Spectrum of SYK model II: Central limit theorem

In our previous paper [R. Feng, G. Tian and D. Wei, Spectrum of SYK model, Peking Math. J. 2 (2019) 41–70], we derived the almost sure convergence of the global density of eigenvalues of random matrices of the SYK model. In this paper, we will prove the central limit theorem for the linear statistics of eigenvalues of the SYK model and compute its variance.

Object Detection in UAV Images via Global Density Fused Convolutional Network

Object detection in Unmanned Aerial Vehicle (UAV) images plays fundamental roles in a wide variety of applications. As UAVs are maneuverable with high speed, multiple viewpoints, and varying altitudes, objects in UAV images are distributed with great heterogeneity, varying in size, with high density, bringing great difficulty to object detection using existing algorithms. To address the above issues, we propose a novel global density fused convolutional network (GDF-Net) optimized for object detection in UAV images. We test the effectiveness and robustness of the proposed GDF-Nets on the VisDrone dataset and the UAVDT dataset. The designed GDF-Net consists of a Backbone Network, a Global Density Model (GDM), and an Object Detection Network. Specifically, GDM refines density features via the application of dilated convolutional networks, aiming to deliver larger reception fields and to generate global density fused features. Compared with base networks, the addition of GDM improves the model performance in both recall and precision. We also find that the designed GDM facilitates the detection of objects in congested scenes with high distribution density. The presented GDF-Net framework can be instantiated to not only the base networks selected in this study but also other popular object detection models.

Modelling Ship Density Using a Molecular Dynamics Approach

Ship density is widely accepted as a basic and major indicator to reflect the marine traffic situation, but it has some limitations in representing the compactness and complexity of ship traffic. To overcoming these limitations, the paper proposes a novel ship density model based on the radial distribution function in molecular dynamics. The proposed model can identify the density and compactness of traffic around each ship and then map the ship density from a microscopic perspective. In addition, the proposed model can identify the global density and the complexity of ship traffic to some extent in the macroscopic perspective. Utilising case studies, the effectiveness of the proposed model is validated through the analysis of ship density in several regions in the Bohai Strait area. The proposed model is developed to help marine surveillance operators gain a better understanding of the traffic situation and to assist them in their work, eventually contributing to navigational safety.