arXiv subjects

Jiang Zhou

Publications and source records attributed to Jiang Zhou.

At least 37 records · Page 2Linked to original sources

arXiv2026

Near-Light Color Photometric Stereo for Mono-Chromatic Non-Lambertian Surfaces

Color photometric stereo enables single-shot surface reconstruction, extending conventional photometric stereo that requires multiple images of a static scene under varying illumination to dynamic scenarios. However, most existing approaches assume ideal distant lighting and Lambertian reflectance, leaving more practical near-light conditions and non-Lambertian surfaces underexplored. To overcome this limitation, we propose a framework that leverages neural implicit representations for depth and BRDF modeling under the assumption of mono-chromaticity (uniform chromaticity and homogeneous material), which alleviates the inherent ill-posedness of color photometric stereo and allows for detailed surface recovery from just one image. Furthermore, we design a compact optical tactile sensor to validate our approach. Experiments on both synthetic and real-world datasets demonstrate that our method achieves accurate and robust surface reconstruction.

cs.CV↗

arXiv2025

Spectral characterizations of local structures of graphs and hypergraphs

In this paper, we give the relationship between spectral radius and local structures of graphs and hypergraphs. Our work shows that certain local subgraphs (subhypergraphs) must occur when the spectral radius ratio is large. We also give spectral bounds on the local vector chromatic number in terms of tensor eigenvalues of graphs.

math.CO↗

arXiv2025

Challenging Multilingual LLMs: A New Taxonomy and Benchmark for Unraveling Hallucination in Translation

Large Language Models (LLMs) have advanced machine translation but remain vulnerable to hallucinations. Unfortunately, existing MT benchmarks are not capable of exposing failures in multilingual LLMs. To disclose hallucination in multilingual LLMs, we introduce a diagnostic framework with a taxonomy that separates Instruction Detachment from Source Detachment. Guided by this taxonomy, we create HalloMTBench, a multilingual, human-verified benchmark across 11 English-to-X directions. We employed 4 frontier LLMs to generate candidates and scrutinize these candidates with an ensemble of LLM judges, and expert validation. In this way, we curate 5,435 high-quality instances. We have evaluated 17 LLMs on HalloMTBench. Results reveal distinct ``hallucination triggers'' -- unique failure patterns reflecting model scale, source length sensitivity, linguistic biases, and Reinforcement-Learning (RL) amplified language mixing. HalloMTBench offers a forward-looking testbed for diagnosing LLM translation failures. HalloMTBench is available in https://huggingface.co/collections/AIDC-AI/marco-mt.

cs.CL↗

arXiv2025

Spherical two-distance sets and graph eigenvalues

A set of unit vectors in $\mathbb{R}^d$ is a called a spherical two-distance set if the inner products of distinct vectors only take two values. In this paper, we give explicit correspondence between spherical two-distance sets and graphs with specific spectral properties, and derive some bounds on the maximum size of spherical two-distance sets.

math.CO↗

arXiv2025

Perron-Frobenius theorem for dual tensors and its applications

The Perron-Frobenius theorem of nonnegative matrices is a classical result on spectral theory of matrices, which has wide applications in many domains. In this paper, we give the Perron-Frobenius theorem for dual tensors, that is, a dual tensor with weakly irreducible nonnegative standard part has a positive dual eigenvalue with a positive dual eigenvector. We give an explicit formula for the dual part of the positive dual eigenvector by using generalized inverses of an $M$-matrix. By considering the natural correspondence between tensors (matrices) and hypergraphs (graphs), some basic properties on the positive dual eigenvalue and positive dual eigenvector of hypergraphs are obtained. As applications, we introduce dual centrality measures for vertices of graphs and hypergraphs. By introducing a dual perturbation, vertices that are tied under eigenvector centrality can be effectively distinguished. In our numerical experiments, by perturbing specific structures, we successfully differentiated vertices in regular graphs and hypergraphs that were previously indistinguishable.

