7 citations · 12 across the 6 of their papers we have counts for
6 papers
Computing real powers of monomial ideals
Pratik Dongre, Benjamin Drabkin, Josiah Lim +5
This paper concerns the exponentiation of monomial ideals. While it is customary for the exponentiation operation on ideals to consider natural powers, we extend this notion to pow…
Consequences of the packing problem
Hrishikesh Bodas, Benjamin Drabkin, Caleb Fong +6
We study several consequences of the packing problem, a conjecture from combinatorial optimization, using algebraic invariants of square-free monomial ideals. While the packing pro…
Convex bodies and asymptotic invariants for powers of monomial ideals
João Camarneiro, Benjamin Drabkin, Duarte Fragoso +5
Continuing a well established tradition of associating convex bodies to monomial ideals, we initiate a program to construct asymptotic Newton polyhedra from decompositions of monom…
Machine learning the real discriminant locus
Edgar A. Bernal, Jonathan D. Hauenstein, Dhagash Mehta +2
Parameterized systems of polynomial equations arise in many applications in science and engineering with the real solutions describing, for example, equilibria of a dynamical syste…
On computing the nonlinearity interval in parametric semidefinite optimization
Jonathan D. Hauenstein, Ali Mohammad-Nezhad, Tingting Tang +1
This paper revisits the parametric analysis of semidefinite optimization problems with respect to the perturbation of the objective function along a fixed direction. We review the…
The loss surface of deep linear networks viewed through the algebraic geometry lens
Dhagash Mehta, Tianran Chen, Tingting Tang +1
By using the viewpoint of modern computational algebraic geometry, we explore properties of the optimization landscapes of the deep linear neural network models. After clarifying o…