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22 pages, 1289 KB  
Article
Evaluating the Quality of Selected Commercial Probiotic Products, Both Dietary Supplements and Foods for Special Medical Purposes
by Anna Zawistowska-Rojek, Justyna Rybak, Paulina Smoleń, Agnieszka Kociszewska, Paweł Rudnicki-Velasquez, Karolina Węgrzyńska, Tomasz Zaręba, Stefan Tyski and Anna Baraniak
Foods 2026, 15(2), 373; https://doi.org/10.3390/foods15020373 - 20 Jan 2026
Abstract
Probiotics are live microorganisms that provide health benefits when administered in adequate amounts. Due to the increasing popularity of probiotic supplements, concerns have arisen regarding their quality, microbial composition, and safety. This study aimed to evaluate the quantitative and qualitative characteristics of the [...] Read more.
Probiotics are live microorganisms that provide health benefits when administered in adequate amounts. Due to the increasing popularity of probiotic supplements, concerns have arisen regarding their quality, microbial composition, and safety. This study aimed to evaluate the quantitative and qualitative characteristics of the selected probiotics available on the Polish market, including both dietary supplements and foods for special medical purposes, and to compare the obtained results with the information provided on the product labels. Fifteen commercial probiotic products were analysed. Viable microorganism counts were determined using the traditional culture-based plate count method and by flow cytometry for selected products. Species identification was performed using MALDI-TOF MS and qPCR, whereas microbiological purity testing was conducted to confirm the absence of pathogenic bacteria. Significant differences were observed between the declared and experimentally determined numbers of viable microorganisms. Only a few products maintained bacterial counts consistent with label claims, while most contained considerably low viable cells. Flow cytometry revealed higher viable cell counts than plate counting, indicating the presence of viable but non-culturable bacteria. The declared species composition of the strains was mostly confirmed, although in several cases, undeclared probiotic microorganisms were identified. All tested products were free from pathogens. The study indicates significant discrepancies in the quality of probiotic supplements available on the Polish market. From a consumer perspective, these findings highlight the importance of verifying probiotic quality and suggest that not all commercial products may guarantee the full range of claimed health benefits. The implementation of standardised analytical procedures and enhanced quality control measures is therefore essential to ensure the product safety, strain authenticity, and reliability of health-related claims. Full article
(This article belongs to the Section Food Microbiology)
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40 pages, 3199 KB  
Article
Scalable Satellite-Assisted Adaptive Federated Learning for Robust Precision Farming
by Sai Puppala and Koushik Sinha
Agronomy 2026, 16(2), 229; https://doi.org/10.3390/agronomy16020229 - 18 Jan 2026
Viewed by 49
Abstract
Dynamic network conditions in precision agriculture motivate a scalable, privacy preserving federated learning architecture that tightly integrates ground-based edge intelligence with a space-assisted hierarchical aggregation layer. In Phase 1, heterogeneous tractors act as intelligent farm nodes that train local models, form capability- and [...] Read more.
