High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

Stationary processes for object detection and non-rigid structure-from-motion

Stationary processes are random variables whose value is a signal and whose distribution is invariant to translation in the domain of the signal. They are intimately connected to convolution, and therefore to the Fourier transform, since the covariance matrix of a stationary process is a Toeplitz matrix, and Toeplitz matrices are the expression of convolution as a linear operator. This thesis utilises this connection in the study of i) efficient training algorithms for object detection and ii) trajectory-based non-rigid structure-from-motion.

Cerebral cortex activation mapping upon electrical muscle stimulation by 32-channel time-domain functional near-infrared spectroscopy

The application of different EMS current thresholds on muscle activates not only the muscle but also peripheral sensory axons that send proprioceptive and pain signals to the cerebral cortex. A 32-channel time-domain fNIRS instrument was employed to map regional cortical activities under varied EMS current intensities applied on the right wrist extensor muscle. Eight healthy volunteers underwent four EMS at different current thresholds based on their individual maximal tolerated intensity (MTI), i.e., 10 % < 50 % < 100 % < over 100 % MTI. Time courses of the absolute oxygenated and deoxygenated hemoglobin concentrations primarily over the bilateral sensorimotor cortical (SMC) regions were extrapolated, and cortical activation maps were determined by general linear model using the NIRS-SPM software. The stimulation-induced wrist extension paradigm significantly increased activation of the contralateral SMC region according to the EMS intensities, while the ipsilateral SMC region showed no significant changes. This could be due in part to a nociceptive response to the higher EMS current intensities and result also from increased sensorimotor integration in these cortical regions.

Functional analysis of missense variants in the TRESK (KCNK18) K+ channel

A loss of function mutation in the TRESK K2P potassium channel (KCNK18), has recently been linked with typical familial migraine with aura. We now report the functional characterisation of additional TRESK channel missense variants identified in unrelated patients. Several variants either had no apparent functional effect, or they caused a reduction in channel activity. However, the C110R variant was found to cause a complete loss of TRESK function, yet is present in both sporadic migraine and control cohorts, and no variation in KCNK18 copy number was found. Thus despite the previously identified association between loss of TRESK channel activity and migraine in a large multigenerational pedigree, this finding indicates that a single non-functional TRESK variant is not alone sufficient to cause typical migraine and highlights the genetic complexity of this disorder. Migraine is a common, disabling neurological disorder with a genetic, environmental and in some cases hormonal component. It is characterized by attacks of severe, usually unilateral and throbbing headache, can be accompanied by nausea, vomiting and photophobia and is clinically divided into two main subtypes, migraine with aura (MA) when a migraine is accompanied by transient and reversible focal neurological symptoms and migraine without aura (MO)1. The multifactorial and clinical heterogeneity of the disorder have considerably hindered the identification of common migraine susceptibility genes and most of our current understanding comes from the studies of familial hemiplegic migraine (FHM), a rare monogenic autosomal dominant form of MA2. So far, the three susceptibility genes that have been convincingly identified in FHM families all encode ion channels or transporters: CACNA1A encoding the α1 subunit of the Cav2.1 calcium channel3, SCN1A encoding the Nav1.1 sodium channel4 and ATP1A2 encoding the α2 subunit of the Na+/K+ pump5. It is believed that mutations in these genes may lead to increased efflux of glutamate and potassium in the synapse and thereby cause migraine by rendering the brain more susceptible to cortical spreading depression (CSD)6 which is thought to play a role in initiating a migraine attack7,8. However, these genes have not to date been implicated in common forms of migraine9. Nevertheless, current opinion suggests that typical migraine, like FHM, is also disorder of neuronal excitability, ion homeostasis and neurotransmitter release10,11,12. Mutations in the SLC4A4 gene encoding the sodium-bicarbonate cotransporter NBCe1, have recently been implicated in several different forms of migraine13, and a variety of genes involved in glutamate homeostasis (PGCP, MTDH14 and LRP115) and a cation channel (TRPM8)15 have also recently been implicated in migraine via genome-wide association studies. Ion channels are therefore highly likely to play an important role in the pathogenesis of typical migraine. TRESK (KCNK18), is a member of the two-pore domain (K2P) family of potassium channels involved in the control of cellular electrical excitability16. Regulation of TRESK activity by the calcium-dependent phosphatase calcineurin17, as well as its expression in dorsal root ganglia (DRG)18 and trigeminal ganglia (TG)19,20 has led to a proposed role for this channel in a variety of pain pathways. In a recent study, a frameshift mutation (F139Wfsx24) in TRESK was identified in a large multigenerational pedigree where it co-segregated perfectly with typical MA and a significant genome-wide linkage LOD score of 3.0. Furthermore, functional analysis revealed that this mutation caused a complete loss of TRESK function and that the truncated subunit was also capable of down regulating wild-type channel function. This therefore highlighted KCNK18 as potentially important candidate gene and suggested that TRESK dysfunction might play a possible role in the pathogenesis of familial migraine with visual aura20. Additional screening for KCNK18 mutations in unrelated sporadic migraine and control cohorts also identified a number of other missense variants; R10G, A34V, C110R, S231P and A233V20. The A233V variant was found only in the control cohort, whilst A34V was identified in a single Australian migraine proband for which family samples were not available, but it was not detected in controls. By contrast, the R10G, C110R, and S231P variants were found in both migraineurs and controls in both cohorts. In this study, we have investigated the functional effect of these variants to further probe the potential association of TRESK dysfunction with typical migraine.

