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15 pages, 2136 KB  
Article
Efficient Time-Domain Dimension Reduction Methods for Simulating Stationary Stochastic Processes
by Guoyu Liu, Shiwei Yin, Xiaojiao Fu and Zixin Liu
Mathematics 2026, 14(5), 875; https://doi.org/10.3390/math14050875 - 5 Mar 2026
Abstract
The high-dimensional stochastic space caused by a large number of random variables remains a significant challenge hindering the practical application of stochastic process simulation in engineering. Although various dimension reduction techniques have been developed, their direct integration into time-domain simulation frameworks remains limited. [...] Read more.
The high-dimensional stochastic space caused by a large number of random variables remains a significant challenge hindering the practical application of stochastic process simulation in engineering. Although various dimension reduction techniques have been developed, their direct integration into time-domain simulation frameworks remains limited. To address this issue, this paper proposes two efficient time-domain dimension reduction methods for simulating stationary stochastic processes. The methods reduce the number of input random variables required for simulation to a single variable, while the randomness of the output stochastic process remains unchanged. The proposed methods are theoretically motivated by spectral decomposition of processes using two distinct strategies and explicitly incorporate the decay characteristics of the impulse response function associated with the stochastic process. Based on this, the random orthogonal functions can be naturally introduced to simulate the stationary stochastic process, which effectively resolves the high-dimensional random variables encountered in conventional time-domain simulations. Furthermore, the incorporation of a number-theoretic method enables uncertainty quantification of stochastic process samples. Numerical simulations demonstrate that the proposed methods reduce the random variable dimension from 2400 to 1 (99.95% reduction). Relative error of the simulated power spectral density remains below 2%, while computational time is reduced by approximately 4% compared with the conventional time-domain methods. These results demonstrate the effectiveness and practical applicability of the proposed approach in engineering stochastic process simulation. Full article
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19 pages, 1774 KB  
Systematic Review
Assessment of Cognitive Emotion Regulation in Gambling Disorder: A Systematic Review of the Literature
by Ioana Ioniță, Mădălina Iuliana Mușat, Bogdan Cătălin and Adela Magdalena Ciobanu
Clin. Pract. 2026, 16(3), 56; https://doi.org/10.3390/clinpract16030056 - 5 Mar 2026
Abstract
Background/Objectives: Gambling disorder (GD) is a behavioral addiction characterized by persistent and repetitive gambling behaviors that cause significant psychological distress and functional impairment. Increasing evidence indicates that difficulties in emotion regulation are a key factor in the development and persistence of GD. This [...] Read more.
Background/Objectives: Gambling disorder (GD) is a behavioral addiction characterized by persistent and repetitive gambling behaviors that cause significant psychological distress and functional impairment. Increasing evidence indicates that difficulties in emotion regulation are a key factor in the development and persistence of GD. This systematic review aimed to summarize and critically evaluate the existing literature on the relationship between emotion regulation strategies and gambling disorder, with a specific focus on studies using the Emotion Regulation Questionnaire (ERQ) and the Cognitive Emotion Regulation Questionnaire (CERQ). Methods: The review was conducted according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA 2020) guidelines. Systematic searches were performed in PubMed and Scopus databases for studies published between 25 October 2015 and 25 October 2025. The methodological quality and risk of bias of the included studies were evaluated using the Joanna Briggs Institute (JBI) Critical Appraisal Checklist and JBI Checklist for Randomized Controlled Trials. Data extraction and synthesis were performed manually by two independent reviewers. Eligible studies included adult participants (≥18 years) diagnosed with gambling disorder or pathological gambling and using the ERQ or CERQ to assess emotion regulation. Results: Nine studies met the inclusion criteria, comprising a total of 607 patients with GD. Across studies, individuals with GD consistently showed reduced cognitive reappraisal, greater expressive suppression, and higher use of maladaptive cognitive strategies such as rumination, catastrophizing, and self-blame. All studies identified impulsivity, emotion dysregulation, alexithymia, or gambling-related cognitive distortions as significant predictors of gambling severity. Neuroimaging evidence from one study further revealed altered activation of frontal regions during negative emotion regulation. Conclusions: This review highlights the central role of emotion regulation in GD. However, the limited available ERQ/CERQ studies in GD were mostly cross-sectional, limiting causal inferences. Second, samples were predominantly male, reducing generalizability to women. Finally, only one study used neurobiological measures, hindering integration of self-report and neural data. These findings emphasize the importance of integrating emotion regulation-based interventions within therapeutic programs for gambling disorder, with ERQ and CERQ being useful tools to assess the pathology. Full article
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25 pages, 3342 KB  
Article
A Novel Spectrum Recognition Model of Spatial Electromagnetic Anomalies Based on VAE-GANGP
by Bin Liu, Jiansheng Bai and Qiongyi Li
Electronics 2026, 15(5), 1062; https://doi.org/10.3390/electronics15051062 - 3 Mar 2026
Abstract
To address the issues of sample imbalance, unstable generation quality, and insufficient feature extraction in spectrum anomaly signal detection under complex electromagnetic environments, this paper proposes a VAE-GANGP identification model that integrates a Variational Autoencoder (VAE) with a Gradient Penalty-based Generative Adversarial Network [...] Read more.
