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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.

Abstract-We present a set of potential function components to assist an automated or semi-automated vehicle in navigating a multi-lane, populated highway. The resulting potential field is constructed as a superposition of disparate functions for lanekeeping, road-staying, speed preference, and vehicle avoidance and passing. The construction of the vehicle avoidance potential is of primary importance, incorporating the structure and protocol of laned highway driving. Particularly, the shape and dimensions of the potential field behind each obstacle vehicle can appropriately encourage control vehicle slowing and/or passing, depending on the cars' velocities and surrounding traffic. Hard barriers on roadway edges and soft boundaries between navigable lanes keep the vehicle on the highway, with a preference to travel in a lane center.

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