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Search Results (358)

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Keywords = Method of Analytical Regularization

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26 pages, 68696 KB  
Article
A Modified Analytical Calculation Model for Mutual Inductance Between Arbitrarily Oriented Solenoid Coils
by Hüseyin Altun and Neslihan Pirinççi
Electronics 2026, 15(13), 2753; https://doi.org/10.3390/electronics15132753 (registering DOI) - 23 Jun 2026
Abstract
Accurate calculation of mutual inductance (MI) between solenoid coils is essential for system design, but complex geometries and spatial arrangements make it challenging. This paper presents a modified analytical method for calculating the MI between two circular-wound air-core solenoid coils arbitrarily oriented in [...] Read more.
Accurate calculation of mutual inductance (MI) between solenoid coils is essential for system design, but complex geometries and spatial arrangements make it challenging. This paper presents a modified analytical method for calculating the MI between two circular-wound air-core solenoid coils arbitrarily oriented in three-dimensional (3D) space. The analytical model used to calculate the MI between two solenoid coils is based on the use of magnetic vector potential (MVP). The helical structure of the solenoid coils is represented by successive coaxial circular filaments arranged along their central axes. Each filament is represented by an equivalent regular polygon with a sufficient number of sides. The proposed approach allows the MI between two solenoid coils to be calculated using a single analytical formula, without imposing restrictions on the relative positions of the coils, while taking lateral and angular misalignments into account. The modified analytical model is validated for accuracy and applicability by comparing its results with experimental measurements and FEM-based simulation results for coil systems with different diameters, turn numbers, and turn pitches. The MI results for various angular and lateral misalignments are in good agreement with experimental measurements and FEM results. The MI calculation model proposed in this work provides a fast and reliable tool for analyzing the electromagnetic behavior of coupled coil systems, designing inductive power transfer systems, and assessing electromagnetic compatibility. Full article
(This article belongs to the Special Issue Wireless Power Transfer: Current Status and Future Prospects)
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20 pages, 1566 KB  
Article
An AI-Driven Management Information System for Employee Attrition Prediction: Enhancing Human Agency Through XGBoost and Explainable AI
by Md Eahia Ansari, Md Tanvir Rahman Tarafder, Abir Chowdhury, Nur Nahar Rimi, Nipa Akter and Khandakar Rabbi Ahmed
Computers 2026, 15(7), 400; https://doi.org/10.3390/computers15070400 (registering DOI) - 23 Jun 2026
Abstract
Employee attrition is a significant organizational challenge associated with substantial financial costs and the erosion of institutional knowledge. This study presents an AI-based Management Information System (MIS) that integrates machine learning (ML) models to forecast employee turnover and support technical interpretability for HR [...] Read more.
Employee attrition is a significant organizational challenge associated with substantial financial costs and the erosion of institutional knowledge. This study presents an AI-based Management Information System (MIS) that integrates machine learning (ML) models to forecast employee turnover and support technical interpretability for HR decision-making. Using the IBM HR Analytics Dataset comprising 1480 employee records with 38 features, we implemented a rigorous preprocessing pipeline—including Synthetic Minority Over-sampling Technique (SMOTE) applied exclusively within training folds to prevent data leakage, one-hot encoding, Z-score normalization, and mean-value imputation. Four ML classifiers—Logistic Regression (LR), Random Forest (RF), Multi-Layer Perceptron (MLP), and XGBoost—were evaluated under a stratified 80/20 split with 5-fold cross-validation. XGBoost achieved the highest performance, attaining an accuracy of 87.83%, a ROC-AUC of 0.94, a PR-AUC of 0.96, and an F1-score of 93.04%, attributed to its sequential boosting mechanism and built-in L1/L2 regularization. Beyond predictive performance, the system incorporates SHapley Additive exPlanations (SHAP) to deliver feature-level transparency, enabling HR professionals to engage in proactive, informed retention interventions while retaining full decision-making authority. Within-dataset comparisons confirm that the proposed framework outperforms prior methods evaluated on the same benchmark; cross-study accuracy comparisons are reported as contextual reference only, given differences in datasets and experimental protocols. The system facilitates human oversight by positioning AI as a decision-support collaborator rather than an autonomous replacement in workforce management. Future work will address real-time deployment, controlled user studies with HR practitioners, and validation with actual organizational HR data. Full article
(This article belongs to the Special Issue Deep Learning and Explainable Artificial Intelligence (2nd Edition))
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17 pages, 1028 KB  
Article
Diet Quality, Healthy Practices, and Psychosocial Functioning Across School Youth, Students, and Adults in Poland: A Cross-Sectional Online Survey
by Klaudia Sochacka, Agata Kotowska and Sabina Lachowicz-Wiśniewska
Nutrients 2026, 18(12), 2022; https://doi.org/10.3390/nu18122022 (registering DOI) - 21 Jun 2026
Viewed by 145
Abstract
Background: This study aimed to compare a limited set of predefined diet-, lifestyle-, knowledge-, and psychosocial indicators across school youth, students, and adults in Poland, and to examine their associations with three predefined outcomes: BMI ≥ 25 kg/m2, poorer mental well-being, [...] Read more.
