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48 pages, 2248 KB  
Article
Transformer-Based Multi-Task Learning with a Task-Aware Weighted Ensemble for Simultaneous Age Estimation and Gender Classification from Facial Images
by Sümeyye Sarıateş and Erdal Özbay
Sensors 2026, 26(18), 5982; https://doi.org/10.3390/s26185982 (registering DOI) - 21 Sep 2026
Abstract
Accurate age estimation and gender classification from facial images remain challenging tasks owing to substantial variations in facial appearance caused by pose, illumination, expression, occlusion, image quality, and age-related morphological changes. Although transformer-based architectures have recently demonstrated remarkable performance in facial analysis, effectively [...] Read more.
Accurate age estimation and gender classification from facial images remain challenging tasks owing to substantial variations in facial appearance caused by pose, illumination, expression, occlusion, image quality, and age-related morphological changes. Although transformer-based architectures have recently demonstrated remarkable performance in facial analysis, effectively exploiting their complementary representation capabilities within a unified multi-task framework remains an open research problem. To address this limitation, this study proposes a transformer-based Multi-task Learning (MTL) framework that jointly performs age estimation and gender classification using a shared feature extraction backbone and task-specific prediction heads. Three state-of-the-art vision transformers, namely Vision Transformer (ViT), Shifted Window Transformer (Swin Transformer), and Data-efficient Image Transformer (DeiT), were independently implemented within the proposed MTL architecture to learn both global contextual information and local facial characteristics. Furthermore, two ensemble learning strategies, namely standard ensemble and Task-aware Weighted Ensemble (TAWE), were developed to exploit the complementary strengths of the individual transformer models. Experiments were conducted on the publicly available UTKFace dataset comprising 15,503 facial images, which were divided into 10,385 training, 1833 validation, and 3285 test samples, while gender balancing was applied during model training to alleviate class imbalance. Age estimation performance was evaluated using Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE), whereas gender classification performance was assessed using Accuracy and F1-score. Experimental results demonstrate that the proposed TAWE achieved the best point estimates among the evaluated ensemble strategies, obtaining an MAE of 4.8905, an RMSE of 6.4674, a gender classification accuracy of 94.86%, and an F1-score of 95.17% for the dataset-defined positive class. Compared with equal-weight averaging, TAWE provided a statistically significant improvement in gender classification accuracy, while the improvement in age estimation was modest and not statistically significant. Full article
39 pages, 12882 KB  
Article
A Multi-Criteria Reanalysis of Electrical-Discharge Diamond Grinding Using Regression Models and DEFMOT
by Nikolay Tonchev, Miroslav Leventov Kokalarov, Ivan Georgiev, Nikolay Hristov and Meglena Delcheva Lazarova
J. Manuf. Mater. Process. 2026, 10(9), 370; https://doi.org/10.3390/jmmp10090370 (registering DOI) - 21 Sep 2026
Abstract
This paper presents an integrated modelling and decision-support reanalysis of a published 24-run experiment on diamond-spark grinding (electrical-discharge diamond grinding) of two hard alloys—the tungsten-free cermet TN-20 and the WC–TiC–Co alloy HS123—machined jointly with C45 steel; no new experiments are performed. Established components [...] Read more.
This paper presents an integrated modelling and decision-support reanalysis of a published 24-run experiment on diamond-spark grinding (electrical-discharge diamond grinding) of two hard alloys—the tungsten-free cermet TN-20 and the WC–TiC–Co alloy HS123—machined jointly with C45 steel; no new experiments are performed. Established components are deliberately combined into one reproducible workflow: quadratic response-surface models fitted by least squares and by minimax (Chebyshev) approximation, validation by prediction-oriented criteria including nested leave-one-out cross-validation of the entire model-selection pipeline, the addressable DEFMOT representation of the 94-factor grid formalized as an ε-constraint procedure, and benchmarking against desirability-function and Pareto analyses. Minimax fitting reduces the maximum absolute residual by 22.5–36.9% at the cost of higher aggregate errors. Nested validation exposes model-selection instability for the TN-20 responses, and a dedicated sensitivity analysis shows that the surrogate-model choice can change the recommended regime: the TN-20 compromise is efficient or one grid step from efficient under all three surrogate families, whereas the preferred HS123 regime shifts qualitatively (including a reversal of the wheel-speed setting) between least-squares and minimax surrogates. A residual-bootstrap analysis propagates data uncertainty through the complete optimization and quantifies how frequently each recommended regime is re-selected. Within the legacy cost basis, point estimates indicate comparable productivity (difference below 9%), an approximately 35% lower specific machining cost for TN-20 and approximately 1.8 times higher diamond consumption; the 95% confidence intervals for the between-material contrasts include zero, so experimental confirmation is required before industrial substitution. The framework quantifies, rather than hides, how surrogate uncertainty propagates into the engineering decision. Full article
(This article belongs to the Special Issue Advances in Machining Processes of Difficult-to-Machine Materials)
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25 pages, 6342 KB  
Article
Early Pest-Stress Detection and Pest-Type Discrimination in Maize Using Multi-Source Physiological and Spectral Data with Stage-Consistency-Constrained Feature Selection
by Tianhua Chen, Jingmin Dang and Yafei Wang
Agriculture 2026, 16(18), 2037; https://doi.org/10.3390/agriculture16182037 - 21 Sep 2026
Abstract
Maize is globally important for food production, while insect pests adversely affect its yield and quality. Multi-source physiological and spectral responses can support early pest identification, but variable correlations and temporal changes in discriminative effects may introduce redundant or stage-specific features, destabilize selection, [...] Read more.
