Tootfinder

Integrable self-adaptive moving mesh schemes for multi-component short pulse type equations under general boundary conditions
Ayako Hori, Ken-ichi Maruno, Yasuhiro Ohta, Bao-Feng Feng
https://arxiv.org/abs/2507.03880

Integrable self-adaptive moving mesh schemes for multi-component short pulse type equations under general boundary conditions
In this paper, we construct integrable self-adaptive moving mesh schemes for multi-component modified short pulse and short pulse equations under general boundary conditions including periodic boundary conditions by using the consistency condition with the hodograph transformation. We also construct multi-soliton solutions expressed by Pfaffian for our self-adaptive moving mesh schemes. Using self-adaptive moving mesh schemes presented in this paper, we perform numerical experiments to evaluate…

iPhone 17 (Pro) und iOS 26: Apple-Event, Ankündigung und Release voraus
In gut einem Monat stellt Apple voraussichtlich die nächste iPhone-Generation vor. Erwartet werden Design-Änderungen und ein Neuling.

PINNs Study for the Bekki-Nozaki Chaos in the Non-linear Schr\"{o}dinger equation
N. Sawado, Y. Shimazaki, Y. Suzuki
https://arxiv.org/abs/2507.05664 …

PINNs Study for the Bekki-Nozaki Chaos in the Non-linear Schrödinger equation
In this paper we study chaotic behavior in the forced dissipative non-linear Schrödinger equation, so called the Bekki-Nozaki equation. Chaotic systems are often seen in a strong sensitivity to initial conditions,leading to error accumulation over time when traditional numerical methods are applied. To address this difficulty, we employ Physics-Informed Neural Networks(PINNs), a mesh-free deep learning framework. PINNs mitigate error accumulation in chaotic systems by solving partial different…

Commuting integrable maps from a deformed D$_4$ cluster algebra
A. N. W. Hone, W. Kim, T. Mase
https://arxiv.org/abs/2508.05270 https://arxiv.org/pdf/2508.…

Commuting integrable maps from a deformed D$_4$ cluster algebra
In this paper we revisit an integrable map of the plane which we obtained recently as a two-parameter family of deformed mutations in the cluster algebra of type D$_4$. The rational first integral for this map defines an invariant foliation of the plane by level curves, and we explain how this corresponds to a rational elliptic surface of rank 2. This leads us to construct another (independent) integrable map, commuting with the first, such that both maps lift to compositions of mutations in an…

Investigating Hallucination in Conversations for Low Resource Languages
Amit Das, Md. Najib Hasan, Souvika Sarkar, Zheng Zhang, Fatemeh Jamshidi, Tathagata Bhattacharya, Nilanjana Raychawdhury, Dongji Feng, Vinija Jain, Aman Chadha
https://arxiv.org/abs/2507.22720

Investigating Hallucination in Conversations for Low Resource Languages
Large Language Models (LLMs) have demonstrated remarkable proficiency in generating text that closely resemble human writing. However, they often generate factually incorrect statements, a problem typically referred to as 'hallucination'. Addressing hallucination is crucial for enhancing the reliability and effectiveness of LLMs. While much research has focused on hallucinations in English, our study extends this investigation to conversational data in three languages: Hindi, Farsi, and Mandari…

LLM-Based Repair of Static Nullability Errors
Nima Karimipour, Michael Pradel, Martin Kellogg, Manu Sridharan
https://arxiv.org/abs/2507.20674 https://arxi…

LLM-Based Repair of Static Nullability Errors
Modern Java projects increasingly adopt static analysis tools that prevent null-pointer exceptions by treating nullness as a type property. However, integrating such tools into large, existing codebases remains a significant challenge. While annotation inference can eliminate many errors automatically, a subset of residual errors -- typically a mix of real bugs and false positives -- often persist and can only be resolved via code changes. Manually addressing these errors is tedious and error-p…

MaCE: General Mass Conserving Dynamics for Cellular Automata
Vassilis Papadopoulos, Etienne Guichard
https://arxiv.org/abs/2507.12306 https://arxiv.org/pdf…

Discovering the dynamics of \emph{Sargassum} rafts' centers of mass
Francisco J. Beron-Vera, Gage Bonner
https://arxiv.org/abs/2507.18771 https://arxiv…

Discovering the dynamics of \emph{Sargassum} rafts' centers of mass
Since 2011, rafts of floating \emph{Sargassum} seaweed have frequently obstructed the coasts of the Intra-Americas Seas. The motion of the rafts is represented by a high-dimensional nonlinear dynamical system. Referred to as the eBOMB model, this builds on the Maxey--Riley equation by incorporating interactions between clumps of \emph{Sargassum} forming a raft and the effects of Earth's rotation. The absence of a predictive law for the rafts' centers of mass suggests a need for machine learning…

Optimal dynamical stabilization
Arnaud Lazarus, Emmanuel Tr\'elat
https://arxiv.org/abs/2508.00006 https://arxiv.org/pdf/2508.00006

Optimal dynamical stabilization
Stability is a fundamental concept that refers to a system's ability to return close to its original state after disturbances. The minimal conditions for stability when system parameters vary in time, though common in physics, have been largely overlooked. Here, we study the minimal amount of periodic stiffness a linear mass-spring system requires to remain stable and apply our findings to optimally trap the upside-down state of a compass in a time-varying magnetic field. We show that the abili…

Piecewise linear cusp bifurcations in ultradiscrete dynamical systems
Shousuke Ohmori, Yoshihiro Yamazaki
https://arxiv.org/abs/2506.23451 https://

Piecewise linear cusp bifurcations in ultradiscrete dynamical systems
We investigate the dynamical properties of cusp bifurcations in max-plus dynamical systems derived from continuous differential equations through the tropical discretization and the ultradiscrete limit. A general relationship between cusp bifurcations in continuous and corresponding discrete systems is formulated as a proposition. For applications of this proposition, we analyze the Ludwig and Lewis models, elucidating the dynamical structure of their ultradiscrete cusp bifurcations obtained fr…