arXiv subjects

Jia Zhou

Publications and source records attributed to Jia Zhou.

At least 19 recordsLinked to original sources

arXiv2026

Dominant-Degree Conditions for Ramsey--Tur\'an Factors of Non-Directed Cycle Orientations

Let $\Cvec$ be a fixed orientation of the cycle $C_\ell$, $\ell\ge3$, which is not directed. For an oriented graph $D$, let $d_D^*(v):=\max\{d_D^+(v),d_D^-(v)\},$ and let \[ \sigore(D):=\min\bigl\{d_D^*(x)+d_D^*(y):x\ne y,\ xy,yx\notin A(D)\bigr\}, \] with $\sigore(D)=\infty$ if the underlying graph of $D$ is complete. We prove that, for every $\mu>0$, there exist $\gamma>0$ and $n_0$ such that every $n\ge n_0$ with $\ell\mid n$ and every $n$-vertex oriented graph $D$ satisfying \[ \alpha(D)\le\gamma n \text{ and } {\sigore(D)\ge\left(\frac34+\mu\right)n} \] contains a $\Cvec$-factor. {Additionally, for every fixed $s\ge2$ and every fixed real constant $C$, we construct arbitrarily large oriented graphs with $\sigore(D)\ge \frac34n+C$ that contain no $C_{2s}^{\ad}$-factor. More precisely, $C:=\frac34\alpha(D)-2$ for $s=2$ and $C:=\frac14\alpha(D)-\frac32$ for $s\ge3$.} This paper develops a weighted reduction framework adapted to dominant degree condition, proves the absorption lemma via closed-cluster merging with even-walk, and derives almost-perfect tiling structures by virtue of Farkas-lemma-based fractional decomposition.

math.CO↗

arXiv2026

A Chv\'atal--Erd\H{o}s type condition for supereulerian digraphs with $\alpha_{2}=4$

A digraph is \textbf{supereulerian} if it contains a spanning closed trail. Let $\alpha_2(D)$ denote the maximum cardinality of a vertex set inducing no 2-cycle. In this paper, we characterize supereulerianity in a strong digraph $D$ with $\alpha_2(D)=4$ by proving that a strong digraph $D$ with $\alpha_2(D)=4$ and $\lambda(D)\ge 2$ is supereulerian if and only if $D$ does not belong to an exceptional family $\mathcal H$ of $2$-arc-strong digraphs with $\alpha_2(D)=4$. Furthermore, every strong digraph satisfying $\alpha_2(D)=4$ and $\lambda(D)\geq3$ is supereulerian.

math.CO↗

arXiv2026

Complexity of Arc-Decompositions involving Perfect Matchings and Cycle Factors

For two digraph properties $P_1$ and $P_2$, a $(P_1,P_2)$-arc-decomposition of a digraph $D$ is a partition $A(D)=A_1\mathbin{\dot\cup}A_2$ such that the spanning subdigraphs $D[A_1]$ and $D[A_2]$ have properties $P_1$ and $P_2$, respectively. For example, a (strong,strong)-arc-decomposition of a digraph $D=(V,A)$ is a partitioning $A=A_1\cup{}A_2$ of $A$ so that each of the spanning digraphs $D_i=(V,A_i)$, $i=1,2$ are strongly connected. We prove that it is NP-complete to decide whether a digraph admits an arc-decomposition with properties $(P_1,P_2)$ where $(P_1,P_2)\in \{$(is a perfect matching, having no odd directed cycle), (perfect matching, strong), (perfect matching, having an out-branching), (is a cycle factor, having no odd directed cycle)$\}$. These results settle some open problems posed by Bang-Jensen, Bessy, Gon\c{c}alves, and Picasarri-Arrieta [Theoret. Comput. Sci. 928 (2022), 167--182].

math.CO↗

arXiv2026

Paths with Prescribed Endpoints in Semicomplete and Locally Semicomplete Digraphs

