arXiv subjects

Zhuoran Du

Publications and source records attributed to Zhuoran Du.

8 recordsLinked to original sources

arXiv2026

DTBench: A Synthetic Benchmark for Document-to-Table Extraction

Document-to-table (Doc2Table) extraction derives structured tables from unstructured documents under a target schema, enabling reliable and verifiable SQL-based data analytics. Although large language models (LLMs) have shown promise in flexible information extraction, their ability to produce precisely structured tables remains insufficiently understood, particularly for indirect extraction that requires complex capabilities such as reasoning and conflict resolution. Existing benchmarks neither explicitly distinguish nor comprehensively cover the diverse capabilities required in Doc2Table extraction. We argue that a capability-aware benchmark is essential for systematic evaluation. However, constructing such benchmarks using human-annotated document-table pairs is costly, difficult to scale, and limited in capability coverage. To address this, we adopt a reverse Table2Doc paradigm and design a multi-agent synthesis workflow to generate documents from ground-truth tables. Based on this approach, we present DTBench, a synthetic benchmark that adopts a proposed two-level taxonomy of Doc2Table capabilities, covering 5 major categories and 13 subcategories. We evaluate several mainstream LLMs on DTBench, and demonstrate substantial performance gaps across models, as well as persistent challenges in reasoning, faithfulness, and conflict resolution. DTBench provides a comprehensive testbed for data generation and evaluation, facilitating future research on Doc2Table extraction. The benchmark is publicly available at https://github.com/ZJU-DAILY/DTBench.

cs.DB↗

arXiv2024

Automatic Spectral Calibration of Hyperspectral Images:Method, Dataset and Benchmark

Hyperspectral image (HSI) densely samples the world in both the space and frequency domain and therefore is more distinctive than RGB images. Usually, HSI needs to be calibrated to minimize the impact of various illumination conditions. The traditional way to calibrate HSI utilizes a physical reference, which involves manual operations, occlusions, and/or limits camera mobility. These limitations inspire this paper to automatically calibrate HSIs using a learning-based method. Towards this goal, a large-scale HSI calibration dataset is created, which has 765 high-quality HSI pairs covering diversified natural scenes and illuminations. The dataset is further expanded to 7650 pairs by combining with 10 different physically measured illuminations. A spectral illumination transformer (SIT) together with an illumination attention module is proposed. Extensive benchmarks demonstrate the SoTA performance of the proposed SIT. The benchmarks also indicate that low-light conditions are more challenging than normal conditions. The dataset and codes are available online:https://github.com/duranze/Automatic-spectral-calibration-of-HSI

cs.CV↗

arXiv2022

Nonexistence of anti-symmetric solutions for fractional Hardy-Hénon System

We study anti-symmetric solutions about the hyperplane $\{x_n=0\}$ to the following fractional Hardy-Hénon system $$ \left\{\begin{aligned} &(-Δ)^{s_1}u(x)=|x|^αv^p(x),\ \ x\in\mathbb{R}_+^n, \\&(-Δ)^{s_2}v(x)=|x|^βu^q(x),\ \ x\in\mathbb{R}_+^n, \\&u(x)\geq 0,\ \ v(x)\geq 0,\ \ x\in\mathbb{R}_+^n, \end{aligned}\right. $$ where $0 2\max\{s_1,s_2\}$. Nonexistence of anti-symmetric solutions are obtained in some appropriate domains of $(p,q)$ under some corresponding assumptions of $α,β$ via the methods of moving spheres and moving planes. Particularly, for the case $s_1=s_2$, one of our results shows that one domain of $(p,q)$, where nonexistence of anti-symmetric solutions with appropriate decay conditions holds true, locates at above the fractional Sobolev's hyperbola under appropriate condition of $α, β$.

math.AP↗

arXiv2022

Classification of solutions to several semi-linear polyharmonic equations and fractional equations

