Tootfinder

Last week, we continued our #ISE2025 lecture on distributional semantics with the introduction of neural language models (NLMs) and compared them to traditional statistical n-gram models.
Benefits of NLMs:
- Capturing Long-Range Dependencies
- Computational and Statistical Tractability
- Improved Generalisation
- Higher Accuracy
@…

Soliton resolution for the coupled complex short pulse equation
Nan Liu, Ran Wang
https://arxiv.org/abs/2505.22210 https://arxiv.org/…

Soliton resolution for the coupled complex short pulse equation
We address the long-time asymptotics of the solution to the Cauchy problem of ccSP (coupled complex short pulse) equation on the line for decaying initial data that can support solitons. The ccSP system describes ultra-short pulse propagation in optical fibers, which is a completely integrable system and posses a $4\times4$ matrix Wadati--Konno--Ichikawa type Lax pair. Based on the $\bar{\partial}$-generalization of the Deift--Zhou steepest descent method, we obtain the long-time asymptotic app…

This https://arxiv.org/abs/2504.20858 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Chaos Meets Attention: Transformers for Large-Scale Dynamical Prediction
Generating long-term trajectories of dissipative chaotic systems autoregressively is a highly challenging task. The inherent positive Lyapunov exponents amplify prediction errors over time. Many chaotic systems possess a crucial property - ergodicity on their attractors, which makes long-term prediction possible. State-of-the-art methods address ergodicity by preserving statistical properties using optimal transport techniques. However, these methods face scalability challenges due to the curse…

This https://arxiv.org/abs/2402.02204 has been replaced.
link: https://scholar.google.com/scholar?q=a

Construction of the Lax pairs for the delay Lotka-Volterra and delay Toda lattice equations and their reductions to delay Painleve equations
The delay Lotka-Volterra and delay Toda lattice equations are delay-differential extensions of the well-known soliton equations, the Lotka-Volterra and Toda lattice equations, respectively. This paper investigates integrable properties of the delay Lotka-Volterra and delay Toda lattice equations, and study the relationships to the already known delay Painleve equations. First, Backlund transformations, Lax pairs and an infinite number of conserved quantities of these delay soliton equations are…