Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

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.

Saturated core high-temperature superconducting fault current limiters as an alternative to conventional series reactors in a distribution grid

Series reactors are used in distribution grids to reduce the short-circuit fault level. Some of the disadvantages of the application of these devices are the voltage drop produced across the reactor and the steep front rise of the transient recovery voltage (TRV), which generally exceeds the rating of the associated circuit breaker. Simulations were performed to compare the characteristics of a saturated core High-Temperature Superconducting Fault Current Limiter (HTS FCL) and a series reactor. The design of the HTS FCL was optimized using the evolutionary algorithm. The resulting Pareto frontier curve of optimum solution is presented in this paper. The results show that the steady-state impedance of an HTS FCL is significantly lower than that of a series reactor for the same level of fault current limiting. Tests performed on a prototype 11 kV HTS FCL confirm the theoretical results. The respective transient recovery voltages (TRV) of the HTS FCL and an air core reactor of comparable fault current limiting capability are also determined. The results show that the saturated core HTS FCL has a significantly lower effect on the rate of rise of the circuit breaker TRV as compared to the air core reactor. The simulations results are validated with shortcircuit test results.

User facilitated congestion and attack mitigation

The IEEE Wireless LAN standard has been a true success story by enabling convenient, efficient and low-cost access to broadband networks for both private and professional use. However, the increasing density and uncoordinated operation of wireless access points, combined with constantly growing traffic demands have started hurting the users' quality of experience. On the other hand, the emerging ubiquity of wireless access has placed it at the center of attention for network attacks, which not only raises users' concerns on security but also indirectly affects connection quality due to proactive measures against security attacks. In this work, we introduce an integrated solution to congestion avoidance and attack mitigation problems through cooperation among wireless access points. The proposed solution implements a Partially Observable Markov Decision Process (POMDP) as an intelligent distributed control system. By successfully differentiating resource hampering attacks from overload cases, the control system takes an appropriate action in each detected anomaly case without disturbing the quality of service for end users. The proposed solution is fully implemented on a small-scale testbed, on which we present our observations and demonstrate the effectiveness of the system to detect and alleviate both attack and congestion situations.

A formal method for attack modelling and detection

This paper presents a formal methodology for attack modeling and detection for networks. Our approach has three phases. First, we extend the basic attack tree approach 1 to capture (i) the temporal dependencies between components, and (ii) the expiration of an attack. Second, using the enhanced attack trees (EAT) we build a tree automaton that accepts a sequence of actions from input stream if there is a traverse of an attack tree from leaves to the root node. Finally, we show how to construct an enhanced parallel automaton (EPA) that has each tree automaton as a subroutine and can process the input stream by considering multiple trees simultaneously. As a case study, we show how to represent the attacks in IEEE 802.11 and construct an EPA for it.

Compaction control of topography and fault network structure along strike-slip faults in sedimentary basins

Strike-slip faults commonly display structurally complex areas of positive or negative topography. Understanding the development of such areas has important implications for earthquake studies and hydrocarbon exploration. Previous workers identified the key factors controlling the occurrence of both topographic modes and the related structural styles. Kinematic and stress boundary conditions are of first-order relevance. Surface mass transport and material properties affect fault network structure. Experiments demonstrate that dilatancy can generate positive topography even under simple-shear boundary conditions. Here, we use physical models with sand to show that the degree of compaction of the deformed rocks alone can determine the type of topography and related surface fault network structure in simple-shear settings. In our experiments, volume changes of ∼5% are sufficient to generate localized uplift or subsidence. We discuss scalability of model volume changes and fault network structure and show that our model fault zones satisfy geometrical similarity with natural flower structures. Our results imply that compaction may be an important factor in the development of topography and fault network structure along strike-slip faults in sedimentary basins.

Trends in the Australian gender wage differential over the 1980s : some evidence on the effectiveness of legislative reform

The article examines the legislative reforms incorporating the Sex Discrimination Act and the Affirmative Action Act introduced during the 1980s. We utilise the Australian Bureau of Statistics Income Distribution Surveys 1981–82 and 1989–90 to reflect pre- and post-legislative reform. The article adopts the Brown, Moon and Zoloth (1980) methodology which treats both the wage and occupational status of the individual as endogenously determined. In the current context this is a particularly flexible framework allowing one to capture both the direct and indirect effects of the legislative reforms. The indirect effect refers to the narrowing of the gender wage gap associated with legislative manipulation of the male-female occupational distributions. The results contrast the slow convergence in the gender wage gap during the 1980s with the much faster pace of the 1970s. The article concludes that despite the focus of the 1980s legislation on employment equity, changes in the male-female occupational distribution over the period are small and the associated impact on gender wage convergence is also small.

The use of a Riesz fractional differential-based approach for texture enhancement in image processing

Abstract: Texture enhancement is an important component of image processing, with extensive application in science and engineering. The quality of medical images, quantified using the texture of the images, plays a significant role in the routine diagnosis performed by medical practitioners. Previously, image texture enhancement was performed using classical integral order differential mask operators. Recently, first order fractional differential operators were implemented to enhance images. Experiments conclude that the use of the fractional differential not only maintains the low frequency contour features in the smooth areas of the image, but also nonlinearly enhances edges and textures corresponding to high-frequency image components. However, whilst these methods perform well in particular cases, they are not routinely useful across all applications. To this end, we applied the second order Riesz fractional differential operator to improve upon existing approaches of texture enhancement. Compared with the classical integral order differential mask operators and other fractional differential operators, our new algorithms provide higher signal to noise values, which leads to superior image quality.

