GPU accelerated algorithms for computing matrix function vector products with applications to exponential integrators and fractional diffusion

The efficient computation of matrix function vector products has become an important area of research in recent times, driven in particular by two important applications: the numerical solution of fractional partial differential equations and the integration of large systems of ordinary differential equations. In this work we consider a problem that combines these two applications, in the form of a numerical solution algorithm for fractional reaction diffusion equations that after spatial discretisation, is advanced in time using the exponential Euler method. We focus on the efficient implementation of the algorithm on Graphics Processing Units (GPU), as we wish to make use of the increased computational power available with this hardware. We compute the matrix function vector products using the contour integration method in [N. Hale, N. Higham, and L. Trefethen. Computing Aα, log(A), and related matrix functions by contour integrals. SIAM J. Numer. Anal., 46(5):2505–2523, 2008]. Multiple levels of preconditioning are applied to reduce the GPU memory footprint and to further accelerate convergence. We also derive an error bound for the convergence of the contour integral method that allows us to pre-determine the appropriate number of quadrature points. Results are presented that demonstrate the effectiveness of the method for large two-dimensional problems, showing a speedup of more than an order of magnitude compared to a CPU-only implementation.

Investigation of drive-train dynamics of mechanical transmissions incorporating cycloidal drives

Cycloidal drives are compact, high-ratio gear transmission systems used in a wide range of mechanical applications from conveyor drives to articulated robots. This research hypothesises that these drives can be successfully applied in dynamic loading situations and thereby focuses on the understanding of differences between static and dynamic loading conditions where load varies with time. New methods of studying the behaviour of these drives under static and dynamic loading circumstances were developed, leading to novel understanding and knowledge. A new model was developed to facilitate research and development on Cycloidal drives with potential benefits for manufacturing, robotics and mechanical-process-industries worldwide.

Characteristics and alteration origins of matrix minerals in volcaniclastic kimberlite of the Muskox pipe (Nunavut, Canada)

The matrix of volcaniclastic kimberlite (VK) from the Muskox pipe (Northern Slave Province, Nunavut, Canada) is interpreted to represent an overprint of an original clastic matrix. Muskox VK is subdivided into three different matrix mineral assemblages that reflect differences in the proportions of original primary matrix constituents, temperature of formation and nature of the altering fluids. Using whole rock X-ray fluorescence (XRF), whole rock X-ray diffraction (XRD), microprobe analyses, back-scatter electron (BSE) imaging, petrography and core logging, we find that most matrix minerals (serpentine, phlogopite, chlorite, saponite, monticellite, Fe-Ti oxides and calcite) lack either primary igneous or primary clastic textures. The mineralogy and textures are most consistent with formation through alteration overprinting of an original clastic matrix that form by retrograde reactions as the deposit cools, or, in the case of calcite, by precipitation from Ca-bearing fluids into a secondary porosity. The first mineral assemblage consists largely of serpentine, phlogopite, calcite, Fe-Ti oxides and monticellite and occurs in VK with relatively fresh framework clasts. Alteration reactions, driven by deuteric fluids derived from the juvenile constituents, promote the crystallisation of minerals that indicate relatively high temperatures of formation (> 400 °C). Lower-temperature minerals are not present because permeability was occluded before the deposit cooled to low temperatures, thus shielding the facies from further interaction with fluids. The other two matrix mineral assemblages consist largely of serpentine, phlogopite, calcite, +/- diopside, and +/- chlorite. They form in VK that contains more country rock, which may have caused the deposit to be cooler upon emplacement. Most framework components are completely altered, suggesting that larger volumes of fluids drove the alteration reactions. These fluids were likely of meteoric provenance and became heated by the volcaniclastic debris when they percolated into the VK infill. Most alteration reactions ceased at temperatures > 200 °C, as indicated by the absence or paucity of lower-temperature phases in most samples, such as saponite. Recognition that Muskox VK contains an original clastic matrix is a necessary first step for evaluating the textural configuration, which is important for reconstructing the physical processes responsible for the formation of the deposit.

