arXiv subjects

Haiqi Zhang

Publications and source records attributed to Haiqi Zhang.

9 recordsLinked to original sources

arXiv2026

Neumann--Dirichlet eigenvalue comparison at the first Dirichlet threshold in the plane

Let $Ω\subset\mathbb R^2$ be a bounded connected Lipschitz domain, and let $\{μ_j(Ω)\}_{j\geq1}$ and $\{λ_j(Ω)\}_{j\geq1}$ denote the Neumann and Dirichlet Laplacian eigenvalues, respectively, counted with multiplicity. We prove that $$ μ_3(Ω)<λ_1(Ω), $$ thereby removing the simple-connectivity assumption from the previously known planar result at the first Dirichlet threshold. We also establish a three-spectrum counting inequality relating the Dirichlet, Neumann, and conductivity spectra.

math.SP↗

arXiv2026

Sharp ratios for low-index Neumann eigenvalues on convex domains

Let $Ω\subset\mathbb{R}^N$ be a bounded open convex set, and let $0=μ_0(Ω)<μ_1(Ω)\le μ_2(Ω)\le\cdots$ be the Neumann eigenvalues of the Laplacian, repeated according to multiplicity. We prove the sharp bounds $$ μ_2(Ω)\le 4μ_1(Ω),\qquad μ_3(Ω)\le 9μ_1(Ω). $$ The first estimate resolves a problem attributed to Henrot, while the second gives the next sharp case predicted by the one-dimensional model. The constants are optimal in every dimension.

math.AP↗

arXiv2026

The Ashbaugh--Benguria reciprocal-gap conjecture for Dirichlet eigenvalues

We prove the Ashbaugh--Benguria reciprocal-gap conjecture for the Dirichlet Laplacian in every dimension $N\ge2$. Specifically, if $Ω\subset\mathbb R^N$ is a bounded domain and $$ 0<λ_1(Ω)<λ_2(Ω)\leλ_3(Ω)\le\cdots $$ are its Dirichlet eigenvalues, then $$ \sum_{i=1}^{N} \frac{λ_1(Ω)} {λ_{i+1}(Ω)-λ_1(Ω)} \ge \frac{N}{j_{N/2,1}^2/j_{N/2-1,1}^2-1}, $$ where $j_{μ,1}$ denotes the first positive zero of the Bessel function $J_μ$ of the first kind of order $μ$. We also characterize the equality case: equality holds precisely when $Ω$ agrees with a Euclidean ball up to a set of Sobolev $H^1$-capacity zero. In particular, among bounded Lipschitz domains, equality holds if and only if $Ω$ is a Euclidean ball.

math.AP↗

arXiv2026

A sharp fixed-volume product inequality for the first $N$ nonzero Steklov eigenvalues

We prove a sharp fixed-volume product inequality for the first $N$ nonzero Steklov eigenvalues of bounded Lipschitz domains in $\mathbb R^N$. More precisely, if $N\ge2$ and $Ω\subset\mathbb R^N$ is a bounded Lipschitz domain, then $$ \prod_{j=1}^N σ_j(Ω)\le \frac{ω_N}{|Ω|}, $$ where $0=σ_0(Ω)<σ_1(Ω)\leσ_2(Ω)\le\cdots$ are the Steklov eigenvalues of $Ω$, and $ω_N$ denotes the volume of the unit ball in $\mathbb R^N$. This extends the convex-domain theorem of Henrot, Philippin, and Safoui to arbitrary bounded Lipschitz domains, and in particular settles the remaining higher-dimensional case of a problem posed by Henrot.

math.AP↗

arXiv2025

LLMTaxo: Leveraging Large Language Models for Constructing Taxonomy of Factual Claims from Social Media

