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.

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.

A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if an s-stage SRK contains Stratonovich integrals up to order p then the strong order of the SRK cannot exceed min{(p + 1)/2, (s - 1)/2), p greater than or equal to 2, s greater than or equal to 3 or 1 if p = 1.

Performance characterization of VGCF/epoxy nanocomposite sensors under static load cycles and in static structural health monitoring

Compared to conventional metal-foil strain gauges, nanocomposite piezoresistive strain sensors have demonstrated high strain sensitivity and have been attracting increasing attention in recent years. To fulfil their ultimate success, the performance of vapor growth carbon fiber (VGCF)/epoxy nanocomposite strain sensors subjected to static cyclic loads was evaluated in this work. A strain-equivalent quantity (resistance change ratio) in cantilever beams with intentionally induced notches in bending was evaluated using the conventional metal-foil strain gauges and the VGCF/epoxy nanocomposite sensors. Compared to the metal-foil strain gauges, the nanocomposite sensors are much more sensitive to even slight structural damage. Therefore, it was confirmed that the signal stability, reproducibility, and durability of these nanocomposite sensors are very promising, leading to the present endeavor to apply them for static structural health monitoring.

Advanced practice nursing role development : factor analysis of a modified role delineation tool

Aim his study reports the use of exploratory factor analysis to determine construct validity of a modified advanced practice role delineation tool. Background Little research exists on specific activities and domains of practice within advanced practice nursing roles, making it difficult to define service parameters of this level of nursing practice. A valid and reliable tool would assist those responsible for employing or deploying advanced practice nurses by identifying and defining their service profile. This is the third paper from a multi-phase Australian study aimed at assigning advanced practice roles. Methods A postal survey was conducted of a random sample of state government employed Registered nurses and midwives, across various levels and grades of practice in the state of Queensland, Australia, using the modified Advanced Practice Role Delineation tool. Exploratory factor analysis, using principal axis factoring was undertaken to examine factors in the modified tool. Cronbach’s alpha coefficient determined reliability of the overall scale and identified factors. Results There were 658 responses (42% response rate). The five factors found with loadings of ≥.400 for 40 of the 41 APN activities were similar to the five domains in the Strong model. Cronbach’s alpha coefficient was .94 overall and for the factors ranged from 0.83 to 0.95. Conclusion Exploratory factor analysis of the modified tool supports validity of the five domains of the original tool. Further investigation will identify use of the tool in a broader healthcare environment.

Effect of driving conditions and suspension parameters on dynamic load-sharing of longitudinal-connected air suspensions

The objective of this research was to investigate the effects of driving conditions and suspension parameters on dynamic load-sharing of longitudinal-connected air suspensions of a tri-axle semi-trailer. A novel nonlinear model of a multi-axle semi-trailer with longitudinal-connected air suspension was formulated based on fluid mechanics and thermodynamics and was validated through test results. The effects of driving conditions and suspension parameters on dynamic load-sharing and road-friendliness of the semi-trailer were analyzed. Simulation results indicate that the road-friendliness metric-DLC (dynamic load coefficient) is not always in accordance with the load-sharing metric-DLSC (dynamic load-sharing coefficient). The effect of employing larger air lines and connectors on the DLSC optimization ratio gives varying results as road roughness increases and as driving speed increases. When the vehicle load reduces, or the static pressure increases, the DLSC optimization ratio declines monotonically. The results also indicate that if the air line diameter is always assumed to be larger than the connector diameter, the influence of air line diameter on load-sharing is more significant than that of the connector.

Load-unloading response of intact and artificially degraded articular cartilage correlated with near infrared (NIR) absorption spectra

The conventional mechanical properties of articular cartilage, such as compressive stiffness, have been demonstrated to be limited in their capacity to distinguish intact (visually normal) from degraded cartilage samples. In this paper, we explore the correlation between a new mechanical parameter, namely the reswelling of articular cartilage following unloading from a given compressive load, and the near infrared (NIR) spectrum. The capacity to distinguish mechanically intact from proteoglycan-depleted tissue relative to the "reswelling" characteristic was first established, and the result was subsequently correlated with the NIR spectral data of the respective tissue samples. To achieve this, normal intact and enzymatically degraded samples were subjected to both NIR probing and mechanical compression based on a load-unload-reswelling protocol. The parameter δ(r), characteristic of the osmotic "reswelling" of the matrix after unloading to a constant small load in the order of the osmotic pressure of cartilage, was obtained for the different sample types. Multivariate statistics was employed to determine the degree of correlation between δ(r) and the NIR absorption spectrum of relevant specimens using Partial Least Squared (PLS) regression. The results show a strong relationship (R(2)=95.89%, p<0.0001) between the spectral data and δ(r). This correlation of δ(r) with NIR spectral data suggests the potential for determining the reswelling characteristics non-destructively. It was also observed that δ(r) values bear a significant relationship with the cartilage matrix integrity, indicated by its proteoglycan content, and can therefore differentiate between normal and artificially degraded proteoglycan-depleted cartilage samples. It is therefore argued that the reswelling of cartilage, which is both biochemical (osmotic) and mechanical (hydrostatic pressure) in origin, could be a strong candidate for characterizing the tissue, especially in regions surrounding focal cartilage defects in joints.

