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.

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.

Practising inspired leadership : the use of applied theatre 'prophetical' in the Executive Leadership Development Program for Queensland Health

The Executive Leadership Development Program embarked upon by Queensland Health as a part of the major reform program is discussed. The second stage of the program has begun and the main aim is to ensure leadership development across the organization.

The educational affordances of generative media in arts education

Network Jamming systems provide real-time collaborative media performance experiences for novice or inexperienced users. In this paper we will outline the theoretical and developmental drivers for our Network Jamming software, called jam2jam. jam2jam employs generative algorithmic techniques with particular implications for accessibility and learning. We will describe how theories of engagement have directed the design and development of jam2jam and show how iterative testing cycles in numerous international sites have informed the evolution of the system and its educational potential. Generative media systems present an opportunity for users to leverage computational systems to make sense of complex media forms through interactive and collaborative experiences. Generative music and art are a relatively new phenomenon that use procedural invention as a creative technique to produce music and visual media. These kinds of systems present a range of affordances that can facilitate new kinds of relationships with music and media performance and production. Early systems have demonstrated the potential to provide access to collaborative ensemble experiences to users with little formal musical or artistic expertise.This presentation examines the educational affordances of these systems evidenced by field data drawn from the Network Jamming Project. These generative performance systems enable access to a unique kind of music/media’ ensemble performance with very little musical/ media knowledge or skill and they further offer the possibility of unique interactive relationships with artists and creative knowledge through collaborative performance. Through the process of observing, documenting and analysing young people interacting with the generative media software jam2jam a theory of meaningful engagement has emerged from the need to describe and codify how users experience creative engagement with music/media performance and the locations of meaning. In this research we observed that the musical metaphors and practices of ‘ensemble’ or collaborative performance and improvisation as a creative process for experienced musicians can be made available to novice users. The relational meanings of these musical practices afford access to high level personal, social and cultural experiences. Within the creative process of collaborative improvisation lie a series of modes of creative engagement that move from appreciation through exploration, selection, direction toward embodiment. The expressive sounds and visions made in real-time by improvisers collaborating are immediate and compelling. Generative media systems let novices access these experiences with simple interfaces that allow them to make highly professional and expressive sonic and visual content simply by using gestures and being attentive and perceptive to their collaborators. These kinds of experiences present the potential for highly complex expressive interactions with sound and media as a performance. Evidence that has emerged from this research suggest that collaborative performance with generative media is transformative and meaningful. In this presentation we draw out these ideas around an emerging theory of meaningful engagement that has evolved from the development of network jamming software. Primarily we focus on demonstrating how these experiences might lead to understandings that may be of educational and social benefit.

Art and the sublime : the paradox of indeterminacy unknowing and (dis)orientation in the presentation of the unpresentable

the (dis)orientation of thought in its encounter with art can be understood as the direct result of an encounter with indeterminacy as a lack in meaning. As an artist I am aware of how this indeterminacy impacts on the perceived value and authority of the artistic voice and in particular its value as a research voice. This paper explores this indeterminacy of meaning, as a profound and disturbing unknowing characteristic of the sublime and argues its value to advanced thought and for any methodological understanding of practice-led research. Lyotard described the sublime as an ‘understanding’ through which art and its associated practices may be able to resist an all too easy assimilation by the public as just a consumer commodity. His thought represents an attempt to both politically and philosophically understand art’s, and particularly abstract painting’s, affect as a state of profound and positive unknowing. To talk of the sublime in art is to speak of the suspension of any comfortable certainty in being and instead to engage with the real as a limit to meaning and knowing. It is to talk of the presentation of the unpresentable as a momentary but significant dissolution of representation. This understanding of the sublime is then further explored through the cultural phenomena of the monochrome painting and applied to the work of the two contemporary artists, Franz Erhard Walter and Günter Umberg. Initially the monochrome was understood as an attempt to go beyond traditional representation and present the unpresentable. In the one hundred years or so since that initial move this understanding has broadened. The monochrome now presents itself as a genre or even project within visual art but it still has much to teach us. In the concretely abstract and performative artworks of Franz Erhard Walter and Günter Umberg, traces of this ambition remain and their work can be seen to pose questions probing our understandings and experiences of artistic meaning, its value and the real.

