A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Beyond Gauss: Image-set matching on the Riemannian manifold of PDFs

State-of-the-art image-set matching techniques typically implicitly model each image-set with a Gaussian distribution. Here, we propose to go beyond these representations and model image-sets as probability distribution functions (PDFs) using kernel density estimators. To compare and match image-sets, we exploit Csiszar´ f-divergences, which bear strong connections to the geodesic distance defined on the space of PDFs, i.e., the statistical manifold. Furthermore, we introduce valid positive definite kernels on the statistical manifold, which let us make use of more powerful classification schemes to match image-sets. Finally, we introduce a supervised dimensionality reduction technique that learns a latent space where f-divergences reflect the class labels of the data. Our experiments on diverse problems, such as video-based face recognition and dynamic texture classification, evidence the benefits of our approach over the state-of-the-art image-set matching methods.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

Fallen Awake

Photo from process: David Megarrity, albury 2007 - example of convergence of writing/design/perfomance/video RESEARCH COMPONENT Fallen Awake was a practice-led research process that opened the development process to the influence of collaborative authorship across artforms. The project focused on of how multiple artforms and artists converge their vision into a singular text, in the context of collaborative authorship. The work also uncovered new questions relating to the dream-life of children. The stimulus for the work was a selection of verbal statements by three-year-olds, raising complex ethical questions as the project progressed about the child’s voice, mediated by the adult artist, for the eventual presentation to a child audience. With the text emergent and open to influence, this project raised other questions related to the lived experience of children, dreaming, creative play and the development of consciousness. It pushed the creative process to experiment with associative, rather then causal narratives, and to negotiate the challenges this raises for traditional story structures and the development processes that usually shape them. It led to the consideration of each artforms and artist as equal contributors in the development of story: traditionally the province of the sole author. The outcomes appeared in various artforms, none of which was live-performance based. An ‘artist’s book’ by the designer, a ‘video treatment’ - a DVD capturing the approach to the performance and a script for an innovative large-scale performance. Fallen Awake was developed with the assistance of Strut & Fret Production House, Arts Queensland, and HotHouse Theatre, Albury Wodonga, through their ‘Month in the Country’ initiative.

Static load modelling and voltage stability indices

This paper analyzes the performance of some of the widely used voltage stability indices, namely, singular value, eigenvalue, and loading margin with different static load models. Well-known ZIP model is used to represent loads having components with different power to voltage sensitivities. Studies are carried out on a 10-bus power system and the New England 39-bus power system models. The effects of variation of load model on the performance of the voltage stability indices are discussed. The choice of voltage stability index in the context of load modelling is also suggested in this paper.

Village green

For a communal garden in Copenhagen, Stig L. Andersson uses grasses of varying texture and height, creating a new view or spatial experience from every angle. The idea of vegetation texture being an important constituent of planting design is pervasive. Gardening books tell aspiring designers that "colour, texture and form" are the central aspects of planting arrangements. While these elements contribute to this language, they have tended to limit the language of planting to a singular, two dimensional paradigm, where planting is designed in static elevation. This has developed from a perennial-border approach demonstrated by the early 20th century garden designer Gertrude Jekyll, where the viewer is parallel to the bed, and the planting is layered to address this view. If one were to characterise the difference between a garden design and a landscape architectural approach, the latter would seem self-conscious in its use of space, movement and vision.

Interview with Dr. Young-Ki Paik, President of the Human Proteome Organization (HUPO): Pharmacoproteomics and the approaching wave of “Proteomics Diagnostics”

Dr. Young-Ki Paik directs the Yonsei Proteome Research Center in Seoul, Korea and was elected as the President of the Human Proteome Organization (HUPO) in 2009. In the December 2009 issue of the Current Pharmacogenomics and Personalized Medicine (CPPM), Dr. Paik explains the new field of pharmacoproteomics and the approaching wave of “proteomics diagnostics” in relation to personalized medicine, HUPO’s role in advancing proteomics technology applications, the HUPO Proteomics Standards Initiative, and the future impact of proteomics on medicine, science, and society. Additionally, he comments that (1) there is a need for launching a Gene-Centric Human Proteome Project (GCHPP) through which all representative proteins encoded by the genes can be identified and quantified in a specific cell and tissue and, (2) that the innovation frameworks within the diagnostics industry hitherto borrowed from the genetics age may require reevaluation in the case of proteomics, in order to facilitate the uptake of pharmacoproteomics innovations. He stresses the importance of biological/clinical plausibility driving the evolution of biotechnologies such as proteomics,instead of an isolated singular focus on the technology per se. Dr. Paik earned his Ph.D. in biochemistry from the University of Missouri-Columbia and carried out postdoctoral work at the Gladstone Foundation Laboratories of Cardiovascular Disease, University of California at San Francisco. In 2005, his research team at Yonsei University first identified and characterized the chemical structure of C. elegans dauer pheromone (daumone) which controls the aging process of this nematode. He is interviewed by a multidisciplinary team specializing in knowledge translation, technology regulation, health systems governance, and innovation analysis.

