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.

System level tests of transformer differential protection using an IEC 61850 process bus

The IEC 61850 family of standards for substation communication systems were released in the early 2000s, and include IEC 61850-8-1 and IEC 61850-9-2 that enable Ethernet to be used for process-level connections between transmission substation switchyards and control rooms. This paper presents an investigation of process bus protection performance, as the in-service behavior of multi-function process buses is largely unknown. An experimental approach was adopted that used a Real Time Digital Simulator and 'live' substation automation devices. The effect of sampling synchronization error and network traffic on transformer differential protection performance was assessed and compared to conventional hard-wired connections. Ethernet was used for all sampled value measurements, circuit breaker tripping, transformer tap-changer position reports and Precision Time Protocol synchronization of sampled value merging unit sampling. Test results showed that the protection relay under investigation operated correctly with process bus network traffic approaching 100% capacity. The protection system was not adversely affected by synchronizing errors significantly larger than the standards permit, suggesting these requirements may be overly conservative. This 'closed loop' approach, using substation automation hardware, validated the operation of protection relays under extreme conditions. Digital connections using a single shared Ethernet network outperformed conventional hard-wired solutions.

Spreading peak demand for urban rail transit through differential fare policy : a review of empirical evidence

More evenly spread demand for public transport throughout a day can reduce transit service provider‟s total asset and labour costs. A plausible peak spreading strategy is to increase peak fare and/or to reduce off-peak fare. This paper reviews relevant empirical studies for urban rail systems, as rail transit plays a key role in Australian urban passenger transport and experiences severe peak loading variability. The literature is categorised into four groups: a) passenger opinions on willingness to change time for travel, b) valuations of displacement time using stated preference technique, c) simulations of peak spreading based on trip scheduling models, and: d) real-world cases of peak spreading using differential fare. Policy prescription is advised to take into account impacts of traveller‟s time flexibility and joint effects of mode shifting and peak spreading. Although focusing on urban rail, arguments in this paper are relevant to public transport in general with values to researchers and practitioners.

Differential pathologic variables and outcomes across the spectrum of adenocarcinoma of the esophagogastric junction

Background Adenocarcinoma of the esophagogastric junction (AEG) as described by Siewert et al. is classified as one entity in the latest (7th Edition) American Joint Cancer Committee/International Union Against Cancer (AJCC/UICC) manual, compared with the previous mix of esophageal and gastric staging systems. The origin of AEG tumors, esophageal or gastric, and their biology remain controversial, particularly for AEG type II (cardia) tumors. Methods We adapted a large prospective database (n = 520: 180 type I, 182 type II, 158 type III) to compare AEG tumors under the new TNM system Pathological variables associated with prognosis were compared (pT, pN, stage, differentiation, R status, lymphovascular invasion, perineural involvement, number of positive nodes, percent of positive nodes, and tumor length), as well as overall survival. Results Compared with AEG type I tumors, type II and type III tumors had significantly (p\0.05) more advanced pN stages, greater number and percentage of positive nodes, poorer differentiation, more radial margin involvement, and more perineural invasion. In AEG type I, 14/180 patients (8%) had[6 involved nodes (pN3), compared with 16 and 30% of patients classified type II and III, respectively. Median survival was significantly (p = 0.03) improved for type I patients (38 months) compared with those with tumors classified as type II (28 months) and type III (24 months). In multivariate analysis node positivity and pN staging but not AEG site had an impact on survival. Conclusions In this series AEG type I is associated with more favorable pathologic features and improved outcomes compared with AEG type II and III. This may reflect earlier diagnosis, but an alternative possibility, that type I may be a unique paradigm with more favorable biology, requires further study. © Société Internationale de Chirurgie 2010.