Parallel linear system solution and its application to railway power network simulation

The Streaming SIMD extension (SSE) is a special feature embedded in the Intel Pentium III and IV classes of microprocessors. It enables the execution of SIMD type operations to exploit data parallelism. This article presents improving computation performance of a railway network simulator by means of SSE. Voltage and current at various points of the supply system to an electrified railway line are crucial for design, daily operation and planning. With computer simulation, their time-variations can be attained by solving a matrix equation, whose size mainly depends upon the number of trains present in the system. A large coefficient matrix, as a result of congested railway line, inevitably leads to heavier computational demand and hence jeopardizes the simulation speed. With the special architectural features of the latest processors on PC platforms, significant speed-up in computations can be achieved.

A parallel solution to linear systems

Streaming SIMD Extensions (SSE) is a unique feature embedded in the Pentium III and IV classes of microprocessors. By fully exploiting SSE, parallel algorithms can be implemented on a standard personal computer and a theoretical speedup of four can be achieved. In this paper, we demonstrate the implementation of a parallel LU matrix decomposition algorithm for solving linear systems with SSE and discuss advantages and disadvantages of this approach based on our experimental study.

Coasting control of train operation by genetic algorithm

Balancing between the provision of high quality of service and running within a tight budget is one of the biggest challenges for most metro railway operators around the world. Conventionally, one possible approach for the operator to adjust the time schedule is to alter the stop time at stations, if other system constraints, such as traction equipment characteristic, are not taken into account. Yet it is not an effective, flexible and economical method because the run-time of a train simply cannot be extended without limitation, and a balance between run-time and energy consumption has to be maintained. Modification or installation of a new signalling system not only increases the capital cost, but also affects the normal train service. Therefore, in order to procure a more effective, flexible and economical means to improve the quality of service, optimisation of train performance by coasting point identification has become more attractive and popular. However, identifying the necessary starting points for coasting under the constraints of current service conditions is no simple task because train movement is attributed by a large number of factors, most of which are non-linear and inter-dependent. This paper presents an application of genetic algorithms (GA) to search for the appropriate coasting points and investigates the possible improvement on computation time and fitness of genes.

Processing load and the use of concrete representations and strategies for solving linear equations

This paper is a report of students' responses to instruction which was based on the use of concrete representations to solve linear equations. The sample consisted of 21 Grade 8 students from a middle-class suburban state secondary school with a reputation for high academic standards and innovative mathematics teaching. The students were interviewed before and after instruction. Interviews and classroom interactions were observed and videotaped. A qualitative analysis of the responses revealed that students did not use the materials in solving problems. The increased processing load caused by concrete representations is hypothesised as a reason.

Low frequency of CHEK2 1100delC allele in Australian multiple-case breast cancer families : functional analysis in heterozygous individuals

A protein-truncating variant of CHEK2, 1100delC, is associated with a moderate increase in breast cancer risk. We have determined the prevalence of this allele in index cases from 300 Australian multiple-case breast cancer families, 95% of which had been found to be negative for mutations in BRCA1 and BRCA2. Only two (0.6%) index cases heterozygous for the CHEK2 mutation were identified. All available relatives in these two families were genotyped, but there was no evidence of co-segregation between the CHEK2 variant and breast cancer. Lymphoblastoid cell lines established from a heterozygous carrier contained approximately 20% of the CHEK2 1100delC mRNA relative to wild-type CHEK2 transcript. However, no truncated CHK2 protein was detectable. Analyses of expression and phosphorylation of wild-type CHK2 suggest that the variant is likely to act by haploinsufficiency. Analysis of CDC25A degradation, a downstream target of CHK2, suggests that some compensation occurs to allow normal degradation of CDC25A. Such compensation of the 1100delC defect in CHEK2 might explain the rather low breast cancer risk associated with the CHEK2 variant, compared to that associated with truncating mutations in BRCA1 or BRCA2.

