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A mixed Laguerre-Legendre spectral collocation schemes is constructed for initial-boundary value problem of the nonlinear Fokker-Planck nonhomogeneous equations and the linear Fokker-Planck homogeneous equation by using the Laguerre interpolation functions in velocity, and the Legendre interpolation functions in time, which is a bivariate Lagrange interpolation approximation function based on Legendre and Laguerre Gauss quadrature notes. The original problem is changed into a matrix equation and solved by Newton iteration. Numerical experiments show that the algorithm has high accuracy and efficiency.

Multifactorial diseases demand therapeutics that can modulate multiple targets for enhanced safety and efficacy, yet the clinical approval of multitarget drugs remains rare. The integration of machine learning (ML) and deep learning (DL) in drug discovery has revolutionized virtual screening. This study investigates the synergy between ML/DL methodologies, molecular representations, and data augmentation strategies. Notably, we found that SVM can match or even surpass the performance of state-of-the-art DL methods. However, conventional data augmentation often involves a trade-off between the true positive rate and false positive rate. To address this, we introduce Negative-Augmented PU-bagging (NAPU-bagging) SVM, a novel semi-supervised learning framework. By leveraging ensemble SVM classifiers trained on resampled bags containing positive, negative, and unlabeled data, our approach is capable of managing false positive rates while maintaining high recall rates. We applied this method to the identification of multitarget-directed ligands (MTDLs), where high recall rates are critical for compiling a list of interaction candidate compounds. Case studies demonstrate that NAPU-bagging SVM can identify structurally novel MTDL hits for ALK-EGFR with favorable docking scores and binding modes, as well as pan-agonists for dopamine receptors. The NAPU-bagging SVM methodology should serve as a promising avenue to virtual screening, especially for the discovery of MTDLs. [ABSTRACT FROM AUTHOR]

Addressing the issue of incorrect and missed detections caused by the complex types, uneven scales, and small sizes of defect targets in transmission lines, this paper proposes a defect-detection method based on cross-scale feature fusion, PGE-YOLO. Firstly, feature extraction is enriched by replacing the convolutional blocks in the backbone network that need to be cascaded and fused using the Par_C2f network module, which incorporates a parallel network (ParNet). Secondly, a four-layer efficient multi-scale attention (EMA) mechanism is incorporated into the network's neck to address long and short dependency issues. This enhancement aims to improve global information retention by employing parallel substructures and integrating cross-space feature information. Finally, the paradigm of generalized feature fusion (GFPN) is introduced and reconfigured to develop a novel CE-GFPN. This model effectively integrates shallow feature information with deep feature information to enhance the capability of feature fusion and improve detection performance. Using a real transmission line multi-defect dataset from UAV aerial photography and the CPLID dataset, ablation and comparison experiments with various models demonstrated that our model achieved superior results. Compared to the initial YOLOv8n model, our model increased the detection accuracy by 6.6% and 1.2%, respectively, while ensuring there is no surge in the number of parameters. This ensures that the real-time and accuracy requirements for defect detection in the industry are satisfied. [ABSTRACT FROM AUTHOR]