10 papers
Graph statistics: An emerging discipline in non-Euclidean data analysis
Rongling Wu, Shing-Tung Yau
The explosive growth of complex data has catalyzed the emergence of graph statistics as a fundamentally new discipline in data science. Unlike traditional statistics, which operate…
Iterative construction of Hermitian-Einstein metrics on stable bundles
Jiaxuan Fan, Zhiyao Xiong, Xiaokui Yang +1
Let be a stable holomorphic vector bundle over a compact Kähler (or Gauduchon) manifold . We show that for any real number and any initial Hermitian metric …
The prescribed Hermitian-Yang-Mills flow II
Zhiyao Xiong, Xiaokui Yang, Shing-Tung Yau
We prove an analogue of the classical Donaldson-Uhlenbeck-Yau theorem by using the prescribed Hermitian-Yang-Mills flow. Let be a holomorphic vector bundle over a compact Kähle…
Existence of twisted Hermitian-Einstein metrics on unstable vector bundles
Mingwei Wang, Xiaokui Yang, Shing-Tung Yau
In this paper, we demonstrate that twisted Hermitian-Einstein metrics on holomorphic vector bundles exist without obstruction. More precisely, for an arbitrary holomorphic vector b…
The prescribed Hermitian-Yang-Mills flow I
Zhiyao Xiong, Xaokui Yang, Shing-Tung Yau
In this paper, we introduce a broad class of flows, including the prescribed Hermitian-Yang-Mills flow: where…
Existence of Hermitian metrics with prescribed Hermitian-Yang-Mills tensors I
Mingwei Wang, Xiaokui Yang, Shing-Tung Yau
In this paper, we solve the prescribed Hermitian-Yang-Mills tensor problem. Let be a holomorphic vector bundle over a compact Kähler manifold . Suppose that there e…
Routine Blood Biomarkers Reveal a Preclinical Continuum of Multiple Myeloma Risk
Bingjie Li, Jiadai Xu, Yiqing Sun +4
Multiple myeloma (MM) is preceded by a long preclinical phase spanning decades, yet scalable, non-specialist tools to identify individuals at elevated risk before end-organ damage…
Rapid general Electromagnetic Analysis with computational conformal geometry via Conformal Energy Minimization
Pengcheng Wan, Zhong-Heng Tan, S. T. Chui +2
We recently found that the electromagnetic scattering problem can be very fast in an approach expressing the fields in terms of orthonormal basis functions. In this paper we apply…
RC-positivity, Schwarz's lemma and comparison theorems
Zhiyao Xiong, Xiaokui Yang, Shing-Tung Yau
It is well-known that the classical Schwarz lemma yields an explicit comparison of two Hermitian metrics with uniform constant negative curvature bounds through holomorphic maps be…
Eigenvalues of the Hodge Laplacian on digraphs
Alexander Grigor'yan, Yong Lin, S. -T. Yau +1
This paper aims to compute and estimate the eigenvalues of the Hodge Laplacians on directed graphs. We have devised a new method for computing Hodge spectra with the following two…