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24 pages, 1276 KB  
Article
A Patient Simulator to Enable the Design of Fractional-Order PID Controllers for Depth of Hypnosis
by Ada M. Tudor, Alin C. Malita, Marcian D. Mihai, Erwin T. Hegedus, Isabela R. Birs and Cristina I. Muresan
Fractal Fract. 2026, 10(6), 407; https://doi.org/10.3390/fractalfract10060407 - 15 Jun 2026
Viewed by 90
Abstract
According to data from the World Federation of Societies of Anesthesiologists, numerous countries across Asia and Africa have fewer than one anaesthesiologist per 100,000 people. Upskilling nurse anaesthetists in these regions is critical to improving clinical outcomes, and interactive virtual patient simulators offer [...] Read more.
According to data from the World Federation of Societies of Anesthesiologists, numerous countries across Asia and Africa have fewer than one anaesthesiologist per 100,000 people. Upskilling nurse anaesthetists in these regions is critical to improving clinical outcomes, and interactive virtual patient simulators offer a safe environment to explore complex clinical scenarios. This paper introduces an advanced general anaesthesia patient simulator engineered to bridge the accessibility gap left by existing platforms, which often require expert programming knowledge and restrict users to manual titration. Our simulator features an intuitive graphical user interface optimised for clinical education and natively supports both manual and closed-loop anaesthesia administration. The platform includes a suite of pre-designed controllers, specifically standard PIDs and two distinct fractional-order FO-PID variants, highlighting a novel robust FO-PID framework engineered to mitigate high patient variability. The deployment of these embedded controllers is demonstrated via a Depth of Hypnosis regulation case study and validated across a diverse cohort of 19 virtual patients. Closed-loop evaluation reveals that while the standard PID achieves a lower average mean squared error during the maintenance phase, the fractional-order alternatives deliver significantly superior robustness and inter-patient consistency. Ultimately, integrating this simulator into clinical training frameworks offers a viable pathway to reduce nursing workload and enhance patient safety through optimised automated drug delivery. Full article
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41 pages, 26866 KB  
Article
Dynamic Mixed Reality Interfaces for Industry 4.0: An Asset Administration Shell Approach
by Tomáš Sedláček, Erik Kučera, Oto Haffner, Martin Pajpach and Martin Michalovič
Electronics 2026, 15(12), 2648; https://doi.org/10.3390/electronics15122648 - 15 Jun 2026
Viewed by 98
Abstract
The ongoing evolution of Industry 4.0 technologies necessitates novel and effective modes of human–machine interaction within production environments. This work presents a modular approach to the design and implementation of graphical user interfaces (GUI) in mixed reality, leveraging the Asset Administration Shell (AAS) [...] Read more.
The ongoing evolution of Industry 4.0 technologies necessitates novel and effective modes of human–machine interaction within production environments. This work presents a modular approach to the design and implementation of graphical user interfaces (GUI) in mixed reality, leveraging the Asset Administration Shell (AAS) standard. The proposed method enables the dynamic rendering of GUI elements in a Mixed Reality setting based on structured data retrieved from an AAS server. Developed for the Microsoft HoloLens 2 using the Unity engine and the Microsoft Reality Toolkit 3 (MRTK3), the system allows for the spatial placement of interface components either at predefined coordinates or in relation to specific elements of a production line model. Additionally, it incorporates a real-time distributed architecture utilizing OPC UA PubSub and MQTT protocols for processing and visualising live data. The prototype demonstrates the viability of using AAS as a flexible framework for defining and generating GUI components in immersive environments and lays the groundwork for further research into standardised, easily deployable user interface solutions for industrial applications. Full article
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11 pages, 2256 KB  
Article
Time to Meaningful Clinical Response Across Approved and Emerging Therapies for Antihistamine-Refractory Chronic Spontaneous Urticaria: A Network Meta-Analysis
by Sarayu Balachandar, Dylan R. Clapp and Alan B. Fleischer
J. Clin. Med. 2026, 15(12), 4622; https://doi.org/10.3390/jcm15124622 - 14 Jun 2026
Viewed by 181
Abstract
Background/Objectives: Several novel biologics and small-molecule therapies have emerged for the treatment of antihistamine-refractory chronic spontaneous urticaria (CSU), yet no study has directly compared their speed of response. This study aims to provide indirect evidence on the relative time to meaningful clinical [...] Read more.
