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20 pages, 4695 KB  
Review
Dual-Mechanism Synergistic Regulation and Performance Optimization of Lead Sulfide Quantum Dot Coatings in Optoelectronic Memristors
by Ru Li, Xinhe Jiang, Xuhao Zhao, Huiyun Zhang, Qingyu Xu and Guangyu Wang
Coatings 2026, 16(6), 715; https://doi.org/10.3390/coatings16060715 (registering DOI) - 15 Jun 2026
Abstract
Lead sulfide quantum dots (PbS QDs), as a functional-layer coating, enable non-volatile integration and neuromorphic computing in memristive structures to address the von Neumann bottleneck. Herein, the dual-interface mechanism of PbS QDs in the memristor film structure is reviewed. First, the local electric [...] Read more.
Lead sulfide quantum dots (PbS QDs), as a functional-layer coating, enable non-volatile integration and neuromorphic computing in memristive structures to address the von Neumann bottleneck. Herein, the dual-interface mechanism of PbS QDs in the memristor film structure is reviewed. First, the local electric field enhancement effect generates tip electrode-like structures in the coating film through QD-mediated spatial charge gradients, thereby enabling precise control over the nucleation and growth of conductive filaments (CFs). As a result, the consistency of switching voltages and the thermal stability at elevated temperatures are significantly improved. Conversely, the anion reservoir effect exploits surface dangling bonds on QDs to efficiently capture anions from the dielectric layer, thereby synergistically regulating vacancy migration kinetics. This process enables zero-initialization behavior and ultra-low-power operation. In addition, the spatial distribution design and density modulation of QDs further reinforce both mechanisms. The structural optimization of QD/dielectric interface engineering can simultaneously improve cycling endurance and resistive switching uniformity. Furthermore, modification of QD surface chemistry through ligand decoration and passivation suppresses the stochasticity of ionic diffusion while improving the linearity of synaptic weight updates. This interfacial engineering strategy utilizing QDs as coating films advances the development of high-performance photonic–electronic systems for memory–computing convergence. Full article
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24 pages, 1770 KB  
Article
Volt–Var Self-Optimizing Control of Distribution Networks Based on the BOST-GRPO Algorithm Under Stability Constraints
by Zewen Li, Weiming Chen, Yuanliang Fan, Yibo Li, Xinghua Huang, Xinxin Wu and Ling Yang
Electronics 2026, 15(12), 2655; https://doi.org/10.3390/electronics15122655 (registering DOI) - 15 Jun 2026
Abstract
High penetration of distributed photovoltaic (PV) generation has intensified voltage violations and stochastic voltage fluctuations in distribution networks, while existing voltage–var control methods still have limitations in terms of communication dependence, scalability, and edge deployment. To address these issues, this paper proposes a [...] Read more.
High penetration of distributed photovoltaic (PV) generation has intensified voltage violations and stochastic voltage fluctuations in distribution networks, while existing voltage–var control methods still have limitations in terms of communication dependence, scalability, and edge deployment. To address these issues, this paper proposes a stability-constrained voltage–var self-optimizing control method for distribution networks based on the Bandit-Guided Online Self-Tuning Group Relative Policy Optimization (BOST-GRPO) algorithm. First, based on the LinDistFlow linearized power-flow model, a communication-free, decentralized, and locally observable reinforcement learning control environment is constructed, enabling each node to independently generate reactive power regulation commands using only local voltage measurements. Second, a contraction-mapping-based stability constraint is embedded into the policy output layer, theoretically guaranteeing the local exponential convergence of nodal voltage deviations around the equilibrium point and reducing the risk of voltage instability caused by overly aggressive policy actions. Meanwhile, device capacity constraints are incorporated into the policy output through a tanh-based action mapping, ensuring the physical feasibility of control commands. On this basis, BOST-GRPO realizes the online self-tuning of key hyperparameters within a single training process through a Bandit-guided mechanism, thereby avoiding the repeated training overhead caused by traditional offline hyperparameter tuning. Simulation results on the IEEE 33-bus system show that the proposed method outperforms benchmark reinforcement learning algorithms in final test cost, voltage deviation suppression, steady-state error, and regulation speed. Further tests under sensitivity matrix mismatch, different initial voltage disturbance intensities, and the extended IEEE 69-bus system demonstrate that the proposed method achieves good robustness and scalability. Full article
(This article belongs to the Special Issue Renewable Energy Integration and Energy Management in Smart Grid)
17 pages, 5112 KB  
Article
Path Planning for an Unmanned Wing-in-Ground-Effect Craft Using a Hybrid ISSA-GWO Algorithm
by Yuan Chen, Yong Zhang and Yiheng Wang
Drones 2026, 10(6), 464; https://doi.org/10.3390/drones10060464 (registering DOI) - 15 Jun 2026
Abstract
A novel hybrid ISSA-GWO (Improved Sparrow Search Algorithm–Grey Wolf Optimizer) is proposed for the path planning of Unmanned Wing-in-Ground-Effect Craft (UWIGC), integrating ground-effect constraints and island-reef environments into a unified optimization framework. Leveraging its exceptional ultra-low-altitude flight capability and high economic efficiency, the [...] Read more.