Dynamic network conditions in precision agriculture motivate a scalable, privacy preserving federated learning architecture that tightly integrates ground-based edge intelligence with a space-assisted hierarchical aggregation layer. In Phase 1, heterogeneous tractors act as intelligent farm nodes that train local models, form capability- and task-aware clusters, and employ Network Quality Index (NQI)-driven scheduling, similarity-based check pointing, and compressed transmissions to cope with highly variable 3G/4G/5G connectivity. In Phase 2, cluster drivers synchronize with Low Earth Orbit (LEO) and Geostationary Earth Orbit (GEO) satellites that perform regional and global aggregation using staleness- and fairness-aware weighting, while end-to-end Salsa20 + MAC encryption preserves the confidentiality and integrity of all model updates. Across two representative tasks—nutrient prediction and crop health assessment—our full hierarchical system matches or exceeds centralized performance (e.g., AUC 0.92 vs. 0.91 for crop health) while reducing uplink traffic by ∼90% relative to vanilla FedAvg and cutting the communication energy proxy by more than 4×. The proposed fairness-aware GEO aggregation substantially narrows regional performance gaps (standard deviation of AUC across regions reduced from 0.058 to 0.017) and delivers the largest gains in low-connectivity areas (AUC 0.74 → 0.88). These results demonstrate that coupling on-farm intelligence with multi-orbit federated aggregation enables near-centralized model quality, strong privacy guarantees, and communication efficiency suitable for large-scale, connectivity-challenged agricultural deployments. Full article
(This article belongs to the Collection AI, Sensors and Robotics for Smart Agriculture)
11 pages, 1772 KB  
Article
Species and Functional Trait Determinants of Biochar Carbon Retention: Insights from Uniform Smoldering Experiments
by Jingyuan Wang
Forests 2026, 17(1), 116; https://doi.org/10.3390/f17010116 - 14 Jan 2026
Viewed by 116
Abstract
Understanding the influence of tree species and their intrinsic traits on biochar yield and carbon retention is essential for optimizing the conversion of biomass to biochar in carbon-negative systems. While it is well-established that pyrolysis temperature and broad feedstock categories significantly affect biochar [...] Read more.
Understanding the influence of tree species and their intrinsic traits on biochar yield and carbon retention is essential for optimizing the conversion of biomass to biochar in carbon-negative systems. While it is well-established that pyrolysis temperature and broad feedstock categories significantly affect biochar properties, the extent of species-level variation within woody biomass under standardized pyrolysis conditions remains insufficiently quantified. Here, we synthesized biochar from seven common subtropical tree species at 600 °C under oxygen-limited smoldering conditions and quantified three key indices: biochar yield (Y), carbon recovery efficiency (ηC), and carbon enrichment factor (EC). We further examined the relationships of these indices with feedstock characteristics (initial carbon content, wood density) and functional group identity (conifer vs. broadleaf). Analysis of variance revealed significant interspecific differences in ηC but weaker effects on Y, indicating that species identity primarily governs carbon retention rather than total mass yield. Broadleaf species (Liquidambar formosana, Castanea mollissima) exhibited consistently higher ηC and EC than conifers (Pinus massoniana, P. elliottii), reflecting higher lignin content and wood density that favor aromatic char formation. Principal component and cluster analyses clearly separated coniferous and broadleaf taxa, accounting for over 80% of total variance in carbon-related traits. Regression models showed that feedstock carbon content, biochar carbon content, and wood density together explained 15.5% of the variance in ηC, with feedstock carbon content exerting a significant negative effect, whereas wood density correlated positively with carbon retention. These findings demonstrate that tree species and their functional traits jointly determine carbon fixation efficiency during smoldering. High initial carbon content alone does not guarantee enhanced carbon recovery; instead, wood density and lignin-derived structural stability dominate retention outcomes. Our results underscore the need for trait-based feedstock selection to improve biochar quality and carbon sequestration potential, and provide a mechanistic framework linking species identity, functional traits, and carbon stabilization in biochar production. Full article
(This article belongs to the Section Forest Ecology and Management)
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23 pages, 6177 KB  
Article
Hierarchical and Robust Intelligent Design System for Aircraft Skin Die Face of Stretch Forming
by Xilei Zhang, Haijiao Kong, Zhen Wang, Yang Wei, Yuqi Liu and Zhibing Zhang
Metals 2026, 16(1), 94; https://doi.org/10.3390/met16010094 - 14 Jan 2026
Viewed by 212
Abstract
Most aircraft skin components are typical sheet metal components, and stretch forming serves as the primary forming process. The die face is the core foundation for both the finite element simulation and mold trial. Due to the intricate geometric characteristics of aircraft skin [...] Read more.