Inducing shades of meaning by matrix methods : a first step towards thematic analysis of opinion

This article explores two matrix methods to induce the ``shades of meaning" (SoM) of a word. A matrix representation of a word is computed from a corpus of traces based on the given word. Non-negative Matrix Factorisation (NMF) and Singular Value Decomposition (SVD) compute a set of vectors corresponding to a potential shade of meaning. The two methods were evaluated based on loss of conditional entropy with respect to two sets of manually tagged data. One set reflects concepts generally appearing in text, and the second set comprises words used for investigations into word sense disambiguation. Results show that for NMF consistently outperforms SVD for inducing both SoM of general concepts as well as word senses. The problem of inducing the shades of meaning of a word is more subtle than that of word sense induction and hence relevant to thematic analysis of opinion where nuances of opinion can arise.

Space and Cyberspace: on the enclosure of consciousness

In this chapter I argue that the global privatisation of elctromagnetic spectrum marks this period as historically unique. I also put forward conceptual categories for understanding the nature of an emergent cybereconomy. They correspond to classical conceptions of property, value and labour, but in no way treat these categories as singular, simple or unproblematic. From a perspective informed largely by Marx’s critique of classical political economy, I frame the creation of a global cyberspace as the enclosure, or “privatisation”, of conscious activity. I argue that a full and formally defined cyberspace, at least as it is currenty conceived of, must prefigure the eventual alienation of human social existence at its most fundamental and definitive level: consciousness.

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

Professional education in built environment and design

Early and rich conversations with a range of stakeholders – academics, professionals and graduates in their early years of practice – quickly clarified that the singular challenge for most parties centres on the ways in which courses prepare graduates for the pace, diversity and flux of contemporary professional practice.---------In pursuing understanding of this central challenge this study has focused on new graduates in BED disciplines by canvassing their views and those of two other major stakeholder groups (academic staff and professional practitioners in the disciplines studied). The first crucial years of a young graduate’s life in the workforce are shaped by a number of factors including the quality of the transition-to-work experience. The quality of this life-shaping transition is dependent on a range of factors including the ways in which graduates are educated in universities, their personal developmental characteristics and those of the professional people around them and the preparedness of workplaces and other professional groups to guide new recruits through the transition experience. This study makes recommendations about how the variations in transition experience, resulting from the vagaries of all these factors across a range of worksites, may be better understood, perhaps normalised, and, at least, supported. . Early and rich conversations with a range of stakeholders – academics, professionals and graduates in their early years of practice – quickly clarified that the singular challenge for most parties centres on the ways in which courses prepare graduates for the pace, diversity and flux of contemporary professional practice. The study proceeded through literature review, focus group interviews, national online survey and workshops. Through all these methods a number of challenges and factors essential to the transition experience, and the quality of education which precedes it, were identified. Firstly the study found further evidence of the importance of higher-order graduate capabilities, namely, the development of judgment, critical enquiry and strategic thinking. Alongside these capabilities the importance of the development of emotional intelligence, particularly interpersonal and social skills, was stressed by all stakeholders. At the time of writing the global economic crisis was providing challenges to the sector and its young graduates. This phenomenon proved the value of the development of resilience and persistence in graduates, the education system was called upon by all stakeholders as a place where the future-proofing of neophytes would ensure that the unknown challenges of the future could also be confronted. The study found that the challenges of transition to work are best supported by authentic undergraduate experiences both on and off campus, inside and outside classrooms, and that commencing professional life is made easier for new graduates when university courses and workplace settings develop, sustain and support high standards and high expectations of students. All these findings indicate the importance of stakeholder expectations, roles and responsibilities in respect of the transition-to-work experience. Whilst full agreement about how these things should occur is not necessary, a process (amongst stakeholders) which seeks value alignment around transition through discussion, debate and agenda-setting would probably assist to address what is seen as a major challenge in built environment and design education.

Trace, a novel and exegesis

Trace concerns writing-walking and walking-writing. The multiple voices of both novel and exegesis assemble a rhizomic map of a walk and create a never-entirely-certain wandering look upon a woman walking, rather than a single cocksure gaze. Trace explores the aesthetics of Western walking literature and the various nostalgias inherent in that tradition. Trace wonders how lost a character can become on a walk and whether a walk is itself a kind of becoming. In the undefined liminal space where the urban bleeds into the rural, Trace challenges the singular perspective of the dominating gaze with a wandering look, which aims to make an original contribution to both the walk in literature and to exegetical form.

Defibrillator

Defibrillator is a 16’41” musical work for solo performer, laptop computer and electric guitar. The electric guitar is processed in real-time by digital signal processing network in software, with gestural control provided by a foot-operated pedal board. --------- The work is informed by a range of ideas from the genres of electroacoustic music, western art music, popular music and cinematic sound. It seeks to fluidly cross and hybridise musical practices from these diverse sonic traditions and to develop a compositional language that draws upon multiple genres, but at the same time resists the ability to be located within a singular genre. Musical structures and sonic markers which form genre are ruptured at strategic levels of the musical structure in order to allow for a cross flow of concepts between genres. The process of rupture is facilitated by the practical implementation of music and sound reception theories into the compositional process. -------- The piece exhibits the by-products of a composer born into a media saturated environment, drawing on a range of musical and sonic traditions, actively seeking to explore the liminal space in between these traditions. The project stems from the author's research interests in locating points of connection between traditions of experimentation in diverse musical and sonic traditions arising from the broad uptake of media technologies in the early 20th century.