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17 pages, 2941 KB  
Article
Hybrid Drift-Flux and Deep Learning Framework for Accurate Multiphase Flowrate Prediction via Multi-Modal ERT/ECT Fusion in Horizontal Wells
by Qingsheng Zhang, Fei Xu, Jianxiong Li, Xiaomin Liu, Aihua Liu and Xiuwu Wang
Processes 2026, 14(13), 2054; https://doi.org/10.3390/pr14132054 (registering DOI) - 24 Jun 2026
Abstract
Accurate multiphase flow measurement in horizontal wells is fundamentally challenged by the antagonistic electrical responses of water and gas: Electrical Resistance Tomography (ERT) loses sensitivity to thin liquid films, while Electrical Capacitance Tomography (ECT) suffers signal saturation in conductive water, preventing either modality [...] Read more.
Accurate multiphase flow measurement in horizontal wells is fundamentally challenged by the antagonistic electrical responses of water and gas: Electrical Resistance Tomography (ERT) loses sensitivity to thin liquid films, while Electrical Capacitance Tomography (ECT) suffers signal saturation in conductive water, preventing either modality from covering the full operating envelope alone. This study proposes a physics-guided hybrid modeling framework that integrates multi-modal ERT/ECT sensing to achieve high-precision flowrate inversion. The framework utilizes a corrected multi-modal fusion algorithm, achieving a liquid holdup MAPE of 2.5 ± 0.5% representing a nearly two-fold improvement over the best single-modality system (Direct ERT, 4.5%). For velocity estimation, an optimized cross-correlation method yields results with ± 3.0% error, incorporating multi-sensor and multi-sequence fusion. A key finding is that deep neural networks exhibit Architectural Phase Specialization: multi-branch architectures (MB-DNN) perform strongly on localized, heterogeneous liquid structures (2.0% liquid error), whereas fully-connected architectures (FC-DNN) excel at capturing the global patterns of the continuous gas core (1.2% gas error). By hybridizing a calibrated drift-flux physical model with these phase-specialized DNNs, the framework achieves overall averaged errors of 1.8% for gas and 1.5% for liquid across the full experimental envelope. The proposed framework was evaluated on 444,313 experimental samples and subsequently validated in a three-month industrial trial at the Puguang gas field under extreme conditions (26 MPa, 80 °C), where it maintained a prediction error of ± 2.3%. This work establishes a scalable, physically consistent paradigm for intelligent hydrocarbon production monitoring. Full article
(This article belongs to the Topic Petroleum and Gas Engineering, 2nd edition)
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41 pages, 11772 KB  
Article
An Uncertainty-Aware Computational Framework for Dimensional Error Prediction in Ceramic Additive Manufacturing Under Variable Material and Process Conditions
by Mahmoud AlJamal, Nawal Louzi, Mohammad Q. Al-Jamal, Luay Tahat, Ala Mughaid and Qasim Aljamal
Computation 2026, 14(7), 144; https://doi.org/10.3390/computation14070144 (registering DOI) - 24 Jun 2026
Abstract
Ceramic additive manufacturing offers strong potential for fabricating geometrically complex and application-specific components, yet achieving reliable dimensional fidelity remains challenging because dimensional deviation is governed by highly coupled material, process, thermal, and environmental factors. To address this problem, this study proposes an uncertainty-aware [...] Read more.
