On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein.

Evolving noisy oscillatory dynamics in genetic regulatory networks

We introduce a genetic programming (GP) approach for evolving genetic networks that demonstrate desired dynamics when simulated as a discrete stochastic process. Our representation of genetic networks is based on a biochemical reaction model including key elements such as transcription, translation and post-translational modifications. The stochastic, reaction-based GP system is similar but not identical with algorithmic chemistries. We evolved genetic networks with noisy oscillatory dynamics. The results show the practicality of evolving particular dynamics in gene regulatory networks when modelled with intrinsic noise.

An example of cognitive obstacles in advanced integration: the case of scalar line integrals

Cognitive obstacles that arise in the teaching and learning of scalar line integrals, derived from cognitive aids provided to students when first learning about integration of single variable functions are described. A discussion of how and why the obstacles cause students problems is presented and possible strategies to overcome the obstacles are outlined.

On the oscillatory behavior of transient Rayleigh Benard convection of air for 2D channel flow at moderate Rayleigh numbers

Unsteady numerical simulation of Rayleigh Benard convection heat transfer from a 2D channel is performed. The oscillatory behavior is attributed to recirculation of ascending and descending flows towards the core of the channel producing organized rolled motions. Variation of the parameters such as Reynolds number, channel outlet flow area and inclination of the channel are considered. Increasing Reynolds number (for a fixed Rayleigh number), delays the generation of vortices. The reduction in the outflow area leads to the later and the less vortex generation. As the time progresses, more vortices are generated, but the reinforced mean velocity does not let the eddies to enter the core of the channel. Therefore, they attach to the wall and reduce the heat transfer area. The inclination of the channel (both positive and negative) induces the generated vortices to get closer to each other and make an enlarged vortex.

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.

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.