Scholars@Duke

• Background
• 

  Education, Training, & Certifications

  • Ph.D., Princeton University 2013
• 

  Duke Appointment History

  • Scholar In Residence of Mathematics, Mathematics, Trinity College of Arts & Sciences 2017
• 

  Academic Positions Outside Duke

  • Gibbs Assistant Professor, Yale University. 2015 - 2017
• Research
• 

  Selected Grants

  • CDS&E: Structure-aware Representation Learning using Deep Networks awarded by  National Science Foundation 2018 - 2021
  • Collaborative Research: Geometric Analysis and Computation of Generative Models awarded by  National Science Foundation 2018 - 2021
• Publications & Artistic Works
• 

  Selected Publications

  • Academic Articles

    • Cheng, X, Rachh, M, and Steinerberger, S. "On the diffusion geometry of graph Laplacians and applications." Applied and Computational Harmonic Analysis 46, no. 3 (May 2019): 674-688.  Full Text
    • Cheng, X, Mishne, G, and Steinerberger, S. "The geometry of nodal sets and outlier detection." Journal of Number Theory 185 (April 2018): 48-64.  Full Text
    • Lu, J, Lu, Y, Wang, X, Li, X, Linderman, GC, Wu, C, Cheng, X, Mu, L, Zhang, H, Liu, J, Su, M, Zhao, H, Spatz, ES, Spertus, JA, Masoudi, FA, Krumholz, HM, and Jiang, L. "Prevalence, awareness, treatment, and control of hypertension in China: data from 1·7 million adults in a population-based screening study (China PEACE Million Persons Project)." The Lancet 390, no. 10112 (December 2017): 2549-2558.  Full Text
    • Pragier, G, Greenberg, I, Cheng, X, and Shkolnisky, Y. "A Graph Partitioning Approach to Simultaneous Angular Reconstitution." Ieee Transactions on Computational Imaging 2, no. 3 (September 2016): 323-334.  Full Text
    • Zhang, T, Cheng, X, and Singer, A. "Marčenko–Pastur law for Tyler’s M-estimator." Journal of Multivariate Analysis 149 (July 2016): 114-123.  Full Text
    • Cheng, X, Chen, X, and Mallat, S. "Deep Haar scattering networks." Information and Inference 5, no. 2 (June 2016): 105-133.  Full Text
    • Boumal, N, and Cheng, X. "Concentration of the Kirchhoff index for Erdős–Rényi graphs." Systems & Control Letters 74 (December 2014): 74-80.  Full Text
    • CHENG, XIUYUAN, and SINGER, AMIT. "THE SPECTRUM OF RANDOM INNER-PRODUCT KERNEL MATRICES." Random Matrices: Theory and Applications 02, no. 04 (October 2013): 1350010-1350010.  Full Text
    • E, W, Zhou, X, and Cheng, X. "Subcritical bifurcation in spatially extended systems." Nonlinearity 25, no. 3 (March 1, 2012): 761-779.  Full Text
    • Lin, L, Cheng, X, E, W, Shi, A-C, and Zhang, P. "A numerical method for the study of nucleation of ordered phases." Journal of Computational Physics 229, no. 5 (March 2010): 1797-1809.  Full Text
    • Cheng, X, Lin, L, E, W, Zhang, P, and Shi, A-C. "Nucleation of Ordered Phases in Block Copolymers(Published online)." Physical Review Letters 104, no. 14.  Full Text

  • Conference Papers

    • Qiu, Q, Cheng, X, Calderbank, AR, and Sapiro, G. "DCFNet: Deep Neural Network with Decomposed Convolutional Filters." : JMLR.org, 2018.
    • Cheng, X, Shaham, U, Dror, O, Jaffe, A, Nadler, B, Chang, J, and Kluger, Y. "A Deep Learning Approach to Unsupervised Ensemble Learning." The 33rd International Conference on Machine Learning (ICML '16).: PMLR, June 2016.
    • Chen, X, Cheng, X, and Mallat, S. "Unsupervised Deep Haar Scattering on Graphs." 2014.
    • Yan, B, Sarkar, P, and Cheng, X. "Provable estimation of the number of blocks in block models." : PMLR,.  Link to Item
• Teaching & Mentoring
• 

  Recent Courses

  • MATH 532: Basic Analysis II 2019
  • MATH 561: Numerical Linear Algebra, Optimization and Monte Carlo Simulation 2019
  • MATH 493: Research Independent Study 2018
  • MATH 631: Measure and Integration 2018
  • MATH 790-90: Minicourse in Advanced Topics 2018
  • MATH 690-40: Topics in Probability Theory 2017
  • STA 690-40: Topics in Probability Theory 2017
• 

  Teaching Activities

  • In Fall 2017, I am teaching the graduate-level course Math 690 Topics in Data Analysis and Computation. I am teaching Math 532 Basic Analysis II in Spring 2018.

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