We show that the distance of a link $K$ with respect to a bridge surface of any genus determines a lower bound on the genus of essential surfaces and…

We examine the fraction of massive ($M_{*}>10^{10} M_{\odot}$), compact star-forming galaxies (cSFGs) that host an active galactic nucleus (AGN) at $…

In [14] Manes studies the possible periods of rational numbers under iteration of maps of the form

Let $P\in\mathbb Q[t,x]$ be a polynomial in two variables with rational coefficients, and let $G$ be the Galois group of $P$ over the field $\mathbb …

In quantum physics, disturbance due to a measurement is not negligible. This requires the time parameter $t$ in the Schr\"odinger or Heisenberg equat…

We report a systematic experimental and numerical study of the expansion of ultra-cold Rydberg plasmas. Specifically, we have measured the asymptotic…

Making accurate motion prediction of surrounding agents such as pedestrians and vehicles is a critical task when robots are trying to perform autonom…

Attaching a 2-handle to a genus two or greater boundary component of a 3-manifold is a natural generalization of Dehn filling a torus boundary compon…

We propose an improved methodology to constrain spatial variations of the fine structure constant using clusters of galaxies. We use the {\it Planck}…

This work defines seven new combinatorial game rulesets based on satisfying Boolean formulas. Two of these are trivial in that the players do not have any choices to make. The other five are all computationally difficult (PSPACE-complete) to determi…

Consider QBF, the Quantified Boolean Formula problem, as a combinatorial game ruleset. The problem is rephrased as determining the winner of the game…

In this section we prove Theorem 1.4.

Consider an algebraic number field, $K$, and its ring of integers, $\mathcal{O}_K$. There exists a smallest $B_K>1$ such that for any $x>1$ we can fi…

We have measured the asymptotic expansion velocities of ultra-cold plasmas (UNPs) which evolve from cold, dense, samples of Rydberg rubidium atoms us…

We prove that knots obtained by attaching a band to a split link satisfy the cabling conjecture. We also give new proofs that unknotting number one k…

Boring is an operation which converts a knot or two-component link in a 3--manifold into another knot or two-component link. It generalizes rational …

We extend techniques due to Pardon to show that there is a lower bound on the distortion of a knot in $\mathbb{R}^3$ proportional to the minimum of t…

An equivalent definition of the Fibonacci numbers is that they are the unique sequence such that every integer can be written uniquely as a sum of no…

Performing deep learning on end-user devices provides fast offline inference results and can help protect the user's privacy. However, running models…

Having developed the theoretical and algorithmic material that form the core of this article, we proceed to apply our results to study the exceptional sets of two sample polynomials, one with an infinite exceptional set and one with a finite excepti…

Let $P(T,X)$ be an irreducible polynomial in two variables with rational coefficients. It follows from Hilbert's Irreducibility Theorem that for most…

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