Abstract. We construct and study a natural homeomorphism between the moduli space of polynomial cubic differentials of degree d on the complex plane and the space of projective equivalence classes of oriented convex polygons with d + 3 vertices. This map arises from the construction of a complete hyperbolic affine sphere with prescribed Pick differential, and can be seen as an analogue of the Labourie-Loftin parameterization of convex RP 2 structures on a compact surface by the bundle of holomorphic cubic differentials over Teichmüller space.

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We show that grafting any fixed hyperbolic surface defines a homeomorphism from the space of measured laminations to Teichmüller space, complementing a result of Scannell-Wolf on grafting by a fixed lamination. This result is used to study the relationship between the complex-analytic and geometric coordinate systems for the space of complex projective (CP 1 ) structures on a surface.We also study the rays in Teichmüller space associated to the grafting coordinates, obtaining estimates for extremal and hyperbolic length functions and their derivatives along these grafting rays.30F60; 30F10, 30F40, 32G15, 57M50

Background In Victoria, Australia, emergency calls requesting an ambulance have been increasing at a rate higher than population growth. While most of these calls are for genuine emergencies, many do not require an immediate ambulance response. A collaborative research approach was undertaken to address this issue. The aim of this paper was to evaluate the effectiveness of applying a behaviour change approach to this challenge by first addressing antecedents of behaviour (attitudes, awareness and knowledge). Methods The project included a formative research phase to inform the design of a mass media campaign and subsequent evaluation of the campaign. Results Results indicated that the campaign was successful in increasing community attitudes towards ambulances as being for emergencies only, particularly among those familiar with the campaign material and with other health service options (such as telephone advice lines). Conclusions These findings provide support for adopting the Forum approach to increase the chances that a mass media campaign will achieve its stated objectives. Recommendations for future campaign activities are discussed. Electronic supplementary material The online version of this article (10.1186/s12961-019-0430-5) contains supplementary material, which is available to authorized users.