Bearing fault prognosis based on health state probability estimation

In condition-based maintenance (CBM), effective diagnostic and prognostic tools are essential for maintenance engineers to identify imminent fault and predict the remaining useful life before the components finally fail. This enables remedial actions to be taken in advance and reschedule of production if necessary. All machine components are subjected to degradation processes in real environments and they have certain failure characteristics which can be related to the operating conditions. This paper describes a technique for accurate assessment of the remnant life of bearings based on health state probability estimation and historical knowledge embedded in the closed loop diagnostics and prognostics system. The technique uses the Support Vector Machine (SVM) classifier as a tool for estimating health state probability of machine degradation process to provide long term prediction. To validate the feasibility of the proposed model, real life fault historical data from bearings of High Pressure-Liquefied Natural Gas (HP-LNG) pumps were analysed and used to obtain the optimal prediction of remaining useful life (RUL). The results obtained were very encouraging and showed that the proposed prognosis system based on health state probability estimation has the potential to be used as an estimation tool for remnant life prediction in industrial machinery.

The N550K/H mutations in FGFR2 confer differential resistance to PD173074, dovitinib and ponatinib ATP-competitive inhibitors

We sought to identify fibroblast growth factor receptor 2 (FGFR2) kinase domain mutations that confer resistance to the pan-FGFR inhibitor, dovitinib, and explore the mechanism of action of the drug-resistant mutations. We cultured BaF3 cells overexpressing FGFR2 in high concentrations of dovitinib and identified fourteen dovitinib-resistant mutations, including the N550K mutation observed in 25% of FGFR2mutant endometrial cancers (EC). Structural and biochemical in vitro kinase analyses, together with BaF3 proliferation assays, showed that the resistance mutations elevate the intrinsic kinase activity of FGFR2. BaF3 lines were used to assess the ability of each mutation to confer cross-resistance to PD173074 and ponatinib. Unlike PD173074, ponatinib effectively inhibited all the dovitinib-resistant FGFR2 mutants except the V565I gatekeeper mutation, suggesting ponatinib but not dovitinib targets the active conformation of FGFR2 kinase. EC cell lines expressing wild-type FGFR2 were relatively resistant to all inhibitors. Whereas EC cell lines expressing mutated FGFR2 showed differential sensitivity. Within the FGFR2mutant cell lines, 3/7 showed marked resistance to PD173074 and relative resistance to dovitinib and ponatinib. This suggests that alternative mechanisms distinct from kinase domain mutations are responsible for intrinsic resistance in these three EC lines. Finally, overexpression of FGFR2N550K in JHUEM-2 cells (FGFR2C383R) conferred resistance (~5 fold) to PD173074, providing independent data that FGFR2N550K can be associated with drug resistance. Biochemical in vitro kinase analyses also shows ponatinib is more effective than dovitinib at inhibiting FGFR2N550K. We propose tumors harboring mutationally activated FGFRs should be treated with FGFR inhibitors that specifically bind the active kinase.

A UKF-based estimation strategy for actuator fault detection of UASs

This paper presents a recursive strategy for online detection of actuator faults on a unmanned aerial system (UAS) subjected to accidental actuator faults. The proposed detection algorithm aims to provide a UAS with the capability of identifying and determining characteristics of actuator faults, offering necessary flight information for the design of fault-tolerant mechanism to compensate for the resultant side-effect when faults occur. The proposed fault detection strategy consists of a bank of unscented Kalman filters (UKFs) with each one detecting a specific type of actuator faults and estimating correspond- ing velocity and attitude information. Performance of the proposed method is evaluated using a typical nonlinear UAS model and it is demonstrated in simulations that our method is able to detect representative faults with a sufficient accuracy and acceptable time delay, and can be applied to the design of fault-tolerant flight control systems of UASs.

Is quality more important if you’re quirky? A review of the literature on differential susceptibility to childcare environments

Evidence concerning the impact of child care on child development suggests that higher-quality environments, particularly those that are more responsive, predict more favourable social and behavioural outcomes. However, the extent of this effect is not as great as might be expected. Impacts on child outcomes are, at best, modest. One recent explanation emerging from a new theoretical perspective of development, differential susceptibility theory, is that a minority of children are more reactive to both positive and negative environments, while the majority are relatively unaffected. These 'quirky' children have temperamental traits that are more extreme, and are often described in research studies as having 'difficult temperaments'. This paper reviews the literature on such children and argues for the need for further research to identify components of childcare environments that optimise the potential of these more sensitive, quirky individuals.

Female concentration and the gender wage differential in the United Kingdom

The paper utilizes the methodology proposed by Johnson and Solon (American Economic Review, 76 (5), 1117-1125, 1986) to examine the impact of job segregation on the gender wage gap in the UK in 1991. The results suggest that despite implementation of the UK 1983 Equal Pay Amendment there remains clear evidence that male/female workers in female dominated jobs continue to earn less for work of ‘similar worth’ than their counterparts in male dominated jobs within the same firm. This conclusion is insensitive to whether one adopts an occupation or firm based measure of gender concentration.