Ship trajectory prediction is a complex time series forecasting problem that necessitates models capable of accurately capturing both long-term trends and short-term fluctuations in vessel movements. While existing deep learning models excel in short-term predictions, they struggle with long-sequence time series forecasting (LSTF) due to difficulties in capturing long-term dependencies, resulting in significant prediction errors. This paper proposes the Informer-TP method, leveraging Automatic Identification System (AIS) data and based on the Informer model, to enhance the ability to capture long-term dependencies, thereby improving the accuracy of long-term ship trajectory predictions. Firstly, AIS data are preprocessed and divided into trajectory segments. Secondly, the time series is separated from the trajectory data in each segment and input into the model. The Informer model is utilized to improve long-term ship trajectory prediction ability, and the output mechanism is adjusted to enable predictions for each segment. Finally, the proposed model’s effectiveness is validated through comparisons with baseline models, and the influence of various sequence lengths $L_{token}$ on the Informer-TP model is explored. Experimental results show that compared with other models, the proposed model exhibits the lowest Mean Squared Error, Mean Absolute Error, and Haversine distance in long-term forecasting, demonstrating that the model can effectively capture long-term dependencies in the trajectories, thereby improving the accuracy of long-term vessel trajectory predictions. This provides an effective and feasible method for ensuring ship navigation safety and advancing intelligent shipping.

Named entity recognition (NER) is particularly challenging for medical texts due to the high domain specificity, abundance of technical terms, and sparsity of data in this field. In this work, we propose a novel attention layer, called the “ontology attention layer”, that enhances the NER performance of a language model for clinical text by utilizing an ontology consisting of conceptual classes related to the target entity set. The proposed layer computes the relevance between each input token and the classes in the ontology and then fuses the encoded token vectors and the class vectors to enhance the token vectors by explicit superior knowledge. In our experiments, we apply the proposed layer to various language models for an NER task based on a Chinese clinical dataset to evaluate the performance of the layer. We also investigate the influence of the granularity of the classes utilized in the ontology attention layer. The experimental results show that the proposed ontology attention layer improved F1 scores by 0.4% to 0.5%. The results suggest that the proposed method is an effective approach to improving the NER performance of existing language models for clinical datasets.

This paper presents an algorithm for effectively maintaining the minimum spanning tree in dynamic weighted undirected graphs. The algorithm efficiently updates the minimum spanning tree when the underlying graph structure changes. By identifying the portion of the original tree that can be preserved in the updated tree, our algorithm avoids recalculating the minimum spanning tree from scratch. We provide proof of correctness for the proposed algorithm and analyze its time complexity. In general scenarios, the time complexity of our algorithm is comparable to that of Kruskal’s algorithm. However, the experimental results demonstrate that our algorithm outperforms the approach of recomputing the minimum spanning tree by using Kruskal’s algorithm, especially in medium- and large-scale dynamic graphs where the graph undergoes iterative changes.

Vessel trajectory prediction is important in maritime traffic safety and emergency management. Vessel trajectory prediction using vessel automatic identification system (AIS) data has attracted wide attention. Deep learning techniques have been widely applied to vessel trajectory prediction tasks due to their advantages in fine-grained feature learning and time series modelling. However, most deep learning-based methods use a unified approach for modelling AIS data, ignoring the diversity of AIS data and the impact of noise on prediction performance due to environmental factors. To address this issue, this study introduces a method consisting of temporal convolutional network (TCN), convolutional neural network (CNN) and convolutional long short-term memory (ConvLSTM) to predict vessel trajectories, called TCC. The model employs TCN to capture the complex correlation of the time series, utilises CNN to capture the fine-grained covariate features and then captures the dynamics and complexity of the trajectory sequences through ConvLSTM to predict vessel trajectories. Experiments are conducted on real public datasets, and the results show that the TCC model proposed in this paper outperforms the existing baseline algorithms with high accuracy and robustness in vessel trajectory prediction.

The minimum dominating tree (MDT) problem consists of finding a minimum weight subgraph from an undirected graph, such that each vertex not in this subgraph is adjacent to at least one of the vertices in it, and the subgraph is connected without any ring structures. This paper presents a dual-neighborhood search (DNS) algorithm for solving the MDT problem, which integrates several distinguishing features, such as two neighborhoods collaboratively working for optimizing the objective function, a fast neighborhood evaluation method to boost the searching effectiveness, and several diversification techniques to help the searching process jump out of the local optimum trap thus obtaining better solutions. DNS improves the previous best-known results for four public benchmark instances while providing competitive results for the remaining ones. Several ingredients of DNS are investigated to demonstrate the importance of the proposed ideas and techniques.

Vessel trajectory prediction (VTP) plays a critical role in maritime safety and intelligent navigation. Existing methods struggle to simultaneously capture long-term dependencies and nonlinear dynamic patterns in vessel movements. To address this challenge, we propose MKAIS, a novel trajectory prediction model that integrates the selective state space modeling capability of Mamba with the strong nonlinear representation power of Kolmogorov–Arnold Networks (KAN). Specifically, we design a feature-separated embedding strategy for AIS inputs (longitude, latitude, speed over ground, course over ground), followed by an MKAN module that jointly models global temporal dependencies and nonlinear dynamics. Experiments on the public ct_dma dataset demonstrate that MKAIS outperforms state-of-the-art baselines (LSTM, Transformer, TrAISformer, Mamba), achieving up to 16.65% improvement in the Haversine distance over 3 h prediction horizons. These results highlight the effectiveness and robustness of MKAIS for both short-term and long-term vessel trajectory prediction.