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23 pages, 1354 KB  
Article
Unsupervised Deep Representation Learning and Probabilistic Clustering for the Systems-Level Discovery of Germline Mutation Signatures in Pediatric Cancers
by Fahimeh Palizban, Michael E. March, Xiang Wang, James Snyder, Fengxiang Wang, Frank Mentch, Yeshwanth Mahesh, Alexandria Thomas, Deborah J. Watson, Huiqi Qu, John Connolly, Amir Hossein Saeidian, Hassan Vahidnezhad, Joseph Glessner and Hakon Hakonarson
Biomedicines 2026, 14(7), 1438; https://doi.org/10.3390/biomedicines14071438 (registering DOI) - 24 Jun 2026
Abstract
Background/Aims: While pathogenic germline variants play a critical role in pediatric cancer susceptibility, traditional clinical genetics primarily focuses on single-gene interpretations. Transitioning to a systems-level analysis of inherited variation can uncover shared biological vulnerabilities, informing genetic counseling, surveillance, and targeted therapeutics. This study [...] Read more.
Background/Aims: While pathogenic germline variants play a critical role in pediatric cancer susceptibility, traditional clinical genetics primarily focuses on single-gene interpretations. Transitioning to a systems-level analysis of inherited variation can uncover shared biological vulnerabilities, informing genetic counseling, surveillance, and targeted therapeutics. This study aims to implement an unsupervised machine learning framework to identify and characterize Germline Mutation Signatures (GMS) across diverse pediatric malignancies, elucidating latent genomic patterns that reveal shared oncogenic mechanisms. Methods: We analyzed germline whole-exome and whole-genome sequencing (WES/WGS) data from a retrospective cohort of 420 pediatric cancer patients and matched non-cancer controls. Variants were deeply annotated to capture multi-dimensional features, including predicted pathogenicity, splice-site disruption, regulatory impact, population frequency, and sequence context. To enable robust modeling, we integrated an augmented feature set encompassing evolutionary constraint, loss-of-function intolerance, and compositionally normalized substitution spectra. These high-dimensional annotations were processed using a deep autoencoder for non-linear representation learning, followed by Gaussian Mixture Modeling (GMM) of the latent space. Results: The framework delineated 13 signatures (GMS1–GMS13), yielding an optimal Davies–Bouldin index of 1.051. These signatures map to fundamental biological processes, including DNA repair deficiencies, transcription-coupled damage, replication stress, and aberrant RNA regulation. Crucially, these GMSs transcend traditional tissue-of-origin classifications, manifesting across multiple distinct cancer types. This observation indicates convergent germline etiologies and suggests potential shared susceptibilities to pathway-directed therapies. Conclusions: The discovery of these cross-cancer signatures provides a scalable, biologically interpretable framework for decoding inherited pediatric cancer risk. While the therapeutic mapping networks identified are currently exploratory and serve as a hypothesis-generating foundation, this deep learning-driven paradigm establishes a robust basis for stratified precision medicine. Pending prospective clinical validation, this approach holds significant translational potential to move beyond single-gene paradigms toward unified, systems-level precision oncology strategies. Full article
(This article belongs to the Section Cancer Biology and Oncology)
13 pages, 1332 KB  
Article
Practical 3D Reconstruction and 3D Printing of Veterinary CT Scans in Small Animals: A Technical Demonstration with Reader-Based Validation in Canine Cranial Trauma
by Yuan Chai and Luxin Lou
Vet. Sci. 2026, 13(7), 610; https://doi.org/10.3390/vetsci13070610 (registering DOI) - 24 Jun 2026
Abstract
Traumatic fractures are common in small animal emergency care, yet subtle fracture lines may be difficult to identify accurately using routine three-dimensional reconstruction workflows, particularly when access to specialized software is limited. This study describes the use of the open-source platform Three-Dimensional Slicer [...] Read more.
