学术报告（张奕堃 9.23）

 摘要：On megaparsec scales, matter in our Universe is not uniformly distributed but rather forms a complicated large-scale network structure called the cosmic web. Among its intricate characteristics, the one-dimensional cosmic filaments are of great research interest because they dominate the cosmic web in terms of matter and provide a valuable insight into the evolution of nearby galaxies.

In this talk, we present a novel statistical framework of recovering the cosmic filaments from galaxy samples in the Sloan Digital Sky Survey (SDSS). In particular, we model these one-dimensional structures through directional density ridges, which can be practically identified by our proposed Directional Subspace Constrained Mean Shift (DirSCMS) algorithm. The algorithm and statistical framework behind it take into account the nonlinear geometry of a celestial sphere on which the galaxy samples lie and thus lead to less biased estimators of the underlying filament structures. We also prove the statistical consistency of our filament estimator based on directional kernel density estimator and the linear convergence results of our proposed filament-finding algorithm. Finally, we briefly discuss how to generalize our framework to recover the cosmic filaments in the 3D (Right Ascension, Declination, Redshift) space.

The talk is based on my recent works with Prof. Yen-Chi Chen and Prof. Rafael S. de Souza.

Notes: I will make the talk content accessible to a general audience, and students at all levels are more than welcome to attend.

Reference:

[1] Yikun Zhang and Yen-Chi Chen. Kernel Smoothing, Mean Shift, and Their Learning Theory with

Directional Data. Journal of Machine Learning Research, 22(154):1−92, 2021. URL:

https://jmlr.org/papers/v22/20-1194.html.

[2] Yikun Zhang and Yen-Chi Chen. Linear Convergence of the Subspace Constrained Mean Shift

Algorithm: From Euclidean to Directional Data. Information and Inference: A Journal of the IMA, 2022.

URL: https://academic.oup.com/imaiai/advance-article-abstract/doi/

10.1093/imaiai/iaac005/6563418.

[3] Yikun Zhang and Yen-Chi Chen. The EM Perspective of Directional Mean Shift Algorithm. arXiv:2101.10058, 2021. https://arxiv.org/abs/2101.10058.

[4] Yikun Zhang and Yen-Chi Chen. Mode and Ridge Estimation in Euclidean and Directional Product Spaces: A Mean Shift Approach. arXiv:2110.08505, 2021. https://arxiv.org/abs/2110.08505.

[5] Yikun Zhang, Rafael S. de Souza, and Yen-Chi Chen. SCONCE: A Cosmic Web Finder for Spherical and Conic Geometries. arXiv:2207.07001, 2022. https://arxiv.org/abs/2207.07001.