Antibiotic Resistance in Escherichia coli Iron Transport Mutants

Studies previously completed on Escherichia coli mutants suggested the possibility of iron uptake as an influence on the antibiotic resistance seen in different strains. The research focused on the TonB energy transduction system and its contributions to efflux-mediated antibiotic resistance. To test the hypothesis that iron uptake has an influence on antibiotic resistance in Escherichia coli, the sensitivity to a variety of antibiotics was evaluated in strains of E. coli lacking genes that relate to the uptake of iron or the efflux system that is necessary for the uptake of iron. To test the efflux systems TolC and TonB were compared with the strains that had those genes removed and then tested against three different antibiotics. No significant correlation was found between the ∆tolC and ∆tonB mutants. Understanding the efflux systems, outer membrane integrity, energy transduction systems, and iron uptake of the gram-negative E. coli is important for the antibiotic resistance that is becoming more common in the healthcare system and public health

A Tropical Count of Binodal Cubic Surfaces

There are 280 binodal cubic surfaces passing through 17 general points. For the typically used tropical point conditions, we show that 214 of these give tropicalizations such that the nodes are separated on the tropical cubic surface.Comment: 21 pages, 11 figure

A tropical count of binodal cubic surfaces

There are 280 binodal cubic surfaces passing through 17 general points. For points in Mikhalkin position, we show that 214 of these give tropicalizations such that the nodes are separated on the tropical cubic surface

Voronoi Cells in Metric Algebraic Geometry of Plane Curves

Voronoi cells of varieties encode many features of their metric geometry. We prove that each Voronoi or Delaunay cell of a plane curve appears as the limit of a sequence of cells obtained from point samples of the curve. We use this result to study metric features of plane curves, including the medial axis, curvature, evolute, bottlenecks, and reach. In each case, we provide algebraic equations defining the object and, where possible, give formulas for the degrees of these algebraic varieties. We show how to identify the desired metric feature from Voronoi or Delaunay cells, and therefore how to approximate it by a finite point sample from the variety.Comment: 23 pages, 14 figure

The slack realization space of a matroid

We introduce a new model for the realization space of a matroid, which is obtained from a variety defined by a saturated determinantal ideal, called the slack ideal, coming from the vertex-hyperplane incidence matrix of the matroid. This is inspired by a similar model for the slack realization space of a polytope. We show how to use these ideas to certify non-realizability of matroids, and describe an explicit relationship to the standard Grassmann-Pl\"ucker realization space model. We also exhibit a way of detecting projectively unique matroids via their slack ideals by introducing a toric ideal that can be associated to any matroid.Comment: 23 pages, 8 figure