A novel hybrid ISSA-GWO (Improved Sparrow Search Algorithm–Grey Wolf Optimizer) is proposed for the path planning of Unmanned Wing-in-Ground-Effect Craft (UWIGC), integrating ground-effect constraints and island-reef environments into a unified optimization framework. Leveraging its exceptional ultra-low-altitude flight capability and high economic efficiency, the UWIGC offers unique advantages in maritime missions such as island patrol and rapid replenishment. However, its path planning faces the dual challenge of precise obstacle avoidance and ultra-low-altitude maintenance, due to the obstacle distribution in island regions and the altitude window constraints inherent to ground-effect flight. To address this, the proposed method integrates the swarm intelligence of the Sparrow Search Algorithm and employs a self-destruction mechanism to escape local optima. Furthermore, it combines the hierarchical guidance of the Grey Wolf Optimizer to enhance convergence accuracy. The algorithm incorporates ground-effect maintenance constraints and an island-reef threat model, and it smooths the final path using cubic B-spline curves. Simulation results demonstrate that the proposed algorithm outperforms the standard Sparrow Search Algorithm, Grey Wolf Optimizer, and Particle Swarm Optimization in terms of convergence speed, optimization accuracy, and obstacle avoidance success rate. It is capable of generating a feasible, safe, and smooth path, thereby supporting the autonomous navigation of UWIGC in island reef waters. Full article
(This article belongs to the Special Issue Swarm Intelligence-Inspired Planning and Control for Drones)
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15 pages, 3554 KB  
Article
GL-SeqNet: Global–Local Fusion for Intra-Cluster Tomato Harvesting Sequence Optimization
by Zhichao Meng, Shan Du, Bo Wang, Jun Pan, Dong Hu, Xiaoqiang Du and Qinghua Yang
Agriculture 2026, 16(12), 1322; https://doi.org/10.3390/agriculture16121322 (registering DOI) - 15 Jun 2026
Abstract
Tomato harvesting in protected horticulture is a critical task that faces challenges due to labor shortages, high environmental stress in greenhouses, and the complex nature of clustered fruit arrangements. This study proposes the global–local sequence ranking network (GL-SeqNet), a novel model designed to [...] Read more.
Tomato harvesting in protected horticulture is a critical task that faces challenges due to labor shortages, high environmental stress in greenhouses, and the complex nature of clustered fruit arrangements. This study proposes the global–local sequence ranking network (GL-SeqNet), a novel model designed to optimize intra-cluster tomato harvesting sequences by integrating global and local features using a deep learning approach. GL-SeqNet fuses the global structural information of tomato clusters with local fruit attributes to dynamically update the harvesting sequence, ensuring the optimal target is selected at each step. The model features a dual-stream architecture, comprising separate global and local backbones, and utilizes a ranking head for prioritizing intra-cluster targets. An AI-based image object-removal tool was used to simulate the dynamic structural changes within a cluster during harvesting, facilitating the creation of a state evolution dataset. The experimental results showed that the best overall performance was achieved with a global resolution of 112 × 112 and a local resolution of 56 × 56, yielding a Top-1 accuracy of 0.950, a position match rate (PMR) of 0.970, and an inference time of only 22.6 ms, along with faster convergence. The results underscore the potential of global and local fusion strategies and ranking-based learning for effective harvesting sequence optimization. Full article
(This article belongs to the Section Artificial Intelligence and Digital Agriculture)
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21 pages, 1972 KB  
Article
Feedforward Neural Network-Based MPC Optimized by Hybrid Fractional PSO–SQP for Trajectory Tracking of Autonomous Vehicles
by Fahad Alotaibi, Habib Dhahri, Saleh Almohaimeed and Awais Mahmood
Automation 2026, 7(3), 95; https://doi.org/10.3390/automation7030095 (registering DOI) - 15 Jun 2026
Abstract
Background/Objective: Autonomous vehicles (AVs) require control algorithms capable of handling complex and dynamic environments while satisfying multiple conflicting objectives such as safety, comfort, energy efficiency, and trajectory accuracy. Model predictive control (MPC) offers a principled framework for multi-constraint optimization, yet its real-time feasibility [...] Read more.
