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Keywords = dual space

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14 pages, 248 KB  
Article
The Studies of (Dual) Fusion Frames on Hilbert Space and Generalization of the Index Set
by Fangfang Dong and Ruichang Pei
Mathematics 2025, 13(19), 3164; https://doi.org/10.3390/math13193164 - 2 Oct 2025
Abstract
In this paper, we begin with the classical concept of tight frames in Hilbert spaces. First, we introduce the orthogonal projection P between H and θ(H) (the range of the frame transform θ associated with a traditional tight frame) and [...] Read more.
In this paper, we begin with the classical concept of tight frames in Hilbert spaces. First, we introduce the orthogonal projection P between H and θ(H) (the range of the frame transform θ associated with a traditional tight frame) and investigate the relationship between P and θ. We then explore fusion frames and extend the index set to an infinite set through a concrete example. Second, we examine the role of orthogonal projections in fusion frames with particular emphasis on robustness and redundancy illustrated by examples. Finally, we study dual fusion frames and establish several important results, especially concerning the relationship between the frame operators of two types of dual fusion frames. Full article
16 pages, 13271 KB  
Article
Smartphone-Based Estimation of Cotton Leaf Nitrogen: A Learning Approach with Multi-Color Space Fusion
by Shun Chen, Shizhe Qin, Yu Wang, Lulu Ma and Xin Lv
Agronomy 2025, 15(10), 2330; https://doi.org/10.3390/agronomy15102330 - 2 Oct 2025
Abstract
To address the limitations of traditional cotton leaf nitrogen content estimation methods, which include low efficiency, high cost, poor portability, and challenges in vegetation index acquisition owing to environmental interference, this study focused on emerging non-destructive nutrient estimation technologies. This study proposed an [...] Read more.
To address the limitations of traditional cotton leaf nitrogen content estimation methods, which include low efficiency, high cost, poor portability, and challenges in vegetation index acquisition owing to environmental interference, this study focused on emerging non-destructive nutrient estimation technologies. This study proposed an innovative method that integrates multi-color space fusion with deep and machine learning to estimate cotton leaf nitrogen content using smartphone-captured digital images. A dataset comprising smartphone-acquired cotton leaf images was processed through threshold segmentation and preprocessing, then converted into RGB, HSV, and Lab color spaces. The models were developed using deep-learning architectures including AlexNet, VGGNet-11, and ResNet-50. The conclusions of this study are as follows: (1) The optimal single-color-space nitrogen estimation model achieved a validation set R2 of 0.776. (2) Feature-level fusion by concatenation of multidimensional feature vectors extracted from three color spaces using the optimal model, combined with an attention learning mechanism, improved the validation R2 to 0.827. (3) Decision-level fusion by concatenating nitrogen estimation values from optimal models of different color spaces into a multi-source decision dataset, followed by machine learning regression modeling, increased the final validation R2 to 0.830. The dual fusion method effectively enabled rapid and accurate nitrogen estimation in cotton crops using smartphone images, achieving an accuracy 5–7% higher than that of single-color-space models. The proposed method provides scientific support for efficient cotton production and promotes sustainable development in the cotton industry. Full article
(This article belongs to the Special Issue Crop Nutrition Diagnosis and Efficient Production)
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22 pages, 7838 KB  
Article
Bifurcation Analysis and Solitons Dynamics of the Fractional Biswas–Arshed Equation via Analytical Method
by Asim Zafar, Waseem Razzaq, Abdullah Nazir, Mohammed Ahmed Alomair, Abdulaziz S. Al Naim and Abdulrahman Alomair
Mathematics 2025, 13(19), 3147; https://doi.org/10.3390/math13193147 - 1 Oct 2025
Abstract
This paper investigates soliton solutions of the time-fractional Biswas–Arshed (BA) equation using the Extended Simplest Equation Method (ESEM). The model is analyzed under two distinct fractional derivative operators: the β-derivative and the M-truncated derivative. These approaches yield diverse solution types, including [...] Read more.