Background/Objectives: Several novel biologics and small-molecule therapies have emerged for the treatment of antihistamine-refractory chronic spontaneous urticaria (CSU), yet no study has directly compared their speed of response. This study aims to provide indirect evidence on the relative time to meaningful clinical response across approved and investigational therapies using a Bayesian network meta-analysis. Methods: Phase 2 and phase 3 randomized controlled trials reporting UAS7 scores in a graphical format for antihistamine-refractory CSU were included. The primary outcome was the mean time in weeks to minimal clinically important difference (MCID), defined as a UAS7 reduction of 10 points. Data were extracted using WebPlotDigitizer (v4.7) and analyzed via Bayesian random-effects network meta-analysis in MetaInsight (v6.4.0), with placebo as the reference node. Results: All drugs except rilzabrutinib 400 mg daily demonstrated faster mean time to MCID than placebo. Fenebrutinib had the fastest mean time to MCID (0.67–0.76 weeks), and tezepelumab the slowest (5.41–5.65 weeks). Only omalizumab 300 mg every 4 weeks, dupilumab 300 mg every 2 weeks, and ligelizumab 72 mg and 120 mg every 4 weeks achieved statistically significant reductions compared with placebo. All treatments had wide credible intervals reflecting limited direct comparisons. Conclusions: This is the first network meta-analysis comparing time to meaningful symptom control across therapies for antihistamine-refractory CSU. Omalizumab, dupilumab, and ligelizumab demonstrated statistically significant reductions in time to MCID compared with placebo. Head-to-head trials with standardized outcome reporting would enable more definitive comparative conclusions. Full article
(This article belongs to the Section Dermatology)
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38 pages, 29624 KB  
Article
Prediction of Scour Hole Geometry Downstream of Ski-Jump Spillways Using Novel Intelligent Computational Machine Learning Models
by Mehrshad Samadi, Aydin Shishegaran, Mina Torabi and Zohreh Sheikh Khozani
Forecasting 2026, 8(3), 49; https://doi.org/10.3390/forecast8030049 - 12 Jun 2026
Viewed by 209
Abstract
The ski-jump spillway is an energy-dissipating structure that discharges extra water beyond the dam’s capacity. The scour process occurs below spillways due to the collision of the water jet with high energy. It is critical to acquire information on scour holes to improve [...] Read more.
