Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

Complementarity and the uncertainty principle as aesthetic principles : the practice and performance of The Physics Project

Using the generative processes developed over two stages of creative development and the performance of The Physics Project at the Loft at the Creative Industries Precinct at the Queensland University of Technology (QUT) from 5th – 8th April 2006 as a case study, this exegesis considers how the principles of contemporary physics can be reframed as aesthetic principles in the creation of contemporary performance. The Physics Project is an original performance work that melds live performance, video and web-casting and overlaps an exploration of personal identity with the physics of space, time, light and complementarity. It considers the acts of translation between the language of physics and the language of contemporary performance that occur via process and form. This exegesis also examines the devices in contemporary performance making and contemporary performance that extend the reach of the performance, including the integration of the live and the mediated and the use of metanarratives.

Service staff attitudes, organisational practices and performance drivers

We provide conceptual and empirical insights elucidating how organizational practices influence service staff attitudes and behaviors and how the latter set affects organizational performance drivers. Our analyses suggest that service organizations can enhance their performance by putting in place strategies and practices that strengthen the service-oriented behaviors of their employees and reduce their intentions to leave the organization. Improved performance is accomplished through both the delivery of high quality services (enhancing organizational effectiveness) and the maintenance of frontline staff(increasing organizational efficiency). Specifically, service-oriented business strategies in the form of organizational-level service orientation and practices in the form of training directly influence the manifest service-oriented behaviors of staff. Training also indirectly affects the intention of frontline staff to leave the organization; it increases job satisfaction, which, in turn has an impact on affective commitment. Both affective and instrumental commitment were hypothesized to reduce the intentions of frontline staff to leave the organization, however only affective commitment had a significant effect.

The new wave : a Brisbane perspective : La Boite Theatre Company's distinctive contribution

In 1967 Brisbane Repertory Theatre made a decision that was to change the city's cultural landscape in a significant and lasting way. Faced with crippling theatre rental costs, Brisbane Rep. found a realistic solution by converting one of its properties - an old Queenslander - into a unique theatre space. The theatre-in-the box that emerged, aptly called La Boite, opened on 23 June 1967 with a production of John Osborne's Look Back in Anger. This experimental space excited the imagination of a new, younger audience not previously interested in Brisbane Rep's essentially conservative fare. It attracted a new group of directors and actors keen to be part of a changing repertoire that embraced more radical, non-mainstream productions, some of which were of Australian plays. The decade after 1967 was a period of change and development unprecedented in La Boite's history. Since then the company has sustained and grown its commitment to Australian plays and the commissioning of new works. To what extent was this most significance moment in La Boite's transformational journey influenced by southern 'new waves' of change? With the benefit of hindsight, it is now time for a re-consideration of Brisbane's distinctive contribution to the New Wave.

Impromptu : an interactive programming environment for composition and performance

Interactive development environments are making a resurgence. The traditional batch style of programming, edit -> compile -> run, is slowly being reevaluated by the development community at large. Languages such as Perl, Python and Ruby are at the heart of a new programming culture commonly described as extreme, agile or dynamic. Musicians are also beginning to embrace these environments and to investigate the opportunity to use dynamic programming tools in live performance. This paper provides an introduction to Impromptu, a new interactive development environment for musicians and sound artists.

"Men at play : masculinities in Australian theater since the 1950s" -- By Jonathan Bollen, Adrian Kiernander and Bruce Parr

Adopting a thematic rather than chronological arrangement, this co-authored book surveys representations of men and masculinity in post-war Australian theater. Its searching and sophisticated analyses draw upon playscripts, critical records and archival material, including screen versions of stage productions. The study is organized around two distinct periods of Australian theater history: the 1950s to 1970, during which time a national theatremovement flourished, and the mid-1980s onward.Whilst some attention is given to different genres, discussion centers primarily on realist works from the mainstream. Several plays usually omitted from orthodox theater histories, such as Barry Pree’s A Fox in the Night (1959), are given detailed treatments.

