We present three reduced integrable hierarchies of nonlocal integrable NLS type equations from a vector integrable hierarchy associated with a matrix Lie algebra, not being A type. Three similarity transformations are taken to keep the invariance of the transformed zero curvature equations. The key step is to formulate a solution to a reduced stationary zero curvature equation so that the zero curvature formulation works for a reduced case.

To quantitatively estimate the risk of power system operation under extreme rainfall, a multi-scenario stochastic risk assessment method is proposed. First, a scenario generation scheme considering waterlogged faults of power facilities is constructed based on the storm water management model (SWMM) and the extreme learning machine method. These scenarios will be merged to several typical scenario sets for further processing. The outage of power facilities will induce power flow transfer which may consequently lead to transmission lines’ thermal limit violation. Semi-invariant and Gram-Charlier level expansion methods are adopted to analytically depict the probability density function and cumulative probability function of each line’s power flow. The optimal solution is performed by a particle swarm algorithm to obtain proper load curtailment at each bus, and consequently the violation probability of line thermal violations can be controlled within an allowable range. The volume of load curtailment as well as their importance are considered to quantitatively access the risk of power supply security under extreme precipitation scenarios. The effectiveness of the proposed method is verified in case studies based on the IEEE 24-bus system.

Water area segmentation in remote sensing is of great importance for flood monitoring. To overcome some challenges in this task, we construct the Water Index and Polarization Information (WIPI) multi-modality dataset and propose a multi-Modality Fusion and Gated multi-Filter U-Net (MFGF-UNet) convolutional neural network. The WIPI dataset enhances the water information and reduces the data dimension. In particular, the Cloud-Free label provided in the database effectively mitigates the issue of scarcity of labeled samples Since a single form or uniform kernel size cannot handle the variety in size and shape of water bodies, we proposed the gated multi-filter inception (GMF-Inception) module in our MFGF-UNet. Moreover, we utilize the attention mechanism by introducing the Gated Channel Transform (GCT) skip connection and integrating GCT into GMF- Inception to further improve model performance. Extensive experiments on three benchmarks, including WIPI, Chengdu and GF2020 datasets demonstrate that our method achieves favorable performance with lower complexity and better robustness against six competing approaches. For example, on WIPI, Chengdu and GF2020 datasets, the proposed MFGF-UNet model achieves F1 of 0.9191, 0.7410, and 0.8421, respectively, which average F1 on three datasets is 0.0045 higher than the U-Net model and reduces 62% average GFLOPs. New WIPI dataset, code and trained models have been released on GitHub