Most aircraft skin components are typical sheet metal components, and stretch forming serves as the primary forming process. The die face is the core foundation for both the finite element simulation and mold trial. Due to the intricate geometric characteristics of aircraft skin components and iterative revisions caused by stretch forming process adjustments and product design changes, the die face design of aircraft skin components is inherently time-intensive, highly complex, and prone to instability. To address these issues, a Hierarchical and Hybrid Association Method (HHAM) based on a robust updating mechanism and hybrid associations is proposed for the intelligent design system. HHAM can significantly enhance the stability and efficiency of die face design. Specifically, the hierarchical and automatic updating process of HHAM, incorporating robust error handling mechanisms, is the core methodology that guarantees the stability of complex and iterative die face design for aircraft skin. Moreover, the inter-module hybrid association, which integrates parametric modeling and automatic connection techniques, eliminates the instability in die face design updating caused by feature and topology variations. Additionally, robust geometric algorithms for wireframe modeling effectively improve the surface quality and generation success rate of the die face. The intelligent design system developed based on the CATIA platform has been successfully applied in two professional aircraft skin component manufacturing enterprises. Case studies and industrial application practices verify the effectiveness of the proposed system, achieving a 72.7% improvement in design efficiency and a 70.27% reduction in the risk of die face update errors. Full article
(This article belongs to the Special Issue Sheet Metal Forming Processes)
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22 pages, 2909 KB  
Article
Study on Quality of AI Service Guarantee in Digital Twin Networks for XR Scenarios
by Jinfei Zhou, Yuehong Gao, Xinyao Wang, Yiran Li and Ziqi Zhao
Electronics 2026, 15(2), 344; https://doi.org/10.3390/electronics15020344 - 13 Jan 2026
Viewed by 120
Abstract
In line with the trend of “native intelligence”, artificial intelligence (AI) will be more deeply integrated into communication networks in the future. Quality of AI service (QoAIS) will become an important factor in measuring the performance of native AI wireless networks. Networks should [...] Read more.
In line with the trend of “native intelligence”, artificial intelligence (AI) will be more deeply integrated into communication networks in the future. Quality of AI service (QoAIS) will become an important factor in measuring the performance of native AI wireless networks. Networks should reasonably allocate multi-dimensional resources to ensure QoAIS for users. Extended Reality (XR) is one of the important application scenarios for future 6G networks. To ensure both the accuracy and latency requirements of users for AI services are met, this paper proposes a resource allocation algorithm called Asynchronous Multi-Agent Deep Deterministic Policy Gradient with Independent State and Action (A-MADDPG-ISA). The proposed algorithm supports agents to use different dimensional state spaces and action spaces; therefore, it enables agents to address different strategy issues separately and makes the algorithm design more flexible. The actions of different agents are executed asynchronously, enabling actions outputted earlier to be transmitted as additional information to other agents. The simulation results show that the proposed algorithm has a 10.41% improvement compared to MADDPG (Multi-Agent Deep Deterministic Policy Gradient). Furthermore, to overcome the limitations of directly applying AI or manual rule-based schemes to real networks, this research establishes a digital twin network (DTN) system and designs pre-validation functionality. The DTN system contributes to better ensuring users’ QoAIS. Full article
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21 pages, 3102 KB  
Article
An Enhanced Hybrid Astar Path Planning Algorithm Using Guided Search and Corridor Constraints
by Na Che, Xianwei Zeng, Jian Zhao, Haiyan Wang and Qinsheng Du
Sensors 2026, 26(2), 379; https://doi.org/10.3390/s26020379 - 7 Jan 2026
Viewed by 161
Abstract
Aiming at the problems of large search space, unstable computational efficiency, and lack of safety of generated paths in complex environments of traditional HybridA* algorithms, this paper proposes an improved HybridA* algorithm based on Voronoi diagrams and safe corridors (GCHybridA*) to overcome these [...] Read more.
