Orthogonal time–frequency space (OTFS) modulation has emerged as a promising technology to alleviate the effects of the Doppler shifts in high-mobility environments. As a prerequisite to demodulation and signal processing, automatic modulation classification (AMC) is essential for OTFS systems. However, a very limited number of works have focused on this issue. In this paper, we propose a novel AMC approach for OTFS systems. We build a dual-stream convolutional neural network (CNN) model to simultaneously capture multi-domain signal features, which substantially enhances recognition accuracy. Moreover, we propose a differentiated embedded pilot structure that incorporates information about distinct modulation schemes to further improve the separability of modulation types. The results of the extensive experiments carried out show that the proposed approach can achieve high classification accuracy even under low signal-to-noise ratio (SNR) conditions and outperform the state-of-the-art baselines.

In this paper, we investigate the memory effects introduced by the time-fractional Schrödinger equation proposed by Naber on quantum entanglement and quantum dense coding under amplitude damping noise. Two formulations are analyzed: one with fractional operations applied to the imaginary unit and one without. Numerical results show that the formulation without fractional operations on the imaginary unit may be more suitable for describing non-Markovian (power-law) behavior in dissipative environments. This finding provides a more physically meaningful interpretation of the memory effects in time-fractional quantum dynamics and indirectly addresses fundamental concerns regarding the violation of unitarity and probability conservation in such frameworks. Our work offers a new perspective for the application of fractional quantum mechanics to realistic open quantum systems and shows promise in supporting the theoretical modeling of decoherence and information degradation.

Hybrid deep learning frameworks integrating convolutional neural networks (CNNs) and Transformer-based attention mechanisms have recently achieved promising results in synthetic aperture radar (SAR) ship detection. However, they still suffer from inherent limitations, including missed detections of small-scale ships under large variations in target scales, multiplicative speckle noise, and complex sea clutter interference. To address these issues, this paper proposes ACmixSAR-YOLO11, a SAR ship detection framework built upon YOLO11. The proposed model incorporates three complementary improvements to enhance feature representation and multi-scale detection capability. First, an ACmixSAR module is designed by integrating convolutional operations with self-attention mechanisms. This design strengthens feature discriminability. Second, a SARNoiseGate gating mechanism is embedded into the ACmixSAR module, which is designed to suppress low signal-to-noise ratio (SNR) feature responses while preserving discriminative ship features. Third, we develop a scale-weighted complete intersection over union (SW-CIoU) loss function, which assigns adaptive regression weights based on target sizes to rebalance the optimization across small, medium, and large ships. All improvements below are reported as relative percentage changes. Experimental results on the SSDD dataset demonstrate that the proposed ACmixSAR-YOLO11 outperforms the original YOLO11 Baseline, achieving a 1.50% increase in precision, a 0.15% growth in recall, a 1.47% enhancement in mAP@0.5, and a 4.26% promotion in mAP@0.5:0.95. Significance testing was applied to mAP@0.5 only (paired one-sided t-test, p = 0.0058 < 0.01); the other three metrics are reported as three-seed means and spreads. As supplementary evidence, experiments on HRSID show improved recall, mAP@0.5 and mAP@0.5:0.95 under conventional patch-level splitting at the cost of slightly reduced precision. However, this patch-level performance gain is partially inflated by scene overlap between training and test patches. Further validation on a strictly leakage-free scene-level split of HRSID shows that the overall mAP@0.5 gain diminishes to within random seed fluctuation, while improvements in mAP@0.5:0.95 and precision remain observable. These results demonstrate that the proposed framework effectively enhances detection accuracy with a moderate parameter increase (9.69 M → 11.75 M) while maintaining real-time inference.