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math.AT2025
Dowker's theorem for higher-order relations
Vin de Silva, Chad Giusti, Vladimir Itskov +5
Given a relation between two sets, Dowker's Theorem (1952) states that the homology groups of two associated simplicial complexes, now known as Dowker comp…
math.AT2023
On the spectrum of the Hodge Laplacian on sequences
Hannah Santa Cruz Baur, Vladimir Itskov
Hodge Laplacians have been previously proposed as a natural tool for understanding higher-order interactions in networks and directed graphs. Here we introduce a Hodge-theoretic ap…
math.AT2020
A Topological Approach to Inferring the Intrinsic Dimension of Convex Sensing Data
Min-Chun Wu, Vladimir Itskov
We consider a common measurement paradigm, where an unknown subset of an affine space is measured by unknown continuous quasi-convex functions. Given the measurement data, can one…