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20 pages, 2643 KB  
Article
An Operation Mode Analysis Method for Power Systems with High-Proportion Renewable Energy Integration Based on Autoencoder Clustering
by Ying Zhao, Lianle Qin, Liangsong Zhou, Huaiyuan Zong and Xinxin Guo
Sustainability 2026, 18(3), 1698; https://doi.org/10.3390/su18031698 - 6 Feb 2026
Abstract
With the integration of high-proportion renewable energy, the operation modes of the power system are becoming increasingly complex and diverse. The typical operation modes selected with manual experience cannot comprehensively represent system operating characteristics. To more accurately analyze system operating characteristics, an analysis [...] Read more.
With the integration of high-proportion renewable energy, the operation modes of the power system are becoming increasingly complex and diverse. The typical operation modes selected with manual experience cannot comprehensively represent system operating characteristics. To more accurately analyze system operating characteristics, an analysis method for power system operation modes based on autoencoder clustering is proposed. Compared to other clustering methods, the autoencoder clustering method can adapt to data of different types and structures, extract features and perform clustering in a reduced-dimensional space, and suppress noise in the data to a certain extent. First, multi-dimensional analysis metrics for power system operation modes are proposed. The metrics are used to evaluate system characteristics such as cleanliness, security, flexibility, and adequacy. The evaluation metrics for clustering are designed based on the metrics. Second, an operation mode analysis framework is constructed. The framework uses an autoencoder to extract implicit coupling relationships between system operation variables. The encoded feature vectors are used for clustering, which helps to find the internal similarities of the operation modes. Regulation resources such as pumped hydro storage are also considered in the framework. Finally, the proposed method is tested on the IEEE 39-node system. In the test, the comparison of clustering evaluation metrics and operation mode analysis errors shows that the proposed method has the best clustering performance and operation mode analysis effect compared to other clustering methods. The results prove that the proposed method can effectively extract the inner correlations and coupling relations of high-dimensional operating vectors, form consistent operation mode clusters, select typical operation modes, and accurately assess the characteristics and risks of the power system with high-proportion renewable energy integration. This paper helps to build a stronger power system that can integrate a higher proportion of renewable energy, replace fossil fuel generation, and contribute to a higher level of sustainable development. Full article
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14 pages, 2237 KB  
Article
Dynamic Parameter Identification of a Hip Exoskeleton Using RLS-GA
by Wentao Sheng, Yunxia Cao, Farzan Ghalichi, Li Ding and Tianyu Gao
Actuators 2026, 15(2), 106; https://doi.org/10.3390/act15020106 - 6 Feb 2026
Abstract
Lower-limb exoskeletons require accurate dynamic models to achieve stable and compliant human–robot interactions. However, least-squares-based identification often relies on demanding experiments and may yield limited accuracy for exoskeletons with non-standard structures and actuator-induced uncertainties. This paper proposes a two-stage dynamic parameter identification method [...] Read more.
Lower-limb exoskeletons require accurate dynamic models to achieve stable and compliant human–robot interactions. However, least-squares-based identification often relies on demanding experiments and may yield limited accuracy for exoskeletons with non-standard structures and actuator-induced uncertainties. This paper proposes a two-stage dynamic parameter identification method that integrates recursive least squares (RLS) and a genetic algorithm (GA), denoted as RLS-GA. RLS is first executed offline to estimate the variation ranges of the inertial parameter vector and to construct a finite, physically meaningful search space. GA then refines the parameters within these bounds by minimizing the regression residual norm. Experiments on a hip exoskeleton show that RLS-GA achieves higher identification accuracy than LS and unconstrained GA, while converging faster than GA under identical conditions. Full article
(This article belongs to the Section Actuators for Robotics)
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24 pages, 6092 KB  
Article
Dual-Output, Hybrid-Clamped, Quasi-Five-Level Inverter and Its Modulation Strategy
by Rutian Wang, Jiahui Wei and Yang Yu
Energies 2026, 19(3), 856; https://doi.org/10.3390/en19030856 - 6 Feb 2026
Abstract
This paper proposes a novel, dual-output, hybrid-clamped, quasi-five-level inverter (DO-HC-FLI) topology, capable of providing two independent AC voltage outputs with adjustable frequency and amplitude. Derived from a dual-output, active, neutral-point-clamped, three-level inverter, the proposed topology introduces three additional switches per phase to create [...] Read more.
