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math.PR2010★ 91 cited
Persistent Homology for Random Fields and Complexes
Robert J. Adler, Omer Bobrowski, Matthew S. Borman +2
We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to un…
math.PR2010★ 31 cited
Euler Integration of Gaussian Random Fields and Persistent Homology
Omer Bobrowski, Matthew Strom Borman
In this paper we extend the notion of the Euler characteristic to persistent homology and give the relationship between the Euler integral of a function and the Euler characteristi…