Background: This study aimed to compare a limited set of predefined diet-, lifestyle-, knowledge-, and psychosocial indicators across school youth, students, and adults in Poland, and to examine their associations with three predefined outcomes: BMI ≥ 25 kg/m2, poorer mental well-being, and high stress/overload. Diet quality, daily health-related practices, psychosocial well-being, and stress/overload may co-occur across different life stages, but online survey data require a focused analytical framework to avoid overinterpretation. Methods: This cross-sectional anonymous online survey included 360 respondents: 154 school youth aged 15–19 years, 127 students aged 20–29 years, and 79 adults aged 30 years or older. Dietary assessment was based on the KomPAN questionnaire and included the pro-healthy diet index, non-healthy diet index, and Diet Quality Index. Study-specific scores were used for knowledge, healthy practices, psychosocial well-being, and stress/overload. Analyses were restricted to predefined group comparisons, selected correlations, and three whole-sample adjusted logistic regression models. Results: Adults had the highest BMI and waist/hip circumference, whereas school youth showed the highest non-healthy diet index and more frequent high processed-food intake. Among the knowledge and psychosocial indicators, only obesity knowledge differed significantly between groups, with the highest mean value among students. Stress/overload was inversely associated with psychosocial well-being, and DQI was positively associated with psychosocial well-being after adjustment for age, sex, and group. In adjusted whole-sample models, BMI ≥ 25 kg/m2 was positively associated with age and DQI and inversely associated with physical activity frequency and regular meals; the positive DQI–BMI association was interpreted cautiously as potentially reflecting reverse causality, reporting bias, or compensatory dietary modification among respondents with excess body weight. Poorer mental well-being was associated with higher stress/overload and inversely associated with DQI, physical activity frequency, and family meals. High stress/overload was positively associated with highly processed food intake and inversely associated with regular meals. Conclusions: The findings suggest that diet quality, behavioral regularity, and psychosocial burden may be more informative than knowledge alone when describing health-related profiles across age-defined groups. Because the study was cross-sectional, self-reported, anonymous, and based on a modest sample, the results should be interpreted as preliminary and hypothesis-generating rather than causal. Full article
(This article belongs to the Special Issue Nutritional Psychiatry: Eating Behaviors and Mental Health Outcomes)
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30 pages, 6376 KB  
Article
Automatic Tuning and Matching for NMR Probes Based on Physics-Informed Conditional Neural Processes
by Zhida Zhai, Zhenggang Li, Ying He, Yaohong Wang, Chenjun Zhu, Weifeng Wu, Yitong Lin and Huijun Sun
Sensors 2026, 26(12), 3724; https://doi.org/10.3390/s26123724 - 11 Jun 2026
Viewed by 127
Abstract
The NMR resonator is the sensor responsible for transmitting RF pulses and receiving detection signals, and its tuning and matching are crucial to acquiring high-sensitivity NMR signals. Automated tuning and matching (ATM) is therefore essential for rapid, accurate, and continuously efficient testing. Existing [...] Read more.