Background/Objective: Autonomous vehicles (AVs) require control algorithms capable of handling complex and dynamic environments while satisfying multiple conflicting objectives such as safety, comfort, energy efficiency, and trajectory accuracy. Model predictive control (MPC) offers a principled framework for multi-constraint optimization, yet its real-time feasibility remains challenging for nonlinear vehicle dynamics. Methods: This paper presents a feedforward neural network (FNN)-based MPC framework for autonomous vehicle trajectory tracking. The FNN approximates the coupled vehicle dynamics and visual preview error model using an algebraic sum of log-sigmoid functions. Three adaptive FNN parameter sets, namely, the scaling factor, convergence parameter, and time-shifting parameter, are jointly optimized using a hybrid algorithm that combines the global search capability of fractional particle swarm optimization (FPSO) with the local refinement of sequential quadratic programming (SQP). Results: Comprehensive scenario-based simulations are performed to evaluate trajectory tracking dynamics under dry conditions with an adhesion coefficient of 0.8 and a vehicle mass of 1723 kg moving at a speed of 80 km/h. The results are quantitatively compared with a traditional PID controller and a structurally comparable MPC framework from the literature under identical simulation conditions; related DRL- and RL-based methods are discussed qualitatively for contextual orientation only. The stability, reliability, and computational complexity of the proposed framework are examined based on the mean square error, fitness value, and computational budget in GFLOPs for 100 independent runs. Conclusions: The proposed FNN-based MPC framework demonstrates improved tracking accuracy and optimizer reliability in simulation. While the present results indicate promising computational behavior, real-time deployment will require further validation on embedded automotive hardware and under closed-loop real-time constraints. Full article
(This article belongs to the Special Issue AI-Enhanced Measurement and Control for Robotic Systems)
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30 pages, 1935 KB  
Article
Factors Influencing Water and Sweet Beverage Purchasing Decisions and Behaviours Among Low-Income Households in Four Peri-Urban Communities in Accra: An Exploratory Study
by Christopher Delali Amegah, Gloria Adobea Odei Obeng-Amoako, Shu Wen Ng, Monica Lambon-Quayefio and Seth Adu-Afarwuah
Int. J. Environ. Res. Public Health 2026, 23(6), 799; https://doi.org/10.3390/ijerph23060799 (registering DOI) - 15 Jun 2026
Abstract
Background: In May 2023, Ghana implemented a 20% ad valorem tax on bottled water and sweet beverages (SBs), replacing a 17.5% tax; sachet water remained untaxed. The effect on low-income consumers’ purchasing decisions and consumption patterns remains poorly understood. Objective: We aimed to [...] Read more.
