arXiv subjects
Publications and source records attributed to Ethan White.
We study arrangements of intervals in $\mathbb{R}^2$ for which many pairs form trapezoids. We show that any set of intervals forming many trapezoids must have underlying algebraic structure, which we characterise. This leads to some unexpected examples of sets of intervals forming many trapezoids, where an important role is played by degree 2 curves.
One of the first beings affected by changes in the climate are trees, one of our most vital resources. In this study tree species interaction and the response to climate in different ecological environments is observed by applying a joint species distribution model to different ecological domains in the United States. Joint species distribution models are useful to learn inter-species relationships and species response to the environment. The climates' impact on the tree species is measured through species abundance in an area. We compare the model's performance across all ecological domains and study the sensitivity of the climate variables. With the prediction of abundances, tree species populations can be predicted in the future and measure the impact of climate change on tree populations.
We show the existence of infinitesimally rigid bipartite unit-bar frameworks in $\mathbb{R}^d$. We also construct unit-bar frameworks with girth up to 12 that are infinitesimally rigid in the plane. This answers problems proposed by Maehara.