Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPE-NST), which involve the Caputo time fractional derivative (CTFD) of order α ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ ∈ (1, 2). Approximating the CTFD and RSFD using the L1-algorithm and shifted Grunwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

Functional status, postural stability and falls among older adults with glaucoma

Visual impairment is an important contributing factor in falls among older adults, which is one of the leading causes of injury and injury-related death in this population. Visual impairment is also associated with greater disability among older adults, including poorer health-related quality of life, increased frailty and reduced postural stability. The majority of this evidence, however, is based on measures of central visual function, rather than peripheral visual function. As such, there is comparatively limited research on the associations between peripheral visual function, disability and falls, and even fewer studies involving older adults with specific diseases which affect peripheral visual function, the most common of which is glaucoma. Glaucoma is one of the leading causes of irreversible vision loss among older adults, affecting around 3 per cent of adults aged over 60 years. The condition is characterised by retinal nerve fibre loss, primarily affecting peripheral visual function. Importantly, the number of older adults with glaucomatous visual impairment is projected to increase as the ageing population grows. The first component of the thesis examined the cross-sectional association between glaucomatous visual impairment and health-related quality of life (Study 1a), functional status (Study 1b) and postural stability (Study 1c) among older adults. A cohort of 74 community-dwelling adults with glaucoma (mean age 74.2 ± 5.9 years) was recruited and completed a baseline assessment. A number of visual function measures was assessed, including central visual function (visual acuity and contrast sensitivity), motion sensitivity, retinal nerve fibre analysis and monocular and binocular visual field measures (monocular 24-2 and binocular integrated visual fields (IVF): IVF-60 and IVF-120). The analyses focused on the associations between the outcomes measures and severity and location of visual field loss, as this is the primary visual function affected by glaucoma. In Study 1a, we examined the association between visual field loss and health-related quality of life, measured by the Short Form 36-item Health Survey (SF-36). Greater binocular visual field loss, on both IVF measures, was associated with lower SF-36 physical component scores, adjusted for age and gender (Pearson's r =|0.32| to |0.36|, p<0.001). Furthermore, inferior visual field loss was more strongly associated with the SF-36 physical component than superior field loss. No association was found between visual field loss and SF-36 mental component scores. The association between visual field loss and functional status was examined in Study 1b. Functional status outcomes measures included a physical activity questionnaire (Physical Activity Scale for the Elderly, PASE), performance tests (six-minute walk test, timed up and go test and lower leg strength) and an overall functional status score. Significant, but weak, correlations were found between binocular visual field loss and PASE and overall functional status scores, adjusted for age and gender (Pearson's r =|0.24| to |0.33|, p<0.05). Greater inferior visual field loss, independent of superior visual field loss, was significantly associated with poorer physical performance results and lower overall functional status scores. In Study 1c, we examined the association between visual field loss and postural stability, using a swaymeter device which recorded body movement during four conditions: eyes open and closed, on a firm and foam surface. Greater binocular visual field loss was associated with increased postural sway, both on firm and foam surfaces, independent of age and gender (Pearson’s r =|0.44| to |0.46|, p <0.001). Furthermore, inferior visual field was a stronger contributor to postural stability, more so than the superior visual field, particularly on the foam condition with the eyes open. Greater visual field loss was associated with a reduction in the visual contribution to postural sway, which underlies the observed association with postural sway. The second component of the thesis examined the association between severity and location of visual field loss and falls during a 12-month longitudinal follow-up. The number of falls was assessed prospectively using monthly fall calendars. Of the 71 participants who successfully completed the follow up (mean age 73.9 ± 5.7 years), 44% reported one or more falls, and around 20% reported two or more falls. After adjusting for age and gender, every 10 points missed on the IVF-120 increased the rate of falls by 25% (rate ratio 1.25, 95% confidence interval 1.08 - 1.44) or every 5dB reduction in IVF-60 increased the rate of falls by 47% (rate ratio 1.47, 95% confidence interval 1.16 - 1.87). Inferior visual field loss was a significant predictor of falls, more so than superior field loss, highlighting the importance of the inferior visual field area in safe and efficient navigation. Further analyses indicated that postural stability, more so than functional status, may be a potential mediating factor in the relationship between visual field loss and falls. Future research is required to confirm this causal pathway. In addition, the use of topical beta-blocker medications was not associated with an increased rate of falls in this cohort, compared with the use of other topical anti-glaucoma medications. In summary, greater binocular visual field loss among older adults with glaucoma was associated with poorer health-related quality of life in the physical domain, reduced functional status, greater postural instability and higher rates of falling. When the location of visual field loss was examined, inferior visual field loss was consistently more strongly associated with these outcomes than superior visual field loss. Insights gained from this research improve our understanding of the association between glaucomatous visual field loss and disability, and its link with falls among older adults. The clinical implications of this research include the need to include visual field screening in falls risk assessments among older adults and to raise awareness of these findings to eye care practitioners and adults with glaucoma. The findings also assist in developing further research to examine strategies to reduce disability and prevent falls among older adults with glaucoma to promote healthy ageing and independence for these individuals.

