🍩 Database of Original & Non-Theoretical Uses of Topology

1. Interdisciplinary Approaches to Automated Obstructive Sleep Apnea Diagnosis Through High-Dimensional Multiple Scaled Data Analysis (2019)

   Giseon Heo, Kathryn Leonard, Xu Wang, Yi Zhou

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   • Medicine
   • Obstructive sleep apnea
   • Innovate
   • Clustering
   • Persistent homology
   • Principal component analysis
   • Random forest

2. Using Persistent Homology and Dynamical Distances to Analyze Protein Binding (2016)

   Violeta Kovacev-Nikolic, Peter Bubenik, Dragan Nikolić, Giseon Heo

   Abstract

   Persistent homology captures the evolution of topological features of a model as a parameter changes. The most commonly used summary statistics of persistent homology are the barcode and the persistence diagram. Another summary statistic, the persistence landscape, was recently introduced by Bubenik. It is a functional summary, so it is easy to calculate sample means and variances, and it is straightforward to construct various test statistics. Implementing a permutation test we detect conformational changes between closed and open forms of the maltose-binding protein, a large biomolecule consisting of 370 amino acid residues. Furthermore, persistence landscapes can be applied to machine learning methods. A hyperplane from a support vector machine shows the clear separation between the closed and open proteins conformations. Moreover, because our approach captures dynamical properties of the protein our results may help in identifying residues susceptible to ligand binding; we show that the majority of active site residues and allosteric pathway residues are located in the vicinity of the most persistent loop in the corresponding filtered Vietoris-Rips complex. This finding was not observed in the classical anisotropic network model.

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   • Molecular dynamics
   • Protein Binding
   • Point cloud
   • Persistent homology
   • Topological landscape