Multivariate Time series forecasting is crucial in domains such as transportation, meteorology, and finance, especially for predicting extreme weather events. State-of-the-art methods predominantly rely on Transformer architectures, which utilize attention mechanisms to capture temporal dependencies. However, these methods are hindered by quadratic time complexity, limiting the model's scalability with respect to input sequence length. This significantly restricts their practicality in the real world. Mamba, based on state space models (SSM), provides a solution with linear time complexity, increasing the potential for efficient forecasting of sequential data. In this study, we propose UmambaTSF, a novel long-term time series forecasting framework that integrates multi-scale feature extraction capabilities of U-shaped encoder-decoder multilayer perceptrons (MLP) with Mamba's long sequence representation. To improve performance and efficiency, the Mamba blocks introduced in the framework adopt a refined residual structure and adaptable design, enabling the capture of unique temporal signals and flexible channel processing. In the experiments, UmambaTSF achieves state-of-the-art performance and excellent generality on widely used benchmark datasets while maintaining linear time complexity and low memory consumption.

The aim of this paper is to design a deep learning-based model to predict proximal femoral strength using multi-view information fusion. Method: We developed new models using multi-view variational autoencoder (MVAE) for feature representation learning and a product of expert (PoE) model for multi-view information fusion. We applied the proposed models to an in-house Louisiana Osteoporosis Study (LOS) cohort with 931 male subjects, including 345 African Americans and 586 Caucasians. With an analytical solution of the product of Gaussian distribution, we adopted variational inference to train the designed MVAE-PoE model to perform common latent feature extraction. We performed genome-wide association studies (GWAS) to select 256 genetic variants with the lowest p-values for each proximal femoral strength and integrated whole genome sequence (WGS) features and DXA-derived imaging features to predict proximal femoral strength. Results: The best prediction model for fall fracture load was acquired by integrating WGS features and DXA-derived imaging features. The designed models achieved the mean absolute percentage error of 18.04%, 6.84% and 7.95% for predicting proximal femoral fracture loads using linear models of fall loading, nonlinear models of fall loading, and nonlinear models of stance loading, respectively. Compared to existing multi-view information fusion methods, the proposed MVAE-PoE achieved the best performance. Conclusion: The proposed models are capable of predicting proximal femoral strength using WGS features and DXA-derived imaging features. Though this tool is not a substitute for FEA using QCT images, it would make improved assessment of hip fracture risk more widely available while avoiding the increased radiation dosage and clinical costs from QCT.