Dictionary learning and sparse coding on Grassmann manifolds : an extrinsic solution

Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping, which enables us to devise a closed-form solution for updating a Grassmann dictionary, atom by atom. Furthermore, to handle non-linearity in data, we propose a kernelised version of the dictionary learning algorithm. Experiments on several classification tasks (face recognition, action recognition, dynamic texture classification) show that the proposed approach achieves considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelised Affine Hull Method and graph-embedding Grassmann discriminant analysis.

The once-and-for-all withdrawal of the Liverpool Care Pathway in the UK : what are the implications for Australia?

This Perspective reflects on the withdrawal of the Liverpool Care Pathway in the UK, and its implications for Australia. Integrated care pathways are documents which outline the essential steps of multidisciplinary care in addressing a specific clinical problem. They can be used to introduce best clinical practice, to ensure that the most appropriate management occurs at the most appropriate time and that it is provided by the most appropriate health professional. By providing clear instructions, decision support and a framework for clinician-patient interactions, care pathways guide the systematic provision of best evidence-based care. The Liverpool Care Pathway (LCP) is an example of an integrated care pathway, designed in the 1990s to guide care for people with cancer who are in their last days of life and are expected to die in hospital. This pathway evolved out of a recognised local need to better support non-specialist palliative care providers’ care for patients dying of cancer within their inpatient units. Historically, despite the large number of people in acute care settings whose treatment intent is palliative, dying patients receiving general hospital acute care tended to lack sufficient attention from senior medical staff and nursing staff. The quality of end-of-life care was considered inadequate, therefore much could be learned from the way patients were cared for by palliative care services. The LCP was a strategy developed to improve end-of-life care in cancer patients and was based on the care received by those dying in the palliative care setting.

Free for all : a case study examining implementation factors of one-to-one device programs

Despite significant investment in school one-to-one device programs, little is known about which aspects of program implementation work and why. Through a comparison of two implementation models, adopter-diffusion and saturation, and using existing data from the One Laptop per Child Australia laptop program, we explored how factors of implementation may affect device diffusion, learning and educational outcomes, and program sustainability in schools. In this article we argue that more focused research into implementation of one-to-one device programs, moving beyond comparisons of “devices versus without devices,” is needed to provide reliable data to inform future program funding and advance this area of research.

Undulating matter : a topology of the studio

With specific reference to the writing of Dan Graham and the experiences of creative practice, this paper will elaborate an account of studio practice as a topology - a theory drawn from mathematics in which space is understood not as a static field but in terms of properties of connectedness, movement and differentiation. This paper will trace a brief sequence of topological formulations to draw together the expression of topology as form and its structural dimension as a methodology in the specific context of the author’s studio practice. In so doing, this paper seeks to expand the notion of topology in art beyond its association with Conceptual Art of the 1960s and 70s to propose that topology provides a dynamic theoretical model for apprehending the generative ‘logic’ that gives direction and continuity to the art-making process.

Is unsupervised exercise following breast cancer safe for all women?

One in eight women living in developed countries will be diagnosed with breast cancer before the age of 85, with the mean age at first diagnosis approximately 60 years. Stage I represents just under 50% of diagnoses, while 45% of cases are diagnosed at later stages (stages II to IV; the remainder being unknown stage). Breast cancer continues to be the most common cause of cancer-related deaths in women , and although survival for women with stage I disease is high (98% 5-year relative survival), survival is significantly lower for those diagnosed with more advanced disease stage (i.e., stages II to IV, 83%; an unknown stage, 50%) .

All-environment visual place recognition with SMART

This paper presents Sequence Matching Across Route Traversals (SMART); a generally applicable sequence-based place recognition algorithm. SMART provides invariance to changes in illumination and vehicle speed while also providing moderate pose invariance and robustness to environmental aliasing. We evaluate SMART on vehicles travelling at highly variable speeds in two challenging environments; firstly, on an all-terrain vehicle in an off-road, forest track and secondly, using a passenger car traversing an urban environment across day and night. We provide comparative results to the current state-of-the-art SeqSLAM algorithm and investigate the effects of altering SMART’s image matching parameters. Additionally, we conduct an extensive study of the relationship between image sequence length and SMART’s matching performance. Our results show viable place recognition performance in both environments with short 10-metre sequences, and up to 96% recall at 100% precision across extreme day-night cycles when longer image sequences are used.

The continuing decline of science and mathematics enrolments in Australian high schools

Is there a crisis in Australian science and mathematics education? Declining enrolments in upper secondary Science and Mathematics courses have gained much attention from the media, politicians and high-profile scientists over the last few years, yet there is no consensus amongst stakeholders about either the nature or the magnitude of the changes. We have collected raw enrolment data from the education departments of each of the Australian states and territories from 1992 to 2012 and analysed the trends for Biology, Chemistry, Physics, two composite subject groups (Earth Sciences and Multidisciplinary Sciences), as well as entry, intermediate and advanced Mathematics. The results of these analyses are discussed in terms of participation rates, raw enrolments and gender balance. We have found that the total number of students in Year 12 increased by around 16% from 1992 to 2012 while the participation rates for most Science and Mathematics subjects, as a proportion of the total Year 12 cohort, fell (Biology (-10%), Chemistry (-5%), Physics (-7%), Multidisciplinary Science (-5%), intermediate Mathematics (-11%), advanced Mathematics (-7%) in the same period. There were increased participation rates in Earth Sciences (+0.3%) and entry Mathematics (+11%). In each case the greatest rates of change occurred prior to 2001 and have been slower and steadier since. We propose that the broadening of curriculum offerings, further driven by students' self-perception of ability and perceptions of subject difficulty and usefulness, are the most likely cause of the changes in participation. While these continuing declines may not amount to a crisis, there is undoubtedly serious cause for concern.