This paper investigates soliton solutions of the time-fractional Biswas–Arshed (BA) equation using the Extended Simplest Equation Method (ESEM). The model is analyzed under two distinct fractional derivative operators: the β-derivative and the M-truncated derivative. These approaches yield diverse solution types, including kink, singular, and periodic-singular forms. Also, in this work, a nonlinear second-order differential equation is reconstructed as a planar dynamical system in order to study its bifurcation structure. The stability and nature of equilibrium points are established using a conserved Hamiltonian and phase space analysis. A bifurcation parameter that determines the change from center to saddle-type behaviors is identified in the study. The findings provide insight into the fundamental dynamics of nonlinear wave propagation by showing how changes in model parameters induce qualitative changes in the phase portrait. The derived solutions are depicted via contour plots, along with two-dimensional (2D) and three-dimensional (3D) representations, utilizing Mathematica for computational validation and graphical illustration. This study is motivated by the growing role of fractional calculus in modeling nonlinear wave phenomena where memory and hereditary effects cannot be captured by classical integer-order approaches. The time-fractional Biswas–Arshed (BA) equation is investigated to obtain diverse soliton solutions using the Extended Simplest Equation Method (ESEM) under the β-derivative and M-truncated derivative operators. Beyond solution construction, a nonlinear second-order equation is reformulated as a planar dynamical system to analyze its bifurcation and stability properties. This dual approach highlights how parameter variations affect equilibrium structures and soliton behaviors, offering both theoretical insights and potential applications in physics and engineering. Full article
23 pages, 24448 KB  
Article
YOLO-SCA: A Lightweight Potato Bud Eye Detection Method Based on the Improved YOLOv5s Algorithm
by Qing Zhao, Ping Zhao, Xiaojian Wang, Qingbing Xu, Siyao Liu and Tianqi Ma
Agriculture 2025, 15(19), 2066; https://doi.org/10.3390/agriculture15192066 - 1 Oct 2025
Abstract
Bud eye identification is a critical step in the intelligent seed cutting process for potatoes. This study focuses on the challenges of low testing accuracy and excessive weighted memory in testing models for potato bud eye detection. It proposes an improved potato bud [...] Read more.
Bud eye identification is a critical step in the intelligent seed cutting process for potatoes. This study focuses on the challenges of low testing accuracy and excessive weighted memory in testing models for potato bud eye detection. It proposes an improved potato bud eye detection method based on YOLOv5s, referred to as the YOLO-SCA model, which synergistically optimizing three main modules. The improved model introduces the ShuffleNetV2 module to reconstruct the backbone network. The channel shuffling mechanism reduces the model’s weighted memory and computational load, while enhancing bud eye features. Additionally, the CBAM attention mechanism is embedded at specific layers, using dual-path feature weighting (channel and spatial) to enhance sensitivity to key bud eye features in complex contexts. Then, the Alpha-IoU function is used to replace the CloU function as the bounding box regression loss function. Its single-parameter control mechanism and adaptive gradient amplification characteristics significantly improve the accuracy of bud eye positioning and strengthen the model’s anti-interference ability. Finally, we conduct pruning based on the channel evaluation after sparse training, accurately removing redundant channels, significantly reducing the amount of computation and weighted memory, and achieving real-time performance of the model. This study aims to address how potato bud eye detection models can achieve high-precision real-time detection under the conditions of limited computational resources and storage space. The improved YOLO-SCA model has a size of 3.6 MB, which is 35.3% of the original model; the number of parameters is 1.7 M, which is 25% of the original model; and the average accuracy rate is 95.3%, which is a 12.5% improvement over the original model. This study provides theoretical support for the development of potato bud eye recognition technology and intelligent cutting equipment. Full article
(This article belongs to the Section Artificial Intelligence and Digital Agriculture)
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21 pages, 4247 KB  
Article
Diverging Carbon Balance and Driving Mechanisms of Expanding and Shrinking Cities in Transitional China
by Jiawei Lei, Keyu Luo, Le Xia and Zhenyu Wang
Atmosphere 2025, 16(10), 1155; https://doi.org/10.3390/atmos16101155 - 1 Oct 2025
Abstract
The synergy between carbon neutrality and urbanization is essential for effective climate governance and socio-ecological intelligent transition. From the perspective of coupled urban dynamic evolution and carbon metabolism systems, this study integrates the Sen-MK trend test and the geographical detector model to explore [...] Read more.
