Modelling: promoting creativity whilst forging links between science education and design and technology education

Educational reforms in many countries currently call for the development of knowledge-based societies. In particular, emphasis is placed on the promotion of creativity, especially in the areas of science education and of design and technology education. In this paper, perceptions of the nature of creativity and of the conditions for its realization are discussed. The notion of modelling as a creative act is outlined and the scope for using modelling as a bridge between science education and design and technology education explored. A model for the creative act of modelling is proposed and its major aspects elaborated upon. Finally, strategies for forging links between the two subjects are outlined.

Semi-automatic annotation and retrieval of visual content using the topic map technology

There are still major challenges in the area of automatic indexing and retrieval of multimedia content data for very large multimedia content corpora. Current indexing and retrieval applications still use keywords to index multimedia content and those keywords usually do not provide any knowledge about the semantic content of the data. With the increasing amount of multimedia content, it is inefficient to continue with this approach. In this paper, we describe the project DREAM, which addresses such challenges by proposing a new framework for semi-automatic annotation and retrieval of multimedia based on the semantic content. The framework uses the Topic Map Technology, as a tool to model the knowledge automatically extracted from the multimedia content using an Automatic Labelling Engine. We describe how we acquire knowledge from the content and represent this knowledge using the support of NLP to automatically generate Topic Maps. The framework is described in the context of film post-production.

Numerical modelling of two-way propagation of non-linear dispersive waves

We describe and implement a fully discrete spectral method for the numerical solution of a class of non-linear, dispersive systems of Boussinesq type, modelling two-way propagation of long water waves of small amplitude in a channel. For three particular systems, we investigate properties of the numerically computed solutions; in particular we study the generation and interaction of approximate solitary waves.

Mathematical modelling for the digital society

We argue the case for a new branch of mathematics and its applications: Mathematics for the Digital Society. There is a challenge for mathematics, a strong “pull” from new and emerging commercial and public activities; and a need to train and inspire a generation of quantitative scientists who will seek careers within the associated sectors. Although now going through an early phase of boiling up, prior to scholarly distillation, we discuss how data rich activities and applications may benefit from a wide range of continuous and discrete models, methods, analysis and inference. In ten years time such applications will be common place and associated courses may be embedded within the undergraduate curriculum.

Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

Neural networks for linear control: an analysis

This paper considers the use of radial basis function and multi-layer perceptron networks for linear or linearizable, adaptive feedback control schemes in a discrete-time environment. A close look is taken at the model structure selected and the extent of the resulting parameterization. A comparison is made with standard, nonneural network algorithms, e.g. self-tuning control.