title: Euler integration over definable functions.
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.
authors.affiliation: Bell Laboratories, Murray Hill, NJ 07974, USA.
authors.forename: Yuliy
authors.initials: Y
authors.lastname: Baryshnikov
authors.forename: Robert
authors.initials: R
authors.lastname: Ghrist
mesh_terms: D008962:Models, Theoretical; D009622:Noise