To address the issues of sample imbalance, unstable generation quality, and insufficient feature extraction in spectrum anomaly signal detection under complex electromagnetic environments, this paper proposes a VAE-GANGP identification model that integrates a Variational Autoencoder (VAE) with a Gradient Penalty-based Generative Adversarial Network (GAN-GP). First, the VAE is employed to encode the original spectrum, generating structured latent features that follow a standard normal distribution. This replaces the random noise input in traditional GANs, significantly enhancing the semantic consistency of generated samples and training stability. Second, an adversarial training mechanism based on Wasserstein distance with gradient penalty (WGAN-GP) is introduced, effectively mitigating mode collapse and gradient vanishing, thereby improving the model’s capability to fit complex signal distributions. Furthermore, a multi-objective optimization function combining reconstruction error and adversarial loss is constructed, establishing an end-to-end integrated framework for feature learning, signal reconstruction, and anomaly discrimination. Experiments are conducted using a synthetic dataset comprising various modulation types and simulated environments with different signal-to-noise ratios for systematic validation. The results demonstrate that the spectrum data generated by VAE-GANGP closely matches the distribution of real signals. Under AWGN-dominated synthetic test conditions, the model achieves an anomaly detection accuracy of 98.1%. When evaluated under more realistic channel impairments (phase noise, multipath, impulsive interference), the model maintains competitive performance, outperforming existing methods and demonstrating promising potential for practical electromagnetic spectrum monitoring. Its performance significantly surpasses traditional detection methods and single deep learning models, providing a highly reliable and adaptive solution for spatial electromagnetic spectrum anomaly detection. Full article
(This article belongs to the Section Artificial Intelligence)
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17 pages, 458 KB  
Article
Acute Effects of Percussive Massage Intensity on Change-of-Direction Performance, Vertical Jump Kinetics, and Neuromuscular Performance Across Morning and Evening Sessions in Trained Male Football Players
by Özgür Eken, İlinsu Demiralp, Birgül Arslanoğlu, Tahir Volkan Aslan, İsmihan Eken, Burak Yagin and Monira I. Aldhahi
Medicina 2026, 62(3), 439; https://doi.org/10.3390/medicina62030439 - 26 Feb 2026
Viewed by 193
Abstract
Background and Objectives: Percussive massage devices (PMDs) are increasingly used as warm-up tools to enhance neuromuscular performance; however, evidence regarding the optimal intensity and its interaction with circadian variation remains limited. This study examined the acute effects of two percussive massage intensities (low: [...] Read more.