We study two open path problems with prescribed endpoints posed by Bang-Jensen and Gutin. The first asks for a longest $(x,y)$-path in a semicomplete digraph. The second asks whether a locally semicomplete digraph has a Hamiltonian $(x,y)$-path. For semicomplete digraphs, we solve the first problem when the endpoints lie in different strong components. We also prove that if a non-Hamiltonian longest $(x,y)$-path omits a set of vertices, then these vertices together with $x$ and $y$ have a Hamiltonian $(y,x)$-path. This gives an equivalent cycle problem. We then give an exact algorithm that runs in polynomial time when the number of omitted vertices is fixed. For locally semicomplete digraphs, we determine the possible endpoints in the connected nonstrong case. Known results then leave only strong, nonsemicomplete, non-$4$-strong digraphs unresolved. Every such digraph of order at least five has a strong vertex cut of size at most three. Two examples show that a spanning directed path together with a vertex-disjoint directed cycle is not sufficient, and that vertices of one strong component need not occur consecutively on a Hamiltonian path.

math.CO↗

arXiv2026

Sparse spanning $k$-strong oriented subdigraphs in split digraphs

Jackson and Thomassen conjectured that every $2k$-strong digraph admits a spanning $k$-strong oriented subdigraph [Ann. N. Y. Acad. Sci. 555 (1989) 402-412]. The conjecture holds for $k=1$ but other than some partial results that have been obtained for general $k$ in some special families of digraphs, including symmetric digraphs, the conjecture remains wide open in general. Even the existence of an integer $K$ such that every $K$-strong digraph has a 2-strong spanning oriented subdigraph is open. As a natural optimization counterpart, the minimum spanning $k$-strong subdigraph (MSSS$_k$) problem, is to find the minimum number of arcs in a spanning $k$-strong subdigraph of a $k$-strong digraph. This problem is NP-hard already for $k=1$ as it generalizes the hamiltonian cycle problem. In this paper, we address both problems simultaneously for the class of split digraphs, by constructing sparse spanning $k$-strong oriented subdigraphs. Specifically, we prove that every $k$-strong split digraph $D = (V_1, V_2; A)$ with minimum semi-degree {$\delta^0(D)\geq 26k+15$} contains a spanning $k$-strong oriented subdigraph with no more than $kn+k|V_1|+98k^2+38k+3$ arcs, where $kn + k|V_1|$ is tight and the $k^{2}$ term is tight up to a constant factor. For the class of $k$-strong tournaments with minimum semi-degree at least $26k+15$ our results improve the bound obtained by Kang in [Combin. Probab. Comput., 27:892-907, 2018].

math.CO↗

arXiv2026

Ramsey--Tur\'an Factors of Non-directed Oriented Cycles in Oriented Graphs

Let $\overrightarrow{C}$ be any orientation of the cycle $C_{\ell}$ which is not directed. We prove that, for every integer $\ell\ge3$ and every $\mu>0$, there is a real $\gamma$ such that every sufficiently large oriented graph $D$ with $\ell\mid |D|$, minimum semidegree at least $(1/4+\mu)|D|$ and independence number at most $\gamma |D|$ has a $\overrightarrow{C}$-factor. The constant $1/4$ is asymptotically tight. This proof establishes Ramsey-Tur\'an type lattice absorption lemmas and an almost covering theorem via the oriented tree embedding lemma under chromatic number constraints.

math.CO↗

arXiv2026

Quadruply Bonded Mo2 Molecules: An Innate Emitter-Resonator Quantum System in Free Space

In recent decades, significant progress has been made in constructing and studying individual quantum systems based on two level atoms (molecules) and photons. Here we demonstrate that the quadruply bonded Mo2 unit, with a MoMo bond distance as short as 2.1A, functions as an innate emitter resonator molecular quantum system capable of trapping visible light photons between the two molybdenum atoms under ambient conditions, thereby generating an intense quantized local electromagnetic field with an extremely small mode volume. The resonance fluorescence spectra of three Mo2 complexes indicate that the intermetallic Mo-Mo charge transfer transition is coherently coupled to the local scattering field, exhibiting vacuum Rabi splitting and Mollow triplets. Resonant coupling of single molecules and N-molecule ensembles to the scattered light through sideband excitation produces a sequence of discrete optical modes spanning a broad wavelength range, with polaritonic transitions identical to those observed in Ni2 based systems. These results establish the Mo2 molecule as an independent emitter resonator integrated quantum system that enables quantum optical experiments in free space using conventional spectroscopic instrumentation. This work extends quantum electrodynamics into molecular science, providing new insights into metal metal bonding, molecular physics, and light matter interactions.

