2 citations · 3 across the 8 of their papers we have counts for
5 papers · 1 filter
About finite differential tropical basis for linear ODE's
Stefano Mereta, Alejandro Vargas
We formulate several open questions regarding the tropicalization of linear ODEs, aiming primarily to develop methods for calculating the radius of convergence of their classical s…
On the identifiability and semi-algebraicity of ReLU neuromanifolds
Axel Flinth, Stefano Mereta, Michele Pernice
We study several aspects of the semi-algebraicity of the neuromanifold of a feedforward ReLU neural network. We prove that in…
The fundamental theorem of tropical differential algebra for formal Puiseux series
Sebastian Falkensteiner, Stefano Mereta
The fundamental theorem of tropical differential algebra has been established for formal power series solutions of systems of algebraic differential equations. It has been shown th…
The Fundamental theorem of tropical differential algebra over nontrivially valued fields and the radius of convergence of nonarchimedean differential equations
Francesco Gallinaro, Stefano Mereta
We prove a fundamental theorem for tropical partial differential equations, analogous to the fundamental theorem of tropical geometry in this context. We extend results from Aroca…
A general framework for tropical differential equations
Jeffrey Giansiracusa, Stefano Mereta
We construct a general framework for tropical differential equations based on idempotent semirings and an idempotent version of differential algebra. Over a differential ring equip…