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23 pages, 850 KB  
Article
A Federated Recommendation System with a Dual-Layer Multi-Head Attention Network and Regularization Strategy
by Qianxiao Yue and Xiangrong Tong
Entropy 2025, 27(11), 1112; https://doi.org/10.3390/e27111112 - 28 Oct 2025
Abstract
Federated recommendation (FedRec) aims to provide effective recommendation services while preserving user privacy. However, in a federated setting, a single user cannot access other users’ interaction data. With limited local interactions, existing FedRec models struggle to fully exploit interaction information to learn users’ [...] Read more.
Federated recommendation (FedRec) aims to provide effective recommendation services while preserving user privacy. However, in a federated setting, a single user cannot access other users’ interaction data. With limited local interactions, existing FedRec models struggle to fully exploit interaction information to learn users’ preferences. Moreover, training recommendation models in decentralized FedRec scenarios suffer from a risk of overfitting. To address the above issues, we propose a federated recommendation system with a dual-layer multi-head attention network and regularization strategy (FedDMR). First, FedDMR initializes clients’ local recommendation models. Subsequently, clients perform local training based on their private data. Our dual-layer multi-head attention network is designed to perform attention-weighted interactions on user and item embeddings, progressively capturing local interaction information and generating interaction-aware embeddings, thereby enriching users’ feature representations for modeling personalized preferences. Then, a regularization strategy is employed to guide updates to clients’ models by constraining their deviation from the global parameters, which effectively mitigates overfitting caused by limited local data and enhances the generalizability of the models. Finally, the server aggregates the clients’ uploaded parameters for this round. The entire training process is implemented through the federated learning framework. Experimental results on three datasets demonstrate that FedDMR achieves an average improvement of 2.63% in AUC and precision compared to the recent federated recommendation baselines. Full article
34 pages, 3112 KB  
Article
Artificial Intelligence Applied to Soil Compaction Control for the Light Dynamic Penetrometer Method
by Jorge Rojas-Vivanco, José García, Gabriel Villavicencio, Miguel Benz, Antonio Herrera, Pierre Breul, German Varas, Paola Moraga, Jose Gornall and Hernan Pinto
Mathematics 2025, 13(21), 3359; https://doi.org/10.3390/math13213359 - 22 Oct 2025
Viewed by 169
Abstract
Compaction quality control in earthworks and pavements still relies mainly on density-based acceptance referenced to laboratory Proctor tests, which are costly, time-consuming, and spatially sparse. Lightweight dynamic cone penetrometer (LDCP) provides rapid indices, such as qd0 and qd1, [...] Read more.
Compaction quality control in earthworks and pavements still relies mainly on density-based acceptance referenced to laboratory Proctor tests, which are costly, time-consuming, and spatially sparse. Lightweight dynamic cone penetrometer (LDCP) provides rapid indices, such as qd0 and qd1, yet acceptance thresholds commonly depend on ad hoc, site-specific calibrations. This study develops and validates a supervised machine learning framework that estimates qd0, qd1, and Zc directly from readily available soil descriptors (gradation, plasticity/activity, moisture/state variables, and GTR class) using a multi-campaign dataset of n=360 observations. While the framework does not remove the need for the standard soil characterization performed during design (e.g., W, γd,field, and RCSPC), it reduces reliance on additional LDCP calibration campaigns to obtain device-specific reference curves. Models compared under a unified pipeline include regularized linear baselines, support vector regression, Random Forest, XGBoost, and a compact multilayer perceptron (MLP). The evaluation used a fixed 80/20 train–test split with 5-fold cross-validation on the training set and multiple error metrics (R2, RMSE, MAE, and MAPE). Interpretability combined SHAP with permutation importance, 1D partial dependence (PDP), and accumulated local effects (ALE); calibration diagnostics and split-conformal prediction intervals connected the predictions to QA/QC decisions. A naïve GTR-average baseline was added for reference. Computation was lightweight. On the test set, the MLP attained the best accuracy for qd1 (R2=0.794, RMSE =5.866), with XGBoost close behind (R2=0.773, RMSE =6.155). Paired bootstrap contrasts with Holm correction indicated that the MLP–XGBoost difference was not statistically significant. Explanations consistently highlighted density- and moisture-related variables (γd,field, RCSPC, and W) as dominant, with gradation/plasticity contributing second-order adjustments; these attributions are model-based and associational rather than causal. The results support interpretable, computationally efficient surrogates of LDCP indices that can complement density-based acceptance and enable risk-aware QA/QC via conformal prediction intervals. Full article
(This article belongs to the Special Issue Artificial Intelligence and Data Science, 2nd Edition)
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17 pages, 1523 KB  
Article
A Hybrid Model Combining Signal Decomposition and Inverted Transformer for Accurate Power Transformer Load Prediction
by Shuguo Gao, Chenmeng Xiang, Yanhao Zhou, Haoyu Liu, Lujian Dai, Tianyue Zhang and Yi Yin
Appl. Sci. 2025, 15(20), 11241; https://doi.org/10.3390/app152011241 - 20 Oct 2025
Viewed by 299
Abstract
Transformer load is a key factor influencing its aging and service life. Accurately predicting load trends is crucial for assisting load redistribution. This study proposes a hybrid model called RIME-VMD-TCN-iTransformer to forecast the trend of transformer load. In this model, RIME (Randomized Improved [...] Read more.
