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.

Games for change and transformative learning : an ethnographic case study

This thesis aims to contribute to a better understanding of how serious games/games for change function as learning frameworks for transformative learning in an educational setting. This study illustrates how the meaning-making processes and learning with and through computer gameplay are highly contingent, and are significantly influenced by the uncertainties of the situational context. The study focuses on SCAPE, a simulation game that addresses urban planning and sustainability. SCAPE is based on the real-world scenario of Kelvin Grove Urban Village, an inner city redevelopment area in Brisbane, Queensland, Australia. The game is embedded within an educational program, and I thus account for the various gameplay experiences of different school classes participating in this program. The networks emerging from the interactions between students/players, educators, facilitators, the technology, the researcher, as well as the setting, result in unanticipated, controversial, and sometimes unintended gameplay experiences and outcomes. To unpack play, transformative learning and games, this study adopts an ecological approach that considers the magic circle of gameplay in its wider context. Using Actor-Network Theory as the ontological lens for inquiry, the methods for investigation include an extensive literature review, ethnographic participant observation of SCAPE, as well as student and teacher questionnaires, finishing with interviews with the designers and facilitators of SCAPE. Altogether, these methods address my research aim to better understand how the heterogeneous actors engage in the relationships in and around gameplay, and illustrate how their conflicting understandings enable, shape or constrain the (transformative) learning experience. To disentangle these complexities, my focus continuously shifts between the following modes of inquiry into the aims „h To describe and analyse the game as a designed artefact. „h To examine the gameplay experiences of players/students and account for how these experiences are constituted in the relationships of the network. „h To trace the meaning-making processes emerging from the various relations of players/students, facilitators, teachers, designers, technology, researcher, and setting, and consider how the boundaries of the respective ecology are configured and negotiated. „h To draw out the implications for the wider research area of game-based learning by using the simulation game SCAPE as an example for introducing gameplay to educational settings. Accounting in detail for five school classes, these accounts represent, each in its own right, distinct and sometimes controversial forms of engagement in gameplay. The practices and negotiations of all the assembled human and non-human actors highlight the contingent nature of gameplay and learning. In their sum, they offer distinct but by no means exhaustive examples of the various relationships that emerge from the different assemblages of human and non-human actors. This thesis, hence, illustrates that game-based learning in an educational setting is accompanied by considerable unpredictability and uncertainty. As ordinary life spills and leaks into gameplay experiences, group dynamics and the negotiations of technology, I argue that overly deterministic assertions of the game¡¦s intention, as well as a too narrowly defined understanding of the transformative learning outcome, can constrain our inquiries and hinder efforts to further elucidate and understand the evolving uncertainties around game-based learning. Instead, this thesis posits that playing and transformative learning are relational effects of the respective ecology, where all actors are networked in their (partial) enrolment in the process of translation. This study thus attempts to foreground the rich opportunities for exploring how game-based learning is assembled as a network of practices.

GameFlow heuristics for designing and evaluating real-time strategy games

The GameFlow model strives to be a general model of player enjoyment, applicable to all game genres and platforms. Derived from a general set of heuristics for creating enjoyable player experiences, the GameFlow model has been widely used in evaluating many types of games, as well as non-game applications. However, we recognize that more specific, low-level, and implementable criteria are potentially more useful for designing and evaluating video games. Consequently, the research reported in this paper aims to provide detailed heuristics for designing and evaluating one specific game genre, real-time strategy games. In order to develop these heuristics, we conducted a grounded theoretical analysis on a set of professional game reviews and structured the resulting heuristics using the GameFlow model. The resulting 165 heuristics for designing and evaluating real-time strategy games are presented and discussed in this paper.

Spotting the difference : identifying player opponent preferences in FPS games

This paper describes a study designed to understand player responses to artificially intelligent opponents in multi-player First Person Shooter games. It examines the player's ability to tell the difference between artificially intelligent opponents and other human players, and investigates the players' perceptions of these opponents. The study examines player preferences in this regard and identifies the significance of the cues and signs players use to categorise an opponent as artificial or human.

Personality, motivation and video games

This study explored relationships between personality, video game preference and gaming experiences. Two hundred and thirty-five participants completed an online survey in which they recalled a recent gaming experience, and provided measures of personality and their gaming experience via the Player Experience of Need Satisfaction (PENS) measure. Relationships between game genre, personality and gaming experience were found. Results are interpreted with reference to the validity of the PENS, current models of video gaming motivations and enjoyment, and sub-groups of people that may be more vulnerable to possible negative effects of games.

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.

