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A note on N-soliton solutions for the viscid incompressible Navier-Stokes differential equation
Rensley A. Meulens
https://arxiv.org/abs/2506.23697 https:/…

A note on N-soliton solutions for the viscid incompressible Navier-Stokes differential equation
Repetitive curling of the incompressible viscid Navier-Stokes differential equation leads to a higher-order diffusion equation. Substituting this equation into the Navier-Stokes differential equation transposes the latter into the Korteweg-de Vries-Burgers equation with the Weierstrass p-function as the soliton solution. However, a higher-order derivative of the studied variable produces the so-called N-soliton solution, which is comparable to the N-soliton solution of the Kadomtsev-Petviashvil…

Mitigating Object Hallucinations via Sentence-Level Early Intervention
Shangpin Peng, Senqiao Yang, Li Jiang, Zhuotao Tian
https://arxiv.org/abs/2507.12455

Mitigating Object Hallucinations via Sentence-Level Early Intervention
Multimodal large language models (MLLMs) have revolutionized cross-modal understanding but continue to struggle with hallucinations - fabricated content contradicting visual inputs. Existing hallucination mitigation methods either incur prohibitive computational costs or introduce distribution mismatches between training data and model outputs. We identify a critical insight: hallucinations predominantly emerge at the early stages of text generation and propagate through subsequent outputs. To …

This https://arxiv.org/abs/2503.21224 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Efficient Learning for Entropy-Regularized Markov Decision Processes via Multilevel Monte Carlo
Designing efficient learning algorithms with complexity guarantees for Markov decision processes (MDPs) with large or continuous state and action spaces remains a fundamental challenge. We address this challenge for entropy-regularized MDPs with Polish state and action spaces, assuming access to a generative model of the environment. We propose a novel family of multilevel Monte Carlo (MLMC) algorithms that integrate fixed-point iteration with MLMC techniques and a generic stochastic approximat…

Exact Distributions for the Solutions of the Compressible Viscous Navier Stokes Differential Equations: An Application in the Aeronautical Industry
Rensley A. Meulens
https://arxiv.org/abs/2506.23932

Exact Distributions for the Solutions of the Compressible Viscous Navier Stokes Differential Equations: An Application in the Aeronautical Industry
Wind tunnels and linearized turbulence and boundary-layer models have been so far necessary to simulate and approximate the stationery lift and drag forces on (base-mounted) airfoils by means of statistically determined or approximated values of the relevant situational coefficients as the drag and lift coefficients.To improve this process, we introduce transient and exact formulae to separate these forces in advance by means of the solutions found from the fluid dynamics model of the Navier St…