Transformer load is a key factor influencing its aging and service life. Accurately predicting load trends is crucial for assisting load redistribution. This study proposes a hybrid model called RIME-VMD-TCN-iTransformer to forecast the trend of transformer load. In this model, RIME (Randomized Improved Marine Predators Algorithm) is employed to enhance decomposition stability, VMD (Variational Mode Decomposition) is used to address the non-stationary characteristics of the load sequence, TCN (Temporal Convolutional Network) extracts local temporal dependencies, and iTransformer (Inverted Transformer) captures global inter-variable correlations. First, the variational mode decomposition algorithm is applied to mitigate the non-stationary characteristics of the signal, followed by the RIME to further enhance the orderliness of the intrinsic mode functions. Subsequently, the TCN-iTransformer model is utilized to predict each intrinsic mode function individually, and the prediction results of all intrinsic mode functions are reconstructed to obtain the final forecast. The findings indicate that the intrinsic mode functions obtained through RIME-VMD exhibit no spectral aliasing and can decompose abrupt time-series signals into stable and regular frequency components. Compared to other hybrid models, the proposed model demonstrates superior responsiveness to changes in time-series trends and achieves the lowest prediction error across various transformer capacity scenarios. These results highlight the model’s superior accuracy and generalization capability in handling abrupt signals, underscoring its potential for preventing unexpected transformer events. Full article
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31 pages, 5190 KB  
Article
MDF-YOLO: A Hölder-Based Regularity-Guided Multi-Domain Fusion Detection Model for Indoor Objects
by Fengkai Luan, Jiaxing Yang and Hu Zhang
Fractal Fract. 2025, 9(10), 673; https://doi.org/10.3390/fractalfract9100673 - 18 Oct 2025
Viewed by 269
Abstract
With the rise of embodied agents and indoor service robots, object detection has become a critical component supporting semantic mapping, path planning, and human–robot interaction. However, indoor scenes often face challenges such as severe occlusion, large-scale variations, small and densely packed objects, and [...] Read more.