The ski-jump spillway is an energy-dissipating structure that discharges extra water beyond the dam’s capacity. The scour process occurs below spillways due to the collision of the water jet with high energy. It is critical to acquire information on scour holes to improve the dam’s safety and related components. Machine learning (ML) techniques have successfully demonstrated their effectiveness for modeling scour in hydraulic engineering. The present research considers novel approaches of ML models for estimating the scour hole geometries below ski-jump bucket spillways. This study investigates the capability of two novel feature-engineering approaches, namely Stronger Variable Creator Machine (SVCM) and High Correlated Variables Creator Machine (HCVCM), along with Gene Expression Programming (GEP) and their hybrid forms (SVCM+GEP and HCVCM+GEP), which were employed to predict normalized scour depth, scour length, and scour width below ski-jump spillways. Statistical metrics, graphical analyses, the Rank Mean (RM) method, the cross-validation approach, and U95 index were used for the evaluation and reliability assessment of the proposed ML models. The results showed that hybrid ML models consistently outperformed individual algorithms. The results indicated that the SVCM+GEP method with RM=1.83 and 1.50 had the highest performance compared to other methods for the prediction of DsDw and LsDw, respectively. In addition, the HCVCM+GEP method with RM=1.33 was the best model for the prediction of WsDw. In comparison with the conventional regression-based equations and previously reported ML methods, the proposed hybrid approaches improved the prediction results. In addition, the cross-validation method confirmed the robustness and generalization capability of the suggested hybrid ML models. The superior performance of the hybrid models is attributed to their ability to capture complex nonlinear interactions among hydraulic and geometric variables. The developed SVCM/HCVCM+GEP models provide accurate approaches for predicting scour parameters in hydraulic structures. Full article
(This article belongs to the Section Environmental Forecasting)
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44 pages, 1250 KB  
Article
Accelerating Active Learning for Image Classification Through FPGA-Based Implementation
by Angelo Barbieri, Christopher A. Flores, Wladimir Valenzuela and Francisco Saavedra
Sensors 2026, 26(12), 3743; https://doi.org/10.3390/s26123743 - 12 Jun 2026
Viewed by 154
Abstract
Image sensors produce high-dimensional visual data for classification algorithms. Deep Neural Networks (DNNs) achieve high accuracy but require large labeled datasets and computational and energy resources, limiting their use in embedded systems. Active Learning (ALrn) can reduce labeling effort by selecting samples based [...] Read more.
Image sensors produce high-dimensional visual data for classification algorithms. Deep Neural Networks (DNNs) achieve high accuracy but require large labeled datasets and computational and energy resources, limiting their use in embedded systems. Active Learning (ALrn) can reduce labeling effort by selecting samples based on informativeness scores, but it remains computationally expensive, especially for high-dimensional images. This work presents a hardware-accelerated approach for the instance selection stage based on a query strategy in uncertainty-based ALrn for image classification using a novel in-line top-k selection algorithm that avoids conventional sorting and reduces memory and computational requirements. The algorithm is implemented on an Xilinx ZYNQ-7000 System on Chip (SoC) using a Field Programmable Gate Array (FPGA)-based accelerator operating at 110 MHz, interfacing with an embedded Advanced RISC Machine (ARM) processor for data acquisition and communication via the Python Productivity for Zynq (PYNQ) framework. Experiments on diverse multiclass datasets demonstrate correctness within an ALrn setting, showing negligible performance deviation in the learning curves compared to software baselines. The accelerator achieves speedup of 231.7× and 22.9× over software baseline and optimized software implementation of the proposed algorithm, respectively, in query-strategy computation while consuming only 0.473 W, substantially lower than conventional Central Processing Unit (CPU)- and Graphics Processing Unit (GPU)-based platforms. These results demonstrate the efficiency and extensibility of the proposed accelerator across alternative ALrn designs and hardware platforms, where the computational cost of instance selection scales with the size of the unlabeled pool. Full article
(This article belongs to the Section Intelligent Sensors)
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20 pages, 20013 KB  
Article
Large Language Models as Semantic Evaluators of Embedded Correlation Substructures
by Adam Dudáš and Peter Babic
AppliedMath 2026, 6(6), 94; https://doi.org/10.3390/appliedmath6060094 - 11 Jun 2026
Viewed by 118
Abstract
Graphical methods of correlation analysis, such as correlation n-ptychs or hotspots, focus on the identification of the strength and direction of functional relationships between sets of attributes in multidimensional datasets. Since these correlation structures only take into account values of the attributes, [...] Read more.