The NMR resonator is the sensor responsible for transmitting RF pulses and receiving detection signals, and its tuning and matching are crucial to acquiring high-sensitivity NMR signals. Automated tuning and matching (ATM) is therefore essential for rapid, accurate, and continuously efficient testing. Existing NMR ATM methods still primarily rely on iterative search strategies, whose dominant cost arises from repeated hardware measurements and waiting periods, often requiring multiple measurement cycles before convergence. The emergence of in situ NMR detection of high-concentration ionic samples has further increased the demand for real-time, rapid ATM with a large dynamic range, posing a major challenge to conventional approaches. This paper proposes a physics-informed few-shot learning method for automatic tuning and matching over wideband and multi-resonance-frequency NMR scenarios. The tuning-and-matching problem is formulated as a structure and frequency-conditioned function regression task, and a conditional neural process (CNP) is introduced to learn cross-task priors and directly predict the states of tunable components from only a small number of real-machine context measurements. A physics regularizer based on the local sensitivity of the input impedance is further designed to impose stronger penalties on errors under high-Q narrowband operating conditions without relying on proprietary analytical circuit models. Simulation studies and real NMR experiments are conducted on multiple circuit topologies and multiple target frequencies using only a small number of NMR samples. The results demonstrate consistent improvements in key metrics, including accuracy of tuning and matching and the number of collected real-machine samples required per task. In particular, with only 100 sampled tuning/matching capacitor points and 20 on-hardware collected samples, the proposed method already delivers satisfactory tuning-and-matching performance. The method achieves an attractive accuracy–cost tradeoff across both cross-topology and cross-frequency scenarios, and shows strong potential for few-shot, rapid, real-time detection. Full article
(This article belongs to the Section Intelligent Sensors)
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15 pages, 594 KB  
Article
Trace-Level Determination of ACE Inhibitors in Wastewater of Al-Kharj Governorate Using Solid-Phase Extraction–Capillary Electrophoresis Aided by Field Amplified Sample Stacking: A Sustainable Analytical Approach
by Alhumaidi B. Alabbas and Sherif A. Abdel-Gawad
Chemosensors 2026, 14(6), 129; https://doi.org/10.3390/chemosensors14060129 - 4 Jun 2026
Viewed by 210
Abstract
Particularly in regions experiencing rapid industrial and healthcare development, the presence of pharmaceutical residues in wastewater is becoming an increasingly pressing environmental concern. In this study, an analytical method was developed to quantify lisinopril (LIS), ramipril (RAM), and enalapril (ENA) in wastewater while [...] Read more.
Particularly in regions experiencing rapid industrial and healthcare development, the presence of pharmaceutical residues in wastewater is becoming an increasingly pressing environmental concern. In this study, an analytical method was developed to quantify lisinopril (LIS), ramipril (RAM), and enalapril (ENA) in wastewater while being both sensitive and inexpensive. To improve the precision and accuracy of the measurements, propranolol (PRO) was used as an internal standard. To achieve dual preconcentration and enhanced sensitivity, the method integrates filed amplified sample stacking (FASS) with solid-phase extraction (SPE) before capillary electrophoresis (CE) in a synergistic way. Important experimental factors such the composition of the background electrolyte (BGE), pH, injection settings, stacking efficiency, and selection of the SPE sorbent were meticulously calibrated. Under ideal circumstances, the SPE-CE-FASS method demonstrated remarkable linearity within the concentration range of 10–1000 ng L−1 (R2 > 0.999), an outstanding level of accuracy (intra- and inter-day RSD < 6%), and satisfactory recovery percents (90–97%) in real wastewater samples. This method offers an eco-friendly and cost-effective alternative to liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) by reducing waste, using less solvent, and providing enough sensitivity for trace-level analysis. Hence, it is very suitable for the regular monitoring of angiotensin converting enzyme (ACE) inhibitors in complex wastewater matrices. Full article
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27 pages, 3787 KB  
Article
Direct Surface-Based Meshing and Measurement-Driven Cutter Edge Reconstruction for Cylindrical Gear Skiving
by Wei-Jen Chen and Zhang-Hua Fong
Machines 2026, 14(6), 641; https://doi.org/10.3390/machines14060641 - 2 Jun 2026
Viewed by 210
Abstract
Most existing analytical models for gear skiving define the cutting edge indirectly through hypothetical generating gears. This abstraction introduces an inherent geometric inconsistency between the theoretical cutting edge and the true conical rake surface of the cutter, limiting prediction accuracy and hindering measurement-driven [...] Read more.
