Results 1 to 10 of about 4,696,446 (251)
Deep learning as Ricci flow [PDF]
Scientific ReportsDeep neural networks (DNNs) are powerful tools for approximating the distribution of complex data. It is known that data passing through a trained DNN classifier undergoes a series of geometric and topological simplifications.
Anthony Baptista +5 more
doaj +6 more sources
Matrix Li-Yau-Hamilton estimates under Ricci flow and parabolic frequency. [PDF]
Calc Var Partial Differ Equ, 2023 We prove matrix Li–Yau–Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Ricci flow.
Li X, Zhang QS.
europepmc +3 more sources
Rendiconti Lincei, Matematica e Applicazioni, 2021 We give a survey on the Chern-Ricci flow, a parabolic flow of Hermitian metrics on complex manifolds. We emphasize open problems and new directions.
Valentino Tosatti, B. Weinkove
semanticscholar +4 more sources
Yamabe constant evolution and monotonicity along the conformal Ricci flow
AIMS Mathematics, 2022 We investigate the Yamabe constant's behaviour in a conformal Ricci flow. For conformal Ricci flow metric g(t), t∈[0,T), the time evolution formula for the Yamabe constant Y(g(t)) is derived.
Yanlin Li +3 more
doaj +2 more sources
Community Detection on Networks with Ricci Flow. [PDF]
Sci Rep, 2019 Many complex networks in the real world have community structures – groups of well-connected nodes with important functional roles. It has been well recognized that the identification of communities bears numerous practical applications.
Ni CC, Lin YY, Luo F, Gao J.
europepmc +3 more sources
Charting cellular differentiation trajectories with Ricci flow
Nature Communications, 2023 Complex biological processes, such as cellular differentiation, require intricate rewiring of intra-cellular signalling networks. Previous characterisations revealed a raised network entropy underlies less differentiated and malignant cell states.
Anthony Baptista +2 more
doaj +2 more sources
Cobordism, singularities and the Ricci flow conjecture [PDF]
Journal of High Energy Physics, 2023 In the following work, an attempt to conciliate the Ricci flow conjecture and the Cobordism conjecture, stated as refinements of the Swampland distance conjecture and of the No global symmetries conjecture respectively, is presented.
David Martín Velázquez +2 more
doaj +2 more sources
Advances in Nonlinear Analysis, 2023 In the present work, we find the Lie point symmetries of the Ricci flow on an n-dimensional manifold, and we introduce a method in order to reutilize these symmetries to obtain the Lie point symmetries of particular metrics.
López Enrique +2 more
doaj +3 more sources
The spinorial energy for asymptotically Euclidean Ricci flow [PDF]
Advanced Nonlinear Studies, 2023 This article introduces a functional generalizing Perelman’s weighted Hilbert-Einstein action and the Dirichlet energy for spinors. It is well defined on a wide class of noncompact manifolds; on asymptotically Euclidean manifolds, the functional is shown
Baldauf Julius, Ozuch Tristan
doaj +2 more sources
High genus surface parameterization using the Euclidean Ricci flow method [PDF]
Scientific ReportsThe parameterization of surfaces, which is related to many frontier problems in mathematics, has long been a challenge for scientists and engineers.
Yuan-guang Wang
doaj +2 more sources