Practice-led research and the innovation agenda : beyond the postgraduate research degree in the arts, design and media

The rise of the ‘practice-led’ research approach has given us a new way of understanding what creative practice in art, design and media can do in the academy and the world— it can materialise new ideas and forms into being as a form of experimental research. Yet, to date, attention around the world, and especially in Australia, has been chiefly directed at the postgraduate research degrees, most notably the PhD or doctoral equivalents. Recent mapping projects and surveys of practice-led research in Australia reveal much about the institutional conditions of higher degree researchers, supervisors, examiners and research training (Baker et al 2009; Evans et al 2003; Dally et al 2004; Paltridge et al 2009; Phillips et al 2009). Given this focus, we might well ask: is the practice-led approach destined to be a part of the higher degree ghetto only, or does it have an afterlife? What is the place of ‘practice-led’ beyond the postgraduate degree? After all postgraduate researchers do not remain postgraduates forever, and perhaps the practice-led approach to research may have benefits in wider university, professional and communal contexts.

State of the arts and innovation : before and after the review of the national innovation system

This article examines the relationship between the arts and national innovation policy in Australia, pivoting around the Venturous Australia report released in September 2008 as part of the Review of the National Innovation System (RNIS). This came at a time of optimism that the arts sector would be included in Australia’s federal innovation policy. However, despite the report’s broad vision for innovation and specific commentary on the arts, the more ambitious hopes of arts sector advocates remained unfulfilled. This article examines the entwining discourses of creativity and innovation which emerged globally and in Australia prior to the RNIS, before analysing Venturous Australia in terms of the arts and the ongoing science-and-technology bias to innovation policy. It ends by considering why sector-led policy research and lobbying has to date proved unsuccessful and then suggests what public policy development is now needed.

“Filling out the forms was a nightmare” : project evaluation and the reflective practitioner in community theatre in contemporary Northern Ireland

Since the Good Friday Agreement of 1998, large sums have been invested in community theatre projects in Northern Ireland, in the interests of conflict transformation and peace building. While this injection of funds has resulted in an unprecedented level of applied theatre activity, opportunities to maximise learning from this activity are being missed. It is generally assumed that project evaluation is undertaken at least partly to assess the degree of success of projects against important social objectives, with a view to learning what works, what does not, and what might work in the future. However, three ethnographic case studies of organisations delivering applied theatre projects in Northern Ireland indicate that current processes used to evaluate such projects are both flawed and inadequate for this purpose. Practitioners report that the administrative work involved in applying for and justifying funding is onerous, burdensome, and occurs at the expense of artistic activity. This is a very real concern when the time and effort devoted to ‘filling out the forms’ does not ultimately result in useful evaluative information. There are strong disincentives for organisations to report honestly on their experiences of difficulties, or undesirable impacts of projects, and this problem is not transcended by the use of external evaluators. Current evaluation processes provide little opportunity to capture unexpected benefits of projects, and small but significant successes which occur in the context of over-ambitious objectives. Little or no attempt is made to assess long-term impacts of projects on communities. Finally, official evaluation mechanisms fail to capture the reflective practice and dialogic analysis of practitioners, which would richly inform future projects. The authors argue that there is a need for clearer lines of communication, and more opportunities for mutual learning, among stakeholders involved in community development. In particular, greater involvement of the higher education sector in partnership with government and non-government agencies could yield significant benefits in terms of optimizing learning from applied theatre project evaluations.

