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.

The role of intermediaries in the implementation and development of asynchronous rural access

In Orissa state, India, the DakNet system supports asynchronous Internet communication between an urban hub and rural nodes. DakNet is noteworthy in many respects, not least in how the system leverages existing transport infrastructure. Wi-Fi transceivers mounted on local buses send and receive user data from roadside kiosks, for later transfer to/from the Internet via wireless protocols. This store-and-forward system allows DakNet to offer asynchronous communication capacity to rural users at low cost. The original ambition of the DakNet system was to provide email and SMS facilities to rural communities. Our 2008 study of the communicative ecology surrounding the DakNet system revealed that this ambition has now evolved – in response to market demand – to the extent that e-shopping (rather than email) has become the primary driver behind the DakNet offer.

Quantum memory

New models of human cognition inspired by quantum theory could underpin information technologies that are better aligned with howwe recall information.

Enabling Open Access to Public Sector Information With Creative Commons Licences : The Australian Experience

This chapter considers how open content licences of copyright-protected materials – specifically, Creative Commons (CC) licences - can be used by governments as a simple and effective mechanism to enable reuse of their PSI, particularly where materials are made available in digital form online or distributed on disk.

Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

Executive control of working memory in schizophrenia

There is considerable evidence that working memory impairment is a common feature of schizophrenia. The present study assessed working memory and executive function in 54 participants with schizophrenia, and a group of 54 normal controls matched to the patients on age, gender and estimated premorbid IQ, using traditional and newer measures of executive function and two dual tasks—Telephone Search with Counting and the Memory Span and Tracking Task. Results indicated that participants with schizophrenia were significantly impaired on all standardised measures of executive function with the exception of a composite measure of the Trail Making Test. Results for the dual task measures demonstrated that while the participants with schizophrenia were unimpaired on immediate digit span recall over a 2-min period, they recalled fewer digit strings and performed more poorly on a tracking task (box-crossing task) compared with controls. In addition, participants with schizophrenia performed more poorly on the tracking task when they were required to simultaneously recall digits strings than when they performed this task alone. Contrary to expectation, results of the telephone search task under dual conditions were not significantly different between groups. These results may reflect the insufficient complexity of the tone-counting task as an interference task. Overall, the present study showed that participants with schizophrenia appear to have a restricted impairment of their working memory system that is evident in tasks in which the visuospatial sketchpad slave system requires central executive control.

Personal Access Tutor - helping students to learn MS Access

The paper describes Personal Access Tutor (PAT),an Intelligent Tutoring System which helps students to learn how to create forms and reports in MS Access. We present the architecture and components of PAT and also the services that PAT provides to the students. Results for an external (system) evaluation of PAT (both qualitative and quantitative data) are presented and discussed.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Open Access and Public Sector Information : Policy Developments in Australia and Key Jurisdictions

This book chapter considers recent developments in Australia and key jurisdictions both in relation to the formation of a national information strategy and the management of legal rights in public sector information.

E-learning and access : getting behind the hype

Rapid advances in information and communications technology (ICT) - particularly the development of online technologies -have transformed the nature of economic, social and cultural relations across the globe. In the context of higher education in post-industrial societies, technological change has had a significant impact on university operating environments. In a broad sense, technological advancement has contributed significantly to the increasing complexity of global economies and societies, which is reflected in the rise of lifelong learning discourses with which universities are engaging. More specifically, the ever-expanding array of ICT available within the university sector has generated new management and pedagogical imperatives for higher education in the information age.