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…

The real-world data is often susceptible to label noise, which might constrict the effectiveness of the existing state of the art algorithms for ordinal regression. Existing works on ordinal regression do not take label noise into account. We propose a theoretically grounded approach for class conditional label noise i…

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…