4 papers
On a polynomial positivity question of Collins, Dykema, and Torres-Ayala related to the Bessis-Moussa-Villani Conjecture
Edward D. Kim, Joe Miller, Laura Zinnel
We construct sum of squares certificates of non-negativity for two families of polynomials appearing as a variant by Collins, Dykema, and Torres-Ayala to Häegele's reformulation of…
Automatic Dynamic Parallelotope Bundles for Reachability Analysis of Nonlinear Systems
Edward Kim, Stanley Bak, Parasara Sridhar Duggirala
Reachable set computation is an important technique for the verification of safety properties of dynamical systems. In this paper, we investigate reachable set computation for disc…
Counterexamples to Siegel's Conjecture
Kean P. Fallon, Madisyn Janusiak, Edward D. Kim +1
We prove that the intersection of a Hirsch polytope and a cube may be a non-Hirsch polytope.
Tail diameter upper bounds for polytopes and polyhedra
J. Mackenzie Gallagher, Edward D. Kim
In 1992, Kalai and Kleitman proved a quasipolynomial upper bound on the diameters of convex polyhedra. Todd and Sukegawa-Kitahara proved tail-quasipolynomial bounds on the diameter…