Evaluation of spectral and texture features for object-based vegetation species classification using Support Vector Machines

The use of appropriate features to characterize an output class or object is critical for all classification problems. This paper evaluates the capability of several spectral and texture features for object-based vegetation classification at the species level using airborne high resolution multispectral imagery. Image-objects as the basic classification unit were generated through image segmentation. Statistical moments extracted from original spectral bands and vegetation index image are used as feature descriptors for image objects (i.e. tree crowns). Several state-of-art texture descriptors such as Gray-Level Co-Occurrence Matrix (GLCM), Local Binary Patterns (LBP) and its extensions are also extracted for comparison purpose. Support Vector Machine (SVM) is employed for classification in the object-feature space. The experimental results showed that incorporating spectral vegetation indices can improve the classification accuracy and obtained better results than in original spectral bands, and using moments of Ratio Vegetation Index obtained the highest average classification accuracy in our experiment. The experiments also indicate that the spectral moment features also outperform or can at least compare with the state-of-art texture descriptors in terms of classification accuracy.

The effects of muscle fatigue on knee function during landing

The human knee acts as a sophisticated shock absorber during landing movements. The ability of the knee to perform this function in the real world is remarkable given that the context of the landing movement may vary widely between performances. For this reason, humans must be capable of rapidly adjusting the mechanical properties of the knee under impact load in order to satisfy many competing demands. However, the processes involved in regulating these properties in response to changing constraints remain poorly understood. In particular, the effects of muscle fatigue on knee function during step landing are yet to be fully explored. Fatigue of the knee muscles is significant for 2 reasons. First, it is thought to have detrimental effects on the ability of the knee to act as a shock absorber and is considered a risk factor for knee injury. Second, fatigue of knee muscles provides a unique opportunity to examine the mechanisms by which healthy individuals alter knee function. A review of the literature revealed that the effect of fatigue on knee function during landing has been assessed by comparing pre and postfatigue measurements, with fatigue induced by a voluntary exercise protocol. The information is limited by inconsistent results with key measures, such as knee stiffness, showing varying results following fatigue, including increased stiffness, decreased stiffness or failure to detect any change in some experiments. Further consideration of the literature questions the validity of the models used to induce and measure fatigue, as well as the pre-post study design, which may explain the lack of consensus in the results. These limitations cast doubt on the usefulness of the available information and identify a need to investigate alternative approaches. Based on the results of this review, the aims of this thesis were to: • evaluate the methodological procedures used in validation of a fatigue model • investigate the adaptation and regulation of post-impact knee mechanics during repeated step landings • use this new information to test the effects of fatigue on knee function during a step-landing task. To address the aims of the thesis, 3 related experiments were conducted that collected kinetic, kinematic and electromyographic data from 3 separate samples of healthy male participants. The methodologies involved optoelectronic motion capture (VICON), isokinetic dynamometry (System3 Pro, BIODEX) and wireless surface electromyography (Zerowire, Aurion, Italy). Fatigue indicators and knee function measures used in each experiment were derived from the data. Study 1 compared the validity and reliability of repetitive stepping and isokinetic contractions with respect to fatigue of the quadriceps and hamstrings. Fifteen participants performed 50 repetitions of each exercise twice in randomised order, over 4 sessions. Sessions were separated by a minimum of 1 week’s rest, to ensure full recovery. Validity and reliability depended on a complex interaction between the exercise protocol, the fatigue indicator, the individual and the muscle of interest. Nevertheless, differences between exercise protocols indicated that stepping was less effective in eliciting valid and reliable changes in peak power and spectral compression, compared with isokinetic exercise. A key finding was that fatigue progressed in a biphasic pattern during both exercises. The point separating the 2 phases, known as the