Ceramic additive manufacturing offers strong potential for fabricating geometrically complex and application-specific components, yet achieving reliable dimensional fidelity remains challenging because dimensional deviation is governed by highly coupled material, process, thermal, and environmental factors. To address this problem, this study proposes an uncertainty-aware computational framework for dimensional error prediction in ceramic 3D printing under variable material and process conditions. The contribution is positioned as a system-level integration of established learning, uncertainty estimation, calibration, and reliability-interpretation components within a ceramic additive manufacturing dimensional-error prediction workflow, rather than as a fundamental methodological breakthrough. The validation is conducted using the publicly available Ceramic 3D Printing Process Control Dataset, a 1000-sample tabular dataset, and the resulting findings are therefore interpreted as dataset-specific computational evidence rather than direct proof of industrial deployment readiness. The methodology begins with a structured data-driven preprocessing pipeline that transforms the Ceramic 3D Printing Process Control Dataset into a multi-condition feature space through data cleaning, one-hot material encoding, min–max normalization, and engineered descriptors capturing extrusion–speed balance, thermal gradients, cooling intensity, deposition density, and material-conditioned interactions. A multi-branch deep computational architecture is then developed to encode material, process, thermal-environmental, and engineered-feature streams separately, followed by adaptive cross-condition fusion to learn nonlinear dependencies across ceramic printing regimes. To improve reliability beyond deterministic regression, the framework jointly models aleatoric and epistemic uncertainty and incorporates calibration refinement to align predictive confidence with observed error behavior, thereby enabling preliminary reliability-oriented interpretation of stable and high-risk operating conditions. Experimental results demonstrate that the full model achieves the best overall within-dataset performance, with a test MAE of 0.0118, RMSE of 0.0172, R2=0.999, MAPE of 1.74%, calibration error of 0.003, PICP of 0.996, reliability score of 0.992, and a stable prediction rate of 98.7%. Although these values indicate strong predictive behavior under the current structured dataset, the exceptionally high R2 should be interpreted cautiously because external experimental validation, larger measured datasets, and cross-machine ceramic printing trials are still required. These findings show that the proposed framework provides an effective system-level computational strategy for dataset-specific reliability-aware dimensional quality prediction in ceramic additive manufacturing and offers a preliminary data-driven foundation for uncertainty-aware intelligent process optimization. Full article
(This article belongs to the Special Issue Computational Methods in Structural Optimization)
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26 pages, 2791 KB  
Article
Constituent-Material-Anchored Continual Learning for Full Stress–Strain Prediction of Multi-Material PETG/PC-ABS MEX Laminates
by Ramachandran Avala Subramanian, Mahalingam Nainaragaram Ramasamy, Michal Prauzek, Quoc-Phu Ma, Jaromir Konecny and Ales Sliva
Polymers 2026, 18(13), 1573; https://doi.org/10.3390/polym18131573 (registering DOI) - 24 Jun 2026
Abstract
Predicting the tensile response of multi-material parts produced by material extrusion (MEX) remains difficult because the final behavior depends on both the constituent polymers and the quality and arrangement of dissimilar interfaces. This study introduces a constituent-material-anchored, phase-aware continual-learning framework for full stress–strain [...] Read more.
Predicting the tensile response of multi-material parts produced by material extrusion (MEX) remains difficult because the final behavior depends on both the constituent polymers and the quality and arrangement of dissimilar interfaces. This study introduces a constituent-material-anchored, phase-aware continual-learning framework for full stress–strain curve prediction of PETG/PC-ABS laminate coupons. Experimentally measured PETG and PC-ABS reference curves were combined through a rule-of-mixtures baseline; an XGBoost residual model then learned pointwise corrections using strain, baseline stress, mechanical phase label, and PETG thickness fraction as inputs. Validation used five PETG reference coupons, five PC-ABS reference coupons, five C1 laminate coupons, two C2 out-of-distribution coupons, and three coupons for each model-suggested Rank 1–3 architecture. UTS agreement alone was not sufficient: Rank 2 had a zero-shot UTS error of only 0.18% but a full-curve RMSE of 20.74%. After the first architecture-specific coupon was introduced, RMSE decreased from 12.34% to 2.72% for C1, from 18.60% to 6.38% for C2, from 21.04% to 6.93% for Rank 1, from 20.74% to 7.50% for Rank 2, and from 19.40% to 7.48% for Rank 3. The framework therefore provides a data-efficient, interpretable proof of concept for laminate screening and tensile-curve prediction, while its broader statistical robustness and extension to other loading modes require larger datasets. Full article
(This article belongs to the Section Polymer Processing and Engineering)
25 pages, 4535 KB  
Article
Evaluation of a Locally Registered UAV Photogrammetry and Smartphone LiDAR Workflow for Scan-to-BIM Documentation of an Existing Building
by Merve Uluçay Temel and Bayram Ali Temel
Buildings 2026, 16(13), 2512; https://doi.org/10.3390/buildings16132512 (registering DOI) - 24 Jun 2026
Abstract
The digital documentation of existing buildings is particularly important when original construction drawings or reliable as-built records are unavailable. This study evaluates the feasibility and selected dimensional consistency of a locally registered Scan-to-BIM workflow integrating unmanned aerial vehicle (UAV) photogrammetry for exterior documentation [...] Read more.
