Scholars@Duke
Ling Zhou

Ling Zhou

Phillip Griffiths Assistant Research Professor
Mathematics

Selected Publications

Persistent homotopy groups of metric spaces

Journal Article Journal of Topology and Analysis · October 1, 2025 In this paper, we study notions of persistent homotopy groups of compact metric spaces. We pay particular attention to the case of fundamental groups, for which we obtain a more precise description via a persistent version of the notion of discrete fundame ... Full text Cite

Persistent cup product structures and related invariants

Journal Article Journal of Applied and Computational Topology · March 2024 AbstractOne-dimensional persistent homology is arguably the most important and heavily used computational tool in topological data analysis. Additional information can be extracted from datasets by studying multi-dimensiona ... Full text Cite

EPHEMERAL PERSISTENCE FEATURES AND THE STABILITY OF FILTERED CHAIN COMPLEXES

Journal Article Journal of Computational Geometry · January 1, 2024 We strengthen the usual stability theorem for Vietoris-Rips (VR) persistent homology of finite metric spaces by building upon constructions due to Usher and Zhang in the context of filtered chain complexes. The information present at the level of filtered ... Full text Cite

Persistent Cup-Length

Conference · July 4, 2021 Cohomological ideas have recently been injected into persistent homology and have for example been used for accelerating the calculation of persistence diagrams by the software Ripser. The cup product operation which is available at cohomology level give ... Full text Link to item Cite

Reducing parameter space for neural network training

Journal Article Theoretical and Applied Mechanics Letters · March 2020 Full text Cite

Generalized Fourier Transforms Associated with the Oscillator Representation

Journal Article Journal of Fourier Analysis and Applications · October 2019 Full text Cite