Computational aspects of the numerical solution of SDEs

In the last 30 to 40 years, many researchers have combined to build the knowledge base of theory and solution techniques that can be applied to the case of differential equations which include the effects of noise. This class of ``noisy'' differential equations is now known as stochastic differential equations (SDEs). Markov diffusion processes are included within the field of SDEs through the drift and diffusion components of the Itô form of an SDE. When these drift and diffusion components are moderately smooth functions, then the processes' transition probability densities satisfy the Fokker-Planck-Kolmogorov (FPK) equation -- an ordinary partial differential equation (PDE). Thus there is a mathematical inter-relationship that allows solutions of SDEs to be determined from the solution of a noise free differential equation which has been extensively studied since the 1920s. The main numerical solution technique employed to solve the FPK equation is the classical Finite Element Method (FEM). The FEM is of particular importance to engineers when used to solve FPK systems that describe noisy oscillators. The FEM is a powerful tool but is limited in that it is cumbersome when applied to multidimensional systems and can lead to large and complex matrix systems with their inherent solution and storage problems. I show in this thesis that the stochastic Taylor series (TS) based time discretisation approach to the solution of SDEs is an efficient and accurate technique that provides transition and steady state solutions to the associated FPK equation. The TS approach to the solution of SDEs has certain advantages over the classical techniques. These advantages include their ability to effectively tackle stiff systems, their simplicity of derivation and their ease of implementation and re-use. Unlike the FEM approach, which is difficult to apply in even only two dimensions, the simplicity of the TS approach is independant of the dimension of the system under investigation. Their main disadvantage, that of requiring a large number of simulations and the associated CPU requirements, is countered by their underlying structure which makes them perfectly suited for use on the now prevalent parallel or distributed processing systems. In summary, l will compare the TS solution of SDEs to the solution of the associated FPK equations using the classical FEM technique. One, two and three dimensional FPK systems that describe noisy oscillators have been chosen for the analysis. As higher dimensional FPK systems are rarely mentioned in the literature, the TS approach will be extended to essentially infinite dimensional systems through the solution of stochastic PDEs. In making these comparisons, the advantages of modern computing tools such as computer algebra systems and simulation software, when used as an adjunct to the solution of SDEs or their associated FPK equations, are demonstrated.

Optimal H∞ insulin injection control for blood glucose regulation in diabetic patients

The theory of H/sup /spl infin// optimal control has the feature of minimizing the worst-case gain of an unknown disturbance input. When appropriately modified, the theory can be used to design a "switching" controller that can be applied to insulin injection for blood glucose (BG) regulation. The "switching" controller is defined by a collection of basic insulin rates and a rule that switches the insulin rates from one value to another. The rule employed an estimation of BG from noisy measurements, and the subsequent optimization of a performance index that involves the solution of a "jump" Riccati differential equation and a discrete-time dynamic programming equation. With an appropriate patient model, simulation studies have shown that the controller could correct BG deviation using clinically acceptable insulin delivery rates.

Reaching out to promote physical activity in Australia: a statewide randomized controlled trial of a stage-targeted intervention

Purpose. This study examined the broader use of a print-media intervention, which was previously shown to be effective at promoting physical activity to participants recruited from a regional Australian community, as a strategy suitable for a more diverse statewide population sample.
Methods. Participants were randomly selected adults who responded to a telephone interview conducted by the New South Wales Health Department and consented to Participate in a randomized controlled trial. Consenters were allocated to either intervention (n = 361) or control (n = 358) conditions. The intervention, a personalized letter plus stage-targeted booklets, was sent 1 week postbaseline. Data were collected via telephone interview at baseline and 2 and 8 months and were analyzed using repeated measures analysis of variance (ANOVA) and mean squared statistics.
Results. The groups were similar at baseline (mean age 43 +/- 3 years; 64 % women). Process evaluation showed high intervention recall (76 % at 2 months) and high follow-up response rates (> 85 % at 8 months) were achieved. Nonsignificant increases in physical activity were observed (Fl,719 = 2.18, p = .14).
Discussion. A single mailing of stage-targeted print materials was not effective in promoting increases in physical activity among participants selected from the statewide population. Future research could examine how the effectiveness of print media might be enhanced, possibly by using supplementary media, community-based prompts, or other incentives.