The digital documentation of existing buildings is particularly important when original construction drawings or reliable as-built records are unavailable. This study evaluates the feasibility and selected dimensional consistency of a locally registered Scan-to-BIM workflow integrating unmanned aerial vehicle (UAV) photogrammetry for exterior documentation and smartphone LiDAR for interior data capture. A two-storey reinforced-concrete building with unavailable original project documentation was selected as a single case study. Exterior images were acquired using a DJI Mavic 3E (DJI, Shenzhen, China), while interior spaces were scanned using an iPhone 16 Pro Max (Apple Inc., Cupertino, CA, USA) and Polycam v5.1.5 in LiDAR mode. The UAV images were processed in Agisoft Metashape Professional 2.2.0 to generate the exterior photogrammetric point cloud, and the smartphone LiDAR data were organised with this dataset in Autodesk ReCap Pro 2025. Both point clouds were then used as geometric references for creating a geometry-oriented as-is BIM model in Autodesk Revit 2025. To evaluate selected dimensional consistency, 32 independent field measurements collected using a steel tape measure and a laser distance meter were compared with corresponding BIM-derived dimensions. The dimensional comparison yielded a mean absolute error (MAE) of 29.56 mm, a root mean square error (RMSE) of 31.21 mm, a maximum absolute error (MaxAE) of 46.00 mm, and a mean signed error (MSE) of +29.56 mm. These results indicate centimetre-level dimensional consistency for the selected validation dimensions, with a small systematic positive offset in the BIM-derived dimensions. The workflow can support preliminary geometric documentation and general as-is BIM for a small existing building, but it does not demonstrate survey-grade georeferencing, full registration accuracy, modelling reproducibility, or general applicability without further testing. Full article
(This article belongs to the Section Construction Management, and Computers & Digitization)
15 pages, 445 KB  
Article
A Step Forward in Post-Mortem Interval Estimation: Multivariate Analysis of Ammonium, Albumin, and Potassium Levels in Vitreous Humor
by Martina Focardi, Beatrice Defraia, Ilenia Bianchi, Barbara Gualco, Andrea Costantino, Rossella Grifoni, Alessandra Fanelli, Tiziana Biagioli, Costanza Bossi, Vilma Pinchi and Luisa Lanzilao
Diagnostics 2026, 16(13), 1970; https://doi.org/10.3390/diagnostics16131970 (registering DOI) - 24 Jun 2026
Abstract
Background/Objectives: Accurate post-mortem interval (PMI) estimation remains challenging in forensic pathology. Although potassium (K+) is the most well-validated single biomarker in vitreous humor (VH), multivariate approaches may enhance precision by capturing the complex cascade of post-mortem biochemical changes. This study aimed [...] Read more.
Background/Objectives: Accurate post-mortem interval (PMI) estimation remains challenging in forensic pathology. Although potassium (K+) is the most well-validated single biomarker in vitreous humor (VH), multivariate approaches may enhance precision by capturing the complex cascade of post-mortem biochemical changes. This study aimed to develop and validate a multivariate PMI estimation model incorporating three biochemical markers—potassium, ammonium (NH4+), and albumin (ALB)—in vitreous humor using automated clinical chemistry platforms for practical forensic application. Methods: Vitreous humor samples from 38 autopsy cases with documented PMIs (39.5–285 h; mean, 105.5 h) were analyzed for K+ (Cobas C8000), NH4+ (Cobas C8000), and ALB (Immage 800 nephelometry). Univariate and multivariate regression analyses were performed, with the residual standard error (RSE) as the primary measure of accuracy. Model validation was conducted by back-calculating PMI in four samples completely distinct from the training cohort. Results: All three analytes demonstrated strong individual correlations with PMI (R2: K+ = 0.88, ALB = 0.78, NH4+ = 0.69; all p < 0.001). The multivariate regression model [PMI = 40.25[Alb] + 0.01573[NH4+] + 5.339[K+] − 53.032] yielded an RMSE of ±15.5 h (MSE = 240.25 h2), outperforming potassium-only models (RMSE = ±22.6 h). Although NH4+ showed limited statistical significance in the multivariate model (p = 0.128), its inclusion improved overall predictive accuracy. External validation in an independent cohort of four subjects (distinct from the 38 subjects in the training set) demonstrated a mean absolute error (MAE) of 20.4 h. Conclusions: The multivariate approach combining K+, NH4+, and ALB in VH improves PMI estimation accuracy compared with single-marker methods. The use of automated clinical chemistry platforms enhances reproducibility and facilitates practical implementation in forensic laboratories. Full article
(This article belongs to the Section Forensic Diagnostics)
16 pages, 2071 KB  
Article
Determining the Impedance of an Eddy Current Probe Placed over a Defect-Free Conductive Cylinder with a Centred Circular Hole
by Grzegorz Tytko, Yike Xiang and Yao Luo
Materials 2026, 19(13), 2718; https://doi.org/10.3390/ma19132718 (registering DOI) - 24 Jun 2026
Abstract
The measurement of a probe impedance performed during eddy current inspections enables detection of flaws in electrically conductive materials. A correct interpretation of the measured impedance values constitutes a key aspect that determines the effectiveness of the inspections, and for this purpose, mathematical [...] Read more.