Traumatic fractures are common in small animal emergency care, yet subtle fracture lines may be difficult to identify accurately using routine three-dimensional reconstruction workflows, particularly when access to specialized software is limited. This study describes the use of the open-source platform Three-Dimensional Slicer for computed tomography-based reconstruction and three-dimensional printing in a small dog with cranial trauma, with emphasis on documenting a practical and reproducible workflow through voxel resampling. Imaging data were imported into the software, bone structures were segmented using a rapid workflow, voxel spacing was resampled for smoother surface visualization by volume resampling, and the reconstructed model was processed for physical printing. Digital models of different resolutions were generated within minutes, and a life-size skull model was successfully fabricated using fused deposition modeling in less than three hours at a material cost of under one United States dollar. The enhanced model provided an intuitive representation of fracture morphology and spatial relationships compared with routine reconstruction alone. These findings demonstrate that open-source software combined with low-cost printing can provide a rapid, affordable, and user-friendly approach for practical skeletal reconstruction in small animals, with practical value for fracture assessment, preoperative planning, and broader use in resource-limited veterinary settings. Full article
(This article belongs to the Special Issue Medical Imaging in Veterinary Musculoskeletal Diagnosis)
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24 pages, 8059 KB  
Article
Information-Theoretic Channel Selection and Spatiotemporal Deep Learning for Early Fault Detection in Microsatellite Thermal Control Systems
by Weijian Pang, Jun Zhou, Jingwen Xu and Xinian Zhi
Entropy 2026, 28(7), 725; https://doi.org/10.3390/e28070725 (registering DOI) - 24 Jun 2026
Abstract
Early fault detection in microsatellite thermal control systems (TCS) faces fundamental challenges: high-dimensional redundant telemetry channels, overlapping multi-scale periodicities that obscure anomaly signatures, and severely limited daily data downlink (1–2 passes per day) that restricts the temporal window for diagnosis. Existing data-driven approaches [...] Read more.
Early fault detection in microsatellite thermal control systems (TCS) faces fundamental challenges: high-dimensional redundant telemetry channels, overlapping multi-scale periodicities that obscure anomaly signatures, and severely limited daily data downlink (1–2 passes per day) that restricts the temporal window for diagnosis. Existing data-driven approaches either rely on supervised learning, requiring labeled fault data that are scarce in practice, or employ univariate analysis that fails to capture inter-sensor spatial correlations. To address these limitations, this paper introduces a hybrid framework integrating information-theoretic feature selection and spatiotemporal deep learning. The Generalized Maximum Information Coefficient (GMIC) quantifies nonlinear dependencies between temperature channels for key channel selection, reducing dimensionality by 82% while preserving diagnostic information. A dual-level Seasonal Trend Decomposition (STL) method disentangles orbital-periodic dynamics from diurnal cycles, effectively isolating distinct thermal characteristics at multiple timescales. Each decomposed component is modeled using Convolutional Neural Network–Long Short-Term Memory (CNN-LSTM) networks to capture spatiotemporal dependencies for accurate temperature prediction. An adaptive threshold-based weighted error fusion mechanism enables early fault detection within a single day of telemetry data. Experimental validation on real satellite telemetry data demonstrates that the proposed framework achieves high-precision fault detection across multiple fault types using a minimal set of temperature channels, significantly outperforming existing benchmarks in both prediction accuracy and detection reliability. Full article
(This article belongs to the Section Signal and Data Analysis)
25 pages, 1136 KB  
Article
Traffic Characteristics-Guided Progressive Method for Fixed-Time Traffic Signal Optimization
by Haichao Guo, Yuanhao Hu, Ziru Zhao and Yunpeng Wu
Electronics 2026, 15(13), 2786; https://doi.org/10.3390/electronics15132786 (registering DOI) - 24 Jun 2026
Abstract
In the field of urban traffic management, optimizing traffic signals at intersections is crucial for enhancing traffic flow efficiency. Despite advances in intelligent traffic signal control strategies through deep reinforcement learning (DRL), practical deployment challenges persist, such as abrupt changes in signal phases [...] Read more.