Engaging students in authoring and playing computer games

Computer games have become a commonplace but engaging activity among students. They enjoy playing computer games as they can perform larger-than-life activities virtually such as jumping from great heights, flying planes, and racing cars; actions that are otherwise not possible in real life. Computer games also offer user interactivity which gives them a certain appeal. Considering this appeal, educators should consider integrating computer games into student learning and to encourage students to author computer games of their own. It is thought that students can be engaged in learning by authoring and using computer games and can also gain essential skills such as collaboration, teamwork, problem solving and deductive reasoning. The research in this study revolves around building student engagement through the task of authoring computer games. The study aims to demonstrate how the creation and sharing of student-authored educational games might facilitate student engagement and how ICT (information and communication technology) plays a supportive role in student learning. Results from this study may lead to the broader integration of computer games into student learning and contribute to similar studies. In this qualitative case study, based in a state school in a low socio-economic area west of Brisbane, Australia, students were selected in both junior and senior secondary classes who have authored computer games as a part of their ICT learning. Senior secondary students (Year 12 ICT) were given the task of programming the games, which were to be based on Mathematics learning topics while the junior secondary students (Year 8 ICT) were given the task of creating multimedia elements for the games. A Mathematics teacher volunteered to assist in the project and provided guidance on the inclusion of suitable Mathematics curricular content into these computer games. The student-authored computer games were then used to support another group of Year 8 Mathematics students to learn the topics of Area, Volume and Time. Data was collected through interviews, classroom observations and artefacts. The teacher researcher, acting in the role of ICT teacher, coordinated with the students and the Mathematics teacher to conduct this study. Instrumental case study was applied as research methodology and Third Generation Activity Theory served as theoretical framework for this study. Data was analysed adopting qualitative coding procedures. Findings of this study indicate that having students author and play computer games promoted student engagement and that ICT played a supportive role in learning and allowed students to gain certain essential skills. Although this study will suggest integrating computer games to support classroom learning, it cannot be presumed that computer games are an immediate solution for promoting student engagement.

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.

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.

Physical performance profile of sub-elite juvenile Gaelic Games players and the prevalence of a Relative Age Effect (RAE)

Gaelic Games are the indigenous sports played in Ireland, the most popular being Gaelic football and hurling. The games are contact sports and the physical demands are thought to be similar to those of Australian Rules football, rugby union, rugby league, field hockey, and lacrosse (Delahunt et al., 2011). The difference in chronological age between children in a single age group is known as relative age and its consequences as the RAE, whereby younger players are disadvantaged (Del Campo et al., 2010). The purpose of this study was to describe the physical and performance profile of sub-elite juvenile Gaelic Games players and to establish if a RAE is present in this cohort and any influence physiological moderator variables may have on this. Following receipt of ethical approval (EHSREC11-45), six sub-elite county development squads (Under-14/15/16 age groups, male, n=115) volunteered to partake in the study. Anthropometric data including skin folds and girths were collected. A number of field tests of physical performance including 5 and 20m speed, vertical and broad jump distance, and an estimate of VO2max were carried out. Descriptive data are presented as Mean SD. Juvenile sub-elite Gaelic Games players aged 14.53 0.82 y were 172.87 7.63 cm tall, had a mass of 64.74 11.06 kg, a BMI of 21.57 2.82 kg.m-2 and 9.22 4.78 % body fat. Flexibility, measured by sit and reach was 33.62 6.86 cm and lower limb power measured by vertical and broad jump were 42.19 5.73 and 191.16 25.26 cm, respectively. Participant time to complete 5m, 20m and an agility test (T-Test) was 1.12 0.07, 3.31 0.30 and 9.31 0.55 s respectively. Participant’s estimated VO2max was 48.23 5.05 ml.kg.min-1. Chi-Square analysis of birth month by quartile (Q1 = January-March) revealed that a RAE was present in this cohort, whereby an over-representation of players born in Q1 compared with Q2, Q3 and Q4 was evident (2 = 14.078, df = 3, p = 0.003). Kruskal-Wallis analysis of the data revealed no significant difference in any of the performance parameters based on quartile of birth (Alpha level = 0.05).This study provides a physical performance profile of juvenile sub-elite Gaelic Games players, comparable with those of other sports such as soccer and rugby. This novel data can inform us of the physical requirements of the sport. The evidence of a RAE is similar to that observed in other contact sports such as soccer and rugby league (Carling et al, 2009; Till et al, 2010). Although a RAE exists in this cohort, this cannot be explained by any physical/physiological moderator variables. Carling C et al. (2009). Scandinavian Journal of Medicine and Science in Sport 19, 3-9. Delahunt E et al. (2011). Journal of Athletic Training 46, 241-5. Del Campo DG et al. (2010). Journal of Sport Science and Medicine 9, 190-198. Delorme N et al. (2010). European Journal of Sport Science 10, 91-96. Till K et al. (2010). Scandinavian Journal of Medicine and Science in Sports 20, 320-329.

The SCOOT experience : games in place : collaborative interventions in socio-spatial practices

The principal focus of this thesis is the representation of a significant creative practice in relation to the design and installation of the Location-Based Game, SCOOT. This project demonstrates new understandings relating to the contingencies and potentials for transferring positive aspects of digital gameplay to everyday physical environments in an effort to reveal hidden histories and revitalise peoples’ interactions with their local urban spaces.