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 | |
| State | Published - May 25 2010 |
| Externally published | Yes |
Keywords
- Definable functions
- Euler characteristic
- O-minimal structures
- Sensor network
ASJC Scopus subject areas
- General