Increased intra-cortical porosity reduces bone stiffness and strength in pediatric patients with osteogenesis imperfecta

Osteogenesis imperfecta (OI) is a heritable disease occurring in one out of every 20,000 births. Although it is known that Type I collagen mutation in OI leads to increased bone fragility, the mechanism of this increased susceptibility to fracture is not clear. The aim of this study was to assess the microstructure of cortical bone fragments from patients with osteogenesis imperfecta (OI) using polarized light microscopy, and to correlate microstructural observations with the results of previously performed mechanical compression tests on bone from the same source. Specimens of cortical bone were harvested from the lower limbs of three (3) OI patients at the time of surgery, and were divided into two groups. Group 1 had been subjected to previous micro-mechanical compression testing, while Group 2 had not been subjected to any prior testing. Polarized light microscopy revealed disorganized bone collagen architecture as has been previously observed, as well as a large increase in the areal porosity of the bone compared to typical values for healthy cortical bone, with large (several hundred micron sized), asymmetrical pores. Importantly, the areal porosity of the OI bone samples in Group 1 appears to correlate strongly with their previously measured apparent Young's modulus and compressive strength. Taken together with prior nanoindentation studies on OI bone tissue, the results of this study suggest that increased intra-cortical porosity is responsible for the reduction in macroscopic mechanical properties of OI cortical bone, and therefore that in vivo imaging modalities with resolutions of ~ 100 μm or less could potentially be used to non-invasively assess bone strength in OI patients. Although the number of subjects in this study is small, these results highlight the importance of further studies in OI bone by groups with access to human OI tissue in order to clarify the relationship between increased porosity and reduced macroscopic mechanical integrity.

Treatment of proximal interphalangeal joint flexion contracture: Combined static and dynamic orthotic intervention compared with other therapy intervention: randomized controlled trial

Purpose To test the effectiveness of static and dynamic orthoses using them as an exclusive treatment for proximal interphalangeal (PIP) joint flexion contracture compared with other hand therapy conservative treatments described in the literature. Methods 60 patients who used orthoses were compared with a control group that received other hand therapy treatments. Clinical assessments were measured before the experiment and 3 months after and included active PIP joint extension and function. Results A significant improvement in the extension active range of motion at the PIP joint in the second measurement was found in both groups, but it was significantly greater in the experimental group. Improvement in function (Disabilities of the Arm, Shoulder, and Hand score) between the first and second assessment was similar in the control and experimental groups. Conclusions Using night progressive static and daily dynamic orthoses as an exclusive treatment during the proliferative phase led to significant improvements in the PIP joint active extension, but the improvement did not correlate with increased function as perceived by the patient.

Hierarchical clustering of the genetic connectivity matrix reveals the network topology of gene action on brain microstructure: An N=531 twin study

Genetic correlation (rg) analysis determines how much of the correlation between two measures is due to common genetic influences. In an analysis of 4 Tesla diffusion tensor images (DTI) from 531 healthy young adult twins and their siblings, we generalized the concept of genetic correlation to determine common genetic influences on white matter integrity, measured by fractional anisotropy (FA), at all points of the brain, yielding an NxN genetic correlation matrix rg(x,y) between FA values at all pairs of voxels in the brain. With hierarchical clustering, we identified brain regions with relatively homogeneous genetic determinants, to boost the power to identify causal single nucleotide polymorphisms (SNP). We applied genome-wide association (GWA) to assess associations between 529,497 SNPs and FA in clusters defined by hubs of the clustered genetic correlation matrix. We identified a network of genes, with a scale-free topology, that influences white matter integrity over multiple brain regions.

Assessment of dynamic susceptibility contrast cerebral blood flow response to amphetamine challenge: A human pharmacological magnetic resonance imaging study at 1.5 and 4 T

Pharmacological MRI (phMRI) techniques can be used to monitor the neurophysiological effects of central nervous system (CNS) active drugs. In this study, we investigated whether dynamic susceptibility contrast (DSC) perfusion imaging employing the use of superparamagnetic iron oxide nanoparticles (Resovist) could be used to measure hemodynamic response to d-amphetamine challenge in human subjects at both 1.5 and 4 T. Significant changes in cerebral blood flow (CBF) were found in focal regions associated with the nigrostriatal circuit and mesolimbic and mesocortical dopaminergic pathways. More significant CBF responses were found at higher field strength, mainly within striatal structures. The results from this study indicate that DSC perfusion imaging using Resovist can be used to assess the efficacy of CNS-active drugs and may play a role in the development of novel psychiatric therapies at the preclinical level. © 2005 Wiley-Liss, Inc.

