arXiv research

This paper studies HOMFLY polynomials of specific and infinite classes of knots.

A bundle with base $B$ and fibre $F$ aspherical closed surfaces has a section if and only if the action $:π_1(B)\to{Out}(π_1(F))$ factors through $Aut(π_1(F))$ and a cohomology class is 0. We simplify and make more explicit the latter condition. We also show that the transgression $d^2_{2,0}$ in the homology LHS spectr…

The paper proves a factorization theorem for harmonic maps between Riemann surfaces and manifolds.

Suppose that $f$ is a homomorphism from the mapping class group $\mathcal{M}(N_{g,n})$ of a nonorientable surface of genus $g$ with $n$ boundary components, to $\mathrm{GL}(m,\mathbb{C})$. We prove that if $g\ge 5$, $n\le 1$ and $m\le g-2$, then $f$ factors through the abelianization of $\mathcal{M}(N_{g,n})$, which is…

Over the last decade there has been increasing concern about the biases embodied in traditional evaluation methods for Natural Language Processing/Learning, particularly methods borrowed from Information Retrieval. Without knowledge of the Bias and Prevalence of the contingency being tested, or equivalently the expecta…

Analyzes the differential expansion of knot polynomials, focusing on its applicability and modifications.

We study the combinatorial pure exploration problem Best-Set in stochastic multi-armed bandits. In a Best-Set instance, we are given $n$ arms with unknown reward distributions, as well as a family $\mathcal{F}$ of feasible subsets over the arms. Our goal is to identify the feasible subset in $\mathcal{F}$ with the maxi…