Straightening Out Copyright Preemption

Straightening out planar poly-line drawings

This paper addresses the following question: Given a planar poly-line drawing of a graph, can we “straighten it out”, i.e., convert it to a planar straight-line drawing, while keeping some features unchanged? We show that any y-monotone poly-line drawing can be straightened out while maintaining y-coordinates and height. The width may increase much, but we also show that on some graphs exponent...

Straightening out rectangular di erential inclusions

In this paper, the classic straightening out theorem from di erential geometry is used to derive necessary and su cient conditions for locally converting rectangular di erential inclusions to constant rectangular di erential inclusions. Both scalar and coupled di erential inclusions are considered. The results presented in this paper have use in the area of computer aided veri cation of hybrid ...

Contracts, Copyright and Preemption in a Digital World

Straightening out the LINEs: LINE-1 orthologous loci.

The L1Hs preTa subfamily of long interspersed elements (LINEs) originated after the divergence of human and chimpanzee and is therefore found only in the human genome. Thirty-three of the 254 L1Hs preTa elements are polymorphic for the absence/presence of the insertion, making them useful markers for studying human population genetics. The problem of homoplasy, however, can diminish the value o...

Straightening out Trajectories near Singular Points of Implicit Differential Equations

Under appropriate assumptions, it is shown that there is a di eomorphism that transforms solutions of the implicit di erential equation