math.CO↗

arXiv2024

Unified bounds for the independence number of graph powers

For a graph $G$, its $k$-th power $G^k$ is constructed by placing an edge between two vertices if they are within distance $k$ of each other. The $k$-independence number $α_k(G)$ is defined as the independence number of $G^k$. By using general semidefinite programming and polynomial methods, we derive sharp bounds for the $k$-independence number of a graph, which extend and unify various existing results. Our work also allows us to easily derive some new bounds for $α_k(G)$.

math.CO↗

arXiv2024

Weak Factorizations of the Hardy Spaces in Terms of Multilinear Calderón-Zygmund Operators on Ball Banach Function Spaces

In this paper, our main purpose is to establish a weak factorization of the classical Hardy spaces in terms of a multilinear Calderón-Zygmund operator on the ball Banach function spaces. Furthermore, a new characterization of the BMO space via the boundedness of the commutator generated by the multilinear Calderón-Zygmund operator is also obtained. The results obtained in this paper have generality. As examples, we apply the above results to weighted Lebesgue space, variable Lebesgue space, Herz space, mixed-norm Lebesgue space, Lorentz space and so on.

math.FA↗

arXiv2024

Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on slice spaces

Let $0<t<\infty$, $0<α<n$, $1<p<r<\infty$ and $1<q<s<\infty$. In this paper, we prove that $b\in B M O\left(\mathbb{R}^{n}\right)$ if and only if the commutator $[b, T_{Ω,α}]$ generated by the fractional integral operator with the rough kernel $T_{Ω,α}$ and the locally integrable function $b$ is bounded from the slice space $(E_{p}^{q})_{t}(\mathbb{R}^{n})$ to $(E_{r}^{s})_{t}(\mathbb{R}^{n})$. Meanwhile, we also show that $b\in Lip_β(\mathbb{R}^{n}) $($0<β<1)$ if and only if the commutator $\left[b, T_{Ω,α}\right]$ is bounded from $(E_{p}^{q})_{t}(\mathbb{R}^{n})$ to $(E_{r}^{s})_{t}(\mathbb{R}^{n})$.

math.FA↗

arXiv2024

Hyponormal block Toeplitz operators with non-harmonic symbols on the weighted Bergman space

In this paper, we discuss hyponormal block Toeplitz operators $T_Φ$ over the vector-valued weighted Bergman space $A_α^2\left(\mathbb{C}^n\right)$. And two conditions about hyponormal block Toeplitz operators $T_Φ$ on $A_α^2\left(\mathbb{C}^n\right)$ were discussed separately, where $ Φ(z)=A z^p \bar{z}^q + B z^s \bar{z}^t $, $A,B$ are any n-order complex square matrices.

math.FA↗

arXiv2024

Characterization of BMO spaces via commutators of fractional maximal function on Lorentz spaces

Let $0 \leq α<n$ and $b$ be the locally integrable function. In this paper, we consider the maximal commutator of fractional maximal function $M_{b,α}$ and the nonlinear commutator of fractional maximal function $[b, M_α]$ on Lorentz spaces. We give some necessary and sufficient conditions for the boundedness of the commutators $M_{b,α}$ and $[b, M_α]$ on Lorentz spaces when the function $b$ belongs to BMO spaces, by which some new characterizations of certain subclasses of BMO spaces are obtained.

math.FA↗

arXiv2024

Characterization of Lipschitz functions via commutators of maximal operators on slice spaces

Let $0 \leq α<n$, $M_α$ be the fractional maximal operator, $M^{\sharp}$ be the sharp maximal operator and $b$ be the locally integrable function. Denote by $[b, M_α]$ and $[b, M^{\sharp}]$ be the commutators of the fractional maximal operator $M_α$ and the sharp maximal operator $M^{\sharp}$. In this paper, we show some necessary and sufficient conditions for the boundedness of the commutators $[b, M_α]$ and $[b, M^{\sharp}]$ on slice spaces when the function $b$ is the Lipschitz function, by which some new characterizations of the non-negative Lipschitz function are obtained

math.FA↗

arXiv2024

Generalized Campanato Space Over Non-homogeneous Space and Its Applications

The authors introduce generalized Campanato space with regularized condition over non-homogeneous space, and study its basic properties including the John-Nirenberg inequality and equivalent characterizations. As applications, the boundedness of fractional type Marcinkiewicz integral operator and its commutator on generalized Morrey space over non-homogeneous space is obtained.