Differential expression of VEGF ligands and receptors in prostate cancer

BACKGROUND Prostate cancer disseminates to regional lymph nodes, however the molecular mechanisms responsible for lymph node metastasis are poorly understood. The vascular endothelial growth factor (VEGF) ligand and receptor family have been implicated in the growth and spread of prostate cancer via activation of the blood vasculature and lymphatic systems. The purpose of this study was to comprehensively examine the expression pattern of VEGF ligands and receptors in the glandular epithelium, stroma, lymphatic vasculature and blood vessels in prostate cancer. METHODS The localization of VEGF-A, VEGF-C, VEGF-D, VEGF receptor (VEGFR)-1, VEGFR-2, and VEGFR-3 was examined in cancerous and adjacent benign prostate tissue from 52 subjects representing various grades of prostate cancer. RESULTS Except for VEGFR-2, extensive staining was observed for all ligands and receptors in the prostate specimens. In epithelial cells, VEGF-A and VEGFR-1 expression was higher in tumor tissue compared to benign tissue. VEGF-D and VEGFR-3 expression was significantly higher in benign tissue compared to tumor in the stroma and the endothelium of lymphatic and blood vessels. In addition, the frequency of lymphatic vessels, but not blood vessels, was lower in tumor tissue compared with benign tissue. CONCLUSIONS These results suggest that activation of VEGFR-1 by VEGF-A within the carcinoma, and activation of lymphatic endothelial cell VEGFR-3 by VEGF-D within the adjacent benign stroma may be important signaling mechanisms involved in the progression and subsequent metastatic spread of prostate cancer. Thus inhibition of these pathways may contribute to therapeutic strategies for the management of prostate cancer.

A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature. Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models. This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest. The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

Parameter estimation of thrust models of uninhabited airborne systems

This paper presents a method for the estimation of thrust model parameters of uninhabited airborne systems using specific flight tests. Particular tests are proposed to simplify the estimation. The proposed estimation method is based on three steps. The first step uses a regression model in which the thrust is assumed constant. This allows us to obtain biased initial estimates of the aerodynamic coeficients of the surge model. In the second step, a robust nonlinear state estimator is implemented using the initial parameter estimates, and the model is augmented by considering the thrust as random walk. In the third step, the estimate of the thrust obtained by the observer is used to fit a polynomial model in terms of the propeller advanced ratio. We consider a numerical example based on Monte-Carlo simulations to quantify the sampling properties of the proposed estimator given realistic flight conditions.

Characterising transiting exoplanets by way of differential photometry

This paper describes a simple activity for plotting and characterising the light curve from an exoplanet transit event by way of differential photometry analysis. Using free digital imaging software, participants analyse a series of telescope images with the goal of calculating various exoplanet parameters, including its size, orbital radius and habitability. The activity has been designed for a high-school or undergraduate university level and introduces fundamental concepts in astrophysics and an understanding of the basis for exoplanetary science, the transit method and digital photometry.

Mandatory Reporting Laws and Identification of Child Abuse and Neglect: Consideration of Differential Maltreatment Types, and a Cross-Jurisdictional Analysis of Child Sexual Abuse Reports

Mandatory reporting laws have been created in many jurisdictions as a way of identifying cases of severe child maltreatment on the basis that cases will otherwise remain hidden. These laws usually apply to all four maltreatment types. Other jurisdictions have narrower approaches supplemented by differential response systems, and others still have chosen not to enact mandatory reporting laws for any type of maltreatment. In scholarly research and normative debates about mandatory reporting laws and their effects, the four major forms of child maltreatment—physical abuse, sexual abuse, emotional abuse, and neglect—are often grouped together as if they are homogenous in nature, cause, and consequence. Yet, the heterogeneity of maltreatment types, and different reporting practices regarding them, must be acknowledged and explored when considering what legal and policy frameworks are best suited to identify and respond to cases. A related question which is often conjectured upon but seldom empirically explored, is whether reporting laws make a difference in case identification. This article first considers different types of child abuse and neglect, before exploring the nature and operation of mandatory reporting laws in different contexts. It then posits a differentiation thesis, arguing that different patterns of reporting between both reporter groups and maltreatment types must be acknowledged and analysed, and should inform discussions and assessments of optimal approaches in law, policy and practice. Finally, to contribute to the evidence base required to inform discussion, this article conducts an empirical cross-jurisdictional comparison of the reporting and identification of child sexual abuse in jurisdictions with and withoutmandatory reporting, and concludes that mandatory reporting laws appear to be associated with better case identification.

