The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Stochastic gauges in quantum dynamics for many-body simulations

Quantum dynamics simulations can be improved using novel quasiprobability distributions based on non-orthogonal Hermitian kernel operators. This introduces arbitrary functions (gauges) into the stochastic equations. which can be used to tailor them for improved calculations. A possible application to full quantum dynamic simulations of BEC's is presented. (C) 2001 Elsevier Science B.V. All rights reserved.

Perceived constraints and social support for active leisure among mothers with young children

Evidence suggests that women who are mothers of young children have lower levels of physical activity than women of similar age who do not have children (Brown, Lee, Mishra, & Bauman, 2000). The purposes of this study were to explore the factors that constrain mothers of young children from being more physically active, and the relationship between physical activity and levels of social support available to the women. The empirical basis for this examination was provided through a study of activity levels and barriers to physical activity experienced by a sample of 543 mothers of young children from differing socioeconomic backgrounds. The data indicate that: (a) more than two-thirds of the mothers were inadequately active in their leisure time for health benefit; (b) while the vast majority of mothers expressed a desire to be more active, they were inhibited in their ability to act out their leisure preferences by a combination of structural (e.g., lack of time, money, energy) and ideological influences (e.g., sense of commitment to others); (c) access to social support (from partners, family, and friends) was seen to place some women in a better position than others to negotiate constraints that inhibit leisure participation; and (d) within groups of varying socioeconomic status (SES) there was wide variation in the amount of time spent each week in active leisure.

Let your feet do the walking: constraints on the stability of bipedal coordination

In this paper we consider whether the behaviour of the neural circuitry that controls lower limb movements in humans is shaped primarily by the spatiotemporal characteristics of bipedal gait patterns, or by selective pressures that are sensitive to considerations of balance and energetics. During the course of normal locomotion, the full dynamics of the neural circuitry are masked by the inertial properties of the limbs. In the present study, participants executed bipedal movements in conditions in which their feet were either unloaded or subject to additional inertial loads. Two patterns of rhythmic coordination were examined. In the in-phase mode, participants were required to flex their ankles and extend their ankles in synchrony. In the out-of-phase mode, the participants flexed one ankle while extending the other and vice versa. The frequency of movement was increased systematically throughout each experimental trial. All participants were able to maintain both the in-phase and the out-of-phase mode of coordination, to the point at which they could no longer increase their frequency of movement. Transitions between the two modes were not observed, and the stability of the out-of-phase and in-phase modes of coordination was equivalent at all movement frequencies. These findings indicate that, in humans, the behaviour of the neural circuitry underlying coordinated movements of the lower limbs is not constrained strongly by the spatiotemporal symmetries of bipedal gait patterns.

Stochastic Schrodinger equation approach to quantum noise in resonant tunneling current

We apply the quantum trajectory method to current noise in resonant tunneling devices. The results from dynamical simulation are compared with those from unconditional master equation approach. We show that the stochastic Schrodinger equation approach is useful in modeling the dynamical processes in mesoscopic electronic systems.

Predictions of quantum mechanics and stochastic electrodynamics in travelling wave second harmonic generation

We show that stochastic electrodynamics and quantum mechanics give quantitatively different predictions for the quantum nondemolition (QND) correlations in travelling wave second harmonic generation. Using phase space methods and stochastic integration, we calculate correlations in both the positive-P and truncated Wigner representations, the latter being equivalent to the semi-classical theory of stochastic electrodynamics. We show that the semiclassical results are different in the regions where the system performs best in relation to the QND criteria, and that they significantly overestimate the performance in these regions. (C) 2001 Published by Elsevier Science B.V.

The stochastic design of force-minimized compact magnets for high-field magnetic resonance imaging applications

New designs for force-minimized compact high-field clinical MRI magnets are described. The design method is a modified simulated annealing (SA) procedure which includes Maxwell forces in the error function to be minimized. This permits an automated force reduction in the magnet designs while controlling the overall dimensions of the system. As SA optimization requires many iterations to achieve a final design, it is important that each iteration in the procedure is rapid. We have therefore developed a rapid force calculation algorithm. Novel designs for short 3- and 4-T clinical MRI systems are presented in which force reduction has been invoked. The final designs provide large homogeneous regions and reduced stray fields in remarkable short magnets. A shielded 4-T design that is approximately 30% shorter than current designs is presented. This novel magnet generates a full 50-cm diameter homogeneous region.

Patchy populations in stochastic environments: Critical number of patches for persistence

We introduce a model for the dynamics of a patchy population in a stochastic environment and derive a criterion for its persistence. This criterion is based on the geometric mean (GM) through time of the spatial-arithmetic mean of growth rates. For the population to persist, the GM has to be greater than or equal to1. The GM increases with the number of patches (because the sampling error is reduced) and decreases with both the variance and the spatial covariance of growth rates. We derive analytical expressions for the minimum number of patches (and the maximum harvesting rate) required for the persistence of the population. As the magnitude of environmental fluctuations increases, the number of patches required for persistence increases, and the fraction of individuals that can be harvested decreases. The novelty of our approach is that we focus on Malthusian local population dynamics with high dispersal and strong environmental variability from year to year. Unlike previous models of patchy populations that assume an infinite number of patches, we focus specifically on the effect that the number of patches has on population persistence. Our work is therefore directly relevant to patchily distributed organisms that are restricted to a small number of habitat patches.

Model specification tests in nonparametric stochastic regression models

In this paper, we consider testing for additivity in a class of nonparametric stochastic regression models. Two test statistics are constructed and their asymptotic distributions are established. We also conduct a small sample study for one of the test statistics through a simulated example. (C) 2002 Elsevier Science (USA).

Syntactic and pragmatic constraints on processing relative clauses

Thc oen itninteureasc ttioo nb eo fa pcreangtmraal tiiscs uaen di ns ymnotadcetlisc ocfo nsestnrtaeinnctse processing. It is well established that object relatives (1) are harder to process than subject relatives (2). Passivization, other things being equal, increases sentence complexity. However, one of the functions of the passive construction is to promote an NP into the role of subject so that it can be more easily bound to the head NP in a higher clause. Thus, (3) is predicted to be marginally preferred over (1). Passiviazation in this instance may be seen as a way of avoiding the object relative construction. 1. The pipe that the traveller smoked annoyed the passengers. 2. The traveller that smoked the pipe annoyed the passengers. 3.The pipe that was smoked by the traveller annoyed the 4.The traveller that the pipe was smoked by annoyed the 5.The traveller that the lady was assaulted by annoyed the In (4) we have relativization of an NP which has been demoted by passivization to the status of a by-phrase. Such relative clauses may only be obtained under quite restrictive pragmatic conditions. Many languages do not permit relativization of a constituent as low as a by-phrase on the NP accessibility hierarchy (Comrie, 1984). The factors which determine the acceptability of demoted NP relatives like (4-5) reflect the ease with which the NP promoted to subject position can be taken as a discourse topic. We explored the acceptability of sentences such as (1-5) using pair-wise judgements of samddifferent meaning, accompanied by ratings of easeof understanding. Results are discussed with reference to Gibsons DLT model of linguistic complexity and sentence processing (Gibson, 2000)

Predictor-corrector methods of Runge-Kutta type for stochastic differential equations

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge-Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditions of the PC methods using stochastic implicit RK correctors with strong global order 1.0 and 1.5. A two-stage implicit RK method with strong global order 1.0 and a four-stage implicit RK method with strong global order 1.5 used as the correctors are constructed in this paper. The mean-square stability properties and numerical results of the PC methods based on these two implicit RK correctors are reported.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.