math.FA↗

arXiv2024

Unified bounds for the independence number of graphs

The Hoffman ratio bound, Lovász theta function and Schrijver theta function are classical upper bounds for the independence number of graphs, which are useful in graph theory, extremal combinatorics and information theory. By using generalized inverses and eigenvalues of graph matrices, we give bounds for independence sets and the independence number of graphs. Our bounds unify the Lovász theta function, Schrijver theta function and Hoffman-type bounds, and we obtain the necessary and sufficient conditions of graphs attaining these bounds. Our work leads to some simple structural and spectral conditions for determining a maximum independent set, the independence number, the Shannon capacity and the Lovász theta function of a graph.

math.CO↗

arXiv2024

A combinatorial problem related to the classical probability

In the classical probability model, let $f(n)$ be the maximum number of pairwise independent events for the sample space with $n$ sample points. The determination of $f(n)$ is equivalent to the problem of determining the maximum cardinality of specific intersecting families on the set $\{1,2,\ldots,n\}$ . We show that $f(n)\leq n+1$, and $f(n)=n+1$ if there exists a Hadamard matrix of order $n$.

math.CO↗

arXiv2024

An Erdős-Stone type result for high-order spectra of graphs

Erdős-Stone Theorem is a well-known result in extremal graph theory which determines the asymptotic behaviour of maximum number of edges in an $n$-vertex $H$-free graph. In 2009, Nikiforov gave a spectral version of Erdős-Stone Theorem. In this paper, we obtain a tensor's spectral version of Erdős-Stone Theorem.

math.CO↗

arXiv2023

Interpolation on Convex-set Valued Lebesgue Spaces and its Applications

In this paper, we obtain two interpolation theorems on convex-set valued Lebesgue spaces, which generalize the Marcinkiewicz interpolation theorem and Riesz-Thorin interpolation theorem on classical Lebesgue spaces, respectively. As applications, we obtain the boundedness of convex-set valued fractional averaging operators and fractional maximal operators, and prove the reverse factorization property of matrix weights.

math.FA↗

arXiv2023

A characterization of mixed $λ$-central $\mathrm{BMO}$ space via the commutators of Hardy type operators

In this paper, we give a characterization of mixed $λ$-central bounded mean oscillation space $\mathrm{CBMO}^{\vec{q},λ}(\mathbb{R}^{n})$ via the boundedness of the commutators of $n$-dimensional Hardy operator $\mathcal{H}$ and its dual operator $\mathcal{H}^{*}$ on mixed Lebesgue space $L^{\vec{p}}(\mathbb{R}^{n})$. In addition, we also establish the boundedness of commutators $\mathcal{H}_{b}$ and $\mathcal{H}^{*}_{b}$ generated with $\mathrm{CBMO}^{\vec{q},λ}(\mathbb{R}^{n})$ function $b$ on mixed $λ$-central Morrey space $\mathcal{B}^{\vec{q},λ}(\mathbb{R}^{n})$, respectively.

math.FA↗

arXiv2023

Characterizations of the mixed central Campanato spaces via the commutator operators of Hardy type

The purpose of this paper is to establish some characterizations of mixed central Campanato space $\mathfrak{C}^{\vec{p},λ}(\mathbb{R}^{n})$, via the boundedness of the commutator operators of Hardy type. Unlike the case $λ\geq0$, there are some technical difficulties caused by $λ<0$ to be overcome. In addition, an extra assumption called as the mixed version of the reverse Hölder class be required in the proof of the converse characterization. Moreover, some further interesting conclusions for the Hardy type operators on mixed $λ$-central Morrey space $\mathcal{B}^{\vec{p},λ}(\mathbb{R}^{n})$ are also derived.

math.FA↗