This paper proposes a novel, dual-output, hybrid-clamped, quasi-five-level inverter (DO-HC-FLI) topology, capable of providing two independent AC voltage outputs with adjustable frequency and amplitude. Derived from a dual-output, active, neutral-point-clamped, three-level inverter, the proposed topology introduces three additional switches per phase to create dynamic switching paths. This expands the available range of DC-side voltage outputs and significantly improves the utilization rate of the DC–link voltage. Additionally, by adopting an asymmetric DC–link voltage configuration, the output line voltage levels of the conventional four-level inverter are increased to a number comparable to that of a five-level inverter. The front-end stage employs a hybrid series-parallel architecture, integrating dual Buck circuits with DC power sources. This configuration supplies the subsequent inverter stage with DC voltage levels at an optimal asymmetric ratio. In conjunction with a dual-output space vector pulse width modulation (SVPWM) strategy, the proposed system can collaboratively optimize the output voltage level characteristics of the inverter stage. Furthermore, a comprehensive analysis and comparison with other multilevel inverters are presented to demonstrate the superiority of the proposed topology. Finally, simulations and experiments are conducted to validate the effectiveness and feasibility of the proposed topology and modulation strategy. Full article
(This article belongs to the Section F: Electrical Engineering)
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15 pages, 282 KB  
Article
Rigidity and Conformal Characterizations of Noncompact Gradient Schouten Solitons
by Ali H. Alkhaldi, Fatemah Mofarreh, Huda M. Alshanbari and Akram Ali
Mathematics 2026, 14(3), 562; https://doi.org/10.3390/math14030562 - 4 Feb 2026
Viewed by 65
Abstract
This paper studies the conformal geometry of complete gradient Schouten solitons (GSSs) admitting closed conformal vector fields (CVFs). We establish rigidity and characterization results for nonparallel, homothetic closed CVFs under the assumption that the gradient of the scalar curvature is parallel to the [...] Read more.
This paper studies the conformal geometry of complete gradient Schouten solitons (GSSs) admitting closed conformal vector fields (CVFs). We establish rigidity and characterization results for nonparallel, homothetic closed CVFs under the assumption that the gradient of the scalar curvature is parallel to the CVF. It is shown that such manifolds are isometric to Euclidean space. Moreover, complete noncompact GSSs with constant scalar curvature are locally conformally flat in dimension four and have harmonic Weyl curvature in higher dimensions. Finally, we prove that these manifolds are totally umbilical if and only if their scalar curvature is constant, and they form warped products with space forms. Full article
31 pages, 12211 KB  
Article
Multi-Dimensional Detection Capability Analysis of Surface and Surface-to-Tunnel Transient Electromagnetic Methods Based on the Spectral Element Method
by Danyu Li, Xin Huang, Xiaoyue Cao, Liangjun Yan, Zhangqian Chen and Qingpu Han
Appl. Sci. 2026, 16(3), 1560; https://doi.org/10.3390/app16031560 - 4 Feb 2026
Viewed by 66
Abstract
The transient electromagnetic (TEM) method is a key detection and monitoring technology for safe coal-mine production. Surface TEM depth penetration is limited by real geological conditions and transmitter–receiver hardware performance. Compared with the surface TEM method, the tunnel TEM method can enhance the [...] Read more.
