Timeseries representation underpin our ability to understand and predict the change of natural system. Series are often predicated on our choice of highly redundant factors, and in fact, the system is driven by a much smaller set of latent intrinsic keys. It means that a better representation of data makes points in phase space clearly for researchers. Specially, a 2D structure of timeseries could combine the trend and correlation characters of different periods in timeseries together, which provides more clear information for top tasks. In this work, the effectiveness of 2D structure of timeseries is investigated in clustering tasks. There are 4 kinds of methods that the Recurrent Plot (RP), the Gramian Angular Summation Field (GASF), the Gramian Angular Differential Field (GADF) and the Markov Transition Field (MTF) have been adopted in the analysis. By classifying the CSI300 and S&P500 indexes, we found that the RP imaging series are valid in recognizing abnormal fluctuations of financial timeseries, as the silhouette values of clusters are over 0.6 to 1. Compared with segment methods, the 2D models have the lowest instability value of 0. It verifies that the SIFT features of RP images take advantage of the volatility of financial series for clustering tasks.

Imaging time series have become an important method for constructing pattern features. The idea that transforming the original 1D time series into a 2D image makes properties from different levels in a spanned space. It realizes to analyze short-term autoregression and long-term relations of points at the same time. In this work, an image-time-series-based attention scheme has been investigated by high-frequency forecasting tasks with S&P500 and CSI300 datasets. By comparing non-parametric models and parametric models, as well as deep learning models, the proposed methods take the least residual. The MSE of the model in predicting the next 15 min’ logarithmic indices is 0.0038, and the MSPE value is 0.0001. Besides, the pattern-based CNN model has the fastest convergence rate when predicting the volatility at the same accuracy level. It verifies that the image representation of time series makes the potential information more efficient in analyzing financial time series.

In this article, we construct an evaluation index system based on the DPSIRM framework to determine the water resources carrying capacity of Shiyan City. Then, we use an obstacle model to calculate and analyze the factors that constrain the improvement in the water resources carrying capacity in the city. The research results are as follows: (1) The water resources carrying capacity of Shiyan City was on the rise during 2011–2021, and the water resources carrying capacity of Shiyan City was continuously improved. (2) The management system is the primary obstacle subsystem, followed by the driving force system, the response system, the pressure system, the state system, and the influence system. (3) Among the specific factors, the top three obstacles are sewage treatment investment, the proportion of guaranteed harvest area in drought and flood, and the average annual fertilizer applied per unit of cultivated land. These primary factors restrict Shiyan City from improving its water resources carrying capacity. This study has important practical significance for understanding the resilience of the water system in Shiyan City; exploring the changes in the water resources carrying capacity and its obstacle factors; and guiding the development, utilization, and management of water resources in Shiyan City.

Traditional disease retrieval and localization for plant leaves typically demand substantial human resources and time. In this study, an intelligent approach utilizing deep hash convolutional neural networks (DHCNN) is presented to address these challenges and enhance retrieval performance. By integrating a collision-resistant hashing technique, this method demonstrates an improved ability to distinguish highly similar disease features, achieving over 98.4% in both precision and true positive rate (TPR) for single-plant disease retrieval on crops like apple, corn and tomato. For multi-plant disease retrieval, the approach further achieves impressive Precision of 99.5%, TPR of 99.6% and F-score of 99.58% on the augmented PlantVillage dataset, confirming its robustness in handling diverse plant diseases. This method ensures precise disease retrieval in demanding conditions, whether for single or multiple plant scenarios.

In this paper, we investigate several two-parameter weak Orlicz–Hardy martingale spaces generated by the $p$-convex and $q$-concave functions, and establish their atomic decomposition theorems. Using the atomic decomposition, we obtain a sufficient condition for the boundedness of a sublinear operator defined on the two-parameter weak Orlicz–Hardy martingale spaces. Furthermore, the dual spaces of the two-parameter weak Orlicz–Hardy martingale spaces are considered.