A wide area monitoring system based load restoration method

Restoring a large-scale power system has always been a complicated and important issue. A lot of research work has been done on different aspects of the whole power system restoration procedure. However, more time will be required to complete the power system restoration process in an actual situation if accurate and real-time system data cannot be obtained. With the development of the wide area monitoring system (WAMS), power system operators are capable of accessing to more accurate data in the restoration stage after a major outage. The ultimate goal of the system restoration is to restore as much load as possible while in the shortest period of time after a blackout, and the restorable load can be estimated by employing WAMS. Moreover, discrete restorable loads are employed considering the limited number of circuit-breaker operations and the practical topology of distribution systems. In this work, a restorable load estimation method is proposed employing WAMS data after the network frame has been reenergized, and WAMS is also employed to monitor the system parameters in case the newly recovered system becomes unstable again. The proposed method has been validated with the New England 39-Bus system and an actual power system in Guangzhou, China.

Numerical studies of load bearing LSF walls under realistic design fire conditions

Fire safety of light gauge steel frame (LSF) stud walls is important in the design of buildings. Currently LSF walls are increasingly used in the building industry, and are usually made of cold-formed and thin-walled steel studs that are fire-protected by two layers of plasterboard on both sides. Many experimental and numerical studies have been undertaken to investigate the fire performance of load bearing LSF walls under standard fire conditions. However, the standard time-temperature curve does not represent the fire load present in typical residential and commercial buildings that include considerable amount of thermoplastic materials. Real building fires are unlikely to follow a standard time-temperature curve. However, only limited research has been undertaken to investigate the fire performance of load bearing LSF walls under realistic design fire conditions. Therefore in this research, finite element thermal models of the traditional LSF wall panels without cavity insulation and the new LSF composite wall panels were developed to simulate their fire performance under recently developed realistic design fire curves. Suitable thermal properties were proposed for plasterboards and insulations based on laboratory tests and literature review. The developed models were then validated by comparing their thermal performance results with available results from realistic design fire tests, and were later used in parametric studies. This paper presents the details of the developed finite element thermal models of load bearing LSF wall panels under realistic design fire time-temperature curves and the re-sults. It shows that finite element thermal models can be used to predict the fire performance of load bearing LSF walls with varying configurations of insulations and plasterboards under realistic design fires. Failure times of load bearing LSF walls were also predicted based on the results from finite element thermal analyses.

Exploring the validity and predictive power of an extended volunteer functions inventory within the context of episodic skilled volunteering by retirees

The current study examined the structure of the volunteer functions inventory within a sample of older individuals (N = 187). The career items were replaced with items examining the concept of continuity of work, a potentially more useful and relevant concept for this population. Factor analysis supported a four factor solution, with values, social and continuity emerging as single factors and enhancement and protective items loading together on a single factor. Understanding items did not load highly on any factor. The values and continuity functions were the only dimensions to emerge as predictors of intention to volunteer. This research has important implications for understanding the motivation of older adults to engage in contemporary volunteering settings.

Attitudes, Ideologies and Self-Organisation : Information Load Minimisation in Multi-Agent Decision Making

Sophisticated models of human social behaviour are fast becoming highly desirable in an increasingly complex and interrelated world. Here, we propose that rather than taking established theories from the physical sciences and naively mapping them into the social world, the advanced concepts and theories of social psychology should be taken as a starting point, and used to develop a new modelling methodology. In order to illustrate how such an approach might be carried out, we attempt to model the low elaboration attitude changes of a society of agents in an evolving social context. We propose a geometric model of an agent in context, where individual agent attitudes are seen to self-organise to form ideologies, which then serve to guide further agent-based attitude changes. A computational implementation of the model is shown to exhibit a number of interesting phenomena, including a tendency for a measure of the entropy in the system to decrease, and a potential for externally guiding a population of agents towards a new desired ideology.