The transient electromagnetic (TEM) method is a key detection and monitoring technology for safe coal-mine production. Surface TEM depth penetration is limited by real geological conditions and transmitter–receiver hardware performance. Compared with the surface TEM method, the tunnel TEM method can enhance the depth of exploration to some extent, but it is constrained by the limited working space of the roadway, which makes it difficult to perform the area-wide and multi-line data acquisition, and thus the lateral detection resolution is directly compromised. Consequently, either surface or tunnel TEM alone suffers inherent limitations. The multidimensional surface and surface-to-tunnel TEM method employs a single large-loop transmitter and records electromagnetic (EM) signals both on the surface and in the tunnel, enabling joint data interpretation. The joint TEM observation method effectively addresses the limitations by using a single observation mode, with the goal of achieving high-precision detection. To investigate the detection capabilities of the joint surface and surface-to-tunnel TEM method, we propose a three-dimensional (3D) joint surface and surface-to-tunnel TEM forward modeling method based on the spectral element method (SEM). The SEM, using high-order vector basis functions, enables high-precision modeling of TEM responses with complex geo-electric earth models. The accuracy of the SEM is validated through comparisons with one-dimensional (1D) TEM semi-analytical solutions. To further reveal TEM response characteristics and multi-dimensional resolution under joint surface and tunnel detection modes, we construct several typical 3D geo-electric earth models and apply the SEM algorithm to simulate the TEM responses. We systematically analyze the horizontal and vertical resolution of 3D earth model targets at different decay times. The numerical results demonstrate that surface multi-line TEM surveying can accurately delineate the lateral extent of the target body, while vertical in-tunnel measurements are crucial for identifying the top and bottom interfaces of geological targets adjacent to the tunnel. Finally, the theoretical modeling results demonstrate that compared to individual TEM methods, the multi-dimensional joint surface and tunnel TEM observation yields superior target spatial information and markedly improves TEM detection efficacy under complex conditions. The 3D TEM forward modeling based on the SEM provides the theoretical foundation for subsequent 3D inversion and interpretation of surface-to-surface and surface-to-tunnel joint TEM data. Full article
15 pages, 884 KB  
Article
AI-Driven Typography: A Human-Centered Framework for Generative Font Design Using Large Language Models
by Yuexi Dong and Mingyong Gao
Information 2026, 17(2), 150; https://doi.org/10.3390/info17020150 - 3 Feb 2026
Viewed by 94
Abstract
This paper presents a human-centered, AI-driven framework for font design that reimagines typography generation as a collaborative process between humans and large language models (LLMs). Unlike conventional pixel- or vector-based approaches, our method introduces a Continuous Style Projector that maps visual features from [...] Read more.
This paper presents a human-centered, AI-driven framework for font design that reimagines typography generation as a collaborative process between humans and large language models (LLMs). Unlike conventional pixel- or vector-based approaches, our method introduces a Continuous Style Projector that maps visual features from a pre-trained ResNet encoder into the LLM’s latent space, enabling zero-shot style interpolation and fine-grained control of stroke and serif attributes. To model handwriting trajectories more effectively, we employ a Mixture Density Network (MDN) head, allowing the system to capture multi-modal stroke distributions beyond deterministic regression. Experimental results show that users can interactively explore, mix, and generate new typefaces in real time, making the system accessible for both experts and non-experts. The approach reduces reliance on commercial font licenses and supports a wide range of applications in education, design, and digital communication. Overall, this work demonstrates how LLM-based generative models can enhance creativity, personalization, and cultural expression in typography, contributing to the broader field of AI-assisted design. Full article
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30 pages, 1510 KB  
Article
An Improved Mantis Search Algorithm for Solving Optimization Problems
by Yanjiao Wang and Tongchao Dou
Biomimetics 2026, 11(2), 105; https://doi.org/10.3390/biomimetics11020105 - 2 Feb 2026
Viewed by 111
Abstract
The traditional mantis search algorithm (MSA) suffers from limitations such as slow convergence and a high likelihood of converging to local optima in complex optimization scenarios. This paper proposes an improved mantis search algorithm (IMSA) to overcome these issues. An adaptive probability conversion [...] Read more.