With the rise of embodied agents and indoor service robots, object detection has become a critical component supporting semantic mapping, path planning, and human–robot interaction. However, indoor scenes often face challenges such as severe occlusion, large-scale variations, small and densely packed objects, and complex textures, making existing methods struggle in terms of both robustness and accuracy. This paper proposes MDF-YOLO, a multi-domain fusion detection framework based on Hölder regularity guidance. In the backbone, neck, and feature recovery stages, the framework introduces the CrossGrid Memory Block, Hölder-Based Regularity Guidance–Hierarchical Context Aggregation module, and Frequency-Guided Residual Block, achieving complementary feature modeling across the state space, spatial domain, and frequency domain. In particular, the HG-HCA module uses the Hölder regularity map as a guiding signal to balance the dynamic equilibrium between the macro and micro paths, thus achieving adaptive coordination between global consistency and local discriminability. Experimental results show that MDF-YOLO significantly outperforms mainstream detectors in metrics such as mAP@0.5, mAP@0.75, and mAP@0.5:0.95, achieving values of 0.7158, 0.6117, and 0.5814, respectively, while maintaining near real-time inference efficiency in terms of FPS and latency. Ablation studies further validate the independent and synergistic contributions of CGMB, HG-HCA, and FGRB in improving small-object detection, occlusion handling, and cross-scale robustness. This study demonstrates the potential of Hölder regularity and multi-domain fusion modeling in object detection, offering new insights for efficient visual modeling in complex indoor environments. Full article
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18 pages, 776 KB  
Article
A Comprehensive Approach to Identifying the Parameters of a Counterflow Heat Exchanger Model Based on Sensitivity Analysis and Regularization Methods
by Salimzhan Tassanbayev, Gulzhan Uskenbayeva, Aliya Shukirova, Korlan Kulniyazova and Igor Slastenov
Processes 2025, 13(10), 3289; https://doi.org/10.3390/pr13103289 - 14 Oct 2025
Viewed by 219
Abstract
The study presents a robust methodology for simultaneous state and parameter estimation in nonlinear thermal systems, demonstrated on a counter-current heat exchanger model operating with nitrogen under industrial conditions. To address challenges of ill-conditioning and parameter correlation, local sensitivity analysis is combined with [...] Read more.
The study presents a robust methodology for simultaneous state and parameter estimation in nonlinear thermal systems, demonstrated on a counter-current heat exchanger model operating with nitrogen under industrial conditions. To address challenges of ill-conditioning and parameter correlation, local sensitivity analysis is combined with regularization through optimal parameter subset selection using orthogonalization and D-optimal experimental design. The Unscented Kalman Filter (UKF) is employed to jointly estimate the augmented state vector in real time, leveraging high-fidelity dynamic simulations generated in Unisim Design with the Peng–Robinson equation of state. The proposed framework achieves high estimation accuracy and numerical stability, even under limited sensor availability and measurement noise. Monte Carlo simulations confirm robustness to ±2.5% uncertainty in initial conditions, while residual autocorrelation analysis validates estimator optimality. The approach provides a practical solution for real-time monitoring and model-based control in industrial heat exchangers and offers a generalizable strategy for building identifiable, noise-resilient models of complex nonlinear systems. Full article
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30 pages, 5508 KB  
Article
Phase-Aware Complex-Spectrogram Autoencoder for Vibration Preprocessing: Fault-Component Separation via Input-Phasor Orthogonality Regularization
by Seung-yeol Yoo, Ye-na Lee, Jae-chul Lee, Se-yun Hwang, Jae-yun Lee and Soon-sup Lee
Machines 2025, 13(10), 945; https://doi.org/10.3390/machines13100945 - 13 Oct 2025
Viewed by 292
Abstract
We propose a phase-aware complex-spectrogram autoencoder (AE) for preprocessing raw vibration signals of rotating electrical machines. The AE reconstructs normal components and separates fault components as residuals, guided by an input-phasor phase-orthogonality regularization that defines parallel/orthogonal residuals with respect to the local signal [...] Read more.
We propose a phase-aware complex-spectrogram autoencoder (AE) for preprocessing raw vibration signals of rotating electrical machines. The AE reconstructs normal components and separates fault components as residuals, guided by an input-phasor phase-orthogonality regularization that defines parallel/orthogonal residuals with respect to the local signal phase. We use a U-Net-based AE with a mask-bias head to refine local magnitude and phase. Decisions are based on residual features—magnitude/shape, frequency distribution, and projections onto the normal manifold. Using the AI Hub open dataset from field ventilation motors, we evaluate eight representative motor cases (2.2–5.5 kW: misalignment, unbalance, bearing fault, belt looseness). The preprocessing yielded clear residual patterns (low-frequency floor rise, resonance-band peaks, harmonic-neighbor spikes), and achieved an area under the receiver operating characteristic curve (ROC-AUC) = 0.998–1.000 across eight cases, with strong leave-one-file-out generalization and good calibration (expected calibration error (ECE) ≤ 0.023). The results indicate that learning to remove normal structure while enforcing phase consistency provides an unsupervised front-end that enhances fault evidence while preserving interpretability on field data. Full article
(This article belongs to the Section Machines Testing and Maintenance)
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27 pages, 3092 KB  
Article
Energy Audit of Road Lighting Installations as a Tool for Improving Efficiency and Visual Safety Conditions
by Marek Kurkowski, Tomasz Popławski, Henryk Wachta and Dominik Węclewski
Energies 2025, 18(20), 5357; https://doi.org/10.3390/en18205357 - 11 Oct 2025
Viewed by 304
Abstract
This study presents an analysis of the condition of street lighting based on a selected typical installation in one of the 1459 rural communes in Poland. The analysis was carried out on the basis of publicly available statistical data, local government reports, and [...] Read more.
