Three points do not determine a (pseudo-) plane

Three-clustering of Points in the Plane Three-clustering of Points in the Plane

Given n points in the plane, we partition them into three classes such that the maximum distance between two points in the same class is minimized. The algorithm takes O(n log n) time.

Inflection Points on Real Plane Curves Having Many Pseudo-Lines

A pseudo-line of a real plane curve C is a global real branch of C(R) that is not homologically trivial in P(R). A geometrically integral real plane curve C of degree d has at most d− 2 pseudo-lines, provided that C is not a real projective line. Let C be a real plane curve of degree d having exactly d − 2 pseudo-lines. Suppose that the genus of the normalization of C is equal to d− 2. We show ...

Do We Know What We Do not Know? A Response to Celine Bonnet

A Polynomial Number of Random Points Does Not Determine the Volume of a Convex Body

We show that there is no algorithm which, provided a polynomial number of random points uniformly distributed over a convex body in R n, can approximate the volume of the body up to a constant factor with high probability.

Three-Way Systems Do Not Exist

We argue that argument encoding systems that seem to involve three syntactic core cases (nominative/absolutive, ergative, accusative) are actually common ergative or accusative systems syntactically, with overt case markers for each of the two cases that disappear in intransitive contexts. Based on evidence from Kham, Djapu, Nez Perce, Upriver Halkomelem, Dyirbal, and Pitjantjatjara, we show th...