The traditional mantis search algorithm (MSA) suffers from limitations such as slow convergence and a high likelihood of converging to local optima in complex optimization scenarios. This paper proposes an improved mantis search algorithm (IMSA) to overcome these issues. An adaptive probability conversion factor is designed, which adaptively controls the proportion of individuals entering the search phase and the attack phase so that the algorithm can smoothly transition from large-scale global exploration to local fine search. In the search phase, a probability update strategy based on both subspace and full space is designed, significantly improving the adaptability of the algorithm to complex problems by dynamically adjusting the search range. The elite population screening mechanism, based on Euclidean distance and fitness double criteria, is introduced to provide dual guidance for the evolution direction of the algorithm. In the attack stage, the base vector adaptive probability selection mechanism is designed, and the algorithm’s pertinence in different optimization stages is enhanced by dynamically adjusting the base vector selection strategy. Finally, in the stage of sexual cannibalism, the directed random disturbance update method of inferior individuals is adopted, and the population is directly introduced through the non-greedy replacement strategy, which effectively overcomes the loss of population diversity. The experimental results of 29 test functions on the CEC2017 test set demonstrate that the IMSA exhibits significant advantages in convergence speed, calculation accuracy, and stability compared to the original MSA and the five best meta-heuristic algorithms. Full article
(This article belongs to the Section Biological Optimisation and Management)
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22 pages, 9179 KB  
Article
GA-HRNet: High-Precision Building Extraction for Individualization of Oblique Photogrammetry 3D Models
by Jiacui Zou, Yongchuan Zhang, Feng Li, Ruibing Wang, Jiajun Wu and Yang Qiao
Appl. Sci. 2026, 16(3), 1486; https://doi.org/10.3390/app16031486 - 2 Feb 2026
Viewed by 90
Abstract
Building individualization is a critical preprocessing step for refined applications of oblique photogrammetry 3D models, yet existing semantic segmentation methods encounter accuracy bottlenecks when applied to ultra-high-resolution orthophotos. To overcome this challenge, this study constructs an automated technical framework following a workflow from [...] Read more.
Building individualization is a critical preprocessing step for refined applications of oblique photogrammetry 3D models, yet existing semantic segmentation methods encounter accuracy bottlenecks when applied to ultra-high-resolution orthophotos. To overcome this challenge, this study constructs an automated technical framework following a workflow from orthophoto generation to high-precision semantic segmentation, and finally to dynamic 3D rendering. The framework comprises three stages: (1) converting the 3D model into a 2D orthophoto to ensure that the extracted building contours can be precisely registered with the original 3D model in space; (2) utilizing the proposed Gated-ASPP High-Resolution Network (GA-HRNet) to extract building contours, enhancing segmentation accuracy by synergizing HRNet’s spatial detail preservation capability with ASPP’s multi-scale context awareness; (3) mapping the extracted 2D vector contours back to the 3D model and achieving interactive building individualization via dynamic rendering technology. Evaluated on a custom-built Hong Kong urban building dataset, GA-HRNet achieved an Intersection over Union (IoU) of 91.25%, an F1-Score of 95.41%, a Precision of 93.31%, and a Recall of 97.70%. Its performance surpassed that of various comparative models, including FCN, U-Net, MBR-HRNet, and others, with an IoU lead of 1.46 to 5.62 percentage points. This method enables precise building extraction and dynamic highlighting within 3D scenes, providing an efficient and reliable technical path for the refined application of large-scale urban oblique photogrammetry models. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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24 pages, 3305 KB  
Article
A Refined Method for Inspecting the Verticality of Thin Tower Structures Using the Marching Square Algorithm
by Mingduan Zhou, Guanxiu Wu, Yuhan Qin, Zihan Zhou, Qiao Song, Shiqi Lin, Lu Qin, Peng Yan and Shufa Li
Buildings 2026, 16(3), 604; https://doi.org/10.3390/buildings16030604 - 2 Feb 2026
Viewed by 142
Abstract
Conducting regular verticality inspections for thin tower structures is essential for ensuring structural safety, extending service life, and optimizing operation and maintenance strategies. However, the traditional theodolite inspection method, as a commonly used technique for verticality assessment, still has certain limitations, including strict [...] Read more.