Graphical methods of correlation analysis, such as correlation n-ptychs or hotspots, focus on the identification of the strength and direction of functional relationships between sets of attributes in multidimensional datasets. Since these correlation structures only take into account values of the attributes, situations arise when the relationship is coincidental, meaning that there is no real-world causality between the values of the observed attributes but these values still exhibit significant correlation. This problem of correlation analysis as a whole motivates the need for semantic evaluation of significant relationships identified using its methods—a task that could potentially be time- and resource-intensive when conducted manually. However, modern results in the large language model area provide tools for the automatization of such tasks. Hence, this work focuses on the design and implementation of a novel large language model-based method for semantic evaluation of correlation structures embedded in a correlation graph, specifically correlation n-ptychs for n{3, 4, 5} and correlation hotspots. In the method, the large language model is automatically prompted to assess the semantic nature of relationships in the set of correlation substructures of the dataset, identify their real-world relevance, and visualize the result in the form of a Semantic evaluation card. The proposed approach is evaluated using two benchmarking datasets focusing on the visualization method used in the model, large language model interaction with the correlation substructures, and comparative analysis with previously used tools in the area. Full article
(This article belongs to the Special Issue Feature Papers in AppliedMath)
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22 pages, 1055 KB  
Article
Multi-Criteria Optimization in the Mining Industry Using a Genetic Algorithm
by Diana Novak, Yuriy Kozhubaev, Dmitry Kazanin, Roman Dorovskih and Georgiy Molodtsov
Automation 2026, 7(3), 87; https://doi.org/10.3390/automation7030087 - 9 Jun 2026
Viewed by 177
Abstract
The present article discusses the application of genetic algorithms (GA) for solving multi-criteria optimization (MCO) problems in underground mining. It has been demonstrated that GAs are highly effective in identifying Pareto-optimal solutions in scenarios involving multiple conflicting criteria, specifically the simultaneous minimization of [...] Read more.
The present article discusses the application of genetic algorithms (GA) for solving multi-criteria optimization (MCO) problems in underground mining. It has been demonstrated that GAs are highly effective in identifying Pareto-optimal solutions in scenarios involving multiple conflicting criteria, specifically the simultaneous minimization of equipment failure rate, energy consumption, and repair costs. The article presents the main approaches to solving MCO problems, a brief overview of the most popular algorithms, such as NSGA-II and SPEA2, and their improved versions. The proposed algorithm, implemented in Python 3.11 using the DEAP library, incorporates adaptive crossover, enhanced diversity preservation, and problem-specific initialization. Quantitative analysis shows that the proposed algorithm achieves a Hypervolume Indicator of 0.796, representing a 7.2% improvement over standard SPEA2, with an 18.3% reduction in Inverted Generational Distance (IGD), indicating superior convergence to the true Pareto front. The algorithm identifies optimal trade-offs between conflicting objectives—for example, a 15% reduction in energy consumption correlates with a 10% increase in failure rate—providing decision-makers with quantified insights for operational planning. The novel idea is the use of an adaptive crossover strategy, a composite diversity maintenance technique, and application-specific initialization—all of which have not been used before for optimizing underground mining machinery. A visual analysis of the results, employing a graphical representation of the Pareto front, confirmed that the proposed approach enables experts to make informed decisions based on production priorities. Full article
(This article belongs to the Section Control Theory and Methods)
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18 pages, 1093 KB  
Article
Finite-Sample Diagnostics for Random-Effects Misspecification in Poisson Generalized Linear Mixed Models
by Jairo A. Ángel and Jorge I. Vélez
Mathematics 2026, 14(12), 2042; https://doi.org/10.3390/math14122042 - 8 Jun 2026
Viewed by 129
Abstract
Poisson mixed-effects models are essential for analyzing repeated count data, relying on latent random effects to account for unobserved heterogeneity and longitudinal dependence. However, the validity of likelihood-based inference in these models is highly sensitive to the specification of both the fixed-effects structure [...] Read more.
