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Betti number signatures of homogeneous Poisson point processes

Robins, Vanessa


The Betti numbers are fundamental topological quantities that describe the k-dimensional connectivity of an object: β0 is the number of connected components and βk effectively counts the number of k-dimensional holes. Although they are appealing natural descriptors of shape, the higher-order Betti numbers are more difficult to compute than other measures and so have not previously been studied per se in the context of stochastic geometry or statistical physics. As a mathematically tractable...[Show more]

CollectionsANU Research Publications
Date published: 2006-12-11
Type: Journal article
Source: Physical Review E-Statistical, Nonlinear and Soft Matter Physics
DOI: 10.1103/PhysRevE.74.061107


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