Fractions, reunitisation and the number-line representation

Centre for Mathematics and Science Education, QUT, Brisbane, Australia This paper reports on a study in which Years 6 and 10 students were individually interviewed to determine their ability to unitise and reunitise number lines used to represent mixed numbers and improper fractions. Only 16.7% of the students (all Year 6) were successful on all three tasks and, in general, Year 6 students outperformed Year 8 students. The interviews revealed that the remaining students had incomplete, fragmented or non-existent structural knowledge of mixed numbers and improper fractions, and were unable to unitise or reunitise number lines. The implication for teaching is that instruction should focus on providing students with a variety of fraction representations in order to develop rich and flexible schema for all fraction types (mixed numbers, and proper and improper fractions).

Energy polarization and popular representation: Evidence from the Russian Duma

In this article we introduce the term “energy polarization” to explain the politics of energy market reform in the Russian Duma. Our model tests the impact of regional energy production, party cohesion and ideology, and electoral mandate on the energy policy decisions of the Duma deputies (oil, gas, and electricity bills and resolution proposals) between 1994 and 2003. We find a strong divide between Single-Member District (SMD) and Proportional Representation (PR) deputies High statistical significance of gas production is demonstrated throughout the three Duma terms and shows Gazprom's key position in the post-Soviet Russian economy. Oil production is variably significant in the two first Dumas, when the main legislative debates on oil privatization occur. There is no constant left–right continuum, which is consistent with the deputies' proclaimed party ideology. The pro- and anti-reform poles observed in our Poole-based single dimensional scale are not necessarily connected with liberal and state-oriented regulatory policies, respectively. Party switching is a solid indicator of Russia's polarized legislative dynamics when it comes to energy sector reform.

Representation and learning of visual information for pose recognition

Recovering position from sensor information is an important problem in mobile robotics, known as localisation. Localisation requires a map or some other description of the environment to provide the robot with a context to interpret sensor data. The mobile robot system under discussion is using an artificial neural representation of position. Building a geometrical map of the environment with a single camera and artificial neural networks is difficult. Instead it would be simpler to learn position as a function of the visual input. Usually when learning images, an intermediate representation is employed. An appropriate starting point for biologically plausible image representation is the complex cells of the visual cortex, which have invariance properties that appear useful for localisation. The effectiveness for localisation of two different complex cell models are evaluated. Finally the ability of a simple neural network with single shot learning to recognise these representations and localise a robot is examined.

Effect of representation size and visual ambiguity on RatSLAM system performance

RatSLAM is a vision-based SLAM system based on extended models of the rodent hippocampus. RatSLAM creates environment representations that can be processed by the experience mapping algorithm to produce maps suitable for goal recall. The experience mapping algorithm also allows RatSLAM to map environments many times larger than could be achieved with a one to one correspondence between the map and environment, by reusing the RatSLAM maps to represent multiple sections of the environment. This paper describes experiments investigating the effects of the environment-representation size ratio and visual ambiguity on mapping and goal navigation performance. The experiments demonstrate that system performance is weakly dependent on either parameter in isolation, but strongly dependent on their joint values.

RatSLAM on the edge : revealing a coherent representation from an overloaded rat brain

The RatSLAM system can perform vision based SLAM using a computational model of the rodent hippocampus. When the number of pose cells used to represent space in RatSLAM is reduced, artifacts are introduced that hinder its use for goal directed navigation. This paper describes a new component for the RatSLAM system called an experience map, which provides a coherent representation for goal directed navigation. Results are presented for two sets of real world experiments, including comparison with the original goal memory system's performance in the same environment. Preliminary results are also presented demonstrating the ability of the experience map to adapt to simple short term changes in the environment.

Schematic Representation of Case Study Research Designs

Aim. The paper is a report of a study to demonstrate how the use of schematics can provide procedural clarity and promote rigour in the conduct of case study research. Background. Case study research is a methodologically flexible approach to research design that focuses on a particular case – whether an individual, a collective or a phenomenon of interest. It is known as the 'study of the particular' for its thorough investigation of particular, real-life situations and is gaining increased attention in nursing and social research. However, the methodological flexibility it offers can leave the novice researcher uncertain of suitable procedural steps required to ensure methodological rigour. Method. This article provides a real example of a case study research design that utilizes schematic representation drawn from a doctoral study of the integration of health promotion principles and practices into a palliative care organization. Discussion. The issues discussed are: (1) the definition and application of case study research design; (2) the application of schematics in research; (3) the procedural steps and their contribution to the maintenance of rigour; and (4) the benefits and risks of schematics in case study research. Conclusion. The inclusion of visual representations of design with accompanying explanatory text is recommended in reporting case study research methods.

A statistical framework for natural feature representation

This paper presents a robust stochastic framework for the incorporation of visual observations into conventional estimation, data fusion, navigation and control algorithms. The representation combines Isomap, a non-linear dimensionality reduction algorithm, with expectation maximization, a statistical learning scheme. The joint probability distribution of this representation is computed offline based on existing training data. The training phase of the algorithm results in a nonlinear and non-Gaussian likelihood model of natural features conditioned on the underlying visual states. This generative model can be used online to instantiate likelihoods corresponding to observed visual features in real-time. The instantiated likelihoods are expressed as a Gaussian mixture model and are conveniently integrated within existing non-linear filtering algorithms. Example applications based on real visual data from heterogenous, unstructured environments demonstrate the versatility of the generative models.