9 citations · 51 across the 15 of their papers we have counts for
17 papers
Hands-on Tropical Geometry
Herbert Gangl, Yue Ren, Ziva Urbancic
This is a guide on how to create 3d printable models of tropical surfaces, curves, and combinations thereof. It uses Polymake to construct bounded models of the tropical objects, a…
On intersections and stable intersections of tropical hypersurfaces
Yue Ren
We prove that every connected component of an intersection of tropical hypersurfaces contains a point of their stable intersection unless their stable intersection is empty. This i…
Generic root counts and flatness in tropical geometry
Paul Alexander Helminck, Yue Ren
We use tropical and non-archimedean geometry to study the generic number of solutions of families of polynomial equations over a parameter space . In particular, we are interest…
Sharp bounds for the number of regions of maxout networks and vertices of Minkowski sums
Guido Montúfar, Yue Ren, Leon Zhang
We present results on the number of linear regions of the functions that can be represented by artificial feedforward neural networks with maxout units. A rank-k maxout unit is a f…
Computing zero-dimensional tropical varieties via projections
Paul Görlach, Yue Ren, Leon Zhang
We present an algorithm for computing zero-dimensional tropical varieties using projections. Our main tools are fast unimodular transforms of lexicographical Gröbner bases. We prov…
Detecting tropical defects of polynomial equations
Paul Görlach, Yue Ren, Jeff Sommars
We introduce the notion of tropical defects, certificates that a system of polynomial equations is not a tropical basis, and provide two algorithms for finding them in affine space…