arXiv subjects

Fanfei Meng

Publications and source records attributed to Fanfei Meng.

At least 19 recordsLinked to original sources

arXiv2026

On the pointwise convergence of NLS flow on $ \S^2 $

In this paper, we study the almost everywhere convergence of the cubic nonlinear Schr\"odinger flow to the initial data on $\mathbb S^2$, \begin{equation*} iu_t + \Delta_g u = |u|^2u, \quad (t,x)\in\R\times \S^2. \end{equation*} Inspired by the randomization method and the ansatz introduced by Burq, Camps, Sun, and Tzvetkov [Preprint, arXiv:2404.18229], we prove almost sure pointwise convergence almost everywhere for the nonlinear solution at very low regularity. This extends Compaan-Luc\`a-Staffilani [Int. Math. Res. Not. IMRN, (1) (2021), 596--647] to the spherical setting. We also provide a new necessary condition for the associated $L^p$ maximal estimate for the linear Schr\"odinger equation on $\S^2$. More precisely, we show that the $L^p$ maximal estimate fails for $s<\frac{1}{2}-\frac{1}{2p}$ with $p\ge 2$. In the special case $p=3$, our result matches the corresponding range in the $\R^2$ case, up to the endpoint, and improves the previous result of Chen-Duong-Lee-Yan [J. Math. Pures Appl. 163 (2022), 433--449].

math.AP↗

arXiv2026

Customizing ChatGPT for Second Language Speaking Practice: Genuine Support or Just a Marketing Gimmick?

ChatGPT, with its customization features and Voice Mode, has the potential for more engaging and peresonalized ESL (English as a Second Language) education. This study examines the efficacy of customized ChatGPT conversational features in facilitating ESL speaking practices, comparing the performance of four versions of ChatGPT Voice Mode: uncustomized Standard mode, uncustomized Advanced mode, customized Standard mode, and customized Advanced mode. Customization was guided by prompt engineering principles and grounded in relevant theories, including Motivation Theory, Culturally Responsive Teaching (CRT), Communicative Language Teaching (CLT), and the Affective Filter Hypothesis. Content analysis found that customized versions generally provided more balanced feedback and emotional support, contributing to a positive and motivating learning environment. However, cultural responsiveness did not show significant improvement despite targeted customization efforts. These initial findings suggest that customization could enhance ChatGPT's capacity as a more effective language tutor, with the standard model already capable of meeting the learning needs. The study underscores the importance of prompt engineering and AI literacy in maximizaing AI's potential in language learning.

cs.HC↗

arXiv2025

Asymptotic behavior of mass-critical Schr\"odinger equation in $ \mathbb{R}$

In this paper, we study the long-time behavior for the mass-critical nonlinear Schr\"odinger equation on the line \[ i\partial_t u + \partial_x^2 u = |u|^4 u, u(0, x) = u_0 \in L_x^2(\Bbb R). \] The global well-posedness and scattering for this equation was solved in Dodson [Amer. J. Math. (2016)]. Inspired by the pioneering work of Killip-Visan-Zhang [Amer. J. Math. (2021)], we show that solution can be approximated by a finite-dimensional Hamiltonian system. This system is the nonlinear Schr\"odinger equation on the rescaled torus $\Bbb R/(L_n\Bbb Z)$ with Fourier truncated nonlinear term. To prove this, we introduce the Fourier truncated mass-critical NLS on $\mathbb{R}$. First, we establish the uniformly global space-time bound for this truncated model on $\mathbb{R}$. Second, we show that the truncated NLS on rescaled torus can be approximated by the truncated equation on $\Bbb R$. Then, using the Gromov theorem, we can show the non-squeezing property for the truncated NLS on torus. The last step to show the non-squeezing property for original NLS is to connect the solution with truncated nonlinearity and a single equation in $\mathbb{R}$, which can be done by performing the nonlinear profile decomposition. Our second result is to study the homogenization of the mass-critical inhomogeneous NLS, where we add a $L^\infty$ function $h(nx)$ in front of the nonlinear term. Based on the method of Ntekoume [Comm. PDE, (2020)], we give the sufficient condition on $h$ such that the scattering holds for this inhomogeneous model and show that the solution to inhomogeneous converges to the homogeneous model when $n\to\infty$. As a corollary, we can transfer the non-squeezing property from homogeneous model to inhomogeneous.

