Doing so, we answer questions first introduced in doi.org/10.1016/j.ce... through a systematic exploration of sign patterns in the associated oriented matroids. The Maple implemtation of this algorithm is available at git.mpi-cbg.de/scholten/fea...

We prove certain 4-species ecological networks cannot achieve stable coexistence, no matter the parameters. The proof uses combinatorial insights from oriented matroid theory to study feasibility/stability constraints algorithmically 🔍

How do you know if species can coexist? The feasible-stable equilibria of Lotka-Volterra systems form semialgebraic sets in parameter space. We recast this using Plücker coordinates & the Grassmannian - opening new computational approaches to ecological networks.

🔍 New algorithm finds ALL local minimizers of functions on tensorized domains using only noisy function evaluations!

Combines approximation theory + computer algebra.

Implemented in Julia package GlobTim

#optimization #mathematics #Julia #computeralgebra