A potential role for lamellar insulin-like growth factor-1 receptor in the pathogenesis of hyperinsulinaemic laminitis

The reason why a sustained high concentration of insulin induces laminitis in horses remains unclear. Cell proliferation occurs in the lamellae during insulin-induced laminitis and in other species high concentrations of insulin can activate receptors for the powerful cell mitogen, insulin-like growth factor (IGF)-1. The first aim of this study was to determine if IGF-1 receptors (IGF-1R) are activated in the hoof during insulin-induced laminitis. Gene expression for IGF-1R and the insulin receptor (InsR) was measured using qRT-PCR, in lamellar tissue from control horses and from horses undergoing a prolonged euglycaemic, hyperinsulinaemic clamp (p-EHC), during the mid-developmental (24 h) and acute (46 h) phases of insulin-induced laminitis. Gene expression for both receptors was decreased 13–32-fold (P < 0.05) at both time-points in the insulin-treated horses. A second aim was to determine if the down-regulation of the receptor genes could be accounted for by an increase in circulating IGF-1. Serum IGF-1 was measured at 0, 10, 25 and 46 h post-treatment in horses given a p-EHC for approximately 46 h, and in matched controls administered a balanced, electrolyte solution. There was no increase in serum IGF-1 concentrations during the p-EHC, consistent with down-regulation of both receptors by insulin. Stimulation of the IGF-1R by insulin may lead to inappropriate lamellar epidermal cell proliferation and lamellar weakening, a potential mechanism for hyperinsulinaemic laminitis. Targeting this receptor may provide insights into the pathogenesis or identify a novel therapy for hyperinsulinaemic laminitis.

Insulin and the insulin-like growth factor system : a novel theory for hyperinsulinemic laminitis pathogenesis

Research into hyperinsulinemic laminitis has progressed significantly in recent years with the use of the prolonged-euglycemic, hyperinsulinemic clamp (p-EHC). Previous investigations of laminitis pathophysiology have focused on digital vascular dysfunction, inflammation, altered glucose metabolism within the lamellae, and lamellar basement membrane breakdown by metalloproteinases. The etiopathogenesis of laminitis occurring in association with hyperinsulinemia is yet to be fully characterized, but it may not involve these mechanisms. Insulin stimulates cellular proliferation and can also affect other body systems, such as the insulin-like growth factor (IGF) system. Insulin-like growth factor-1 (IGF-1) is structurally homologous to insulin and, like insulin, binds with strong affinity to a specific tyrosine kinase receptor on the cell surface to produce its effects, which include promoting cell proliferation. Receptors for IGF-1 (IGF-1R) are present in the lamellar epidermis. An alternative theory for the pathogenesis of hyperinsulinemic laminitis is that uncontrolled cell proliferation, mediated through both the insulin receptor (InsR) and IGF-1R, leads to lengthening, weakening, and failure of the lamellae. An analysis of the proliferative activity of lamellar epidermal cells during the developmental and acute phases of hyperinsulinemic laminitis, and lamellar gene expression of the InsR and IGF-1R was undertaken.

Reduction in resting plasma granulysin as a marker of increased training load

Granulysin is a cytolytic granule protein released by natural killer cells and activated cytotoxic T lymphocytes. The influence of exercise training on circulating granulysin concentration is unknown, as is the relationship between granulysin concentration, natural killer cell number and natural killer cell cytotoxicity. We examined changes in plasma granulysin concentration, natural killer cell number and cytotoxicity following acute exercise and different training loads. Fifteen highly trained male cyclists completed a baseline 40-km cycle time trial (TT401) followed by five weeks of normal training and a repeat time trial (TT402). The cyclists then completed four days of high intensity training followed by another time trial (TT403) on day five. Following one final week of normal training cyclists completed another time trial (TT404). Fasting venous blood was collected before and after each time trial to determine granulysin concentration, natural killer cell number and natural killer cell cytotoxicity. Granulysin concentration increased significantly after each time trial (P<0.001). Pre-exercise granulysin concentration for TT403 was significantly lower than pre-exercise concentration for TT401 (-20.3 +/- 7.5%, P<0.026), TT402 (-16.7 +/- 4.3%, P<0.003) and 7T404 (-21 +/- 4.2%, P<0.001). Circulating natural killer cell numbers also increased significantly post-exercise for each time trial (P<0.001), however there was no significant difference across TT40 (P>0.05). Exercise did not significantly alter natural killer cell cytotoxicity on a per cell basis, and there were no significant differences between the four time trials. In conclusion, plasma granulysin concentration increases following moderate duration, strenuous exercise and is decreased in response to a short-term period of intensified training.