The measurement of a probe impedance performed during eddy current inspections enables detection of flaws in electrically conductive materials. A correct interpretation of the measured impedance values constitutes a key aspect that determines the effectiveness of the inspections, and for this purpose, mathematical models are employed. Such models, which are becoming more and more frequently an integral part of eddy current measurement systems, enable carrying out the calculation of the probe impedance, through depicting the measurements being performed. What offer the shortest calculation time while maintaining high accuracy are analytical solutions. In this paper, to the best of the authors’ knowledge, this is the first time an analytical model of an eddy current probe placed over a small diameter cylinder containing a hole has been presented. The final formulas were obtained using the truncated region eigenfunction expansion (TREE) method, and then implemented in Matlab. The calculated values of the probe resistance and reactance were compared with the measurement results obtained for cylinders with a through defect. The tests were conducted on components made of several conductive materials with different geometric dimensions. The measurement error in all of the tests was small, i.e., it did not exceed 3% across the entire frequency range. The proposed solution can be used in defectoscopy for eddy current testing of tubes, pucks, washers, and any cylindrical elements. Full article
(This article belongs to the Special Issue Non-Destructive Testing in Industrial Applications)
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19 pages, 7318 KB  
Article
Multi-Platform Software for Electrical and Microstructural Analysis of Silicon Solar Cell Metallization
by Małgorzata Musztyfaga-Staszuk, Dušan Pudiš and Rafał Honysz
Materials 2026, 19(13), 2717; https://doi.org/10.3390/ma19132717 (registering DOI) - 24 Jun 2026
Abstract
This paper presents proprietary, multi-platform software developed in Python for analyzing the electrical and microstructural properties of silicon solar cell metallization. Utilizing a sample set of 20 commercial solar cells, electrical resistivity and contact resistance measurements obtained via the potential difference method were [...] Read more.
This paper presents proprietary, multi-platform software developed in Python for analyzing the electrical and microstructural properties of silicon solar cell metallization. Utilizing a sample set of 20 commercial solar cells, electrical resistivity and contact resistance measurements obtained via the potential difference method were correlated with high-resolution topographic data from AFM, SEM, and CLSM. This process enabled the quantification of how specific features, such as surface roughness and finger height, directly influence electrical performance. The developed algorithms offer high-fidelity predictive capabilities, with relative errors below 4%. This “virtual laboratory” serves as a transformative research and educational tool, allowing for complex materials analysis while avoiding the necessity for destructive testing. Full article
(This article belongs to the Section Energy Materials)
54 pages, 2648 KB  
Article
The Education–Sustainability Paradox: Asymmetric Associations Between Human Capital Expansion and Social and Environmental Sustainable Development Goals
by Oksana Liashenko, Tomasz Wołowiec, Olena Pavlova, Kostiantyn Pavlov, Oleksandr Shubalyi, Oksana Drebot, Oksana Novosad and Bohdan Samoilenko
Sustainability 2026, 18(13), 6452; https://doi.org/10.3390/su18136452 (registering DOI) - 24 Jun 2026
Abstract
The proposition that expanding education uniformly advances the 2030 Agenda is widely held in policy discourse—embedded in SDG 4, amplified by UNESCO, and routinely invoked in national development strategies. This paper shows that this proposition holds only partially. Using a balanced panel of [...] Read more.
