Using inclusion-exclusion, we can write the indicator function of a union of finitely many balls as an alternating sum of indicator functions of common intersections of balls. We...
The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the p...
David Cohen-Steiner, Herbert Edelsbrunner, John Ha...
A plane algebraic curve can be represented as the zero-set of a polynomial in two - or if one takes homogenous coordinates: three - variables. The coefficients of the polynomial de...
This paper investigates the homography which transforms a set of points in projective space when undergoing a rigid translation, termed a projective translation. A representation ...
A projective plane is called a translation plane if there exists a line L such that the group of elations with axis L acts transitively on the points not on L. A translation plane...