In the field of urban traffic management, optimizing traffic signals at intersections is crucial for enhancing traffic flow efficiency. Despite advances in intelligent traffic signal control strategies through deep reinforcement learning (DRL), practical deployment challenges persist, such as abrupt changes in signal phases and significant hardware costs. This paper proposes a novel Traffic Characteristics-Guided Progressive optimization (TCGP) method that builds on classical fixed-time traffic signals. It is based on the classic fixed-time and quickly optimizes the green time ratio of intersection traffic lights by integrating the relationship between green light duration and traffic flow. Then, it efficiently explores the traffic signal cycle duration of a single intersection. Using a progressive optimization strategy, TCGP addresses the “curse of dimensionality” problem caused by a large number of intersections. TCGP ensures compatibility with traditional control methods and offers performance comparable to state-of-the-art DRL approaches, with competitive stability and computational efficiency. Evaluations with public datasets and real traffic data from Zhengzhou, Henan, China, confirm TCGP’s competitive performance and adaptability. This contributes fresh perspectives to the modernization of urban traffic systems. Full article
28 pages, 1063 KB  
Article
Automatic Oral Cancer Detection Using Improved Honey Badger Algorithm-Based Feature Selection
by Nebras Sobahi, Yagmur Olmez, Osman Fatih Koparır, Muammer Turkoglu, Adalet Çelebi, Yazyd Alghamedi and Abdulkadir Şengür
Diagnostics 2026, 16(13), 1969; https://doi.org/10.3390/diagnostics16131969 (registering DOI) - 24 Jun 2026
Abstract
Background/Objectives: Oral cancer is one of the most common types of cancer, with high mortality rates if not detected early. Traditional diagnostic methods based on clinical examination rely on experience, leading to delays in early and reliable diagnosis. In recent years, medical imaging [...] Read more.
Background/Objectives: Oral cancer is one of the most common types of cancer, with high mortality rates if not detected early. Traditional diagnostic methods based on clinical examination rely on experience, leading to delays in early and reliable diagnosis. In recent years, medical imaging and AI-based computer-aided diagnostic systems have shown promising results in the automated identification of oral cancer. In particular, the efficient management of high-dimensional feature spaces in machine learning and deep learning approaches directly impacts classification performance. In this context, metaheuristic-based feature selection technics is a critical component because of eliminating redundant and irrelevant features. To address these challenges, this study proposes a metaheuristic-based feature selection method to reduce feature dimensionality and enhance the classification performance of oral cancer detection. Methods: This study proposes an improved Honey Badger Algorithm-based feature selection approach for the automated detection of oral cancer. In the proposed method, the distance vector used in the HBA method has been redefined to improve the balance between exploration and exploitation. Additionally, a new Cauchy mutation-based migration strategy was integrated into the proposed method to increase diversity in the search space and avoid getting stuck in local minima. The continuous-valued iHBA method was discretized with a modified sin–cos transfer function for feature selection. Oral cancer images were filtered using the CLAHE method, and after extracting deep features with the ResNet50 architecture, the proposed metaheuristic-based method was used to select discriminative features. Results: The proposed method was first tested for reliability and limitations through repeated runs on problems with different characteristics, such as unimodal and multimodal classical test functions. Then, the method was applied to extract significant features for oral cancer detection using a Histopathological Imaging Database containing 1224 histopathological oral tissue images at 100× and 400× magnification levels from 230 patients. The proposed approach was assessed in terms of accuracy, precision, recall, F1-score, and convergence curves in comparison with various classical feature selection techniques, such as wrapper-based, filter-based, and embedded-based methods, as well as other metaheuristic-based methods. The experimental results demonstrated that the suggested strategy outperformed both traditional feature selection techniques and alternative metaheuristic approaches. Conclusions: The effectiveness of the proposed method in improving diagnostic accuracy was evaluated through comprehensive experimental analyses. The obtained findings show that the proposed iHBA-based feature selection approach can reduce feature dimensionality, eliminate redundant and irrelevant features, and improve the classification performance of oral cancer detection. Therefore, the proposed method provides an effective and competitive computer-aided diagnostic framework for the automated classification of histopathological oral cancer images. Full article
(This article belongs to the Section Machine Learning and Artificial Intelligence in Diagnostics)
31 pages, 6618 KB  
Review
Perovskite Manganites: An Overview of Synthesis, Classification, Characterization, and Applications
by Marzhan Nurbekova, Mukhametkali Mataev, Moldir Abdraimova, Zhanar Tursyn, Zhadyra Durmenbayeva and Zamira Sarsenbaeva
Int. J. Mol. Sci. 2026, 27(13), 5709; https://doi.org/10.3390/ijms27135709 (registering DOI) - 24 Jun 2026
Abstract
Perovskite manganites (AMnO3) and perovskite-like manganites (A’1−xAxMnO3) are complex oxide materials that have attracted significant attention from the scientific community in recent years due to their structural flexibility, mixed-valence state, tunable electronic configuration, and multifunctional [...] Read more.
