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Fractional stochastic differential equations (FSDEs) are powerful tools for modeling real-world phenomena, as they incorporate both memory effects and stochastic noise. A central focus in their analysis is establishing the well-posedness and regularity of solutions. Moreover, the averaging principle offers a systematic approach to simplify complex dynamical systems by approximating their behavior through time-averaged models. In this paper, we develop a theoretical framework for a class of FSDEs involving the Hilfer–Katugampola derivative. Our main contributions include proving the well-posedness and regularity of solutions, establishing a generalized averaging principle, and demonstrating real-life applications solved via the Euler–Maruyama method. All numerical simulations were conducted using the Python programming language (version 3.11). These results are formulated for the

\tilde{P}

th moment, providing a unified analysis that extends existing findings. Full article

(This article belongs to the Special Issue Fractional Calculus and Fractional Differential Equations: Theory and Applications)

14 pages, 1727 KB

Open AccessArticle

Postural and Muscular Responses to a Novel Multisensory Relaxation System in Children with Autism Spectrum Disorder: A Pilot Feasibility Study

by Laura Zaliene, Daiva Mockeviciene, Eugenijus Macerauskas, Vytautas Zalys and Migle Dovydaitiene

Children 2025, 12(11), 1455; https://doi.org/10.3390/children12111455 (registering DOI) - 26 Oct 2025

Abstract

Background: Children with autism spectrum disorder (ASD) frequently show postural abnormalities and elevated muscle tone, which can hinder participation in education and rehabilitation. Evidence on the immediate physiological effects of standardized multisensory environments is limited. Objective: To evaluate feasibility, safety and short-term physiological/postural responses to an automated multisensory smart relaxation system in children with severe ASD. Methods: In a single-session pilot across three sites, 30 children (27 boys; 6–16 years) underwent pre–post postural observation and bilateral surface EMG of the upper trapezius, biceps brachii and rectus abdominis. The system delivered parameterized sound, vibration, and mild heat. EMG was normalized to a quiet-sitting baseline. Results: The intervention was well tolerated with no adverse events. Most children sat independently (25/30; 80%) and a majority stood up unaided after the session (24/30; 76.9%). Postural profiles reflected common ASD features (neutral trunk 76%, forward head 52%, rounded/protracted shoulders 46%), while limb behavior was predominantly calm (73%). Normalized EMG amplitudes were low, with no significant pre–post changes and no meaningful left–right asymmetries (all p > 0.05; Cohen’s d < 0.20), indicating physiological calmness rather than tonic co-contraction. Conclusions: A single session with a smart multisensory relaxation system was safe, feasible, and physiologically calming for children with severe ASD, without increasing postural or muscular tension. The platform’s standardization and objective monitoring support its potential as a short-term calming adjunct before therapy or classroom tasks. Larger, gender-balanced, multi-session trials with behavioral outcomes are warranted. Full article

(This article belongs to the Section Global Pediatric Health)

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18 pages, 5624 KB

Open AccessArticle

Exploring the Role of Rhizobacteria in Sorghum bicolor Adaptation to Combined Drought and Heat Stress

by Alec Magaisa, Elizabeth Ngadze, Tshifhiwa Paris Mamphogoro, Martin Philani Moyo and Casper Nyaradzai Kamutando

Microorganisms 2025, 13(11), 2454; https://doi.org/10.3390/microorganisms13112454 (registering DOI) - 26 Oct 2025