Maize is globally important for food production, while insect pests adversely affect its yield and quality. Multi-source physiological and spectral responses can support early pest identification, but variable correlations and temporal changes in discriminative effects may introduce redundant or stage-specific features, destabilize selection, and increase model complexity. This study proposed a stage-consistency-constrained feature selection method (SCCFS), in which stage consistency denotes the persistence of discriminative ability across the 2–12 h observation groups. Jointing-stage maize plants were assigned to healthy control, mechanical damage, leaf-feeding pest, or stem-boring pest treatments. Gas exchange, chlorophyll fluorescence, spectral indices, and 400–1000 nm ASD reflectance provided 613 candidate variables for pest detection and pest-type identification. SCCFS evaluated overall discrimination, temporal persistence, and resampling repeatability, and determined compact subsets through forward selection and the one-standard-error rule. Using shrinkage linear discriminant analysis (LDA), SCCFS achieved Macro-F1 values of 0.9639 for pest detection and 0.9926 for pest-type identification. Out-of-fold (OOF) Shapley additive explanations (SHAP) analysis of the radial-basis-function support vector machine (SVM-RBF) models identified relative electron transport rate (rETR), transpiration rate (Tr), operating efficiency of photosystem II photochemistry (Fq′/Fm′), and stomatal conductance (Gs) as key contributors to pest detection, and intercellular CO2 concentration (Ci), relative electron transport rate (rETR), normalized difference vegetation index (NDVI), and photochemical reflectance index (PRI) as key contributors to pest-type identification. For pest detection and pest-type identification, the Nogueira stability indices were 0.6946 and 0.8227, respectively, and the mean absolute Spearman correlation coefficients were 0.3016 and 0.4625, respectively. SCCFS retained pest diagnostic performance while yielding compact, temporally persistent, and low-redundancy subsets, providing a compact variable representation for maize pest identification under the tested greenhouse conditions. Full article
(This article belongs to the Section Crop Protection, Diseases, Pests and Weeds)
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22 pages, 6454 KB  
Article
A Knowledge-Driven Intelligent Agent for Automated Quantity Checking of Concrete Bridge Structures
by Yi Li, Boxu Tian, Qing Liu, Yingce Zhao, Bo Liu, Jiang Yu, Xunkun Gong, Wenliang Qian and Wenli Chen
Appl. Sci. 2026, 16(18), 9366; https://doi.org/10.3390/app16189366 (registering DOI) - 21 Sep 2026
Abstract
Automated quantity checking directly from two-dimensional bridge drawings remains challenging because the required information is distributed across structural views, detail drawings, and tables, while recognition errors may propagate into deterministic engineering calculations. This study proposes a knowledge-driven intelligent agent for automated quantity checking [...] Read more.