Perovskite manganites (AMnO3) and perovskite-like manganites (A’1−xAxMnO3) are complex oxide materials that have attracted significant attention from the scientific community in recent years due to their structural flexibility, mixed-valence state, tunable electronic configuration, and multifunctional properties. This review systematically analyzes the synthesis methods, structural classification, and physicochemical characterization of perovskite manganites, as well as their magnetic, optical, electrical, dielectric, and catalytic properties. The influence of solid-state reactions, sol–gel, Pechini, hydrothermal, co-precipitation, microwave, and other mild chemical approaches on phase purity, morphology, particle size, and oxygen stoichiometry was examined. The structural diversity of perovskite and perovskite-like manganites, including simple ABO3, double perovskites, multilayer, and low-dimensional systems, was characterized in relation to their functional properties. The review discussed the capabilities of methods for synthesizing and analyzing morphological properties, demonstrating the role of doping, cation substitution, oxygen vacancies, and Jahn–Teller distortions in controlling material properties. Prospects for the application of perovskite manganites in spintronics, magnetocaloric cooling, photocatalysis, gas-sensing devices, and energy conversion and storage systems were analyzed. This review highlights the structure–property–application relationship in perovskite manganites. Full article
22 pages, 11565 KB  
Article
Three-Dimensional Mixed-Mode Fracture Analysis in Finite Structures Using a Generalized Domain Integral: Crack Front Energy Partition and Thickness Effects
by Soliman El kabir, Rostand Moutou Pitti and Naman Recho
Appl. Sci. 2026, 16(13), 6347; https://doi.org/10.3390/app16136347 (registering DOI) - 24 Jun 2026
Abstract
This paper presents a three-dimensional generalization of the M-integral, formulated as an interaction integral based on a bilinear strain energy density, for the mixed-mode decoupling of crack front energies in finite structural components. The proposed Mθ3D integral combines real and [...] Read more.
This paper presents a three-dimensional generalization of the M-integral, formulated as an interaction integral based on a bilinear strain energy density, for the mixed-mode decoupling of crack front energies in finite structural components. The proposed Mθ3D integral combines real and virtual mechanical fields within a local spherical reference frame, enabling the separate evaluation of mode I (opening), mode II (in-plane shear) and mode III (out-of-plane shear) energy release rates along arbitrary crack front lines. The theoretical framework, derived from Noether’s theorem and the virtual work principle, is implemented in the Cast3M finite element code using a toroidal integration domain with a local theta weighting function. Numerical validations are conducted on the Mixed-Mode Crack Growth (MMCG) specimen, a geometry representative of structural components subjected to combined tension and shear. Three key findings are demonstrated: (i) practical domain independence is achieved for all three fracture modes; (ii) the three-dimensional approach converges to the plane-stress solution for thin specimens and reveals significant deviations from plane-strain assumptions; (iii) even under nominally mode I + II loading, a non-negligible mode III component emerges due to Poisson-induced out-of-plane effects, with magnitude increasing at free surfaces and for thicker geometries. These results indicate that finite-thickness and out-of-plane effects can significantly affect the partition of fracture energy between modes. For the MMCG configuration investigated here, the three-dimensional formulation shows the limitations of two-dimensional assumptions and provides an energetic basis for the analysis of mixed-mode fracture in finite-thickness components. Full article
(This article belongs to the Special Issue Application of Fracture Mechanics in Structures)
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35 pages, 4742 KB  
Review
Advances in Modeling Multiple Myeloma Within the Bone Marrow Tumor Microenvironment for Exploration of Current and Emerging Therapies
by Charlotte E. J. Toomes, Oliver G. Best, Timothy Hollenberg, Rose Turner, Claudine S. Bonder and Barbara J. McClure
Cancers 2026, 18(13), 2050; https://doi.org/10.3390/cancers18132050 (registering DOI) - 24 Jun 2026
Abstract
Multiple Myeloma (MM) is a hematological malignancy characterized by the clonal proliferation and survival of neoplastic plasma cells (PCs) within the bone marrow (BM), where disease progression is critically supported by interactions with the BM tumor microenvironment (TME). Despite significant advances in therapeutic [...] Read more.
