arXiv subjects
Publications and source records attributed to Hongliang Lu.
For fixed integers $k\ge3$ and $1\le d\le k-1$ and sufficiently large $n\in k\mathbb N$, we establish the sharp minimum $d$-degree thresholds that forces perfect matching in every $n$-vertex $k$-uniform hypergraphs. This was conjectued by Treglown and Zhao, and the $d=1$ case was conjectued by K\"uhn, Osthus and Treglown.
Energy feasibility under wind uncertainty is a critical safety issue for low-altitude air-ground delivery. In truck-UAV systems, UAVs complete assigned deliveries and safely return to a mobile truck or depot, while wind-induced propulsion costs vary online and are only partially observable. Existing routing methods often rely on static or deterministic energy models, which may underestimate headwind, crosswind, battery-voltage, and return-feasibility risks. This paper proposes Energy-Aware Wind-Resilient Routing (EWR), an online risk-sensitive planning framework for wind-aware and energy-safe UAV routing. The delivery environment is represented as a time-dependent directed energy graph whose edge costs are updated using delayed noisy wind estimates, payload states, and conservative uncertainty margins. Experiments using synthetic delivery graphs with replayed wind logs from a public truck-UAV delivery dataset show that EWR improves mission success rates and reduces wind-induced return failures.
Vision-Language-Action (VLA) models transform representations from pretrained vision-language models (VLMs) into robot actions, yet the interface that routes intermediate VLM features into action decoders remains underexplored. Existing designs either expose only a narrow part of the representation hierarchy or rigidly match each decoder block to one VLM layer, restricting access to complementary task evidence across depths. We introduce LIRA, a local cross-layer action-conditioning mechanism that formulates VLM-to-action conditioning as depth-aware information routing. LIRA operates on task-token features and LIRA Query features derived from intermediate VLM states, then assigns each Parallel Fusion Block a depth-aligned local window centered on its corresponding VLM layer. Parallel Fusion Blocks aggregate neighboring LIRA Query features and integrate them with task-token features and proprioceptive inputs before action prediction. This routing interface leaves the backbone architecture, action decoder, and supervised training recipe unchanged. Across LIBERO, LIBERO-Plus, CALVIN ABC$\rightarrow$D, and real-world manipulation, LIRA improves the principal aggregate metrics over the VLA-Adapter baseline under the same 0.5B-parameter configuration. In zero-shot transfer to LIBERO-Plus, LIRA increases average success from 59.1% to 78.0%, an 18.9-point gain indicating improved robustness under controlled distribution shifts.
A balanced $k$-partite $k$-graph is a $k$-uniform hypergraph such that every edge intersects each partition class in exactly one vertex, where each partition class has size $n$. Lo and Markstr\"om (2014) determined the minimum vertex-degree threshold for perfect matchings in balanced \(3\)-partite \(3\)-graphs. In this paper, we determine the minimum vertex-degree threshold for balanced \(4\)-partite \(4\)-graphs. The proof relies on a reduction framework for \(k\)-partite \(k\)-graphs, through which the existence of a perfect fractional matching is converted into a finite-dimensional optimization problem.
In this note, we resolve the remaining open case of a conjecture by Han and Zhao concerning the codegree threshold for Hamilton $\ell$-cycles in $k$-uniform hypergraphs. Specifically, we prove that for integers $k\ge 3$, $3k/4\le \ell<k$, with $k\not\equiv 0 \pmod{k-\ell}$, and for all sufficiently large $n$ divisible by $k-\ell$, every $n$-vertex $k$-uniform hypergraph $H$ satisfying \[ \delta_{k-1}(H)\ge \frac{n}{(k-\ell)\left\lceil \frac{k}{k-\ell}\right\rceil} \] contains a Hamilton $\ell$-cycle. Our proof builds on the framework of Gan, Han and Xu, and refines their argument to obtain, at the exact threshold, the required family of paths.