Abstract

Although rhizobacteria are known to improve plant adaptation to abiotic stressors, their possible contribution to the inherent resilience exhibited by crops such as Sorghum bicolor is still poorly quantified. Here, three sorghum pre-release lines and three check varieties were established and evaluated at two low-altitude sites of less than 600 masl. Treatments were laid out in a randomized complete block design, replicated two times. Twenty-four rhizospheric soil samples comprising six sorghum genotypes with two replications across two sites were collected, processed using Zymo Research DNA extraction protocols, and the 16S rRNA amplicon sequences were generated for bacterial diversity quantifications following the Divisive Amplicon Denoising Algorithm 2 (DADA2) workflow. Grain yield data were also recorded and expressed in tonnes per hectare. Rhizobacteria recruitment and GY performance significantly (p < 0.05) varied with sorghum genotypes. Bacterial abundance significantly (p < 0.05) associated with sorghum grain yield performance with Actinobacteriota and Firmicutes being identified to be of economic importance, explaining between 52.23 and 85.64% of the variation in grain yield performance. The modelled relationships between rhizobacteria and grain yield performance revealed R² predicted values of up to 75.25% and a 10-fold R² of 75.54%, implying no model overfitting. Sorghum genotypes did not consistently exhibit direct variation between genetic worth values and grain yield performance. Superior grain yield performers, namely ICSV111IN, CHITICHI, and SV4, consistently associated with high incidences of occurrence of the bacteria phyla Chloroflexi (class = Chloroflexia) and Firmicutes (class = Bacilli), whilst integrating the conventional selection method with microbial diversity data, changed the genotype performance ranking, in which all the three pre-release lines, namely, IESV91070DL, ASARECA12-3-1, and ICSV111IN, exhibited superiority over the check varieties. The results demonstrated that the inherent stress resilience exhibited by some sorghum genotypes under climate change-induced stresses such as CDHS may be influenced by specific bacterial taxa recruited in the rhizosphere environment of the plants. Hence, more effort should be made to further exploit these beneficial plant–microbe interactions for enhanced sorghum productivity under abiotic stress conditions. Full article

(This article belongs to the Special Issue Advances in the Plant Microbiome: Rhizosphere, Endosphere and Phyllosphere)

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13 pages, 320 KB

Open AccessArticle

Sharp Unified Smoothness Theory for Cavalieri Estimation via Fourier Decay

by Francisco-Javier Soto

Axioms 2025, 14(11), 786; https://doi.org/10.3390/axioms14110786 (registering DOI) - 26 Oct 2025

Abstract

Cavalieri estimation is a widely used technique in stereology (applied geometric sampling) for approximating the volume of a solid by sampling cross-sectional areas along a fixed axis. Classical theory shows that, under systematic equidistant sampling (the well-known Cavalieri estimator), the variance decay depends on the smoothness of the area function, which is essentially measured by the number of continuous derivatives. This paper focuses on the natural assumptions under which the theory holds. We first obtain sharp and explicit variance rates: when the Fourier decay is of order s > 1/2, the variance of the Cavalieri estimator decays as t^2s with a constant independent of t. Building on this, we show that the smoothness condition expressed in terms of the algebraic Fourier decay subsumes both integer- and fractional-order frameworks used to date. Finally, we establish a matching converse showing that, under general assumptions, no broader smoothness framework extends the theory; that is, any algebraic variance decay implies the corresponding Fourier decay. Full article

(This article belongs to the Special Issue Numerical Analysis, Approximation Theory and Related Topics)

25 pages, 10646 KB

Open AccessArticle

A Multimodal Fusion Method for Weld Seam Extraction Under Arc Light and Fume Interference

by Lei Cai and Han Zhao

J. Manuf. Mater. Process. 2025, 9(11), 350; https://doi.org/10.3390/jmmp9110350 (registering DOI) - 26 Oct 2025

Abstract

During the Gas Metal Arc Welding (GMAW) process, intense arc light and dense fumes cause local overexposure in RGB images and data loss in point clouds, which severely compromises the extraction accuracy of circular closed-curve weld seams. To address this challenge, this paper proposes a multimodal fusion method for weld seam extraction under arc light and fume interference. The method begins by constructing a weld seam edge feature extraction (WSEF) module based on a synergistic fusion network, which achieves precise localization of the weld contour by coupling image arc light-removal and semantic segmentation tasks. Subsequently, an image-to-point cloud mapping-guided Local Point Cloud Feature extraction (LPCF) module was designed, incorporating the Shuffle Attention mechanism to enhance robustness against noise and occlusion. Building upon this, a cross-modal attention-driven multimodal feature fusion (MFF) module integrates 2D edge features with 3D structural information to generate a spatially consistent and detail-rich fused point cloud. Finally, a hierarchical trajectory reconstruction and smoothing method is employed to achieve high-precision reconstruction of the closed weld seam path. The experimental results demonstrate that under severe arc light and fume interference, the proposed method achieves a Root Mean Square Error below 0.6 mm, a maximum error not exceeding 1.2 mm, and a processing time under 5 s. Its performance significantly surpasses that of existing methods, showcasing excellent accuracy and robustness. Full article