The proposition that expanding education uniformly advances the 2030 Agenda is widely held in policy discourse—embedded in SDG 4, amplified by UNESCO, and routinely invoked in national development strategies. This paper shows that this proposition holds only partially. Using a balanced panel of 193 countries observed over 2000–2023, we estimate 96 two-way fixed-effects regressions connecting eight measures of education—spanning expenditure, enrolment, completion, attainment, and accumulated stock—to twelve Sustainable Development Goal outcomes. The estimates reveal a pronounced block asymmetry. On the social side, educational expansion is a robust correlate of progress against poverty: a one-standard-deviation increase in secondary enrolment is associated with a 0.16-log-point lower $2.15/day extreme-poverty headcount and a 4.35-point lower value on the 0–100 SDG-1 composite, both significant at p < 0.001. On the environmental side, the same education measure is associated with a coefficient of β = +0.048 (p = 0.014) on production-based CO2 per capita and β = −0.260 (p = 0.031) on forest area—associations that are statistically significant but directionally perverse, though small in magnitude (approximately 0.05–0.26 SD on the standardised outcome). Higher schooling is also associated with higher within-country inequality (β = +0.71 on the Gini, p = 0.006). The asymmetry survives Driscoll–Kraay standard errors, Oster sensitivity bounds, and two-year lagged specifications. The findings qualify the optimistic narrative that frames education as a uniform instrument for sustainable development: schooling is a robust predictor of social-block progress, but appears insufficient on its own for environmental progress and is best understood as a complement to, rather than a substitute for, dedicated environmental policy. The 2030 architecture may benefit from differentiated instrument–goal pairs rather than reliance on any single instrument across all goals. Full article
19 pages, 5593 KB  
Article
Comparative Feasibility of Transmission and Metal-Backed Microwave Architectures for Meter-Referenced Grain Moisture Monitoring
by Qinyi Xiao, Xingbao Lyu, Yiqun Ma, Guijiang Liu, Chengxun Yuan, Jingfeng Yao and Zhongxiang Zhou
Appl. Sci. 2026, 16(13), 6348; https://doi.org/10.3390/app16136348 (registering DOI) - 24 Jun 2026
Abstract
Grain moisture content is a key variable for safe storage, drying control, and quality management. Microwave sensing is attractive because water strongly modulates the complex relative permittivity (ε* = ε′ – ″) of granular agricultural products, thereby shaping broadband [...] Read more.
Grain moisture content is a key variable for safe storage, drying control, and quality management. Microwave sensing is attractive because water strongly modulates the complex relative permittivity (ε* = ε′ – ″) of granular agricultural products, thereby shaping broadband scattering-parameter spectra. This study presents a meter-referenced feasibility evaluation of an interpretable S-parameter–permittivity–moisture chain using a vector network analyzer over 2–18 GHz. Wheat, maize, and mung bean were prepared at six moisture levels, and the moisture values were referenced to two commercial grain moisture meters (MC_ref) to represent rapid on-site benchmarking rather than absolute gravimetric moisture determination. Therefore, the reported errors should be interpreted as commercial-meter-referenced calibration indicators rather than absolute gravimetric moisture prediction accuracy. Two free-space configurations were compared on the same platform: a two-horn transmission setup under controlled packing and a metal-backed double-pass reflection setup intended to represent single-sided access under loose bulk packing. After SOLT calibration and empty-holder background normalization, ε′ and ε″ were retrieved via complex-domain nonlinear least-squares fitting of physics-based slab models to measured S21 spectra. The results show that moisture-dependent dielectric responses were grain- and configuration-dependent. In particular, ε″ generally provided a more robust moisture-sensitive feature in the free-space transmission configuration, whereas the optimal single-parameter predictor in the metal-backed configuration differed among grains. A mid-band frequency window of approximately 8–16 GHz provided more stable inversion by avoiding low-frequency coupling artefacts and high-frequency signal-to-noise degradation. The metal-backed configuration preserved moisture trends but yielded lower effective ε′ values, likely due to increased air fraction under loose packing. These results indicate that packing state, grain type, and frequency-window selection are critical factors for transferring microwave moisture calibration from laboratory measurements to practical grain-handling scenarios. Full article
45 pages, 4257 KB  
Article
Stochastic Temperature Modeling Using the Ornstein-Uhlenbeck Process for Fractional Dimensional Weather Derivative Pricing in Climate Risk Management
by Sukono, Gumgum Darmawan, Muhamad Deni Johansyah, Igif Gimin Prihanto, Hadi Kardoyo, Hendy Gunawan, Syafrizal Maludin, Astrid Sulistya Azahra, Moch Panji Agung Saputra and Norizan Mohamed
Mathematics 2026, 14(13), 2257; https://doi.org/10.3390/math14132257 (registering DOI) - 24 Jun 2026
Abstract
Temperature variability and weather-related fluctuations significantly affect the energy, agricultural, and industrial sectors that are highly sensitive to meteorological changes. These conditions may lead to financial losses caused by demand fluctuations and operational disruptions. This study aims to develop a fractional weather-derivative pricing [...] Read more.
