arXiv subjects

Jia Zhou

Publications and source records attributed to Jia Zhou.

At least 19 recordsLinked to original sources

arXiv2026

Two-block paths in oriented graphs under the Ore-type condition

Stein conjectured that for every positive integer $k$, every oriented graph with minimum semi-degree greater than $k/2$ contains every oriented path of length $k$ [Springer Optim.Appl. 165 (2020), 459--486]. For directed paths this is a classical result of Jackson (1981). The two-block case of the conjecture was established by Chen, Hou and Zhou (2025). In this paper we prove the two-block analogue of Jackson's theorem. For all positive integers $s$ and $r$, let $P(s,r)$ be the oriented path consisting of two directed paths of lengths $s$ and $r$ with a common terminal vertex, and let $Q(s,r)$ be its reverse. We show that for all $K\ge3$ and all $s,r\ge1$ with $s+r\le K$, every oriented graph $D$ with $δ(D)\ge K$ and $d_D^+(u)+d_D^-(v)\ge K-1$ for every ordered pair of distinct vertices $(u,v)\notin A(D)$ contains both $P(s,r)$ and $Q(s,r)$. Our result is the two-block analogue of Jackson's theorem, and it extends the two-block result of Chen, Hou and Zhou. The proof iterates a shift of the terminal vertex of a longest path.

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. We prove that it is NP-complete to decide whether a digraph admits an arc-decomposition with properties $(P_1,P_2)$ where $(P_1,P_2)\in \{$(perfect matching, having no odd cycle), (perfect matching, strong), (perfect matching, having an out-branching), (cycle factor, having no odd cycle)$\}$. All four problems remain NP-complete even when restricted to strongly connected digraphs. We also prove that every strongly connected digraph with minimum semi-degree at least three contains two vertex-disjoint cycles whose simultaneous arc deletion leaves the digraph strongly connected. These results settle some open problems posed by Bang-Jensen, Bessy, Gonçalves, and Picasarri-Arrieta [Theoret. Comput. Sci. 928 (2022), 167--182].

math.CO↗

arXiv2026

MCSplat: Multi-View Photometric and Geometric Consistent Feed-Forward Gaussian Splatting for Driving Scenes

Driving-scene reconstruction via feed-forward Gaussian splatting from sparse multi-view images remains challenging due to two factors. First, cross-camera photometric inconsistency, caused by variations in exposure, ISP, and illumination, can be incorrectly absorbed into Gaussian geometry. Second, unreliable local geometric supervision arises from normal-based constraints near depth discontinuities. To address these issues, we present \textbf{MCSplat}, a multi-view consistent feed-forward Gaussian splatting framework for driving scenes. MCSplat constructs a canonical appearance space from depth-guided multi-camera correspondences to decouple geometry learning from camera-specific appearance. A multi-scale Bilateral Grid Transformer restores raw camera appearance from canonical renderings, enabling photometric supervision without contaminating Gaussian geometry. To improve local geometric reliability, we estimate Fisher-information-based uncertainty from photometric sensitivity and use it to adaptively weight surface-oriented self-supervision. Extensive experiments demonstrate improved reconstruction quality and generalization across driving datasets. Geometry-oriented evaluations further reveal enhanced cross-view depth consistency and local surface-normal agreement, while qualitative results show fewer geometric artifacts and more coherent structures across overlapping views.

cs.CV↗

arXiv2026

A linear bound for a connectivity partition in graphs

Kühn and Osthus proved that, for every positive integer $\ell$, every $2^{16}\ell^2$-connected graph $G$ has a partition $V(G)=S\cup T$ such that $G[S]$ and $G[T]$ are $\ell$-connected and $d_T(v)\geq \ell$ for every $v\in S$. And they asked whether the quadratic bound can be replaced by a linear bound. In this paper, we answer this question in the affirmative by proving that every $641\ell$-connected graph $G$ has a partition $V(G)=S\cup T$ such that $G[S]$ and $G[T]$ are $\ell$-connected and $d_T(v)\ge \ell$ for every $v\in S$. The proof integrates the Moser-Tardos resampling algorithm.

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

Ramsey--Turán 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 $μ>0$, there is a real $γ$ such that every sufficiently large oriented graph $D$ with $\ell\mid |D|$, minimum semidegree at least $(1/4+μ)|D|$ and independence number at most $γ|D|$ has a $\overrightarrow{C}$-factor. The constant $1/4$ is asymptotically tight. This proof establishes Ramsey-Turán type lattice absorption lemmas and an almost covering theorem via the oriented tree embedding lemma under chromatic number constraints.

math.CO↗

arXiv2026

Dominant-Degree Conditions for Ramsey--Turán 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 $μ>0$, there exist $γ>0$ and $n_0$ such that every $n\ge n_0$ with $\ell\mid n$ and every $n$-vertex oriented graph $D$ satisfying \[ α(D)\leγn \text{ and } {\sigore(D)\ge\left(\frac34+μ\right)n} \] 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, $C:=\frac34α(D)-2$ for $s=2$ and $C:=\frac14α(D)-\frac32$ 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 Chvátal--Erdős type condition for supereulerian digraphs with $α_{2}=4$

A digraph is \textbf{supereulerian} if it contains a spanning closed trail. Let $α_2(D)$ denote the maximum cardinality of a vertex set inducing no 2-cycle. In this paper, we characterize supereulerianity in a strong digraph $D$ with $α_2(D)=4$ by proving that a strong digraph $D$ with $α_2(D)=4$ and $λ(D)\ge 2$ is supereulerian if and only if $D$ does not belong to an exceptional family $\mathcal H$ of $2$-arc-strong digraphs with $α_2(D)=4$. Furthermore, every strong digraph satisfying $α_2(D)=4$ and $λ(D)\geq3$ is supereulerian.

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 {$δ^0(D)\geq 26k+15$} 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

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

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↗

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

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↗