Author

Shu-Cheng Cao

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Preprint Aug 2026

CLEARMIND: Closed-Form Laplacian Embeddings of Arakelov-Green Resistance for Morphological Intrinsic Neuronal Distances

It is proved that for points of the graph this problem is solved by geodesics: the squared tropical polarization distance equals the path metric minus the Arakelov-Green (AG) distance, an effective-resistance kernel given in closed form by the Laplacian pseudoinverse.

Yuyang Zhang, Weihang Xu, Xuehai Zhou et al. · 0 citations

#machine learning Preprint Aug 2026

Tropical Algebraic Geometry for Neuronal Representations: An Arakelov-Green Measure Based Descriptor for Graph Learning

The quantitative analysis of 3D neuronal morphologies requires capturing both graph topology and spatial geometry. Current message-passing Graph Neural Networks (GNNs) are bounded by the 1-Weisfeiler-Lehman (1-WL) test, limiting their ability to capture cycles induced by spatial proximities. To address this, we propose...

Yuyang Zhang, Weihang Xu, Xuehai Zhou et al. · 0 citations