Temperature variability and weather-related fluctuations significantly affect the energy, agricultural, and industrial sectors that are highly sensitive to meteorological changes. These conditions may lead to financial losses caused by demand fluctuations and operational disruptions. This study aims to develop a fractional weather-derivative pricing model based on temperature dynamics by integrating the Ornstein–Uhlenbeck (OU) process, the classical Black–Scholes model (BSM), and the fractional Black–Scholes model (fBSM). Daily temperature data from 2016 to 2025 obtained from the Bandung Geophysical Station, West Java, Indonesia, were used as the basis of analysis. Temperature dynamics were modeled using an OU process, and parameter estimation was conducted using Ordinary Least Squares (OLS). The strike price was determined using Historical Burn Analysis (HBA), whereas weather-derivative pricing was performed using call and put option approaches under both the BSM and fBSM frameworks, incorporating the Hurst parameter to capture long-term memory effects. The results indicate that the fractional Black–Scholes model analytical solution is obtained using the Daftardar–Gejji Aboodh method. Furthermore, the OU process successfully captured daily temperature dynamics, yielding a Mean Absolute Percentage Error (MAPE) of 4.344% and a Root Mean Square Error (RMSE) of 1.396 C, indicating high predictive accuracy across both relative and absolute error measures. In addition, the fBSM consistently generated higher option values than the classical BSM, particularly under higher observed temperatures during the study period and at higher strike prices. These findings demonstrate that long-term memory significantly influences effective volatility and option valuation. This study is expected to contribute to the development of weather derivative models that more realistically represent temperature dynamics and to serve as a reference for weather derivative pricing, hedging, and decision-making, as well as for more measurable, systematic, and sustainable climate-related financial analysis using derivative pricing frameworks. Full article
27 pages, 489 KB  
Systematic Review
Concurrent Validity and Reliability of Inertial Sensor-Based Wearables for Quantifying Spatial–Temporal Gait Parameters After Stroke: A Systematic Review
by Víctor Martínez-Pozo, David Barbado, Carmina Díaz-Marín, Jonatan García-Campos, Carles Blasco-Peris, Pablo Ros-Arlanzón, Luis Moreno-Navarro, Ivo D. Popivanov, Shima Mehrabian-Spasova, Lachezar Traykov, Bernardino Morillo-Merino, Elisabeth García-Alonso and Diana Salas-Gómez
Brain Sci. 2026, 16(7), 662; https://doi.org/10.3390/brainsci16070662 (registering DOI) - 24 Jun 2026
Abstract
This systematic review examined the validity and reliability of wearable inertial sensor systems to quantify spatiotemporal gait parameters in post-stroke adults, a population in which gait asymmetry and altered motor control challenge accurate measurement. Sixteen studies involving 300 participants were included. Spatial parameters [...] Read more.
This systematic review examined the validity and reliability of wearable inertial sensor systems to quantify spatiotemporal gait parameters in post-stroke adults, a population in which gait asymmetry and altered motor control challenge accurate measurement. Sixteen studies involving 300 participants were included. Spatial parameters gait speed, cadence, and step/stride length showed consistently good-to-excellent agreement with reference systems (ICC 0.85–0.98; 95% LoA ±0.03–0.08 m/s for gait speed, ±4–10 steps/min for cadence, and ±3–8 cm for step/stride length) and high test–retest reliability. Temporal parameters demonstrated greater heterogeneity, with larger errors and lower concordance (ICC 0.40–0.85; LoA ±0.04–0.12 s), particularly for swing time (ICC 0.40–0.70; LoA up to ±0.15 s). Paretic-side measurements showed 10–20% lower concordance and 30–50% wider limits of agreement compared with the non-paretic side, although within-subject reliability remained moderate to high. No consistent influence of sensor number on measurement accuracy was observed. Overall, wearable inertial sensors provide robust estimates of spatial gait parameters, whereas temporal outcomes especially swing time remain limited due to challenges in gait event detection under stroke-related biomechanical alterations. These findings highlight the need for standardized protocols and improved algorithms to enhance comparability across studies and support broader clinical adoption. Full article
(This article belongs to the Section Neurorehabilitation)
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17 pages, 1326 KB  
Article
A New Estimator of Kullback–Leibler Divergence via Shannon Entropy
by Mehmet Sıddık Çadırcı and Martin Singull
Entropy 2026, 28(7), 720; https://doi.org/10.3390/e28070720 (registering DOI) - 24 Jun 2026
Abstract
We examine the estimation of the Kullback–Leibler (KL) divergence and the use of the goodness-of-fit test for multivariate normality. Our starting point is the maximum entropy principle for Shannon entropy: among all distributions with a fixed mean vector and covariance matrix, the multivariate [...] Read more.