Most existing analytical models for gear skiving define the cutting edge indirectly through hypothetical generating gears. This abstraction introduces an inherent geometric inconsistency between the theoretical cutting edge and the true conical rake surface of the cutter, limiting prediction accuracy and hindering measurement-driven compensation. To address this limitation, this study proposes a unified analytical and measurement-driven framework for cylindrical gear skiving that eliminates the generating-gear assumption entirely. A direct surface-based meshing formulation is developed by enforcing positional coincidence and tangential compatibility directly on the cutter’s conical rake surface, ensuring strict geometric consistency with the physical cutting mechanism. To incorporate real cutter deviations, a tension-controlled spline reconstruction method is introduced to recover smooth and curvature-stable cutting edge curves from noisy three-dimensional measurement data, overcoming the oscillation and instability commonly associated with high-order polynomial fitting. By integrating direct surface-based meshing, spline-regularized reconstruction, and CNC-oriented kinematics within a single formulation, this work establishes a complete digital chain for precision skiving cutter modeling, simulation, and compensation, providing a practical foundation for advanced tool design and manufacturing optimization. Full article
(This article belongs to the Section Machine Design and Theory)
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19 pages, 270 KB  
Article
Capability Assessment for Diet and Activity (CADA) and Its Influencing Factors Among Healthcare Workers in the Jazan Region, Saudi Arabia, 2026: A Cross-Sectional Study
by Yahya H. Almalki, Amal J. Alfaifi, Abdullah A. Mosawa, Abdulrahman M. Mahzara and Mohammed H. Abutaleb
Healthcare 2026, 14(11), 1530; https://doi.org/10.3390/healthcare14111530 - 1 Jun 2026
Viewed by 281
Abstract
Background: Adopting a healthy lifestyle through a balanced diet and regular physical activity is essential for chronic disease prevention, but healthcare workers face occupational constraints that may limit such behaviors. This study assessed perceived capability for healthy diet and physical activity among [...] Read more.
Background: Adopting a healthy lifestyle through a balanced diet and regular physical activity is essential for chronic disease prevention, but healthcare workers face occupational constraints that may limit such behaviors. This study assessed perceived capability for healthy diet and physical activity among healthcare workers in the Jazan region of Saudi Arabia using the Capability Assessment for Diet and Activity (CADA) instrument and examined associated factors. Methods: A cross-sectional analytical study was conducted in 2026 in governmental healthcare facilities in the Jazan Health Cluster. A structured electronic questionnaire collected sociodemographic, occupational, and health-related data alongside the 34-item CADA. Total, Diet and Physical Activity CADA scores (1–5) were analyzed using descriptive statistics and multivariable ordinary least squares regression adjusted for sex, education, profession, and workplace; standardized coefficients and Cohen’s f2 were reported. Results: A total of 601 healthcare workers participated. Internal consistency was good (Cronbach’s α = 0.84 for the full scale). Mean Total CADA was 3.28 ± 0.80 (scale midpoint 3.0); perceived Diet capability (3.45 ± 0.85) was higher than perceived Physical Activity capability (3.11 ± 0.85). Female sex was independently associated with lower Physical Activity CADA (β = −0.16; 95% CI −0.32 to −0.01; p = 0.042). Bachelor’s and board/doctoral qualifications were associated with higher Total CADA (β = 0.20; 95% CI 0.02 to 0.38; p = 0.026 and β = 0.33; 95% CI 0.07 to 0.58; p = 0.013, respectively). Compared with hospital-based participants, those in primary healthcare centers had lower Total (β = −0.19; 95% CI −0.32 to −0.05; p = 0.007), Diet (β = −0.17; 95% CI −0.31 to −0.02; p = 0.024) and Physical Activity (β = −0.21; 95% CI −0.35 to −0.06; p = 0.006) CADA scores. Effect sizes were small (|β*| ≤ 0.16; R2 = 0.076–0.082; Cohen’s f2 = 0.08–0.09). Conclusions: As CADA captures perceived capability, these findings reflect self-perception rather than objectively measured behavior; longitudinal studies combining CADA with validated behavioral instruments are warranted to clarify whether perceived capability translates into actual dietary and physical-activity behaviors in healthcare workers, and to evaluate whether workplace-based interventions targeting time pressure and access to supportive environments improve both perceived capability and measured behavior. Full article
12 pages, 713 KB  
Article
Laser-Assisted Self-Monitoring of Blood Glucose: Analytical Performance, Clinical Accuracy, and Usability of the HandyRay-Glu System
by Minsup Lim, JunMin Lee, Ji A Seo and Sun-Young Ko
Diagnostics 2026, 16(11), 1700; https://doi.org/10.3390/diagnostics16111700 - 31 May 2026
Viewed by 264
Abstract
Background/Objectives: Diabetes mellitus is a major global health burden, and inadequate glycemic control increases the risk of microvascular and macrovascular complications. Self-monitoring of blood glucose (SMBG) is essential for diabetes management, but conventional finger-prick sampling may reduce adherence due to pain and [...] Read more.