Poisson mixed-effects models are essential for analyzing repeated count data, relying on latent random effects to account for unobserved heterogeneity and longitudinal dependence. However, the validity of likelihood-based inference in these models is highly sensitive to the specification of both the fixed-effects structure and the distributional assumptions of the random effects. While diagnostics based on the information matrix equality (IME) provide a theoretical framework for detecting misspecification, their high dimensionality and reliance on second-order derivatives often result in numerical instability and poor finite-sample performance in nonlinear settings. Here we introduce the Contrast of Information by Volume (CIV) test, a low-dimensional information-based diagnostic test for Poisson generalized linear mixed models (GLMMs). By integrating the scalar CIV statistics with novel graphical diagnostics, our approach facilitates the interpretation of specification errors in the random-effects structure. We derive the asymptotic behaviour of the CIV statistics under local misspecification and evaluate their properties through Monte Carlo simulations. To ensure robust inference in moderate samples, a parametric bootstrap procedure is employed for size calibration. Simulation results demonstrate that the CIV diagnostics maintain accurate Type I error control and achieve competitive power against common misspecification, including heteroskedasticity, correlation, and heavy-tailed random-effect distributions. Compared to traditional IME diagnostics, estimator-comparison tests, and GMM-based procedures, the CIV approach offers a superior balance between finite-sample stability and detection power. Finally, an empirical application illustrates the utility of the CIV framework in diagnosing latent misspecification and guiding the selection of random-effects covariance structures in applied research. Full article
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33 pages, 1190 KB  
Article
The Minimal Geometric Deformation Method to Construct Anisotropic Solutions for Polytropic Configurations
by Tayyab Naseer, Muhammad Sharif, Aleena Tehreem, Komal Hassan and Ahmed Emara
Math. Comput. Appl. 2026, 31(3), 99; https://doi.org/10.3390/mca31030099 - 7 Jun 2026
Viewed by 137
Abstract
The minimal geometric deformation method is applied on Einstein–Maxwell field equations in this study to obtain two novel exact anisotropic solutions for polytropic configurations. A static spherically symmetric seed structure penetrated by the anisotropic fluid distribution is taken into consideration in order to [...] Read more.
The minimal geometric deformation method is applied on Einstein–Maxwell field equations in this study to obtain two novel exact anisotropic solutions for polytropic configurations. A static spherically symmetric seed structure penetrated by the anisotropic fluid distribution is taken into consideration in order to accomplish this goal. The gravitational interaction of the new Lagrangian density is then coupled with the initial fluid configuration, representing an additional matter source. We obtain the field equations that correspond to the associated charged fluid sources. Two separate decoupled systems are developed when the field equations are subjected to a radial transformation. By applying the distinct constraints, each system’s solution is determined individually. The entire fluid configuration is then generated by combining these solutions via a certain linear combination. The constraints needed to determine the integration constants in the internal solutions are provided by junction conditions at the interface between the interior and exterior geometry. The suggested models are then verified by comparing them graphically under the observational data from the CenX3 candidate star. In conclusion, for certain values of the decoupling parameter, our derived relativistic solutions satisfy established physical acceptability requirements. Full article
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19 pages, 61900 KB  
Article
FasterNetFire: A Cost-Effective Fast Neural Network for Forest Fire Detection with Partial Convolution
by Gongsuo Chen, Annop Tananchana, Laihong Jiang, Xiangbing Zhou, Lei Mu and Wu Deng
Forests 2026, 17(6), 672; https://doi.org/10.3390/f17060672 - 31 May 2026
Viewed by 225
Abstract
Forest fires occur frequently around the world due to extreme weather conditions of high temperatures and drought. Vision-based convolutional neural networks (CNNs) have greatly improved forest fire detection accuracy. However, slow inference speed severely restricts real-time deployment in actual forest scenes. Existing models [...] Read more.
