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Logarithmic Voronoi cells for Gaussian models

JOURNAL OF SYMBOLIC COMPUTATION (2024)

Voronoi cells of varieties

Diego Cifuentes et al.

Summary: Every real algebraic variety results in a Voronoi decomposition of its ambient Euclidean space, where each Voronoi cell is a convex semialgebraic set in the normal space of the variety at a point. The algebraic boundaries of these Voronoi cells are calculated in the study.

JOURNAL OF SYMBOLIC COMPUTATION (2022)

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Article Mathematics, Applied

Maximum Likelihood Degree, Complete Quadrics, and C*-Action

Mateusz Michalek et al.

Summary: This study focuses on the maximum likelihood (ML) degree of linear concentration models in algebraic statistics and its connection to an intersection problem on the variety of complete quadrics. The authors are able to provide an explicit and basic formula for the ML-degree, despite its computational complexity. The variety of complete quadrics is considered an exact analogue for symmetric matrices of the permutohedron variety for diagonal matrices.

SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY (2021)

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Article Mathematics, Applied