Dynamic advertising under vertical product differentiation

We investigate a dynamic advertising model where product quality is endogenous. In the differential game between single-product firms, there exists a parameter range where the low-quality firm uses a more efficient advertising technology and earns higher profits than the rival. Moreover, we show that equilibrium qualities are the same under duopoly, multiproduct monopoly, and social planning, the only distortion being concerned with the output levels.

A multifaceted pharmacist intervention to improve antihypertensive adherence: a cluster-randomized, controlled trial (HAPPy trial)

About half of all patients taking antihypertensives discontinue treatment by 12 months. There is potential for substantial health gains at both individual and population levels through improved treatment adherence. The objective was to evaluate a community pharmacist intervention to improve adherence with antihypertensive medicines with a view to improving blood pressure (BP) control.

Reduced order functional observers with application to partial state estimation of linear systems with input delay

Reduced order multi-functional observer design for multi-input multi-utput (MIMO) linear time-invariant (LTI) systems with constant delayed inputs is studied. This research is useful in the input estimation of LTI systems with actuator delay, as well as system monitoring and fault detection of these systems. Two approaches for designing an asymptotically stable functional observer for the system are proposed: delay-dependent and delay-free. The delay-dependent observer is infinite-dimensional, while the delay-free structure is finite-dimensional. Moreover, since the delay-free observer does not require any information on the time delay, it is more practical in real applications. However, the delay-dependent observer contains less restrictive assumptions and covers more variety of systems. The proposed observer design schemes are novel, simple to implement, and have improved numerical features compared to some of the other available approaches to design (unknown-input) functional observers. In addition, the proposed observers usually possess lower order than ordinary Luenberger observers, and the design schemes do not need the observability or detectability requirements of the system. The necessary and sufficient conditions of the existence of an asymptoticobserver in each scenario are explored. The extensions of the proposed observers to systems with multiple delayed-inputs are also discussed. Several numerical examples and simulation results are employed to support our theories.

School based education programme to reduce salt intake in children and their families (School-EduSalt): cluster randomised controlled trial

Objective To determine whether an education programme targeted at schoolchildren could lower salt intake in children and their families. Design Cluster randomised controlled trial, with schools randomly assigned to either the intervention or control group. Setting 28 primary schools in urban Changzhi, northern China. Participants 279 children in grade 5 of primary school, with mean age of 10.1; 553 adult family members (mean age 43.8). Intervention Children in the intervention group were educated on the harmful effects of salt and how to reduce salt intake within the schools' usual health education lessons. Children then delivered the salt reduction message to their families. The intervention lasted for one school term (about 3.5 months). Main outcome measures The primary outcome was the difference between the groups in the change in salt intake (as measured by 24 hour urinary sodium excretion) from baseline to the end of the trial. The secondary outcome was the difference between the two groups in the change in blood pressure. Results At baseline, the mean salt intake in children was 7.3 (SE 0.3) g/day in the intervention group and 6.8 (SE 0.3) g/day in the control group. In adult family members the salt intakes were 12.6 (SE 0.4) and 11.3 (SE 0.4) g/day, respectively. During the study there was a reduction in salt intake in the intervention group, whereas in the control group salt intake increased. The mean effect on salt intake for intervention versus control group was -1.9 g/day (95% confidence interval -2.6 to -1.3 g/day; P<0.001) in children and -2.9 g/day (-3.7 to -2.2 g/ day; P<0.001) in adults. The mean effect on systolic blood pressure was -0.8 mm Hg (-3.0 to 1.5 mm Hg; P=0.51) in children and -2.3 mm Hg (-4.5 to -0.04 mm Hg; P<0.05) in adults. Conclusions An education programme delivered to primary school children as part of the usual curriculum is effective in lowering salt intake in children and their families. This offers a novel and important approach to reducing salt intake in a population in which most of the salt in the diet is added by consumers.

