation (e.g. small, large) may have contributed to the differences in receiving benefits reported in prior studies in this domain. The alleged differences in organisational performance are empirically measured using a prior validated model, using five constructs and fortytwo sub-constructs. Information is gathered from three hundred and ten respondents representing twenty-seven public sector organisations. Results suggests that (1) larger organisations have received more benefits compared to small organisations, (2) small organisations demonstrated higher reliance on their ERP systems, (3) employment cohorts demonstrate significant differences in perceived benefits in small and large organisations.

Characterization of expiration air jets and droplet size distributions immediately at the mouth opening

Size distributions of expiratory droplets expelled during coughing and speaking and the velocities of the expiration air jets of healthy volunteers were measured. Droplet size was measured using the Interferometric Mie imaging (IMI) technique while the Particle Image Velocimetry (PIV) technique was used for measuring air velocity. These techniques allowed measurements in close proximity to the mouth and avoided air sampling losses. The average expiration air velocity was 11.7 m/s for coughing and 3.9 m/s for speaking. Under the experimental setting, evaporation and condensation effects had negligible impact on the measured droplet size. The geometric mean diameter of droplets from coughing was 13.5m and it was 16.0m for speaking (counting 1 to 100). The estimated total number of droplets expelled ranged from 947 – 2085 per cough and 112 – 6720 for speaking. The estimated droplet concentrations for coughing ranged from 2.4 - 5.2cm-3 per cough and 0.004 – 0.223 cm-3 for speaking.

Size distribution and sites of origin of droplets expelled during expiratory activities

A new Expiratory Droplet Investigation System (EDIS) was used to conduct the most comprehensive program of study to date, of the dilution corrected droplet size distributions produced during different respiratory activities.----- Distinct physiological processes were responsible for specific size distribution modes. The majority of particles for all activities were produced in one or more modes, with diameters below 0.8 µm. That mode occurred during all respiratory activities, including normal breathing. A second mode at 1.8 µm was produced during all activities, but at lower concentrations.----- Speech produced particles in modes near 3.5 µm and 5 µm. The modes became most pronounced during continuous vocalization, suggesting that the aerosolization of secretions lubricating the vocal chords is a major source of droplets in terms of number.----- Non-eqilibrium droplet evaporation was not detectable for particles between 0.5 and 20 μm implying that evaporation to the equilibrium droplet size occurred within 0.8 s.