Low altitude uncrewed aerial vehicles (UAVs) are expected to facilitate the development of aerial-ground integrated intelligent transportation systems and unlocking the potential of the emerging low-altitude economy. However, several critical challenges persist, including the dynamic optimization of network resources and UAV trajectories, limited UAV endurance, and imperfect channel state information (CSI). In this paper, we offer new insights into low-altitude economy networking by exploring intelligent UAV-assisted vehicle-to-everything communication strategies aligned with UAV energy efficiency. Particularly, we formulate an optimization problem of joint channel allocation, power control, and flight altitude adjustment in UAV-assisted vehicular networks. Taking CSI feedback delay into account, our objective is to maximize the vehicle-to-UAV communication sum rate while satisfying the UAV's long-term energy constraint. To this end, we first leverage Lyapunov optimization to decompose the original long-term problem into a series of per-slot deterministic subproblems. We then propose a diffusion-based deep deterministic policy gradient (D3PG) algorithm, which innovatively integrates diffusion models to determine optimal channel allocation, power control, and flight altitude adjustment decisions. Through extensive simulations using real-world vehicle mobility traces, we demonstrate the superior performance of the proposed D3PG algorithm compared to existing benchmark solutions.

Graph sampling plays an important role in data mining for large networks. Specifically, larger networks often correspond to lower sampling rates. Under the situation, traditional traversal-based samplings for large networks usually have an excessive preference for densely-connected network core nodes. Aim at this issue, this paper proposes a sampling method for unknown networks at low sampling rates, called SLSR, which first adopts a random node sampling to evaluate a degree threshold, utilized to distinguish the core from periphery, and the average degree in unknown networks, and then runs a double-layer sampling strategy on the core and periphery. SLSR is simple that results in a high time efficiency, but experimental evaluation confirms that the proposed method can accurately preserve many critical structures of unknown large networks with low sampling rates and low variances.

Graph sampling based Graph Convolutional Networks (GCNs) decouple the sampling from the forward and backward propagation during minibatch training, which exhibit good scalability in terms of layer depth and graph size. We propose HIS_GCNs, a hierarchical importance graph sampling based learning method. By constructing minibatches using sampled subgraphs, HIS_GCNs gives attention to the importance of both core and periphery nodes/edges. Specifically, it preserves the centrum of the core to most minibatches, which maintains connectivity between periphery nodes, and samples periphery edges without core node interference, in order to keep more long chains composed entirely of low-degree nodes in the same minibatch. In addition, we verify the effectiveness of HIS_GCNs in reducing node embedding variance and chain information loss. Experiments on GCNs and other Graph Neural Networks (GNNs) with node classification tasks on five large-scale graphs confirm superior performance of the proposed hierarchical importance sampling method in both accuracy and training time.

We extended the surface element method proposed by Reitan and Higgins for calculating the capacitance of cubes, subdividing each face of a cube into up to $600 \times 600$ Subsquares. When each face was divided into \(90 \times 90\) Subsquares, the capacitance of the unit cube reached a maximum value of $0.6608$ cm ($0.7352$ pF). We further applied this method to compute the capacitance of hollow cylinders by dividing them into $q$ annular rings (each $1$ cm in width), with each ring subdivided into $m$ square elements ( $1$ cm side length). The capacitance of hollow cylinders under varying $q/m$ ratios was calculated and compared with Lekner's numerical results and Cavendish's experimental measurements, showing excellent agreement with both.

Graph sampling-based Graph Convolutional Networks (GCNs) decouple sampling from forward and backward propagation during minibatch training, enhancing scalability with respect to layer depth and graph size. We propose HIS_GCNs, a hierarchical importance sampling-based learning method. By constructing minibatches using sampled subgraphs, HIS_GCNs focuses on the importance of both the core and periphery in a scale-free training graph. Specifically, it preserves the centrum of the core in most minibatches, which maintains connectivity between periphery nodes, and samples periphery edges without core node interference, which allows longer chains composed entirely of low-degree nodes remain within the same minibatch. HIS_GCNs can maximize the discrete Ricci curvature (i.e., Ollivier-Ricci curvatures) of the edges in a subgraph, enabling preservation of important chains for information propagation. This approach can achieve a low node embedding variance and a high convergence speed. Diverse experiments on Graph Neural Networks (GNNs) with node classification tasks confirmed the superior performance of HIS_GCNs in terms of both accuracy and training time. Open-source code (this https URL).