A projective plane is equivalent to a disk with antipodal points identiied. A graph is projective planar if it can be drawn on the projective plane with no crossing edges. A linear time algorithm for projective planar embedding has been described by Mohar 20]. We provide a new approach that takes O(n 2) time is but much easier to implement. 1 Description of the problem A graph G consists of a s...

An open partition p [Cod09a, Cod09b] of a tree T is a partition of the vertices of T with the property that, for each block B of p, the upset of B is a union of blocks of p. This paper deals with the number, NP(n), of open partitions of the tree, Vn, made of two chains with n points each, that share the root. We prove that the number of such partitions is given by the formula NPn = k=1 n  j...

A common approach to automatic quad layout generation on surfaces is to, in a first stage, decide the positioning of irregular vertices, followed by finding sensible edges connecting these vertices and partitioning surface into quadrilateral patches second stage. While this two-step reduces problem's complexity, separation also limits result quality. In worst case, set fixed stage without consi...

An understanding of feather moult, an important process in the life cycle birds, lags behind that other avian life‐history events. This lag includes a lack scientific attention, but surprisingly also basic knowledge regarding moult strategy many bird species. situation is particularly astonishing light fact feathers are unique characteristic birds. Currently, there two main terminology systems ...

What roles do syntax and semantics have in the grammar of a language? What are the consequences of these roles for syntactic structure, and why does it matter? We sketch the Simpler Syntax Hypothesis, which holds that much of the explanatory role attributed to syntax in contemporary linguistics is properly the responsibility of semantics. This rebalancing permits broader coverage of empirical l...