Optimum position of steel outrigger system for high rise composite buildings subjected to wind loads

The responses of composite buildings under wind loads clearly become more critical as the building becomes taller, less stiff and more lightweight. When the composite building increases in height, the stiffness of the structure becomes more important factor and introduction to belt truss and outrigger system is often used to provide sufficient lateral stiffness to the structure. Most of the research works to date is limited to reinforced concrete building with outrigger system of concrete structure, simple building plan layout, single height of a building, one direction wind and single level of outrigger arrangement. There is a scarcity in research works about the effective position of outrigger level on composite buildings under lateral wind loadings when the building plan layout, height and outrigger arrangement are varied. The aim of this paper is to determine the optimum location of steel belt and outrigger systems by using different arrangement of single and double level outrigger for different size, shape and height of composite building. In this study a comprehensive finite element modelling of composite building prototypes is carried out, with three different layouts (Rectangular, Octagonal and L shaped) and for three different storey (28, 42 and 57-storey). Models are analysed for dynamic cyclonic wind loads with various combination of steel belt and outrigger bracings. It is concluded that the effectiveness of the single and double level steel belt and outrigger bracing are varied based on their positions for different size, shape and height of composite building.

A dynamic real time scheduling methodology for the emergency department

This project constructs a scheduling solution for the Emergency Department. The schedules are generated in real-time to adapt to new patient arrivals and changing conditions. An integrated scheduling formulation assigns patients to beds and treatment tasks to resources. The schedule efficiency is assessed using waiting time and total care time experienced by patients. The solution algorithm incorporates dispatch rules, meta-heuristics and a new extended disjunctive graph formulation which provide high quality solutions in a fast time-frame for real time decision support. This algorithm can be implemented in an electronic patient management system to improve patient flow in the Emergency Department.

Somewhere between haste and delay... Investigating the interactions of road users and pedestrians in a dynamic rail level crossing environment

There are currently 23,500 level crossings in Australia, broadly divided into one of two categories: active level crossings which are fully automatic and have boom barriers, alarm bells, flashing lights, and pedestrian gates; and passive level crossings, which are not automatic and aim to control road and pedestrianised walkways solely with stop and give way signs. Active level crossings are considered to be the gold standard for transport ergonomics when grade separation (i.e. constructing an over- or underpass) is not viable. In Australia, the current strategy is to annually upgrade passive level crossings with active controls but active crossings are also associated with traffic congestion, largely as a result of extended closure times. The percentage of time level crossings are closed to road vehicles during peak periods increases with the rise in the frequency of train services. The popular perception appears to be that once a level crossing is upgraded, one is free to wipe their hands and consider the job done. However, there may also be environments where active protection is not enough, but where the setting may not justify the capital costs of grade separation. Indeed, the associated congestion and traffic delay could compromise safety by contributing to the risk taking behaviour by motorists and pedestrians. In these environments it is important to understand what human factor issues are present and ask the question of whether a one size fits all solution is indeed the most ergonomically sound solution for today’s transport needs.

A dynamic navigation model for unmanned aircraft systems and an application to autonomous front-on environmental sensing and photography using low-cost sensor systems

This paper presents an unmanned aircraft system (UAS) that uses a probabilistic model for autonomous front-on environmental sensing or photography of a target. The system is based on low-cost and readily-available sensor systems in dynamic environments and with the general intent of improving the capabilities of dynamic waypoint-based navigation systems for a low-cost UAS. The behavioural dynamics of target movement for the design of a Kalman filter and Markov model-based prediction algorithm are included. Geometrical concepts and the Haversine formula are applied to the maximum likelihood case in order to make a prediction regarding a future state of a target, thus delivering a new waypoint for autonomous navigation. The results of the application to aerial filming with low-cost UAS are presented, achieving the desired goal of maintained front-on perspective without significant constraint to the route or pace of target movement.

Shear strength and stiffness of crest-fixed steel claddings

Diaphragm action of crest-fixed profiled steel claddings is present in low-rise buildings whether the designer acknowledges it or not. For the designers to take advantage of the diaphragm strength of the crest-fixed steel claddings in the design of low-rise buildings in a similar manner to valley-fixed claddings, and to design the buildings based on the true behaviour rather than the assumed behaviour, shear/racking behaviour of the three trapezoidal and corrugated steel claddings commonly used at present was investigated using large scale experiments. Crest-fixed claddings (up to a maximum size of 6 x 6.2m) with different aspect ratio and fastening systems were tested to failure, based on which suitable shear strength and stiffness values have been proposed for these claddings as they are used at present. A simple analytical model combined with basic connection data from small scale experiments was used to predict the shear strength of tested panels. Currently attempts are being made to develop general design formulae to determine shear strength and stiffness of crest-fixed steel claddings...