transition point, demonstrated superior between-test reliability during the isokinetic protocol, compared with stepping. However, a correction factor should be used to accurately apply this technique to the study of fatigue during landing. Study 2 examined alterations in knee function during repeated landings, with a different sample (N =12) performing 60 consecutive step landing trials. Each landing trial was separated by 1-minute rest periods. The results provided new information in relation to the pre-post study design in the context of detecting adjustments in knee function during landing. First, participants significantly increased or decreased pre-impact muscle activity or post-impact mechanics despite environmental and task constraints remaining unchanged. This is the 1st study to demonstrate this effect in healthy individuals without external feedback on performance. Second, single-subject analysis was more effective in detecting alterations in knee function compared to group-level analysis. Finally, repeated landing trials did not reduce inter-trial variability of knee function in some participants, contrary to assumptions underpinning previous studies. The results of studies 1 and 2 were used to modify the design of Study 3 relative to previous research. These alterations included a modified isokinetic fatigue protocol, multiple pre-fatigue measurements and singlesubject analysis to detect fatigue-related changes in knee function. The study design incorporated new analytical approaches to investigate fatiguerelated alterations in knee function during landing. Participants (N = 16) were measured during multiple pre-fatigue baseline trial blocks prior to the fatigue model. A final block of landing trials was recorded once the participant met the operational fatigue definition that was identified in Study 1. The analysis revealed that the effects of fatigue in this context are heavily dependent on the compensatory response of the individual. A continuum of responses was observed within the sample for each knee function measure. Overall, preimpact preparation and post-impact mechanics of the knee were altered with highly individualised patterns. Moreover, participants used a range of active or passive pre-impact strategies to adapt post-impact mechanics in response to quadriceps fatigue. The unique patterns identified in the data represented an optimisation of knee function based on priorities of the individual. The findings of these studies explain the lack of consensus within the literature regarding the effects of fatigue on knee function during landing. First, functional fatigue protocols lack validity in inducing fatigue-related changes in mechanical output and spectral compression of surface electromyography (sEMG) signals, compared with isokinetic exercise. Second, fatigue-related changes in knee function during landing are confounded by inter-individual variation, which limits the sensitivity of group-level analysis. By addressing these limitations, the 3rd study demonstrated the efficacies of new experimental and analytical approaches to observe fatigue-related alterations in knee function during landing. Consequently, this thesis provides new perspectives into the effects of fatigue in knee function during landing. In conclusion: • The effects of fatigue on knee function during landing depend on the response of the individual, with considerable variation present between study participants, despite similar physical characteristics. • In healthy males, adaptation of pre-impact muscle activity and postimpact knee mechanics is unique to the individual and reflects their own optimisation of demands such as energy expenditure, joint stability, sensory information and loading of knee structures. • The results of these studies should guide future exploration of adaptations in knee function to fatigue. However, research in this area should continue with reduced emphasis on the directional response of the population and a greater focus on individual adaptations of knee function.

Effect of pH on the uptake of arsenate and vanadate and the stability of these anions in alkaline solutions – a Raman spectroscopic study

Hydrotalcites have been synthesised using three different pH solutions to assess the effect of pH on the uptake of arsenate and vanadate. The ability of these hydrotalcites to remove vanadate and arsenate from solution has been determined by ICP-OES. Raman spectroscopy is used to monitor changes in the anionic species for hydrotalcites synthesised at different pH values. The results show a reduction in the concentration of arsenate and vanadate anions that are removed in extremely alkaline solutions. Hydrotalcites containing arsenate and vanadate are stable in solutions up to pH 10. Exposure of these hydrotalcites to higher pH values results in the removal of large percentages of arsenate and vanadate from the hydrotalcite interlayer.