quant-ph↗

arXiv2026

K-Arc-Strong Orientations Of Semicomplete Digraphs

Results by Jackson and Frank imply that every 2k-arc-strong digraph D contains a spanning k-arc-strong oriented subdigraph. This is best possible, even for very dense digraphs. A digraph is semicomplete if at least one of the arcs xy,yx is present for every pair of distinct vertices x,y. A tournament has exactly one of xy,yx for every such pair. Clearly every semicomplete digraph D contains a spanning tournament T which is obtained by deleting one arc from every 2-cycle of D. We prove that every (2k-1)-arc-strong semicomplete digraph on at least 2k+1 vertices contains a spanning k-arc-strong tournament. Both bounds 2k-1 and 2k+1 are best possible. The proof uses Frank's general orientation theorem for graphs as well as counting arguments based on the semicomplete structure.

math.CO↗

arXiv2026

Highly connected spanning oriented subdigraphs in generalizations of semicomplete digraphs

Let $k$ be a positive integer. Jackson and Thomassen conjectured in 1989 that there exists an integer function $f(k)$ such that every $f(k)$-strong digraph admits a spanning $k$-strong oriented subdigraph. They even conjectured that one can take $f(k)=2k$ [Ann. N. Y. Acad. Sci. 555 (1989) 402-412]. Already the existence of $f(2)$ is open for general digraphs. Thomassen proved that $f(2)=4$ for symmetric digraphs. For general $k$, the existence of $f(k)$ was only known for locally semicomplete digraphs and quasi-transitive digraphs. Guo proved that every ${(3k-2)}$-strong locally semicomplete digraph contains a spanning $k$-strong local tournament [Discrete Appl. Math. 79 (1997) 119--125]. One can deduce from Guo's result that we have $f(k)\leq 3k-2$ for quasi-transitive digraphs. In this paper, we prove the existence of $f(k)$ for two subclasses of the semicomplete multipartite digraphs, namely extended semicomplete digraphs and semicomplete split digraphs. We prove that every $(4k+1)$-strong extended semicomplete digraph contains a spanning $k$-strong oriented subdigraph and every $5k$-strong semicomplete split digraph contains a spanning $k$-strong oriented subdigraph. The first result implies that for the large class of digraphs which can be obtained from some semicomplete digraph $S$ on at least 3 vertices by substituting arbitrary digraphs for each vertex of $S$ we also have $f(k)\leq 4k+1$.

math.CO↗

arXiv2026

Confidence Intervals for the Risk Difference in Combined Unilateral and Bilateral Data Incorporating a Distribution-Based Approach

Combined unilateral and bilateral binary outcomes frequently arise in studies involving paired organs. The risk difference is a clinically interpretable measure for comparing treatment effects between groups. Existing confidence interval methods are primarily based on asymptotic normality and may fail to adequately reflect finite-sample distributional features, particularly skewness. To address this issue, we propose a distribution-based confidence interval derived from the probability distribution of the risk difference estimator and a modified MOVER procedure that accounts for intra-subject correlation. Their performances are compared with those of commonly used asymptotic methods through extensive simulation studies. Across a broad range of parameter settings, all methods exhibited satisfactory performance as sample size increased. The proposed distribution-based interval achieved coverage probabilities close to the nominal level with interval widths comparable to those of existing procedures. In small sample settings, it was able to capture skewness in the sampling distribution that was not reflected by methods relying on asymptotic normality. Analyses of two real-world datasets demonstrated the practical applicability of the competing methods and yielded consistent inferential conclusions. The proposed approach provides an alternative framework for interval estimation of the risk difference in studies involving combined unilateral and bilateral binary outcomes.

stat.ME↗

arXiv2026

Symmetry energy of baryon- and neutron-rich nuclear matter

Based on the relativistic mean-field model and assuming $G$-parity invariance, we have studied the equation of state of baryon- and neutron-rich matter produced in low-energy relativistic heavy-ion collisions. Similar to the traditional isospin symmetry energy, we define the baryon-antibaryon symmetry energy characterizing the energy difference due to the baryon-antibaryon asymmetry. The potential difference between nucleons and antinucleons is correlated with the potential contribution of the baryon-antibaryon symmetry energy mainly from the vector interaction in baryon-rich matter. The isospin symmetry energy is considerably reduced even with a small fraction of antinucleons compared to the traditional case with only nucleons. A more attractive antineutron potential than antiproton potential is observed, and the isospin splitting of the mean-field potential for antinucleons is found to be intrinsically larger than that for nucleons in baryon- and neutron-rich matter.