Background: In May 2023, Ghana implemented a 20% ad valorem tax on bottled water and sweet beverages (SBs), replacing a 17.5% tax; sachet water remained untaxed. The effect on low-income consumers’ purchasing decisions and consumption patterns remains poorly understood. Objective: We aimed to explore factors influencing water and SB purchasing behaviours among low-income households in four peri-urban Accra communities. Methods: This study employed a convergent parallel mixed-methods design. Four focus group discussions (n = 36) and a cross-sectional survey (n = 43) were conducted among purposively sampled household primary shoppers in early 2025 across Oyarifa, Teiman, Kweiman, and Danfa. Data were analysed thematically and descriptively. Results: Of 43 participants, 67% were female and 65% had junior high school education. Water insecurity was common (60%), and sachet water was the main drinking source (77%). SB purchasing was driven by taste and convenience, while sachet water choices were linked to perceived safety, price, and availability. Tax awareness was moderate (56%); many perceived bottled water taxation as unfair and reported intentions to switch to cheaper local alternatives. Conclusions: Limited tax awareness and perceived inequities suggest the need for policy refinements to better align fiscal measures with public health objectives. Full article
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12 pages, 395 KB  
Article
Research on Logistics Distribution Center Location Problem Based on Genetic Variation Firefly Algorithm
by Lang Yang, Changan Ren, Zhangwei Yu and Mengya Ma
Algorithms 2026, 19(6), 481; https://doi.org/10.3390/a19060481 (registering DOI) - 15 Jun 2026
Abstract
The selection of locations for logistics distribution centers poses a significant challenge in logistics network planning. Traditional methods often demonstrate limited accuracy in solutions and a tendency to become trapped in local optima when addressing large-scale, multi-constraint location models. To address these shortcomings, [...] Read more.
The selection of locations for logistics distribution centers poses a significant challenge in logistics network planning. Traditional methods often demonstrate limited accuracy in solutions and a tendency to become trapped in local optima when addressing large-scale, multi-constraint location models. To address these shortcomings, this study introduces a firefly algorithm enhanced by genetic mutation strategies (GVFA) to optimize the location of distribution centers. Within the framework of the standard firefly algorithm, we incorporate an adaptive step-size decay mechanism and a mutation operator. The movement step size adjusts dynamically based on iteration counts, while a mutation probability of 5% is implemented to maintain population diversity, effectively reducing the risk of premature convergence. A specialized boundary-handling strategy ensures that the search process remains within the feasible solution space, guiding the population toward the global optimum. Experiments were conducted using latitude–longitude coordinates and logistics demand data from 159 Cainiao Post stations in Hengyang City, resulting in the construction of a location model aimed at minimizing total costs. The findings confirm the efficiency and stability of our method in optimizing distribution center locations, thereby providing a novel intelligent optimization approach for the siting of logistics distribution centers. Full article
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26 pages, 4334 KB  
Article
RKF-YOLO: A Lightweight Dual-Task Model for Illegal Parking Detection and License Plate Recognition on Edge Devices
by Hao Chen, Yao Li, Yong Jia, Guangle Yao and Ruipeng Zhu
Electronics 2026, 15(12), 2638; https://doi.org/10.3390/electronics15122638 (registering DOI) - 15 Jun 2026
Abstract
To address the joint requirements of illegal parking detection and license plate recognition under complex traffic scenarios and limited edge-device resources, this study proposes RKF-YOLO, a lightweight dual-task model based on improved YOLOv11n that integrates Rep-CSP structural optimization, knowledge-transfer-enhanced training (KTET), and Focal-CIoU [...] Read more.
To address the joint requirements of illegal parking detection and license plate recognition under complex traffic scenarios and limited edge-device resources, this study proposes RKF-YOLO, a lightweight dual-task model based on improved YOLOv11n that integrates Rep-CSP structural optimization, knowledge-transfer-enhanced training (KTET), and Focal-CIoU loss. Compared with YOLOv11n, RKF-YOLO reduces parameters and FLOPs by 38.2% and 38.1%, respectively, while improving mAP@0.5 and mAP@0.5:0.95 by 0.6 and 1.1 percentage points for parking detection; for plate detection, Focal-CIoU improves mAP@0.5:0.95 by 1.3 percentage points and contributes to a recognition accuracy of 95.7%. The unified framework uses a shared backbone and task-oriented detection heads to support vehicle-level illegal parking detection and license-plate-oriented localization. Rep-CSP enhances multi-scale feature representation, asymmetric channel reduction with feature compensation reduces redundant computation, and KTET improves convergence through optimizer and learning-rate migration. Deployment on RK3588 achieves 59.5 FPS for parking detection and 95.1% recognition accuracy, demonstrating real-time performance and practical applicability on resource-constrained edge devices. Full article
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26 pages, 2861 KB  
Article
Artificial Intelligence Adoption, Administrative Efficiency, and E-Citizen Integration in Spanish Local Government: A PLS-SEM Analysis
by Abayomi Ogunrinde, José Luis Montes-Botella and Carmen De-Pablos-Heredero
Adm. Sci. 2026, 16(6), 284; https://doi.org/10.3390/admsci16060284 (registering DOI) - 13 Jun 2026
Abstract
How does artificial intelligence (AI) adoption shape administrative efficiency and e-citizen integration in local governments, and what role does professional development play in mediating these relationships? Drawing on a survey of 500 municipal employees across Spanish municipalities, this study employs partial least squares [...] Read more.
