arXiv subjects

Li Yong

Publications and source records attributed to Li Yong.

7 recordsLinked to original sources

arXiv2025

Nekhoroshev type stability for non-local semilinear Schr\"odinger equations

This paper investigates Nekhoroshev-type stability for solutions of ultra-differentiable regularity in Schr\"odinger equations with non-local nonlinear terms, employing the method of rational normal forms. We establish the first rigorous results for logarithmic ultra-differentiable regularity in infinite-dimensional Hamiltonian systems without external parameters. Under Gevrey class regularity assumptions, we achieve the stability times matching Bourgain's conjectured optimal stability time in \cite{B04}. Furthermore, we introduce a novel global vector field norm adapted to the rational normal form framework. This norm eliminate the need for degree tracking during the iteration process, thereby enabling a unified treatment of nonlinear terms.

math.AP↗

arXiv2025

Almost global existence for Ultra-differential Hamiltonian in $L^2$ space

This paper combines the decay of high modes with the smallness introduced by high orders, leading to a normal form lemma for infinite-dimensional Hamiltonian systems under ultra-differentiable regularity. We prove the sub-exponential stability time of a wide class of Hamiltonian PDEs, including the Schr\"odinger equation with convolution potentials, fractional-order Schr\"odinger equations, and beam equations with metrics. When the conditions are equivalent to previous ones, the stability time we obtain reaches Bourgain's predicted optimal bound. Furthermore, we approach earlier results under lower conditions. These results are discussed within a general framework we propose, which applies to the ultra-differential class.

math.AP↗

arXiv2024

Human Behavior Simulation: Objectives, Methodologies, and Open Problems

In recent years, human behavior simulation has drawn increasing attention from both academia and industry. The reasons fall into two aspects. First, simulation serves as a critical tool for understanding human behaviors, which has become one of the most important research topics in the history. Second, researchers have gradually reached a consensus that simulation, especially human behavior simulation, is critical for real-world decision-making systems. As a result, lots of human behavior simulation research and applications have sprung up across numerous disciplines in the past few years. In addition to the traditional methods, such as building mathematical and physical models, leveraging the recent advances of deep learning techniques -- especially the nascent Large Language Model technology -- for accurate human behavior simulation has also been one of the hottest research topics. In this study, we provide a comprehensive review of the latest research advancements in human behavior simulation. We summarize the objectives, problem formulations, and commonly used methods and discuss the consistency in the development of related research in different disciplines, which reveals the gaps and opportunities for high-impact research in this promising direction.

cs.HC↗

arXiv2024

DCMSA: Multi-Head Self-Attention Mechanism Based on Deformable Convolution For Seismic Data Denoising

When dealing with seismic data, diffusion models often face challenges in adequately capturing local features and expressing spatial relationships. This limitation makes it difficult for diffusion models to remove noise from complex structures effectively. To tackle this issue, we propose a novel convolutional attention mechanism Multi-head Self-attention mechanism based on Deformable convolution (DCMSA) achieving efficient fusion of diffusion models with convolutional attention. The implementation of DCMSA is as follows: First, we integrate DCMSA into the UNet architecture to enhance the network's capability in recognizing and processing complex seismic data. Next, the diffusion model utilizes the UNet enhanced with DCMSA to process noisy data. The results indicate that this method addresses the shortcomings of diffusion models in capturing local features and expressing spatial relationships effectively, proving superior to traditional diffusion models and standard neural networks in noise suppression and preserving meaningful seismic data information.

physics.geo-ph↗

arXiv2024

Poisson stability of solutions for stochastic evolution equations driven by fractional Brownian motion

In this paper, we study the problem of Poisson stability of solutions for stochastic semi-linear evolution equation driven by fractional Brownian motion \mathrm{d} X(t)= \left( AX(t) + f(t, X(t)) \right) \mathrm{d}t + g\left(t, X(t)\right)\mathrm{d}B^H_{Q}(t), where A is an exponentially stable linear operator acting on a separable Hilbert space \mathbb{H}, coefficients f and g are Poisson stable in time, and B^H_Q (t) is a Q-cylindrical fBm with Hurst index H. First, we establish the existence and uniqueness of the solution for this equation. Then, we prove that under the condition where the functions f and g are sufficiently "small", the equation admits a solution that exhibits the same character of recurrence as f and g. The discussion is further extended to the asymptotic stability of these Poisson stable solutions. Finally, we include an example to validate our results.

math.DS↗

arXiv2024

Fine-tuning Large Language Model (LLM) Artificial Intelligence Chatbots in Ophthalmology and LLM-based evaluation using GPT-4

Purpose: To assess the alignment of GPT-4-based evaluation to human clinician experts, for the evaluation of responses to ophthalmology-related patient queries generated by fine-tuned LLM chatbots. Methods: 400 ophthalmology questions and paired answers were created by ophthalmologists to represent commonly asked patient questions, divided into fine-tuning (368; 92%), and testing (40; 8%). We find-tuned 5 different LLMs, including LLAMA2-7b, LLAMA2-7b-Chat, LLAMA2-13b, and LLAMA2-13b-Chat. For the testing dataset, additional 8 glaucoma QnA pairs were included. 200 responses to the testing dataset were generated by 5 fine-tuned LLMs for evaluation. A customized clinical evaluation rubric was used to guide GPT-4 evaluation, grounded on clinical accuracy, relevance, patient safety, and ease of understanding. GPT-4 evaluation was then compared against ranking by 5 clinicians for clinical alignment. Results: Among all fine-tuned LLMs, GPT-3.5 scored the highest (87.1%), followed by LLAMA2-13b (80.9%), LLAMA2-13b-chat (75.5%), LLAMA2-7b-Chat (70%) and LLAMA2-7b (68.8%) based on the GPT-4 evaluation. GPT-4 evaluation demonstrated significant agreement with human clinician rankings, with Spearman and Kendall Tau correlation coefficients of 0.90 and 0.80 respectively; while correlation based on Cohen Kappa was more modest at 0.50. Notably, qualitative analysis and the glaucoma sub-analysis revealed clinical inaccuracies in the LLM-generated responses, which were appropriately identified by the GPT-4 evaluation. Conclusion: The notable clinical alignment of GPT-4 evaluation highlighted its potential to streamline the clinical evaluation of LLM chatbot responses to healthcare-related queries. By complementing the existing clinician-dependent manual grading, this efficient and automated evaluation could assist the validation of future developments in LLM applications for healthcare.

cs.AI↗

arXiv2013

Longitudinal Single Bunch Instability Study on BEPCII

In order to study the single bunch longitudinal instability in BEPCII, experiments on the positron ring (BPR) for the bunch lengthening phenomenon were made. By analyzing the experimental data based on Gao's theory, the longitudinal loss factor for the bunch are obtained. Also, the total wake potential and the beam current threshold are estimated.

physics.acc-ph↗