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.

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.

A framework for a dense matching algorithm : Results using matching metrics and order statistic filters

An algorithm for computing dense correspondences between images of a stereo pair or image sequence is presented. The algorithm can make use of both standard matching metrics and the rank and census filters, two filters based on order statistics which have been applied to the image matching problem. Their advantages include robustness to radiometric distortion and amenability to hardware implementation. Results obtained using both real stereo pairs and a synthetic stereo pair with ground truth were compared. The rank and census filters were shown to significantly improve performance in the case of radiometric distortion. In all cases, the results obtained were comparable to, if not better than, those obtained using standard matching metrics. Furthermore, the rank and census have the additional advantage that their computational overhead is less than these metrics. For all techniques tested, the difference between the results obtained for the synthetic stereo pair, and the ground truth results was small.

Order statistic filters for image matching

The rank and census are two filters based on order statistics which have been applied to the image matching problem for stereo pairs. Advantages of these filters include their robustness to radiometric distortion and small amounts of random noise, and their amenability to hardware implementation. In this paper, a new matching algorithm is presented, which provides an overall framework for matching, and is used to compare the rank and census techniques with standard matching metrics. The algorithm was tested using both real stereo pairs and a synthetic pair with ground truth. The rank and census filters were shown to significantly improve performance in the case of radiometric distortion. In all cases, the results obtained were comparable to, if not better than, those obtained using standard matching metrics. Furthermore, the rank and census have the additional advantage that their computational overhead is less than these metrics. For all techniques tested, the difference between the results obtained for the synthetic stereo pair, and the ground truth results was small.

Efficient articulated trajectory reconstruction using dynamic programming and filters

This paper considers the problem of reconstructing the motion of a 3D articulated tree from 2D point correspondences subject to some temporal prior. Hitherto, smooth motion has been encouraged using a trajectory basis, yielding a hard combinatorial problem with time complexity growing exponentially in the number of frames. Branch and bound strategies have previously attempted to curb this complexity whilst maintaining global optimality. However, they provide no guarantee of being more efficient than exhaustive search. Inspired by recent work which reconstructs general trajectories using compact high-pass filters, we develop a dynamic programming approach which scales linearly in the number of frames, leveraging the intrinsically local nature of filter interactions. Extension to affine projection enables reconstruction without estimating cameras.

Using variable speed limits for motorway off-ramp queue protection

Motorway off-ramps are a significant source of traffic congestion and collisions. Heavy diverging traffic to off-ramps slows down the mainline traffic speed. When the off-ramp queue spillbacks onto the mainline, it leads to a major breakdown of the motorway capacity and a significant threat to the traffic safety. This paper proposes using Variable Speed Limits (VSL) for protection of the motorway off-ramp queue and thus to promote safety in congested diverging areas. To support timely activation of VSL in advance of queue spillover, a proactive control strategy is proposed based on a real-time off-ramp queue estimation and prediction. This process determines the estimated queue size in the near-term future, on which the decision to change speed limits is made. VSL can effectively slow down traffic as it is mandatory that drivers follow the changed speed limits. A collateral benefit of VSL is its potential effect on drivers making them more attentive to the surrounding traffic conditions, and prepared for a sudden braking of the leading car. This paper analyses and quantifies these impacts and potential benefits of VSL on traffic safety and efficiency using the microsimulation approach.

Conserved and variable features of gag structure and arrangement in immature retrovirus particles

The assembly of retroviruses is driven by oligomerization of the Gag polyprotein. We have used cryo-electron tomography together with subtomogram averaging to describe the three-dimensional structure of in vitro-assembled Gag particles from human immunodeficiency virus, Mason-Pfizer monkey virus, and Rous sarcoma virus. These represent three different retroviral genera: the lentiviruses, betaretroviruses and alpharetroviruses. Comparison of the three structures reveals the features of the supramolecular organization of Gag that are conserved between genera and therefore reflect general principles of Gag-Gag interactions and the features that are specific to certain genera. All three Gag proteins assemble to form approximately spherical hexameric lattices with irregular defects. In all three genera, the N-terminal domain of CA is arranged in hexameric rings around large holes. Where the rings meet, 2-fold densities, assigned to the C-terminal domain of CA, extend between adjacent rings, and link together at the 6-fold symmetry axis with a density, which extends toward the center of the particle into the nucleic acid layer. Although this general arrangement is conserved, differences can be seen throughout the CA and spacer peptide regions. These differences can be related to sequence differences among the genera. We conclude that the arrangement of the structural domains of CA is well conserved across genera, whereas the relationship between CA, the spacer peptide region, and the nucleic acid is more specific to each genus.