Aiming at the problems of large search space, unstable computational efficiency, and lack of safety of generated paths in complex environments of traditional HybridA* algorithms, this paper proposes an improved HybridA* algorithm based on Voronoi diagrams and safe corridors (GCHybridA*) to overcome these challenges. The method first reduces ineffective node expansion by constructing a Voronoi path away from obstacles and smoothing it, followed by selecting key guidance points to provide stage-like goals for path search. Then, an innovative safe corridor is generated and the path search is restricted to the safe corridor area to guarantee the safety of the path, and an adaptive step-size mechanism is designed to balance the search efficiency and path quality. The experimental results show that the GCHybridA* algorithm significantly outperforms the conventional HybridA* algorithm, with an average reduction of 83.7% in node expansions while maintaining zero potential collision points across all four typical maps. This study provides an innovative and robust solution for efficient and safe path planning in autonomous driving systems. This study provides an innovative and robust solution for global path planning in autonomous driving systems, focusing on static environment navigation with safety guarantees. Full article
(This article belongs to the Section Sensors and Robotics)
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13 pages, 1149 KB  
Article
Monitoring IoT and Robotics Data for Sustainable Agricultural Practices Using a New Edge–Fog–Cloud Architecture
by Mohamed El-Ouati, Sandro Bimonte and Nicolas Tricot
Computers 2026, 15(1), 32; https://doi.org/10.3390/computers15010032 - 7 Jan 2026
Viewed by 237
Abstract
Modern agricultural operations generate high-volume and diverse data (historical and stream) from various sources, including IoT devices, robots, and drones. This paper presents a novel smart farming architecture specifically designed to efficiently manage and process this complex data landscape.The proposed architecture comprises five [...] Read more.
Modern agricultural operations generate high-volume and diverse data (historical and stream) from various sources, including IoT devices, robots, and drones. This paper presents a novel smart farming architecture specifically designed to efficiently manage and process this complex data landscape.The proposed architecture comprises five distinct, interconnected layers: The Source Layer, the Ingestion Layer, the Batch Layer, the Speed Layer, and the Governance Layer. The Source Layer serves as the unified entry point, accommodating structured, spatial, and image data from sensors, Drones, and ROS-equipped robots. The Ingestion Layer uses a hybrid fog/cloud architecture with Kafka for real-time streams and for batch processing of historical data. Data is then segregated for processing: The cloud-deployed Batch Layer employs a Hadoop cluster, Spark, Hive, and Drill for large-scale historical analysis, while the Speed Layer utilizes Geoflink and PostGIS for low-latency, real-time geovisualization. Finally, the Governance Layer guarantees data quality, lineage, and organization across all components using Open Metadata. This layered, hybrid approach provides a scalable and resilient framework capable of transforming raw agricultural data into timely, actionable insights, addressing the critical need for advanced data management in smart farming. Full article
(This article belongs to the Special Issue Computational Science and Its Applications 2025 (ICCSA 2025))
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10 pages, 1644 KB  
Proceeding Paper
Heat Stress in Chillies: Integrating Physiological Responses and Heterosis Breeding Approaches for Enhanced Resilience
by Inaba Hawraa, Muhammad Azam Khan, Muhammad Tahir Akram, Rashid Mehmood Rana, Feroz Ahmed Tipu, Israr Ali, Hina Nawaz and Muhammad Hashir Khan
Biol. Life Sci. Forum 2025, 51(1), 12; https://doi.org/10.3390/blsf2025051012 - 6 Jan 2026
Viewed by 144
Abstract
Chilli (Capsicum annuum) is a popular spice and vegetable crop of significant economic importance that is cultivated worldwide in warm and humid climatic zones. Although chilli is a thermophilic crop, its quality and yield potential are significantly affected due to various [...] Read more.
