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» Quantifying Homology Classes
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STACS
2009
Springer
14 years 2 months ago
Weak MSO with the Unbounding Quantifier
Abstract. A new class of languages of infinite words is introduced, called the maxregular languages, extending the class of ω-regular languages. The class has two equivalent desc...
Mikolaj Bojanczyk
COMPGEOM
2011
ACM
12 years 11 months ago
An output-sensitive algorithm for persistent homology
In this paper, we present the first output-sensitive algorithm to compute the persistence diagram of a filtered simplicial complex. For any Γ > 0, it returns only those homo...
Chao Chen, Michael Kerber
IPSN
2005
Springer
14 years 1 months ago
Coverage and hole-detection in sensor networks via homology
We consider coverage problems in sensor networks of stationary nodes with minimal geometric data. In particular, there are no coordinates and no localization of nodes. We introduc...
Robert Ghrist, Abubakr Muhammad
MFCS
2010
Springer
13 years 6 months ago
Persistent Homology under Non-uniform Error
Using ideas from persistent homology, the robustness of a level set of a real-valued function is defined in terms of the magnitude of the perturbation necessary to kill the classe...
Paul Bendich, Herbert Edelsbrunner, Michael Kerber...
BIRTHDAY
2004
Springer
13 years 11 months ago
On Models for Quantified Boolean Formulas
A quantified Boolean formula is true, if for any existentially quantified variable there exists a Boolean function depending on the preceding universal variables, such that substi...
Hans Kleine Büning, Xishun Zhao