Background/Objectives: Diabetes mellitus is a major global health burden, and inadequate glycemic control increases the risk of microvascular and macrovascular complications. Self-monitoring of blood glucose (SMBG) is essential for diabetes management, but conventional finger-prick sampling may reduce adherence due to pain and repeated skin injury. This study evaluated the analytical performance, clinical accuracy, and usability of a novel laser-assisted blood glucose monitoring system, HandyRay-Glu. Methods: A prospective clinical evaluation study was conducted in accordance with ISO 15197:2013. Capillary blood glucose values obtained using the HandyRay-Glu system were compared with reference measurements generated by the cobas c111 analyzer. Analytical performance was assessed by evaluating repeatability, linearity, hematocrit effect, and interference. Clinical performance was assessed according to ISO 15197:2013 system accuracy criteria, and method comparison was performed using Passing–Bablok regression and Bland–Altman analyses. Usability was evaluated using a structured participant questionnaire. Results: A total of 100 adult participants with diabetes mellitus were included. Overall, 97.8% of results met the ISO 15197:2013 accuracy criteria. Passing–Bablok regression showed strong agreement between HandyRay-Glu and the reference method (y = 1.694 + 0.9859x, r = 0.992). Bland–Altman analysis demonstrated a mean bias of −1.763 mg/dL, with 95% limits of agreement ranging from −29.333 to 25.808 mg/dL. Analytical evaluations showed acceptable repeatability, linearity across the tested measurement range, and no clinically significant interference. More than 97% of participants reported satisfaction with device usability. Conclusions: The HandyRay-Glu system met the performance requirements of ISO 15197:2013 and demonstrated high analytical accuracy, acceptable agreement with the reference method, and favorable usability. Laser-assisted blood sampling combined with electrochemical glucose measurement may offer a potential alternative to conventional SMBG systems, and its possible role in improving patient acceptance of regular monitoring warrants further investigation. Full article
(This article belongs to the Section Point-of-Care Diagnostics and Devices)
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31 pages, 4240 KB  
Systematic Review
Circadian Regulation and Pain: A Systematic Review of the Association Between Rest–Activity Rhythm and Pain-Related Outcomes
by Aline Van Stallen, Manon De deyne, Céline Labie and Liesbet De Baets
Clocks & Sleep 2026, 8(2), 32; https://doi.org/10.3390/clockssleep8020032 - 28 May 2026
Viewed by 361
Abstract
The rest–activity rhythm (RAR) is a key marker of circadian regulation and is commonly assessed using actigraphy. Emerging evidence suggests that characteristics of RAR, such as amplitude, stability, and regularity, may be associated with pain-related outcomes. However, no systematic review has yet synthesized [...] Read more.
The rest–activity rhythm (RAR) is a key marker of circadian regulation and is commonly assessed using actigraphy. Emerging evidence suggests that characteristics of RAR, such as amplitude, stability, and regularity, may be associated with pain-related outcomes. However, no systematic review has yet synthesized this evidence across populations and pain conditions. This systematic review aimed to provide an overview of current approaches to measuring and defining RAR and to examine its associations with pain outcomes in both healthy individuals and clinical populations experiencing acute or chronic pain. A systematic search of PubMed, Web of Science, Scopus, and Embase was conducted, with the final search completed on 20 May 2025. Observational studies reporting associations between at least one RAR characteristic and a pain outcome were eligible. Article selection and risk-of-bias assessment using the ROBINS-E tool were performed independently by two reviewers, and findings were synthesized narratively. Seven cross-sectional studies were included, employing diverse analytic methods such as cosinor and non-parametric analyses. Overall, the findings were heterogeneous, suggesting that associations between RAR and pain vary according to the RAR metric used, the analytical approach, and the population studied. Nevertheless, the evidence generally indicates that more robust and well-consolidated circadian rhythms are associated with lower pain, whereas regularity and timing appear to play more context-dependent roles, highlighting the potential relevance of RAR metrics as modifiable targets and the need for standardized measurement approaches. Full article
(This article belongs to the Section Human Basic Research & Neuroimaging)
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13 pages, 1144 KB  
Case Report
Metabolic, Cardiovascular, and Stress Biomarker Adaptations to Breath-Hold Training in a National-Level Swimmer: A Signal-Generating Single-Case Study
by Gabriella D’Orsi, Paride Vasco, Raffaella R. R. Marzovillo, Natalia Forte, Giulia Scioscia, Giuseppe Cartagena, Luigi A. Marinaccio, Maria L. Torquato, Giuseppe Cibelli and Anna A. Valenzano
J. Funct. Morphol. Kinesiol. 2026, 11(2), 213; https://doi.org/10.3390/jfmk11020213 - 28 May 2026
Viewed by 347
Abstract
Background: Breath-hold training (BHT) has emerged as a novel strategy to enhance metabolic efficiency and autonomic resilience in national-level athletes. This signal-generating single-case study examined physiological and neuroendocrine adaptations to an eight-week BHT program in a nationally ranked competitive swimmer. Methods: [...] Read more.
