Euler integration over definable functions

DOI10.1073/pnas.0910927107zbMath1205.53081arXiv0909.4054OpenAlexW2109673461WikidataQ34006630 ScholiaQ34006630MaRDI QIDQ3073985

Robert W. Ghrist, Yuliy M. Baryshnikov

Publication date: 12 February 2011

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.4054

zbMATH Keywords

Euler characteristicsensor networko-minimal structuresdefinable functions

Mathematics Subject Classification ID

Communication networks in operations research (90B18) Model-theoretic algebra (03C60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Integral geometry (53C65) Semialgebraic sets and related spaces (14P10)

Related Items (9)

Discrete Euler integration over functions on finite categories ⋮ EULER INTEGRATION OF GAUSSIAN RANDOM FIELDS AND PERSISTENT HOMOLOGY ⋮ Discrete Morse theory for computing cellular sheaf cohomology ⋮ Mean geometry for 2D random fields: level perimeter and level total curvature integrals ⋮ Euler characteristic surfaces ⋮ Hadwiger's theorem for definable functions ⋮ Efficient algorithms for computing the Euler-Poincaré characteristic of symmetric semi-algebraic sets ⋮ Topological approach to microcanonical thermodynamics and phase transition of interacting classical spins ⋮ A complexity theory of constructible functions and sheaves

Cites Work

• Integralsätze im Konvexring
• Operations on constructible functions
• Integration of positive constructible functions against Euler characteristic and dimension
• Constructible motivic functions and motivic integration
• Chern classes for singular algebraic varieties
• Integral geometry of tame sets
• Target Enumeration via Euler Characteristic Integrals

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