This study presents an analysis of the condition of street lighting based on a selected typical installation in one of the 1459 rural communes in Poland. The analysis was carried out on the basis of publicly available statistical data, local government reports, and information contained in national and European strategic documents. During the analysis, numerous irregularities and differences in the quality and energy efficiency of the lighting infrastructure were indicated. It was found that outdated sodium luminaires with high energy consumption, low durability, and limited luminous efficacy are used in many cases, which generates significant operating costs and negatively affects the environment. The authors emphasize that a lack of regular and professional lighting audits leads to the suboptimal use of energy resources, an insufficient level of road safety, and failure to adapt lighting to current technical standards and the needs of road users. A lighting audit is a key tool for diagnosing the technical condition, efficiency, and compliance of installations with relevant regulations and recommendations. It also allows for the identification of potential savings and determining the directions of modernization and implementation of energy-saving technologies, such as LED luminaires and intelligent control systems.The presented analysis demonstrates that energy audits are an effective tool for confirming efficiency improvements and enhancing visual safety conditions through better compliance with photometric standards (luminance, lighting uniformity). Direct accident statistics were not within the scope of this study. Full article
(This article belongs to the Section F: Electrical Engineering)
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22 pages, 325 KB  
Article
Global Solutions to the Vlasov–Fokker–Planck Equation with Local Alignment Forces Under Specular Reflection Boundary Condition
by Yanming Chang and Yingzhe Fan
Axioms 2025, 14(10), 760; https://doi.org/10.3390/axioms14100760 - 11 Oct 2025
Viewed by 172
Abstract
In this article, we establish the existence of global mild solutions to the Vlasov–Fokker–Planck equation with local alignment forces under specular reflection boundary conditions in the low-regularity function space Lk1LTLv2. A key difficulty is [...] Read more.
In this article, we establish the existence of global mild solutions to the Vlasov–Fokker–Planck equation with local alignment forces under specular reflection boundary conditions in the low-regularity function space Lk1LTLv2. A key difficulty is that the macroscopic averaged velocity u does not directly possess a dissipative structure in the equation. To overcome this, we rely on the dissipation ub from the linear part, combined with the dissipation of the macroscopic component b derived from the associated macroscopic equation. Moreover, since no direct energy functional is available for u, we fully exploit the dissipative mechanisms of both ub and b when handling the estimates for the nonlinear terms. Full article
(This article belongs to the Special Issue Recent Advances in Differential Equations and Related Topics)
26 pages, 2534 KB  
Article
Consumer Attitudes, Awareness, and Purchase Behaviour for Certified Mountain Products in Romania
by Ancuța Marin, Steliana Rodino, Ruxandra-Eugenia Pop, Vili Dragomir and Marian Butu
Sustainability 2025, 17(19), 8950; https://doi.org/10.3390/su17198950 - 9 Oct 2025
Viewed by 390
Abstract
Interest in consumer behavior regarding agri-food products is growing, particularly in the context of sustainable and local consumption. This study examines consumer perceptions of certified mountain products in Romania, with a specific focus on cow’s milk. A structured survey was conducted among 576 [...] Read more.