Victoria's Child FIRST and IFS differential response system : progress and issues

Differential response has long been utilized by statutory child protection systems in Australia. This article describes the advent and history of Victoria's differential response system, with a particular focus on the Child FIRST and IFS programme. This program entails a partnership arrangement between the Department of Human Services child protection services and community-based, not-for-profit agencies to provide a diverse range of early intervention and prevention services. The findings of a recent external service system evaluation, a judicial inquiry, and the large-scale Child and Family Services Outcomes Survey of parents/carers perspectives of their service experiences are used to critically examine the effectiveness of this differential response approach. Service-user perspectives of the health and wellbeing of children and families are identified, as well as the recognized implementation issues posing significant challenges for the goal of an integrated partnership system. The need for ongoing reform agendas is highlighted along with the policy, program and structural tensions that exist in differential response systems, which are reliant upon partnerships and shared responsibilities for protecting children and assisting vulnerable families. Suggestions are made for utilizing robust research and evaluation that gives voice to service users and promotes their rights and interests.

Maximum principle and numerical method for the multi-term time–space Riesz–Caputo fractional differential equations

The maximum principle for the space and time–space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time–space Riesz–Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor–corrector method combining the L1 and L2 discrete schemes, we present a numerical method for the specified equation. Two examples are given to illustrate the obtained results.

Customer agility, smart shopping apps and their implications: Customer relationship management systems in the digital age

This thesis examines the complementarities and vulnerabilities of customer connectivity that contemporary firms achieved through ubiquitous digital technologies. Taking the example of deployment of smart shopping apps to connect with consumers in the context of Australian retail, the study examines how such customer connectivity positively influences firm performances through firm's customer agility whilst creating implications for firms' digital business strategy through altered customer cognitions. Employing Oliver's (1977) Expectation Confirmation Theory, this study empirically tests a conceptual model involving digital connectivity, digital expectations, experiences and satisfaction of the customers who uses smart shopping apps in Australian consumer retail.

A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems

In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multidimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel mode

Hybrid stiff-string-polynomial basis functions for vibration analysis of high speed rotating beams

A new finite element is developed for free vibration analysis of high speed rotating beams using basis functions which use a linear combination of the solution of the governing static differential equation of a stiff-string and a cubic polynomial. These new shape functions depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. The natural frequencies predicted by the proposed element are compared with an element with stiff-string, cubic polynomial and quintic polynomial shape functions. It is found that the new element exhibits superior convergence compared to the other basis functions.

Precipitation In Small Systems--II. Mean Field Equations More Effective Than Population Balance

Part I (Manjunath et al., 1994, Chem. Engng Sci. 49, 1451-1463) of this paper showed that the random particle numbers and size distributions in precipitation processes in very small drops obtained by stochastic simulation techniques deviate substantially from the predictions of conventional population balance. The foregoing problem is considered in this paper in terms of a mean field approximation obtained by applying a first-order closure to an unclosed set of mean field equations presented in Part I. The mean field approximation consists of two mutually coupled partial differential equations featuring (i) the probability distribution for residual supersaturation and (ii) the mean number density of particles for each size and supersaturation from which all average properties and fluctuations can be calculated. The mean field equations have been solved by finite difference methods for (i) crystallization and (ii) precipitation of a metal hydroxide both occurring in a single drop of specified initial supersaturation. The results for the average number of particles, average residual supersaturation, the average size distribution, and fluctuations about the average values have been compared with those obtained by stochastic simulation techniques and by population balance. This comparison shows that the mean field predictions are substantially superior to those of population balance as judged by the close proximity of results from the former to those from stochastic simulations. The agreement is excellent for broad initial supersaturations at short times but deteriorates progressively at larger times. For steep initial supersaturation distributions, predictions of the mean field theory are not satisfactory thus calling for higher-order approximations. The merit of the mean field approximation over stochastic simulation lies in its potential to reduce expensive computation times involved in simulation. More effective computational techniques could not only enhance this advantage of the mean field approximation but also make it possible to use higher-order approximations eliminating the constraints under which the stochastic dynamics of the process can be predicted accurately.