Chang Liu

Shenghao Zhu, Yifei Chen, Shuo Jiang et al.

Neurogliomas are among the most aggressive forms of cancer, presenting considerable challenges in both treatment and monitoring due to their unpredictable biological behavior. Magnetic resonance imaging (MRI) is currently the preferred method for diagnosing and monitoring gliomas. However, the lack of specific imaging techniques often compromises the accuracy of tumor segmentation during the imaging process. To address this issue, we introduce the XLSTM-HVED model. This model integrates a hetero-modal encoder-decoder framework with the Vision XLSTM module to reconstruct missing MRI modalities. By deeply fusing spatial and temporal features, it enhances tumor segmentation performance. The key innovation of our approach is the Self-Attention Variational Encoder (SAVE) module, which improves the integration of modal features. Additionally, it optimizes the interaction of features between segmentation and reconstruction tasks through the Squeeze-Fusion-Excitation Cross Awareness (SFECA) module. Our experiments using the BraTS 2024 dataset demonstrate that our model significantly outperforms existing advanced methods in handling cases where modalities are missing. Our source code is available at https://github.com/Quanato607/XLSTM-HVED.

Qiuqi Li, Chang Liu, Yifei Yang

Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this limitation, we propose a localized DMD (LDMD) framework that improves prediction performance by integrating DMD's strong linear forecasting capabilities with time-domain segmentation techniques. In this framework, the temporal domain is segmented into multiple subintervals, within which snapshot matrices are constructed and localized predictions are performed. We first present the localized DMD method with predefined segmentation, and then explore an adaptive segmentation strategy to further enhance computational efficiency and prediction robustness. Furthermore, we conduct an error analysis that provides the upper bound of the local and global truncation error for the proposed framework. The effectiveness of LDMD is demonstrated on four benchmark problems-Burgers', Allen-Cahn, nonlinear Schrodinger, and Maxwell's equations. Numerical results show that LDMD significantly enhances long-term predictive accuracy while preserving high computational efficiency.