Air quality data， as a typical spatio-temporal data， exhibits complex multi-scale intrinsic characteristics and has abrupt change problem. Concerning the problem that existing air quality prediction methods perform poorly when dealing with air quality prediction tasks containing large amount of abrupt change， a Multi-Granularity abrupt Change Fitting Network （MACFN） for air quality prediction was proposed. Firstly， multi-granularity feature extraction was first performed on the input data according to the periodicity of air quality data in time. Then， a graph convolution network and a temporal convolution network were used to extract the spatial correlation and temporal dependence of the air quality data， respectively. Finally， to reduce the prediction error， an abrupt change fitting network was designed to adaptively learn the abrupt change part of the data. The proposed network was experimentally evaluated on three real air quality datasets， and the Root Mean Square Error （RMSE） decreased by about 11.6%， 6.3%， and 2.2% respectively， when compared to the Multi-Scale Spatial Temporal Network （MSSTN）. The experimental results show that MACFN can efficiently capture complex spatio-temporal relationships and performs better in the task of predicting air quality that is prone to abrupt change with a large magnitude of variability.

Concerning the problem that existing target tracking algorithms mainly use the linear constraint mechanism LADCF （Learning Adaptive Discriminative Correlation Filters）， which easily causes model drift， a correlation filtering based target tracking algorithm with nonlinear temporal consistency was proposed. First， a nonlinear temporal consistency term was proposed based on Stevens’ Law， which aligned closely with the characteristics of human visual perception. The nonlinear temporal consistency term allowed the model to track the target relatively smoothly， thus ensuring tracking continuity and preventing model drift. Next， the Alternating Direction Method of Multipliers （ADMM） was employed to compute the optimal function value， ensuring real-time tracking of the algorithm. Lastly， Stevens’ Law was used for nonlinear filter updating， enabling the filter update factor to enhance and suppress the filter according to the change of the target， thereby adapting to target changes and preventing filter degradation. Comparison experiments with mainstream correlation filtering and deep learning algorithms were performed on four standard datasets. Compared with the baseline algorithm LADCF， the tracking precision and success rate of the proposed algorithm were improved by 2.4 and 3.8 percentage points on OTB100 dataset， and 1.5 and 2.5 percentage points on UAV123 dataset. The experimental results show that the proposed algorithm effectively avoids tracking model drift， reduces the likelihood of filter degradation， has higher tracking precision and success rate， and stronger robustness in complicated situations such as occlusion and illumination changes.

In the realms of intelligent manufacturing and environmental sustainability， the significance of multi-objective scheduling in orchestrating a balance among production efficiency， cost management， and environmental conservation is paramount. Contemporary research indicates that CPU-based scheduling solutions are constrained by suboptimal efficiency and responsiveness， particularly when managing tasks of considerable scale. Consequently， the parallel computational prowess of GPUs heralds a novel avenue for the refinement of extensive flow shop scheduling challenges. For the multi-objective No-Wait Flow shop Scheduling Problem （NWFSP）， with the concurrent objectives of minimizing both the makespan and the Total Energy Consumption （TEC）， a Mixed-Integer Linear Programming model （MILP） was formulated to delineate the problem， and a bespoke GPU-accelerated tensorized evolutionary algorithm named Tensor-GPU-NSGA-Ⅱ was introduced for problem-solving. The ingenuity of Tensor-GPU-NSGA-Ⅱ resides in its tensorized algorithm for the computation of the makespan and TEC within the NWFSP framework， as well as in converting the conventional CPU-based serial individual updating to a GPU-driven parallel population renewal process. Empirical results demonstrate that for a scenario involving 500 jobs and 20 machines， Tensor-GPU-NSGA-Ⅱ realizes an enhancement in computational efficiency by a speedup of 9 761.75 over the traditional NSGA-Ⅱ algorithm. Furthermore， this acceleration efficacy markedly surges as the population scale expands.

In this paper, a new variational model based on Partial Differential Equation (PDE) was proposed to solve the ill-posed problems in the data-fidelity item of the existing key variational approaches to remove multiplicative noise with the theories of total variation and logarithmic transformation. The initial boundary value problem of the PDE associated with the new variational problem was derived and discreted numerically. The numerical experimental results show that the values of Mean Square Error (MSE) are decreased and Peak Signal to Noise Ratio (PSNR) are increased obviously. The ill-posed problem in the data-fidelity item is avoided well at the same time. It makes a good method to solve this problem, and avoids the errors which may appear in the discretization process. The quality of the images restored by the proposed method is not only more favorable, but the new model also eliminates the “step-casing effect”.