Background and Objectives: Percussive massage devices (PMDs) are increasingly used as warm-up tools to enhance neuromuscular performance; however, evidence regarding the optimal intensity and its interaction with circadian variation remains limited. This study examined the acute effects of two percussive massage intensities (low: 28 Hz; moderate: 35 Hz) compared with no massage on change-of-direction (COD) performance, vertical jump kinetics, and neuromuscular variables in trained male football players across morning and evening sessions. Materials and Methods: Eighteen trained male football players completed a randomized, counterbalanced crossover design involving three protocols (no massage, 28 Hz, and 35 Hz) performed in both morning (09:00–11:00) and evening (17:00–19:00) sessions following a standardized warm-up protocol. COD performance (T-Test and Illinois COD Test), countermovement jump height, and model-derived kinetic variables were assessed. Results: Significant main effects of the protocol were observed for T-test performance, jump height, velocity-related variables, and kinetic outcomes (p < 0.001; large effect sizes), with both percussive massage intensities outperforming the no-massage condition. Significant protocol × time-of-day interactions emerged for jump height, force, and impulse-related variables (p < 0.05), indicating greater morning-specific benefits following moderate-intensity (35 Hz) massage. The Illinois COD Test showed no significant protocol-related changes. Conclusions: Acute percussive massage enhances COD performance and vertical jump-related outcomes in trained football players. While both intensities are effective for general performance enhancement, moderate-intensity massage (35 Hz) appears to be more effective for optimizing force–time characteristics and attenuating morning-related performance decrements. These findings support the inclusion of intensity- and time-specific percussive massage strategies in warm-up routines. Full article
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21 pages, 1548 KB  
Article
Observational Comparison of Outcomes of Sandplay Therapy (SPT-SAFE) Versus Dialectical Behavior Therapy (DBT-BI) for Elementary School Students with NSSI and Suicidal Ideation: A Retrospective School-Based Study
by Hyeonjeong Kwak and Unkyoung Ahn
Behav. Sci. 2026, 16(2), 308; https://doi.org/10.3390/bs16020308 - 23 Feb 2026
Viewed by 277
Abstract
Background/Objectives: Suicidal ideation and non-suicidal self-injury (NSSI) among elementary school students represent critical public health concerns that require develop-mentally appropriate, evidence-informed school-based interventions. This study con-ducted a retrospective comparative analysis of two school-based approaches—Sandplay Therapy with Suicidal Ideation and Self-Injury-Focused Engagement (SPT-SAFE) and [...] Read more.
Background/Objectives: Suicidal ideation and non-suicidal self-injury (NSSI) among elementary school students represent critical public health concerns that require develop-mentally appropriate, evidence-informed school-based interventions. This study con-ducted a retrospective comparative analysis of two school-based approaches—Sandplay Therapy with Suicidal Ideation and Self-Injury-Focused Engagement (SPT-SAFE) and a School-based Dialectical Behavior Therapy-informed Brief Intervention (DBT-BI)—for elementary school students presenting with suicidal ideation and NSSI. The objective was to describe pre–post-changes in key outcomes within each intervention and to explore whether outcome trajectories differed between the two approaches in a non-randomized, real-world school-based setting. Methods: This retrospective study analyzed archival clinical records from 109 elementary school students (SPT-SAFE: N = 59; DBT-BI: N = 50) who received services at a school-based suicide prevention center in South Korea between 2022 and 2024. Seven validated outcome measures assessed suicidal ideation, NSSI frequency, depression, anxiety, aggression, impulsiveness, and self-concept at pre- and post-intervention. Pre–post-changes and exploratory between-group differences were examined using 2 × 2 mixed-design ANOVAs (Group × Time interaction), with baseline-adjusted ANCOVAs conducted as complementary analyses. Suicidal ideation was operationalized using the SIQ-JR total score, and NSSI was operationalized using the FASM summed frequency index. Results: Both interventions were associated with significant reductions in suicidal ideation (F = 29.98, p < 0.001, partial η2 = 0.219) and NSSI frequency (F = 15.95, p < 0.001, partial η2 = 0.130), with large within-group effect sizes and no significant Group × Time interactions. Accordingly, between-group differences were limited and should be interpreted as exploratory rather than comparative–effectiveness evidence. Modest between-group differences favoring DBT-BI were observed for self-concept outcomes (F = 4.14, p = 0.044, partial η2 = 0.037; d = −0.39). Conclusions: These findings suggest that both interventions were associated with pre–post-improvements in suicidal ideation and NSSI frequency within a school-based clinical context. Full article
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26 pages, 11745 KB  
Article
Robust Incipient Fault Diagnosis of Rolling Element Bearings Under Small-Sample Conditions Using Refined Multiscale Rating Entropy
by Shiqian Wu, Huiyu Liu and Liangliang Tao
Entropy 2026, 28(2), 240; https://doi.org/10.3390/e28020240 - 19 Feb 2026
Viewed by 175
Abstract
The operational reliability of aero-engines is critically dependent on the health of rolling element bearings, while incipient fault diagnosis remains particularly challenging under small-sample conditions. Although multiscale entropy methods are widely used for complexity analysis, conventional coarse-graining strategies suffer from severe information loss [...] Read more.
