arXiv subjects

Qiang Fei

Publications and source records attributed to Qiang Fei.

3 recordsLinked to original sources

arXiv2025

Critical sinh-Gordon flow with non-negative weight functions

The aim of this article is twofold: one one side we introduce and study the properties of a critical sinh-Gordon type flow \begin{equation*} {\frac{\partial}{\partial t}}e^u=\Delta_gu+8\pi\left({\frac{h_1e^u}{\int_{\Sigma}h_1e^udV_g}}-1\right)-\rho_2\left({\frac{h_2e^{-u}}{\int_{\Sigma}h_2e^{-u}dV_g}}-1\right), \end{equation*} where $\rho_2<8\pi$, $h_1,h_2$ are non-negative weight functions and $\Sigma$ is a closed Riemannian surface. Secondly, under suitable geometric conditions, we prove the convergence of the flow to a solution of the critical sinh-Gordon equation, extending the result of Zhou (2008) to the case of non-negative weights. The argument is based on a careful blow-up analysis. Some remarks about a Toda flow are also given.

math.AP↗

arXiv2025

Text-to-SQL for Enterprise Data Analytics

The introduction of large language models has brought rapid progress on Text-to-SQL benchmarks, but it is not yet easy to build a working enterprise solution. In this paper, we present insights from building an internal chatbot that enables LinkedIn's product managers, engineers, and operations teams to self-serve data insights from a large, dynamic data lake. Our approach features three components. First, we construct a knowledge graph that captures up-to-date semantics by indexing database metadata, historical query logs, wikis, and code. We apply clustering to identify relevant tables for each team or product area. Second, we build a Text-to-SQL agent that retrieves and ranks context from the knowledge graph, writes a query, and automatically corrects hallucinations and syntax errors. Third, we build an interactive chatbot that supports various user intents, from data discovery to query writing to debugging, and displays responses in rich UI elements to encourage follow-up chats. Our chatbot has over 300 weekly users. Expert review shows that 53% of its responses are correct or close to correct on an internal benchmark set. Through ablation studies, we identify the most important knowledge graph and modeling components, offering a practical path for developing enterprise Text-to-SQL solutions.

cs.CL↗

arXiv2024

Existence Results of Singular Toda Systems with Sign-Changing Weight Functions

We consider the existence problem of the following Singular Toda system on a compact Riemann surface $(\Sigma, g)$ without boundary \begin{equation*} \begin{cases} -\Delta_gu_1=2\overline{\rho}_1\Big({\frac{h_1e^{u_1}}{\int_{\Sigma}h_1e^{u_1}dV_g}}-1\Big)-\rho_2\Big({\frac{h_2e^{u_2}}{\int_{\Sigma}h_2e^{u_2}dV_g}}-1\Big)-4\pi\alpha_1(\delta_0-1), -\Delta_gu_2=2\rho_2\big({\frac{h_2e^{u_2}}{\int_{\Sigma}h_2e^{u_2}dV_g}}-1\big)-\overline{\rho}_1\big({\frac{h_1e^{u_1}}{\int_{\Sigma}h_1e^{u_1}dV_g}}-1\big)-4\pi\alpha_2(\delta_0-1), \end{cases} \end{equation*} where $h_1,\,h_2$ are sign-changing smooth functions, $\overline{\rho}_1:=4\pi(1+\overline{\alpha}_1),\,0<\rho_2<4\pi(1+\overline{\alpha}_2),\,\overline{\alpha}_i=\min\{0,\alpha_i\},\,\alpha_i>-1,\,i=1,2$. By relying on the proof framework established in \cite{DJLW}, the Pohozaev identity and the classical blow-up analysis, we prove the existence theorem under some appropriate condition. Our results generalize Jost-Wang's results \cite{JLW} from regular Toda system with positive functions to the singular Toda system involving sign-changing weight functions.

math.AP↗