How does artificial intelligence (AI) adoption shape administrative efficiency and e-citizen integration in local governments, and what role does professional development play in mediating these relationships? Drawing on a survey of 500 municipal employees across Spanish municipalities, this study employs partial least squares structural equation modelling (PLS-SEM), with formal non-linearity testing via Warp3 algorithms, to test a theoretically grounded model. The conceptual framework integrates Digital Transformation Theory and Public Value Theory as primary explanatory lenses, while drawing on the Technology Acceptance Model (TAM) and Total Factor Productivity (TFP) logic as complementary background perspectives that contextualise rather than directly operationalise the micro-level findings. Structural results reveal that AI adoption exerts a strong direct (and statistically linear) effect on perceived administrative efficiency (β = 1.04, p < 0.001; the standardised coefficient exceeding 1.0 and R2 > 1 are a legitimate WarpPLS warp-model fit index rather than evidence of model misspecification: the Warp3 warp functions inflate the variance of predicted efficiency and break the additive identity SST = SSM + SSE, with the high AI–PD collinearity (r ≈ 0.84) as the contributing mechanism (RSCR = 1.000, SSR = 1.000); a comparative re-estimation without the moderation term yields β = 0.87 and R2 = 0.76; we adopt this parsimonious specification (β ≈ 0.87, R2 = 0.76) as the substantively interpretable estimate, with predictive relevance confirmed by a high Stone–Geisser Q2 = 0.685, indicating that the model fits and predicts well rather than overfitting, while simultaneously stimulating professional development (β = 0.84, p < 0.001, R2 = 0.70). Professional development positively predicted both efficiency (β = 0.27, p < 0.001) and e-citizen integration (β = 0.26, p < 0.01). Efficiency is the primary driver of e-citizen integration (β = 0.54, p < 0.001, R2 = 0.53). The proposed moderation of AI adoption by professional development on efficiency was not supported (β = −0.01, p = 0.44), suggesting additive rather than synergistic effects. Model fit was robust (GoF = 0.701; ARS = 0.749; APC = 0.495); convergent and discriminant validity were confirmed by composite reliability, average variance extracted, Fornell–Larcker, and HTMT criteria; and common method bias diagnostics (Harman’s single-factor test, full-collinearity AFVIF, and marker-variable analysis) indicated that systematic method variance was not a material threat. These findings offer micro-empirical evidence of the mechanisms linking AI adoption to citizen service outcomes via a professional development pathway and provide actionable recommendations for Spanish and European municipalities navigating AI-driven governance reform. Full article
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51 pages, 4229 KB  
Article
Blackcap Optimization Algorithm (BCOA): A Novel Metaheuristic Algorithm for Global and Engineering Optimization Problems
by Ali Asghari and Mohammadhossein Mohammadi
Biomimetics 2026, 11(6), 419; https://doi.org/10.3390/biomimetics11060419 (registering DOI) - 13 Jun 2026
Abstract
Metaheuristic algorithms are widely used to find optimal or near-optimal solutions for complex problems by taking inspiration from natural behaviors and processes. Although many different methods have been developed, a common problem in many of them is maintaining a good balance between exploration [...] Read more.