Automated quantity checking directly from two-dimensional bridge drawings remains challenging because the required information is distributed across structural views, detail drawings, and tables, while recognition errors may propagate into deterministic engineering calculations. This study proposes a knowledge-driven intelligent agent for automated quantity checking of concrete bridge structures. A task-specific dataset containing 1362 drawing images is constructed with region-level and parameter-level annotations. A two-stage YOLO method first locates functional regions and then detects parameter-related objects within cropped structural views. The agent coordinates detection, OCR, and table-parsing tools, associates recognized values with parameter types, spatial locations, and bridge components, and organizes them into a unified representation for deterministic rule execution. Human-in-the-loop verification is introduced before calculation to control error propagation. Compared with single-stage detection, the two-stage method increases mAP@0.5 from 0.769 to 0.908, mAP@0.5:0.95 from 0.471 to 0.656, and Recall from 0.664 to 0.792. After verification by bridge design professionals, parameter accuracy increases from 82.77% to 100%, and the overall mean concrete volume error decreases from 23.94% to 2.98%. The framework also produces lower concrete volume errors than three prompt-based large-model baselines across all six evaluated structural types. The methodological novelty lies in integrating region-to-parameter drawing perception, agent-orchestrated heterogeneous information organization, parameter-level human verification, and deterministic engineering rules into a controlled workflow for concrete quantity checking and reinforcement information consistency checking. Full article
(This article belongs to the Section Civil Engineering)
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36 pages, 7286 KB  
Review
Foundation-Model-Assisted Reward Design for Reinforcement Learning: A Review of Reward Program Synthesis, Multimodal Feedback, and Trustworthiness
by Wei Zhu, Jinyin Bai, Rui Tang, Zehao Pang, Mingxi Wang, Chengjie Lu, Tianjin Ni, Hang Liu, Xiangchen Wang, Jinji Zhou, Yanlin Wu, Yongjun Peng, Zongzhe Nie, Shiluo Guo, Qinglin Xu, Kaiyang Kou and Yihao Zhong
Information 2026, 17(9), 925; https://doi.org/10.3390/info17090925 (registering DOI) - 20 Sep 2026
Abstract
Reward functions determine what reinforcement learning agents ultimately optimize, yet reward design for complex tasks has traditionally relied on extensive domain expertise and iterative engineering. Recent large language models and vision–language foundation models have introduced new mechanisms for interpreting task intent, synthesizing reward [...] Read more.
Reward functions determine what reinforcement learning agents ultimately optimize, yet reward design for complex tasks has traditionally relied on extensive domain expertise and iterative engineering. Recent large language models and vision–language foundation models have introduced new mechanisms for interpreting task intent, synthesizing reward programs, evaluating states and trajectories, and refining rewards through policy feedback. This review organizes the emerging literature along three complementary directions: reward program synthesis, multimodal feedback, and feedback-driven reward optimization. We further propose a five-level trustworthiness framework spanning format validity, execution validity, semantic validity, behavioral validity, and structural assurance. Existing evidence shows that foundation models substantially broaden how rewards can be represented and acquired but do not eliminate grounding errors, proxy misalignment, reward hacking, selection bias, or reward-search costs. We therefore examine the field from an end-to-end perspective that jointly considers policy performance, reward fidelity, trustworthiness, computational and human cost, and transfer. Finally, we identify verifiable reward representations, process reward models, budget-aware reward search, and transferable reward knowledge across tasks and multi-agent systems as key directions for future research. Full article
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24 pages, 1824 KB  
Article
Multi-Scale Residual Attention Network for Chinese Speech Recognition Through Collaborative Design
by Yuying Li, Hongjie Wan, Akash Sutradhar and Jianing Qin
Entropy 2026, 28(9), 1037; https://doi.org/10.3390/e28091037 - 20 Sep 2026
Abstract
In recent years, the application of multi-scale residuals and attention mechanisms in automatic speech recognition has made some progress. However, existing speech recognition systems still have critical limitations. Many existing systems fail to adequately capture multi-scale speech features, struggling with representation gaps and [...] Read more.