The operational reliability of aero-engines is critically dependent on the health of rolling element bearings, while incipient fault diagnosis remains particularly challenging under small-sample conditions. Although multiscale entropy methods are widely used for complexity analysis, conventional coarse-graining strategies suffer from severe information loss and unstable estimation when data are extremely limited. To address this, the primary objective of this study is to develop a robust diagnostic framework that ensures feature consistency and classification stability even with minimal training samples. Specifically, this paper proposes an integrated approach combining Refined Time-shifted Multiscale Rating Entropy (RTSMRaE) with an Animated Oat Optimization (AOO)-optimized Extreme Learning Machine (ELM). By introducing a refined time-shift operator and a dual-weight fusion mechanism, RTSMRaE effectively preserves transient impulsive features across multiple scales while suppressing stochastic fluctuations. Meanwhile, the AOO algorithm is employed to optimize the input weights and hidden biases of the ELM, alleviating performance instability caused by random initialization and improving generalization capability. Experimental validation on both laboratory-scale and real-world aviation bearing datasets demonstrates that the proposed RTSMRaE-AOO-ELM framework achieves a diagnostic accuracy of 99.47% with a standard deviation of ±0.48% using only five training samples per class. These results indicate that the proposed method offers superior diagnostic robustness and computational efficiency, providing a promising solution for intelligent condition monitoring in data-scarce industrial environments. Full article
(This article belongs to the Section Multidisciplinary Applications)
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18 pages, 319 KB  
Article
Effects of Extracorporeal Shockwave Therapy on Pain and Mobility in Client-Owned Dogs with Refractory Elbow and Stifle Osteoarthritis: A Randomized Double-Blinded Trial
by Annika Klein, Elena V. Winkler, Yury Zablotski, Monika A. Mille, Frederik Volz and Susanne K. Lauer
Animals 2026, 16(4), 541; https://doi.org/10.3390/ani16040541 - 9 Feb 2026
Viewed by 419
Abstract
Introduction: Extracorporeal shockwave therapy (ESWT) is used as an adjunctive treatment for canine osteoarthritis (OA), but its effects in dogs with treatment-refractory advanced disease remain unclear. This study compared the efficacy of one versus two sessions of focused ESWT administered approximately 28 days [...] Read more.
Introduction: Extracorporeal shockwave therapy (ESWT) is used as an adjunctive treatment for canine osteoarthritis (OA), but its effects in dogs with treatment-refractory advanced disease remain unclear. This study compared the efficacy of one versus two sessions of focused ESWT administered approximately 28 days apart in dogs with refractory elbow or stifle OA. Methods: In this randomized, double-blinded clinical trial, twenty-four client-owned dogs with treatment-refractory elbow (n = 12) or stifle (n = 12) osteoarthritis received ESWT using an identical per-session protocol (X-Trode, 1000 pulses at 0.14 mJ/mm2; PulseVet-Zomedica, Ann Arbor, MI, USA), once (Group L) or twice (Group E). Orthopedic examination, goniometric and limb circumference measurements, and kinetic gait analysis (peak vertical pressure [PVP], vertical impulse [VI]) were performed on days 0, 28, and 56. Owner questionnaires (Canine Brief Pain Inventory [CBPI], Client Specific Outcome Measures [CSOM]) were collected on days 0, 28, 56, and 84. Data were analyzed using chi-squared tests, t-tests, and mixed effects models in R. Results: Age, weight, BCS, and radiographic osteoarthritis severity did not differ between groups at baseline. Improvement was small and limited to selected parameters. Vertical impulse and limb circumference increased more consistently in Group E, whereas peak vertical pressure increased in both groups, including before ESWT in Group L. No sustained or treatment-associated improvement was detected in symmetry variables or joint range of motion. Owner-reported outcomes showed variable patterns without consistent treatment effects. ESWT was well tolerated, and no major adverse events occurred. Conclusion: ESWT produced modest, inconsistent improvements in dogs with treatment-refractory OA, with slightly more consistent effects following two sessions. Therapeutic efficacy appeared limited in this end-stage population. Full article
13 pages, 73269 KB  
Proceeding Paper
Advanced Machine Learning Approaches for Predicting ADHD in Females: A Data-Driven Study Employing the WIDS Dataset
by Parth Patil, Karthik Kamaldinni, Sanjana Patil and Sakshi Gaitonde
Comput. Sci. Math. Forum 2025, 12(1), 17; https://doi.org/10.3390/cmsf2025012017 - 3 Feb 2026
Viewed by 209
Abstract
Attention Deficit/Hyperactivity Disorder (ADHD) is a neurodevelopmental disorder that is found in both children and adults. While this disorder often continues in adulthood, diagnosis can be challenging, particularly in females. Unlike males, who are often diagnosed with ADHD due to their externalizing behaviors [...] Read more.