Exponential stabilization of non-autonomous delayed neural networks via Riccati equations

This paper concerns with the problem of exponential stabilization for a class of non-autonomous neural networks with mixed discrete and distributed time-varying delays. Two cases of discrete time-varying delay, namely (i) slowly time-varying; and (ii) fast time-varying, are considered. By constructing an appropriate Lyapunov-Krasovskii functional in case (i) and utilizing the Razumikhin technique in case (ii), we establish some new delay-dependent conditions for designing a memoryless state feedback controller which stabilizes the system with an exponential convergence of the resulting closed-loop system. The proposed conditions are derived through solutions of some types of Riccati differential equations. Applications to control a class of autonomous neural networks with mixed time-varying delays are also discussed in this paper. Some numerical examples are provided to illustrate the effectiveness of the obtained results.

Changing risk behaviours for non-communicable disease in New Zealand working men - is workplace intervention effective?

Aims. To evaluate the effectiveness of a health promotion
programme targeting dietary behaviours and physical
activity among male hourly-paid workers and to explore
demographic and attitudinal influences on dietary patterns
at baseline.
Methods. A controlled field trial compared workers at one
intervention and one control worksite. The intervention
comprised nutrition displays in the cafeteria and monthly
30-minute workshops for six months. Key outcome
measures at six and twelve-months were self-reported
dietary and lifestyle behaviours, nutrition knowledge, body
mass index (BMI), waist circumference and blood pressure.
Results. 132 men at the intervention site and 121 men at the
control site participated in the study and a high retention rate
(94% at 6-months and 89% at 12-months) was achieved. At
baseline, 40% of the total sample (253) were obese, 30% had
elevated blood pressure, 59% indicated an excessive fat intake
and 92% did not meet the recommended vegetable and fruit
intake. The intervention reduced fat intake, increased
vegetable intake and physical activity, improved nutrition
knowledge and reduced systolic blood pressure when
compared to the control site. There was no difference in
change in mean BMI or waist circumference. Reduction in
BMI was associated with reduction in fat intake.
Discussion. Low intensity workplace intervention can
significantly improve reported health behaviours and
nutrition knowledge although the impact on more
objective measures of risk was variable. A longer duration
or more intensive intervention may be required to achieve
further reduction in risk factors.

Neonatal growth outcomes at birth and one month postpartum following in utero exposure to antidepressant medication

Objective: There is evidence of increasing prescription of antidepressant medication in pregnant women. This has arisen from the recognition of the importance of treating maternal depression. This must be balanced, however, with information on outcomes for infants and children exposed to antidepressants in pregnancy. The aim of the present study was to examine whether neonatal outcomes including gestational age at birth, neonatal growth outcomes at birth and then at 1 month postpartum were altered by in utero exposure to antidepressant medication using a prospective and controlled design.

Method: A prospective case–control study recruited 27 pregnant women taking antidepressant medication and 27 matched controls who were not taking antidepressant medication in pregnancy at an obstetric hospital in Melbourne, Australia. Of the 27 women taking medication, 25 remained on medication in the third trimester. A purpose-designed self-report questionnaire and the Beck Depression Inventory-II were completed in pregnancy, after birth and at one month postpartum. In addition information was collected on exposed and non-exposed infants including Apgar scores, birthweight/length/head circumference and gestational age at birth. Weight/length/head circumference was again collected at 1 month of age.

Results: Infants exposed to antidepressants in utero were eightfold more likely to be born at a premature gestational age, had significantly lower birthweight and were smaller in length and head circumference than non-exposed infants. There was no association between birth outcomes and maternal depression. At 1 month, the difference in weight in the exposed group became significantly greater than the control group.