18 pages, 5688 KB

Open AccessArticle

Method for Suppressing Non-Stationary Interference in the Main-Lobe Based on a Multi-Polarized Array

by Jie Wang, Shujuan Ding, Na Wei, Jinzhi Bi and Rongqiu Zheng

Sensors 2025, 25(21), 6587; https://doi.org/10.3390/s25216587 (registering DOI) - 26 Oct 2025

Abstract

To suppress non-stationary main-lobe interference, we utilized the waveform information of the transmitted signal and proposed an interference suppression method based on a multi-polarized array without the need for calculating the target parameters. This method calculates the steering vector of the target through matched filtering. Additionally, for non-stationary interference whose statistical characteristics change over time, we extract high-energy frequency points from the time–frequency joint domain to obtain the time–frequency covariance matrix for subsequent beamforming. Simulation experiments demonstrate that this method leverages the signal polarization information sensed by the multi-polarized array, effectively suppressing non-stationary main-lobe interference in the polarization domain. This method does not require estimation of the target’s polarization parameters and is more suitable for real-world detection scenarios where the waveform is known. Full article

(This article belongs to the Topic Radar Signal and Data Processing with Applications, 2nd Edition)

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21 pages, 6893 KB

Open AccessArticle

A Multi-Source Data-Driven Fracturing Pressure Prediction Model

by Zhongwei Zhu, Mingqing Wan, Yanwei Sun, Xuan Gong, Biao Lei, Zheng Tang and Liangjie Mao

Processes 2025, 13(11), 3434; https://doi.org/10.3390/pr13113434 (registering DOI) - 26 Oct 2025

Abstract

Accurate prediction of fracturing pressure is critical for operational safety and fracturing efficiency in unconventional reservoirs. Traditional physics-based models and existing deep learning architectures often struggle to capture the intense fluctuations and complex temporal dependencies observed in actual fracturing operations. To address these challenges, this paper proposes a multi-source data-driven fracturing pressure prediction model, a model integrating TCN-BiLSTM-Attention Mechanism (Temporal Convolutional Network, Bidirectional Long Short-Term Memory, Attention Mechanism), and introduces a feature selection mechanism for fracture pressure prediction. This model employs TCN to extract multi-scale local fluctuation features, BiLSTM to capture long-term dependencies, and Attention to adaptively adjust feature weights. A two-stage feature selection strategy combining correlation analysis and ablation experiments effectively eliminates redundant features and enhances model robustness. Field data from the Sichuan Basin were used for model validation. Results demonstrate that our method significantly outperforms baseline models (LSTM, BiLSTM, and TCN-BiLSTM) in mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²), particularly under high-fluctuation conditions. When integrated with slope reversal analysis, it achieves sand blockage warnings up to 41 s in advance, offering substantial potential for real-time decision support in fracturing operations. Full article

(This article belongs to the Special Issue Data-Based Prediction Models in Energy Systems: From Principles to Applications)

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12 pages, 975 KB

Open AccessArticle

Analyzing Shortwave Propagation with a Remote Accessible Software-Defined Ham Radio System

by Gergely Vakulya and Helga Anna Albert-Huszár

Signals 2025, 6(4), 58; https://doi.org/10.3390/signals6040058 (registering DOI) - 26 Oct 2025

Abstract

Ham radio has long been a foundational area of practice in electrical engineering. Advances in signal processing, particularly the advent of software-defined radio (SDR), have revolutionized the field, offering new possibilities and modes of operation. This paper introduces a system designed for long-term collection of shortwave propagation data, leveraging SDR technology. It also presents the analysis of the collected data, demonstrating the system’s potential for advancing research in radio wave propagation. Full article