Background: Breath-hold training (BHT) has emerged as a novel strategy to enhance metabolic efficiency and autonomic resilience in national-level athletes. This signal-generating single-case study examined physiological and neuroendocrine adaptations to an eight-week BHT program in a nationally ranked competitive swimmer. Methods: A national-level 23-year-old female freestyle sprinter (50 m best time = 26.59 s; 100 m = 60.40 s) completed three weekly BHT sessions integrated into her regular training. Pre- and post-intervention assessments included an incremental Mader cycling test with measurements of blood lactate ([La]), heart rate (HR), salivary cortisol (sCort), and salivary alpha-amylase (sAA). Blood chemistry and pulmonary function, including diffusing capacity of the lung for carbon monoxide (DLCO), were also evaluated. Results: Post intervention, the athlete demonstrated reduced [La] and HR at all workloads, a 20 W increase in power at 4 mmol·L−1 [La], and an elevated final workload achieved during the Mader test. Salivary stress biomarkers showed blunted responses with significant reductions in area under the curve and large effect sizes. These changes were observed under standardized pre-analytical conditions and individualized training adjustments. Conclusions: This study highlights coordinated improvements in metabolic, cardiovascular, and stress regulation mechanisms following BHT in a swimmer with verified national-level performance benchmarks. BHT, when applied in sport-specific contexts, may serve as an effective adjunct to high-performance training. Full article
(This article belongs to the Special Issue Innovative Approaches in Monitoring Individual Sports)
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31 pages, 8537 KB  
Article
Physics-Informed Neural Networks for Excited Liquid Sloshing with Beating Response in Two- and Three-Dimensional Rectangular Tanks
by Zhiqiang Luo
Symmetry 2026, 18(6), 917; https://doi.org/10.3390/sym18060917 - 27 May 2026
Viewed by 230
Abstract
This paper applies physics-informed neural networks (PINNs) to laterally excited liquid sloshing in a two-dimensional rectangular tank, where near-resonant forcing (ωe/ω1=0.9) produces a multi-frequency beating response with a period of approximately 10T1. [...] Read more.
This paper applies physics-informed neural networks (PINNs) to laterally excited liquid sloshing in a two-dimensional rectangular tank, where near-resonant forcing (ωe/ω1=0.9) produces a multi-frequency beating response with a period of approximately 10T1. Linearized potential flow theory governs the problem; the network learns the velocity potential φ(x,z,t) while the free-surface elevation η is injected analytically. Two training obstacles specific to forced sloshing are analyzed. First, a zero-solution trap arises because the trivial solution φ^=0 satisfies all equations except the free-surface conditions, whose residuals are roughly 104 times smaller than the Laplace residual; characteristic-scale normalization combined with loss weighting (λD=λK=100) breaks this trap. Second, spectral bias prevents standard MLPs from resolving the three co-existing frequencies (ω1, ωe, Δω); a Fourier time embedding that augments the input from 3 to 9 dimensions overcomes this limitation. Two additional techniques further reduce errors: a hard-wall boundary condition enforced exactly via a cos(πx/B) spatial embedding, which eliminates wall collocation points; and a gradient-enhanced Laplace regularizer ((2φ^)2) that constrains velocity smoothness through third-order automatic differentiation. An ablation study shows that these four techniques progressively reduce the horizontal velocity error from εu=12.46% to 0.84%. Results are validated against a viscous finite-difference benchmark. Over one beating cycle the errors are εη=0.15%, εu=0.84%, and εw=1.65%. A frequency parameter study across ωe/ω1 = 0.5–1.1 gives εη<0.25% and εu<2.3% for all near-resonance cases. For long-time simulation, a time-domain decomposition strategy with transfer learning partitions the domain into one-beat windows; extending to five beating cycles (50T1) yields εu=3.43% and εη=0.30% with no monotonic error accumulation across windows. The methodology is then extended to a three-dimensional rectangular tank (B×W×H) with bi-directional lateral excitation. The 3-D formulation introduces the y-dimension into the Laplace equation (2φ=φxx+φyy+φzz=0), adds transverse wall boundary conditions (φ/y=0) enforced exactly via a cos(πy/W) embedding, and extends the Fourier time embedding from 9 to 16 dimensions to accommodate six physical frequencies. The bi-directional excitation excites both (m,0) and (0,n) modal families, producing a genuinely three-dimensional beating response. Experimental results verify that the proposed methods can be well generalized to three-dimensional scenarios. Within a single beating cycle, the relative errors reach εη=0.24%, εu=1.31%, εv=1.78% and εw=2.32%, with a total training time of 2499 s. By applying time domain decomposition to carry out two-cycle three-dimensional simulations, the model can steadily maintain satisfactory prediction precision across segmented time intervals, achieving overall errors of εη=0.30% and εu=1.32%. Full article
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36 pages, 6407 KB  
Article
A Coupled Multi-Stage Hybrid Framework for BER Prediction and Beam Angle Optimization in Massive MIMO Systems: Combining Classical Regression with Coupled Deep Learning Approaches
by Iacovos Ioannou, Michael Georgiades, Prabagarane Nagaradjane, Ala Khalifeh, Christophoros Christophorou, Marios Raspopoulos and Vasos Vassiliou
Network 2026, 6(2), 35; https://doi.org/10.3390/network6020035 - 27 May 2026
Viewed by 196
Abstract
A coupled multi-stage learning framework is presented for joint bit error rate (BER) prediction and beam angle optimization in massive multiple-input multiple-output (MIMO) systems under a controlled simulation protocol. Unlike purely sequential benchmarking pipelines, the proposed method jointly coordinates BER prediction and beam-angle [...] Read more.