Interest in consumer behavior regarding agri-food products is growing, particularly in the context of sustainable and local consumption. This study examines consumer perceptions of certified mountain products in Romania, with a specific focus on cow’s milk. A structured survey was conducted among 576 respondents from the Bucharest–Ilfov metropolitan area, representing the target population of regular food consumers. The data were analyzed using descriptive and comparative statistical methods in SPSS, including chi-square tests and contingency coefficients, to evaluate consumer awareness, attitudes, and their willingness to pay. The results reveal that although awareness of the “mountain product” label is high (88.9%), its direct influence on purchase decisions remains limited, with price, brand, and origin playing stronger roles. Nevertheless, 95% of respondents expressed willingness to pay a premium price, and over 70% associated mountain certification with health benefits and higher quality. These findings highlight both the potential and current limitations of certification as a market-based tool to support sustainable consumption and the economic resilience of mountain areas. The study contributes empirical evidence from a less explored national context. It offers insights for policymakers, producers, and retailers seeking to strengthen short food supply chains and consumer trust in certified labels. Full article
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17 pages, 905 KB  
Article
The Simplest 2D Quantum Walk Detects Chaoticity
by César Alonso-Lobo, Gabriel G. Carlo and Florentino Borondo
Mathematics 2025, 13(19), 3223; https://doi.org/10.3390/math13193223 - 8 Oct 2025
Viewed by 400
Abstract
Quantum walks are, at present, an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior. For this purpose, we consider an extremely [...] Read more.
Quantum walks are, at present, an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior. For this purpose, we consider an extremely simple model consisting of alternating one-dimensional walks along the two spatial coordinates in bidimensional closed domains (hard wall billiards). The chaotic or regular behavior induced by the boundary shape in the deterministic classical motion translates into chaotic signatures for the quantized problem, resulting in sharp differences in the spectral statistics and morphology of the eigenfunctions of the quantum walker. Indeed, we found, for the Bunimovich stadium—a chaotic billiard—level statistics described by a Brody distribution with parameter δ0.1. This indicates a weak level repulsion, and also enhanced eigenfunction localization, with an average participation ratio (PR)1150 compared to the rectangular billiard (regular) case, where the average PR1500. Furthermore, scarring on unstable periodic orbits is observed. The fact that our simple model exhibits such key signatures of quantum chaos, e.g., non-Poissonian level statistics and scarring, that are sensitive to the underlying classical dynamics in the free particle billiard system is utterly surprising, especially when taking into account that quantum walks are diffusive models, which are not direct quantizations of a Hamiltonian. Full article
(This article belongs to the Section C2: Dynamical Systems)
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24 pages, 29903 KB  
Article
Analyzing Spatiotemporal Patterns of Cultivated Land by Integrating Aggregation Degree and Omnidirectional Connectivity: A Case Study of Daqing City, China
by Yanhong Hang, Zhuocheng Zhang and Xiaoming Li
Land 2025, 14(10), 2000; https://doi.org/10.3390/land14102000 - 6 Oct 2025
Viewed by 369
Abstract
The spatial configuration of cultivated land is crucial for modern agricultural production; therefore, research on cultivated land aggregation and spatial connectivity holds significant importance for enhancing agricultural production efficiency and ensuring food security. This study selected Daqing City, China, as the research area [...] Read more.
The spatial configuration of cultivated land is crucial for modern agricultural production; therefore, research on cultivated land aggregation and spatial connectivity holds significant importance for enhancing agricultural production efficiency and ensuring food security. This study selected Daqing City, China, as the research area and constructed a three-level nested framework of “patch–local–regional” scales. The aggregation degree was calculated through landscape pattern indices and the MSPA model, and connectivity was evaluated using the Omniscape algorithm based on circuit theory to explore the spatiotemporal evolution patterns of cultivated land configuration and analyze their spatial correlations, proposing classified optimization strategies. The results indicate the following: (1) the spatiotemporal distribution characteristics of cultivated land aggregation in Daqing City exhibit a spatial pattern of “high in the north and south, low in the middle,” with an overall declining trend from 2000 to 2020; (2) high-connectivity areas are primarily distributed in Lindian County in the north and Zhaozhou and Zhaoyuan Counties in the south, while low-connectivity areas are concentrated in the central urban area and surrounding regions; (3) the aggregation degree and connectivity demonstrate positive spatial correlation, with the Global Moran’s index increasing from 0.358 in 2000 to 0.413 in 2020; and (4) based on the aggregation degree and connectivity characteristics, the study area can be classified into four types: scattered imbalance–isolated dysfunction, regular imbalance–connected dysfunction, scattered improvement–connected optimization, and regular improvement–connected optimization. This study provides new research perspectives for cultivated land protection. The proposed multi-scale aggregation–connectivity research method and classification system offer important reference value for the efficient utilization and management optimization of cultivated land. Full article
(This article belongs to the Special Issue Spatiotemporal Dynamics and Utilization Trend of Farmland)
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17 pages, 2126 KB  
Article
Explainable Machine Learning Applied to Bioelectrical Impedance for Low Back Pain: Classification and Pain-Score Prediction
by Seungwan Jang, Seung Mo Yoo, Se Dong Min and Changwon Wang
Sensors 2025, 25(19), 6135; https://doi.org/10.3390/s25196135 - 3 Oct 2025
Viewed by 494
Abstract
(1) Background: Low back pain (LBP) is the most prevalent cause of disability worldwide, yet current assessment relies mainly on subjective questionnaires, underscoring the need for objective and interpretable biomarkers. Bioelectrical impedance parameter (BIP), quantified by resistance (R), impedance magnitude (Z), and phase [...] Read more.
