S
Shiping Liu
Researcher at University of Science and Technology of China
Publications - 62
Citations - 1270
Shiping Liu is an academic researcher from University of Science and Technology of China. The author has contributed to research in topics: Curvature & Ricci curvature. The author has an hindex of 16, co-authored 54 publications receiving 964 citations. Previous affiliations of Shiping Liu include Chinese Academy of Sciences & Max Planck Society.
Papers
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Ollivier's Ricci curvature, local clustering and curvature dimension inequalities on graphs
TL;DR: This paper employs a definition of generalized Ricci curvature proposed by Ollivier in a general framework of Markov processes and metric spaces and applied in graph theory by Lin–Yau to derive lower RicCI curvature bounds on graphs in terms of such local clustering coefficients.
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Ollivier–Ricci curvature and the spectrum of the normalized graph Laplace operator
TL;DR: In this article, the spectrum of the normalized Laplace operator ∆ on a finite graph G, 1− (1− k[t]) 1t ≤ λ 1 ≤ · · · ≤ ≥ λN−1 ≤ 1 + ∆ 1 t, ∀ integers t ≥ 1.
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Comparative analysis of two discretizations of Ricci curvature for complex networks
TL;DR: In this paper, the authors performed an empirical comparison of two distinct notions of discrete Ricci curvature for graphs or networks, namely, the Forman-Ricci curvatures and Ollivier-Rriccis.
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Gradient estimates for solutions of the heat equation under Ricci flow
TL;DR: In this article, the authors established first order gradient estimates for positive solutions of the heat equations on complete non-compact or closed Riemannian manifolds under Ricci flows.
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Comparative analysis of two discretizations of Ricci curvature for complex networks
TL;DR: It is shown that if one considers the augmented Forman-Ricci curvature which also accounts for the two-dimensional simplicial complexes arising in graphs, the observed correlation between the two discretizations is even higher, especially, in real networks.