Metaheuristic algorithms are widely used to find optimal or near-optimal solutions for complex problems by taking inspiration from natural behaviors and processes. Although many different methods have been developed, a common problem in many of them is maintaining a good balance between exploration and exploitation and avoiding local optima. To deal with this issue, this paper proposes a new method called the Blackcap Optimization Algorithm (BCOA), which is inspired by the navigation and migration behavior of Blackcap birds. Instead of using complicated distance calculations, the proposed method is based on angular movement vectors. The movement of each search agent is controlled by an angle-based mathematical model that combines the global best angle, a successful neighboring angle, and an adaptive exponential disturbance factor. In addition, the algorithm uses a quasi-genetic path transition mechanism to combine successful parent paths together, along with a territorial competition stage. This structure helps reduce computational cost and improves the balance between exploration and exploitation. The performance of the proposed algorithm is tested on 32 benchmark functions and seven engineering and network optimization problems. The simulation results show that BCOA has a good ability to avoid local optima and can achieve acceptable convergence speed and cost reduction compared to several existing methods. Full article
(This article belongs to the Section Biological Optimisation and Management)
31 pages, 1709 KB  
Article
First Optimal Eighth-Order Families with Multivariable Scalar Weight Functions for Nonlinear Systems and Applications to Fredholm Integral and Semilinear Elliptic Problems
by Alicia Cordero, Miguel A. Leonardo Sepúlveda, Juan R. Torregrosa, Antmel Rodríguez Cabral and Natanael Ureña Castillo
Mathematics 2026, 14(12), 2114; https://doi.org/10.3390/math14122114 (registering DOI) - 13 Jun 2026
Abstract
This paper presents new optimal eighth-order families with weight functions for solving nonlinear systems, obtained as a generalization of the first optimal eighth-order CTT8 method introduced by Cordero, Torregrosa and Triguero-Navarro. The proposed schemes are constructed by combining a Newton-type predictor with high-order [...] Read more.
This paper presents new optimal eighth-order families with weight functions for solving nonlinear systems, obtained as a generalization of the first optimal eighth-order CTT8 method introduced by Cordero, Torregrosa and Triguero-Navarro. The proposed schemes are constructed by combining a Newton-type predictor with high-order correction steps whose weight functions are suitably chosen to preserve optimal convergence while keeping a low computational cost. To the best of our knowledge, this work introduces the first family of optimal eighth-order methods for nonlinear systems, in the sense of the Cordero–Torregrosa conjecture, developed through a weight-function technique. A complete local convergence analysis is carried out under standard smoothness assumptions, proving eighth-order convergence for nondegenerate solutions. The computational efficiency of the proposed methods is also studied and compared with several existing high-order iterative schemes. Numerical experiments on nonlinear systems of different dimensions confirm the theoretical order of convergence and show the robustness of the new families. In addition, a Fredholm integral equation is solved, followed by a semilinear elliptic Dirichlet problem, further illustrating the reliability and computational performance of the proposed weight-function-based methods. Full article
145 pages, 1732 KB  
Article
Statistical Learning of Conditional Single-Index U-Processes Under Local Stationarity and Missing-At-Random Functional Responses
by Salim Bouzebda
Mathematics 2026, 14(12), 2112; https://doi.org/10.3390/math14122112 (registering DOI) - 13 Jun 2026
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Abstract
This paper develops a unified asymptotic theory for conditional single-index U-statistics and the associated conditional U-processes in the setting of locally stationary functional time series subject to missing-at-random response mechanisms. The proposed framework addresses, within a single nonparametric inferential architecture, three [...] Read more.