math.AP↗

arXiv2025

Threshold solutions for the energy-critical NLS system with quadratic interaction

In this paper, we study the Cauchy problem for a quadratic nonlinear Schr\"{o}dinger system in dimension six. In~\cite{GaoMengXuZheng}, the authors classified the behavior of solutions under the energy constraint $E(u) < E(Q)$, where $Q$ denotes the ground state. In this work, we classify the dynamics of radial solutions at the threshold energy $E(u) = E(Q)$.

math.AP↗

arXiv2025

Inaccuracy of an E-Dictionary and Its Influence on Chinese Language Users

Electronic dictionaries have largely replaced paper dictionaries and become central tools for L2 learners seeking to expand their vocabulary. Users often assume these resources are reliable and rarely question the validity of the definitions provided. The accuracy of major E-dictionaries is seldom scrutinized, and little attention has been paid to how their corpora are constructed. Research on dictionary use, particularly the limitations of electronic dictionaries, remains scarce. This study adopts a combined method of experimentation, user survey, and dictionary critique to examine Youdao, one of the most widely used E-dictionaries in China. The experiment involved a translation task paired with retrospective reflection. Participants were asked to translate sentences containing words that are insufficiently or inaccurately defined in Youdao. Their consultation behavior was recorded to analyze how faulty definitions influenced comprehension. Results show that incomplete or misleading definitions can cause serious misunderstandings. Additionally, students exhibited problematic consultation habits. The study further explores how such flawed definitions originate, highlighting issues in data processing and the integration of AI and machine learning technologies in dictionary construction. The findings suggest a need for better training in dictionary literacy for users, as well as improvements in the underlying AI models used to build E-dictionaries.

cs.CL↗

arXiv2024

The dynamics of the focusing NLH with a potential beyond the mass-energy threshold

We study the dynamics of the focusing nonlinear Hartree equation with a Kato potential $$ i\partial_t u +\Delta u - Vu = -(|\cdot|^{-\gamma} \ast |u|^2)u, \quad x \in \mathbb{R}^d $$ under some assumptions on the potential $V$. We prove the blow up versus global existence dichotomy for solutions beyond the threshold, based on the method from Duyckaerts-Roudenko [6]. Furthermore, our result compensates for the one of in [13] below that threshold.

math.AP↗

arXiv2024

Hybrid FedGraph: An efficient hybrid federated learning algorithm using graph convolutional neural network

Federated learning is an emerging paradigm for decentralized training of machine learning models on distributed clients, without revealing the data to the central server. Most existing works have focused on horizontal or vertical data distributions, where each client possesses different samples with shared features, or each client fully shares only sample indices, respectively. However, the hybrid scheme is much less studied, even though it is much more common in the real world. Therefore, in this paper, we propose a generalized algorithm, FedGraph, that introduces a graph convolutional neural network to capture feature-sharing information while learning features from a subset of clients. We also develop a simple but effective clustering algorithm that aggregates features produced by the deep neural networks of each client while preserving data privacy.

cs.LG↗

arXiv2024

Evolution and Efficiency in Neural Architecture Search: Bridging the Gap Between Expert Design and Automated Optimization

The paper provides a comprehensive overview of Neural Architecture Search (NAS), emphasizing its evolution from manual design to automated, computationally-driven approaches. It covers the inception and growth of NAS, highlighting its application across various domains, including medical imaging and natural language processing. The document details the shift from expert-driven design to algorithm-driven processes, exploring initial methodologies like reinforcement learning and evolutionary algorithms. It also discusses the challenges of computational demands and the emergence of efficient NAS methodologies, such as Differentiable Architecture Search and hardware-aware NAS. The paper further elaborates on NAS's application in computer vision, NLP, and beyond, demonstrating its versatility and potential for optimizing neural network architectures across different tasks. Future directions and challenges, including computational efficiency and the integration with emerging AI domains, are addressed, showcasing NAS's dynamic nature and its continued evolution towards more sophisticated and efficient architecture search methods.

