Random Points on an Algebraic Manifold

DOI10.1137/19M1271178zbMath1486.14076arXiv1810.06271MaRDI QIDQ5037571

Orlando Marigliano, Paul Breiding

Publication date: 1 March 2022

Published in: SIAM Journal on Mathematics of Data Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.06271

zbMATH Keywords

samplingstatistical physicsalgebraic geometrytopological data analysisgeometrical probabilityapproximating integrals

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Sampling theory, sample surveys (62D05) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25) Geometries with algebraic manifold structure (51H30) Geometric aspects of numerical algebraic geometry (14Q65) Topological data analysis (62R40)

Related Items (6)

Voronoi cells of varieties ⋮ Sampling and homology via bottlenecks ⋮ The average condition number of most tensor rank decomposition problems is infinite ⋮ Hybrid Monte Carlo methods for sampling probability measures on submanifolds ⋮ Catastrophe in elastic tensegrity frameworks ⋮ Expected centre of mass of the random Kodaira embedding

Uses Software

• HOM4PS
• Macaulay2
• PHCpack
• Matplotlib
• Bertini
• HomotopyContinuation
• GitHub
• Ripser

Cites Work

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• Algorithm 795
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• Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods
• Semidefinite Optimization and Convex Algebraic Geometry
• Rigid continuation paths I. Quasilinear average complexity for solving polynomial systems

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