Heegaard Splittings of Twisted Torus Knots

Little is known on the classification of Heegaard splittings for hyperbolic 3-manifolds. Although Kobayashi gave a complete classification of Heegaard splittings for the exteriors of 2-bridge knots, our knowledge of other classes is extremely limited. In particular, there are very few hyperbolic manifolds that are known to have a unique minimal genus splitting. Here we demonstrate that an infinite class of hyperbolic knot exteriors, namely exteriors of certain "twisted torus knots" originally studied by Morimoto, Sakuma and Yokota, have a unique minimal genus Heegaard splitting of genus two. We also conjecture that these manifolds possess irreducible yet weakly reducible splittings of genus three. There are no known examples of such Heegaard splittings.Comment: 4 pages 8 figure

The effects of viewpoint on the virtual space of pictures

Pictorial displays whose primary purpose is to convey accurate information about the 3-D spatial layout of an environment are discussed. How and how well, pictures can convey such information is discussed. It is suggested that picture perception is not best approached as a unitary, indivisible process. Rather, it is a complex process depending on multiple, partially redundant, interacting sources of visual information for both the real surface of the picture and the virtual space beyond. Each picture must be assessed for the particular information that it makes available. This will determine how accurately the virtual space represented by the picture is seen, as well as how it is distorted when seen from the wrong viewpoint

Fears, constraints, and contracts: the democratic reality for New Zealand’s community and voluntary sector

The important role of community and voluntary sector organisations to democratic debate and policy development is widely acknowledged by governments, academics, and the sector itself. However, our survey of 153 NZ community and voluntary sector groups shows that democratic engagement has been constrained under both Labour-led and National-led governments in the last decade. The ‘contract’ environment dominating funding for social service providers; a lack of understanding and appreciation of those who work in the sector; and, disparaging remarks and treatment of ‘dissenters’ by political elite were major factors constraining democratic debate in NZ. This report was presented at the Community and Voluntary Sector Research Forum, Victoria University of Wellington, 26 March 2013

Educational Psychologists as Scientist Practitioners: A Critical Synthesis of Existing Professional Frameworks by a Consciously Incompetent Trainee

Several professional frameworks have been developed that provide mechanisms to support the application of psychology to problem-solving; thus facilitating the role of educational psychologists as scientist–practitioners. Furthermore, existing frameworks do not have to be viewed in isolation and can be integrated to demonstrate effective and defensible professional standards (Kelly & Marks Woolfson, 2017). This paper is a reflection on practice written by a third-year trainee from Manchester University. It aims to critique five existing frameworks, through casework analysis, and critically synthesise findings to produce a personalised framework based on “what works”. A theoretical model, “The Model of Dynamic Epistemology” (MODE) and a framework to support the application of MODE has been suggested. The paper concludes that an effective professional framework must emphasise positive relationships and shared understanding while maintaining scientific rigour. Finally, limitations have been outlined and future action research into the effect of MODE recommended. Several professional frameworks have been developed that provide mechanisms to support the application of psychology to problem-solving; thus facilitating the role of educational psychologists as scientist–practitioners. Furthermore, existing frameworks do not have to be viewed in isolation and can be integrated to demonstrate effective and defensible professional standards (Kelly & Marks Woolfson, 2017). This paper is a reflection on practice written by a third-year trainee from Manchester University. It aims to critique five existing frameworks, through casework analysis, and critically synthesise findings to produce a personalised framework based on “what works”. A theoretical model, “The Model of Dynamic Epistemology” (MODE) and a framework to support the application of MODE has been suggested. The paper concludes that an effective professional framework must emphasise positive relationships and shared understanding while maintaining scientific rigour. Finally, limitations have been outlined and future action research into the effect of MODE recommended