Chilli (Capsicum annuum) is a popular spice and vegetable crop of significant economic importance that is cultivated worldwide in warm and humid climatic zones. Although chilli is a thermophilic crop, its quality and yield potential are significantly affected due to various abiotic factors, including extremely fluctuating temperatures beyond the optimum temperatures (18–30 °C). Global warming and anthropogenic activities lead to adverse climatic changes, imposing severe stress on growth, development, and productivity. High temperatures above 43–45 °C adversely affect chilli crops, especially during the reproductive stages, by causing immature fruit dropping, poor seed vigour, reduced number of flowers, flower abscission, aborted reproductive organs, reduced fruit set, and significant yield loss by 50%. Therefore, to reduce quantitative and qualitative losses, heat management is necessary from April to June in Pakistan, when the temperature rises beyond 40 °C. For heat management, the hybridisation of heat-resilient and high-yielding genotypes to develop heat-tolerant high-yielding hybrids appears to be a rational approach. These genetically improved hybrids inherit such characteristics that assist in maintaining vigorous growth, fruit quality, and stable yield without significant yield losses even under heat-stressed conditions. Hence, the thermotolerant chilli hybrids developed through hybridisation help to satisfy the escalating demand for chilli and guarantee the financial stability of farmers. Full article
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20 pages, 1542 KB  
Article
Large-Scale Point Cloud Completion Through Registration and Fusion of Object-Level Reconstructions
by Taiming He, Yixuan Fang, Keyuan Li and Lu Yang
Appl. Sci. 2026, 16(1), 554; https://doi.org/10.3390/app16010554 - 5 Jan 2026
Viewed by 230
Abstract
Existing 3D reconstruction algorithms commonly struggle with modeling specific local objects within large-scale scenes, often resulting in a lack of local detail and incomplete geometric structures. While current mainstream point cloud completion methods can restore these missing structures to some degree, they are [...] Read more.
Existing 3D reconstruction algorithms commonly struggle with modeling specific local objects within large-scale scenes, often resulting in a lack of local detail and incomplete geometric structures. While current mainstream point cloud completion methods can restore these missing structures to some degree, they are fundamentally based on generative in-filling, a process that relies on geometric priors learned from large-scale datasets. Consequently, the physical realism and geometric accuracy of the results cannot be guaranteed. To address these limitations, this paper proposes a novel, data-driven framework for point cloud completion. Our core method involves the high-precision, heterogeneous data registration and seamless fusion of an object-level point cloud—reconstructed with high-fidelity appearance and geometry by our optimized Neural Radiance Fields (NeRF) framework—with our target large-scale scene point cloud. By using high-precision, physically based data as a strong prior for geometric completion, we offer an alternative route to conventional generative completion methods. Concurrently, we employ unsupervised evaluation metrics to assess the intrinsic quality of the final results. This work provides a robust and high-fidelity solution to the problem of completing local objects within large-scale scenes. Evaluated on our self-constructed UAV-Recon dataset, the proposed method achieved a Structural Plausibility ≥ 0.995, Geometric Smoothness ≤ 0.19, and Distribution Uniformity ≈ 1.2, offering a robust solution for the high-fidelity completion of local objects within large-scale scenes. Full article
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25 pages, 1829 KB  
Article
A Water Resources Scheduling Model for Complex Water Networks Considering Multi-Objective Coordination
by Hui Bu, Chun Pan, Chunyang Liu, Yu Zhu, Zhuowei Yin, Zhengya Liu and Yu Zhang
Water 2026, 18(1), 124; https://doi.org/10.3390/w18010124 - 5 Jan 2026
Viewed by 257
Abstract
Complex water networks face prominent contradictions among flood control, water supply, and ecological protection, and traditional scheduling models struggle to address multi-dimensional water security challenges. To solve this problem, this study proposes a multi-objective coordinated water resources scheduling model for complex water networks, [...] Read more.
