Related papers: Rhymes in primes
I briefly review the present status of bosonic strings and discretized random surfaces in D>1 which seem to be in a polymer rather than stringy phase. As an explicit example of what happens, I consider the Kazakov-Migdal model with a…
This work, concerning paraphrase identification task, on one hand contributes to expanding deep learning embeddings to include continuous and discontinuous linguistic phrases. On the other hand, it comes up with a new scheme TF-KLD-KNN to…
The theory of planar hyperbolic billiards is already quite well developed by having also achieved spectacular successes. In addition there also exists an excellent monograph by Chernov and Markarian on the topic. In contrast, apart from a…
The world of primes has many gaps between evidence and theorems. Here, we review Legendre's conjecture on primes between consecutive squares and recent progress on the weaker question of primes between consecutive larger powers. Assuming…
Memes are prevalent on the internet and continue to grow and evolve alongside our culture. An automatic understanding of memes propagating on the internet can shed light on the general sentiment and cultural attitudes of people. In this…
An informal and elementary introduction to probability scoring and forecast verification and improvement, slightly extended from Significance 22:3(2025)16, which might be useful for less mathematical readers as a prologue to the classic…
A consequence of Bertrand's postulate, proved by L. Greenfield and S. Greenfield in 1998, assures that the set of integers $\{1,2,\cdots, 2n\}$ can be partitioned into pairs so that the sum of each pair is a prime number for any positive…
We prove that there are infinitely often pairs of primes much closer than the average spacing between primes - almost within the square root of the average spacing. We actually prove a more general result concerning the set of values taken…
This paper is withdrown
Online communities for sports fans have surged in popularity, with Reddit's r/PremierLeague emerging as a focal point for fans of one of the globe's most celebrated sports leagues. This boom has helped the Premier League make significant…
This paper describes the analysis of quantitative characteristics of frequent sets and association rules in the posts of Twitter microblogs related to different event discussions. For the analysis, we used a theory of frequent sets,…
This is a reply to Muff, S. et al. (2022) Rewriting results sections in the language of evidence, Trends in Ecology & Evolution 37, 203-210.
The pursuit of general-purpose artificial intelligence depends on large language models (LLMs) that can handle both structured reasoning and open-ended generation. We present Omni-Thinker, a unified reinforcement learning (RL) framework…
We provide an approach for generating beautiful poetry. Our sonnet-generation algorithm includes several novel elements that improve over the state of the art, leading to metrical, rhyming poetry with many human-like qualities. These novel…
A binary string representation of prime occurrences is a sequence of bits, where $1$ entries encode positions of prime numbers. This is a convenient representation for analysis of prime distribution, since it allows for application of a…
There has been an ongoing race for the past several years to develop the best universal machinelearning interatomic potential. This progress has led to increasingly accurate models for predictingenergy, forces, and stresses, combining…
This paper uses the Yule-Simon model to estimate to what extent the work of chemistry Nobelists and Fields medalist mathematicians is incorporated into the knowledge corpus of their disciplines as measured by Google Scholar inlinks. Due to…
Natural language processing (NLP) has grown significantly since the advent of the Transformer architecture. Transformers have given birth to pre-trained large language models (PLMs). There has been tremendous improvement in the performance…
We consider the problem of finding a maximum popular matching in a many-to-many matching setting with two-sided preferences and matroid constraints. This problem was proposed by Kamiyama (2020) and solved in the special case where matroids…
We generalize recent work of Andrews, Just, and Simay on modular palindromic compositions and anti-palindromic compositions by viewing all compositions partially (modular) palindromic or anti-palindromic. More precisely, we enumerate…