Although many state-of-the-art object detectors have been developed, detecting small and densely packed objects with complicated orientations in remote sensing aerial images remains challenging. For object detection in remote sensing aerial images, different scales, sizes, appearances, and orientations of objects from different categories could most likely enlarge the variance in the detection error. Undoubtedly, the variance in the detection error should have a non-negligible impact on the detection performance. Motivated by the above consideration, in this paper, we tackled this issue, so that we could improve the detection performance and reduce the impact of this variance on the detection performance as much as possible. By proposing a scaled smooth L${}_1$ loss function, we developed a new two-stage object detector for remote sensing aerial images, named Faster R-CNN-NeXt with RoI-Transformer. The proposed scaled smooth L${}_1$ loss function is used for bounding box regression and makes regression invariant to scale. This property ensures that the bounding box regression is more reliable in detecting small and densely packed objects with complicated orientations and backgrounds, leading to improved detection performance. To learn rotated bounding boxes and produce more accurate object locations, a RoI-Transformer module is employed. This is necessary because horizontal bounding boxes are inadequate for aerial image detection. The ResNeXt backbone is also adopted for the proposed object detector. Experimental results on two popular datasets, DOTA and HRSC2016, show that the variance in the detection error significantly affects detection performance. The proposed object detector is effective and robust, with the optimal scale factor for the scaled smooth L${}_1$ loss function being around 2.0. Compared to other promising two-stage oriented methods, our method achieves a mAP of 70.82 on DOTA, with an improvement of at least 1.26 and up to 16.49. On HRSC2016, our method achieves an mAP of 87.1, with an improvement of at least 0.9 and up to 1.4.

In this paper, we introduce a new class of set-valued risk measures which satisfies cash sub-additivity. Dual representation for them is provided. Moreover, we also investigate dynamic set-valued cash sub-additive risk measures and discuss the corresponding multi-portfolio time consistency. The equivalent characterization of the multi-portfolio time consistency is given. Finally, an example is also given to illustrate the introduction of set-valued cash sub-additive risk measures. The present paper can be considered as a set-valued extension of scalar cash sub-additive risk measures introduced by El Karouii and Ravanelli [8].

Inspired by the consideration of some inside and future market information in financial market, a class of anticipated backward doubly stochastic Volterra integral equations (ABDSVIEs) are introduced to induce dynamic risk measures for risk quantification. The theory, including the existence, uniqueness and a comparison theorem for ABDSVIEs, is provided. Finally, dynamic convex risk measures by ABDSVIEs are discussed.

This study addressed the autonomous planning of three-dimensional (3D) underwater inspection paths for autonomous underwater vehicles (AUVs) in marine ranching by integrating differential evolution and particle swarm optimization (PSO) algorithms. First, a modified PSO algorithm incorporating swap operators, mutation, and crossover strategies was employed to enable autonomous obstacle avoidance during the inspection of offshore net cages in fish farms situated within a 3D marine environment. This approach addresses the problem of planning full-traversal paths for multiple inspection points. Second, the performance of the proposed algorithm was assessed through comparative tests with other algorithms. The proposed algorithm demonstrated significant improvements in convergence speed, accuracy, and stability under complex scenarios involving multiple optima and intense oscillations. To validate the superiority and overall planning proficiency of the modified method, an experimental setup comprising of two distinct 3D marine cage environments with a series of checkpoints was utilized. The experimental results demonstrated the ability of the proposed algorithm to generate an optimal path while traversing all inspection points of fish farm offshore net cages. By ensuring the safety of AUVs and closely adhering to the surfaces of offshore net cages during the inspection process, the algorithm exhibits remarkable adaptability to specific application scenarios, effectively mitigating concerns related to local optima and premature convergence.