Hey, folks! I discovered [this image](https://i.4cdn.org/vp/1614460760813.jpg) while looking at different discussions regarding the upcoming Legends: Arceus game. This led me down a bit of a rabbit ...
Automatic polyp segmentation has proven to be immensely helpful for endoscopy procedures, reducing the missing rate of adenoma detection for endoscopists while increasing efficiency. However, classifying a polyp as being neoplasm or not and segmentin...
Recently Yu. Bilu, P. Habegger and L. Kühne proved that no singular modulus can be a unit in the ring of algebraic integers. In this paper we study for which sets S of prime numbers there is no singular modulus that is an S-units. Here we prove that...
We analyze, and prove, the associativity of the new Z_{3} parafermionic chiral algebra which has been announced some time ago, with principal parafermionic fields having the conformal dimension Δ_ψ=8/3. In doing so we have developed a new method fo...
We prove that the pseudoautomorphism group of a blow-up of $\mathbb{P}^3$ at $8$ very general points is trivial. We also establish the injectivity of the Coble representation associated to blow-ups of $\mathbb{P}^3$ at $r\ge 8$ general points, answer...
Let $v_1$, $v_2$, ..., $v_n$ be real numbers whose squares add up to 1. Consider the $2^n$ signed sums of the form $S = \sum \pm v_i$. Holzman and Kleitman (1992) proved that at least 3/8 of these sums satisfy $|S| \le 1$. This 3/8 bound seems to be...
PT6A-27 engines. This was a 680 hp (510 kW) engine that was flat rated to 620 hp (460 kW) for use in the Series 300 Twin Otter. The Series 300 proved to be
For any $n\geq 3$, we prove that there exist equivalences between these apparently unrelated objects: irreducible $n$-dimensional non degenerate projective varieties $X\subset \mathbb P^{2n+1}$ different from rational normal scrolls and 3-covered by...
Fix a number field $k$, integers $\ell, n \geq 2$, and a prime $p$. For all $r \geq 1$, we prove strong unconditional upper bounds on the $r$-th moment of $\ell$-torsion in the ideal class groups of degree $p$ extensions of $k$ and of degree $n$ $S_n...
We prove a highly uniform version of the prime number theorem for a certain class of $L$-functions. The range of $x$ depends polynomially on the analytic conductor, and the error term is expressed in terms of an optimization problem depending explici...
Let $π$ be a unitary cuspidal automorphic representation of $\mathrm{GL}_n$ over a number field, and let $\tildeπ$ be contragredient to $π$. We prove effective upper and lower bounds of the correct order in the short interval prime number theorem...
Lattices generated by lattice points in skeletons of reflexive polytopes are essential in determining the fundamental group and integral cohomology of Calabi-Yau hypersurfaces. Here we prove that the lattice generated by all lattice points in a ref...
For an irreducible character $χ$ of a finite group $G$, let $\mathrm{cod}(χ):=|G: \ker(χ)|/χ(1)$ denote the codegree of $χ$, and let $\mathrm{cod}(G)$ be the set of irreducible character codegrees of $G$. In this note, we prove that if $\ker(χ)...
We prove a p'-version of a classical theorem of Broline and Garrison. As a consequence, we obtain results on p-parts of character codegrees....
Wanna know the fastest way to lose weight that’s still extremely healthy? We have the answer for you! A team of European scientists recently set up a head-to-head battle between five approaches already proven to make wellbeing soar. And when it came to speedy slimming, there was…
Partly Cloudy today with a high of 63°F and a low of 48°F.
Partly Cloudy today with a high of 63°F and a low of 49°F.
In a recent prominent study Worobey et al.\ (2022, Science, 377, pp.\ 951--9) purported to demonstrate statistically that the Huanan Seafood Wholesale Market was the epicenter of the early COVID-19 epidemic. We show that this statistical conclusion i...
L. Lovasz has shown that Sperner's combinatorial lemma admits a generalization involving a matroid defined on the set of vertices of the associated triangulation. Inspired by this result we prove that classical Ky Fan's theorem admits an oriented m...
Address clustering tries to construct the one-to-many mapping from entities to addresses in the Bitcoin system. Simple heuristics based on the micro-structure of transactions have proved very effective in practice. In this paper we describe the prima...