Related papers: Rhymes in primes
Gibbs random fields corresponding to systems of real-valued spins (e.g. systems of interacting anharmonic oscillators) indexed by the vertices of unbounded degree graphs with a certain summability property are constructed. It is proven that…
Room Impulse Response (RIR) prediction at arbitrary receiver positions is essential for practical applications such as spatial audio rendering. We propose Neural Acoustic Multipole Splatting (NAMS), which synthesizes RIRs at unseen receiver…
LLM-generated reviews for scientific papers are gaining considerable traction and are even being officially piloted by major conferences. We have to assume that not only reviewers are using LLM-assistance, but also that authors use LLMs to…
Let $x$ be a positive integer. We give an asymptotic formula for the number of primes in the set $\{\fl{x/n}, 1 \le n \le x\}$ and give some related results.
A new and exciting breakthrough due to Maynard establishes that there exist infinitely many pairs of distinct primes $p_1,p_2$ with $|p_1-p_2|\leq 600$ as a consequence of the Bombieri-Vinogradov Theorem. In this paper, we apply his general…
I describe our understanding of physics near the planck length, in particular the great progress of the last four years in string theory. Superstring theory, and a recent extension called M theory, are leading candidates for a quantum…
In this paper, we prove that there are infinitely many primes of the form $\ell^2 - \ell m + m^2$ such that $2\ell - m$ is also prime. To prove this, we follow along the lines of the work of Fouvry and Iwaniec (1997) who showed that there…
Accurately predicting music popularity is a critical challenge in the music industry, offering benefits to artists, producers, and streaming platforms. Prior research has largely focused on audio features, social metadata, or model…
We describe our system for WNUT-2020 shared task on the identification of informative COVID-19 English tweets. Our system is an ensemble of various machine learning methods, leveraging both traditional feature-based classifiers as well as…
Recent progress in large language models (LLMs) has moved the frontier from puzzle-solving to science-grade reasoning-the kind needed to tackle problems whose answers must stand against nature, not merely fit a rubric. Physics is the…
The common thread behind the recent Nobel Prize in Physics to John Hopfield and those conferred to Giorgio Parisi in 2021 and Philip Anderson in 1977 is disorder. Quoting Philip Anderson: "more is different". This principle has been…
Artificial intelligence (AI) and machine learning (ML) are expanding in popularity for broad applications to challenging tasks in chemistry and materials science. Examples include the prediction of properties, the discovery of new reaction…
Bridging is an anaphoric phenomenon where the referent of an entity in a discourse is dependent on a previous, non-identical entity for interpretation, such as in "There is 'a house'. 'The door' is red," where the door is specifically…
We survey some different results on the digits of prime numbers, giving a simplified proof of weak forms of a result of Maynard and Mauduit-Rivat.
Let $\mathcal{A}'$ be the set of integers missing any three fixed digits from their decimal expansion. We produce primes in a thin sequence by proving an asymptotic formula for counting primes of the form $p = m^2 + \ell^2$, with $\ell \in…
Recent work by Hewitt et al. (2020) provides an interpretation of the empirical success of recurrent neural networks (RNNs) as language models (LMs). It shows that RNNs can efficiently represent bounded hierarchical structures that are…
Results in contact sports like Rugby are mainly interpreted in terms of the ability and/or luck of teams. But this neglects the important role of the {\em motivation} of players, reflected in the effort exerted in the game. Here we present…
In this paper, we prove a theorem on the distribution of primes in cubic progressions on average.
For every quadrilateral sufficiently close to a rectangle, we shall show that it possess a periodic billiard path. This is an REU work done at ICERM in Summer 2012.
Automation of social network data assessment is one of the classic challenges of natural language processing. During the COVID-19 pandemic, mining people's stances from public messages have become crucial regarding understanding attitudes…