Ehrhart-Equivalence, Equidecomposability, and Unimodular Equivalence of Integral Polytopes

no code implementations • 21 Jan 2021 • Fiona Abney-McPeek, Sanket Biswas, Senjuti Dutta, Yongyuan Huang, Deyuan Li, Nancy Xu

In this paper, we establish a relationship between Ehrhart-equivalence and other forms of equivalence: the $\operatorname{GL}_n(\mathbb{Z})$-equidecomposability and unimodular equivalence of two integral $n$-polytopes in $\mathbb{R}^n$.

Combinatorics

Bridging the Gap: Unifying the Training and Evaluation of Neural Network Binary Classifiers

no code implementations • 2 Sep 2020 • Nathan Tsoi, Kate Candon, Deyuan Li, Yofti Milkessa, Marynel Vázquez

In this work, we propose a unifying approach to training neural network binary classifiers that combines a differentiable approximation of the Heaviside function with a probabilistic view of the typical confusion matrix values using soft sets.

General Classification

Ulam Sets in New Settings

no code implementations • 6 Aug 2020 • Tej Bade, Kelly Cui, Antoine Labelle, Deyuan Li

Then, we study Ulam sets in $\mathbb{Z}\times (\mathbb{Z}/n\mathbb{Z})$ and prove regularity for an infinite class of initial sets.

Combinatorics