In recent years, the application of multi-scale residuals and attention mechanisms in automatic speech recognition has made some progress. However, existing speech recognition systems still have critical limitations. Many existing systems fail to adequately capture multi-scale speech features, struggling with representation gaps and often relying on inefficient serial attention mechanisms. Additionally, lightweight models, while efficient, often isolate information within grouped architectures, limiting the global feature interaction necessary for speech recognition. To address these persistent challenges, we introduce MSRDA-GSCA, an architecture that synergistically integrates a Multi-Scale Residual Deep Convolutional Attention (MSRDA) network with a Group Shuffled Co-Attention (GSCA) mechanism. MSRDA uses parallel convolutions with varied kernels and dilations, plus adaptive residual connections, to capture diverse temporal dependencies and align heterogeneous features. Its dual-path attention recalibrates channel and spatial information with element-wise max fusion. GSCA employs sequential position-wise channel and spatial attention with intermediate channel shuffling, enabling cross-group interaction and enhancing global feature synergy. Experiments on THCHS-30 and ST-CMDS datasets show that the proposed model outperforms existing methods in Character Error Rate (CER) and Word Error Rate (WER). Ablation studies confirm the complementarity of MSRDA and GSCA. With only 4.65 M parameters, MSRDA-GSCA achieves high recognition accuracy while maintaining low computational complexity for efficient deployment. Full article
(This article belongs to the Section Signal and Data Analysis)
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23 pages, 1671 KB  
Article
Comparative Evaluation of Classical, Deep, and Quantum Machine Learning for Video-Based Physical Activity Classification
by Andrea Lucía Sulla Valdivia, Jorge Martínez Muñoz, Diego Iquira Becerra, Marco Antonio Cossio Bolaños and José Alfredo Sulla Torres
Appl. Sci. 2026, 16(18), 9344; https://doi.org/10.3390/app16189344 (registering DOI) - 20 Sep 2026
Abstract
Reliable exercise recognition across schools requires models that remain accurate when acquisition conditions change. This study compares classical machine learning, pose-sequence deep learning, and quantum machine learning to classify four standardized physical-fitness exercises: sit-up, biceps curl, sit-and-reach, and horizontal jump. The original repository [...] Read more.
Reliable exercise recognition across schools requires models that remain accurate when acquisition conditions change. This study compares classical machine learning, pose-sequence deep learning, and quantum machine learning to classify four standardized physical-fitness exercises: sit-up, biceps curl, sit-and-reach, and horizontal jump. The original repository contained 2034 videos. A SHA-256 audit of the temporal pose arrays identified 152 exact duplicate copies, all from the same school, leaving 1882 unique videos for the primary analysis. We used YOLO26n-Pose to extract 17 COCO keypoints. We evaluated two input representations: 110 aggregated biomechanical descriptors and 128-step sequences containing 34 local pose coordinates. Model selection and evaluation followed a nested Leave-One-School-Out protocol. Random Forest obtained the highest pooled outer-fold performance (Macro-F1 = 0.9964, accuracy = 0.9968, MCC = 0.9953), with six errors in 1882 videos; XGBoost and RBF-SVC followed with Macro-F1 values of 0.9932 and 0.9881. Among the deep models, BiLSTM, CNN1D, and ST-GCN achieved Macro-F1 values of 0.9711, 0.9666, and 0.9498, respectively. A paired stratified bootstrap supported the Random Forest advantage over XGBoost for Macro-F1, although the Holm-adjusted exact McNemar test for overall correctness was not significant. In exploratory controlled QML experiments, neither QSVC nor VQC exceeded its matched classical baseline under the tested configurations. These results show that compact biomechanical descriptors provide a strong and stable representation for cross-school exercise recognition in this dataset. Full article
(This article belongs to the Special Issue Deep Learning-Based Computer Vision Technology and Its Applications)
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25 pages, 992 KB  
Article
Transformer-Based Solar Irradiance Forecasting Model for Coastal and Microclimate-Sensitive Areas of First District of Batangas
by Jeffrey S. Sarmiento, Dylan Josh D. Lopez and Gerard Francesco De Guzman Apolinario
Energies 2026, 19(18), 4448; https://doi.org/10.3390/en19184448 (registering DOI) - 20 Sep 2026
Abstract
Accurate solar irradiance forecasting is a key prerequisite for reliable solar photovoltaic (PV) operation, effective energy management, and system optimization. Conventional forecasting methods, such as historical averaging, persistence models, and coarse-resolution numerical weather prediction outputs, often exhibit limited performance in coastal and microclimate-sensitive [...] Read more.