Multiple Myeloma (MM) is a hematological malignancy characterized by the clonal proliferation and survival of neoplastic plasma cells (PCs) within the bone marrow (BM), where disease progression is critically supported by interactions with the BM tumor microenvironment (TME). Despite significant advances in therapeutic strategies, MM remains incurable, underscoring the need for improved preclinical models to better understand the disease biology and therapeutic response. This review summarizes current and emerging MM treatment approaches and critically examines the development of models designed to more accurately recapitulate interactions between MM-PCs and the surrounding BM niche. We describe established and emerging modeling platforms, with emphasis on advanced three-dimensional (3D) culture systems and highlight their unique contributions to the preclinical assessment of both existing and novel therapies. The advantages of 3D models, including in vitro and in silico systems, over traditional two-dimensional (2D) models are discussed, alongside a comparative evaluation of scaffold-free and scaffold-based approaches. In addition, the benefits and recent advances in the customization of BM niche simulation using microfluidic technologies and organ-on-a-chip platforms are reviewed. The application of 3D models in MM research is increasingly enabling the study of disease pathogenesis, progression, drug resistance and precision-medicine approaches (informed by biomarker discovery). Although standardized preclinical approaches for evaluating MM therapeutics are currently lacking, the growing imperative to reduce reliance on preclinical animal models highlights the importance of alternate systems. Consequently, the development and adoption of physiologically relevant models that accurately recapitulate MM-PC interactions with the BM TME will be critical for advancing future therapeutic strategies in MM. Full article
(This article belongs to the Special Issue Myeloma and Immunology)
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33 pages, 18461 KB  
Article
Measuring Built Environment Restorativeness and Uncovering Nonlinear Mechanisms via Deep Learning and Multi-Source Visual Perception Data: A Youth-Centered Study in Changsha
by Zhihuan Huang, Jinying Lin, Zhe Zhang and Yu Wang
Buildings 2026, 16(13), 2510; https://doi.org/10.3390/buildings16132510 (registering DOI) - 24 Jun 2026
Abstract
Contemporary buildings and urban spaces are increasingly expected to support psychological well-being—a quality often termed “restorativeness.” Conventional approaches to quantifying restorativeness rely on subjective surveys or coarse green metrics, failing to capture how specific building morphologies and street-level visual configurations shape restorative experiences, [...] Read more.
Contemporary buildings and urban spaces are increasingly expected to support psychological well-being—a quality often termed “restorativeness.” Conventional approaches to quantifying restorativeness rely on subjective surveys or coarse green metrics, failing to capture how specific building morphologies and street-level visual configurations shape restorative experiences, particularly for stress-prone groups such as young adults. This study develops a deep-learning-driven framework linking building visual elements to youth-specific perceived restorativeness, using Changsha, China, as a testbed. The framework comprises three AI-powered modules: the TrueSkill algorithm trains a deep learning model to predict six dimensions of youth perception (e.g., beautiful, clean, safe) from pairwise comparisons of street view images; the Mask2Former architecture segments street-level imagery into 18 building and street attributes; and the XGBoost-SHAP pipeline uncovers nonlinear associations and threshold-like patterns between these attributes and the composite Built Environment Restorativeness Index (BERI). Results reveal three key insights: tree coverage shows a sustained positive association without saturation; building density exhibits a weakening association at high levels, suggesting possible saturation; and road proportion follows a bidirectional pattern, shifting from negative to positive beyond a certain range. Spatially, high BERI zones concentrate where ecological assets and diverse building functions co-occur, while youth perception exhibits systematic mismatches (e.g., “beautiful but not clean,” “safe but not lively”), traceable to imbalances in building form, street furniture, and commercial mix. These findings advance AI-assisted evaluation of built environments by shifting from one-dimensional metrics to interpretable, design-relevant diagnostics, offering a replicable evidence base for crafting youth-responsive buildings and streets. Full article
19 pages, 2720 KB  
Article
Evaluation of Travel–Time Definitions for Thermal Tracer Tomography Under Varying Data Density: A Laboratory Sandbox Study
by Yang Song, Rui Hu, Lirui Fan and Huiyang Qiu
Water 2026, 18(13), 1543; https://doi.org/10.3390/w18131543 (registering DOI) - 24 Jun 2026
Abstract
Travel–time-based thermal tracer tomography (TTT) has emerged as a promising technique for characterizing aquifer heterogeneity. However, the influence of travel–time definitions and data density on inversion performance is not well understood. In this study, we present a controlled two-dimensional sandbox experiment designed to [...] Read more.
