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This https://arxiv.org/abs/2409.12068 has been replaced.
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The repetition threshold for ternary rich words
In 2017, Vesti proposed the problem of determining the repetition threshold for infinite rich words, i.e., for infinite words in which all factors of length $n$ contain $n$ distinct nonempty palindromic factors. In 2020, Currie, Mol, and Rampersad proved a conjecture of Baranwal and Shallit that the repetition threshold for binary rich words is $2 + \sqrt{2}/2$. In this paper, we prove a structure theorem for $16/7$-power-free ternary rich words. Using the structure theorem, we deduce that the …

An analysis of the 2-D isentropic Euler Equations for a generalized polytropic gas law
Lauren M. M. Bonaldo, Talita Mello, Wladimir Neves
https://arxiv.org/abs/2506.23327

An analysis of the 2-D isentropic Euler Equations for a generalized polytropic gas law
In this paper we developed an analysis of the compressible, isentropic Euler equations in two spatial dimensions for a generalized polytropic gas law. The main focus is rotational flows in the subsonic regimes, described through the framework of the Euler equations expressed in self-similar variables and pseudo-velocities. A Bernoulli type equation is derived, serving as a cornerstone for establishing a self-similar system tailored to rotational flows. In the final section, the study extends to…

Transformer Based Multi-Target Bernoulli Tracking for Maritime Radar
Caden Sweeney, Du Yong Kim, Branko Ristic, Brian Cheung
https://arxiv.org/abs/2506.20319

Transformer Based Multi-Target Bernoulli Tracking for Maritime Radar
Multi-target tracking in the maritime domain is a challenging problem due to the non-Gaussian and fluctuating characteristics of sea clutter. This article investigates the use of machine learning (ML) to the detection and tracking of low SIR targets in the maritime domain. The proposed method uses a transformer to extract point measurements from range-azimuth maps, before clustering and tracking using the Labelled mulit- Bernoulli (LMB) filter. A measurement driven birth density design based on…