Conducting regular verticality inspections for thin tower structures is essential for ensuring structural safety, extending service life, and optimizing operation and maintenance strategies. However, the traditional theodolite inspection method, as a commonly used technique for verticality assessment, still has certain limitations, including strict requirements for station setup, the need for high-altitude contact-based operations, and difficulty in accurately resolving the tilt azimuth of the central axis. More importantly, the conventional method provides insufficient understanding of the overall verticality geometric characteristics of thin tower structures, particularly lacking in systematic approaches for characterizing the axis morphology under non-contact, full three-dimensional (3D) perception conditions. Therefore, this study proposes a refined method for inspecting the verticality of thin tower structures using the Marching Square algorithm. The tower body of a tower crane was selected as the experimental subject. Firstly, ground-based LiDAR was employed to scan and acquire the raw point cloud data of the tower crane. After point cloud registration and denoising, high-precision and valid point cloud data of the tower body were obtained. Secondly, a cross-sectional slicing segmentation strategy was designed for the point cloud of the tower body standard sections, and a slice-polygon-contour extraction method based on the Marching Square algorithm was proposed to extract the contour vertices and compute the coordinates of the contour centroids. Finally, a spatial line-fitting algorithm based on the least squares method was proposed to fit a 3D line to the coordinates of the contour centroids, thereby determining the direction vector of the central axis. The direction vector was then subjected to vector operations with the x-axis and z-axis in the station-center space coordinate system to derive the tilt azimuth and tilt angle of the central axis, thereby providing the verticality inspection results of the tower crane. The experimental results indicate that the four cross-section slicing segmentation schemes designed using the proposed method in this study yielded tower crane verticality values of 2.45‰, 2.35‰, 2.20‰, and 2.18‰. All verticality values meet the verticality requirement of no more than 4‰ specified in GB/T 5031-2019 (Tower Cranes). This verifies that the proposed method is feasible and effective, providing a novel, high-precision, and non-contact inspection method for inspecting the anti-overturning stability of thin tower structures. Full article
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27 pages, 9162 KB  
Article
Multi-Domain Incremental Learning for Semantic Segmentation via Visual Domain Prompt in Remote Sensing Data
by Junxi Li, Zhiyuan Yan, Wenhui Diao, Yidan Zhang, Zicong Zhu, Yichen Tian and Xian Sun
Remote Sens. 2026, 18(3), 464; https://doi.org/10.3390/rs18030464 - 1 Feb 2026
Viewed by 220
Abstract
Domain incremental learning for semantic segmentation has gained lots of attention due to its importance for many fields including urban planning and autonomous driving. The catastrophic forgetting problem caused by domain shift has been alleviated by structure expansion of the model or data [...] Read more.
Domain incremental learning for semantic segmentation has gained lots of attention due to its importance for many fields including urban planning and autonomous driving. The catastrophic forgetting problem caused by domain shift has been alleviated by structure expansion of the model or data rehearsal. However, these methods ignore similar contextual knowledge between the new and the old data domain and assume that new knowledge and old knowledge are completely mutually exclusive, which cause the model to be trained in a suboptimal direction. Motivated by the prompt learning, we proposed a new domain incremental learning framework named RS-VDP. The key innovation of RS-VDP is to utilize a visual domain prompt to change the optimization direction from input data space and feature space. First, we designed a domain prompt based on a dynamic location module, which applied a visual domain prompt according to a local entropy map to update the distribution of the input images. Second, in order to filter the feature vectors with high confidence, a representation feature alignment based on an entropy map module is proposed. This module ensures the accuracy and stability of the feature vectors involved in the regularization loss, alleviating the problem of semantic drift. Finally, we introduced a new evaluation metric to measure the overall performance of the incremental learning models, solving the problem that the traditional evaluation metric is affected by the single-task accuracy. Comprehensive experiments demonstrated the effectiveness of the proposed method by significantly reducing the degree of catastrophic forgetting. Full article
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22 pages, 4797 KB  
Article
Surrogate-Based Reconstruction of Structural Damage in Train Collisions: A Systematic Optimization Framework
by Hui Zhao, Dehong Zhang and Ping Xu
Systems 2026, 14(2), 156; https://doi.org/10.3390/systems14020156 - 31 Jan 2026
Viewed by 97
Abstract
Accurate reconstruction of train collision accidents is essential for understanding impact conditions, assessing crashworthiness, and supporting safety improvements. This study proposes a surrogate-based optimization framework for reconstructing structural damage in train collisions from post-accident observations. The pre-impact kinematic state, expressed by a six-dimensional [...] Read more.