Travel–time-based thermal tracer tomography (TTT) has emerged as a promising technique for characterizing aquifer heterogeneity. However, the influence of travel–time definitions and data density on inversion performance is not well understood. In this study, we present a controlled two-dimensional sandbox experiment designed to systematically investigate three travel–time definitions (early-time t10, intermediate t50, and peak-time tpeak) under data-rich (32 travel times) and data-sparse (10 travel times) conditions. The obtained hydraulic conductivity (K) fields are benchmarked against permeameter measurements and a geostatistical inversion that assimilates dense steady-state head observations. The results demonstrate that all three travel–time definitions satisfactorily reproduce the primary layered heterogeneity when abundant travel–time data are available, with t50 and tpeak providing marginally better structural fidelity under data-rich conditions. However, only the early-time t10 definition preserves the spatial continuity of dominant geological structures under data-sparse conditions, exhibiting superior robustness. All TTT inversions systematically underestimate the K ranges and exhibit pronounced range compression, whereas the geostatistical inversion overestimates K and introduces spurious high-value extremes. Forward thermal transport simulations reveal that TTT-derived K fields yield systematically delayed thermal breakthroughs, while the geostatistical inversion yields more accurate predictions. These findings highlight the critical interplay between travel–time diagnostics and observation density. They also underscore the necessity of jointly inverting hydraulic and thermal data to overcome the limitations of single-dataset approaches for reliable aquifer characterization and transport prediction. Full article
(This article belongs to the Special Issue Hydrogeophysical Methods and Hydrogeological Models)
25 pages, 666 KB  
Review
Statistical Methods for Detecting Nonlinear Relationships in Gene Expression and Omics Data: A Review
by Łukasz Huminiecki
Int. J. Mol. Sci. 2026, 27(13), 5700; https://doi.org/10.3390/ijms27135700 (registering DOI) - 24 Jun 2026
Abstract
High-throughput technologies such as RNA-seq and single-cell transcriptomics generate increasingly large and high-dimensional gene expression datasets in which nonlinear dependence structures are common. Because classical methods primarily capture linear associations, they may fail to characterize many biologically relevant patterns of dependence. To address [...] Read more.
High-throughput technologies such as RNA-seq and single-cell transcriptomics generate increasingly large and high-dimensional gene expression datasets in which nonlinear dependence structures are common. Because classical methods primarily capture linear associations, they may fail to characterize many biologically relevant patterns of dependence. To address this limitation, diverse nonlinear dependence measures—including information-theoretic, rank-based, kernel-based, distance-based, copula-based, and clustering-based approaches—have been developed. However, the field remains fragmented, and comparative evaluations are often inconsistent. This review organizes nonlinear methods into major methodological families and critically compares their statistical behavior, strengths, limitations, and characteristic modes of failure. We emphasize that method selection depends on matching inferential objectives to estimator assumptions, analytical constraints, and characteristic failure modes. By identifying recurring trade-offs among flexibility, robustness, interpretability, and computational scalability, we provide scenario-based guidance for method selection in transcriptomics, network inference, and functional genomics. In doing so, we aim to align inferential objectives with analytical requirements, supporting principled and application-specific use of nonlinear dependence methods in modern omics research. Full article
41 pages, 24651 KB  
Article
Dynamical Analysis of Fractional Whitham–Broer–Kaup Systems Under Deterministic and Stochastic Effects
by Atef Abdelkader, Maham Munawar, Adil Jhangeer and Mudassar Imran
Fractal Fract. 2026, 10(7), 426; https://doi.org/10.3390/fractalfract10070426 (registering DOI) - 24 Jun 2026
Abstract
The fractional Whitham–Broer–Kaup model governs nonlinear wave propagation in memory-dependent media, including porous structures, viscoelastic fluids, and irregular seabeds, yet the full dynamical spectrum from quasi-periodicity to deterministic chaos, the role of stochastic forcing, and reliable identification from noisy data remains insufficiently explored, [...] Read more.
