Euler integration over definable functions

Yuliy Baryshnikova; Robert Ghristb

doi:10.1073/pnas.0910927107

Euler integration over definable functions

Research output: Contribution to journal › Article › peer-review

Abstract

We extend the theory of Euler integration from the class of constructible functions to that of "tame" R-valued functions (definable with respect to an o-minimal structure). The corresponding integral operator has some unusual defects (it is not a linear operator); however, it has a compelling Morse-theoretic interpretation. In addition, it is an advantageous setting in which to integrate in applications to diffused and noisy data in sensor networks.

Original language	English (US)
Pages (from-to)	9525-9530
Number of pages	6
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	107
Issue number	21
DOIs	https://doi.org/10.1073/pnas.0910927107
State	Published - May 25 2010
Externally published	Yes

Keywords

Definable functions
Euler characteristic
O-minimal structures
Sensor network

ASJC Scopus subject areas

General

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10.1073/pnas.0910927107

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AB - We extend the theory of Euler integration from the class of constructible functions to that of "tame" R-valued functions (definable with respect to an o-minimal structure). The corresponding integral operator has some unusual defects (it is not a linear operator); however, it has a compelling Morse-theoretic interpretation. In addition, it is an advantageous setting in which to integrate in applications to diffused and noisy data in sensor networks.

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KW - Euler characteristic

KW - O-minimal structures

KW - Sensor network

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Euler integration over definable functions

Abstract

Keywords

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