A coupled multi-stage learning framework is presented for joint bit error rate (BER) prediction and beam angle optimization in massive multiple-input multiple-output (MIMO) systems under a controlled simulation protocol. Unlike purely sequential benchmarking pipelines, the proposed method jointly coordinates BER prediction and beam-angle selection through a shared latent representation, an uncertainty-guided refinement mechanism, a cross-stage consistency loss and alternating optimization. Ten diverse approaches are systematically evaluated across two task-specific stages: Stage 1 examines six classical and adapted methods for BER prediction, including polynomial regression and deep unfolding networks; Stage 2 investigates four machine-learning and generative adversarial network (GAN)-based approaches for angle optimization, including conditional GANs and the proposed Direct-Angle neural network. Stage 3 couples the best-performing methods into a unified hybrid architecture through a shared encoder, explicit consistency regularization and alternating cross-stage updates, thereby producing an integrated beamforming decision strategy rather than an independent cascade. It is shown through the evaluation that the coupled hybrid framework achieves 96.0% overall angle-selection accuracy, a mean BER of 8.0×105 and 100% BER tolerance compliance within ±3 dB. In this framework, a differentiable BER surrogate initialized from a second-degree polynomial-regression teacher is coupled with the proposed Direct-Angle-NN for angle optimization. Relative to the strongest reimplemented literature baseline under the same controlled simulation assumptions, a 33.3% reduction in mean BER is achieved. Ablation experiments show that the coupling mechanism provides a modest but consistent improvement over the decoupled sequential baseline, increasing angle-selection accuracy from 93.5% to 96.0% and reducing mean BER from 1.05×104 to 8.0×105; the shared encoder accounts for the largest part of this gain while the consistency loss adds 0.6 percentage points. These results indicate that the shared encoder, consistency regularization and uncertainty-guided refinement improve the final beamforming decision, although the gain should be interpreted as incremental rather than as a large architectural breakthrough. A spectral efficiency of 38.0 bps/Hz and an energy efficiency of 0.466 Gbps/W are achieved with a power consumption of only 32.6 W. The theoretical discussion is presented as an analytical characterization of BER sensitivity, complemented by a computational-complexity assessment and empirical convergence diagnostics for the alternating optimization, rather than as a formal optimality proof. The effectiveness of the framework across multiple performance metrics is supported by Monte Carlo simulations, while the limitations of the current setup, including perfect CSI, uncoded QPSK, ideal hardware assumptions and a fixed beam codebook, are explicitly discussed. The complete simulation framework, including code and trained models, can be made available by the corresponding author upon reasonable request to facilitate reproducible research in massive MIMO optimization. Full article
(This article belongs to the Special Issue AI-Driven Evolution in Next-Generation Wireless Networks)
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26 pages, 2829 KB  
Article
Inverse Problem of Heat Conduction in a Multilayer Cylindrical System
by Aigul Satybaldina, Bolatbek Rysbaiuly, Aizhan Ydyrys, Sultan Alpar, Korlan Rysbayeva and Auzhan Sakabekov
Symmetry 2026, 18(6), 908; https://doi.org/10.3390/sym18060908 - 26 May 2026
Viewed by 391
Abstract
This study investigates steady-state heat transfer in a three-layer cylindrical system with angular non-uniformity of the temperature field. For the considered geometry, a mathematical model of heat conduction is formulated in cylindrical coordinates with piecewise constant thermophysical properties and continuity conditions at the [...] Read more.
