My current research interests include
topological data analysis,
manifold learning,
fMRI data analysis, and
Euler calculus
My previous research interest was in
harmonic analysis and dispersive partial differential equations.
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Publications: (# indicates the corresponding author; + indicates my advisee; * equal contributions.)
(Topic: topological data analysis.)
Kun Meng #, Jinyu Wang +, Lorin Crawford, and Ani Eloyan.
Randomness of shapes and statistical inference on shapes via the smooth Euler characteristic transform.
Journal of the American Statistical Association (Theory and Methods), 2024.
(Topic: fMRI data analysis.)
Kun Meng # and Ani Eloyan.
Population-level task-evoked functional connectivity via Fourier analysis.
Journal of the Royal Statistical Society Series C: Applied Statistics, 2024.
(Topic: manifold learning.)
Kun Meng # and Ani Eloyan.
Principal manifold estimation via model complexity selection.
Journal of the Royal Statistical Society Series B: Statistical Methodology, 2021.
(Topic: harmonic analysis and dispersive partial differential equations.)
Junfeng Li and Kun Meng.
Global well-posedness for the fifth order Kadomtsev-Petviashvili II equation in three-dimensional space.
Preprints: (# indicates the correspondence author; + indicates my advisee; * equal contributions.)
(Topic: manifold learning.)
Robert Zielinski #, Kun Meng, and Ani Eloyan.
Longitudinal principal manifold estimation.
arXiv preprint arXiv:2407.17450, 2024.
(Topic: algebraic topology and Euler calculus.)
Mattie Ji+ * and Kun Meng * (alphabetical)
Euler characteristics and homotopy types of definable sublevel sets, with applications to topological data analysis.
arXiv preprint arXiv:2309.03142, 2023.
(Topic: topological data analysis.)
Kun Meng #, Mattie Ji +, Jinyu Wang +, Kexin Ding +, Henry Kirveslahti, Ani Eloyan, and Lorin Crawford.
Statistical inference on grayscale images via the Euler-Radon transform.
arXiv preprint arXiv:2308.14249, 2023.
(Topic: topological data analysis.)
Jinyu Wang # +, Kun Meng, and Fenghai Duan.
Hypothesis testing for medical imaging analysis via the smooth Euler characteristic transform.
"Everything is connected by my love of the craft, the thrill of working through ideas and narrowing them down and polishing it all up in the end, editing, waking up in the middle of the night, throwing out the old ideas because you just thought of a newer, better one or a plot device that ties the whole thing together."
--- Taylor Swift (NYU 2022 commencement speech)
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