cs.NE↗

arXiv2023

Sample-based Dynamic Hierarchical Transformer with Layer and Head Flexibility via Contextual Bandit

Transformer requires a fixed number of layers and heads which makes them inflexible to the complexity of individual samples and expensive in training and inference. To address this, we propose a sample-based Dynamic Hierarchical Transformer (DHT) model whose layers and heads can be dynamically configured with single data samples via solving contextual bandit problems. To determine the number of layers and heads, we use the Uniform Confidence Bound while we deploy combinatorial Thompson Sampling in order to select specific head combinations given their number. Different from previous work that focuses on compressing trained networks for inference only, DHT is not only advantageous for adaptively optimizing the underlying network architecture during training but also has a flexible network for efficient inference. To the best of our knowledge, this is the first comprehensive data-driven dynamic transformer without any additional auxiliary neural networks that implement the dynamic system. According to the experiment results, we achieve up to 74% computational savings for both training and inference with a minimal loss of accuracy.

cs.LG↗

arXiv2023

FedEmb: A Vertical and Hybrid Federated Learning Algorithm using Network And Feature Embedding Aggregation

Federated learning (FL) is an emerging paradigm for decentralized training of machine learning models on distributed clients, without revealing the data to the central server. The learning scheme may be horizontal, vertical or hybrid (both vertical and horizontal). Most existing research work with deep neural network (DNN) modelling is focused on horizontal data distributions, while vertical and hybrid schemes are much less studied. In this paper, we propose a generalized algorithm FedEmb, for modelling vertical and hybrid DNN-based learning. The idea of our algorithm is characterised by higher inference accuracy, stronger privacy-preserving properties, and lower client-server communication bandwidth demands as compared with existing work. The experimental results show that FedEmb is an effective method to tackle both split feature & subject space decentralized problems, shows 0.3% to 4.2% inference accuracy improvement with limited privacy revealing for datasets stored in local clients, and reduces 88.9 % time complexity over vertical baseline method.

cs.LG↗

arXiv2023

Optimizing the Passenger Flow for Airport Security Check

Due to the necessary security for the airport and flight, passengers are required to have strict security check before getting aboard. However, there are frequent complaints of wasting huge amount of time while waiting for the security check. This paper presents a potential solution aimed at optimizing gate setup procedures specifically tailored for Chicago OHare International Airport. By referring to queueing theory and performing Monte Carlo simulations, we propose an approach to significantly diminish the average waiting time to a more manageable level. Additionally, our study meticulously examines and identifies the influential factors contributing to this optimization, providing a comprehensive understanding of their impact.

cs.AI↗

arXiv2023

Joint Detection Algorithm for Multiple Cognitive Users in Spectrum Sensing

Spectrum sensing technology is a crucial aspect of modern communication technology, serving as one of the essential techniques for efficiently utilizing scarce information resources in tight frequency bands. This paper first introduces three common logical circuit decision criteria in hard decisions and analyzes their decision rigor. Building upon hard decisions, the paper further introduces a method for multi-user spectrum sensing based on soft decisions. Then the paper simulates the false alarm probability and detection probability curves corresponding to the three criteria. The simulated results of multi-user collaborative sensing indicate that the simulation process significantly reduces false alarm probability and enhances detection probability. This approach effectively detects spectrum resources unoccupied during idle periods, leveraging the concept of time-division multiplexing and rationalizing the redistribution of information resources. The entire computation process relies on the calculation principles of power spectral density in communication theory, involving threshold decision detection for noise power and the sum of noise and signal power. It provides a secondary decision detection, reflecting the perceptual decision performance of logical detection methods with relative accuracy.

eess.SP↗

arXiv2023

Sentiment analysis with adaptive multi-head attention in Transformer

We propose a novel framework based on the attention mechanism to identify the sentiment of a movie review document. Previous efforts on deep neural networks with attention mechanisms focus on encoder and decoder with fixed numbers of multi-head attention. Therefore, we need a mechanism to stop the attention process automatically if no more useful information can be read from the memory.In this paper, we propose an adaptive multi-head attention architecture (AdaptAttn) which varies the number of attention heads based on length of sentences. AdaptAttn has a data preprocessing step where each document is classified into any one of the three bins small, medium or large based on length of the sentence. The document classified as small goes through two heads in each layer, the medium group passes four heads and the large group is processed by eight heads. We examine the merit of our model on the Stanford large movie review dataset. The experimental results show that the F1 score from our model is on par with the baseline model.