Accurate reconstruction of train collision accidents is essential for understanding impact conditions, assessing crashworthiness, and supporting safety improvements. This study proposes a surrogate-based optimization framework for reconstructing structural damage in train collisions from post-accident observations. The pre-impact kinematic state, expressed by a six-dimensional vector of relative offsets, rotations, and impact velocity, is formulated as an inverse problem in which a Sum of Squared Relative Deviations (SSRD) between measured and simulated residual deformations serves as the objective function. A reduced two-vehicle finite element (FE) model is developed to capture the dominant impact dynamics, an Optimal Latin Hypercube Design is used to sample the parameter space, and a Kriging surrogate model is constructed to approximate the response. A simulated annealing algorithm is applied to search for the global minimum. The framework is demonstrated on a real high-speed rear-end collision of electric multiple units. The Kriging model achieves a coefficient of determination of about 0.85, and the optimized kinematic state yields FE-predicted residual deformations that agree with field measurements at key locations to within about 5%. The results show that the method can efficiently reconstruct physically plausible collision scenarios and provide insight into parameter sensitivity and identifiability for railway safety analysis. Full article
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17 pages, 797 KB  
Article
Continued Electromagnetic Signal Classification Based on Vector Space Separation
by Lu Jia, Yan Zhao, Shichuan Chen and Zhijin Zhao
Electronics 2026, 15(3), 613; https://doi.org/10.3390/electronics15030613 - 30 Jan 2026
Viewed by 169
Abstract
Incremental electromagnetic signal classification is crucial in realistic wireless environments where new signal types continuously emerge and historical training data are often unavailable. This paper proposes a model-based incremental learning method driven by vector space separation to mitigate catastrophic forgetting without accessing old-task [...] Read more.
Incremental electromagnetic signal classification is crucial in realistic wireless environments where new signal types continuously emerge and historical training data are often unavailable. This paper proposes a model-based incremental learning method driven by vector space separation to mitigate catastrophic forgetting without accessing old-task samples or requiring semantic information. We show that forgetting is largely caused by insufficient separation between old and new classes in the classifier weight space. To address this issue, we jointly introduce weight normalization, a cosine-similarity separation loss, and regularization, together with cross-entropy supervision for new classes. Based on these designs, we propose an incremental learning method based on vector space separation for electromagnetic signal classification, enabling the model to continually recognize modulation signals without requiring semantic information or access to raw data from previous tasks during incremental updates. Experiments on two simulated modulation datasets under multiple task sequences demonstrate that the proposed method consistently alleviates catastrophic forgetting and achieves stable incremental performance, outperforming baselines while avoiding data rehearsal. Full article
(This article belongs to the Section Circuit and Signal Processing)
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24 pages, 861 KB  
Article
Distinguishability-Driven Voice Generation for Speaker Anonymization via Random Projection and GMM
by Chunxia Wang, Qiuyu Zhang, Yingjie Hu and Huiyi Wei
Big Data Cogn. Comput. 2026, 10(2), 43; https://doi.org/10.3390/bdcc10020043 - 29 Jan 2026
Viewed by 104
Abstract
Speaker anonymization effectively conceals speaker identity in speech signals to protect privacy. To address issues in existing anonymization systems, including reduced voice distinguishability, limited anonymized voices, reliance on an external speaker pool, and vulnerability to privacy leakage against strong attackers, a novel distinguishability-driven [...] Read more.