Accurate solar irradiance forecasting is a key prerequisite for reliable solar photovoltaic (PV) operation, effective energy management, and system optimization. Conventional forecasting methods, such as historical averaging, persistence models, and coarse-resolution numerical weather prediction outputs, often exhibit limited performance in coastal and microclimate-sensitive environments where irradiance is characterized by rapid and nonlinear atmospheric variability. Batangas District 1, a coastal and peninsular region in the Philippines, is particularly influenced by sea–land breeze circulation, convective cloud development, humidity fluctuations, and aerosol transport, resulting in highly non-stationary irradiance patterns and persistent forecasting errors. Although recent advances in deep learning, particularly Transformer-based architectures, have demonstrated strong potential for modeling complex atmospheric time-series, locally developed and validated models for Philippine coastal environments remain scarce. Moreover, this study addresses this gap by developing FAT-Former, a Transformer-based solar irradiance forecasting algorithm designed to capture the microclimatic characteristics of Batangas District 1. The proposed model substantially outperformed the persistence benchmark and demonstrated strong temporal representation capability, achieving the lowest mean peak-time error and preserving 101.30% of the observed variance. However, predictive performance deteriorated under precipitation events and highly variable daylight conditions, while the resulting prediction intervals exhibited under-calibration. These findings suggest that forecasting performance in coastal environments depends not only on model complexity but also on the model’s ability to adapt to rapidly changing atmospheric regimes. All in all, FAT-Former demonstrates the potential of Transformer-based architectures for localized and uncertainty-aware solar irradiance forecasting. Further evaluation across diverse coastal and microclimate-sensitive locations is recommended to assess the model’s robustness, transferability, and broader generalizability. Full article
(This article belongs to the Special Issue Advanced Artificial Intelligence for Photovoltaic Energy Systems)
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31 pages, 3787 KB  
Article
Digital Predistortion of Wideband Power Amplifiers Using Functionally Decoupled Envelope-Assisted Attention-Guided Recurrent Architecture
by Bingwen Qiu, Xiaoyu Li and Yunjie Zhao
Sensors 2026, 26(18), 5945; https://doi.org/10.3390/s26185945 (registering DOI) - 19 Sep 2026
Abstract
Wideband power amplifiers (PAs) operating with high-order modulation signals exhibit strong nonlinear distortion and dynamic memory effects, making real-time digital predistortion (DPD) increasingly challenging under strict computational constraints. This work proposes a functionally decoupled neural DPD architecture, termed EA-CCF-AttGRU, which explicitly separates instantaneous [...] Read more.
Wideband power amplifiers (PAs) operating with high-order modulation signals exhibit strong nonlinear distortion and dynamic memory effects, making real-time digital predistortion (DPD) increasingly challenging under strict computational constraints. This work proposes a functionally decoupled neural DPD architecture, termed EA-CCF-AttGRU, which explicitly separates instantaneous nonlinear feature representation from temporal memory compensation within a unified end-to-end framework. Instead of introducing envelope features, cross-channel fusion, and recurrent attention as isolated modules, the proposed architecture assigns different compensation functions to dedicated components: envelope-assisted augmentation and point-wise cross-channel fusion enhance instantaneous nonlinear representation, while attention-guided recurrent modeling captures dynamic memory effects. A global linear bypass further reduces the burden of nonlinear compensation by preserving the linear transformation. Experimental results under a 160 MHz 1024-ary quadrature amplitude modulation (1024-QAM) baseband excitation with a 10.38 dB peak-to-average power ratio (PAPR) demonstrate that the proposed method achieves an adjacent channel leakage ratio (ACLR) of −65.91 dBc, a normalized mean square error (NMSE) of −57.84 dB, and an error vector magnitude (EVM) of 0.07% with only 6009 trainable parameters. The proposed architecture achieves an effective complexity–performance trade-off for wideband DPD applications and provides potential for future hardware-oriented implementation and synthesis validation. Full article
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32 pages, 4720 KB  
Article
Explainability-Guided Transformer Models for Hourly Cryptocurrency Forecasting: A Comparative Study with SHAP-Based Feature Refinement
by Zeynep Hilal Kilimci and Erçin Dinçer
Mathematics 2026, 14(18), 3402; https://doi.org/10.3390/math14183402 (registering DOI) - 19 Sep 2026
Abstract
Accurate cryptocurrency price forecasting represents an important yet challenging problem in financial time-series analysis due to the highly volatile, nonlinear, and noise-sensitive nature of digital asset markets. Although transformer-based architectures have recently demonstrated strong capabilities in temporal sequence modeling, their behavior under high-frequency [...] Read more.
