A new algorithm is proposed for detection of corners and other high curvature points in planar curves. A corner is deened as a location where a triangle with speciied opening angle and size can be inscribed in the curve. The tests compare the new algorithm to four alternative algorithms for corner detection.

A non-degenerate rectangular subdivision is a subdivision of a rectangle into a set of non-overlapping rectangles S, such that no four rectangles meet in a point. We consider a problem that Katz and colleagues call strong polychromatic four-colouring: Colouring the vertices of the subdivision with four colours, such that each rectangle of S has all colours among its four corners. By considering...

It is shown that the (infinite) tiling problem byWang tiles is undecidable even if the given tile set is deterministic by all four corners, i.e. a tile is uniquely determined by the colors of any two adjacent edges. The reduction is done from the Turing machine halting problem and uses the aperiodic tile set of Kari and Papasoglu. © 2008 Elsevier B.V. All rights reserved.

Co-evolution of phytoplankton C:N:P stoichiometry and the deep ocean N:P ratio T. M. Lenton and C. A. Klausmeier School of Environmental Sciences, University of East Anglia, Norwich NR4 7TJ, UK W. K. Kellogg Biological Station, Michigan State University, Hickory Corners, MI 49060, USA Received: 16 June 2006 – Accepted: 4 July 2006 – Published: 17 July 2006 Correspondence to: T. M. Lenton (t.len...