The theory of zigzag persistence is a substantial extension of persistent homology, and its development has enabled the investigation of several unexplored avenues in the area of topological data analysis. In this paper, we discuss three applications of zigzag persistence: topological bootstrapping, parameter thresholding, and the comparison of witness complexes.

Magnesium oxide nanotubes of finite length are investigated by the Density Functional Theory (DFT) at the B3LYP/6-31G (d) level. The (6, 0) zigzag and (4, 4) armchair of MgO nanotubes were considered and nuclear magnetic resonance properties including isotropic and anisotropic chemical shielding parameters (CSI and CSA) were calculated for 25Mg and 17O atoms of the optimiz...

Magnesium oxide nanotubes of finite length are investigated by the Density Functional Theory (DFT) at the B3LYP/6-31G (d) level. The (6, 0) zigzag and (4, 4) armchair of MgO nanotubes were considered and nuclear magnetic resonance properties including isotropic and anisotropic chemical shielding parameters (CSI and CSA) were calculated for 25Mg and 17O atoms of the optimiz...

Understanding molecular conformation is a first step in understanding the waxing (or formation of crystals) of petroleum fuels. In this work, we study the molecular conformation of typical fuel oils modeled as pure n-alkanes. A multi-scale global optimization methodology based on terrain methods and funneling algorithms is used to find minimum energy molecular conformations of united atom n-alk...