Accurate cryptocurrency price forecasting represents an important yet challenging problem in financial time-series analysis due to the highly volatile, nonlinear, and noise-sensitive nature of digital asset markets. Although transformer-based architectures have recently demonstrated strong capabilities in temporal sequence modeling, their behavior under high-frequency cryptocurrency dynamics and the role of explainability-guided feature refinement remain insufficiently explored. To address this gap, this study presents a comprehensive transformer-based forecasting framework for hourly cryptocurrency price prediction and investigates the impact of explainability-guided feature optimization on forecasting performance, robustness, and interpretability. Five transformer architectures—Vanilla Transformer, Informer, Autoformer, Reformer, and Temporal Fusion Transformer (TFT)—are systematically evaluated across five major cryptocurrency assets: Bitcoin (BTC), Ethereum (ETH), Solana (SOL), Dogecoin (DOGE), and Ripple (XRP). The experimental framework employs Open, High, Low, Close, and Volume (OHLCV) data together with a broad set of engineered technical indicators and evaluates model performance using Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), and the coefficient of determination (R2). To improve interpretability and reduce feature redundancy, SHAP (SHapley Additive exPlanations) and LIME (Local Interpretable Model-agnostic Explanations) are integrated directly into the forecasting pipeline. Based on the resulting explanations, asset-specific feature subsets are constructed, and all models are subsequently retrained using the refined feature representations. The results show that explainability-guided feature refinement provides compact, model-aware, and interpretable feature subsets with competitive forecasting performance; however, its effect on prediction accuracy is dependent on the cryptocurrency asset, transformer architecture, retained feature subset size, and market conditions. Additional robustness, sensitivity, alternative feature-selection, and statistical significance analyses indicate that the SHAP–LIME Top-15 subset should be interpreted as a conservative dimensionality-reduction strategy rather than a universally optimal feature-selection rule. The findings further reveal that transformer architectures incorporating sparse attention, decomposition mechanisms, or gating structures generally provide stronger performance than the Vanilla Transformer under highly volatile hourly market conditions. Overall, the proposed framework demonstrates that combining transformer-based forecasting with explainability-guided feature refinement can support interpretable and parsimonious high-frequency financial time-series modeling, while highlighting the importance of evaluating robustness, feature-selection sensitivity, and statistical variability alongside average forecasting errors. Full article
(This article belongs to the Special Issue Advances in Machine Learning Applied to Financial Economics)
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26 pages, 2566 KB  
Article
A Recentered-Domain Yau–Yau Filter with Reduced-Order FKE Propagation for Nonlinear State Estimation
by Lei Ma, Yuzhong Hu and Xiaoming John Zhang
Mathematics 2026, 14(18), 3401; https://doi.org/10.3390/math14183401 (registering DOI) - 19 Sep 2026
Abstract
Nonlinear filtering can be formulated as the propagation and update of conditional probability densities, but direct numerical propagation of the associated Forward Kolmogorov equation (FKE) over a large fixed domain is computationally expensive. This paper proposes a Recentered-Domain Yau–Yau Filter (RD-YYF) with reduced-order [...] Read more.
Nonlinear filtering can be formulated as the propagation and update of conditional probability densities, but direct numerical propagation of the associated Forward Kolmogorov equation (FKE) over a large fixed domain is computationally expensive. This paper proposes a Recentered-Domain Yau–Yau Filter (RD-YYF) with reduced-order FKE propagation for nonlinear state estimation. The method solves the FKE on a fixed-size local computational window centered at the latest state estimate, thereby concentrating numerical resolution near the dominant posterior density. In the offline stage, physics-informed neural networks (PINNs) generate FKE solution snapshots, principal component analysis constructs a low-dimensional representation of density evolution, and a lightweight residual surrogate maps initial-condition coefficients and the domain center to terminal-solution coefficients. In the online stage, the pretrained surrogate performs per-timestep density prediction within the recentered window, followed by observation update and state estimation. Numerical experiments on two geometrically constrained target-tracking models show that RD-YYF achieves lower tracking errors than the extended Kalman filter and particle filter under matched online evaluation conditions. A fixed-domain ablation further shows that recentering improves density approximation in high-probability regions and reduces offline PINN training epochs. These results indicate that recentered-domain reduced-order FKE propagation is a practical computational strategy for nonlinear density-based filtering. Full article
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31 pages, 6708 KB  
Article
A Rational Canonical Grey Gompertz Forecasting Model Based on the Hausdorff Fractal Derivative
by Li Ji, Derong Xie and Huiming Duan
Fractal Fract. 2026, 10(9), 655; https://doi.org/10.3390/fractalfract10090655 (registering DOI) - 19 Sep 2026
Abstract
Accurately forecasting carbon emission trends in China’s power sector is of great significance for achieving the “dual-carbon” goals, optimizing the energy structure, and formulating low-carbon development strategies. This paper aims to develop a forecasting method capable of effectively characterizing the long-term evolutionary patterns [...] Read more.