The synergy between carbon neutrality and urbanization is essential for effective climate governance and socio-ecological intelligent transition. From the perspective of coupled urban dynamic evolution and carbon metabolism systems, this study integrates the Sen-MK trend test and the geographical detector model to explore the spatial–temporal differentiation patterns and driving mechanisms of carbon balance across 337 prefecture-level cities in China from 2012 to 2022. The results reveal a spatial–temporal mismatch between carbon emissions and carbon storage, forming an asymmetric carbon metabolism pattern characterized by “expansion-dominated and shrinkage-dissipative” dynamics. Carbon compensation rates exhibit a west–high to east–low gradient distribution, with hotspots of expansionary cities clustered in the southwest, while shrinking cities display a dispersed pattern from the northwest to the northeast. Based on the four-quadrant carbon balance classification, expansionary cities are mainly located in the “high economic–low ecological” quadrant, whereas shrinking cities concentrate in the “low economic–high ecological” quadrant. Industrial structure and population scale serve as the dual-core drivers of carbon compensation. Expansionary cities are positively regulated by urbanization rates, while shrinking cities are negatively constrained by energy intensity. These findings suggest that differentiated regulation strategies can help optimize carbon governance within national territorial space. Full article
(This article belongs to the Section Air Quality)
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21 pages, 2749 KB  
Article
Performance Analysis of an Optical System for FSO Communications Utilizing Combined Stochastic Gradient Descent Optimization Algorithm
by Ilya Galaktionov and Vladimir Toporovsky
Appl. Syst. Innov. 2025, 8(5), 143; https://doi.org/10.3390/asi8050143 - 30 Sep 2025
Abstract
Wavefront aberrations caused by thermal flows or arising from the quality of optical components can significantly impair wireless communication links. Such aberrations may result in an increased error rate in the received signal, leading to data loss in laser communication applications. In this [...] Read more.
Wavefront aberrations caused by thermal flows or arising from the quality of optical components can significantly impair wireless communication links. Such aberrations may result in an increased error rate in the received signal, leading to data loss in laser communication applications. In this study, we explored a newly developed combined stochastic gradient descent optimization algorithm aimed at compensating for optical distortions. The algorithm we developed exhibits linear time and space complexity and demonstrates low sensitivity to variations in input parameters. Furthermore, its implementation is relatively straightforward and does not necessitate an in-depth understanding of the underlying system, in contrast to the Stochastic Parallel Gradient Descent (SPGD) method. In addition, a developed switch-mode approach allows us to use a stochastic component of the algorithm as a rapid, rough-tuning mechanism, while the gradient descent component is used as a slower, more precise fine-tuning method. This dual-mode operation proves particularly advantageous in scenarios where there are no rapid dynamic wavefront distortions. The results demonstrated that the proposed algorithm significantly enhanced the total collected power of the beam passing through the 10 μm diaphragm that simulated a 10 μm fiber core, increasing it from 0.33 mW to 2.3 mW. Furthermore, the residual root mean square (RMS) aberration was reduced from 0.63 μm to 0.12 μm, which suggests a potential improvement in coupling efficiency from 0.1 to 0.6. Full article
(This article belongs to the Section Information Systems)
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22 pages, 6708 KB  
Article
Enhanced Model Predictive Speed Control of PMSMs Based on Duty Ratio Optimization with Integrated Load Torque Disturbance Compensation
by Tarek Yahia, Abdelsalam A. Ahmed, M. M. Ahmed, Amr El Zawawi, Z. M. S. Elbarbary, M. S. Arafath and Mosaad M. Ali
Machines 2025, 13(10), 891; https://doi.org/10.3390/machines13100891 - 30 Sep 2025
Abstract
This paper proposes an enhanced Model Predictive Direct Speed Control (MPDSC) framework for Permanent Magnet Synchronous Motor (PMSM) drives, integrating duty ratio optimization and load torque disturbance compensation to significantly improve both transient and steady-state performance. Traditional finite-control-set MPC strategies, which apply a [...] Read more.
