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Xinyue Luo

Publications and source records attributed to Xinyue Luo.

7 recordsLinked to original sources

Safe and Adaptive Cloud Healing: Verifying LLM-Generated Recovery Plans with a Neural-Symbolic World Model

As the scale and complexity of cloud-based AI systems continue to escalate, ensuring service reliability through rapid fault detection and adaptive recovery has become a critical challenge. While existing approaches integrate Large Language Models (LLMs) for semantic understanding and Deep Reinforcement Learning (DRL) for policy optimization, they often rely on sequential, loosely coupled architectures that underutilize the generative and reasoning capabilities of LLMs. In this paper, we propose a paradigm shift with PASE, a Planning-Aware Semantic self-healing engine, a novel fault self-healing framework that reconceptualizes recovery as a neuro-symbolic program synthesis task. PASE employs an LLM as a core Plan Synthesis Engine to generate structured recovery plans from a library of semantic primitives. A Neural-Symbolic World Model verifies plan feasibility through simulation, while a Meta-Prompt Optimizer, trained via DRL, learns to generate optimal prompts that guide the LLM's planning process. This tight reason-plan-verify-adapt loop enables dynamic, context-aware recovery strategy generation beyond predefined action spaces. Experiments on a real-world cloud fault injection dataset demonstrate that PASE significantly outperforms state-of-the-art methods, reducing average system recovery time by over 40% and improving fault detection accuracy in unknown fault scenarios. Our framework advances autonomous system management by unifying LLM-based reasoning with model-assisted verification and meta-learned guidance.

cs.AI

Inverse source problems with reduced interior data for a coupled reaction-diffusion system

We consider a two-component semilinear reaction-diffusion system in a bounded spatial domain $\Omega$ over a time interval $(0,T)$, which governs the water density $u(x,t)$ and the vegetation biomass density $v(x,t)$ for $x\in\Omega$ and $0<t<T$. In this system, called the Klausmeier-Gray-Scott model, we assume that an unknown source depends only on the spatial variable and appears in the reaction-diffusion equation for $u$. The main subject is the inverse source problem of determining a source term from limited data on $(u,v)$. We establish two kinds of stability estimates by means of Carleman estimates. First, a Carleman estimate with a singular weight yields a Lipschitz stability estimate for the inverse source problem from data consisting of a snapshot $u(\cdot,t_0)$ in $\Omega$ and $(u,v)$ in a subdomain $\omega$ over a time interval. Second, without assuming boundary data, we prove a H\"older stability estimate in any interior subdomain $\Omega_0$ satisfying $\overline{\Omega_0}\subset\Omega$. We further study how much the observation data can be reduced while preserving uniqueness and stability in the inverse problem under suitable additional conditions.

math.AP

Anti-Ramsey Number of Stars in 3-uniform hypergraphs

An edge-colored hypergraph is called \emph{a rainbow hypergraph} if all the colors on its edges are distinct. Given two positive integers $n,r$ and an $r$-uniform hypergraph $\mathcal{G}$, the anti-Ramsey number $ar_r(n,\mathcal{G})$ is defined to be the minimum number of colors $t$ such that there exists a rainbow copy of $\mathcal{G}$ in any exactly $t$-edge-coloring of the complete $r$-uniform hypergraph of order $n$. Let $ \mathcal{F}_k $ denote the 3-graph ($k$-star) consisting of $k$ edges sharing exactly one vertex. Tang, Li and Yan \cite{YTG} determined the value of $ar_3(n,\mathcal{F}_3)$ when $n\geq 20$. In this paper, we determine the anti-Ramsey number $ar_3(n,\mathcal{F}_{k+1})$, where $k\geq 3$ and $n> \frac{5}{2}k^3+\frac{15}{2}k^2+26k-3$.

math.CO

Anti-Ramsey number of intersecting cliques

An edge-colored graph is called a rainbow graph if all its edges have distinct colors. The anti-Ramsey number $ar(n, G)$, for a graph $G$ and a positive integer $n$, is defined as the minimum number of colors $r$ such that every exact $r$-edge-coloring of the complete graph $K_n$ contains at least one rainbow copy of $G$. A $(k, r)$-fan graph, denoted $F_{k, r}$, is a graph composed of $k$ cliques each of size $r$, all intersecting at exactly one common vertex. In this paper, we determine $ar(n, F_{k, r})$ for $n \geq 256r^{16}(k+1)^5$, $k \geq 1$, and $r \geq 2$.

math.CO

New Bounds on the Anti-Ramsey Number of Independent Triangles

An edge-colored graph is called \textit{rainbow graph} if all the colors on its edges are distinct. Given a positive integer $n$ and a graph $G$, the \textit{anti-Ramsey number} $ar(n,G)$ is defined to be the minimum number of colors $r$ such that there exists a rainbow copy of $G$ in any exactly $r$-edge-coloring of $K_n$. Wu et al. (Anti-Ramsey numbers for vertex-disjoint triangles, \emph{Discrete. Math.}, \textbf{346} (2022), 113123) determined the anti-Ramsey number $ar(n, kK_3)$ for $n\geq 2k^2-k+2 $. In this paper, we extend this result by improving the lower bound on $n$ to $n\geq 15k+57$.

math.CO

Anti-Ramsey Number of Friendship Graphs

An edge-colored graph is called \textit{rainbow graph} if all the colors on its edges are distinct. For a given positive integer $n$ and a family of graphs $\mathcal{G}$, the anti-Ramsey number $ar(n, \mathcal{G})$ is the smallest number of colors $r$ required to ensure that, no matter how the edges of the complete graph $K_n$ are colored using exactly $r$ colors, there will always be a rainbow copy of some graph $G$ from the family $\mathcal{G}$. A friendship graph $F_k$ is the graph obtained by combining $k$ triangles that share a common vertex. In this paper, we determine the anti-Ramsey number $ar(n, \{F_k\})$ for large values of $n$. Additionally, we also determine the $ar(n, \{K_{1,k}, kK_2\}$, where $K_{1,k}$ is a star graph with $ k+1$ vertices and $kK_2$ is a matching of size $k$.

math.CO

Prediction of the Economic Behavior of Fishery Biotechnology Companies Based on Machine Learning-Based Deep Metacellular Automata

Ocean warming significantly affects the fishing industry, with species like Scottish herring and mackerel migrating northwards. Our research, a fusion of artificial intelligence, data science, and operations research, addresses this crisis. Using Long Short Term Memory networks, we forecast sea surface temperatures (SST) and model fish migratory patterns with Enhanced Cellular Automata. A corrective factor within our model adjusts for human impact on SST, guiding diverse mitigation scenarios. We apply operational research to strategize responses, including the modernization of fishing vessels as a less costly alternative to relocation. Our data-driven approach, suggesting fleet modernization, strategic relocation, and product diversification, offers an effective approach to mitigating the threats to the ocean warming phenomenon.

stat.AP