Accurate 4D trajectory prediction and closed-loop tracking are essential for Unmanned Aerial Vehicle (UAV) swarms to achieve safe and efficient operations in complex low-altitude environments such as urban airspaces, industrial sites, and indoor facilities. However, this task remains challenging due to intrinsic nonlinearity of UAV swarm dynamics and strict real-time constraints of swarm formation control. To address these challenges, we propose a unified framework that couples coarse-to-fine trajectory forecasting with uncertainty-aware Distributed Nonlinear Model Predictive Control (DNMPC). Our approach features two key innovations: 1) a dimension-decoupled trajectory prediction module that reduces computational complexity by forecasting axis-wise motion, and 2) a diffusion-based residual dynamics refinement module that captures temporally correlated dynamic uncertainties. These refined predictions are then integrated into a DNMPC loop to ensure formation stability. We also introduce a synchronized multi-scenario 4D UAV swarm dataset spanning six representative airspace scenarios. The dataset contains over \textbf{7,900} frames of synchronized three-UAV trajectories with frame-level annotations of speed intention and target sector. Extensive experiments demonstrate that our approach outperforms state-of-the-art baselines, reducing trajectory tracking error by up to \textbf{10-15\%} and achieving sub-\textbf{0.07\,m} average tracking error in complex urban and industrial environments, while maintaining real-time inference speeds of 34 FPS (sub-30 ms latency) suitable for agile flight.
Let $H$ be a 3-partite 3-uniform hypergraph whose three vertex classes all have size $n$. For a vertex $v \in V(H)$, the link graph $N_H(v)$ is defined on $V(H)\setminus\{v\}$ with edge set $\{e\setminus\{v\}: v\in e\in E(H)\}$, and we denote by $\rho(N_H(v))$ its spectral radius. We prove that for every $\alpha>0$ there exists $n_0$ such that for all $n\ge n_0$ the following holds: if \[ \rho\bigl(N_H(v)\bigr) > \left(\frac{\sqrt{2}}{2}+\alpha\right)n \] for every vertex $v\in V(H)$, then $H$ contains a perfect matching. This spectral condition is asymptotically best possible.
Strongly correlated quantum states, such as charge density waves (CDWs), are exquisitely sensitive to Fermi surface topology and lattice symmetry, and are typically quenched by heavy carrier doping. In two-dimensional (2D) systems, however, macroscopic geometric curvature emerges as a novel structural degree of freedom to modulate microscopic quantum coherence. This raises a compelling physical question: can non-Euclidean geometric deformations compete with extreme electronic perturbations to reshape, or even revive, a quenched macroscopic quantum order? Here, by constructing monolayer TiSe$_2$-NbSe$_2$ heterostructure on a BLG/SiC substrate for the first time, we report the curvature-driven revival of a frustrated charge order in a non-Euclidean space. Low-temperature angle-resolved photoemission spectroscopy (ARPES) reveals a massive interfacial charge transfer, which destroys the global Fermi surface nesting and completely suppresses the long-range CDW order in Euclidean flat regions. Strikingly, high-resolution scanning tunneling microscopy (STM) reveals that a novel, non-linear CDW state miraculously survives, remaining strictly localized within morphologically distorted, non-Euclidean nanoscale curved regions. Atomistic simulations unravel the structural origin of this phenomenon, demonstrating that interfacial twist and lattice mismatch spontaneously generate a corrugated superlattice.
Vision-Language-Action (VLA) models have demonstrated promising capability in autonomous driving, highlighting the potential of unified multimodal architectures for jointly modeling perception and planning. However, how current VLA-based driving behavior is grounded in visual information remains poorly understood. Existing evaluation protocols mainly focus on aggregate performance metrics, lacking structured and practical diagnostics to quantify visual-behavior dependency. In this work, we introduce a structured multi-level visual perturbation framework to analyze visual-behavior dependency in VLA-based driving models systematically. The framework organizes controlled visual perturbations along three complementary dimensions: channellevel degradation, information-level disruption, and structurelevel modification. We apply it to VLA-based driving systems and evaluate behavioral responses under both open-loop trajectory prediction and interactive closed-loop safety evaluation. Experimental results reveal evaluation-dependent dependency patterns and uneven visual grounding across abstraction levels. These findings call for more structured analyses and principled design of VLA driving models to better understand how visual information shapes behavior and develop safer, more robust systems.
Recent feed-forward models have significantly advanced geometry perception for inferring dense 3D structure from sensor observations. However, its essential capabilities remain fragmented across multiple incompatible paradigms, including online perception, offline reconstruction, multi-modal integration, long-horizon scalability, and metric-scale estimation. We present UniT, a unified model built upon a novel Group Autoregressive Transformer, which reformulates these seemingly disparate capabilities within a single framework. The key idea is to treat groups of sensor observations as the basic autoregressive units and predict the corresponding point maps in an anchor-free and scale-adaptive manner. More specifically, diverse view configurations in both online and offline settings are naturally unified within a single group autoregression process. By varying the group size, online mode operates over multiple autoregressive steps with single-frame groups, whereas offline mode aggregates a multi-frame group in a single forward pass. Meanwhile, a queue-style KV caching mechanism ensures bounded autoregressive memory over long horizons. This is enabled by reducing long-range dependencies on early frames through anchor-free relational modeling, thereby allowing outdated memory to be discarded on the fly. To improve metric-scale generalization across scenes, a scale-adaptive geometry loss is further introduced within this framework. It couples relative geometric constraints with a partial absolute scale term, implicitly regularizing global scale and inducing a progressive transition from scale-invariant geometry to metric-scale solutions. Together with a dedicated modal attention module for integrating auxiliary modalities, UniT achieves state-of-the-art performance in unified geometry perception, as validated on ten benchmarks spanning seven representative tasks.