(1) Background: Low back pain (LBP) is the most prevalent cause of disability worldwide, yet current assessment relies mainly on subjective questionnaires, underscoring the need for objective and interpretable biomarkers. Bioelectrical impedance parameter (BIP), quantified by resistance (R), impedance magnitude (Z), and phase angle (PA), reflects tissue hydration and cellular integrity and may provide physiological correlates of pain; (2) Methods: This cross-sectional study used lumbar BIP and demographic characteristics from 83 participants (38 with lumbar BIP and 45 normal controls). We applied Extreme Gradient Boosting (XGBoost), a regularized tree-based machine learning (ML) algorithm, with stratified five-fold cross-validation. Model interpretability was ensured using SHapley Additive exPlanations (SHAP), which provide global importance rankings and local feature attributions. Outcomes included classification of LBP versus healthy status and regression-based prediction of pain scales: the Visual Analog Scale (VAS), Oswestry Disability Index (ODI), and Roland–Morris Disability Questionnaire (RMDQ); (3) Results: The classifier achieved high discrimination (ROC–AUC = 0.996 ± 0.009, sensitivity = 0.950 ± 0.068, specificity = 0.977 ± 0.049). Pain prediction showed best performance for VAS (R2 = 0.70 ± 0.14; mean absolute error = 1.23 ± 0.27), with weaker performance for ODI and RMDQ; (4) Conclusions: These findings suggest that explainable ML models applied to BIP could discriminate between LBP and healthy groups and could estimate pain intensity, providing an objective complement to subjective assessments. Full article
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22 pages, 3598 KB  
Article
Research on Denoising Methods for Magnetocardiography Signals in a Non-Magnetic Shielding Environment
by Biao Xing, Xie Feng and Binzhen Zhang
Sensors 2025, 25(19), 6096; https://doi.org/10.3390/s25196096 - 3 Oct 2025
Viewed by 541
Abstract
Magnetocardiography (MCG) offers a noninvasive method for early screening and precise localization of cardiovascular diseases by measuring picotesla-level weak magnetic fields induced by cardiac electrical activity. However, in unshielded magnetic environments, geomagnetic disturbances, power-frequency electromagnetic interference, and physiological/motion artifacts can significantly overwhelm effective [...] Read more.
Magnetocardiography (MCG) offers a noninvasive method for early screening and precise localization of cardiovascular diseases by measuring picotesla-level weak magnetic fields induced by cardiac electrical activity. However, in unshielded magnetic environments, geomagnetic disturbances, power-frequency electromagnetic interference, and physiological/motion artifacts can significantly overwhelm effective magnetocardiographic components. To address this challenge, this paper systematically constructs an integrated denoising framework, termed “AOA-VMD-WT”. In this approach, the Arithmetic Optimization Algorithm (AOA) adaptively optimizes the key parameters (decomposition level K and penalty factor α) of Variational Mode Decomposition (VMD). The decomposed components are then regularized based on their modal center frequencies: components with frequencies ≥50 Hz are directly suppressed; those with frequencies <50 Hz undergo wavelet threshold (WT) denoising; and those with frequencies <0.5 Hz undergo baseline correction. The purified signal is subsequently reconstructed. For quantitative evaluation, we designed performance indicators including QRS amplitude retention rate, high/low frequency suppression amount, and spectral entropy. Further comparisons are made with baseline methods such as FIR and wavelet soft/hard thresholds. Experimental results on multiple sets of measured MCG data demonstrate that the proposed method achieves an average improvement of approximately 8–15 dB in high-frequency suppression, 2–8 dB in low-frequency suppression, and a decrease in spectral entropy ranging from 0.1 to 0.6 without compromising QRS amplitude. Additionally, the parameter optimization exhibits high stability. These findings suggest that the proposed framework provides engineerable algorithmic support for stable MCG measurement in ordinary clinic scenarios. Full article
(This article belongs to the Section Biomedical Sensors)
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28 pages, 379 KB  
Article
Completeness and Cocompleteness Transfer for Internal Group Objects with Geometric Obstructions
by Jian-Gang Tang, Nueraminaimu Maihemuti, Jia-Yin Peng, Yimamujiang Aisan and Ai-Li Song
Mathematics 2025, 13(19), 3155; https://doi.org/10.3390/math13193155 - 2 Oct 2025
Viewed by 255
Abstract
This work establishes definitive conditions for the inheritance of categorical completeness and cocompleteness by categories of internal group objects. We prove that while the completeness of Grp(C) follows unconditionally from the completeness of the base category C, cocompleteness requires [...] Read more.