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28 pages, 1656 KB

Open AccessArticle

Developing a Real-Time Public Opinion Analysis System for Women’s Reemployment in Taiwan: A Digital Transformation Approach to Policy Innovation

by Chin-Hui Hsiao, Kuo-Jung Lin, Yu-Ting Lee, Shih-Teng Lin and Li-Ping Chen

Systems 2025, 13(11), 952; https://doi.org/10.3390/systems13110952 (registering DOI) - 26 Oct 2025

Abstract

Declining fertility and population aging intensify labor shortages, making women’s reemployment after caregiving a policy priority. Using Taiwan as a case study, this study develops a real-time public opinion analysis system to complement delayed surveys and capture emerging barriers in labor-market reintegration. Drawing on 2022–2024 social media posts, the system applies sentiment co.mputing, clustering, and algorithmic attention to map four phases: withdrawal, intention, search, and reintegration. Findings show that younger women stress flexibility and childcare, while older returnees prioritize skill renewal and confidence rebuilding; sectoral variation supports life-cycle and clockspeed theories. Policy recommendations emphasize subsidies, training, quotas, and street-level implementation. Beyond technical contributions, the study embeds digital transformation (DT) into labor governance, showing a shift from as-is retrospective surveys to to-be-real-time monitoring. This transformation enhances policy agility, inclusiveness, and alignment with citizens’ lived experiences. The system thus functions as both a tool for rapid intervention and a DT-driven theoretical lens extending reemployment scholarship, offering transferable insights for aging societies. Full article

(This article belongs to the Special Issue Organizational Digital Innovation and Transformation in Enterprise and Government Strategies)

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26 pages, 784 KB

Open AccessFeature PaperArticle

Degenerate Fractals: A Formal and Computational Framework for Zero-Dimension Attractors

by Ion Andronache

Mathematics 2025, 13(21), 3407; https://doi.org/10.3390/math13213407 (registering DOI) - 26 Oct 2025

Abstract

This paper analyzes the extreme limit of iterated function systems (IFSs) when the number of contractions drops to one and the resulting attractors reduce to a single point. While classical fractals have a strictly positive fractal dimension, the degenerate case

D = 0

[...] Read more.

D = 0

has been little explored. Starting from the question “what happens to a fractal when its complexity collapses completely?”, Moran’s similarity equation becomes tautological (

r^{s} = 1

with solution

s = {dim}_{M} = 0

) and that only the Hausdorff and box-counting definitions allow an exact calculation. Based on Banach’s fixed point theorem and these definitions, we prove that the attractor of a degenerate IFS is a singleton with

{dim}_{H} = {dim}_{B} = 0

. We develop a reproducible computational methodology to visualize the collapse in dimensions 1–3 (the Iterated Line Contraction—1D/Iterated Square Contraction—2D/Iterated Cube Contraction—3D families), including deterministic and stochastic variants, and we provide a Python script 3.9. The theoretical and numerical results show that the covering box-counting retains unity across all generations, confirming the zero-dimension element and the stability of the phenomenon under moderate perturbations. We conclude that degenerate fractals are an indispensable benchmark for validating fractal dimension estimators and for studying transitions to attractors with positive dimensions. Full article

(This article belongs to the Special Issue Advances in Fractal Geometry and Applications)

31 pages, 1563 KB

Open AccessArticle

Artificial Intelligence-Assisted Determination of Suitable Age Values for Children’s Books

by Feyza Nur Kılıçaslan, Burkay Genç, Fatih Saglam and Arif Altun

Appl. Sci. 2025, 15(21), 11438; https://doi.org/10.3390/app152111438 (registering DOI) - 26 Oct 2025

Abstract

Identifying age-appropriate books for children is a complex task that requires balancing linguistic, cognitive, and thematic factors. This study introduces an artificial intelligence–supported framework to estimate the Suitable Age Value (SAV) of Turkish children’s books targeting the 2–18-year age range. We employ repeated, [...] Read more.