Diffusion and rectified flow (RF) models generate high-fidelity images and videos, but their iterative velocity-field evaluations are computationally expensive. Existing caching methods accelerate sampling by skipping timesteps, yet their coarse approximations introduce accumulated errors over long skip intervals and degrade quality under aggressive acceleration. We propose TACache (Trajectory-Aware Cache), a training-free acceleration framework following a skip-then-compensate paradigm. TACache performs an orthogonal decomposition of discrete velocity acceleration along the RF trajectory into a parallel component and an orthogonal residual, isolating the magnitude and directional sources of per-step approximation error. The framework operates in two stages: offline, cumulative variation thresholds on the magnitude and direction indicators yield the skip schedule and bound how far each skip interval may extend; online, at each skipped step the offline statistics are combined with the sample's historical orthogonal direction to reconstruct the skipped velocity without additional model evaluations. Experiments on BAGEL, FLUX.1-dev, and Wan2.1-1.3B show that TACache achieves up to 4.14 speedup on text-to-image generation and 2.11 speedup on text-to-video generation, with consistent improvements over prior cache-based methods on all reference-based fidelity metrics. Code will be released soon.
Optimization modeling is the process of translating real-world decision problems, often described in natural language, into formal mathematical formulations and executable solver code. While recent advances in large language models have shown promise in automating this process, most existing approaches remain one-shot: a model produces a formulation once, without executing it, conditioning on solver feedback, or iteratively revising errors. This stands in sharp contrast to real-world optimization modeling, which is inherently interactive and proceeds through repeated solve-debug-revise cycles. We introduce PEARL, a system for interactive optimization modeling that uses Python execution and mathematical programming solvers inside this loop. Rather than relying on a fixed repair workflow, PEARL learns when to test partial models, how to revise from solver diagnostics, and when to stop. It operates in a multi-turn tool-integrated setting where intermediate execution results, feasibility signals, and solution checks are used to improve both formulations and solver code before finalization. Across diverse optimization benchmarks, PEARL substantially improves verified solve rates over strong one-shot and tool-augmented baselines; notably, our PEARL-Qwen3-\textbf{4B} model outperforms the much larger DeepSeek-V3.2-\textbf{685B} in both macro- and micro-averaged accuracy on optimization modeling tasks.
Benchmarks within the OpenClaw ecosystem have thus far evaluated exclusively assistant-level tasks, leaving the academic-level capabilities of OpenClaw largely unexamined. We introduce AcademiClaw, a bilingual benchmark of 80 complex, long-horizon tasks sourced directly from university students' real academic workflows -- homework, research projects, competitions, and personal projects -- that they found current AI agents unable to solve effectively. Curated from 230 student-submitted candidates through rigorous expert review, the final task set spans 25+ professional domains, ranging from olympiad-level mathematics and linguistics problems to GPU-intensive reinforcement learning and full-stack system debugging, with 16 tasks requiring CUDA GPU execution. Each task executes in an isolated Docker sandbox and is scored on task completion by multi-dimensional rubrics combining six complementary techniques, with an independent five-category safety audit providing additional behavioral analysis. Experiments on six frontier models show that even the best achieves only a 55\% pass rate. Further analysis uncovers sharp capability boundaries across task domains, divergent behavioral strategies among models, and a disconnect between token consumption and output quality, providing fine-grained diagnostic signals beyond what aggregate metrics reveal. We hope that AcademiClaw and its open-sourced data and code can serve as a useful resource for the OpenClaw community, driving progress toward agents that are more capable and versatile across the full breadth of real-world academic demands. All data and code are available at https://github.com/GAIR-NLP/AcademiClaw.
