Applied Mathematics

  1. Learning Manifold Diffusion Semigroups from Graph Transition Matrices
    (Xiuyuan Cheng and Nan Wu),submitted. arXiv:2605.25383
  2. Improved Convergence Rate of kNN Graph Laplacians: Differentiable Self-tuned Affinity
    (Xiuyuan Cheng, Yixuan Tan and Nan Wu), submitted. arXiv:2410.23212
  3. Boundary Detection Algorithm Inspired by Locally Linear Embedding
    (Pei-Cheng Kuo and Nan Wu), SIAM Journal on Mathematics of Data Science, Volume 7, Number 4 (2025), 1857--1881. arXiv:2406.18456
  4. Data-driven Efficient Solvers for Langevin Dynamics on Manifold in High Dimensions
    (Yuan Gao, Jian-Guo Liu and Nan Wu), Applied and Computational Harmonic Analysis, Volume 62, January (2023), 261-309. arXiv:2005.12787
  5. Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation
    (Xiuyuan Cheng and Nan Wu), Applied and Computational Harmonic Analysis, Volume 61, November (2022), 132-190. arXiv:2101.09875
  6. When Locally Linear Embedding Hits Boundary
    (Hau-Tieng Wu and Nan Wu), Journal of Machine Learning Research, Volume 24, Number 69, (2023), 1-80. arXiv:1811.04423
  7. Spectral Convergence of Graph Laplacian and Heat Kernel Reconstruction in $L^\infty$ from Random Samples
    (David B Dunson, Hau-Tieng Wu, and Nan Wu), Applied and Computational Harmonic Analysis, Volume 55, November (2021), 282-336.arXiv:1912.05680
  8. Connecting Dots-from Local Covariance to Empirical Intrinsic Geometry and Locally Linear Embedding
    (John Malik, Chao Shen, Hau-Tieng Wu, and Nan Wu), Pure and Applied Analysis, Volume 1, No. 4, (2019), 515-542. arXiv:1804.02811

Statistics

  1. Inferring Manifolds using Gaussian Processes
    (David B Dunson and Nan Wu), Biometrika, Volume 113, Number 2, (2026). arXiv:2110.07478
  2. Adaptive Bayesian Regression on Data with Low Intrinsic Dimensionality
    (Tao Tang, Nan Wu, Xiuyuan Cheng and David B Dunson), Annals of Statistics, Volume 54, Number 2, (2026),1080-1099. arXiv:2407.09286
  3. Graph Based Gaussian Process on Restricted Domains
    (David B Dunson, Hau-Tieng Wu and Nan Wu), Journal of the Royal Statistical Society: Series B (Statistical Methodology), Volume 84, Issue 2, (2022), 414–439. arXiv:2010.07242
  4. Strong Uniform Consistency with Rates for Kernel Density Estimators with General Kernels on Manifolds
    (Hau-Tieng Wu and Nan Wu), Information and Inference: a Journal of the IMA, Volume 11, Issue 2, June (2022), 781–799. arXiv:2007.06408
  5. Think Globally and Fit Locally Under the Manifold Setup: Asymptotic Analysis of Locally Linear Embedding
    (Hau-Tieng Wu and Nan Wu), Annals of Statistics, Volume 46, Number 6B, (2018), 3805-3837.arXiv:1703.04058

Pure Differential Geometry

  1. Length of a Shortest Closed Geodesic in Manifolds of Dimension Four
    (Nan Wu and Zhifei Zhu), Journal of Differential Geometry, Volume 122, Number 3,(2022)， 519-564. arXiv:1702.07033
  2. An Upper Bound for the Smallest Area of a Minimal Surface in Manifolds of Dimension Four
    (Nan Wu and Zhifei Zhu), Journal of Geometric Analysis, Volume 30, (2020)， 573-600.