arXiv subjects

Rui Tong

Publications and source records attributed to Rui Tong.

5 recordsLinked to original sources

arXiv2026

Average Local Independence and the Spanning-Tree Leaf Number: A Proof of Graffiti.pc Conjecture 2

We prove Graffiti.pc Conjecture 2, a 1996 conjecture listed as open on the \emph{Written on the Wall II} page marked ``Last update 7/23/26.'' Let $G$ be a finite simple connected graph. For $v\in V(G)$, let $I(v)=\alpha(G[N_G(v)])$, and let $I_{\mathrm{avg}}(G)$ be the average of these local independence numbers. The conjecture states that the maximum number $L_s(G)$ of leaves in a spanning tree of $G$ satisfies $L_s(G)\ge 2\bigl(I_{\mathrm{avg}}(G)-1\bigr)$. We establish this inequality by extracting a triangle-free spanning subgraph that retains at least half of the total local-independence mass. A degree-square argument then produces a double star with sufficiently many leaves, and this tree extends to a spanning tree without losing leaves. Balanced complete bipartite graphs show that the bound is sharp.

math.CO↗

arXiv2025

Manifold Percolation: from generative model to Reinforce learning

Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution. We propose that continuum percolation is uniquely suited to this support analysis, as the sampling process effectively projects high-dimensional density estimation onto a geometric counting problem on the support. In this work, we establish a rigorous correspondence between the topological phase transitions of random geometric graphs and the underlying data manifold in high-dimensional space. By analyzing the relationship between our proposed Percolation Shift metric and FID, we show that this metric captures structural pathologies, such as implicit mode collapse, where standard statistical metrics fail. Finally, we translate this topological phenomenon into a differentiable loss function that guides training. Experimental results confirm that this approach not only prevents manifold shrinkage but also fosters a form of synergistic improvement, where topological stability becomes a prerequisite for sustained high fidelity in both static generation and sequential decision making.

stat.ML↗

arXiv2024

Unlocking the Potential: Benchmarking Large Language Models in Water Engineering and Research

Recent advancements in Large Language Models (LLMs) have sparked interest in their potential applications across various fields. This paper embarked on a pivotal inquiry: Can existing LLMs effectively serve as "water expert models" for water engineering and research tasks? This study was the first to evaluate LLMs' contributions across various water engineering and research tasks by establishing a domain-specific benchmark suite, namely, WaterER. Herein, we prepared 983 tasks related to water engineering and research, categorized into "wastewater treatment", "environmental restoration", "drinking water treatment and distribution", "sanitation", "anaerobic digestion" and "contaminants assessment". We evaluated the performance of seven LLMs (i.e., GPT-4, GPT-3.5, Gemini, GLM-4, ERNIE, QWEN and Llama3) on these tasks. We highlighted the strengths of GPT-4 in handling diverse and complex tasks of water engineering and water research, the specialized capabilities of Gemini in academic contexts, Llama3's strongest capacity to answer Chinese water engineering questions and the competitive performance of Chinese-oriented models like GLM-4, ERNIE and QWEN in some water engineering tasks. More specifically, current LLMs excelled particularly in generating precise research gaps for papers on "contaminants and related water quality monitoring and assessment". Additionally, they were more adept at creating appropriate titles for research papers on "treatment processes for wastewaters", "environmental restoration", and "drinking water treatment". Overall, this study pioneered evaluating LLMs in water engineering and research by introducing the WaterER benchmark to assess the trustworthiness of their predictions. This standardized evaluation framework would also drive future advancements in LLM technology by using targeting datasets, propelling these models towards becoming true "water expert".

cs.CL↗

arXiv2018

Type-II Dirac photons at the metasurfaces

Topological characteristics of energy bands, such as Dirac/Weyl nodes, have attracted substantial interest in condensed matter systems as well as in classical wave systems. Among these energy bands, the type-II Dirac point is a nodal degeneracy with tilted conical dispersion, leading to a peculiar crossing dispersion in the constant energy plane. Such nodal points have recently been found in electronic materials. The analogous topological feature in photonic systems remains a theoretical curiosity, with experimental realization expected to be challenging. Here, we experimentally realize the type-II Dirac point using a planar metasurface architecture, where the band degeneracy point is protected by the underlying mirror symmetry of the metasurface. Gapless edge modes are found and measured at the boundary between the different domains of the symmetry-broken metasurface. Our work shows that metasurfaces are simple and practical platforms for realizing electromagnetic type-II Dirac points, and their planar structure is a distinct advantage that facilitates applications in two-dimensional topological photonics.

physics.app-ph↗

arXiv2017

A metasurface with bidirectional hyperbolic surface modes and positionsensing applications

We theoretically and experimentally studied resonance-induced hyperbolic metasurfaces, proving that it is an efficient way to introduce Fano-resonance and decreasethe Q-factor in our system in order to create hyperbolic iso-frequency contours (IFCs) along two orthogonal directions. The metasurface with a continuous topological transition for such IFCs has been designed and experimentally implemented. In particular, two independent selfcollimation frequencies corresponding to the transition frequencies in orthogonal directions. As a consequence, we experimentally demonstrated that the metasurface can function as a position- sensor by utilizing the bidirectional hyperbolic surface waves, opening a new avenue for position-sensing.

physics.app-ph↗