This work establishes definitive conditions for the inheritance of categorical completeness and cocompleteness by categories of internal group objects. We prove that while the completeness of Grp(C) follows unconditionally from the completeness of the base category C, cocompleteness requires C to be regular, cocomplete, and admit a free group functor left adjoint to the forgetful functor. Explicit limit and colimit constructions are provided, with colimits realized via coequalizers of relations induced by group axioms over free group objects. Applications demonstrate cocompleteness in topological groups, ordered groups, and group sheaves, while Lie groups serve as counterexamples revealing necessary analytic constraints—particularly the impossibility of equipping free groups on non-discrete manifolds with smooth structures. Further results include the inheritance of regularity when the free group functor preserves finite products, the existence of internal hom-objects in locally Cartesian closed settings, monadicity for locally presentable C, and homotopical extensions where model structures on Grp(M) reflect those of M. This framework unifies classical category theory with geometric obstruction theory, resolving fundamental questions on exactness transfer and enabling new constructions in homotopical algebra and internal representation theory. Full article
18 pages, 2019 KB  
Article
Low-Velocity Impact Behavior of PLA BCC Lattice Structures: Experimental and Numerical Investigation with a Novel Dimensionless Index
by Giuseppe Iacolino, Giuseppe Mantegna, Emilio V. González, Giuseppe Catalanotti, Calogero Orlando, Davide Tumino and Andrea Alaimo
Materials 2025, 18(19), 4574; https://doi.org/10.3390/ma18194574 - 1 Oct 2025
Viewed by 505
Abstract
Lattice structures are lightweight architected materials particularly suitable for aerospace and automotive applications due to their ability to combine mechanical strength with reduced mass. Among various topologies, Body-Centered Cubic (BCC) lattices are widely employed for their geometric regularity and favorable strength-to-weight ratio. Advances [...] Read more.
Lattice structures are lightweight architected materials particularly suitable for aerospace and automotive applications due to their ability to combine mechanical strength with reduced mass. Among various topologies, Body-Centered Cubic (BCC) lattices are widely employed for their geometric regularity and favorable strength-to-weight ratio. Advances in Additive Manufacturing (AM) have enabled the precise and customizable fabrication of such complex architectures, reducing material waste and increasing design flexibility. This study investigates the low-velocity impact behavior of two polylactic acid (PLA)-based BCC lattice panels differing in strut diameter: BCC1.5 (1.5 mm) and BCC2 (2 mm). Experimental impact tests and finite element simulations were performed to evaluate their energy absorption (EA) capabilities. In addition to conventional global performance indices, a dimensionless parameter, D, is introduced to quantify the ratio between local plastic indentation and global displacement, allowing for a refined characterization of deformation modes and structural efficiency. Results show that BCC1.5 absorbs more energy than BCC2, despite the latter’s higher stiffness. This suggests that thinner struts enhance energy dissipation under dynamic loading. Despite minor discrepancies, numerical simulations provide accurate estimations of EA and support the robustness of the D index within the examined configuration, highlighting its potential to deformation heterogeneity. Full article
(This article belongs to the Section Manufacturing Processes and Systems)
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