4 papers
Asymptotics of a planar isoperimetric problem with a white-noise volume term
Xiaopeng Cheng, Felix Otto, Matteo Palmieri
In this work we study the maximal ratio between the white noise integrated over a set and the perimeter of the set, which can be seen as a random isoperimetric problem, and app…
Optimal Sampling and Reconstruction of Graph Signals in the Fractional Fourier Domain
Xiaopeng Cheng, Zhichao Zhang, Yangfan He
Graph signal sampling and reconstruction are commonly formulated in the graph Fourier transform (GFT) domain. However, the reconstruction performance may be limited when practical…
MPFSR-Enhanced GNNs: Spectral Graph Neural Networks Enhancement Through Learnable Multiple-Parameter Graph Fractional Fourier Transforms
Manjun Cui, Xiaopeng Cheng, Yangfan He +1
Graph neural networks (GNNs) excel in processing non-Euclidean data, but traditional spectral GNNs rely on static bases and fundamentally lack active spectral regulation. Although…
Boundary Reconstruction for the Anisotropic Fractional Calderón Problem
Xiaopeng Cheng, Angkana Rüland
In this article, we provide a boundary reconstruction result for the anisotropic fractional Calderón problem and its associated degenerate elliptic extension into the upper half pl…