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math.ST2024
Community detection with the Bethe-Hessian
Ludovic Stephan, Yizhe Zhu
The Bethe-Hessian matrix, introduced by Saade, Krzakala, and Zdeborová (2014), is a Hermitian matrix designed for applying spectral clustering algorithms to sparse networks. Rather…
math.CO2024
Regular bipartite decompositions of pseudorandom graphs
Asaf Ferber, Bryce Frederickson, Dingjia Mao +2
In 1972, Kotzig proved that for every even , the complete graph can be decomposed into edge-disjoint regular bipartite spanning subgraphs, which is b…
math.AP2024
Second order Sobolev regularity for normalized parabolic -Laplace equations via the algebraic structure
Yuqing Wang, Yizhe Zhu
Denote by the Laplacian and by the -Laplacian. A fundamental inequality is proved for the algebraic structure of : for every ,…