cs.CL↗

arXiv2022

Scattering For three waves Nonlinear Schr\"odinger System with mass-resonance in 5D

In this paper, we study the dynamics behavior of the NLS system with three waves interaction in the energy space $H^1(\mathbb{R}^5) \times H^1(\mathbb{R}^5)\times H^1(\mathbb{R}^5) $. Inspired by B. Dodson and J. Murphy in \cite{Dodson2018}, we establish an interaction Morawetz estimate for the NLS system, together with the criterion which proved by Tao-Dodson--Murphy we can get the scattering under the ground state in energy space with mass-resonance. Under the radial assumption, we can remove the mass-resonance condition.

math.AP↗

arXiv2021

Model-based Reinforcement Learning for Service Mesh Fault Resiliency in a Web Application-level

Microservice-based architectures enable different aspects of web applications to be created and updated independently, even after deployment. Associated technologies such as service mesh provide application-level fault resilience through attribute configurations that govern the behavior of request-response service -- and the interactions among them -- in the presence of failures. While this provides tremendous flexibility, the configured values of these attributes -- and the relationships among them -- can significantly affect the performance and fault resilience of the overall application. Furthermore, it is impossible to determine the best and worst combinations of attribute values with respect to fault resiliency via testing, due to the complexities of the underlying distributed system and the many possible attribute value combinations. In this paper, we present a model-based reinforcement learning workflow towards service mesh fault resiliency. Our approach enables the prediction of the most significant fault resilience behaviors at a web application-level, scratching from single service to aggregated multi-service management with efficient agent collaborations.

cs.DC↗

arXiv2021

On the energy-critical quadratic nonlinear Schr\"odinger system with three waves

In this article, we consider the dynamics of the energy-critical quadratic nonlinear Schr\"odinger system $\[ \left\{ \begin{aligned} & i u^1_t + \kappa_1 \Delta u^1 = -\overline{u^2}u^3, \\ & i u^2_t + \kappa_2 \Delta u^2 = -\overline{u^1}u^3, \\ & i u^3_t + \kappa_3 \Delta u^3 = -u^1u^2, \\ \end{aligned} \right. \qquad (t, x) \in \R \times \R^6 \] in energy-space $ {\dot H}^1 \times {\dot H}^1\times{\dot H}^1 $, where the sign of potential energy can not be determined. We prove the scattering theory with mass-resonance (or with radial initial data) below ground state via concentration compactness method. We discover a family of new physically conserved quantities with mass-resonance which play an important role in the proof of scattering.

math.AP↗

arXiv2021

Long time behaviors for the inhomogeneous NLS with a potential in $\mathbb{R}^3$

In this article, we aim to study the scattering of the solution to the focusing inhomogeneous nonlinear Schr\"odinger equation with a potential of form \begin{align*} i\partial_t u+\Delta u- Vu=-|x|^{-b}|u|^{p-1}u \end{align*} in the energy space $H^1(\R^3)$. We prove a scattering criterion, and then we use it together with Morawetz estimate to show the scattering theory, which generalizes the results of Dinh \cite{DD} to the non-radial symmetric case.

math.AP↗

arXiv2021

Scattering theory For Quadratic Nonlinear Schr\"odinger System in dimension six

In this paper, we study the solutions to the energy-critical quadratic nonlinear Schr\"odinger system in ${\dot H}^1\times{\dot H}^1$, where the sign of its potential energy can not be determined directly. If the initial data ${\rm u}_0$ is radial or non-radial but satisfies the mass-resonance condition, and its energy is below that of the ground state, using the compactness/rigidity method, we give a complete classification of scattering versus blowing-up dichotomies depending on whether the kinetic energy of ${\rm u}_0$ is below or above that of the ground state.

math.AP↗