Speaker anonymization effectively conceals speaker identity in speech signals to protect privacy. To address issues in existing anonymization systems, including reduced voice distinguishability, limited anonymized voices, reliance on an external speaker pool, and vulnerability to privacy leakage against strong attackers, a novel distinguishability-driven voice generation for speaker anonymization via random projection and the Gaussian Mixture Model (GMM) is proposed. This method first applies the random projection to lower the dimensionality of the X-vectors from an external speaker pool, and then constructs a GMM in the reduced dimensional space to fit the generative model. By sampling from this generative model, anonymous speaker identity representations are generated, ultimately synthesizing anonymized speech that maintains both intelligibility and distinguishability. To ensure the anonymized speech remains sufficiently distinguishable from the original and prevents excessive similarity, a cosine similarity check is implemented between the original X-vector and pseudo-X-vector. Experimental results on the VoicePrivacy Challenge datasets demonstrate that the proposed method not only effectively protects speaker privacy across different attack scenarios but also preserves speech content integrity while significantly enhancing speaker distinguishability between original speakers and their corresponding pseudo-speakers, as well as among different pseudo-speakers. Full article
(This article belongs to the Topic Generative AI and Interdisciplinary Applications)
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19 pages, 6479 KB  
Article
Excitonic Effects and Antiferromagnetism in the Doped-Biased AB-Stacked Bilayer Graphene
by Vardan Apinyan and Tadeusz Kopeć
Crystals 2026, 16(2), 95; https://doi.org/10.3390/cryst16020095 - 29 Jan 2026
Viewed by 179
Abstract
We consider the direct orbital effect of an external magnetic field on the motion of electrons in reciprocal space in AB-stacked bilayer graphene subjected to a perpendicular magnetic field and an external electric field. For this purpose, the Peierls substitution is implemented using [...] Read more.
We consider the direct orbital effect of an external magnetic field on the motion of electrons in reciprocal space in AB-stacked bilayer graphene subjected to a perpendicular magnetic field and an external electric field. For this purpose, the Peierls substitution is implemented using the symmetric gauge for the vector potential, and the electronic dispersion is reconstructed. The Lorentz potential arising from the Lorentz force acting on the electrons is included in the calculations. The effective chemical potential method is employed to incorporate the effects of Hubbard on-site repulsion, the external electric field, and Landau quantization of the allowed electronic states in reciprocal space. Local canted antiferromagnetic states are discussed, and their coexistence with excitonic states is found. Full article
(This article belongs to the Section Inorganic Crystalline Materials)
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27 pages, 1408 KB  
Article
A Fuzzy Granular K-Means Clustering Method Driven by Gaussian Membership Functions
by Junjie Huang, Biyun Lan, Haibo Huang, Tiancai Huang and Yumin Chen
Mathematics 2026, 14(3), 462; https://doi.org/10.3390/math14030462 - 28 Jan 2026
Viewed by 94
Abstract
The K-means clustering algorithm is widely applied in various clustering tasks due to its high computational efficiency and simple implementation. However, its performance significantly deteriorates when dealing with non-convex structures, fuzzy boundaries, or noisy data, as it relies on the assumption that clusters [...] Read more.
The K-means clustering algorithm is widely applied in various clustering tasks due to its high computational efficiency and simple implementation. However, its performance significantly deteriorates when dealing with non-convex structures, fuzzy boundaries, or noisy data, as it relies on the assumption that clusters are spherical or linearly separable. To address these limitations, this paper proposes a Gaussian membership-driven fuzzy granular K-means clustering method. In this approach, multi-function Gaussian membership functions are used for fuzzy granulation at the single-feature level to generate fuzzy granules, while fuzzy granule vectors are constructed in the multi-feature space. A novel distance metric for fuzzy granules is defined along with operational rules, for which axiomatic proof is provided. This Gaussian-based granulation enables effective modeling of nonlinear separability in complex data structures, leading to the development of a new fuzzy granular K-means clustering framework. Experimental results on multiple public UCI datasets demonstrate that the proposed method significantly outperforms traditional K-means and other baseline methods in clustering tasks involving complex geometric data (e.g., circular and spiral structures), showing improved robustness and adaptability. This offers an effective solution for clustering data with intricate distributions. Full article
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