5 \times 5

cross-validation and report out-of-fold (OOF) metrics with 95% confidence intervals for a dataset of 300 Turkish children’s books. As classical baselines, linear/ElasticNet, SVR, Random Forest (RF), and XGBoost are trained on the engineered features; we also evaluate a rule-based Ateşman readability baseline. For text, we use a frozen dbmdz/bert-base-turkish-uncased encoder inside two hybrid variants, Concat and Attention-gated, with fold-internal PCA and metadata selection; augmentation is applied only to the training folds. Finally, we probe a few-shot LLM pipeline (GPT-4o-mini) and a convex blend of RF and LLM predictions. A few-shot LLM markedly outperforms the zero-shot model, and zero-shot performance is unreliable. Among hybrids, Concat performs better than Attention-gated, yet both trail our best classical baseline. A convex RF + LLM blend, learned via bootstrap out-of-bag sampling, achieves a lower RMSE/MAE than either component and a slightly higher QWK. The Ateşman baseline performance is substantially weaker. Overall, the findings were as follows: feature-based RF remains a strong baseline, few-shot LLMs add semantic cues, blending consistently helps, and simple hybrid concatenation beats a lightweight attention gate under our small-N regime. Full article

(This article belongs to the Special Issue Machine Learning-Based Feature Extraction and Selection: 2nd Edition)

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25 pages, 5132 KB

Open AccessArticle

Collaborative Estimation of Lithium Battery State of Charge Based on the BiLSTM-AUKF Fusion Model

by Rui Wang, Lele Liu, Honghou Zhang, Qifeng Qian, Lingchao Xiao, Qiansheng Qiu, Chao Tan and Fujian Yang

Energies 2025, 18(21), 5624; https://doi.org/10.3390/en18215624 (registering DOI) - 26 Oct 2025

Abstract

To address the issue of decreased accuracy in lithium battery state of charge (SOC) estimation caused by parameter mismatches, modeling error accumulation, and sensitivity to noise, this paper proposes a collaborative estimation method. The proposed method combines a Bayesian optimization (BO)-tuned dual-input bidirectional long short-term memory network (BiLSTM) with an adaptive unscented Kalman filter (AUKF) based on the Sage–Husa adaptive strategy. First, a dual-input BiLSTM network is constructed using a multi-layer cascaded BiLSTM to extract time-dependent features. This network fuses both temporal and static features to perform an initial SOC prediction, while BO is employed to adaptively optimize the network’s hyperparameters. Second, the BiLSTM prediction outputs and the physical model are incorporated into the AUKF framework to achieve real-time iterative SOC estimation. Multi-scenario experiments conducted on the University of Maryland CALCE battery dataset demonstrated that the proposed method achieved a mean absolute error (MAE) below 0.6% and a root mean square error (RMSE) less than 0.8%. This method effectively enhances the robustness and noise immunity of SOC estimation in dynamic scenarios, providing a high-precision state estimation solution for battery management systems. Full article

16 pages, 6905 KB

Open AccessArticle

A Hybrid Fuzzy-PSO Framework for Multi-Objective Optimization of Stereolithography Process Parameters

by Mohanned M. H. AL-Khafaji, Abdulkader Ali Abdulkader Kadauw, Mustafa Mohammed Abdulrazaq, Hussein M. H. Al-Khafaji and Henning Zeidler

Micromachines 2025, 16(11), 1218; https://doi.org/10.3390/mi16111218 (registering DOI) - 26 Oct 2025

Abstract

Additive manufacturing is driving a significant change in industry, extending beyond prototyping to the inclusion of printed parts in final designs. Stereolithography (SLA) is a polymerization technique valued for producing highly detailed parts with smooth surface finishes. This study presents a hybrid intelligent framework for modeling and optimizing the SLA 3D printer process’s parameters for Acrylonitrile Butadiene Styrene (ABS) photopolymer parts. The nonlinear relationships between the process’s parameters (Orientation, Lifting Speed, Lifting Distance, Exposure Time) and multiple performance characteristics (ultimate tensile strength, yield strength, modulus of elasticity, Shore D hardness, and surface roughness), which represent complex relationships, were investigated. A Taguchi design of the experiment with an L18 orthogonal array was employed as an efficient experimental design. A novel hybrid fuzzy logic–Particle Swarm Optimization (PSO) algorithm, ARGOS (Adaptive Rule Generation with Optimized Structure), was developed to automatically generate high-accuracy Mamdani-type fuzzy inference systems (FISs) from experimental data. The algorithm starts by customizing Modified Learn From Example (MLFE) to create an initial FIS. Subsequently, the generated FIS is tuned using PSO to develop and enhance predictive accuracy. The ARGOS models provided excellent performances, achieving correlation coefficients (R²) exceeding 0.9999 for all five output responses. Once the FISs were tuned, a multi-objective optimization was carried out based on the weighted sum method. This step helped to identify a well-balanced set of parameters that optimizes the key qualities of the printed parts, ensuring that the results are not just mathematically ideal, but also genuinely helpful for real-world manufacturing. The results showed that the proposed hybrid approach is a robust and highly accurate method for the modeling and multi-objective optimization of the SLA 3D process. Full article

