Revisiting Over-smoothing and Over-squashing using Ollivier's Ricci Curvature [PDF]
International Conference on Machine Learning, 2022 Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing. These issues prohibit the ability of GNNs to model complex graph interactions by limiting their effectiveness in taking ...
K. Nguyen +5 more
semanticscholar +1 more source
Weighted Ricci curvature in Riemann-Finsler geometry [PDF]
AUT Journal of Mathematics and Computing, 2021 Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold.
Zhongmin Shen
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Radiometric Constraints on the Timing, Tempo, and Effects of Large Igneous Province Emplacement
Geophysical Monograph Series, Page 27-82., 2021 Exploring the links between Large Igneous Provinces and dramatic environmental impact
An emerging consensus suggests that Large Igneous Provinces (LIPs) and Silicic LIPs (SLIPs) are a significant driver of dramatic global environmental and biological changes, including mass extinctions.
Jennifer Kasbohm +2 more
wiley +3 more sources
Minkowski inequality on complete Riemannian manifolds with nonnegative Ricci curvature [PDF]
Analysis & PDE, 2021 In this paper we consider Riemannian manifolds of dimension at least $3$, with nonnegative Ricci curvature and Euclidean Volume Growth. For every open bounded subset with smooth boundary we establish the validity of an optimal Minkowski Inequality.
L. Benatti +2 more
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On the projective Ricci curvature [PDF]
Science China Mathematics, 2020 The notion of the Ricci curvature is defined for sprays on a manifold. With a volume form on a manifold, every spray can be deformed to a projective spray. The Ricci curvature of a projective spray is called the projective Ricci curvature. In this paper, we introduce the notion of projectively Ricci-flat sprays.
Zhongmin Shen, Liling Sun, Liling Sun
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Generalized surgery on Riemannian manifolds of positive Ricci curvature [PDF]
Transactions of the American Mathematical Society, 2021 The surgery theorem of Wraith states that positive Ricci curvature is preserved under surgery if certain metric and dimensional conditions are satisfied.
Philipp Reiser
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Frontiers in Aging Neuroscience, 2023 IntroductionGeometry-inspired notions of discrete Ricci curvature have been successfully used as markers of disrupted brain connectivity in neuropsychiatric disorders, but their ability to characterize age-related changes in functional connectivity is ...
Yasharth Yadav +8 more
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FORMAN–RICCI CURVATURE FOR HYPERGRAPHS [PDF]
Advances in Complex Systems, 2021 Hypergraphs serve as models of complex networks that capture more general structures than binary relations. For graphs, a wide array of statistics has been devised to gauge different aspects of their structures. Hypergraphs lack behind in this respect.
Peter F. Stadler +6 more
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On the Almost $\eta-$Ricci Solitons on Pseudosymmetric Lorentz Generalized Sasakian Space Forms
Universal Journal of Mathematics and Applications, 2023 In this paper, we consider Lorentz generalized Sasakian space forms admitting almost $\eta-$Ricci solitons in some curvature tensors. Ricci pseudosymmetry concepts of \ Lorentz generalized Sasakian space forms admitting $\eta-$Ricci soliton have ...
Mehmet Atçeken, Tuğba Mert
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Almost $\eta-$Ricci Solitons on Pseudosymmetric Lorentz Sasakian Space Forms
Communications in Advanced Mathematical Sciences, 2023 In this paper, we consider pseudosymmetric Lorentz Sasakian space forms admitting almost $\eta-$Ricci solitons in some curvature tensors. Ricci pseudosymmetry concepts of Lorentz Sasakian space forms admits $\eta-$Ricci soliton have introduced according ...
Mehmet Atçeken, Tuğba Mert
doaj +1 more source