TAFE Governance Transitions Prophetical

Drama staff from QUT Creative Industries were commissioned by the Dept of Education, Training and the Arts (DETA) to devise a tailor made and highly targeted staff development program for TAFE Queensland Institute Directors and senior managers. The program was designed to assist these senior staff to address a range of change and governance issues in the context of TAFE Queensland’s transition to statutory authority status. In responding to this brief, the QUT team utilised an original applied performance technique known as a ‘Prophetical’ to research, devise and present an interactive case study to TAFE Institute Directors and senior managers. This particular Prophetical portrayed a senior staff team at the fictitious Massey Institute of TAFE, confronted by an escalating series of crises as they try to manage the transition to the fundamentally different business model of a statutory authority.

Changing musical emotion : a computational rule system for modifying score and performance

When communicating emotion in music, composers and performers encode their expressive intentions through the control of basic musical features such as: pitch, loudness, timbre, mode, and articulation. The extent to which emotion can be controlled through the systematic manipulation of these features has not been fully examined. In this paper we present CMERS, a Computational Music Emotion Rule System for the control of perceived musical emotion that modifies features at the levels of score and performance in real-time. CMERS performance was evaluated in two rounds of perceptual testing. In experiment I, 20 participants continuously rated the perceived emotion of 15 music samples generated by CMERS. Three music works, each with five emotional variations were used (normal, happy, sad, angry, and tender). The intended emotion by CMERS was correctly identified 78% of the time, with significant shifts in valence and arousal also recorded, regardless of the works’ original emotion.

La Boite The Story of an Australian Theatre Company

Since its genesis in 1925, La Boite has never been afraid of change. Despite controversies, crises and crippling set-backs that should have closed its stage doors many times, La Boite - which began life as the Brisbane Repertory Theatre Society - has proved itself an extraordinary survivor. When the opportunity came to build its own theatre, its inspired choice of theatre-in-the-round gave Brisbane an iconic performance space that attracted a whole new generation of actors, directors and designers and placed La Boite at the forefront of contemporary theatre practice. The place, in Katharine Brisbane’s words, “to see the red meat of theatre”. Always enterprising, with gritty determination it became a professional theatre company of national significance; and early in the new millennium triumphantly re-located to its new home at The Roundhouse Theatre. La Boite –The Story of an Australian Theatre Company both interrogates and celebrates the history of Queensland’s oldest theatre company. Highlighting the roles key people played in its evolution – particularly four remarkable women – Christine Comans explores La Boite’s colourful past, its cultural significance to Brisbane, and its vibrant and enduring role in the nation’s theatrical history.

Devising a scenographic approach in Jonzi D's Hip Hop theatre

Jonzi D, one of the leading Hip Hop voices in the UK, creates contemporary theatrical works that merge dance, street art, original scored music and contemporary rap poetry, to create theatrical events that expand a thriving sense of a Hip Hop nation with citizens in the UK, throughout southern Africa and the rest of the world. In recent years Hip Hop has evolved as a performance genre in and of itself that not only borrows from other forms but vitally now contributes back to the body of contemporary practice in the performing arts. As part of this work Jonzi’s company Jonzi D Productions is committed to creating and touring original Hip Hop theatre that promotes the continuing development and awareness of a nation with its own language, culture and currency that exists without borders. Through the deployment of a universal voice from the local streets of Johannesburg and the East End of London, Jonzi D creates a form of highly energized performance that elevates Hip Hop as great democratiser between the highly developed global and under resourced local in the world. It is the staging of this democratised and technologised future (and present), that poses the greatest challenge for the scenographer working with Jonzi and his company, and the associated deprogramming and translation of the artists particular filmic vision to the stage, that this discussion will explore. This paper interrogates not only how a scenographic strategy can support the existence of this work but also how the scenographer as outsider can enter and influence this nation.

Singing the blues : developing a cabaret performance on depression

This paper will discuss the researcher’s practice-led study within the field of contemporary cabaret performance. The project is focussed on transforming personal stories of depression into cabaret with the aims of raising community awareness of the issue. In the process, the research aims to explore innovations within the field of cabaret. Interviews conducted with individuals who have suffered from depression are being used as ‘inspiration points’ for the development of the performance. This paper will provide a short contextual review for the project and introduce the researcher’s creative process. For the purposes of this research, cabaret has been defined as performances of songs and dialogue in direct-address with the audience. Cabaret performances merge ‘high’ and ‘low’ art forms (often including satirical comedy), and are generally performed in small-scale venues. The accessible, intimate and light-hearted nature of cabaret offers unique opportunities for the discussion of social issues.