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The persistent Betti numbers are used in topological data analysis (TDA) to infer the scales at which topological features appear and disappear in the filtration of a topological space. Understanding the statistical foundations of these descriptors, and their corresponding barcodes, is thus an...
In this paper we decompose the rational homology of the ordered configuration space of n open unit-diameter disks in the infinite strip of width 2 as a direct sum of induced...
Path homology is a topological invariant for directed graphs, which is sensitive to their asymmetry and can discern between digraphs which are indistinguishable to the directed flag complex. In Erdős–Rényi directed random graphs, the first Betti number undergoes two distinct transitions,...
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