27 citations · 79 across the 17 of their papers we have counts for
17 papers
Hidden critical and Morse equivalence behind duality: Theory and Applications
Dong Zhang
The aim of this paper is to establish critical duality theory for ratios of nonnegative homogeneous convex functions (shorten for RC functions) and differences of convex functions…
There is no going back: Properties of the non-backtracking Laplacian
Raffaella Mulas, Dong Zhang, Giulio Zucal
We prove new properties of the non-backtracking graph and the non-backtracking Laplacian for graphs. In particular, among other results, we prove that two simple graphs are isomorp…
Cheeger inequalities on simplicial complexes
Jürgen Jost, Dong Zhang
Cheeger-type inequalities in which the decomposability of a graph and the spectral gap of its Laplacian mutually control each other play an important role in graph theory and netwo…
Nodal domain theorems for -Laplacians on signed graphs
Chuanyuan Ge, Shiping Liu, Dong Zhang
We establish various nodal domain theorems for -Laplacians on signed graphs, which unify most of the existing results on nodal domains of graph -Laplacians and arbitrary symm…
Petals and Books: The largest Laplacian spectral gap from 1
Jürgen Jost, Raffaella Mulas, Dong Zhang
We prove that, for any connected graph on vertices, the spectral gap from the value with respect to the normalized Laplacian is at most . Moreover, we show that…
Homological eigenvalues of graph -Laplacians
Dong Zhang
Inspired by persistent homology in topological data analysis, we introduce the homological eigenvalues of the graph -Laplacian , which allows us to analyse and classify non…
Discrete-to-Continuous Extensions: piecewise multilinear extension, min-max theory and spectral theory
Jürgen Jost, Dong Zhang
We introduce the homogeneous and piecewise multilinear extensions and the eigenvalue problem for locally Lipschitz function pairs, in order to develop a systematic framework for re…
Discrete-to-Continuous Extensions: Lovász extension, optimizations and eigenvalue problems
Jürgen Jost, Dong Zhang
In this paper, we use various versions of Lovász extension to systematically derive continuous formulations of problems from discrete mathematics. This will take place in the follo…
Coloring the normalized Laplacian for oriented hypergraphs
Aida Abiad, Raffaella Mulas, Dong Zhang
The independence number, coloring number and related parameters are investigated in the setting of oriented hypergraphs using the spectrum of the normalized Laplace operator. For t…
-Laplace Operators for Oriented Hypergraphs
Jürgen Jost, Raffaella Mulas, Dong Zhang
The -Laplacian for graphs, as well as the vertex Laplace operator and the hyperedge Laplace operator for the general setting of oriented hypergraphs, are generalized. In particu…
Khintchine inequality on normed spaces and the application to Banach-Mazur distance
Xin Luo, Dong Zhang
We establish variant Khintchine inequalities on normed spaces of Hanner type and cotype, in which the Rademacher distribution corresponding to classical Khintchine inequality is re…
Spectral Theory of Laplace Operators on Oriented Hypergraphs
Raffaella Mulas, Dong Zhang
Several new spectral properties of the normalized Laplacian defined for oriented hypergraphs are shown. The eigenvalue and the case of duplicate vertices are discussed; two Cou…
Discrete-to-Continuous Extensions: Lovász extension and Morse theory
Jürgen Jost, Dong Zhang
This is the first of a series of papers that develop a systematic bridge between constructions in discrete mathematics and the corresponding continuous analogs. In this paper, we e…
Spectrum of signless 1-Laplacian on simplicial complexes
Xin Luo, Dong Zhang
We introduce the signless 1-Laplacians and the dual Cheeger constants on simplicial complexes. The connection of its spectrum to the combinatorial properties like independence numb…
Non-crossing chords of a polygon with forbidden positions
Dongyi Wei, Demin Zhang, Dong Zhang
In this paper, we systematically study non-crossing chords of simple polygons in the plane. We first introduce the reduced Euler characteristic of a family of line-segments, and su…
Dual Cheeger Constants, Signless 1-Laplacians and Maxcut
Sihong Shao, Chuan Yang, Dong Zhang
The first nontrivial lower bound of the worst-case approximation ratio for the maxcut problem was achieved via the dual Cheeger problem, whose optimal value is referred to the dual…
The -Laplacian Cheeger Cut: Theory and Algorithms
K. C. Chang, Sihong Shao, Dong Zhang
This paper presents a detailed review of both theory and algorithms for the Cheeger cut based on the graph -Laplacian. In virtue of the cell structure of the feasible set, we pr…