Morse Theory for Filtrations and Efficient Computation of Persistent Homology

By Konstantin Mischaikow, Vidit Nanda. Discrete & Computational Geometry, 2013

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Topological Consistency via Kernel Estimation (2014, background): “Note that there are several efficient algorithms to compute persistent homology that can also be used here (see [23, 34, 43]).”
Deep Learning with Topological Signatures (2017, methodology): “All experiments were implemented in PyTorch 3 , DIPHA 4 and Perseus [21].”
Clique topology reveals intrinsic geometric structure in neural correlations (2015, methodology): “The resulting lists are then input into Perseus, a computational topology software package implemented by Vidit Nanda ( 27 ); this software builds on work by Mishaikow and Nanda ( 28 ) using discrete Morse theory to reduce the sizes of simplicial complexes before performing persistent homology compu”
Persistent homology analysis of protein structure, flexibility and folding (2014, methodology): “General filtration processes To construct a simplicial homology from a set of point cloud data, a filtration process is required [42–46].”