This research delves into the strategies employed by firms to compete through effective management of their online reputation and sales. We analyze a market comprising multiple firms operating within a platform, with each firm striving to enhance its ratings and sales performance. We transform the problem into a stochastic differential game model that incorporates online ratings and sales in the competition among multiple decision-makers. The resulting system of coupled HJB equations becomes high-dimensional, with the nonlinearity and coupling nature of the equations posing challenges for traditional numerical methods. To address this challenge, we propose a machine learning algorithm, which constitutes one of the main contributions of this paper. We train the neural networks using stochastic gradient descent, where spatiotemporal points are sampled randomly to enforce the partial differential equations together with the prescribed boundary and initial conditions. We reformulate the above problem as a deep learning task by leveraging random sampling to eliminate the need for grid construction. We theoretically demonstrate the convergence of the proposed machine learning algorithm, ensuring the validity and reliability of numerical results. Our results provide valuable insights for platform executives and participating companies regarding equilibrium strategies and investment decisions.
Observed differences between paddy and upland croplands in soil organic carbon (SOC) and soil inorganic carbon (SIC) may reflect environmental and data-provenance imbalances rather than land-use effects. We reconstructed independent SOC and SIC profile datasets across China, harmonized depths, and separated full-sample comparisons from a prespecified comparable subset. Among all topsoil SOC profiles retained after applying the inclusion criteria (334 paddy, 347 upland), the median Upland-minus-Paddy contrast was −2.12 g kg−1; within the shared subset (97/95), it attenuated to −0.35 g kg−1 (95% interval, −1.74 to 1.55). For 97 paddy soils, changing only the land-use indicator to upland while holding observed soil and environment states fixed yielded a mean SOC contrast of −0.58 g kg−1 (joint 95% interval, −1.02 to −0.15), with 78.4% negative. A layer-resolved Extra Trees S-learner supported this scenario with out-of-fold R2 = 0.72 and mean R2 = 0.72 across ten spatial partitions. The shared topsoil SIC subset retained only 9 paddy and 7 upland profiles, so adjusted SIC could not be estimated. Aridity index (AI) stratification showed the strongest negative SOC contrast in more humid high-AI croplands (−1.08 g kg−1; −1.62 to −0.56), whereas low- and middle-AI strata crossed zero; the high-minus-middle difference was −1.29 g kg−1 (−2.09 to −0.60). Among comparable croplands, observed topsoil SOC differed little between paddy and upland fields, but model predictions indicated lower SOC under upland land use, particularly in humid regions. These results suggest a modest SOC advantage of paddy croplands, while SIC differences remain unresolved.
Accuracy and timeliness of forestry monitoring are critical for reliable resource assessment and early warning of pest and disease outbreaks. While drone technologies are increasingly used for forestry monitoring, current applications often lack systematic planning. Monitoring operations rely heavily on manual experience, resulting in low efficiency, redundant coverage, and coverage gaps. To address the trade-off between coverage completeness and operational timeliness in large and topographically complex forests, we investigate a truck-drone collaborative forestry monitoring framework that jointly optimizes vehicle routes, candidate docking points, and unmanned aerial vehicle (UAV or drone) coverage paths. The dual objectives of our model are to maximize coverage and minimize total operational time subject to road-network and engineering constraints. To this end, the monitoring region is gridded in a projected coordinate system. Non-monitoring units (e.g., villages, farmlands) identified through remote sensing and field surveys are excluded to reduce redundant searches and monitoring. Road network data serves as constraints for vehicle access and docking point selection. We propose a Fix-and-Optimize (FO) iterative decomposition to decouple and alternately solve two coupledsubproblems: docking-point combination selection and sub-region partitioning. Under fixed task region division, clustering-based sampling and variable neighborhood search optimization are performed for docking point combinations. Under fixed docking points, isolated block detection and local redistribution are conducted for sub-regions, and a genetic algorithm is used to optimize the heading angles of boustrophedon flight paths for efficient coverage routes. To improve the solution efficiency for large-scale cases, we devise a mechanism for maintaining and parallel evaluating the Pareto front. In the case study of Qingyuan, China, the proposed method reduces total operational time by 30.06 % at the same coverage level compared with the current manual planning scheme. The Pareto front also reveals a clear trade-off: coverage gains diminish sharply beyond approximately 55 UAV flights, and the 55-flight scheme achieves 96.6 % coverage while reducing the number of sorties by 16.7 % with only a 3.4 % coverage loss relative to the 66-flight full-coverage scheme. Our framework provides a quantitative tool for decision-makers to balance coverage goals with resource constraints, enabling more efficient and effective large-scale forestry monitoring.
Multimodal sentiment analysis aims to improve sentiment prediction by integrating affective cues from heterogeneous modalities such as text, acoustics, and vision. However, most existing methods directly interact or fuse the raw modality representations, lacking sufficient denoising capability and failing to fully exploit multi-level semantic affective information. Consequently, noise and redundancy are prone to be introduced, which restricts the modeling of fine-grained affective cues. Moreover, existing methods generally lack fine-grained selective modeling in cross-modal interaction and fusion, making it difficult to adaptively regulate modality contributions across feature dimensions. To address these issues, we propose a Hierarchical Query Denoising and Text-Guided Dimension-Wise Gated Fusion framework for multimodal sentiment analysis, termed HQDF. Specifically, a hierarchical query denoising module is first constructed, where learnable query tokens progressively interact with multi-level semantic representations to extract sentiment-relevant information while suppressing noise and redundancy. Next, a text-anchored interaction module uses the textual representation as a semantic anchor to retrieve acoustic and visual cues, which are then incorporated to refine the textual representation for subsequent fusion. Finally, an interaction-aware dimension-wise gated fusion module is developed to adaptively weight cross-modally enhanced representations at the feature-dimension level, enabling fine-grained cross-modal selection and fusion. Experimental results on CMU-MOSI and CMU-MOSEI demonstrate the competitiveness of the proposed method. Ablation studies and visualization analyses further verify the effectiveness of the proposed modules.
Intercropping is an effective cropping pattern that improves crop yields, soil properties and soil organic carbon (SOC) stocks. Nitrogen (N) deposition is one of the global environmental changes. However, under increasing N deposition, how paddy intercropping affects SOC fractions and stability remain unclear. In this study, a four-year paddy experiment was conducted with three cropping patterns and two levels of N deposition. The cropping patterns included rice monoculture (RM), water mimosa monoculture (WM), and rice–water mimosa intercropping (RWI), which were subjected to low N deposition (LN, 40 kg N ha⁻¹ yr⁻¹) or high N deposition (HN, 120 kg N ha⁻¹ yr⁻¹). The results showed that, under LN conditions, RWI significantly increased the milled rice rate and reduced the chalky rice rate by 40.74% compared with RM. Meanwhile, RWI significantly increased SOC content, mineral-bound organic carbon (MAOC) content, the MAOC/SOC ratio, and carbon pool index by 13.85%, 27.16%, 11.77%, and 13.54% compared with RM under LN conditions, respectively. Besides, at LN level, RWI significantly increased the proportion of small soil macroaggregates by 30.03% compared to RM. However, these positive effects of RWI were not observed under HN conditions. Instead, WM exhibited greater potential for SOC accumulation and stability under HN conditions. Overall, the effects of paddy intercropping on SOC sequestration and stability largely depend on N deposition level. Our findings provide new insights into how paddy intercropping regulates SOC sequestration and stability under increasing N deposition and offer a practical strategy for enhancing soil carbon storage in paddy ecosystems.
