Unmanned Aerial Vehicles (UAVs) and Automated Guided Vehicles (AGVs) increasingly collaborate in logistics, surveillance, inspection tasks and etc. However, existing simulators often focus on a single domain, limiting cross-domain study. This paper presents the SkyRover, a modular simulator for UAV-AGV multi-agent pathfinding (MAPF). SkyRover supports realistic agent dynamics, configurable 3D environments, and convenient APIs for external solvers and learning methods. By unifying ground and aerial operations, it facilitates cross-domain algorithm design, testing, and benchmarking. Experiments highlight SkyRover’s capacity for efficient pathfinding and high-fidelity simulations in UAV-AGV coordination. We believe the SkyRover fills a key gap in MAPF research. Project is available at https://sites.google.com/view/mapf3d/home.

Langevin Dynamics (LD) and its discrete proposal have been widely applied in the field of Combinatorial Optimization (CO). Both sampling-based and data-driven approaches have benefited significantly from these methods. However, LD's reliance on Gaussian noise limits its ability to escape narrow local optima, requires costly parallel chains, and performs poorly in rugged landscapes or with non-strict constraints. These challenges have impeded the development of more advanced approaches. To address these issues, we introduce Fractional Langevin Dynamics (FLD) for CO, replacing Gaussian noise with $\alpha$-stable L\'evy noise. FLD can escape from local optima more readily via L\'evy flights, and in multiple-peak CO problems with high potential barriers it exhibits a polynomial escape time that outperforms the exponential escape time of LD. Moreover, FLD coincides with LD when $\alpha = 2$, and by tuning $\alpha$ it can be adapted to a wider range of complex scenarios in the CO fields. We provide theoretical proof that our method offers enhanced exploration capabilities and improved convergence. Experimental results on the Maximum Independent Set, Maximum Clique, and Maximum Cut problems demonstrate that incorporating FLD advances both sampling-based and data-driven approaches, achieving state-of-the-art (SOTA) performance in most of the experiments.

The development of sensor technology has resulted in the accumulation of extensive spatiotemporal traffic information, which holds great potential for predicting traffic patterns and improving traffic management strategies. Nevertheless, dealing with missing data poses a significant challenge for the intelligent traffic system (ITS). To address this issue, this study employs a nonconvex smoothly clipped absolute deviation (SCAD) penalty customized for tensors to surrogate tensor rank and incorporates the deep plug-and-play (PnP) prior into the low-rank tensor completion (LRTC) model. An efficient iterative framework is formulated to integrate these penalties into the alternating direction method of multipliers (ADMM) method. Moreover, two imputation methods, namely LRTC-SCAD and LRTC-SCAD-DeepPnP, are developed, affirming that the LRTC-SCAD method ensures convergence to the global optimum. We conduct simulated experiments using real-world traffic datasets, and our proposed methods outperform state-of-the-art imputation methods. For instance, on the Portland dataset, LRTC-SCAD achieves a noteworthy 9.86% improvement in mean absolute percentage error (MAPE) compared to the cutting-edge LRTC method while consuming only 28.26% of its total running time. Similarly, on the PeMS dataset, LRTC-SCAD-DeepPnP achieves an average 11.59% enhancement in MAPE, with visually compelling improvements in imputation results, further validating its efficacy in maintaining local consistency. The code is available athttps://github.com/peterchen96/LRTC_DeepPnP.

Abstract. The [Formula: see text]-blow-up of a given graph is obtained by replacing each edge by a clique of order [Formula: see text] where the new vertices of the cliques are distinct. Liu and Yuan determined the extremal graphs for the 3-blow-ups of a triangle and the [Formula: see text]-blow-ups of any complete graph with order at most [Formula: see text], respectively. We determine the Turán number for the [Formula: see text]-blow-ups of a complete graph with order at least [Formula: see text], completing the study of the extremal graphs for [Formula: see text]-blow-ups of complete graphs.