Forest fires occur frequently around the world due to extreme weather conditions of high temperatures and drought. Vision-based convolutional neural networks (CNNs) have greatly improved forest fire detection accuracy. However, slow inference speed severely restricts real-time deployment in actual forest scenes. Existing models generally adopt group convolution (GConv) or depthwise convolution (DWConv) to reduce computational complexity, which causes frequent memory access and result in a practical inference speed far below theoretical expectations. Therefore, we propose a novel fast neural network named FasterNetFire for forest fire detection, which introduces partial convolution (PConv) as the basic feature extraction operator to reduce redundant computation as well as memory access overhead simultaneously. FasterNetFire is composed of four cascaded stages, each stage contains several stacked FasterNet Blocks, and the core of each FasterNet Block is an inverted residual module built upon PConv. The proposed network significantly improves inference efficiency while maintaining the effectiveness of spatial feature extraction. Experiments conducted on the FD and Foggia’s fire detection dataset demonstrate that our FasterNetFire achieves an impressive inference speed of up to 290 frames per second (FPS) on graphics processing unit (GPU) platforms. Compared with current representative methods, its inference speed is 4.5× and 4× faster than that of EFDNet and DFAN. Furthermore, FasterNetFire achieves the best results among 17 state-of-the-art methods, achieving an excellent balance between detection accuracy and real-time response performance. This advantage fully verifies the high efficiency of PConv in vision forest fire detection tasks and provides a novel lightweight solution for real-time monitoring and early warning of forest fires in resource-constrained environments. Full article
(This article belongs to the Section Natural Hazards and Risk Management)
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18 pages, 6465 KB  
Article
PokerOWL: A Multi-Agent Poker Environment for Benchmarking Open-World Learning
by Min-Hsueh Chiu, Navapat Nananukul and Mayank Kejriwal
Appl. Sci. 2026, 16(11), 5458; https://doi.org/10.3390/app16115458 - 31 May 2026
Viewed by 414
Abstract
In complex task environments in both nature and human society, structuralviolations of expectation (VoE) occur with non-trivial frequency. Agents that are designed to operate in such environments must be capable of open-world learning (OWL), defined as the ability to detect and accommodate out-of-distribution [...] Read more.
In complex task environments in both nature and human society, structuralviolations of expectation (VoE) occur with non-trivial frequency. Agents that are designed to operate in such environments must be capable of open-world learning (OWL), defined as the ability to detect and accommodate out-of-distribution inputs, as well as more complex structural VoEs, without requiring extensive and offline re-training. Until recently, OWL research was relatively constrained and limited to areas such as anomaly detection and concept drift. More recently, agent-based OWL research has witnessed much interest from across the community. To support this research, not just for developing OWL algorithms, but also evaluating them, there is a need for multi-agent environments where structural VoEs can be generated, and controlled experiments can be run with relative ease. To address this need, we propose a resource called PokerOWL, a platform that is supported on the Gymnasium infrastructure, which is extensively used in the reinforcement learning and AI game-playing communities. PokerOWL supports both a rich VoE generator and a graphical interface for facilitating development and evaluation of OWL methods. Using an extensive set of experiments and a Poker-playing agent based on Deep Q-Networks, we use PokerOWL to demonstrate how even state-of-the-art agents can struggle to generalize to novel situations without additional OWL capabilities. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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35 pages, 6455 KB  
Article
Comparative Kinematics and Static Analysis of Regular and Irregular Hexagonal Stewart–Gough Platform Configurations
by Tony Punnoose Valayil and Tarek H. Mokhtar
Technologies 2026, 14(6), 312; https://doi.org/10.3390/technologies14060312 - 22 May 2026
Viewed by 401
Abstract
The Stewart–Gough Platform (SGP) is a spatial parallel manipulator offering high accuracy, rigidity, and adaptability, with applications spanning medical systems, marine engineering, agriculture, manufacturing, entertainment, aerospace, and architectural installations. This paper presents a comparative analytical and computational study of three SGP configurations: the [...] Read more.