Complex water networks face prominent contradictions among flood control, water supply, and ecological protection, and traditional scheduling models struggle to address multi-dimensional water security challenges. To solve this problem, this study proposes a multi-objective coordinated water resources scheduling model for complex water networks, taking the Taihu Lake Basin as a typical case. First, a multi-objective optimization indicator system covering flood control, water supply, and aquatic ecological environment was constructed, including 12 key indicators such as drainage efficiency of key outflow hubs and water supply guarantee rate. Second, a dynamic variable weighting strategy was adopted to convert the multi-objective optimization problem into a single-objective one by adjusting indicator weights according to different scheduling periods. Finally, a combined solving mode integrating a basin water quantity-quality model and a joint scheduling decision model was established, optimized using the particle swarm optimization (PSO) algorithm. Under the 1991-Type 100-Year Return Period Rainfall scenario, three scheduling schemes were designed: a basic scheduling scheme and two enhanced discharge schemes modified by lowering the drainage threshold of the Xinmeng River Project. Simulation and decision results show that the enhanced discharge scheme with the lowest drainage threshold achieves the optimal performance with an objective function value of 98.8. Compared with the basic scheme, it extends the flood season drainage days of the Jiepai Hub from 32 to 43 days, increases the average flood season discharge of the Xinmeng River to the Yangtze River by 9.5%, and reduces the maximum water levels of Wangmuguan, Fangqian, Jintan, and Changzhou (III) stations by 5 cm, 5 cm, 4 cm, and 4 cm, respectively. This model effectively overcomes technical bottlenecks such as conflicting multi-objectives and complex water system structures, providing theoretical and technical support for multi-objective coordinated scheduling of water resources in complex water networks. Full article
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16 pages, 2031 KB  
Article
Cooperative 4D Trajectory Prediction and Conflict Detection in Integrated Airspace
by Xin Ma, Linxin Zheng, Jiajun Zhao and Yuxin Wu
Algorithms 2026, 19(1), 32; https://doi.org/10.3390/a19010032 - 1 Jan 2026
Viewed by 187
Abstract
In order to effectively ensure the flight safety of unmanned aerial vehicles (UAVs) and effectively deal with the risk of integrated airspace operation, this study carried out a series of key technology exploration and verification. In terms of data processing, Density-based spatial clustering [...] Read more.
In order to effectively ensure the flight safety of unmanned aerial vehicles (UAVs) and effectively deal with the risk of integrated airspace operation, this study carried out a series of key technology exploration and verification. In terms of data processing, Density-based spatial clustering of applications with noise (DBSCAN) clustering method is used to preprocess the characteristics of UAV automatic dependent surveillance–broadcast (ADS-B) data, effectively purify the data from the source, eliminate the noise and outliers of track data in spatial dimension and spatial-temporal dimension, significantly improve the data quality and standardize the data characteristics, and lay a reliable and high-quality data foundation for subsequent trajectory analysis and prediction. In terms of trajectory prediction, the convolutional neural networks-bidirectional gated recurrent unit (CNN-BiGRU) trajectory prediction model is innovatively constructed, and the integrated intelligent calculation of ‘prediction-judgment’ is successfully realized. The output of the model can accurately and prospectively judge the conflict situation and conflict degree between any two trajectories, and provide core and direct technical support for trajectory conflict warning. In the aspect of conflict detection, the performance of the model and the effect of conflict detection are fully verified by simulation experiments. By comparing the predicted data of the model with the real track data, it is confirmed that the CNN-BiGRU prediction model has high accuracy and reliability in calculating the distance between aircraft. At the same time, the preset conflict detection method is used for further verification. The results show that there is no conflict risk between the UAV and the manned aircraft in integrated airspace during the full 800 s of terminal area flight. In summary, the trajectory prediction model and conflict detection method proposed in this study provide a key technical guarantee for the construction of an active and accurate integrated airspace security management and control system, and have important application value and reference significance for improving airspace management efficiency and preventing flight conflicts. Full article
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20 pages, 2951 KB  
Article
Vibration-Excited Combined Harvester for Dual Harvesting of Ears and Stalks: Design and Experiments
by Xinxin Wang, Yang Wang, Qian Wang, Xiang Li, Ruo Liu, Junlin Liu, Yansong Gong, Yushuai Liu and Duanyang Geng
Agriculture 2026, 16(1), 104; https://doi.org/10.3390/agriculture16010104 - 31 Dec 2025
Viewed by 246
Abstract
Aiming at the reliability of ear picking and the consistency of stalk chopping length in the process of corn ear and stalk harvesting, a new type of corn harvester with both ear and stalk harvesting based on exciting ear picking was developed. Based [...] Read more.