Inferior visual field reductions are associated with poorer functional status among older adults with glaucoma

Purpose: To examine the relationship between visual impairment and functional status in a community-dwelling sample of older adults with glaucoma. Methods: This study included 74 community-dwelling older adults with open-angle glaucoma (aged 74 ± 6 years). Assessment of central vision included high-contrast visual acuity and Pelli-Robson contrast sensitivity. Binocular integrated visual fields were derived from merged monocular Humphrey Field Analyser visual field plots. Functional status outcome measures included physical performance tests (6-min walk test, timed up and go test and lower limb strength), a physical activity questionnaire (Physical Activity Scale for the Elderly) and an overall functional status score. Correlation and linear regression analyses, adjusting for age and gender, examined the association between visual impairment and functional status outcomes. Results: Greater levels of visual impairment were significantly associated with lower levels of functional status among community-dwelling older adults with glaucoma, independent of age and gender. Specifically, lower levels of visual function were associated with slower timed up and go performance, weaker lower limb strength, lower self-reported physical activity, and lower overall functional status scores. Of the components of vision examined, the inferior visual field and contrast factors were the strongest predictors of these functional outcomes, whereas the superior visual field factor was not related to functional status. Conclusions: Greater visual impairment, particularly in the inferior visual field and loss of contrast sensitivity, was associated with poorer functional status among older adults with glaucoma. The findings of this study highlight the potential links between visual impairment and the onset of functional decline. Interventions which promote physical activity among older adults with glaucoma may assist in preventing functional decline, frailty and falls, and improve overall health and well-being.

Vision based control for fixed wing UAVs inspecting locally linear infrastructure using skid-to-turn maneuvers

The following paper proposes a novel application of Skid-to-Turn maneuvers for fixed wing Unmanned Aerial Vehicles (UAVs) inspecting locally linear infrastructure. Fixed wing UAVs, following the design of manned aircraft, traditionally employ Bank-to-Turn maneuvers to change heading and thus direction of travel. Commonly overlooked is the effect these maneuvers have on downward facing body fixed sensors, which as a result of bank, point away from the feature during turns. By adopting Skid-to-Turn maneuvers, the aircraft is able change heading whilst maintaining wings level flight, thus allowing body fixed sensors to maintain a downward facing orientation. Eliminating roll also helps to improve data quality, as sensors are no longer subjected to the swinging motion induced as they pivot about an axis perpendicular to their line of sight. Traditional tracking controllers that apply an indirect approach of capturing ground based data by flying directly overhead can also see the feature off center due to steady state pitch and roll required to stay on course. An Image Based Visual Servo controller is developed to address this issue, allowing features to be directly tracked within the image plane. Performance of the proposed controller is tested against that of a Bank-to-Turn tracking controller driven by GPS derived cross track error in a simulation environment developed to simulate the field of view of a body fixed camera.

Safety enhancement of operator protection systems on self-propelled mining equipment

In the long term, with development of skill, knowledge, exposure and confidence within the engineering profession, rigorous analysis techniques have the potential to become a reliable and far more comprehensive method for design and verification of the structural adequacy of OPS, write Nimal J Perera, David P Thambiratnam and Brian Clark. This paper explores the potential to enhance operator safety of self-propelled mechanical plant subjected to roll over and impact of falling objects using the non-linear and dynamic response simulation capabilities of analytical processes to supplement quasi-static testing methods prescribed in International and Australian Codes of Practice for bolt on Operator Protection Systems (OPS) that are post fitted. The paper is based on research work carried out by the authors at the Queensland University of Technology (QUT) over a period of three years by instrumentation of prototype tests, scale model tests in the laboratory and rigorous analysis using validated Finite Element (FE) Models. The FE codes used were ABAQUS for implicit analysis and LSDYNA for explicit analysis. The rigorous analysis and dynamic simulation technique described in the paper can be used to investigate the structural response due to accident scenarios such as multiple roll over, impact of multiple objects and combinations of such events and thereby enhance the safety and performance of Roll Over and Falling Object Protection Systems (ROPS and FOPS). The analytical techniques are based on sound engineering principles and well established practice for investigation of dynamic impact on all self propelled vehicles. They are used for many other similar applications where experimental techniques are not feasible.