Accurately forecasting carbon emission trends in China’s power sector is of great significance for achieving the “dual-carbon” goals, optimizing the energy structure, and formulating low-carbon development strategies. This paper aims to develop a forecasting method capable of effectively characterizing the long-term evolutionary patterns and short-term dynamic features of carbon emissions in China’s power sector. However, existing models struggle to simultaneously describe the nonlinear S-shaped growth trend, periodic fluctuations, and long-term memory effects inherent in carbon emission time series. To address these issues, this paper proposes a rational canonical form grey Gompertz forecasting model based on the Hausdorff fractional derivative. By introducing a rational canonical form matrix structure, this model enhances the capability of the grey Gompertz model to represent multi-scale periodic information, and incorporates the Hausdorff fractional derivative to characterize the non-local dynamic features during the time-series evolution, thereby improving the model’s adaptability to complex nonlinear carbon emission sequences. Taking the quarterly and semi-annual carbon emission data of China’s power sector as the research object, simulation and forecasting experiments under various time scales and sample settings were conducted to verify the effectiveness of the new model, and a comparative analysis was performed against traditional grey models, fractional-order grey models, and statistical forecasting models. The results indicate that the model possesses certain advantages in structural representation and dynamic memory mechanisms, exhibiting high forecasting accuracy and stability across different time scales. The full-sample mean absolute percentage errors (MAPEs) were all below 3%, and the MAPEs of the optimal schemes for quarterly and semi-annual data reached 0.8353% and 0.0491%, respectively. Finally, the model was utilized to effectively forecast the carbon emissions of China’s power sector for the 2026–2027 period. Full article
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31 pages, 11638 KB  
Article
SApneaNet: Adaptive Squeeze-and-Excitation-Based CNN–Transformer Network with AGFF for Sleep Apnea Event Detection Using ECG Images Under IoMT
by Innocent Tujyinama, Bessam Abdulrazak and Rachid Hedjam
Sensors 2026, 26(18), 5936; https://doi.org/10.3390/s26185936 (registering DOI) - 19 Sep 2026
Abstract
Background and Objective: Obstructive sleep apnea (OSA) is a fatal widespread sleep-related breathing disorder and a major risk factor for cardiovascular and cerebrovascular diseases, significantly impacting older adults’ health worldwide. Due to the risk of such complications, timely and accurate identification of OSA [...] Read more.
Background and Objective: Obstructive sleep apnea (OSA) is a fatal widespread sleep-related breathing disorder and a major risk factor for cardiovascular and cerebrovascular diseases, significantly impacting older adults’ health worldwide. Due to the risk of such complications, timely and accurate identification of OSA is crucial. Polysomnography is considered the most accurate technique for detecting OSA; however, it is limited by its complexity and multi-channel requirements. A promising alternative is electrocardiogram (ECG)-based diagnosis, which continuously monitors heart rhythm and captures subtle cardiac changes associated with OSA. Nevertheless, existing ECG-based approaches still face challenges related to complex feature engineering, limited capture of complementary temporal–spectral information and global dependencies, along with inadequate feature recalibration and fusion, which can restrict OSA detection. Thus, further improvements are still required to achieve clinically reliable performance. Methods: To address these challenges, this study proposes SApneaNet, a novel advanced deep learning method for detecting OSA events using ECG signals. The proposed approach employs the continuous wavelet transform (CWT) to convert ECG signals into RGB log-scalograms, enabling the simultaneous analysis of temporal and frequency-domain features. The generated RGB log-scalograms are then fed into a deep CNN encoder with adaptive squeeze-and-excitation (ASE), followed by a transformer and an adaptive gated feature fusion (AGFF) architecture. In this framework, to improve OSA detection performance, the CNN extracts rich local features, the ASE module performs channel-wise recalibration to enhance feature representations, the transformer performs data-parallel processing and captures global contextual dependencies, and the AGFF mechanism adaptively emphasizes informative features while suppressing less relevant ones. Results: The experimental results on the Apnea-ECG dataset showed that the model achieved a sensitivity of 94.7%, specificity of 95.2%, F1-score of 93.5%, accuracy of 95.1%, Cohen’s kappa of 89.4%, and an area under the receiver operating characteristic (ROC) curve (AUC) of 0.989 for per-segment classification. Furthermore, for per-recording classification, the model achieved an accuracy of 100.0%, a mean absolute error (MAE) of 2.025, and a Pearson correlation coefficient (PCC) of 0.992. Overall, the experimental results demonstrated that the proposed model achieved excellent and competitive performance compared with other advanced state-of-the-art methods for OSA classification. Conclusions: The proposed model demonstrates strong efficacy in OSA detection, providing a novel and robust alternative to conventional diagnostic methods. The model’s reliable and consistent diagnostic performance highlights its potential for integration into practical OSA diagnostic systems, including home-based health monitoring devices and clinical decision-support tools. Full article
(This article belongs to the Special Issue Biosignal Sensing Analysis (EEG, EMG, ECG, PPG) (3rd Edition))
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20 pages, 6917 KB  
Article
A Reduced-Order Equivalent-Dipole Model for DC Stray Magnetic Fields
by Carlo Silano, Raffaele Fresa, Vincenzo Paolo Loschiavo and Antonio Quercia
Appl. Sci. 2026, 16(18), 9298; https://doi.org/10.3390/app16189298 (registering DOI) - 19 Sep 2026
Abstract
Accurate characterization of stray magnetic fields is essential in high-field devices, where external fields may affect diagnostics and personnel safety. Although finite-element models provide high-fidelity solutions, they may require extensive preprocessing and discretization of large source-free regions, making repeated evaluations costly when the [...] Read more.