Aiming at the reliability of ear picking and the consistency of stalk chopping length in the process of corn ear and stalk harvesting, a new type of corn harvester with both ear and stalk harvesting based on exciting ear picking was developed. Based on the vertical cutting table, the machine realizes the excitation of the ear during the process of stalk transportation by rotating the eight-edged special-shaped pick-up roll, and the stable and orderly transportation of stalks before cutting is realized by the way of clamping and conveying with the rear rollers. By analyzing the configuration and parameter determination methods of the main working parts, the high-efficiency and low-loss harvest of the ear was realized, and the consistency of the cut length of the stalk was guaranteed. A discrete element model (DEM) of ear-bearing maize plants was established using EDEM (version 2024, Altair Engineering, Troy, MI, USA) simulation software, and a five-factor, three-level quadratic orthogonal rotation experiment was conducted based on Response Surface Methodology (RSM). The simulation results indicated that the optimal operational quality was achieved under the following parameters: a header angle of 10°, a snapping roller speed of 942 rpm, a clamping roller speed of 215 rpm, and a moving blade speed of 1450 rpm. Furthermore, multiple sets of field trials were conducted at various forward speeds to validate these findings. The mean values of seed loss rate, ear loss rate, and seed breakage rate are 0.51%, 0.55%, and 0.32%, respectively, for the harvester at operating speeds of 4 km/h, 6 km/h, 8 km/h, and 10 km/h. The σ values are 97%, 98%, 97%, and 98%. The field harvesting performance indexes meet the requirements of technical specifications for evaluating the operation quality of corn combine harvester, and meet the design requirements of low loss, high efficiency, and consistency of stem chopping length. Full article
(This article belongs to the Section Agricultural Technology)
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30 pages, 623 KB  
Article
Resource Allocation for Network Slicing in 5G/RSU Integrated Networks with Multi-User and Multi-QoS Services
by Kun Song, Hanxiao Jiang, Jining Liu and Wai Kin (Victor) Chan
Mathematics 2026, 14(1), 159; https://doi.org/10.3390/math14010159 - 31 Dec 2025
Viewed by 341
Abstract
Network slicing in 5G systems enables different Quality of Service (QoS) for heterogeneous Vehicle-to-Everything (V2X) applications, yet efficiently allocating resource blocks from both 5G base stations and roadside units (RSUs) across multiple slices remains challenging. Existing approaches either pre-assign users to slices or [...] Read more.
