Symmetry

Lane detection, as one of the key real-time tasks in vehicle tracking, often faces numerous challenges due to the complex shapes and inherent symmetry of lane lines. Aiming at the requirements of high accuracy and real-time performance of the lane detection, this paper proposes an adaptive structural optimization and enhanced receptive field network for lane detection (ASO-ERFNet). Specifically, we propose a Multi-receptive Field Fusion Layer (MFFL) that optimizes the structure of the pooling operation to fully utilize its hierarchical characteristics, leverage the symmetry of lane layouts, and precisely preserve the spatial geometric properties of lane lines. Then, we design a Dynamic Cross Attention Mechanism (DCAM) that can adaptively adjust convolutional kernel weights, thereby further enhancing detection precision. In addition, compared with the existing single-feature extraction networks, we propose a Dual-Perception Network (DPNet) that fuses features from different scale levels through a U-shaped structure. The experimental findings show that compared with state-of-the-art methods, our model obtains superior performance, achieving the best results in six scenes, such as normal and crowded scenes. Specifically, our method achieved 76.61% and 79.90% performance in crowded and shadow scenes, respectively, while reducing the false positive rate by 22.90% in cross scenes. Moreover, with an average processing time of only 5.5 ms per frame, our method achieves an F1 score of 96.65% on the TuSimple dataset and 76.23% on the CULane dataset. These results indicate that our model effectively balances detection accuracy and speed by leveraging lane symmetry, providing an efficient and reliable solution for lane detection in vehicle tracking.

Quantum watermarking is a technique that embeds specific information into a quantum carrier for the purpose of digital copyright protection. In this paper, we propose a novel color image watermarking algorithm that integrates quantum discrete wavelet transform with Sinusoidal–Tent mapping and baker mapping. Initially, chaotic sequences are generated using Sinusoidal–Tent mapping to determine the channels suitable for watermark embedding. Subsequently, a one-level quantum Haar wavelet transform is applied to the selected channel to decompose the image. The watermarked image is then scrambled via discrete baker mapping, and the scrambled image is embedded into the High-High subbands. The invisibility of the watermark is evaluated by calculating the peak signal-to-noise ratio, Structural similarity index measure, and Learned Perceptual Image Patch Similarity, with comparisons made against the color histogram. The robustness of the proposed algorithm is assessed through the calculation of Normalized Cross-Correlation. In the simulation results, PSNR is close to 63, SSIM is close to 1, LPIPS is close to 0.001, and NCC is close to 0.97. This indicates that the proposed watermarking algorithm exhibits excellent visual quality and a robust capability to withstand various attacks. Additionally, through ablation study, the contribution of each technique to overall performance was systematically evaluated.

This study introduces a unified and methodologically symmetric comparative framework for multivariate cryptocurrency forecasting, addressing long-standing inconsistencies in prior research where model families, feature sets, and preprocessing pipelines differ across studies. Under an identical and rigorously controlled experimental setup, we benchmark six deep learning architectures—LSTM, GPT-2, Informer, Autoformer, Temporal Fusion Transformer (TFT), and a Vanilla Transformer—together with four widely used econometric models (ARIMA, VAR, GARCH, and a Random Walk baseline). All models are evaluated using a shared multivariate feature space composed of more than forty technical indicators, identical normalization procedures, harmonized sliding-window formations, and aligned temporal splits across five high-liquidity assets (BTC, ETH, XRP, XLM, and SOL). The experimental results show that transformer-based architectures consistently outperform both the recurrent baseline and classical econometric models across all assets. This superiority arises from the ability of attention mechanisms to capture long-range temporal dependencies and adaptively weight informative time steps, whereas recurrent models suffer from vanishing-gradient limitations and restricted effective memory. The best-performing deep learning models achieve MAPE values of 0.0289 (BTC, GPT-2), 0.0198 (ETH, Autoformer), 0.0418 (XRP, Informer), 0.0469 (XLM, Informer), and 0.0578 (SOL, TFT), substantially improving upon the performance of both LSTM and all econometric baselines. These findings highlight the effectiveness of attention-based architectures in modeling volatility-driven nonlinear dynamics and establish a reproducible, symmetry-preserving benchmark for future research in deep-learning-based financial forecasting.