Single-stranded DNA-binding protein hSSB1 is critical for genomic stability

Single-strand DNA (ssDNA)-binding proteins (SSBs) are ubiquitous and essential for a wide variety of DNA metabolic processes, including DNA replication, recombination, DNA damage detection and repair1. SSBs have multiple roles in binding and sequestering ssDNA, detecting DNA damage, stimulating nucleases, helicases and strand-exchange proteins, activating transcription and mediating protein–protein interactions. In eukaryotes, the major SSB, replication protein A (RPA), is a heterotrimer1. Here we describe a second human SSB (hSSB1), with a domain organization closer to the archaeal SSB than to RPA. Ataxia telangiectasia mutated (ATM) kinase phosphorylates hSSB1 in response to DNA double-strand breaks (DSBs). This phosphorylation event is required for DNA damage-induced stabilization of hSSB1. Upon induction of DNA damage, hSSB1 accumulates in the nucleus and forms distinct foci independent of cell-cycle phase. These foci co-localize with other known repair proteins. In contrast to RPA, hSSB1 does not localize to replication foci in S-phase cells and hSSB1 deficiency does not influence S-phase progression. Depletion of hSSB1 abrogates the cellular response to DSBs, including activation of ATM and phosphorylation of ATM targets after ionizing radiation. Cells deficient in hSSB1 exhibit increased radiosensitivity, defective checkpoint activation and enhanced genomic instability coupled with a diminished capacity for DNA repair. These findings establish that hSSB1 influences diverse endpoints in the cellular DNA damage response.

A biologically inspired object spectral-texture descriptor and its application to vegetation classification in power-line corridors

The use of appropriate features to represent an output class or object is critical for all classification problems. In this paper, we propose a biologically inspired object descriptor to represent the spectral-texture patterns of image-objects. The proposed feature descriptor is generated from the pulse spectral frequencies (PSF) of a pulse coupled neural network (PCNN), which is invariant to rotation, translation and small scale changes. The proposed method is first evaluated in a rotation and scale invariant texture classification using USC-SIPI texture database. It is further evaluated in an application of vegetation species classification in power line corridor monitoring using airborne multi-spectral aerial imagery. The results from the two experiments demonstrate that the PSF feature is effective to represent spectral-texture patterns of objects and it shows better results than classic color histogram and texture features.

CYR61 (CCN1) protein expression during fracture healing in an ovine tibial model and its relation to the mechanical fixation stability

The formation of new blood vessels is a prerequisite for bone healing. CYR61 (CCN1), an extracellular matrix-associated signaling protein, is a potent stimulator of angiogenesis and mesenchymal stem cell expansion and differentiation. A recent study showed that CYR61 is expressed during fracture healing and suggested that CYR61 plays a significant role in cartilage and bone formation. The hypothesis of the present study was that decreased fixation stability, which leads to a delay in healing, would lead to reduced CYR61 protein expression in fracture callus. The aim of the study was to quantitatively analyze CYR61 protein expression, vascularization, and tissue differentiation in the osteotomy gap and relate to the mechanical fixation stability during the course of healing. A mid-shaft osteotomy of the tibia was performed in two groups of sheep and stabilized with either a rigid or semirigid external fixator, each allowing different amounts of interfragmentary movement. The sheep were sacrificed at 2, 3, 6, and 9 weeks postoperatively. The tibiae were tested biomechanically and histological sections from the callus were analyzed immunohistochemically with regard to CYR61 protein expression and vascularization. Expression of CYR61 protein was upregulated at the early phase of fracture healing (2 weeks), decreasing over the healing time. Decreased fixation stability was associated with a reduced upregulation of the CYR61 protein expression and a reduced vascularization at 2 weeks leading to a slower healing. The maximum cartilage callus fraction in both groups was reached at 3 weeks. However, the semirigid fixator group showed a significantly lower CYR61 immunoreactivity in cartilage than the rigid fixator group at this time point. The fraction of cartilage in the semirigid fixator group was not replaced by bone as quickly as in the rigid fixator group leading to an inferior histological and mechanical callus quality at 6 weeks and therefore to a slower healing. The results supply further evidence that CYR61 may serve as an important regulator of bone healing.