Cross-domain crowd counting has shown progressively improved performance. However, most methods fail to explicitly consider the transferability of different features between source and target domains. In this paper, we propose an innovative explicit Invariant Feature induced Cross-domain Knowledge Transformation framework to address the inconsistent domain-invariant features of different domains. The main idea is to explicitly extract domain-invariant features from both source and target domains, which builds a bridge to transfer more rich knowledge between two domains. The framework consists of three parts, global feature decoupling (GFD), relation exploration and alignment (REA), and graph-guided knowledge enhancement (GKE). In the GFD module, domain-invariant features are efficiently decoupled from domain-specific ones in two domains, which allows the model to distinguish crowds features from backgrounds in the complex scenes. In the REA module both inter-domain relation graph (Inter-RG) and intra-domain relation graph (Intra-RG) are built. Specifically, Inter-RG aggregates multi-scale domain-invariant features between two domains and further aligns local-level invariant features. Intra-RG preserves taskrelated specific information to assist the domain alignment. Furthermore, GKE strategy models the confidence of pseudolabels to further enhance the adaptability of the target domain. Various experiments show our method achieves state-of-theart performance on the standard benchmarks. Code is available at https://github.com/caiyiqing/IF-CKT.

Modern crowd counting methods in natural scenes, even when video datasets are available, are mostly based on images. Because of background interference or occlusion in the scene, these methods can easily lead to mutations and instability in density prediction. There has been minimal research on how to exploit the inherent consistency among adjacent frames to achieve high estimation accuracy of video sequences. In this study, we explore the long-term global temporal consistency in the video sequence and propose a novel Global Representation Guided Adaptive Fusion Network (GRGAF) for video crowd counting. The primary aim is to establish a long-term temporal representation among consecutive frames to guide the density estimation of local frames, which can alleviate the prediction instability caused by background noise and occlusions in crowd scenes. Moreover, in order to further enforce the temporal consistency, we apply the generative adversarial learning scheme and design a global-local joint loss, which can make the estimated density maps more temporally coherent. Extensive experiments on four challenging video-based crowd counting datasets (FDST, DroneCrowd, MALL and UCSD) demonstrate that our method makes effective use of spatio-temporal information of video and outperforms the other state-of-the-art approach.

In reality, complex scene plagues numerous scene graph generation models because realistic scene contains myriad of objects and complicated relationships. Most current methods suffer poor performance when encountering complex scenes. We find that there are two principal reasons for this phenomenon. First, the construction of graph loses sight of the hierarchy of objects. Second, there exists redundant information in feature optimization. To facilitate this issue, this paper proposes an innovative dual-hierarchy graph convolutional network (DH-GCN), which is a conceptually elegant and efficient top-down approach. In specific, DH-GCN leverages salient object detector to hierarchize objects and give gist nodes more accurate representation. Moreover, the dual-hierarchy message propagation is designed to refine the representation hierarchically and eliminate redundant information. Systematic experiments on Visual Genome dataset show the superiority of our method over strong baseline methods.

Unsupervised cross-domain counting research using synthetic datasets becomes imminent when considering the laborious labeling for supervised methods. However, the existing methods only focus on learning domain shared knowledge to narrow the gap between the source domain and target domain (inter-domain gap). Nevertheless, these methods do not consider the enormous distribution gap among the target domain data itself (intra-domain gap). In this paper, we propose a two-step domain adaptation method with multi-level feature response branches, which further uses the intra-domain knowledge to strengthen the target domain’s adaptability. Specifically, we first use different feature response branches to learn inter-domain knowledge more robustly, reducing the prediction inconsistency of different scenarios. Subsequently, the trained model is used to generate pseudo-labels for the target domain. The entire model was retrained by using pseudo-labels. Various experiments on synthetic dataset GCC and three real public datasets validate our proposed method’s availability with higher accuracy.

Hajós conjectured in 1961 that every $k$-chromatic graph contains a $K_k$-subdivision. In this paper, we consider the subdivision of $K_5^-$ and prove that every 4-connected graph contains a $K_5^-$-subdivision. This may make progress for the case k=5 of the Hajós' conjecture.