nucl-th↗

arXiv2026

Parameter Efficient Multi-Class Intelligent Scheduling for Multimodal Online Distributed Industrial Anomaly Detection

Industrial anomaly detection has attracted significant attention as a fundamental challenge in industrial systems. The rapid advancement of heterogeneous industrial sensors has driven industrial anomaly detection from unimodal to multimodal paradigms. However, existing methods are primarily designed for centralized and offline settings, overlooking the distributed and continuously generated data characteristic of real-world industrial environments. With the advancement of edge intelligence, modern edge devices are increasingly capable of not only data acquisition but also distributed model training, enabling collaborative intelligence across the system. Industrial anomaly detection represents a critical application in this context. Motivated by these challenges, we propose a novel framework termed Multimodal Online Distributed Industrial Anomaly Detection (MODIAD). We first present a comprehensive workflow for MODIAD and then formulate a Multi-class Intelligent Scheduling (MIS) problem to coordinate cross class model updates by balancing data sufficiency and class update frequency. To efficiently solve this problem, we design a Sequential Marginal Gain Greedy (SMG) algorithm that enables effective multi-class training under resource constraints. Furthermore, to improve the computational and communication efficiency during training, we propose an Resource Efficient Class-Wise Low Rank Adaptation (REC-LoRA) strategy, which significantly reduces system overhead while preserving detection performance. Extensive experiments on two representative multimodal industrial anomaly detection datasets, MVTec 3D-AD and Eyecandies demonstrate that the proposed approach achieves superior performance and efficiency under the MODIAD scenario.

cs.LG↗

arXiv2026

Can LLMs Act as Historians? Evaluating Historical Research Capabilities of LLMs via the Chinese Imperial Examination

While Large Language Models (LLMs) have increasingly assisted in historical tasks such as text processing, their capacity for professional-level historical reasoning remains underexplored. Existing benchmarks primarily assess basic knowledge breadth or lexical understanding, failing to capture the higher-order skills, such as evidentiary reasoning,that are central to historical research. To fill this gap, we introduce ProHist-Bench, a novel benchmark anchored in the Chinese Imperial Examination (Keju) system, a comprehensive microcosm of East Asian political, social, and intellectual history spanning over 1,300 years. Developed through deep interdisciplinary collaboration, ProHist-Bench features 400 challenging, expert-curated questions across eight dynasties, accompanied by 10,891 fine-grained evaluation rubrics. Through a rigorous evaluation of 18 LLMs, we reveal a significant proficiency gap: even state-of-the-art LLMs struggle with complex historical research questions. We hope ProHist-Bench will facilitate the development of domain-specific reasoning LLMs, advance computational historical research, and further uncover the untapped potential of LLMs. We release ProHist-Bench at https://github.com/inclusionAI/ABench/tree/main/ProHist-Bench.

cs.CL↗

arXiv2026

KG-CMI: Knowledge graph enhanced cross-Mamba interaction for medical visual question answering

Medical visual question answering (Med-VQA) is a crucial multimodal task in clinical decision support and telemedicine. Recent methods fail to fully leverage domain-specific medical knowledge, making it difficult to accurately associate lesion features in medical images with key diagnostic criteria. Additionally, classification-based approaches typically rely on predefined answer sets. Treating Med-VQA as a simple classification problem limits its ability to adapt to the diversity of free-form answers and may overlook detailed semantic information in those answers. To address these challenges, we propose a knowledge graph enhanced cross-Mamba interaction (KG-CMI) framework, which consists of a fine-grained cross-modal feature alignment (FCFA) module, a knowledge graph embedding (KGE) module, a cross-modal interaction representation (CMIR) module, and a free-form answer enhanced multi-task learning (FAMT) module. The KG-CMI learns cross-modal feature representations for images and texts by effectively integrating professional medical knowledge through a graph, establishing associations between lesion features and disease knowledge. Moreover, FAMT leverages auxiliary knowledge from open-ended questions, improving the model's capability for open-ended Med-VQA. Experimental results demonstrate that KG-CMI outperforms existing state-of-the-art methods on three Med-VQA datasets, i.e., VQA-RAD, SLAKE, and OVQA. Additionally, we conduct interpretability experiments to further validate the framework's effectiveness.