Attention Deficit/Hyperactivity Disorder (ADHD) is a neurodevelopmental disorder that is found in both children and adults. While this disorder often continues in adulthood, diagnosis can be challenging, particularly in females. Unlike males, who are often diagnosed with ADHD due to their externalizing behaviors (i.e., impulsive nature), most females show inattentive symptoms (i.e., in focusing, disorganization), which makes this disorder hard to detect. This paper proposes a machine learning approach to detect ADHD among females. The Wids Datathon 2025 provides three datasets: categorical data, quantitative data, and function connectomes. It contains information on 1213 participants who are seeking to take a test to detect ADHD. Categorical data includes 10 attributes, quantitative data has 19 attributes, and functional connectomes contain 19,901 attributes which are relevant to studying the participants’ overall condition. By combining both XGBoost and Random Forest, an accuracy of 79.42% was achieved. The results show that machine learning algorithms can help in improving ADHD detection in females, leading to better diagnoses in future. Full article
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11 pages, 704 KB  
Article
Effects of a Carbohydrate + Caffeine Beverage on Game Performance, Blood Glucose and Perceived Effort in Collegiate Women Soccer Players
by Andrew R. Jagim, Abby Ambrosius, Makenna Carpenter, Joesi Krieger, Lochlan Charley, Jennifer B. Fields, Margaret T. Jones and Chad Kerksick
Appl. Sci. 2026, 16(3), 1523; https://doi.org/10.3390/app16031523 - 3 Feb 2026
Viewed by 226
Abstract
Carbohydrate availability and caffeine ingestion have been shown to elicit improvements in performance independently of one another. The purpose of the study was to examine the effect of a carbohydrate + caffeine beverage on performance and perceived effort in soccer players. Forty-three collegiate [...] Read more.
Carbohydrate availability and caffeine ingestion have been shown to elicit improvements in performance independently of one another. The purpose of the study was to examine the effect of a carbohydrate + caffeine beverage on performance and perceived effort in soccer players. Forty-three collegiate women’s soccer athletes were recruited to participate during a single day of simulated match play, in which each team played once. Athletes consumed either a carbohydrate + caffeine (Experimental) beverage or a control (Control) beverage (flavored water) during half-time in a double-blind, placebo-controlled, randomized control trial design. Prior to and after each game, Ratings of Perceived Exertion (RPE) and blood glucose levels were assessed. Heart rate, training impulse (TRIMP), total distance covered, high-speed distance, and velocity were recorded. Blood glucose levels after the match simulation were positively associated with total distance (r = 0.434; p = 0.01), distance per minute (r = 0.439; p < 0.01), average velocity (r = 0.438; p = 0.01), and TRIMP (r = 0.404; p = 0.018) during the second half. There was a significant main effect for half regarding blood glucose (p < 0.001), total distance (p < 0.001), high-speed distance (p < 0.001), and TRIMP (p = 0.046). There was a significant half × condition effect for blood glucose (p = 0.05). Pairwise comparisons indicated the Experimental beverage condition resulted in a +27 mg/dL (95% CI: −3.6, 58.8) difference compared to the Control beverage following the 2nd Half. In the current study, consumption of the carbohydrate + caffeine beverage during half-time resulted in higher blood glucose levels post-game compared to placebo; however, the experimental beverage did not influence the total distance covered, average velocities, average heart rate, or TRIMP values during the second half of simulated match play. Full article
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17 pages, 2842 KB  
Article
Using Neural Networks to Generate a Basis for OFDM Acoustic Signal Decomposition in Non-Stationary Underwater Media to Provide for Reliability and Energy Efficiency
by Aleksandr Yu. Rodionov, Lyubov G. Statsenko, Andrey A. Chusov, Denis A. Kuzin and Mariia M. Smirnova
Acoustics 2026, 8(1), 10; https://doi.org/10.3390/acoustics8010010 - 2 Feb 2026
Viewed by 259
Abstract
The high peak-to-average power ratio (PAPR) in classical high-speed digital data transmission systems with orthogonal frequency division multiplexing (OFDM) limits energy efficiency and communication range. This paper proposes a method for randomizing OFDM signals via frequency coding using synthesized pseudorandom sequences with improved [...] Read more.
