Tootfinder

The number of primes not in a numerical semigroup
Yong-Gao Chen, Hui Zhu
https://arxiv.org/abs/2506.03625 https://arxiv.org/pdf/2506.…

The number of primes not in a numerical semigroup
For two coprime positive integers $a,b$, let $π^* (a, b)$ be the number of primes that cannot be represented as $au+bv$, where $u,v$ are nonnegative integers. In this paper, we prove that $π^* (a, b)\ge 0.014 π(ab-a-b)$ and pose following conjecture: $π^* (a, b)\ge \frac 12 π(ab-a-b)$, where $π(x)$ denotes the number of primes not exceeding $x$. This conjecture is confirmed for $1\le a\le 8$.

This https://arxiv.org/abs/2504.10914 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qfi…

Breaking the Trend: How to Avoid Cherry-Picked Signals
Our empirical results, illustrated in Fig.5, show an impressive fit with the pretty complex theoritical Sharpe formula of a Trend following strategy depending on the parameter of the signal, which was derived by Grebenkov and Serror (2014). That empirical fit convinces us that a mean-reversion process with only one time scale is enough to model, in a pretty precise way, the reality of the trend-following mechanism at the average scale of CTAs and as a consequence, using only one simple EMA, app…

Harmony-Aware Music-driven Motion Synthesis with Perceptual Constraint on UGC Datasets
Xinyi Wu, Haohong Wang, Aggelos K. Katsaggelos
https://arxiv.org/abs/2506.07076

Harmony-Aware Music-driven Motion Synthesis with Perceptual Constraint on UGC Datasets
With the popularity of video-based user-generated content (UGC) on social media, harmony, as dictated by human perceptual principles, is critical in assessing the rhythmic consistency of audio-visual UGCs for better user engagement. In this work, we propose a novel harmony-aware GAN framework, following a specifically designed harmony evaluation strategy to enhance rhythmic synchronization in the automatic music-to-motion synthesis using a UGC dance dataset. This harmony strategy utilizes refin…