4 papers
Algebra of Path Integrals on Digraphs
Shing-Tung Yau, Mengmeng Zhang, Yunpeng Zi
In this paper, we extend the iterated path integrals from smooth manifolds to digraphs and develop the associated algebraic and geometric structures. Iterated path integrals on a d…
Quantum Topological Analysis on Digraphs
Yunpeng Zi, Muchun Yang, D. L. Zhou
Quantum algorithms for topological data analysis provide significant advantages over the best known classical algorithms. Unlike previous work on simplicial complexes built from po…
New Aspects of Analyzing Amyloid Fibrils
Xiaoxi Lin, Yunpeng Zi, Fengling Li +1
This is a summary of mathematical tools we used in research of analyzing the structure of proteins with amyloid form \cite{xi2024Top}. We defined several geometry indicators on the…
On the Monodromy and Period Map of the Winger Pencil
Yunpeng Zi
The sextic plane curves that are invariant under the standard action of the icosahedral group on the projective plane make up a pencil of genus ten curves (spanned by a sum of six…