Ensuring energy feasibility under wind uncertainty is critical for the safety and reliability of UAV delivery missions. In realistic truck-drone logistics systems, UAVs must deliver parcels and safely return under time-varying wind conditions that are only partially observable during flight. However, most existing routing approaches assume static or deterministic energy models, making them unreliable in dynamic wind environments. We propose Battery-Efficient Routing (BER), an online risk-sensitive planning framework for wind-sensitive truck-assisted UAV delivery. The problem is formulated as routing on a time dependent energy graph whose edge costs evolve according to wind-induced aerodynamic effects. BER continuously evaluates return feasibility while balancing instantaneous energy expenditure and uncertainty-aware risk. The approach is embedded in a hierarchical aerial-ground delivery architecture that combines task allocation, routing, and decentralized trajectory execution. Extensive simulations on synthetic ER graphs generated in Unreal Engine environments and quasi-real wind logs demonstrate that BER significantly improves mission success rates and reduces wind-induced failures compared with static and greedy baselines. These results highlight the importance of integrating real-time energy budgeting and environmental awareness for UAV delivery planning under dynamic wind conditions.
Let $\gamma$ be a constant such that $0 < \gamma < 1$, and let $n$ be a sufficiently large integer. Consider a $3$-uniform hypergraph $H$ on $n$ vertices. In 2013, K\"{u}hn, Osthus, and Treglown, along with Khan independently, proved that for large enough $n$ with $n\equiv 0\pmod{3}$, if $\delta_1(H)\geq\binom{2n/3}{2}$, then $H$ admits a perfect matching. For any vertex $v\in V(H)$, we define $N_H(v)$ as the $2$-graph with vertex set $V(H)\setminus\{v\}$ and edge set $E(N_H(v)) = \{e\subseteq V(H)\setminus\{v\}: e\cup \{v\}\in E(H)\}$. In this paper, we show that if $\rho(N_H(v)) > (2/3+\gamma)n$ for all $v\in V(H)$, where $\rho(N_H(v))$ denotes the spectral radius of $N_H(v)$, then $H$ has a perfect matching. This bound is asymptotically tight. Furthermore, for integer $s$ satisfying $n\geq 3s+3$, we establish that if \[ \rho(N_H(v))>\frac{1}{2}(s-1+\sqrt{(s-1)^2+4s(n-s-1)})\] holds for every $v\in V(H),$ then $H$ admits a fractional matching of size $s+1$. Notably, this second spectral bound is tight.
Let $n, r, s$ be three positive integers such that $n\geq 2s+5$. Let $K_r$ denote the complete graph of order $r$. Given a graph $F$, the anti-Ramsey number $ar(n,F)$ is defined as the minimum number $C$ such that any edge-coloring of $K_n$ with exactly $C$ colors contains a rainbow copy of $F$. Let $H$ be an edge-colored graph on $K_n$ with at least $g(n,s)$ colors, where \[ g(n,s)=\max\left\{ \binom{n}{2} - \binom{n - s + 1}{2} + 5, \binom{2s - 1}{2} + n + 1 \right\}. \] In this paper, we establish a stability type result for the anti-Ramsey number of matchings. Specifically, if $H$ does not have a rainbow matching of size $s+2$, then $H$ contains either a monochromatic complete graph $K_{n-s}$ or a monochromatic $K_{n - 2s - 1} \vee \overline{K_{2s + 1}}$.
Participatory urban sensing leverages human mobility for large-scale urban data collection, yet existing methods typically rely on centralized optimization and assume homogeneous participants, resulting in rigid assignments that overlook personal preferences and heterogeneous urban contexts. We propose MAPUS, an LLM-based multi-agent framework for personalized and fair participatory urban sensing. In our framework, participants are modeled as autonomous agents with individual profiles and schedules, while a coordinator agent performs fairness-aware selection and refines sensing routes through language-based negotiation. Experiments on real-world datasets show that MAPUS achieves competitive sensing coverage while substantially improving participant satisfaction and fairness, promoting more human-centric and sustainable urban sensing systems.
A famous conjecture of Erd\H{o}s asserts that for $k\ge 3$, the maximum number of edges in an $n$-vertex $k$-uniform hypergraph without $s+1$ pairwise disjoint edges is $\max\{\binom{n}{k}-\binom{n-s}{k},\binom{sk+k-1}{k}\}$. This problem has been central in extremal combinatorics, with substantial progress in the literature, including a complete solution for $k=3$ due to the first author. In this paper, we make progress towards the $4$-uniform case, proving the conjecture for $n\ge 5s$ and sufficiently large $n$, thereby taking a first step analogous to the $3$-uniform case. The main technical contribution is a stability result of independent interest. We further apply this stability to resolve two new instances of conjectures on the minimum $d$-degree threshold for matchings in $5$- and $6$-uniform hypergraphs, in a strengthened form.