The high peak-to-average power ratio (PAPR) in classical high-speed digital data transmission systems with orthogonal frequency division multiplexing (OFDM) limits energy efficiency and communication range. This paper proposes a method for randomizing OFDM signals via frequency coding using synthesized pseudorandom sequences with improved autocorrelation properties, obtained through machine learning, to minimize PAPR in complex, non-stationary hydroacoustic channels for communicating with underwater robotic systems. A neural network architecture was developed and trained to generate codes of up to 150 elements long based on an analysis of patterns in previously found best short sequences. The obtained class of OFDM signals does not require regular and accurate estimation of channel parameters while remaining resistant to various types of impulse noise, Doppler shifts, and significant multipath interference typical of the underwater environment. The attained spectral efficiency values (up to 0.5 bits/s/Hz) are relatively high for existing hydroacoustic communication systems. It has been shown that the peak power of such multi-frequency information transmission systems can be effectively reduced by an average of 5–10 dB, which allows for an increase in the communication range compared to classical OFDM methods in non-stationary hydrological conditions at acceptable bit error rates (from 10−2 to 10−3 and less). The effectiveness of the proposed methods of randomization with synthesized codes and frequency coding for OFDM signals was confirmed by field experiments at sea on the shelf, over distances of up to 4.2 km, with sea waves of up to 2–3 Beaufort units and mutual movement of the transmitter and receiver. Full article
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21 pages, 9088 KB  
Article
GMM-Enhanced Mixture-of-Experts Deep Learning for Impulsive Dam-Break Overtopping at Dikes
by Hanze Li, Yazhou Fan, Luqi Wang, Xinhai Zhang, Xian Liu and Liang Wang
Water 2026, 18(3), 311; https://doi.org/10.3390/w18030311 - 26 Jan 2026
Viewed by 281
Abstract
Impulsive overtopping generated by dam-break surges is a critical hazard for dikes and flood-protection embankments, especially in reservoirs and mountainous catchments. Unlike classical coastal wave overtopping, which is governed by long, irregular wave trains and usually characterized by mean overtopping discharge over many [...] Read more.