Functional and advanced functional and causal relationship diagrams for remote condition monitoring

Analysing the condition of an asset is a big challenge as there can be many aspects which can contribute to the overall functional reliability of the asset that have to be considered. In this paper we propose a two-step functional and causal relationship diagram (FCRD) to address this problem. In the first step, the FCRD is designed to facilitate the analysis of the condition of an asset by evaluating the interdependence (functional and causal) relationships between different components of the asset with the help of a relationship diagram. This is followed by the advanced FCRD (AFCRD) which refines the information from the FCRD into a comprehensive and manageable format. This new two-step methodology for asset condition monitoring is tested and validated for the case of a water treatment plant. © IMechE 2012.

The relationship between chronic disease self-efficacy and nutritional status, functional ability and quality of life in older adults at risk of hospital readmission

Background and significance: Older adults with chronic diseases are at increasing risk of hospital admission and readmission. Approximately 75% of adults have at least one chronic condition, and the odds of developing a chronic condition increases with age. Chronic diseases consume about 70% of the total Australian health expenditure, and about 59% of hospital events for chronic conditions are potentially preventable. These figures have brought to light the importance of the management of chronic disease among the growing older population. Many studies have endeavoured to develop effective chronic disease management programs by applying social cognitive theory. However, limited studies have focused on chronic disease self-management in older adults at high risk of hospital readmission. Moreover, although the majority of studies have covered wide and valuable outcome measures, there is scant evidence on examining the fundamental health outcomes such as nutritional status, functional status and health-related quality of life. Aim: The aim of this research was to test social cognitive theory in relation to self-efficacy in managing chronic disease and three health outcomes, namely nutritional status, functional status, and health-related quality of life, in older adults at high risk of hospital readmission. Methods: A cross-sectional study design was employed for this research. Three studies were undertaken. Study One examined the nutritional status and validation of a nutritional screening tool; Study Two explored the relationships between participants. characteristics, self-efficacy beliefs, and health outcomes based on the study.s hypothesized model; Study Three tested a theoretical model based on social cognitive theory, which examines potential mechanisms of the mediation effects of social support and self-efficacy beliefs. One hundred and fifty-seven patients aged 65 years and older with a medical admission and at least one risk factor for readmission were recruited. Data were collected from medical records on demographics, medical history, and from self-report questionnaires. The nutrition data were collected by two registered nurses. For Study One, a contingency table and the kappa statistic was used to determine the validity of the Malnutrition Screening Tool. In Study Two, standard multiple regression, hierarchical multiple regression and logistic regression were undertaken to determine the significant influential predictors for the three health outcome measures. For Study Three, a structural equation modelling approach was taken to test the hypothesized self-efficacy model. Results: The findings of Study One suggested that a high prevalence of malnutrition continues to be a concern in older adults as the prevalence of malnutrition was 20.6% according to the Subjective Global Assessment. Additionally, the findings confirmed that the Malnutrition Screening Tool is a valid nutritional screening tool for hospitalized older adults at risk of readmission when compared to the Subjective Global Assessment with high sensitivity (94%), and specificity (89%) and substantial agreement between these two methods (k = .74, p < .001; 95% CI .62-.86). Analysis data for Study Two found that depressive symptoms and perceived social support were the two strongest influential factors for self-efficacy in managing chronic disease in a hierarchical multiple regression. Results of multivariable regression models suggested advancing age, depressive symptoms and less tangible support were three important predictors for malnutrition. In terms of functional status, a standard regression model found that social support was the strongest predictor for the Instrumental Activities of Daily Living, followed by self-efficacy in managing chronic disease. The results of standard multiple regression revealed that the number of hospital readmission risk factors adversely affected the physical component score, while depressive symptoms and self-efficacy beliefs were two significant predictors for the mental component score. In Study Three, the results of the structural equation modelling found that self-efficacy partially mediated the effect of health characteristics and depression on health-related quality of life. The health characteristics had strong direct effects on functional status and body mass index. The results also indicated that social support partially mediated the relationship between health characteristics and functional status. With regard to the joint effects of social support and self-efficacy, social support fully mediated the effect of health characteristics on self-efficacy, and self-efficacy partially mediated the effect of social support on functional status and health-related quality of life. The results also demonstrated that the models fitted the data well with relative high variance explained by the models, implying the hypothesized constructs under discussion were highly relevant, and hence the application for social cognitive theory in this context was supported. Conclusion: This thesis highlights the applicability of social cognitive theory on chronic disease self-management in older adults at risk of hospital readmission. Further studies are recommended to validate and continue to extend the development of social cognitive theory on chronic disease self-management in older adults to improve their nutritional and functional status, and health-related quality of life.