Conclusion: Antidepressant exposure in utero may affect gestational age at birth and neonatal outcomes independently of antenatal maternal depression. Further studies are needed to examine whether these findings vary according to the type of antidepressant prescribed and follow up growth and development in exposed infants beyond 1 month.

On backwards and forwards reachable sets bounding for perturbed time-delay systems

Linear systems with interval time-varying delay and unknown-but-bounded disturbances are considered in this paper. We study the problem of finding outer bound of forwards reachable sets and inter bound of backwards reachable sets of the system. Firstly, two definitions on forwards and backwards reachable sets, where initial state vectors are not necessary to be equal to zero, are introduced. Then, by using the Lyapunov-Krasovskii method, two sufficient conditions for the existence of: (i) the smallest possible outer bound of forwards reachable sets; and (ii) the largest possible inter bound of backwards reachable sets, are derived. These conditions are presented in terms of linear matrix inequalities with two parameters need to tuned, which therefore can be efficiently solved by combining existing convex optimization algorithms with a two-dimensional search method to obtain optimal bounds. Lastly, the obtained results are illustrated by four numerical examples.

Robust adaptive backstepping excitation controller design for simple power system models with external disturbances

This paper presents a nonlinear robust adaptive excitation controller design for a simple power system model where a synchronous generator is connected to an infinite bus. The proposed controller is designed to obtain the adaption laws for estimating critical parameters of synchronous generators which are considered as unknown while providing the robustness against the bounded external disturbances. The convergence of different physical quantities of a single machine infinite bus (SMIB) system, with the proposed control scheme, is ensured through the negative definiteness of the derivative of Lyapunov functions. The effects of external disturbances are considered during formulation of Lyapunov function and thus, the proposed excitation controller can ensure the stability of the SMIB system under the variation of critical parameters as well as external disturbances including noises. Finally, the performance of the proposed scheme is investigated with the inclusion of external disturbances in the SMIB system and its superiority is demonstrated through the comparison with an existing robust adaptive excitation controller. Simulation results show that the proposed scheme provides faster responses of physical quantities than the existing controller.

An investigation into using SAP-PS as a multidimensional project control system (MPCS)

This paper investigates the effectiveness of using a corporate enterprise resource planning (ERP) system as a multi-dimensional project control system (MPCS) to monitor and control the work performed on projects, meet the needs and expectations of the project managers and support the requirements of other key stakeholders. A qualitative approach i.e. case study interviews and literature review accompanied by a quantitative computer system validation test approach was deployed. The results from this study suggest that the corporate ERP system is effective at monitoring and controlling the project stakeholder success criteria within a fully integrated environment. The system does however need to be setup and configured for the purpose of MPCS. This study contributes to the field by providing empirical evidence that corporate ERP systems are likely one of the only systems truly capable of solving the age old problem of how to expand the traditional singular dimensional approaches commonly used in project control, thus multiple control dimensions are integrated with each other and other business systems to form a multi-dimensional project control system.

Possibilities to include in numerical simulation stochastic and discontinuous phenomena occurring in material

Simulation of materials processing has to face new difficulties regarding proper description of various discontinuous and stochastic phenomena occurring in materials. Commonly used rheological models based on differential equations treat material as continuum and are unable to describe properly several important phenomena. That is the reason for ongoing search for alternative models, which can account for non-continuous structure of the materials and for the fact, that various phenomena in the materials occur in different scales from nano to mezo. Accounting for the stochastic character of some phenomena is an additional challenge. One of the solutions may be the coupled Cellular Automata (CA) – Finite Element (FE) multi scale model. A detailed discussion about the advantages given by the developed multi scale CAFE model for strain localization phenomena in contrast to capabilities provided by the conventional FE approaches is a subject of this work. Results obtained from the CAFE model are supported by the experimental observations showing influence of many discontinuities existing in the real material on macroscopic response. An immense capabilities of the CAFE approach in comparison to limitations of the FE method for modeling of real material behavior is are shown this work as well.