2 citations · 3 across the 8 of their papers we have counts for
9 papers
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…
Three lectures on tropical algebra
Jeffrey Giansiracusa, Kevin Kuehn, Stefano Mereta +1
This document is a slightly expanded version of a series of talks given by J. Giansiracusa at the workshop `Geometry over semirings' at Universitat Autònoma de Barcelona in July 20…
Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry
Giovanni Luca Marchetti, Vahid Shahverdi, Stefano Mereta +2
In this position paper, we promote the study of function spaces parameterized by machine learning models through the lens of algebraic geometry. To this end, we focus on algebraic…
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…
Higher-dimensional cubical sliding puzzles
Moritz Beyer, Stefano Mereta, Érika Roldán +1
We introduce higher-dimensional cubical sliding puzzles that are inspired by the classical 15 Puzzle from the 1880s. In our puzzles, on a -dimensional cube, a labeled token can…
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…
From pre-trusses to skew braces
Tomasz Brzeziński, Stefano Mereta, Bernard Rybołowicz
The notion of a pre-truss, that is, a set that is both a heap and a semigroup is introduced. Pre-trusses themselves as well as pre-trusses in which one-sided or two-sided distribut…