Multivariate time series (MTS) forecasting aims to predict future patterns by extracting features from multivariate history. Predominant methods face challenges in learning spatial dependencies while capturing long-term trends and local details, leading to suboptimal performance in MTS forecasting. To address this problem, we propose a Patch-Aware graph Network with Dual Alignment (PANDA) of features in both time and frequency domain. Specifically, we utilize a patch-aware graph neural network to extract spatio-temporal dependencies. Additionally, dual alignment is employed for multi-perspective optimization. By performing multi-view joint optimization, our model reduces feature redundancy and improves the extraction of structured spatio-temporal patterns. Extensive experiments demonstrate that PANDA achieves superior forecasting accuracy in both long- and short-time series forecasting. Code is available at this repository: https://github.com/lichen0620/PANDA.

Based on temporal variations in the celestial tidal force (CTF) at the hypocenter of the Ms 7.1 Yushu earthquake, we analyzed the relationship between the earthquake and the phase change in the CTF. Then, using atmospheric temperature data from the National Center for Environmental Prediction Final Operational Global Analysis (NCEP-FNL) dataset, we introduced a three-dimensional spatial distribution method to stratify atmospheric thermodynamic anomalies. We further explored the relationship between the CTF, atmospheric temperature, and seismic activity, and the results show that the phase change of the continuous enhancement of atmospheric temperature is temporally quasi-synchronous with the continuous change in the CTF from peak to trough and this method successfully captures the synchronous migration of atmospheric temperature anomalies associated with two adjacent earthquakes. As the Yushu earthquake approached, warming became concentrated, transitioning from a scattered distribution to the Ganzi–Yushu seismogenic fracture zone. After the earthquake, the warming distribution underwent significant bifurcation and offset steering, and a new significant earthquake occurred in Nerong in the new warming region formed along the Zadoi – Shanglaxiu seismogenic fault zone. The vertical multi-layer structures of the thermal anomaly show that the spatial expansion pattern, intensity, and extent of atmospheric warming with increasing altitude are consistent with the atmospheric thermodynamic properties of ground-to-atmosphere heating, leading to near-surface atmospheric warming, lifting, diffusion, and extinction, showing the primary warming of the subsurface heat source. In general, the CTF changes the tectonic environment, induces earthquakes, and changes the atmospheric temperature, and the temperature anomaly reflects that the tectonic stress in the seismogenic zones has entered a critical state. Therefore, the atmospheric warming data extracted using Tidal Force Potential Analysis (TFFA) can be used to monitor the stress state and indicate seismogenic regions for the earthquake induced by the CTF. The results of the synergistic time –space –intensity evolution of atmospheric warming due to seismic activity can also provide a new parameter that can complement studies of regional atmospheric changes due to the effects of tectonic activity.

A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic specifications only using observation samples and without the knowledge of the model, and provide a probabilistic guarantee on the satisfaction of the specification. We first propose the theoretical results for using non-parametric estimation to estimate an asymptotic upper bound for the \emph{Lipschitz constant} of the stochastic system, which can determine a finite abstraction of the system. Our results prove that the asymptotic convergence rate of the estimation is $O(n^{-\frac{1}{3+d}})$, where $d$ is the dimension of the system and n is the data scale. We then construct interval Markov decision processes using two different data-driven methods, namely non-parametric estimation and empirical estimation of transition probabilities, to perform formal verification against a given temporal logic specification. Multiple case studies are presented to validate the effectiveness of the proposed methods.

Order-preserving pattern (OPP) mining is a type of sequential pattern mining method in which a group of ranks of time series is used to represent an OPP. This approach can discover frequent trends in time series. Existing OPP mining algorithms consider data points at different time to be equally important; however, newer data usually have a more significant impact, while older data have a weaker impact. We therefore introduce the forgetting mechanism into OPP mining to reduce the importance of older data. This paper explores the mining of OPPs with forgetting mechanism (OPF) and proposes an algorithm called OPF-Miner that can discover frequent OPFs. OPF-Miner performs two tasks, candidate pattern generation and support calculation. In candidate pattern generation, OPF-Miner employs a maximal support priority strategy and a group pattern fusion strategy to avoid redundant pattern fusions. For support calculation, we propose an algorithm called support calculation with forgetting mechanism, which uses prefix and suffix pattern pruning strategies to avoid redundant support calculations. The experiments are conducted on nine datasets and 12 alternative algorithms. The results verify that OPF-Miner is superior to other competitive algorithms. More importantly, OPF-Miner yields good clustering performance for time series, since the forgetting mechanism is employed.

BACKGROUND: A Raman spectroscopy method can quickly and accurately measure the concentration of ofloxacin in solution. This method has the advantages of accuracy and rapidity over traditional detection methods. However, the manual analysis methods for the collected Raman spectral data often ignore the nonlinear characteristics of the data and cannot accurately predict the concentration of the target sample. METHODS: To address this drawback, this paper proposes a novel kernel-Huber loss function that combines the Huber loss function with the Gaussian kernel function. This function is used with an improved genetic algorithm-convolutional neural network (GA-CNN) to model and predict the Raman spectral data of different concentrations of ofloxacin in solution. In addition, the paper introduces recurrent neural networks (RNN), long short-term memory (LSTM), bidirectional long short-term memory (BiLSTM) and gated recurrent units (GRU) models to conduct multiple experiments and use root mean square error (RMSE) and residual predictive deviation (RPD) as evaluation metrics. RESULTS: The proposed method achieved an [Formula: see text] of 0.9989 on the test set data and improved by 3% over the traditional CNN. Multiple experiments were also conducted using RNN, LSTM, BiLSTM, and GRU models and evaluated their performance using RMSE, RPD, and other metrics. The results showed that the proposed method consistently outperformed these models. CONCLUSIONS: This paper demonstrates the effectiveness of the proposed method for predicting the concentration of ofloxacin in solution based on Raman spectral data, in addition to discussing the advantages and limitations of the proposed method, and the study proposes a solution to the problem of deep learning methods for Raman spectral concentration prediction.