This paper develops a unified asymptotic theory for conditional single-index U-statistics and the associated conditional U-processes in the setting of locally stationary functional time series subject to missing-at-random response mechanisms. The proposed framework addresses, within a single nonparametric inferential architecture, three major sources of complexity in modern functional data analysis: infinite-dimensional covariates, smoothly time-varying stochastic dynamics, and incomplete response observations. The methodology is based on a class of kernel-type estimators combining temporal localization, functional single-index smoothing, and inverse-propensity correction. Temporal localization captures the gradual evolution of the underlying regression structure, the single-index projection provides an effective dimension-reduction mechanism for functional covariates, and the propensity adjustment restores the target conditional functional under the MAR sampling scheme. The principal contribution of the paper is the establishment of weak convergence, in a suitable space of bounded functions, for the resulting propensity-adjusted conditional U-process indexed by a general class of measurable kernels. Under absolute regularity conditions, local stationarity assumptions, small-ball probability requirements, entropy restrictions of VC type, and uniform consistency of the propensity-score estimator, the normalized process is shown to converge weakly to a tight centered Gaussian process. The limiting covariance structure explicitly reflects the interaction between temporal smoothing, functional concentration, dependence, and the random loss of responses. In parallel, uniform convergence rates are derived for the associated conditional single-index U-statistic estimators, thereby quantifying the respective contributions of smoothing bias, stochastic fluctuation, local-stationarity approximation error, and missingness-induced variance inflation. A substantial part of the analysis is devoted to the technical difficulties created by the simultaneous presence of dependence, nonstationarity, functional covariates, and incomplete observations. The proofs combine Hoeffding-type decompositions adapted to weighted incomplete data, blocking and coupling arguments for absolutely regular triangular arrays, refined entropy bounds for kernel-indexed function classes, and small-ball probability techniques for functional covariates. The MAR mechanism is incorporated via inverse-propensity weighting, and its effects on the effective sample size, asymptotic variance, and bias structure are made explicit. The theory also provides a rigorous foundation for bandwidth selection through blocked, propensity-adjusted cross-validation and clarifies its relation to the corresponding oracle risk. The proposed framework encompasses a broad class of statistical learning and inference problems involving pairwise or higher-order functionals of functional time series. In particular, it applies to conditional Kendall-type functionals, discrimination problems, metric learning with incomplete labels, and conditional independence testing under local stationarity. A simulation study illustrates the finite-sample behavior of the proposed estimators and supports the theoretical findings across varying regimes of temporal nonstationarity, serial dependence, functional concentration, and response missingness. Overall, the results provide a mathematically rigorous and methodologically flexible foundation for inference from evolving functional data when dependence, infinite dimensionality, and incomplete observation are present simultaneously. Full article
(This article belongs to the Section D1: Probability and Statistics)
17 pages, 463 KB  
Article
Heterogeneous Regional Convergence in the European Union: Club Dynamics, Structural Breaks, and Spatial Spillovers
by Greta Mockevičienė and Mindaugas Butkus
Economies 2026, 14(6), 228; https://doi.org/10.3390/economies14060228 (registering DOI) - 13 Jun 2026
Viewed by 50
Abstract
This study examines income convergence among EU NUTS-2 regions from 2000 to 2023 using a combination of Phillips-Sul (PS) club convergence methodology, β-convergence, and spatial econometric models. The results reveal that regional convergence in Europe is heterogeneous and nonlinear: four stable convergence [...] Read more.
This study examines income convergence among EU NUTS-2 regions from 2000 to 2023 using a combination of Phillips-Sul (PS) club convergence methodology, β-convergence, and spatial econometric models. The results reveal that regional convergence in Europe is heterogeneous and nonlinear: four stable convergence clubs emerge, while overall convergence is rejected. Convergence was faster before 2012 and weakened afterward. A single income threshold and two structural breaks (2005 and 2012) mark shifts in growth dynamics. Spatial models reveal that neighboring regions affect each other’s growth, indicating that regional development in Europe depends on both local conditions and interactions across regions. Full article
(This article belongs to the Section Economic Development)
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168 pages, 1537 KB  
Article
Advanced Statistical Learning: Limit Theorems for Nonparametric Conditional U-Statistics Smoothed by Asymmetric Kernels Under Missing-at-Random Sampling
by Salim Bouzebda
Mathematics 2026, 14(12), 2110; https://doi.org/10.3390/math14122110 (registering DOI) - 12 Jun 2026
Viewed by 128
Abstract
This paper develops a boundary-sensitive asymptotic theory for nonparametric conditional U-statistics smoothed by support-adapted asymmetric kernels when the response variable is subject to Missing-at-Random observation. The problem lies at the intersection of three well-established but traditionally separate lines of research: conditional U [...] Read more.
