User authentication and verification by gait data based on smartphones’ inertial sensors has gradually attracted increasing attention due to their compact size, portability and affordability. However, the existing approaches often require users to walk on a specific road at a normal walking speed to improve recognition accuracy. In order to recognize gaits under unconstrained conditions on where and how users walk, we proposed a Hybrid Deep Learning Network (HDLN), which combined the advantages of a long short-term memory (LSTM) network and a convolutional neural network (CNN) to reliably extract discriminative features from complex smartphone inertial data. The convergence layer of HDLN was optimized through a spatial pyramid pooling and attention mechanism. The former ensured that the gait features were extracted from more dimensions, and the latter ensured that only important gait information was processed while ignoring unimportant data. Furthermore, we developed an APP that can achieve real-time gait recognition. The experimental results showed that HDLN achieved better performance improvements than CNN, LSTM, DeepConvLSTM and CNN+LSTM by 1.9%, 2.8%, 2.0% and 1.3%, respectively. Furthermore, the experimental results indicated our model’s high scalability and strong suitability in real application scenes.

E-commerce retailers bear substantial additional costs arising from high product return rates due to lenient return policies and consumers’ impulsive purchasing. This study aims to accurately predict product return behavior before payment, supporting proactive return management and reducing potential losses. Based on the Graph Transformer, we proposed a novel return prediction model, Returnformer, which focuses on capturing user–product connections represented in topological structures of bipartite graphs. The Returnformer first integrates global topological embeddings into original node features to alleviate structural information loss caused by graph partitioning. It then employs a Graph Transformer to capture long-range user–item dependencies within local subgraphs. In addition, a graph-level attention mechanism is introduced to facilitate the propagation of global return patterns across different subgraphs. Experiments on a real-world e-commerce dataset show that the Returnformer outperforms four machine learning models in terms of prediction accuracy, demonstrating superior performance compared to the state-of-the-art models. The proposed model enables retailers to identify potential return risks prior to payment, thereby supporting timely and proactive preventive interventions.

Accurate forecasting of lottery sales is crucial for strategic planning in volatile consumer markets driven by trend shifts, multi-scale seasonality, and calendar effects. This study proposes a Diagnostic Decomposition–Correction Hybrid (DDC-Hybrid) framework integrating Prophet and SARIMA through a residual diagnostics and correction pipeline. Specifically, Prophet is employed to model long-term trend changes and interpretable holiday impacts, while SARIMA is subsequently used to correct the residual series, capturing short-range temporal dependence that remains statistically significant after decomposition. From an information-theoretic perspective, the framework can be viewed as a two-stage uncertainty reduction process, where decomposition extracts low-frequency informative components and residual correction harvests remaining predictive information. Using monthly lottery sales in China (2008–2025), we conduct a comprehensive evaluation of SARIMA, Prophet, and the proposed hybrid approach. The DDC-Hybrid demonstrates improved predictive accuracy, yielding the lowest error rates. Beyond predictive accuracy, we further examine varying holiday effects through statistical testing. We also find that lottery sales contain a pronounced quadrennial (48-month) seasonal cycle associated with mega-sport events, which improves long-horizon stability. The results suggest that the proposed diagnostic hybrid modeling approach enhances forecasting accuracy and provides practical insights for lottery sales management.