With the rapid expansion of content on social media platforms, analyzing and comprehending online discourse has become increasingly complex. This paper introduces LLMTaxo, a novel framework leveraging large language models for the automated construction of taxonomies of factual claims from social media by generating topics at multiple levels of granularity. The resulting hierarchical structure significantly reduces redundancy and improves information accessibility. We also propose dedicated taxonomy evaluation metrics to enable comprehensive assessment. Evaluations conducted on three diverse datasets demonstrate LLMTaxo's effectiveness in producing clear, coherent, and comprehensive taxonomies. Among the evaluated models, GPT-4o mini consistently outperforms others across most metrics. The framework's flexibility and low reliance on manual intervention underscore its potential for broad applicability.

cs.CL↗

arXiv2025

A Knowledge Graph Informing Soil Carbon Modeling

Soil organic carbon is crucial for climate change mitigation and agricultural sustainability. However, understanding its dynamics requires integrating complex, heterogeneous data from multiple sources. This paper introduces the Soil Organic Carbon Knowledge Graph (SOCKG), a semantic infrastructure designed to transform agricultural research data into a queryable knowledge representation. SOCKG features a robust ontological model of agricultural experimental data, enabling precise mapping of datasets from the Agricultural Collaborative Research Outcomes System. It is semantically aligned with the National Agricultural Library Thesaurus for consistent terminology and improved interoperability. The knowledge graph, constructed in GraphDB and Neo4j, provides advanced querying capabilities and RDF access. A user-friendly dashboard allows easy exploration of the knowledge graph and ontology. SOCKG supports advanced analyses, such as comparing soil organic carbon changes across fields and treatments, advancing soil carbon research, and enabling more effective agricultural strategies to mitigate climate change.

cs.CY↗

arXiv2025

OT-DETECTOR: Delving into Optimal Transport for Zero-shot Out-of-Distribution Detection

Out-of-distribution (OOD) detection is crucial for ensuring the reliability and safety of machine learning models in real-world applications. While zero-shot OOD detection, which requires no training on in-distribution (ID) data, has become feasible with the emergence of vision-language models like CLIP, existing methods primarily focus on semantic matching and fail to fully capture distributional discrepancies. To address these limitations, we propose OT-DETECTOR, a novel framework that employs Optimal Transport (OT) to quantify both semantic and distributional discrepancies between test samples and ID labels. Specifically, we introduce cross-modal transport mass and transport cost as semantic-wise and distribution-wise OOD scores, respectively, enabling more robust detection of OOD samples. Additionally, we present a semantic-aware content refinement (SaCR) module, which utilizes semantic cues from ID labels to amplify the distributional discrepancy between ID and hard OOD samples. Extensive experiments on several benchmarks demonstrate that OT-DETECTOR achieves state-of-the-art performance across various OOD detection tasks, particularly in challenging hard-OOD scenarios.

cs.CV↗

arXiv2025

TrustMap: Mapping Truthfulness Stance of Social Media Posts on Factual Claims for Geographical Analysis

Factual claims and misinformation circulate widely on social media and affect how people form opinions and make decisions. This paper presents a truthfulness stance map (TrustMap), an application that identifies and maps public stances toward factual claims across U.S. regions. Each social media post is classified as positive, negative, or neutral/no stance, based on whether it believes a factual claim is true or false, expresses uncertainty about the truthfulness, or does not explicitly take a position on the claim's truthfulness. The tool uses a retrieval-augmented model with fine-tuned language models for automatic stance classification. The stance classification results and social media posts are grouped by location to show how stance patterns vary geographically. TrustMap allows users to explore these patterns by claim and region and connects stance detection with geographical analysis to better understand public engagement with factual claims.

cs.SI↗

arXiv2024

On Context-aware Detection of Cherry-picking in News Reporting

Cherry-picking refers to the deliberate selection of evidence or facts that favor a particular viewpoint while ignoring or distorting evidence that supports an opposing perspective. Manually identifying cherry-picked statements in news stories can be challenging. In this study, we introduce a novel approach to detecting cherry-picked statements by identifying missing important statements in a target news story using language models and contextual information from other news sources. Furthermore, this research introduces a novel dataset specifically designed for training and evaluating cherry-picking detection models. Our best performing model achieves an F-1 score of about 89% in detecting important statements. Moreover, results show the effectiveness of incorporating external knowledge from alternative narratives when assessing statement importance.

cs.CL↗