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- Gary Gordon
- 2002

We consider a probabilistic antimatroid A on the ground set E, where each element e ∈ E may succeed with probability p e. We focus on the expected rank ER(A) of a subset of E as a polynomial in the p e. General formulas hold for arbitrary antimatroids, and simpler expressions are valid for certain well-studied classes, including trees, rooted trees, posets,… (More)

When the edges in a tree or rooted tree fail with a certain fixed probability, the (greedoid) rank may drop. We compute the expected rank as a polynomial in p and as a real number under the assumption of uniform distribution. We obtain several different expressions for this expected rank polynomial for both trees and rooted trees, one of which is especially… (More)

We define two two-variable polynomials for rooted trees and one two-variable polynomial for unrooted trees, all of which are based on the corank-nullity formulation of the Tutte polynomial of a graph or matroid. For the rooted polynomials, we show that the polynomial completely determines the rooted tree, i.e., rooted trees TI and T, are isomorphic if and… (More)

- Joshua I Molho, Amy E Herr, Bruce P Mosier, Juan G Santiago, Thomas W Kenny, Reid A Brennen +9 others

Chip-based microcolumn separation systems often require serpentine channels to achieve longer separation lengths within a compact area. However, analyte bands traveling through curved channels experience an increased dispersion that can reduce the benefit of increased channel length. This paper presents analytical solutions for dispersions, numerical models… (More)

The greedoid Tutte polynomial of a tree is equivalent to a generating function that encodes information about the number of subtrees with I internal (non-leaf) edges and L leaf edges, for all I and L. We prove that this information does not uniquely determine the tree T by constructing an infinite family of pairs of non-isomorphic caterpillars, each pair… (More)

Derangements are a popular topic in combinatorics classes. We study a generalization to face derangements of the n-dimensional hypercube. These derangements can be classified as odd or even, depending on whether the underlying isometry is direct or indirect, providing a link to abstract algebra. We emphasize the interplay between the geometry, algebra and… (More)

- Yuesheng Zhang, Gary B Gordon
- Molecular cancer therapeutics
- 2004

Many genes, with products involved in the protection of cells against carcinogens, oxidants, and other toxic chemicals, are under the transcriptional control of a simple DNA regulatory element [i.e., the antioxidant response element (ARE)]. One or more functional AREs have been confirmed or are believed to exist in the upstream region of many… (More)

- Gary Gordon, Elizabeth Mcmahon, Thomas H Brylawski
- 1989

We define a two-variable polynomial fa(t, z) for a greedoid G which generalizes the standard one-variable greedoid polynomial A<j(f). Several greedoid invariants (including the number of feasible sets, bases, and spanning sets) are easily shown to be evaluations of fG(t, z). We prove (Theorem 2.8) that when G is a rooted directed arborescence, fo(t, z)… (More)

The notion of activities with respect to spanning trees in graphs was introduced by W.T. Tutte, and generalized to activities with respect to bases in matroids by H. Crapo. We present a further generalization, to activities with respect to arbitrary subsets of matroids. These generalized activities provide a unified view of several different expansions of… (More)

Distinct epidemiological and clinicopathological characteristics of colorectal carcinomas (CRCs) based on their anatomical location suggest different risk factors and pathways of transformation associated with proximal and distal colon carcinogenesis. These differences may reflect distinct biological characteristics of proximal and distal colonic mucosa,… (More)