Impulsive overtopping generated by dam-break surges is a critical hazard for dikes and flood-protection embankments, especially in reservoirs and mountainous catchments. Unlike classical coastal wave overtopping, which is governed by long, irregular wave trains and usually characterized by mean overtopping discharge over many waves, these dam-break-type events are dominated by one or a few strongly nonlinear bores with highly transient overtopping heights. Accurately predicting the resulting overtopping levels under such impulsive flows is therefore important for flood-risk assessment and emergency planning. Conventional cluster-then-predict approaches, which have been proposed in recent years, often first partition data into subgroups and then train separate models for each cluster. However, these methods often suffer from rigid boundaries and ignore the uncertainty information contained in clustering results. To overcome these limitations, we propose a GMM+MoE framework that integrates Gaussian Mixture Model (GMM) soft clustering with a Mixture-of-Experts (MoE) predictor. GMM provides posterior probabilities of regime membership, which are used by the MoE gating mechanism to adaptively assign expert models. Using SPH-simulated overtopping data with physically interpretable dimensionless parameters, the framework is benchmarked against XGBoost, GMM+XGBoost, MoE, and Random Forest. Results show that GMM+MoE achieves the highest accuracy (R2=0.9638 on the testing dataset) and the most centralized residual distribution, confirming its robustness. Furthermore, SHAP-based feature attribution reveals that relative propagation distance and wave height are the dominant drivers of overtopping, providing physically consistent explanations. This demonstrates that combining soft clustering with adaptive expert allocation not only improves accuracy but also enhances interpretability, offering a practical tool for dike safety assessment and flood-risk management in reservoirs and mountain river valleys. Full article
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34 pages, 5362 KB  
Article
Radial Extracorporeal Shock Wave Therapy Versus Multimodal Physical Therapy in Non-Traumatic (Degenerative) Rotator Cuff Tendinopathy with Partial Supraspinatus Tear: A Randomized Controlled Trial
by Zheng Wang, Lan Tang, Ni Wang, Lihua Huang, Christoph Schmitz, Jun Zhou, Yingjie Zhao, Kang Chen and Yanhong Ma
J. Clin. Med. 2026, 15(2), 471; https://doi.org/10.3390/jcm15020471 - 7 Jan 2026
Viewed by 1083
Abstract
Background/Objectives: Non-traumatic (degenerative) rotator cuff tendinopathy with partial supraspinatus tear (NT-RCTT) is a common source of shoulder pain and disability. Comparative evidence between radial extracorporeal shock wave therapy (rESWT) and multimodal physical therapy modalities (PTMs) remains scarce. Methods: In this single-center randomized controlled [...] Read more.
Background/Objectives: Non-traumatic (degenerative) rotator cuff tendinopathy with partial supraspinatus tear (NT-RCTT) is a common source of shoulder pain and disability. Comparative evidence between radial extracorporeal shock wave therapy (rESWT) and multimodal physical therapy modalities (PTMs) remains scarce. Methods: In this single-center randomized controlled trial, 60 adults with MRI-confirmed NT-RCTT were assigned (1:1) to rESWT (one session weekly for six weeks; 2000 impulses per session, 2 bar air pressure, positive energy flux density 0.08 mJ/mm2; 8 impulses per second) or a multimodal PTM program (interferential current, shortwave diathermy and magnetothermal therapy; five sessions weekly for six weeks). All participants performed standardized home exercises. The primary outcome was the American Shoulder and Elbow Surgeons (ASES) total score; secondary outcomes included pain (visual analog scale, VAS), satisfaction, range of motion (ROM), supraspinatus tendon (ST) thickness and acromiohumeral distance (AHD). Assessments were conducted at baseline, and at week 6 (W6) and week 12 (W12) post-baseline. Results: Both interventions significantly improved all outcomes, but rESWT produced greater and faster effects. Mean ASES total scores increased by 31 ± 5 points with rESWT versus 26 ± 6 with PTMs (p < 0.05). VAS pain decreased from 5.2 ± 0.7 to 1.0 ± 0.7 with rESWT and from 5.2 ± 0.8 to 1.7 ± 0.8 with PTMs (p < 0.01). rESWT achieved higher satisfaction and larger gains in abduction, flexion and external rotation. Ultrasound showed reduced ST thickness and increased AHD after rESWT but not after PTMs. No serious adverse events occurred. Conclusions: rESWT yielded superior pain relief, functional recovery and tendon remodeling compared with a multimodal PTM program, with markedly lower treatment time and excellent tolerability. Full article
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28 pages, 2234 KB  
Article
Qualitative Analysis and Applications of Fractional Stochastic Systems with Non-Instantaneous Impulses
by Muhammad Imran Liaqat and Abdelhamid Mohammed Djaouti
Mathematics 2026, 14(2), 224; https://doi.org/10.3390/math14020224 - 7 Jan 2026
Viewed by 199
Abstract
Fractional stochastic differential Equations (FSDEs) with time delays and non-instantaneous impulses describe dynamical systems whose evolution relies not only on their current state but also on their historical context, random fluctuations, and impulsive effects that manifest over finite intervals rather than occurring instantaneously. [...] Read more.
