Tootfinder

Twists arising from torsion points
Lukas Novak
https://arxiv.org/abs/2510.08486 https://arxiv.org/pdf/2510.08486 …

Twists arising from torsion points
Let $p$ be a prime number, $K$ a number field that contains the $p$-th root of unity $ζ_p$, $d$ a $p$-power-free integer and $L=K(\sqrt[p]{d})$. Let $E/K$ be an elliptic curve with full $p$-torsion and $S,T \in E(K)[p]$ be the generators. Define the cocycle $ξ_d : \operatorname{Gal}(\overline{K}/K) \to E$ by \[ ξ_d (σ)= \begin{cases} O, & \text{if } σ(\sqrt[p]{d})=\sqrt[p]{d}, \newline kS, & \text{if } σ(\sqrt[p]{d})=ζ_p^k\sqrt[p]{d}, \end{cases} \] and denote by $H_S^d$ the twist …

Mixed higher-order coupling stabilizes new states
Per Sebastian Skardal, Federico Battiston, Maxime Lucas, Matthew S Mizuhara, Giovanni Petri, Yuanzhao Zhang
https://arxiv.org/abs/2510.09387

Mixed higher-order coupling stabilizes new states
Understanding how higher-order interactions affect collective behavior is a central problem in nonlinear dynamics and complex systems. Most works have focused on a single higher-order coupling function, neglecting other viable choices. Here we study coupled oscillators with dyadic and three different types of higher-order couplings. By analyzing the stability of different twisted states on rings, we show that many states are stable only for certain combinations of higher-order couplings, and th…

Crosslisted article(s) found for nlin.CD. https://arxiv.org/list/nlin.CD/new
[1/1]:
- Collective dynamics on higher-order networks
Battiston, Bick, Lucas, Mill\'an, Skardal, Zhang
…

Scaling with Collapse: Efficient and Predictable Training of LLM Families
Shane Bergsma, Bin Claire Zhang, Nolan Dey, Shaheer Muhammad, Gurpreet Gosal, Joel Hestness
https://arxiv.org/abs/2509.25087

Scaling with Collapse: Efficient and Predictable Training of LLM Families
Effective LLM training relies on *consistency*, meaning that key quantities -- such as final losses and optimal hyperparameters -- scale predictably across model sizes. Qiu et al. (2025) recently showed that this consistency extends beyond scalars: whole training loss curves can *collapse* onto a universal trajectory after a simple normalization. What remains unclear is whether this phenomenon holds for LLM families trained under *practical scaling recipes*, where width, depth, learning rate, b…

Replaced article(s) found for nlin.SI. https://arxiv.org/list/nlin.SI/new
[1/1]:
- Low-dimensional tori in Calogero-Moser-Sutherland systems
Andrii Liashyk, Guorui Ma, Nicolai Reshetikhin, Ivan Sechin

Collective dynamics on higher-order networks
Federico Battiston, Christian Bick, Maxime Lucas, Ana P. Mill\'an, Per Sebastian Skardal, Yuanzhao Zhang
https://arxiv.org/abs/2510.05253

Collective dynamics on higher-order networks
Higher-order interactions that nonlinearly couple more than two nodes are ubiquitous in networked systems. Here we provide an overview of the rapidly growing field of dynamical systems with higher-order interactions, and of the techniques which can be used to describe and analyze them. We focus in particular on new phenomena that emerge when nonpairwise interactions are considered. We conclude by discussing open questions and promising future directions on the collective dynamics of higher-orde…