AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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We prove that the set of bounded ratios $\BR(X)$ on a semialgebraic set $X\subset\R^n_{>0}$ is the convex cone of linear forms that are nonnegative on the tropicalization $\trop(X)$. In particular, it is a rational polyhedral convex cone. For $X$ the set of Lorentzian polynomials with fixed M-convex support, it is the...
Br\"and\'en and Huh showed that Lorentzian polynomials unify Hodge-Riemann relations in combinatorics: their supports are M-convex, and every M-convex set supports a Lorentzian polynomial. Baker, Huh, Kummer, and Lorscheid later proved that, for every $q>0$, the projectivized space $\mathbf{P}\operatorname{L}_J$ of Lor...
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