The fractional Whitham–Broer–Kaup model governs nonlinear wave propagation in memory-dependent media, including porous structures, viscoelastic fluids, and irregular seabeds, yet the full dynamical spectrum from quasi-periodicity to deterministic chaos, the role of stochastic forcing, and reliable identification from noisy data remains insufficiently explored, particularly how the fractional order β influences these regimes. This study addresses these gaps through a comprehensive, multi-method dynamical analysis of a representative nonlinear oscillator embodying key FWBK features. Three-dimensional attractor visualizations, return maps, and surrogate data tests demonstrate a transition from quasi-periodic toroidal attractors to fully developed chaos via torus breakdown, confirming that observed complexity originates from deterministic nonlinearity. Poincaré sections reveal multistability and KAM-type structures, where coexisting attractors depend on initial conditions, while increasing noise progressively disrupts coherent dynamics. The OGY control method effectively stabilizes unstable periodic orbits across chaotic regimes with minimal perturbation, and Lyapunov analysis indicates that stochastic forcing attenuates chaos while enhancing dissipation. The Fokker–Planck framework shows that noise reshapes probability landscapes, driving transitions from unimodal to bimodal distributions. Comparative analysis of SINDy, JMAP and VBA highlights trade-offs in interpretability, computational efficiency, and uncertainty quantification, while an integrated Bayesian–PCE–Sobol approach quantifies parametric uncertainty and reveals time-dependent sensitivity variations. Additionally, the overlapping of soliton solutions extracted via the enhanced modified Sardar sub-equation method reveals structural relationships among soliton families and their stability under interaction. Soliton branches that maintain high overlap under noise correspond to stable regimes, while those losing coherence indicate the onset of chaos. Furthermore, while the reduced dynamics in η-space are independent of β, the fractional order controls spatial compression and temporal scaling in physical coordinates, directly influencing observable wave localization. These results imply that fractional effects can modify chaos transitions, support controllability through OGY, and influence noise–instability interactions depending on β. This framework provides a robust, transferable methodology for analyzing and controlling nonlinear oscillatory systems under deterministic and stochastic conditions, with direct applications to FWBK-based models in coastal engineering, fiber optics, and quantum interference systems. Full article
39 pages, 5906 KB  
Review
Modelling the Mechanical Properties of Architected Cellular Solids for Structural Applications: A Review
by Jorge Luis Flores Alarcón, Rafael Schouwenaars, Armando Ortiz, Leopoldo Ruiz-Huerta, Manuel Farid Azamar and Ignacio Alejandro Figueroa
Materials 2026, 19(13), 2711; https://doi.org/10.3390/ma19132711 (registering DOI) - 24 Jun 2026
Abstract
Among a broad range of promising applications, the use of cellular solids as lightweight structural components is an important field of research that requires reliable predictions of their stiffness and strength. Predictive and general models should not depend on extensive parameter-fitting experiments and [...] Read more.
Among a broad range of promising applications, the use of cellular solids as lightweight structural components is an important field of research that requires reliable predictions of their stiffness and strength. Predictive and general models should not depend on extensive parameter-fitting experiments and should not rely on computationally intensive numerical calculations for each new set of geometric parameters and loading conditions. An overview of models for 2D, 2.5D, and three-dimensional structures will be presented. Most 2D and 2.5D models neglect out-of-plane behaviour and the face sheets used in sandwich panels. 3D studies, mainly by finite element models (FEMs), are often limited to a narrow set of geometries and simple loading conditions. Elastic anisotropy is well covered, but calculating yield surfaces remains a challenge. Simplified models based on structural mechanics are rare and often limited in scope. They offer a flexible, computationally efficient approach for simulating truss-based materials. For more advanced designs, parameter-based FEMs must be developed for any loading condition to facilitate the generalised incorporation of 3D cellular solids in mechanical design. Artificial intelligence and machine learning are promising approaches for making optimal use of experimental and FEM results across multidimensional parameter spaces. Full article
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23 pages, 16049 KB  
Article
Deep Learning Image Steganography Based on Dual-Path Fusion in Frequency and Spatial Domains
by Xiang Meng, Yuexin Li, Wanjia Li, Yiliang Guo, Yanhua Dong and Hongyu Sun
Electronics 2026, 15(13), 2777; https://doi.org/10.3390/electronics15132777 (registering DOI) - 24 Jun 2026
Abstract
Contemporary deep learning-based image steganography techniques for embedding images within images are hindered by inadequate utilization of frequency-domain features and limited steganographic security, restricting their effectiveness in practical privacy protection contexts. To mitigate these limitations, we introduce a frequency–spatial dual-path fusion-based deep steganography [...] Read more.