We examine the estimation of the Kullback–Leibler (KL) divergence and the use of the goodness-of-fit test for multivariate normality. Our starting point is the maximum entropy principle for Shannon entropy: among all distributions with a fixed mean vector and covariance matrix, the multivariate Gaussian distributions uniquely maximize entropy. As a result, the KL divergence from a moment-matched Gaussian distribution to an unknown density can then be written as the entropy difference, which is a suitable information-theoretic measure of divergence from the Gaussian distribution. To estimate, we use k-nearest neighbor (kNN) estimators based on Shannon entropy and KL divergence derived from the Kozachenko–Leonenko approach and subsequent improvements, along with the consistency and L2-convergence results established for these estimators. Motivated by previous entropy-based goodness-of-fit ideas developed for Rényi-type functionals for generalized Gaussian and Student-type models, we describe a KL-based test statistic as being the difference between the entropy of a Gaussian model fitted to the sample mean and covariance and the KL divergence between the unknown entropy and the kNN estimate. The statistic converges to zero for multivariate normality and converges to a strictly positive bound with non-Gaussian alternatives. The results of Monte Carlo simulations conducted across various dimensions and sample sizes indicate that the proposed method provides accurate Type I error control among the alternatives considered and demonstrates promising empirical power. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
21 pages, 3740 KB  
Article
Time-Domain Analysis of Rectangular Pulse Response in Capacitive Impedance Sensing Using Capacitively Coupled Contactless Electrodes
by Damian Wanta, Waldemar T. Smolik, Mikhail Ivanenko, Jacek Kryszyn, Oliwia Makowiecka, Grzegorz Domański, Przemysław Wróblewski, Mateusz Midura and Mateusz Orzechowski
Sensors 2026, 26(13), 3999; https://doi.org/10.3390/s26133999 (registering DOI) - 24 Jun 2026
Abstract
Impulse-based impedance sensing with capacitively coupled electrodes is introduced as a fast, non-contact, and simplified complementary method to conventional capacitive impedance measurements. Unlike frequency-domain methods, the proposed approach derives effective resistive and capacitive properties of a sample from the transient response to a [...] Read more.
Impulse-based impedance sensing with capacitively coupled electrodes is introduced as a fast, non-contact, and simplified complementary method to conventional capacitive impedance measurements. Unlike frequency-domain methods, the proposed approach derives effective resistive and capacitive properties of a sample from the transient response to a single rectangular pulse. The equivalent circuit model comprises three elements: sample resistance, sample capacitance, and electrode coupling capacitance. From this model, analytical expressions of the transient response were derived, enabling accurate simulation of measured signals and providing the basis for both phantom verification and machine learning training. Importantly, the coupling capacitance, typically considered a limitation in contactless methods, is estimated alongside the sample parameters, providing insight into electrode–object coupling conditions. A machine-learning model trained on simulated circuit responses, including noise and temporal variability, is employed as a low-latency estimator for extracting parameters from measured transient signals. Experimental validation was carried out using a configurable lumped-element equivalent circuit and NaCl solutions of controlled conductivity, cross-verified with conductometric measurements and numerical probe simulations. Across a tested conductivity range, the method achieved estimation errors of 2–8%. The proposed approach is intended as a low-latency measurement strategy for simplified capacitively coupled impedance sensing, with potential relevance to future capacitively coupled electrical impedance tomography systems, where rapid acquisition of boundary measurements is prioritized over full frequency-resolved impedance spectroscopy. Full article
(This article belongs to the Special Issue Bioimpedance Measurements and Microelectrodes: Second Edition)
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20 pages, 9790 KB  
Article
Evaluation of the Relationship Between the Level of UVB Irradiation and the Reflectance Spectrum of Leaves and the Content of Steviol Glycosides in Stevia rebaudiana Bertoni
by Alexey P. Dolgalev, Alexander A. Smirnov, Yuri A. Proshkin, Pavel V. Tikhonov, Dmitry A. Burynin, Inna V. Knyazeva, Alina S. Ivanitskikh and Alexander V. Sokolov
AgriEngineering 2026, 8(7), 258; https://doi.org/10.3390/agriengineering8070258 (registering DOI) - 24 Jun 2026
Abstract
Stevia (Stevia rebaudiana Bertoni) is an important source of natural sweeteners. Since its commercial value depends on steviol glycosides, quality assessment primarily involves quantifying these compounds in leaves and shoots. While chromatography is the standard analytical method, it is labor-intensive and time-consuming; [...] Read more.
