Publications (22)
The algebraic degree of the Wasserstein distance
Chiara Meroni, Bernhard Reinke, Kexin Wang
Given two rational univariate polynomials, the Wasserstein distance of their associated measures is an algebraic number. We determine the algebraic degree of the squared Wasserstei…
Linear causal disentanglement via higher-order cumulants
Paula Leyes Carreno, Chiara Meroni, Anna Seigal
Linear causal disentanglement is a recent method in causal representation learning to describe a collection of observed variables via latent variables with causal dependencies betw…
Chebyshev Varieties
Zaïneb Bel-Afia, Chiara Meroni, Simon Telen
Chebyshev varieties are algebraic varieties parametrized by Chebyshev polynomials or their multivariate generalizations. We determine the dimension, degree, singular locus and defi…
Asymptotic number of edge-colored regular graphs
Michael Borinsky, Chiara Meroni, Maximilian Wiesmann
We prove a formula for the asymptotic number of edge-colored regular graphs with a prescribed set of allowed vertex-incidence structures. The formula depends on specific critical p…
Approximation of starshaped sets using polynomials
Chiara Meroni, Jared Miller, Mauricio Velasco
We introduce polystar bodies: compact starshaped sets whose gauge or radial functions are expressible by polynomials, enabling tractable computations, such as that of intersection…
Convex hulls of surfaces in fourspace
Chiara Meroni, Kristian Ranestad, Rainer Sinn
This is a case study of the algebraic boundary of convex hulls of varieties. We focus on surfaces in fourspace to showcase new geometric phenomena that neither curves nor hypersurf…