Some Remarks on the Approximation of Transitional Density in Stochastic Differential Equations

Aijt-Sahalia (2002) introduced a method to estimate transitional probability densities of di®usion processes by means of Hermite expansions with coe±cients determined by means of Taylor series. This note describes a numerical procedure to ¯nd these coe±cients based on the calculation of moments. One advantage of this procedure is that it can be used e®ectively when the mathematical operations required to ¯nd closed-form expressions for these coe±cients are otherwise infeasible.

Report : stochastic analysis of road asset data for maintenance cost prediction

Reliable budget/cost estimates for road maintenance and rehabilitation are subjected to uncertainties and variability in road asset condition and characteristics of road users. The CRC CI research project 2003-029-C ‘Maintenance Cost Prediction for Road’ developed a method for assessing variation and reliability in budget/cost estimates for road maintenance and rehabilitation. The method is based on probability-based reliable theory and statistical method. The next stage of the current project is to apply the developed method to predict maintenance/rehabilitation budgets/costs of large networks for strategic investment. The first task is to assess the variability of road data. This report presents initial results of the analysis in assessing the variability of road data. A case study of the analysis for dry non reactive soil is presented to demonstrate the concept in analysing the variability of road data for large road networks. In assessing the variability of road data, large road networks were categorised into categories with common characteristics according to soil and climatic conditions, pavement conditions, pavement types, surface types and annual average daily traffic. The probability distributions, statistical means, and standard deviation values of asset conditions and annual average daily traffic for each type were quantified. The probability distributions and the statistical information obtained in this analysis will be used to asset the variation and reliability in budget/cost estimates in later stage. Generally, we usually used mean values of asset data of each category as input values for investment analysis. The variability of asset data in each category is not taken into account. This analysis method demonstrated that it can be used for practical application taking into account the variability of road data in analysing large road networks for maintenance/rehabilitation investment analysis.

Relative entropy rate based multiple hidden Markov Model Approximation

This paper proposes a novel relative entropy rate (RER) based approach for multiple HMM (MHMM) approximation of a class of discrete-time uncertain processes. Under different uncertainty assumptions, the model design problem is posed either as a min-max optimisation problem or stochastic minimisation problem on the RER between joint laws describing the state and output processes (rather than the more usual RER between output processes). A suitable filter is proposed for which performance results are established which bound conditional mean estimation performance and show that estimation performance improves as the RER is reduced. These filter consistency and convergence bounds are the first results characterising multiple HMM approximation performance and suggest that joint RER concepts provide a useful model selection criteria. The proposed model design process and MHMM filter are demonstrated on an important image processing dim-target detection problem.

Increasing stochastic perturbations enhances acquisition and learning of complex sport movements

Traditionally, the aquisition of skills and sport movement has been characterised by numerous repetitions of presumed model movement pattern to be acquired by learners. This approach has been questioned by research identifying the presence of individualised movement patterns and the low probability of occurrence of two identical movements within and between individuals. In contrast, the differential learning approach claims advantage for incurring variability in the learning process by adding stochastic perturbations during practice. These ideas are exemplified by data from a high jump experiment which compared the effectiveness of classical and a differential training approach with pre-post test design. Results showed clear advantages for the group with additional stochastic perturbation during the aquisition phase in comparison to classically trained athletes. Analogies to similar phenomenological effects in the neurobiological literature are discussed.

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

Research Monograph: Managing ubiquitous eco cities: telecommunication infrastructure networks, technology convergence and intelligent urban management systems

Efficient and effective urban management systems for Ubiquitous Eco Cities require having intelligent and integrated management mechanisms. This integration includes bringing together economic, socio-cultural and urban development with a well orchestrated, transparent and open decision making mechanism and necessary infrastructure and technologies. In Ubiquitous Eco Cities telecommunication technologies play an important role in monitoring and managing activities over wired, wireless or fibre-optic networks. Particularly technology convergence creates new ways in which the information and telecommunication technologies are used and formed the back bone or urban management systems. The 21st Century is an era where information has converged, in which people are able to access a variety of services, including internet and location based services, through multi-functional devices such as mobile phones and provides opportunities in the management of Ubiquitous Eco Cities. This research paper discusses the recent developments in telecommunication networks and trends in convergence technologies and their implications on the management of Ubiquitous Eco Cities and how this technological shift is likely to be beneficial in improving the quality of life and place of residents, workers and visitors. The research paper reports and introduces recent approaches on urban management systems, such as intelligent urban management systems, that are suitable for Ubiquitous Eco Cities.

Managing ubiquitous eco cities : the role of urban telecommunication infrastructure networks and convergence technologies

A successful urban management system for a Ubiquitous Eco City requires an integrated approach. This integration includes bringing together economic, socio-cultural and urban development with a well orchestrated, transparent and open decision making mechanism and necessary infrastructure and technologies. Rapidly developing information and telecommunication technologies and their platforms in the late 20th Century improves urban management and enhances the quality of life and place. Telecommunication technologies provide an important base for monitoring and managing activities over wired, wireless or fibre-optic networks. Particularly technology convergence creates new ways in which the information and telecommunication technologies are used. The 21st Century is an era where information has converged, in which people are able to access a variety of services, including internet and location based services, through multi-functional devices such as mobile phones and provides opportunities in the management of Ubiquitous Eco Cities. This paper discusses the recent developments in telecommunication networks and trends in convergence technologies and their implications on the management of Ubiquitous Eco Cities and how this technological shift is likely to be beneficial in improving the quality of life and place. The paper also introduces recent approaches on urban management systems, such as intelligent urban management systems, that are suitable for Ubiquitous Eco Cities.

Ourplace : the convergence of locative media and online participatory culture

The trans-locative potential of the Internet has driven the design of many online applications. Online communities largely cluster around topics of interest, which take precedence over participants’ geographical locations. The site of production is often disregarded when creative content appears online. However, for some, a sense of place is a defining aspect of creativity. Yet environments that focus on the display and sharing of regionally situated content have, so far, been largely overlooked. Recent developments in geo-technologies have precipitated the emergence of a new field of interactive media. Entitled locative media, it emphasizes the geographical context of media. This paper argues that we might combine practices of locative media (experiential mapping and geo-spatial annotation) with aspects of online participatory culture (uploading, file-sharing and search categorization) to produce online applications that support geographically ‘located’ communities. It discusses the design considerations and possibilities of this convergence,making reference to an example, OurPlace 3G to 3D, which has to date been developed as a prototype.1 It goes on to discuss the benefits and potential uses of such convergent applications, including the co-production of spatial- emporal narratives of place.

Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.