arXiv research

The 2-rank of a compact Lie group $G$ is the maximal possible rank of the elementary 2-subgroup ${\mathbb Z}_{2}\times... {\mathbb Z}_{2}$ of $G$. The study of 2-ranks (and $p$-rank for any prime $p$) of compact Lie groups was initiated in 1953 by A. Borel and J.-P. Serre. Since then the 2-ranks of compact Lie groups h…

Finite groups with a hyperelliptic involution have a 2-rank of at most 4.

Let $M$ be a compact connected orientable Seifert manifold with hyperbolic orbifold $B_M$, and $f_π: π_1(M)\rightarrowπ_1(M)$ be an automorphism induced by an orientation-reversing homeomorphism $f$ of $M$. We give a bound on the rank of the fixed subgroup of $f_π$, namely, $\rank\fix(f_π)<2\rank π_1(M)$, which is simi…

Let $M$ be a closed, connected, orientable topological four-manifold with $H_1(M)$ nontrivial and free abelian, $b_2(M)\ne 0, 2$, and $χ(M)\ne 0$. We show that if $G$ is a finite group of 2-rank $\le 1$ which admits a homologically trivial, locally linear, effective action on $M$, then $G$ must be cyclic. With addition…

Proposes a deep learning method for robust ordinal regression under label noise.

Given a vertex of interest in a network $G_1$, the vertex nomination problem seeks to find the corresponding vertex of interest (if it exists) in a second network $G_2$. A vertex nomination scheme produces a list of the vertices in $G_2$, ranked according to how likely they are judged to be the corresponding vertex of …

Paper proves optimal decomposition for matrix fields, reducing convex integration steps.

This work tackles uncertainty in multi-agent multi-modal trajectory forecasting.

Scaled gradient descent improves matrix recovery for ill-conditioned matrices with optimal sampling complexity.

We introduce the probably approximately correct (PAC) \emph{Battling-Bandit} problem with the Plackett-Luce (PL) subset choice model--an online learning framework where at each trial the learner chooses a subset of $k$ arms from a fixed set of $n$ arms, and subsequently observes a stochastic feedback indicating prefere…