cs.CV↗

arXiv2026

On the 2-Linkage Problem for Split Digraphs

A digraph is {\bf $ k $-linked} if for arbitary two disjoint vertex sets $\{s_1, \ldots, s_k\}$ and $\{t_1, \ldots, t_k\}$, there exist vertex-disjoint directed paths $P_1, \ldots, P_k$ {such that $P_i$ is a directed path from $s_i$ to $t_i$ for each $i\in [k]$}. A {\bf split digraph} is a digraph $ D = (V_1, V_2; A) $ whose vertex set is a disjoint union of two nonempty sets $ V_1 $ and $ V_2 $ such that $ V_1 $ is an independent set and the subdigraph induced by $ V_2 $ is semicomplete (no pair of non-adjacent vertices). A {\bf semicomplete split digraph} is a split digraph $ D = (V_1, V_2; A) $ in which every vertex in the independent set $ V_1 $ is adjacent to every vertex in $ V_2 $. {Semicomplete split digraphs form an important subclass of the class of semicomplete multipartite digraphs.} In this paper, we prove that every 6-strong split digraph is 2-linked. This solves a problem posed by Bang-Jensen and Wang [J. Graph Theory, 2025]. We also show that every 5-strong semicomplete split digraph is 2-linked. This bound is tight already for semicomplete digraphs.

math.CO↗

arXiv2026

Measuring Neural Network Complexity via Effective Degrees of Freedom

Quantifying the complexity of feed-forward neural networks (FFNNs) remains challenging due to their nonlinear, hierarchical structure and numerous parameters. We apply generalized degrees of freedom (GDF) to measure model complexity in FFNNs with binary outcomes, adapting the algorithm for discrete responses. We compare GDF with both the effective number of parameters derived via log-likelihood cross-validation and the null degrees of freedom of Landsittel et al. Through simulation studies and a real data analysis, we demonstrate that GDF provides a robust assessment of model complexity for neural network models, as it depends only on the sensitivity of fitted values to perturbations in the observed responses rather than on assumptions about the likelihood. In contrast, cross-validation-based estimates of model complexity and the null degrees of freedom rely on the correctness of the assumed likelihood and may exhibit substantial variability. We find that GDF, cross-validation-based measures, and null degrees of freedom yield similar assessments of model complexity only when the fitted model adequately represents the data-generating mechanism. These findings highlight GDF as a stable and broadly applicable measure of model complexity for neural networks in statistical modeling.

stat.ME↗

arXiv2026

Analysis of Stakeholder Involvement in Nuclear Power Plant Cost Overruns and Implications for Contract Structuring

Existing evidence on nuclear power plant construction suggests that individual stakeholders involved in project delivery are often not responsible for all of the cost overruns in their scope of the project, which can lead to costly and time-consuming litigation to determine who is truly at fault for overruns. This study introduces a framework to model the share of overruns caused and received as payment by five stakeholders in a nuclear construction project: equipment suppliers, construction subcontractors, the design and management team, creditors, and the nuclear regulator. We then perform a contract analysis under three common contract structures - fixed-price, cost-plus, and performance-based - to show the profit misallocations that can result, revealing the advantages and disadvantages of each contract type for aligning stakeholder incentives. Regardless of the contract type chosen, strong owner involvement is crucial for project success, and we conclude with specific recommendations for project owners seeking to minimize cost overruns.

econ.GN↗

arXiv2025

Testing Risk Difference of Two Proportions for Combined Unilateral and Bilateral Data

In clinical studies with paired organs, binary outcomes often exhibit intra-subject correlation and may include a mixture of unilateral and bilateral observations. Under Donner's constant correlation model, we develop three likelihood-based test statistics (the likelihood ratio, Wald-type, and score tests) for assessing the risk difference between two proportions. Simulation studies demonstrate good control of type I error and comparable power among the three tests, with the score test showing slightly better stability. Applications to otolaryngologic and ophthalmologic data illustrate the methods. An online calculator is also provided for power analysis and risk difference testing. The score test is recommended for practical use and future studies with combined unilateral and bilateral binary data.

stat.ME↗