Robust subspace recovery by Tyler's M-estimator

This paper considers the problem of robust subspace recovery: given a set of $N$ points in $\mathbb{R}^D$, if many lie in a $d$-dimensional subspace, then can we recover the underlying subspace? We show that Tyler's M-estimator can be used to recover the underlying subspace, if the percentage of the inliers is larger than $d/D$ and the data points lie in general position. Empirically, Tyler's M-estimator compares favorably with other convex subspace recovery algorithms in both simulations and experiments on real data sets

Stable Yang-Mills connections on Special Holonomy Manifolds

We prove that energy minimizing Yang-Mills connections on a compact $G_{2}$-manifold has holonomy equal to $G_{2}$ are $G_{2}$-instantons, subject to an extra condition on the curvature. Furthermore, we show that energy minimizing connections on a compact Calabi-Yau $3$-fold has holonomy equal to $SU(3)$ subject to a similar condition are holomorphic.Comment: Final Version; will be appear in JGP. arXiv admin note: text overlap with arXiv:0808.0667 by other author

“Lost in Translation? Transnational American Rock Music of the Sixties and its Misreading in 1980s China”

Excerpt from The Power of Culture: Encounters between China and the United States, edited by Priscilla Robert