Network slicing in 5G systems enables different Quality of Service (QoS) for heterogeneous Vehicle-to-Everything (V2X) applications, yet efficiently allocating resource blocks from both 5G base stations and roadside units (RSUs) across multiple slices remains challenging. Existing approaches either pre-assign users to slices or rely on population-based metaheuristic algorithms that cannot guarantee deterministic real-time performance within the stringent 20 ms latency requirements of vehicular networks. This study formulates the resource allocation problem as an integer programming model that jointly optimizes slice selection and resource allocation to maximize weighted system transmission rate while satisfying heterogeneous QoS constraints. We develop a constructive heuristic algorithm that employs a hierarchical allocation strategy prioritizing 5G resources before RSU resources, coupled with a backfilling mechanism to exploit the remaining resource block capacity. Numerical experiments across abundant 5G and limited resource scenarios demonstrate the algorithm’s effectiveness. First, comparing against Random baseline validates the optimization model’s value, achieving 21.4–24.9% higher weighted throughput in an abundant 5G scenario and 42.5–51.0% improvement under a limited resource scenario. Second, performance evaluation with 500 users shows the proposed constructive heuristic achieves optimal solutions in abundant 5G resource scenarios and 3.5–5.7% optimality gaps in limited resource scenarios, while maintaining an execution time of under 20 ms, which satisfies real-time requirements and executes faster than Gurobi, Simulated Annealing and Round-Robin. Third, scalability analyses across 400–700 users demonstrate favorable performance scaling, as the optimality gap decreases from 5.3% to 3.4% with execution times consistently below 20 ms. The proposed heuristic achieves the highest service admission count while maintaining near-optimal system weighted transmission rate performance, ranking second only to Gurobi solver. Compared with other baseline algorithms, the proposed heuristic delivers a superior balance between solution quality and computational efficiency, confirming its real-time feasibility for large-scale V2X network deployments. Full article
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7 pages, 290 KB  
Article
Determining the Best Algorithm for the Knapsack Problem with Forfeits
by Peter Cadiz, Yun Lu, Myung Soon Song and Francis J. Vasko
Mathematics 2026, 14(1), 143; https://doi.org/10.3390/math14010143 - 30 Dec 2025
Viewed by 205
Abstract
In 2024, four papers that presented four different solution approaches for the knapsack problem with forfeits (KPF) appeared in the OR literature. However, none of these four solution approaches compared their performance to the other three on a standard set of 120 KPF [...] Read more.
In 2024, four papers that presented four different solution approaches for the knapsack problem with forfeits (KPF) appeared in the OR literature. However, none of these four solution approaches compared their performance to the other three on a standard set of 120 KPF test instances. In this short paper, both empirically and statistically, these four KPF solution approaches are compared. Furthermore, by using the solutions from the best method (HESM) among the four to initialize Gurobi, bounded solutions are obtained. For the 120 KPF test instances, this simple hybrid approach resulted in solutions that, on average, were guaranteed to be within 7% of the optimums. This type of guarantee does not exist for other KPF solution methods in the literature. It is very important for operations research (OR) practitioners that need to ensure the value of their solutions to management to have some guarantee of the quality of these solutions. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)
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22 pages, 4026 KB  
Article
Path Planning and Tracking Control for Unmanned Surface Vehicle Based on Adaptive Differential Evolution Algorithm
by Zhongming Xiao, Jingyi Zhao, Zhengjiang Liu and Guang Yang
Actuators 2026, 15(1), 13; https://doi.org/10.3390/act15010013 - 29 Dec 2025
Viewed by 289
Abstract
With the growing demand for safe obstacle avoidance and precise trajectory tracking in the autonomous navigation of unmanned surface vessels (USVs), this paper investigates an adaptive differential evolution approach for integrated path planning and tracking control. In the path planning stage, an elite [...] Read more.
With the growing demand for safe obstacle avoidance and precise trajectory tracking in the autonomous navigation of unmanned surface vessels (USVs), this paper investigates an adaptive differential evolution approach for integrated path planning and tracking control. In the path planning stage, an elite archive mechanism is first incorporated into the mutation process, and the scaling factor F and crossover rate CR are adaptively adjusted to enhance population diversity and global search capability. Then, the International Regulations for Preventing Collisions at Sea (COLREGs) are embedded into the algorithmic framework to reinforce collision avoidance performance in complex encounter scenarios. A multi-objective fitness function combining six performance criteria is subsequently constructed to evaluate individual path points, thereby identifying high-quality solutions that ensure both safe navigation and route efficiency. In the tracking control stage, the optimally generated reference trajectory is then employed as the input command for the vessel’s motion control subsystem. A fuzzy logic system is introduced to approximate unknown nonlinear dynamics, and an adaptive fuzzy logic controller is designed to guarantee accurate tracking of the planned path. Finally, simulation tests are used to show the algorithm’s efficiency and usefulness. Full article
(This article belongs to the Special Issue Control System of Autonomous Surface Vehicles)
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