The Stewart–Gough Platform (SGP) is a spatial parallel manipulator offering high accuracy, rigidity, and adaptability, with applications spanning medical systems, marine engineering, agriculture, manufacturing, entertainment, aerospace, and architectural installations. This paper presents a comparative analytical and computational study of three SGP configurations: the regular SGP, with regular hexagonal base and top platforms; the Irregular-Parallel SGP, derived from the regular SGP by a novel graphical decomposition-and-modification procedure and characterized by similar symmetric hexagonal platforms with limbs preserved parallel; and the Irregular-Skewed SGP, in which the irregular hexagonal platforms of the Irregular-Parallel SGP are retained, but the limbs are connected in an inclined, alternating clockwise (or anticlockwise) topology. The Irregular–Skewed SGP is free from the constraint singularity that persists in the first two configurations and requires the shortest maximum actuator stroke. Static force analysis shows that the regular SGP and the Irregular–Parallel SGP both exhibit a rank-deficient rigidity matrix (rank = 3) across the geometric scaling range tested (radius ratios 1:2 to 1:10; inter-platform distances 100–1000 mm), whereas the Irregular-Skewed SGP achieves full rank (rank = 6) through inclined limb connectivity and is the only configuration capable of sustaining static equilibrium under the loading conditions examined. The forward kinematics of the Irregular-Parallel SGP is verified against a SolidWorks model: under a 9 mm uniform limb extension, the MATLAB and SolidWorks positions of node 7 agree to within 1.27 mm. The rotational workspace volume is equivalent across the three configurations, but the density of valid solution points within that workspace differs. The workspace within joint limits, alternating compression–tension force partition, and asymmetric stroke economy of the Irregular-Skewed SGP indicate applicability to kinetic facades and transformable interiors in architectural-robotics deployment. Full article
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25 pages, 2510 KB  
Article
ANN-Assisted Sharp Bounds for Higher-Order Euler–Maclaurin Inequalities
by Muhammad Zakria Javed, Muhammad Uzair Awan, Loredana Ciurdariu, Eugenia Grecu and Hala Mostafa
Axioms 2026, 15(5), 358; https://doi.org/10.3390/axioms15050358 - 11 May 2026
Viewed by 263
Abstract
This study presents some novel sharp estimates of the Euler–Maclaurin inequality using a new higher-order derivative Maclaurin identity. By utilizing the properties of convexity and classical inequalities, we exploit various novel tight boundaries of the Euler–Maclaurin inequality. They offer alternatives to measuring the [...] Read more.
This study presents some novel sharp estimates of the Euler–Maclaurin inequality using a new higher-order derivative Maclaurin identity. By utilizing the properties of convexity and classical inequalities, we exploit various novel tight boundaries of the Euler–Maclaurin inequality. They offer alternatives to measuring the sharp bounds of the mean integral of the higher-order differentiable mappings. In order to prove the importance and precision of the key findings, we apply graphical and numerical techniques. Another important section evaluates the behavior and validity of inequalities using a neural network model. The method is not only utilized to authenticate the results but also brings out the practical advancements of the study within a computational framework. The method and results of the article provide an insight and develop a solid connection between inequalities, higher-order derivative convex mappings, numerical analysis, approximation theory, and artificial neural networking. Full article
(This article belongs to the Special Issue Theory and Application of Integral Inequalities, 2nd Edition)
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40 pages, 42122 KB  
Article
Artificial Intelligence for Learning 2D Debris-Flow Dynamics: Application of Fourier Neural Operators and Synthetic Data to a Case Study in Central Italy
by Mauricio Secchi, Antonio Pasculli and Nicola Sciarra
Land 2026, 15(5), 759; https://doi.org/10.3390/land15050759 - 29 Apr 2026
Viewed by 400
Abstract
Physics-based simulation of debris flows over complex terrain is essential for hazard assessment, but repeated numerical integration is costly when many scenarios must be explored. We develop a general deep-learning surrogate modelling framework for two-dimensional (2D) debris-flow propagation, here applied to the Morino–Rendinara [...] Read more.