What's your other job : a census analysis of arts employment in Australia

This report applies CCI’s creative trident methodology with the definition of the arts as established by the Australia Council for the Arts to data sourced from Australia’s national census data (from 1996, 2001 and the most recent one in 2006). Analysis has been conducted on employment, income, gender, age and the nature of employment for artists and arts related workers within and beyond the arts industries, as well as other support workers in the arts industries.

Re-generating the praxis of academic staff development through arts-based learning : beyond paradox

Effective staff development remains a challenge in higher education. This paper examines the non-traditional methodology of arts-based staff development, its potential to foster transformational learning and the practice of professional artistry, through perceptions of program impact. Over a three year period, eighty academics participated in one metropolitan Australian university’s arts-based academic development program. The methodology used one-on-one hermeneutic-based conversations with fifteen self-selected academics and a focus group with twenty other academics from all three years. The paper presents a learning model to engender academic professional artistry. The findings provide developers with support for using a non-traditional strategy of transformational learning.

Developing new alliances in higher education leadership and governance : autopoietic application of the “arts” creative capacities

This paper, underpinned by a framework of autopoietic principles of creativity/innovation and leadership/governance, argues that open forms of creativity in ‘arts’ provide opportunity for impact upon concepts of development, leadership and governance. The alliance of creativity and governance suggests that by examining various understandings of artistic experiences, readers may perceive new understandings of alliance, application and assessment of such experiences. This critical understanding would include assessing whether such experience supports people changing their aspirations as they become what they want to be. Such understanding may also suggest that different applications of the creative capacity of the ‘arts’ offers relevance in alleged ‘non-creative’ areas of academe, particularly in areas of management, leadership and governance. This alliance also offers the possibility of new staff development programs that facilitate learning and building of individual capacity, as well as facilitate congruent development process and policy, particularly within academic organisational structures.

Designing ePortfolios for music postgraduate study : a practice-led inquiry

In this research I have examined how ePortfolios can be designed for Music postgraduate study through a practice led research enquiry. This process involved designing two Web 2.0 ePortfolio systems for a group of five post graduate music research students. The design process revolved around the application of an iterative methodology called Software Develop as Research (SoDaR) that seeks to simultaneously develop design and pedagogy. The approach to designing these ePortfolio systems applied four theoretical protocols to examine the use of digitised artefacts in ePortfolio systems to enable a dynamic and inclusive dialogue around representations of the students work. The research and design process involved an analysis of existing software and literature with a focus upon identifying the affordances of available Web 2.0 software and the applications of these ideas within 21st Century life. The five post graduate music students each posed different needs in relation to the management of digitised artefacts and the communication of their work amongst peers, supervisors and public display. An ePortfolio was developed for each of them that was flexible enough to address their needs within the university setting. However in this first SoDaR iteration data gathering phase I identified aspects of the university context that presented a negative case that impacted upon the design and usage of the ePortfolios and prevented uptake. Whilst the portfolio itself functioned effectively, the university policies and technical requirements prevented serious use. The negative case analysis of the case study found revealed that Access and Control and Implementation, Technical and Policy Constraints protocols where limiting user uptake. From the semistructured interviews carried out as part of this study participant feedback revealed that whilst the participants did not use the ePortfolio system I designed, each student was employing Web 2.0 social networking and storage processes in their lives and research. In the subsequent iterations I then designed a more ‘ideal’ system that could be applied outside of the University context that draws upon the employment of these resources. In conclusion I suggest recommendations about ePortfolio design that considers what the applications of the theoretical protocols reveal about creative arts settings. The transferability of these recommendations are of course dependent upon the reapplication of the theoretical protocols in a new context. To address the mobility of ePortfolio design between Institutions and wider settings I have also designed a prototype for a business card sized USB portal for the artists’ ePortfolio. This research project is not a static one; it stands as an evolving design for a Web 2.0 ePortfolio that seeks to refer to users needs, institutional and professional contexts and the development of software that can be incorporated within the design. What it potentially provides to creative artist is an opportunity to have a dialogue about art with artefacts of the artist products and processes in that discussion.