This paper develops a boundary-sensitive asymptotic theory for nonparametric conditional U-statistics smoothed by support-adapted asymmetric kernels when the response variable is subject to Missing-at-Random observation. The problem lies at the intersection of three well-established but traditionally separate lines of research: conditional U-statistics, asymmetric smoothing on constrained supports, and incomplete-data inference under MAR sampling. The contribution of the paper is not a novelty claim concerning any of these components in isolation. Rather, it consists in deriving a kernel-specific and MAR-aware limit theory for their simultaneous occurrence, where the estimators are nonlinear complete-case ratios of localized U-statistics and the localization devices are point-dependent approximate identities adapted to the geometry of the covariate support. The analysis covers three principal classes of support-respecting smoothers: Dirichlet kernels on the simplex, Bernstein polynomial smoothers, and multivariate beta kernels on hypercubes, with an additional extension to mixed continuous–categorical regressors. These smoothing schemes are not translation-invariant, and their local moments, effective support, normalizing constants and L2-masses vary with the evaluation point, especially near the boundary. Consequently, their incorporation into conditional U-statistics requires more than a direct transfer of ordinary asymmetric-kernel regression theory. The numerator and denominator of the estimators are localized U-statistics whose stochastic expansions are governed by Hoeffding projections, including canonical components that must be controlled uniformly over the conditioning domain. Under regularity, smoothness and positivity assumptions adapted to the MAR setting, we establish uniform consistency, weak and strong uniform convergence rates, stochastic expansions and asymptotic normality. The results are obtained both on fixed compact subsets and on interior regions approaching the boundary, thereby identifying how support geometry enters the bias and stochastic normalizations. A central feature of the theory is the separation between the deterministic effect of complete-case sampling and its stochastic effect. For the complete-case estimator, the natural deterministic equivalent is obtained by replacing the design density f with the effective complete-case density pf, where p is the propensity score. Thus, the MAR mechanism may enter higher-order deterministic bias constants through the local design tilt, whereas the leading stochastic dispersion reflects the loss of effective information through propensity score factors. The precise variance constants and normalizing rates remain kernel-specific, depending on the local L2-structure of the Dirichlet, Bernstein or beta smoothing device. The paper should therefore be viewed as a MAR extension and refinement of the complete-data asymmetric-kernel conditional U-statistic theory. It provides a common probabilistic architecture for several boundary-adapted smoothing schemes while retaining the kernel-dependent bias operators, variance constants, boundary regimes and Hoeffding-projection structures required for sharp asymptotic interpretation. Numerical experiments illustrate the finite-sample behavior predicted by the theory and highlight the interaction between support-adapted smoothing, boundary effects and incomplete response observation. Full article
(This article belongs to the Section D1: Probability and Statistics)
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22 pages, 5125 KB  
Article
Mixed-Mode Dynamic Stress Intensity Factors and Fracture Analysis Using Ordinary State-Based Peridynamics
by Yanyun Ru, Fei Li, Xingyu Li, Caidan Wang, Qianlong Yang, Shuqin Zheng, Lei Zhou and Xu Wang
Materials 2026, 19(12), 2560; https://doi.org/10.3390/ma19122560 (registering DOI) - 12 Jun 2026
Viewed by 69
Abstract
An ordinary state-based peridynamic (OSPD) approach combined with an interaction integral method is proposed to calculate dynamic stress intensity factors (DSIFs) and simulate crack propagation in two-dimensional cracked brittle solids. Numerical investigations are carried out for mode I and mixed-mode cracked plates under [...] Read more.
An ordinary state-based peridynamic (OSPD) approach combined with an interaction integral method is proposed to calculate dynamic stress intensity factors (DSIFs) and simulate crack propagation in two-dimensional cracked brittle solids. Numerical investigations are carried out for mode I and mixed-mode cracked plates under static, quasi-static, and dynamic loading conditions. A local damping scheme is incorporated into the peridynamic equations of motion to achieve convergence in static and quasi-static analyses. The influence of circular holes on DSIFs and crack propagation paths is systematically examined. Quantitative analyses of elastic deformation and quasi-static fracture behavior for mode I and mixed-mode cracks are verified through the uniaxial tension of a slab. The peak values of DSIFs exceed their static counterparts under dynamic loading. Complex dynamic fracture phenomena, including crack branching in both straight and inclined edge cracks, are successfully captured. The results obtained by the OSPD approach are validated through comparisons with theoretical benchmarks and finite element results, demonstrating high accuracy and effectiveness in calculating elastic deformation and stress intensity factors (SIFs), as well as accurately predicting crack propagation paths in quasi-static and dynamic fracture problems in brittle solids. Beyond the benchmark problems, the proposed OSPD approach is particularly well-suited for investigating more complex fracture systems. Full article
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