We are concerned with the following semi-linear polyharmonic equation with integral constraint \begin{align} \left\{\begin{array}{rl} &(-Δ)^pu=u^γ_+ ~~ \mbox{ in }{\mathbb{R}^n},\\ \nonumber &\int_{\mathbb{R}^n}u_+^γdx<+\infty, \end{array}\right. \end{align} where $n>2p$, $p\geq2$ and $p\in\mathbb{Z}$. We obtain for $γ\in(1,\frac{n}{n-2p})$ that any nonconstant solution satisfying certain growth at infinity is radial symmetric about some point in $\mathbb{R}^{n}$ and monotone decreasing in the radial direction. In the case $p=2$, the same results are established for more general exponent $γ\in(1,\frac{n+4}{n-4})$. For the following fractional equation with integral constraint \begin{equation*} \left\{\begin{array}{rl} &(-Δ)^sv=v^γ_+ ~~ \mbox{ in }{\mathbb{R}^n},~~~~\\ &\int_{\mathbb{R}^n}v_+^{\frac{n(γ-1)}{2s}}dx<+\infty,~~~~~ \end{array}\right. \end{equation*} where $s\in(0,1)$, $γ\in (1, \frac{n+2s}{n-2s})$ and $n\geq 2$, we also complete the classification of solutions with certain growth at infinity. In addition, observe that the assumptions of the maximum principle named decay at infinity in \cite{chen} can be weakened slightly. Based on this observation, we classify all positive solutions of two semi-linear fractional equations without integral constraint.

math.AP↗

arXiv2022

Classification of solutions to equations involving Higher-order fractional Laplacian

In this paper, we are concerned with the following equation involving higher-order fractional Lapalacian \begin{equation*} \left\{\begin{aligned} &(-Δ)^{p+{\fracα{2}}}u(x)=u_+^γ~~ \mbox{ in }\mathbb{R}^n,\\ &\int_{\mathbb{R}^n}u_+^γdx<+\infty, \end{aligned}\right. \end{equation*} where $p\geq 1$ is an integer, $0<\alp<2$, $n> 2p+α$ and $γ\in (1,\frac{n}{n-2p-\alp})$. We establish an integral representation formula for any nonconstant classical solution satisfying certain growth at infinity. From this we prove that these solutions are radially symmetric about some point in $\R^n$ and monotone decreasing in the radial direction via method of moving planes in integral forms.

math.AP↗

arXiv2018

Further study on periodic solutions of elliptic equations with a fractional Laplacian

We obtain some existence theorems for periodic solutions to several linear equations involving fractional Laplacian. We also prove that the lower bound of all periods for semilinear elliptic equations involving fractional Laplacian is not larger than some exact positive constant. Hamiltonian identity, Modica-type inequalities and an estimate of the energy for periodic solutions are also established.

math.AP↗

arXiv2015

Asymptotic behavior of positive solutions to a degenerate elliptic equation in the upper half space with a nonlinear boundary condition

We consider positive solutions of the problem \begin{equation} \left\{\begin{array}{l}-\mbox{div}(x_{n}^{a}\nabla u)=0\qquad \mbox{in}\;\;\mathbb{R}_+^n,\\ \frac{\partial u}{\partial ν^a}=u^{q} \qquad \mbox{on}\;\;\partial \mathbb{R}_+^n,\\ \end{array} \right. \end{equation} where $a\in (-1,0)\cup(0,1)$, $q>1$ and $\frac{\partial u}{\partial ν^a}:=-\lim_{x_{n}\rightarrow 0^+}x_{n}^{a}\frac{\partial u}{\partial x_{n}}$. We obtain some qualitative properties of positive axially symmetric solutions in $n\geq3$ for the case $a\in (-1,0)$ under the condition $q\geq\frac{n-a}{n+a-2}$. In particular, we establish the asymptotic expansion of positive axially symmetric solutions.

math.AP↗

arXiv2011

Properties of the extremal solution for a fourth-order elliptic problem

Let $λ^{*}>0$ denote the largest possible value of $λ$ such that $$ \{{array}{lllllll} Δ^{2}u=\fracλ{(1-u)^{p}} & \{in}\ \ B, 0 1$ and $n$ is the exterior unit normal vector. We show that for $λ=λ^{*}$ this problem possesses a unique weak solution $u^{*}$, called the extremal solution. We prove that $u^{*}$ is singular when $n\geq 13$ for $p$ large enough and $1-C_{0}r^{\frac{4}{p+1}}\leq u^{*}(x)\leq 1-r^{\frac{4}{p+1}}$ on the unit ball, where $ C_{0}:=(λ^{*}/\barλ)^{\frac{1}{p+1}}$ and $\barλ:=\frac{8(p-1)}{(p+1)^{2}}[n-\frac{2(p-1)}{p+1}][n-\frac{4p}{p+1}]$. Our results actually complete part of the open problem which \cite{D} lef

math.AP↗