Showing papers by "Chris Peterson published in 2011"
TL;DR: In this article, the authors considered the Plucker embedding of the Grassmann variety of projective k-planes in Pn and showed that the expected dimension of a projective variety is asymptotic to n 2 18.
Abstract: Let Gr(k,n) be the Plucker embedding of the Grassmann variety of projective k-planes in Pn. For a projective variety X, lets(X) denote the variety of its s 1 secant planes. More precisely, �s(X) denotes the Zariski closure of the union of linear spans of s-tuples of points lying on X. We exhibit two functions s0(n) � s1(n) such thats(Gr(2,n)) has the expected dimension whenever n � 9 and either ss0(n) or s1(n) � s. Both s0(n) and s1(n) are asymptotic to n 2 18 . This yields, asymptotically, the typical rank of an element of ^ 3 C n+1 . Finally, we classify all defectives(Gr(k,n)) for s � 6 and provide geometric arguments underlying each defective case.
41 citations
TL;DR: In conclusion, heifers given two doses of PGF at CIDR removal on Day 5, in a 5-d C IDR-CO-Synch protocol, tended to have a higher pregnancy rate than those that received only one dose of P GF.
24 citations
TL;DR: In this article, a numerical algorithm is presented to compute the geometric genus of any one-dimensional irreducible component of an algebraic set, where the most important invariants of a curve are the degree, arithmetic genus and geometric genus.
22 citations
TL;DR: A combination of these tools leads to a numerical method for computing the degrees of Chern classes of smooth projective varieties in P^n.
22 citations
TL;DR: In this paper, the degrees of the Segre classes of a subscheme of complex projective space are computed based on generic residuation and intersection theory, and implemented using the software system Macaulay2.
Abstract: We present a method to compute the degrees of the Segre classes of a subscheme of complex projective space. The method is based on generic residuation and intersection theory. It has been implemented using the software system Macaulay2.
15 citations
01 Dec 2011
TL;DR: The development of the basic mathematical theory of data bundles into practical algorithms will bring fundamentally new tools to bear on the problem of processing large quantities of streaming data.
Abstract: : Over the course of this project we developed a mathematical representation of data, which we refer to as data bundles. This approach provides a mechanism for encoding the data including aspects of the signal that might normally be removed to simplify data processing. Motivated by the mathematics of fiber bundles, a data bundle provides a flexible representation of information that embraces variations that one would normally attempt to limit, or exclude entirely. Such an approach motivates the idea of intelligent data acquisition wherein the state of an object may actually be varied to enrich the data collection process. The data bundle is a natural way to encode information which can then be viewed as a point on a variety of parameter spaces such as Grassmann manifolds, Flag manifolds, or Stiefel manifolds. Each setting provides a different view of the data and similarity measures may be constructed in these settings to optimize discriminatory strength of any classification system. The development of the basic mathematical theory of data bundles into practical algorithms will bring fundamentally new tools to bear on the problem of processing large quantities of streaming data.