Stevia (Stevia rebaudiana Bertoni) is an important source of natural sweeteners. Since its commercial value depends on steviol glycosides, quality assessment primarily involves quantifying these compounds in leaves and shoots. While chromatography is the standard analytical method, it is labor-intensive and time-consuming; it involves multiple processing steps that may cumulatively introduce errors and remains relatively expensive. Although chromatography remains the most accurate method, this exploratory study evaluates the potential of using spectroscopy as an auxiliary method for the approximate assessment of steviol glycoside content. Leaf reflectance spectroscopy could be a simpler and more cost-effective approach. However, relationships between leaf reflectance and steviol glycoside content are indirect and mediated by physiological processes. To account for these indirect dependencies, cumulative UVB exposure was included as an additional feature because it influences both leaf optical properties and plant metabolic processes. A low-cost spectrometer was utilized as the measuring instrument. The study was conducted over a period of three months on 77 S. rebaudiana clones, divided into four groups based on their level of UVB irradiance (control without irradiation, 400, 600, and 800 μW m−2). Based on the collected data, linear and polynomial regression, Random Forest, XGBoost, PLSR, and ElasticNetCV models were trained. Cumulative UVB exposure was found to be the most important feature. Of the spectral features, the most informative for assessing the content of steviol glycosides were spectral indicators in the far-red and near-infrared (NIR) ranges. Our results indicate a detectable relationship, with Random Forest being the best-performing model and achieving a moderate predictive performance (R2 = 0.66). Despite their limited predictive performance, the models demonstrate that leaf reflectance spectra combined with cumulative UVB exposure contain information related to steviol glycoside content. These findings support further investigation of remote sensing approaches for crop quality assessment. Full article
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Article
A Physics-Informed Framework Linking Satellite AOD and Ambient Particulate Matter: A Pilot Study
by Giorgia Proietti Pelliccia, Erika Brattich, Andrea Faggi, Silvana Di Sabatino and Tiziano Maestri
Atmosphere 2026, 17(7), 627; https://doi.org/10.3390/atmos17070627 (registering DOI) - 24 Jun 2026
Abstract
Recently, numerous studies have exploited satellite Aerosol Optical Depth (AOD) to estimate near-surface particulate matter (PM) concentrations, with the aim of overcoming the limited spatial and temporal coverage of ground-based air quality monitoring networks. Despite significant progress, the relationship between AOD and PM [...] Read more.
Recently, numerous studies have exploited satellite Aerosol Optical Depth (AOD) to estimate near-surface particulate matter (PM) concentrations, with the aim of overcoming the limited spatial and temporal coverage of ground-based air quality monitoring networks. Despite significant progress, the relationship between AOD and PM remains highly uncertain, mainly due to the inadequate representation of local aerosol microphysical properties and of hygroscopic growth effects. In particular, satellite AOD is retrieved at ambient relative humidity, whereas standard PM measurements are performed under dry conditions. This study proposes a physics-informed, semi-empirical approach that overcomes these limitations by directly relating satellite AOD to PM measured at ambient humidity. Co-located measurements, from a Light Optical Aerosol Counter (LOAC) in the urban area of Bologna (Po Valley, Italy) during 2023, are used. This study is designed as a pilot application to evaluate the physical consistency of the proposed framework under well-characterised observational conditions, including spatial co-location, temporal matching to satellite overpasses, and exclusion of precipitation and desert dust events. The LOAC provides particle number size distribution and particle-type classification, which are used to estimate key aerosol properties controlling the AOD–PM theoretical relationship, including the Effective Radius, Extinction Efficiency, and aerosol Mass Density. These quantities, together with Mixing Layer Height, are combined within a theoretical framework linking PM and AOD, allowing for the derivation of a physically based scaling coefficient without relying on empirical hygroscopic growth corrections. The results show that using ambient PM2.5 alone already yields a moderate linear correlation with AOD normalized by Mixing Layer Height (Pearson’s R = 0.56) whereas no meaningful correlation is found when using standard dry PM2.5. When aerosol microphysical properties derived from LOAC measurements are incorporated, the correlation substantially improves (R = 0.76), with regression slopes close to unity and reduced errors, independently of the season. These results demonstrate that explicitly accounting for aerosol size and optical properties enhances the physical consistency and robustness of satellite-based PM estimates. The proposed framework also provides a pathway to indirectly derive aerosol hygroscopic growth factors by coupling ambient PM estimates from satellite observations with conventional dry PM measurements. This opens new perspectives for characterizing aerosol–humidity interactions from space and for improving air quality monitoring in regions lacking of dense in situ networks. Full article
(This article belongs to the Section Aerosols)
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