(This article belongs to the Special Issue Emerging Micro Manufacturing Technologies and Applications, 3rd Edition)

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24 pages, 2839 KB

Open AccessArticle

Socio-Spatial Disparities in Urban Green Space Resilience to Flooding: A 20-Year Analysis Across the Southeastern U.S

by Kexin Zhao and Xiaoying Meng

Buildings 2025, 15(21), 3866; https://doi.org/10.3390/buildings15213866 (registering DOI) - 26 Oct 2025

Abstract

While urban green spaces are integral to urban resilience, their long-term dynamics under recurrent flooding have received limited scholarly attention. This study investigates two decades of green space change across 367 counties in the southeastern United States, integrating FEMA disaster records with multi-period land cover data. Employing generalized additive and logistic regression models, the impacts of flood frequency, development intensity, and socioeconomic drivers were assessed. Flood frequency was identified as the primary determinant of urban green space loss. Each additional flood event corresponded to a 0.36% reduction in the five-year green space change rate (p < 0.01), while extreme flood frequency (≥ 10 events) was associated with an 18-fold increase in the odds of long-term degradation. Development intensity exhibited a significant non-linear effect, with loss rates culminating at moderate-to-high intensities. Furthermore, household income functioned as a significant moderator; in extremely flood-prone areas, higher income correlated with enhanced resilience (OR = 0.155, p < 0.05). These findings demonstrate that recurrent floods function as a cumulative pressure. This research highlights the necessity of equitable green infrastructure planning that integrates flood risk with the complex, moderating role of socioeconomic capacity. Full article

(This article belongs to the Section Architectural Design, Urban Science, and Real Estate)

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18 pages, 3092 KB

Open AccessArticle

Adverse-Weather Image Restoration Method Based on VMT-Net

by Zhongmin Liu, Xuewen Yu and Wenjin Hu

J. Imaging 2025, 11(11), 376; https://doi.org/10.3390/jimaging11110376 (registering DOI) - 26 Oct 2025

Abstract

To address global semantic loss, local detail blurring, and spatial–semantic conflict during image restoration under adverse weather conditions, we propose an image restoration network that integrates Mamba with Transformer architectures. We first design a Vision-Mamba–Transformer (VMT) module that combines the long-range dependency modeling of Vision Mamba with the global contextual reasoning of Transformers, facilitating the joint modeling of global structures and local details, thus mitigating information loss and detail blurring during restoration. Second, we introduce an Adaptive Content Guidance (ACG) module that employs dynamic gating and spatial–channel attention to enable effective inter-layer feature fusion, thereby enhancing cross-layer semantic consistency. Finally, we embed the VMT and ACG modules into a U-Net backbone, achieving efficient integration of multi-scale feature modeling and cross-layer fusion, significantly improving reconstruction quality under complex weather conditions. The experimental results show that on Snow100K-S/L, VMT-Net improves PSNR over the baseline by approximately 0.89 dB and 0.36 dB, with SSIM gains of about 0.91% and 0.11%, respectively. On Outdoor-Rain and Raindrop, it performs similarly to the baseline and exhibits superior detail recovery in real-world scenes. Overall, the method demonstrates robustness and strong detail restoration across diverse adverse-weather conditions. Full article

(This article belongs to the Topic Transformer and Deep Learning Applications in Image Processing)

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