Fractional stochastic differential Equations (FSDEs) with time delays and non-instantaneous impulses describe dynamical systems whose evolution relies not only on their current state but also on their historical context, random fluctuations, and impulsive effects that manifest over finite intervals rather than occurring instantaneously. This combination of features offers a more precise framework for capturing critical aspects of many real-world processes. Recent findings demonstrate the existence, uniqueness, and Ulam–Hyers stability of standard fractional stochastic systems. In this study, we extend these results to include systems characterized by FSDEs that incorporate time delays and non-instantaneous impulses. We prove the existence and uniqueness of the solution for this system using Krasnoselskii’s and Banach’s fixed-point theorems. Additionally, we present findings related to Ulam–Hyers stability. To illustrate the practical application of our results, we develop a population model that incorporates memory effects, randomness, and non-instantaneous impulses. This model is solved numerically via the Euler–Maruyama method, and graphical simulations effectively depict the dynamic behavior of the system. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems, 2nd Edition)
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27 pages, 5287 KB  
Review
Recent Advances in Experimental and Numerical Studies on Cloud and Erosion Behaviors in Cavitating Jets
by Nobuyuki Fujisawa
Fluids 2026, 11(1), 14; https://doi.org/10.3390/fluids11010014 - 31 Dec 2025
Viewed by 566
Abstract
Recent advances in experimental techniques for visualizing cloud behavior, pit formation, and erosion in cavitating jets have been reviewed. To characterize the erosion behavior of cavitating jets and clarify their erosion mechanisms, various experimental techniques—such as high-speed imaging, frame difference method, proper orthogonal [...] Read more.
Recent advances in experimental techniques for visualizing cloud behavior, pit formation, and erosion in cavitating jets have been reviewed. To characterize the erosion behavior of cavitating jets and clarify their erosion mechanisms, various experimental techniques—such as high-speed imaging, frame difference method, proper orthogonal decomposition (POD) analysis, pit sensors, polyvinylidene fluoride (PVDF) sensors, laser schlieren imaging, and cross schlieren imaging—have been developed. Experimental results demonstrated that the erosion mechanism of cavitating jets is highly correlated with periodic cloud behaviors, including the growth, shrinkage, and collapse, which generate impulsive pressure on the wall material. This pressure initiates random pits on the wall surface and is associated with the generation of microjets caused by the reentrant-jet mechanism during cloud collapse near the wall. Several shockwaves were generated at peak impulsive pressures when the cavitation cloud collapsed, and a microjet was formed. Some of these experimental findings were successfully reproduced in recent numerical studies; however, further numerical modeling of erosion behavior in cavitating jets is still needed. Furthermore, the behavior of cavitating jets on rough walls requires future study, as the erosion rate is significantly higher than that on smooth walls. Full article
(This article belongs to the Special Issue Feature Reviews for Fluids 2025–2026)
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17 pages, 1132 KB  
Article
Multifractal Random Walk Model for Bursty Impulsive PLC Noise
by Steven O. Awino and Bakhe Nleya
Appl. Sci. 2026, 16(1), 49; https://doi.org/10.3390/app16010049 - 20 Dec 2025
Viewed by 300
Abstract
The indoor low-voltage power line network is characterized by highly irregular interferences, where background noise coexists with bursty impulsive noise originating from household appliances and switching events. Traditional noise models, which are considered monofractal models, often fail to reproduce the clustering, intermittency, and [...] Read more.
The indoor low-voltage power line network is characterized by highly irregular interferences, where background noise coexists with bursty impulsive noise originating from household appliances and switching events. Traditional noise models, which are considered monofractal models, often fail to reproduce the clustering, intermittency, and long-range dependence seen in measurement data. In this paper, a Multifractal Random Walk (MRW) framework tailored for Power Line Communication (PLC) noise modelling is developed. MRW is a continuous time limit process based on discrete-time random walks with stochastic log-normal variance. As such, the formulated MRW framework introduces a stochastic volatility component that modulates Gaussian increments, thus generating heavy-tailed statistics and multifractal scaling laws which are consistent with the measured PLC noise data. Empirical validation is carried out through structure function analysis and covariance of log-amplitudes, both of which reveal scaling characteristics that align well with MRW-simulated predictions. This proposed model captures both the bursty nature and correlation structure of impulsive PLC noise more effectively as compared to the conventional monofractal approaches, thereby providing a mathematically grounded framework for accurate noise generation and the robust system-level performance evaluation of PLC networks. Full article
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