Accurate characterization of stray magnetic fields is essential in high-field devices, where external fields may affect diagnostics and personnel safety. Although finite-element models provide high-fidelity solutions, they may require extensive preprocessing and discretization of large source-free regions, making repeated evaluations costly when the magnetic source is unchanged. This paper proposes a reduced-order equivalent-dipole model that provides an analytical representation of the three-dimensional background stray field after one-time offline calibration. Dipoles are placed at Gauss–Legendre nodes within an auxiliary volume, while symmetry and anti-symmetry conditions are embedded in the source mapping. Their effective moments are identified from magnetic-flux-density data through a regularized linear inverse problem. The method is assessed for the SHiP spectrometer magnet at CERN against a high-fidelity finite-element reference. A controlled comparison of five model orders selects the 125-dipole configuration, reducing the relative vector L2 error on a common three-dimensional evaluation grid from 21.2% for 27 dipoles to 4.59%. An independently generated dense three-dimensional post-selection dataset confirms the accuracy of the selected model, giving a relative vector L2 error of 1.77% for daux0.50 m. The complementary dense mid-plane assessment gives 0.95% over the same validity region. Full article
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19 pages, 1973 KB  
Article
End-to-End Characterization of Cascaded RF/FSO Relaying Under Dust Fading
by Maged Abdullah Esmail
Technologies 2026, 14(9), 592; https://doi.org/10.3390/technologies14090592 (registering DOI) - 19 Sep 2026
Abstract
This paper investigates the performance of a cascaded dual-hop relay system comprising a radio-frequency (RF) hop followed by a free-space optical (FSO) hop. The RF channel was subject to Rayleigh fading, whereas the FSO channel experienced beta-distributed dust-induced irradiance fluctuations based on experimentally [...] Read more.
This paper investigates the performance of a cascaded dual-hop relay system comprising a radio-frequency (RF) hop followed by a free-space optical (FSO) hop. The RF channel was subject to Rayleigh fading, whereas the FSO channel experienced beta-distributed dust-induced irradiance fluctuations based on experimentally obtained channel parameters. A fixed-gain amplify-and-forward (AF) relay was employed, and the FSO link operated using intensity modulation/direct detection (IM/DD) with on–off keying (OOK). Unlike conventional mixed RF/FSO studies that primarily model the optical hop through atmospheric turbulence and pointing errors, this work examined the end-to-end effect of dust-induced fading in a cascaded RF/FSO architecture. An exact integral representation of the end-to-end signal-to-noise ratio (SNR) cumulative distribution function was formulated. A finite-series closed-form approximation of the end-to-end CDF was subsequently obtained, from which corresponding closed-form approximations for the outage probability, the average bit error rate (BER), and the ergodic capacity metric were derived. The accuracy of the proposed approximations was validated through numerical integration and Monte Carlo simulations. The results show that the finite-series expressions provided highly accurate and computationally efficient performance estimates in the moderate- and high-SNR regions, while a measurable deviation may occur under very low-SNR conditions. The developed framework provides useful analytical tools for evaluating cascaded RF/FSO systems operating over beta-distributed dust-fading channels. Full article
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