Hyaluronic acid enhances the mechanical properties of tissue-engineered cartilage constructs

There is a need for materials that are well suited for cartilage tissue engineering. Hydrogels have emerged as promising biomaterials for cartilage repair, since, like cartilage, they have high water content, and they allow cells to be encapsulated within the material in a genuinely three-dimensional microenvironment. In this study, we investigated the mechanical properties of tissue-engineered cartilage constructs using in vitro culture models incorporating human chondrocytes from osteoarthritis patients. We evaluated hydrogels formed from mixtures of photocrosslinkable gelatin-methacrylamide (Gel-MA) and varying concentrations (0–2%) of hyaluronic acid methacrylate (HA-MA). Initially, only small differences in the stiffness of each hydrogel existed. After 4 weeks of culture, and to a greater extent 8 weeks of culture, HA-MA had striking and concentration dependent impact on the changes in mechanical properties. For example, the initial compressive moduli of cell-laden constructs with 0 and 1% HA-MA were 29 and 41 kPa, respectively. After 8 weeks of culture, the moduli of these constructs had increased to 66 and 147 kPa respectively, representing a net improvement of 69 kPa for gels with 1% HA-MA. Similarly the equilibrium modulus, dynamic modulus, failure strength and failure strain were all improved in constructs containing HA-MA. Differences in mechanical properties did not correlate with glycosaminoglycan content, which did not vary greatly between groups, yet there were clear differences in aggrecan intensity and distribution as assessed using immunostaining. Based on the functional development with time in culture using human chondrocytes, mixtures of Gel-MA and HA-MA are promising candidates for cartilage tissue-engineering applications.

Adjustable stiffness, external fixator for the rat femur osteotomy and segmental bone defect models

The mechanical environment around the healing of broken bone is very important as it determines the way the fracture will heal. Over the past decade there has been great clinical interest in improving bone healing by altering the mechanical environment through the fixation stability around the lesion. One constraint of preclinical animal research in this area is the lack of experimental control over the local mechanical environment within a large segmental defect as well as osteotomies as they heal. In this paper we report on the design and use of an external fixator to study the healing of large segmental bone defects or osteotomies. This device not only allows for controlled axial stiffness on the bone lesion as it heals, but it also enables the change of stiffness during the healing process in vivo. The conducted experiments have shown that the fixators were able to maintain a 5 mm femoral defect gap in rats in vivo during unrestricted cage activity for at least 8 weeks. Likewise, we observed no distortion or infections, including pin infections during the entire healing period. These results demonstrate that our newly developed external fixator was able to achieve reproducible and standardized stabilization, and the alteration of the mechanical environment of in vivo rat large bone defects and various size osteotomies. This confirms that the external fixation device is well suited for preclinical research investigations using a rat model in the field of bone regeneration and repair.

Dynamic, invivo, real-time detection of retinal oxidative status in a model of elevated intraocular pressure using a novel, reversibly responsive, profluorescent nitroxide probe

Changes to the redox status of biological systems have been implicated in the pathogenesis of a wide variety of disorders including cancer, Ischemia-reperfusion (I/R) injury and neurodegeneration. In times of metabolic stress e.g. ischaemia/reperfusion, reactive oxygen species (ROS) production overwhelms the intrinsic antioxidant capacity of the cell, damaging vital cellular components. The ability to quantify ROS changes in vivo, is therefore essential to understanding their biological role. Here we evaluate the suitability of a novel reversible profluorescent probe containing a redox-sensitive nitroxide moiety (methyl ester tetraethylrhodamine nitroxide, ME-TRN), as an in vivo, real-time reporter of retinal oxidative status. The reversible nature of the probe's response offers the unique advantage of being able to monitor redox changes in both oxidizing and reducing directions in real time. After intravitreal administration of the ME-TRN probe, we induced ROS production in rat retina using an established model of complete, acute retinal ischaemia followed by reperfusion. After restoration of blood flow, retinas were imaged using a Micron III rodent fundus fluorescence imaging system, to quantify the redox-response of the probe. Fluorescent intensity declined during the first 60 min of reperfusion. The ROS-induced change in probe fluorescence was ameliorated with the retinal antioxidant, lutein. Fluorescence intensity in non-Ischemia eyes did not change significantly. This new probe and imaging technology provide a reversible and real-time response to oxidative changes and may allow the in vivo testing of antioxidant therapies of potential benefit to a range of diseases linked to oxidative stress