This study investigates steady-state heat transfer in a three-layer cylindrical system with angular non-uniformity of the temperature field. For the considered geometry, a mathematical model of heat conduction is formulated in cylindrical coordinates with piecewise constant thermophysical properties and continuity conditions at the interfaces between layers. The direct problem is solved analytically using a Fourier series expansion of the temperature field with respect to the angular coordinate. Based on experimental temperature measurements obtained for various configurations of soil layers, an inverse problem is formulated and solved to reconstruct the thermal conductivities of the individual layers and the heat transfer coefficient at the external boundary. To stabilize the solution, a regularized least-squares approach is employed. The convergence of the recovered parameters with respect to the harmonic number is analyzed, and the averaged reconstructed values are compared with the exact parameters used in the direct problem. The obtained results demonstrate the stability and accuracy of the proposed method, confirming its applicability to the identification of thermophysical parameters in multilayer soil systems based on experimental data. Full article
(This article belongs to the Special Issue Symmetry in Numerical Analysis and Applied Mathematics)
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20 pages, 664 KB  
Article
The k-Beta Logarithmic Function: Theory, Fractional Derivative, and Spectral Numerical Method
by Karima M. Oraby, Amna Mohamed, Youssri Hassan Youssri and Marwa Abdelkhaliq
Mathematics 2026, 14(11), 1808; https://doi.org/10.3390/math14111808 - 23 May 2026
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Abstract
A new generalization of the Logarithmic mean function and Euler’s Beta k-Logarithm function is proposed using the Mittag–Leffler k-function. We study their analytical properties, including functional relations, symmetry relation, inequalities, summation representations, and integral representations. Mellin transformations are established, and a [...] Read more.
A new generalization of the Logarithmic mean function and Euler’s Beta k-Logarithm function is proposed using the Mittag–Leffler k-function. We study their analytical properties, including functional relations, symmetry relation, inequalities, summation representations, and integral representations. Mellin transformations are established, and a generalized k-Beta Logarithmic distribution is presented along with its probabilistic applications. Furthermore, we introduce a novel k-Beta Logarithmic fractional derivative operator of Caputo type and develop a Legendre spectral collocation method with Chebyshev–Gauss–Lobatto nodes for the numerical solution of associated fractional differential equations. Rigorous error analysis in the weighted L2-norm is provided, establishing algebraic convergence for finite-regularity solutions and exponential convergence for analytic solutions. Numerical experiments confirm the theoretical convergence rates and demonstrate the efficiency and spectral accuracy of the proposed scheme. Full article
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Article
Robust Multi-View Ensemble Broad Learning for Semi-Supervised Classification
by Ziyang Dong, Mianfen Lin and Zhiwen Yu
Informatics 2026, 13(5), 75; https://doi.org/10.3390/informatics13050075 - 21 May 2026
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Abstract
In semi-supervised learning scenarios, the presence of limited labeled data and abundant unlabeled samples poses significant challenges to model robustness and generalization. Although the semi-supervised broad learning system (SSBLS) effectively exploits manifold structure through graph Laplacian regularization, its optimization is typically formulated under [...] Read more.
In semi-supervised learning scenarios, the presence of limited labeled data and abundant unlabeled samples poses significant challenges to model robustness and generalization. Although the semi-supervised broad learning system (SSBLS) effectively exploits manifold structure through graph Laplacian regularization, its optimization is typically formulated under the mean square error (MSE) criterion, which is sensitive to noise and outliers. To address this limitation, this paper introduces the maximum mixture correntropy criterion (MMC) into the SSBLS framework and proposes a model termed M2C-SSBLS. By replacing the conventional MSE loss with a mixture correntropy-based objective, the proposed method enhances robustness against non-Gaussian noise and abnormal samples while preserving the computational efficiency and analytical solution property of the BLS. Furthermore, to improve representation diversity and reduce model variance, a multi-view ensemble extension, named EC-SSBLS, is proposed. This method constructs multiple feature views through a random feature subspace strategy, and independently trains an M2C-SSBLS base learner on each subspace. Finally, the predicted results of each view are fused through a voting mechanism. Experiments on benchmark UCI datasets under noise-free, 10% and 20% label noise settings demonstrate that the proposed M2C-SSBLS consistently outperforms conventional SSBLS and other advanced semi-supervised learning approaches. The ensemble extension EC-SSBLS further enhances performance, particularly in noisy environments, validating the effectiveness of combining MMC-based optimization with multi-view ensemble learning. Full article
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