Heteroscedastic probabilistic linear discriminant analysis for manifold learning in video-based face recognition

To recognize faces in video, face appearances have been widely modeled as piece-wise local linear models which linearly approximate the smooth yet non-linear low dimensional face appearance manifolds. The choice of representations of the local models is crucial. Most of the existing methods learn each local model individually meaning that they only anticipate variations within each class. In this work, we propose to represent local models as Gaussian distributions which are learned simultaneously using the heteroscedastic probabilistic linear discriminant analysis (PLDA). Each gallery video is therefore represented as a collection of such distributions. With the PLDA, not only the within-class variations are estimated during the training, the separability between classes is also maximized leading to an improved discrimination. The heteroscedastic PLDA itself is adapted from the standard PLDA to approximate face appearance manifolds more accurately. Instead of assuming a single global within-class covariance, the heteroscedastic PLDA learns different within-class covariances specific to each local model. In the recognition phase, a probe video is matched against gallery samples through the fusion of point-to-model distances. Experiments on the Honda and MoBo datasets have shown the merit of the proposed method which achieves better performance than the state-of-the-art technique.

A variable step-size FxLMS algorithm for feedforward active noise control systems based on a new online secondary path modelling technique

Several approaches have been introduced in literature for active noise control (ANC) systems. Since FxLMS algorithm appears to be the best choice as a controller filter, researchers tend to improve performance of ANC systems by enhancing and modifying this algorithm. This paper proposes a new version of FxLMS algorithm. In many ANC applications an online secondary path modelling method using a white noise as a training signal is required to ensure convergence of the system. This paper also proposes a new approach for online secondary path modelling in feedfoward ANC systems. The proposed algorithm stops injection of the white noise at the optimum point and reactivate the injection during the operation, if needed, to maintain performance of the system. Benefiting new version of FxLMS algorithm and not continually injection of white noise makes the system more desirable and improves the noise attenuation performance. Comparative simulation results indicate effectiveness of the proposed approach.

A new feedback ANC system approach

We propose a new active noise control (ANC) technique. The technique has a feedback structure to have a simple configuration in practical implementation. In this approach, the secondary path is modelled online to ensure convergence of the system as the secondary paths are practically time varying or non-linear. The proposed method consists of two steps: a noise controller which is based on a modified FxLMS algorithm, and a new variable step size (VSS) LMS algorithm which is used to adapt the modelling filter with the secondary path. The proposed algorithm stops injection of the white noise at the optimum point and reactivate the injection during the operation, if needed, to maintain performance of the system. Eliminating continuous injection of the white noise increases the performance of the proposed method significantly and makes it more desirable for practical ANC systems. The computer simulations are presented to show the effectiveness of the proposed method.

Image based visual servo control for fixed wing UAVs tracking linear infrastructure in wind

This paper presents an Image Based Visual Servo control design for Fixed Wing Unmanned Aerial Vehicles tracking locally linear infrastructure in the presence of wind using a body fixed imaging sensor. Visual servoing offers improved data collection by posing the tracking task as one of controlling a feature as viewed by the inspection sensor, although is complicated by the introduction of wind as aircraft heading and course angle no longer align. In this work it is shown that the effects of wind alter the desired line angle required for continuous tracking to equal the wind correction angle as would be calculated to set a desired course. A control solution is then sort by linearizing the interaction matrix about the new feature pose such that kinematics of the feature can be augmented with the lateral dynamics of the aircraft, from which a state feedback control design is developed. Simulation results are presented comparing no compensation, integral control and the proposed controller using the wind correction angle, followed by an assessment of response to atmospheric disturbances in the form of turbulence and wind gusts

Board age and gender diversity : a test of competing linear and curvilinear predictions

We test competing linear and curvilinear predictions between board diversity and performance. The predictions were tested using archival data on 288 organizations listed on the Australian Securities Exchange. The findings provide additional evidence on the business case for board gender diversity and refine the business case for board age diversity.

