Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

An examination of monotony and hypovigilance, independent of fatigue : relevance to road safety

Driving is a vigilance task, requiring sustained attention to maintain performance and avoid crashes. Hypovigilance (i.e., marked reduction in vigilance) while driving manifests as poor driving performance and is commonly attributed to fatigue (Dinges, 1995). However, poor driving performance has been found to be more frequent when driving in monotonous road environments, suggesting that monotony plays a role in generating hypovigilance (Thiffault & Bergeron, 2003b). Research to date has tended to conceptualise monotony as a uni-dimensional task characteristic, typically used over a prolonged period of time to facilitate other factors under investigation, most notably fatigue. However, more often than not, more than one exogenous factor relating to the task or operating environment is manipulated to vary or generate monotony (Mascord & Heath, 1992). Here we aimed to explore whether monotony is a multi-dimensional construct that is determined by characteristics of both the task proper and the task environment. The general assumption that monotony is a task characteristic used solely to elicit hypovigilance or poor performance related to fatigue appears to have led to there being little rigorous investigation into the exact nature of the relationship. While the two concepts are undoubtedly linked, the independent effect of monotony on hypovigilance remains largely ignored. Notwithstanding, there is evidence that monotony effects can emerge very early in vigilance tasks and are not necessarily accompanied by fatigue (see Meuter, Rakotonirainy, Johns, & Wagner, 2005). This phenomenon raises a largely untested, empirical question explored in two studies: Can hypovigilance emerge as a consequence of task and/or environmental monotony, independent of time on task and fatigue? In Study 1, using a short computerised vigilance task requiring responses to be withheld to infrequent targets, we explored the differential impacts of stimuli and task demand manipulations on the development of a monotonous context and the associated effects on vigilance performance (as indexed by respone errors and response times), independent of fatigue and time on task. The role of individual differences (sensation seeking, extroversion and cognitive failures) in moderating monotony effects was also considered. The results indicate that monotony affects sustained attention, with hypovigilance and associated performance worse in monotonous than in non-monotonous contexts. Critically, performance decrements emerged early in the task (within 4.3 minutes) and remained consistent over the course of the experiment (21.5 minutes), suggesting that monotony effects can operate independent of time on task and fatigue. A combination of low task demands and low stimulus variability form a monotonous context characterised by hypovigilance and poor task performance. Variations to task demand and stimulus variability were also found to independently affect performance, suggesting that monotony is a multi-dimensional construct relating to both task monotony (associated with the task itself) and environmental monotony (related to characteristics of the stimulus). Consequently, it can be concluded that monotony is multi-dimensional and is characterised by low variability in stimuli and/or task demands. The proposition that individual differences emerge under conditions of varying monotony with high sensation seekers and/or extroverts performing worse in monotonous contexts was only partially supported. Using a driving simulator, the findings of Study 1 were extended to a driving context to identify the behavioural and psychophysiological indices of monotony-related hypovigilance associated with variations to road design and road side scenery (Study 2). Supporting the proposition that monotony is a multi-dimensional construct, road design variability emerged as a key moderating characteristic of environmental monotony, resulting in poor driving performance indexed by decrements in steering wheel measures (mean lateral position). Sensation seeking also emerged as a moderating factor, where participants high in sensation seeking tendencies displayed worse driving behaviour in monotonous conditions. Importantly, impaired driving performance was observed within 8 minutes of commencing the driving task characterised by environmental monotony (low variability in road design) and was not accompanied by a decline in psychophysiological arousal. In addition, no subjective declines in alertness were reported. With fatigue effects associated with prolonged driving (van der Hulst, Meijman, & Rothengatter, 2001) and indexed by drowsiness, this pattern of results indicates that monotony can affect driver vigilance, independent of time on task and fatigue. Perceptual load theory (Lavie, 1995, 2005) and mindlessness theory (Robertson, Manly, Andrade, Baddley, & Yiend, 1997) provide useful theoretical frameworks for explaining and predicting monotony effects by positing that the low load (of task and/or stimuli) associated with a monotonous task results in spare attentional capacity which spills over involuntarily, resulting in the processing of task-irrelevant stimuli or task unrelated thoughts. That is, individuals – even when not fatigued - become easily distracted when performing a highly monotonous task, resulting in hypovigilance and impaired performance. The implications for road safety, including the likely effectiveness of fatigue countermeasures to mitigate monotony-related driver hypovigilance are discussed.

An implicit RBF meshless approach for time fractional diffusion equations

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

The differential recognition of children’s cultural practices in middle primary literacy classrooms

This paper argues that teachers’ recognition of children’s cultural practices is an important positive step in helping socio-economically disadvantaged children engage with school literacies. Based on twenty-one longitudinal case studies of children’s literacy development over a three-year period, the authors demonstrate that when children’s knowledges and practices assembled in home and community spheres are treated as valuable material for school learning, children are more likely to invest in the work of acquiring school literacies. However they show also that whilst some children benefit greatly from being allowed to draw on their knowledge of popular culture, sports and the outdoors, other children’s interests may be ignored or excluded. Some differences in teachers’ valuing of home and community cultures appeared to relate to gender dimensions.