The course of bone healing is influenced by the initial shear fixation stability

Fracture healing is influenced by fixation stability and experimental evidence suggests that the initial mechanical conditions may determine the healing outcome. We hypothesised that mechanical conditions influence not only the healing outcome, but also the early phase of fracture healing. Additionally, it was hypothesised that decreased fixation stability characterised by an increased shear interfragmentary movement results in a delay in healing. Sixty-four sheep underwent a mid-shaft tibial osteotomy which was treated with either a rigid or a semi-rigid external fixator. Animals were sacrificed at 2, 3, 6 and 9 weeks postoperatively and the fracture callus was analysed using radiological, biomechanical and histological techniques. The tibia treated with semi-rigid fixation showed inferior callus stiffness and quality after 6 weeks. At 9 weeks, the calluses were no longer distinguishable in their mechanical competence. The calluses at 9 weeks produced under rigid fixation were smaller and consisted of a reduced fibrous tissue component. These results demonstrate that the callus formation over the course of healing differed both morphologically and in the rate of development. In this study, we provide evidence that the course of healing is influenced by the initial fixation stability. The semi-rigid fixator did not result in delayed healing, but a less optimal healing path was taken. An upper limit of stability required for successful healing remains unknown, however a limit by which healing is less optimal has been determined.

Stability boundary analysis of the dynamic voltage restorer in weak systems with dynamic loads

In this contribution, a stability analysis for a dynamic voltage restorer (DVR) connected to a weak ac system containing a dynamic load is presented using continuation techniques and bifurcation theory. The system dynamics are explored through the continuation of periodic solutions of the associated dynamic equations. The switching process in the DVR converter is taken into account to trace the stability regions through a suitable mathematical representation of the DVR converter. The stability regions in the Thevenin equivalent plane are computed. In addition, the stability regions in the control gains space, as well as the contour lines for different Floquet multipliers, are computed. Besides, the DVR converter model employed in this contribution avoids the necessity of developing very complicated iterative map approaches as in the conventional bifurcation analysis of converters. The continuation method and the DVR model can take into account dynamics and nonlinear loads and any network topology since the analysis is carried out directly from the state space equations. The bifurcation approach is shown to be both computationally efficient and robust, since it eliminates the need for numerically critical and long-lasting transient simulations.

Thermal stability of the soil minerals destinezite and diadochite Fe3+2(PO4)(SO4)(OH)·6H2O - implications for soils in bush fires

Thermogravimetry combined with evolved gas mass spectrometry has been used to ascertain the stability of the soil minerals destinezite and diadochite. These two minerals are identical except for their morphology. Diadochite is amorphous whereas destinezite is crystalline. Both minerals are found in soils. It is important to understand the stability of these minerals because soils are subject to bush fires especially in Australia. The thermal analysis patterns of the two minerals are similar but not identical. Subtle differences are observed in the DTG patterns. For destinezite, two DTG peaks are observed at 129 and 182°C attributed to the loss of hydration water, whereas only a broad peak with maximum at 84°C is observed for diadochite. Higher temperature mass losses at 685°C for destinezite and 655°C for diadochite, based upon the ion current curves, are due to sulphate decomposition. This research has shown that at low temperatures the minerals are stable but at high temperatures, as might be experienced in a bush fire, the minerals decompose.

Thermal stability of the ‘cave’ mineral brushite CaHPO4•2H2O -mechanism of formation and decomposition

Thermogravimetry combined with evolved gas mass spectrometry has been used to ascertain the stability of the ‘cave’ mineral brushite. X-ray diffraction shows that brushite from the Jenolan Caves is very pure. Thermogravimetric analysis coupled with ion current mass spectrometry shows a mass loss at 111°C due to loss of water of hydration. A further decomposition step occurs at 190°C with the conversion of hydrogen phosphate to a mixture of calcium ortho-phosphate and calcium pyrophosphate. TG-DTG shows the mineral is not stable above 111°C. A mechanism for the formation of brushite on calcite surfaces is proposed, and this mechanism has relevance to the formation of brushite in urinary tracts.