19 citations · 52 across the 11 of their papers we have counts for
11 papers
On The Discrete Morse Functions for Hypergraphs
Shiquan Ren, Chong Wang, Chengyuan Wu +1
A hypergraph can be obtained from a simplicial complex by deleting some non-maximal simplices. In this paper, we study the embedded homology as well as the homology of the (lower-)…
Weighted Simplicial Complexes and Weighted Analytic Torsions
Shiquan Ren, Chengyuan Wu
A weighted simplicial complex is a simplicial complex with values (called weights) on the vertices. In this paper, we consider weighted simplicial complexes with -val…
Discrete Morse Theory for Weighted Simplicial Complexes
Chengyuan Wu, Shiquan Ren, Jie Wu +1
In this paper, we study Forman's discrete Morse theory in the context of weighted homology. We develop weighted versions of classical theorems in discrete Morse theory. A key diffe…
Weighted Fundamental Group
Chengyuan Wu, Shiquan Ren, Jie Wu +1
In this paper, we develop and study the theory of weighted fundamental groups of weighted simplicial complexes. When all weights are 1, the weighted fundamental group reduces to th…
Hodge Decompositions for Weighted Hypergraphs
Shiquan Ren, Chengyuan Wu, Jie Wu
Weighted hypergraphs are generalizations of weighted simplicial complexes. In recent years, weighted Laplacians of weighted simplicial complexes have been studied. In 2016, as a ge…
A Discrete Morse Theory for Hypergraphs
Shiquan Ren, Chong Wang, Chengyuan Wu +1
A hypergraph can be obtained from a simplicial complex by deleting some non-maximal simplices. By [11], a hypergraph gives an associated simplicial complex. By [4], the embedded ho…
Weighted (Co)homology and Weighted Laplacian
Chengyuan Wu, Shiquan Ren, Jie Wu +1
In this paper, we generalize the combinatorial Laplace operator of Horak and Jost by introducing the -weighted coboundary operator induced by a weight function . Our weight f…
Maps on random hypergraphs and random simplicial complexes
Shiquan Ren, Chengyuan Wu, Jie Wu
Let be a simplicial complex. In this paper, we study random sub-hypergraphs and random sub-complexes of . By considering the minimal complex that a sub-hypergraph can be emb…
Computational Tools in Weighted Persistent Homology
Shiquan Ren, Chengyuan Wu, Jie Wu
In this paper, we study further properties and applications of weighted homology and persistent homology. We introduce the Mayer-Vietoris sequence and generalized Bockstein spectra…
Weighted Persistent Homology
Shiquan Ren, Chengyuan Wu, Jie Wu
In this paper we develop the theory of weighted persistent homology. In 1990, Robert J. Dawson was the first to study in depth the homology of weighted simplicial complexes. We gen…
Computing the Homology of Hypergraphs
Shiquan Ren, Chengyuan Wu, Stephane Bressan +1
Hypergraph is a topological model for networks. In order to study the topology of hypergraphs, the homology of the associated simplicial complexes and the embedded homology have be…