Time series forecasting remains challenging in domains such as finance and climate science, where complex interactions among variables often induce spurious correlations. We propose ARCausal, a forecasting framework that integrates transfer entropy (TE)-based causal discovery with Transformer attention modeling. ARCausal introduces a sparse causal masking mechanism derived from TE and refined via vector autoregression (VAR) estimation to capture dynamic causal interactions. The mask suppresses noninformative dependencies and distinguishes autocorrelation from cross-variable causal effects, improving both predictive performance and interpretability. Experiments on nine benchmark datasets demonstrate consistent improvements over strong baselines, achieving up to [Formula: see text] reduction in MSE while maintaining computational efficiency. Visualization results further illustrate the interpretability of the learned causal structures. The code is publicly available at https://github.com/jancely/ARCausal/.

In recent years, multivariate time series forecasting (MTSF) has gained significant attention. And transformer-based models have showed strong performance. However, the quadratic complexity of attention mechanisms leads to inefficiency and high overhead. The Mamba state-space model offers a more efficient alternative with lower complexity and fewer parameters. However, its unilateral nature limits the effective capture of time and feature dimensions. To address this, we propose A Dual-stream Cross-time and Cross-feature with Mamba (DCCMamba) for MTSF. Specifically, we employ a dual-stream structure to extract different information from the time and feature dimensions. One stream encodes data from a feature perspective and passes it through a Mamba layer to capture cross-time information. The other stream encodes the data from the time perspective, decomposes it into trend and seasonal components, and captures cross-feature information using a Mamba layer. Finally, we fuse the cross-feature information and cross-time information to get the final result. Experiments on four public datasets demonstrate that DCCMamba achieves state-of-the-art performance.

Urban traffic flow management faces increasing challenges due to accelerating urbanization. Traffic data collected from roadside sensors contain complex temporal and spatial dependencies that interact simultaneously. Although Graph Neural Networks and Recurrent Neural Networks have been successful in capturing these dependencies, two critical issues remain: 1) Treating all traffic signals equally fails to capture the nuanced spatiotemporal dependencies hidden in time series data; 2) Dynamic traffic conditions hinder the accurate capture of local spatial dependencies, thereby limiting prediction accuracy and reliability. To address these challenges, we propose an innovative model, FDDSGCN. To resolve the first issue, we introduce Fractional Residual Decomposition, which effectively separates traffic data into spatial and temporal signals. For the second issue, we employ Dynamic Spatial-Temporal Graph Convolution with fractional-order weight adjustments to dynamically capture local dependencies. Additionally, the Long Short-Term Dependency module analyzes both long-term and short-term dependencies. Extensive experiments on three public datasets demonstrate the superior performance and practical value of our model.

With the proliferation of the Internet of Things (IoT), a wealth of multivariate time series data is being generated across various domains, creating new demands for accurate and efficient forecasting models. Despite the success of attention-based models in capturing dependencies within time series, they often fail to address two critical challenges: (1) the lag effect between output and input, which can significantly distort predictions, and (2) the limitations of classic trigonometric positional embeddings, which lack scalability and adaptability to diverse temporal patterns. To address these challenges, we propose FPPformer, a novel forecasting model that introduces two key innovations: (i) a Fractional Positional Embedding (FPE), which leverages fractional calculus to enable scalable and adaptive positional representations, and (ii) a Predictive Attention Mechanism (PAM), which explicitly models the lag effect, aligning output and input more effectively. The FPPformer architecture consists of encoder-only structure, with the core of encoder module utilizing the PAM. Experimental results demonstrate that FPPformer significantly improves forecasting perfromance, reducing the mean squared error (MSE) by 28% and the mean absolute error (MAE) by 17% across six datasets spanning four domains -electricity, weather, economy, and transportation -especially on large-scale datasets such as Traffic and Electricity. These results highlight FPPformer’s ability to address fundamental challenges in time series forecasting, providing a new perspective on leveraging positional representations and lag-aware attention mechanisms. The code for this project is available at https://github.com/jancely/FPPformer.

Possessing two manipulators heightens the ability of dual-arm robots (DAR) to conduct complex tasks, while raising hazard that the two manipulators might collide with each other or with other objects. DARs are usually equipped with a collision-free motion planning algorithms (CFMPA) to prevent the two manipulators from colliding. The CFMPA searches the motion paths of robot manipulators, which are expected to be as short and smooth as possible under the premise of ensuring safety. It is important to ensure that the algorithm is correct and efficient. It is not enough to apply traditional test methods to determine whether DARs can work in safety-critical applications. In this paper, theorem proving technology is employed to analyze the correctness and efficiency of a classical CFMPA. The CFMPA is outlined, and then formalized in high order logic with the theorem prover HOL4. An inconsistency in the range of motions of the robot manipulators in the algorithm is discovered. An improved algorithm is therefore proposed. Formal verification with HOL4 proves the correctness and efficiency of the proposed algorithm that has already run on a real DAR as well, in conformity with our expectation.