Mathematics

A critical decision in pre-disaster humanitarian logistics planning is determining the amount of aid to preposition to ensure timely and effective emergency response. To support managers in this process, we propose four mathematical formulations designed to optimize food prepositioning and subsequent distribution while minimizing unmet demand under supply uncertainty. Two formulations adopt the cardinality-constrained approach: one focuses on minimizing unmet demand, and the other incorporates equity in meeting demand. The remaining two formulations are scenario-based, addressing the same objectives with and without equity considerations. To compare the variations in the solutions generated by the proposed formulations and gain a deeper understanding of their behavior and performance, the formulations are applied to synthetic instances. To assist managers in selecting the model that best aligns with their objectives, we provide a summary of the advantages and disadvantages of each formulation. Our results show that considering supply uncertainty has important implications for the total costs, and that having adequate storage capacity may help mitigate the problems caused by this uncertainty.

Precise medical image segmentation plays a vital role in disease diagnosis and clinical treatment. Although U-Net-based architectures and their Transformer-enhanced variants have achieved remarkable progress in automatic segmentation tasks, they still face challenges in complex medical imaging scenarios, particularly around simultaneously modeling fine-grained local details and capturing long-range global contextual information, which limits segmentation accuracy and structural consistency. To address these challenges, this paper proposes a novel medical image segmentation framework termed DA-TransResUNet. Built upon a ResUNet backbone, the proposed network integrates residual learning, Transformer-based encoding, and a dual-attention (DA) mechanism in a unified manner. Residual blocks facilitate stable optimization and progressive feature refinement in deep networks, while the Transformer module effectively models long-range dependencies to enhance global context representation. Meanwhile, the proposed DA-Block jointly exploits local and global features as well as spatial and channel-wise dependencies, leading to more discriminative feature representations. Furthermore, embedding DA-Blocks into both the feature embedding stage and skip connections strengthens information interaction between the encoder and decoder, thereby improving overall segmentation performance. Experimental results on the LiTS2017 dataset and Sliver07 dataset demonstrate that the proposed method achieves incremental improvement in liver segmentation. In particular, on the LiTS2017 dataset, DA-TransResUNet achieves a Dice score of 97.39%, a VOE of 5.08%, and an RVD of −0.74%, validating its effectiveness for liver segmentation.

This paper addresses nonlinear time-varying cascade systems governed by differential equations with finite delay. Several sufficient conditions for asymptotic stability are derived, based on differing assumptions regarding the isolated subsystems and their interconnection. The cascade structure enables the treatment of a broad class of systems while simplifying stability analysis compared to conventional approaches. Moreover, it allows the stabilization problem to be decoupled: under suitable conditions, the asymptotic stability of the overall cascade system follows from the stability properties of its individual subsystems. These properties are typically verified using the direct Lyapunov method. In contrast to existing results, the theorems presented herein apply to an extended class of systems and impose relaxed conditions on the Lyapunov functions employed to establish uniform asymptotic stability. Additionally, new results are provided on semiglobal exponential stability and (non-uniform) asymptotic stability for time-varying cascade systems with delay. Collectively, these contributions broaden the applicability of the direct Lyapunov method to delayed cascade systems.