Physics-based simulation of debris flows over complex terrain is essential for hazard assessment, but repeated numerical integration is costly when many scenarios must be explored. We develop a general deep-learning surrogate modelling framework for two-dimensional (2D) debris-flow propagation, here applied to the Morino–Rendinara area (central Italy) using a three-dimensional (3D) Fourier Neural Operator (FNO) trained on synthetic simulations generated by a validated in-house finite-volume shallow-water solver. The solver reproduces debris-flow propagation over complex terrain and is specifically developed for artificial intelligence (AI) applications. It is based on a depth-averaged 2D formulation using the Harten–Lax–van Leer–Contact (HLLC) approximate Riemann solver, hydrostatic reconstruction, positivity-preserving wet–dry treatment, and Voellmy-type basal friction, and was verified through analytical benchmarks, numerical tests, and back-analyses of real events. The dataset was built from four site-specific release settings derived from real topography, combining different released volumes and bulk densities while preserving local geomorphological and rheological characteristics. Each simulation was stored as a full spatio-temporal tensor and used to train an FNO conditioned on coordinates, topography, friction parameters, bulk density, and initial release thickness. Training used a novel loss to emphasize active-flow areas and improve velocity reconstruction, and was performed using a graphics processing unit (GPU). The surrogate shows effective generalization to within-distribution validation samples, with global relative mean squared errors of 5.49% for flow thickness, 5.34% for velocity component u, and 2.60% for v, and mean R2 values of 0.95, 0.94, and 0.97. For a representative sample, the surrogate predicts the full spatio-temporal solution in 0.52 s, versus about 47 s for the first-order finite-volume solver, corresponding to a speed-up of about 91×, with an even larger gap expected for higher-order solvers, since, whilst the computation time of the solver increases as its complexity increases, the computation time of the FNO remains essentially unchanged. These results indicate that the proposed FNO is a reliable site-specific surrogate for rapid approximation of 2D debris-flow dynamics over real terrain, with potential for uncertainty propagation, Monte Carlo analysis, large-ensemble simulation, and hazard-oriented scenario assessment. Full article
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14 pages, 3280 KB  
Article
New Possibilities of Testing the Darkening of Automatic Welding Filters as Expressed by Switching Time
by Joanna Szkudlarek and Marcin Jachowicz
Appl. Sci. 2026, 16(8), 4045; https://doi.org/10.3390/app16084045 - 21 Apr 2026
Viewed by 326
Abstract
Welders constitute an occupational group that is particularly exposed to high-risk hazards arising from harmful radiation emitted during welding, including ultraviolet (UV) and infrared (IR) radiation, as well as visible (VIS) radiation, whose high intensity causes glare. Effective protection of the eyes and [...] Read more.
Welders constitute an occupational group that is particularly exposed to high-risk hazards arising from harmful radiation emitted during welding, including ultraviolet (UV) and infrared (IR) radiation, as well as visible (VIS) radiation, whose high intensity causes glare. Effective protection of the eyes and face is provided by welding shields equipped with automatic welding filters (AWFs), which activate automatically upon arc ignition. Their switching time is the most important protective parameter, as it has a direct impact on the user’s visual health. The objective of the work is to present a novel test stand for determining AWFs switching and holding times, which provides advanced possibilities for evaluating all types of AWFs. Until now, performance and safety levels have been determined based on numerical values: switching time and hold time. For the first time, it is possible to analyze the darkening and clearing phenomena over time with an interpretation of graphical results. Importantly, it is possible to analyze the symmetry of filter properties, using two measurement channels, which is crucial for binocular and curved (panoramic) AWFs. The results obtained for two types of AWFs mounted in goggles with a one-piece and a binocular visor differ from each other. Switching time differences between the left and right measurement channels were about 6–7% for the one-piece visor goggles (G1) and about 3–4% for the binocular goggles (G2). The dispersion of results confirmed the importance of the two measurement channels, which was not previously practiced. The test stand, designed in accordance with the requirements of the new European standards (EN ISO 18526-2:2020, EN ISO 16321-2:2021), can be used for prototyping and for AWF certification purposes. Full article
(This article belongs to the Special Issue Industrial System Optimization and Intelligent Manufacturing)
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