Contemporary deep learning-based image steganography techniques for embedding images within images are hindered by inadequate utilization of frequency-domain features and limited steganographic security, restricting their effectiveness in practical privacy protection contexts. To mitigate these limitations, we introduce a frequency–spatial dual-path fusion-based deep steganography approach, termed FS-Stego. This method incorporates a frequency–spatial dual-path architecture within the generator network. Specifically, the frequency-domain processing module facilitates feature embedding in the complex domain, while the spatial-domain processing module maintains the image’s structural integrity, thereby enabling the co-optimization of multi-dimensional features. Second, an adaptive fusion module is developed to dynamically adjust the weights of the two paths, while residual connections and attention mechanisms are utilized to mitigate feature loss. Third, a multi-objective loss function is implemented to simultaneously optimize the quality of the stego images and the reconstruction accuracy of the secret images. The proposed method utilizes three open-source datasets as cover images and the LFW dataset as the secret images. Experimental results demonstrate that, compared to existing deep steganographic techniques, the stego and recovered images achieve superior peak signal-to-noise ratios (PSNR) and structural similarity (SSIM). Regarding model efficiency, the number of parameters is reduced to below 0.98 million, significantly enhancing practical performance. The proposed method ensures high-quality image recovery while maintaining steganographic security, thereby offering an effective solution for privacy protection. Full article
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23 pages, 4939 KB  
Article
Vertical Bearing and Load Transfer of Fluidized Solidified Soil Piles in Layered Soft Ground
by Zhikang Wang, Jie Xu, Qianru Ge, Biao Chen, Ruiyan Wang and Tiange Ge
Buildings 2026, 16(13), 2497; https://doi.org/10.3390/buildings16132497 (registering DOI) - 24 Jun 2026
Abstract
Fluidized solidified soil piles combine slurry-like constructability with post-hardening strength development and provide a potential approach for soft ground improvement. This study investigated the vertical bearing behavior and load-transfer mechanism of fluidized solidified soil piles in layered soft ground through field single-pile vertical [...] Read more.
Fluidized solidified soil piles combine slurry-like constructability with post-hardening strength development and provide a potential approach for soft ground improvement. This study investigated the vertical bearing behavior and load-transfer mechanism of fluidized solidified soil piles in layered soft ground through field single-pile vertical static load tests, core drilling, and three-dimensional numerical simulation. The field tests and core drilling provided experimental evidence for evaluating load–settlement behavior, pile integrity, and material strength, while the internal load-transfer mechanism and geometric parameters were mainly interpreted using the numerical model. The field results showed that the Q-s curves exhibited staged deformation characteristics, with relatively stable settlement development during the main loading stage and more pronounced nonlinearity under high load levels. The ultimate vertical bearing capacities of the 10 m and 20 m test piles were 1050 kN and 950 kN, respectively. Core drilling indicated that the two pile groups had similar material strength, suggesting that the bearing capacity difference was mainly associated with the pile toe bearing stratum rather than pile material strength. After comparison with the measured Q-s curves, the numerical analysis showed that the 20 m pile mobilized a longer shaft resistance range and a higher shaft resistance contribution, but its pile toe extended into the lower mucky soil layer, resulting in reduced pile toe resistance. Parametric analysis indicated that increasing pile length does not necessarily improve bearing performance when the pile toe bearing stratum is unfavorable, whereas increasing pile diameter more directly reduces pile head settlement under the same pile toe bearing condition. These findings highlight the need to consider both shaft resistance mobilization and pile toe bearing stratum in the design of fluidized solidified soil piles in layered soft ground. Full article
(This article belongs to the Section Building Materials, and Repair & Renovation)
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