Characterisations of ideal threshold schemes

We characterise ideal threshold schemes from different approaches. Since the characteristic properties are independent to particular descriptions of threshold schemes, all ideal threshold schemes can be examined by new points of view and new results on ideal threshold schemes can be discovered.

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.

Generalized azimuthal shear deformations in compressible isotropic elastic materials

In this article we study the azimuthal shear deformations in a compressible Isotropic elastic material. This class of deformations involves an azimuthal displacement as a function of the radial and axial coordinates. The equilibrium equations are formulated in terms of the Cauchy-Green strain tensors, which form an overdetermined system of partial differential equations for which solutions do not exist in general. By means of a Legendre transformation, necessary and sufficient conditions for the material to support this deformation are obtained explicitly, in the sense that every solution to the azimuthal equilibrium equation will satisfy the remaining two equations. Additionally, we show how these conditions are sufficient to support all currently known deformations that locally reduce to simple shear. These conditions are then expressed both in terms of the invariants of the Cauchy-Green strain and stretch tensors. Several classes of strain energy functions for which this deformation can be supported are studied. For certain boundary conditions, exact solutions to the equilibrium equations are obtained. © 2005 Society for Industrial and Applied Mathematics.

A comparison of stability and bifurcation criteria for inflated spherical elastic shells

The nonlinear stability analysis introduced by Chen and Haughton [1] is employed to study the full nonlinear stability of the non-homogeneous spherically symmetric deformation of an elastic thick-walled sphere. The shell is composed of an arbitrary homogeneous, incompressible elastic material. The stability criterion ultimately requires the solution of a third-order nonlinear ordinary differential equation. Numerical calculations performed for a wide variety of well-known incompressible materials are then compared with existing bifurcation results and are found to be identical. Further analysis and comparison between stability and bifurcation are conducted for the case of thin shells and we prove by direct calculation that the two criteria are identical for all modes and all materials.

On cheating immune secret sharing

The paper addresses the cheating prevention in secret sharing. We consider secret sharing with binary shares. The secret also is binary. This model allows us to use results and constructions from the well developed theory of cryptographically strong boolean functions. In particular, we prove that for given secret sharing, the average cheating probability over all cheating vectors and all original vectors, i.e., 1/n 2n ∑c=1...n ∑α∈V n ρc,α , denoted by ρ, satisfies ρ ≥ ½, and the equality holds if and only if ρc,α satisfies ρc,α= ½ for every cheating vector δc and every original vector α. In this case the secret sharing is said to be cheating immune. We further establish a relationship between cheating-immune secret sharing and cryptographic criteria of boolean functions.This enables us to construct cheating-immune secret sharing.

Global start-ups profile : one size fits all?

Our research aims to answer the research questions “How do we commonly describe the global start-ups profile as evidenced in prior inductive research?” and “Does this global start-ups profile can effectively explain phenomena in Australian global start-up firms?” We systematically review 29 global start-ups (144 firms) qualitative articles to understand descriptive definitions of global-startup firms. We then triangulate this finding with an Australian high-tech firm. Our contribution is to form a descriptive profile of global start-up phenomenon and raise interesting issues that have potentially fruitful findings for both research and practice. This profile might well be just a deviant from the traditional model that describes how firms establish their footprints, first in their domestic markets followed by moves into cross-border activities. Regardless, government agencies, consultants, and entrepreneurs need to understand the phenomenon. Thus we anticipate that this phenomenon will continue to provide interesting issues for pursuit, both by researchers as well as the practitioner community.

Pituitary tumours : all silent on the epigenetics front

Investigation of the epigenome of sporadic pituitary tumours is providing a more detailed understanding of aberrations that characterise this tumour type. Early studies, in this and other tumour types adopted candidate-gene approaches to characterise CpG island methylation as a mechanism responsible for or associated with gene silencing. However, more recently, investigators have adopted approaches that do not require a priori knowledge of the gene and transcript, as example differential display techniques, and also genome-wide, array-based approaches, to 'uncover' or 'unmask' silenced genes. Furthermore, through use of chromatin immunoprecipitation as a selective enrichment technique; we are now beginning to identify modifications that target the underlying histones themselves and that have roles in gene-silencing events. Collectively, these studies provided convincing evidence that change to the tumour epigenome are not simply epiphenomena but have functional consequences in the context of pituitary tumour evolution. Our ability to perform these types of studies has been and is increasingly reliant upon technological advances in the genomics and epigenomics arena. In this context, other more recent advances and developing technologies, and, in particular, next generation or flow cell re-sequencing techniques offer exciting opportunities for our future studies of this tumour type.