Estimating the effects of ambient temperature on mortality : methodological challenges and proposed solutions

The health impacts of exposure to ambient temperature have been drawing increasing attention from the environmental health research community, government, society, industries, and the public. Case-crossover and time series models are most commonly used to examine the effects of ambient temperature on mortality. However, some key methodological issues remain to be addressed. For example, few studies have used spatiotemporal models to assess the effects of spatial temperatures on mortality. Few studies have used a case-crossover design to examine the delayed (distributed lag) and non-linear relationship between temperature and mortality. Also, little evidence is available on the effects of temperature changes on mortality, and on differences in heat-related mortality over time. This thesis aimed to address the following research questions: 1. How to combine case-crossover design and distributed lag non-linear models? 2. Is there any significant difference in effect estimates between time series and spatiotemporal models? 3. How to assess the effects of temperature changes between neighbouring days on mortality? 4. Is there any change in temperature effects on mortality over time? To combine the case-crossover design and distributed lag non-linear model, datasets including deaths, and weather conditions (minimum temperature, mean temperature, maximum temperature, and relative humidity), and air pollution were acquired from Tianjin China, for the years 2005 to 2007. I demonstrated how to combine the case-crossover design with a distributed lag non-linear model. This allows the case-crossover design to estimate the non-linear and delayed effects of temperature whilst controlling for seasonality. There was consistent U-shaped relationship between temperature and mortality. Cold effects were delayed by 3 days, and persisted for 10 days. Hot effects were acute and lasted for three days, and were followed by mortality displacement for non-accidental, cardiopulmonary, and cardiovascular deaths. Mean temperature was a better predictor of mortality (based on model fit) than maximum or minimum temperature. It is still unclear whether spatiotemporal models using spatial temperature exposure produce better estimates of mortality risk compared with time series models that use a single site’s temperature or averaged temperature from a network of sites. Daily mortality data were obtained from 163 locations across Brisbane city, Australia from 2000 to 2004. Ordinary kriging was used to interpolate spatial temperatures across the city based on 19 monitoring sites. A spatiotemporal model was used to examine the impact of spatial temperature on mortality. A time series model was used to assess the effects of single site’s temperature, and averaged temperature from 3 monitoring sites on mortality. Squared Pearson scaled residuals were used to check the model fit. The results of this study show that even though spatiotemporal models gave a better model fit than time series models, spatiotemporal and time series models gave similar effect estimates. Time series analyses using temperature recorded from a single monitoring site or average temperature of multiple sites were equally good at estimating the association between temperature and mortality as compared with a spatiotemporal model. A time series Poisson regression model was used to estimate the association between temperature change and mortality in summer in Brisbane, Australia during 1996–2004 and Los Angeles, United States during 1987–2000. Temperature change was calculated by the current day's mean temperature minus the previous day's mean. In Brisbane, a drop of more than 3 �C in temperature between days was associated with relative risks (RRs) of 1.16 (95% confidence interval (CI): 1.02, 1.31) for non-external mortality (NEM), 1.19 (95% CI: 1.00, 1.41) for NEM in females, and 1.44 (95% CI: 1.10, 1.89) for NEM aged 65.74 years. An increase of more than 3 �C was associated with RRs of 1.35 (95% CI: 1.03, 1.77) for cardiovascular mortality and 1.67 (95% CI: 1.15, 2.43) for people aged < 65 years. In Los Angeles, only a drop of more than 3 �C was significantly associated with RRs of 1.13 (95% CI: 1.05, 1.22) for total NEM, 1.25 (95% CI: 1.13, 1.39) for cardiovascular mortality, and 1.25 (95% CI: 1.14, 1.39) for people aged . 75 years. In both cities, there were joint effects of temperature change and mean temperature on NEM. A change in temperature of more than 3 �C, whether positive or negative, has an adverse impact on mortality even after controlling for mean temperature. I examined the variation in the effects of high temperatures on elderly mortality (age . 75 years) by year, city and region for 83 large US cities between 1987 and 2000. High temperature days were defined as two or more consecutive days with temperatures above the 90th percentile for each city during each warm season (May 1 to September 30). The mortality risk for high temperatures was decomposed into: a "main effect" due to high temperatures using a distributed lag non-linear function, and an "added effect" due to consecutive high temperature days. I pooled yearly effects across regions and overall effects at both regional and national levels. The effects of high temperature (both main and added effects) on elderly mortality varied greatly by year, city and region. The years with higher heat-related mortality were often followed by those with relatively lower mortality. Understanding this variability in the effects of high temperatures is important for the development of heat-warning systems. In conclusion, this thesis makes contribution in several aspects. Case-crossover design was combined with distribute lag non-linear model to assess the effects of temperature on mortality in Tianjin. This makes the case-crossover design flexibly estimate the non-linear and delayed effects of temperature. Both extreme cold and high temperatures increased the risk of mortality in Tianjin. Time series model using single site’s temperature or averaged temperature from some sites can be used to examine the effects of temperature on mortality. Temperature change (no matter significant temperature drop or great temperature increase) increases the risk of mortality. The high temperature effect on mortality is highly variable from year to year.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.