This paper proposes an enhanced Model Predictive Direct Speed Control (MPDSC) framework for Permanent Magnet Synchronous Motor (PMSM) drives, integrating duty ratio optimization and load torque disturbance compensation to significantly improve both transient and steady-state performance. Traditional finite-control-set MPC strategies, which apply a single voltage vector per sampling interval, often suffer from steady-state ripples, elevated total harmonic distortion (THD), and high computational complexity due to exhaustive switching evaluations. The proposed approach addresses these limitations through a novel dual-stage cost function structure: the first cost function optimizes dynamic response via predictive control of speed error, while the second adaptively minimizes torque ripple and harmonic distortion by adjusting the active–zero voltage vector duty ratio without the need for manual weight tuning. Robustness against time-varying disturbances is further enhanced by integrating a real-time load torque observer into the control loop. The scheme is validated through both MATLAB/Simulink R2020a simulations and real-time experimental testing on a dSPACE 1202 rapid control prototyping platform across small- and large-scale PMSM configurations. Experimental results confirm that the proposed controller achieves a transient speed deviation of just 0.004%, a steady-state ripple of 0.01 rpm, and torque ripple as low as 0.0124 Nm, with THD reduced to approximately 5.5%. The duty ratio-based predictive modulation ensures faster settling time, improved current quality, and greater immunity to load torque disturbances compared to recent duty-ratio MPC implementations. These findings highlight the proposed DR-MPDSC as a computationally efficient and experimentally validated solution for next-generation PMSM drive systems in automotive and industrial domains. Full article
(This article belongs to the Section Electrical Machines and Drives)
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18 pages, 2459 KB  
Article
FFMamba: Feature Fusion State Space Model Based on Sound Event Localization and Detection
by Yibo Li, Dongyuan Ge, Jieke Xu and Xifan Yao
Electronics 2025, 14(19), 3874; https://doi.org/10.3390/electronics14193874 - 29 Sep 2025
Abstract
Previous studies on Sound Event Localization and Detection (SELD) have primarily focused on CNN- and Transformer-based designs. While CNNs possess local receptive fields, making it difficult to capture global dependencies over long sequences, Transformers excel at modeling long-range dependencies but have limited sensitivity [...] Read more.
Previous studies on Sound Event Localization and Detection (SELD) have primarily focused on CNN- and Transformer-based designs. While CNNs possess local receptive fields, making it difficult to capture global dependencies over long sequences, Transformers excel at modeling long-range dependencies but have limited sensitivity to local time–frequency features. Recently, the VMamba architecture, built upon the Visual State Space (VSS) model, has shown great promise in handling long sequences, yet it remains limited in modeling local spatial details. To address this issue, we propose a novel state space model with an attention-enhanced feature fusion mechanism, termed FFMamba, which balances both local spatial modeling and long-range dependency capture. At a fine-grained level, we design two key modules: the Multi-Scale Fusion Visual State Space (MSFVSS) module and the Wavelet Transform-Enhanced Downsampling (WTED) module. Specifically, the MSFVSS module integrates a Multi-Scale Fusion (MSF) component into the VSS framework, enhancing its ability to capture both long-range temporal dependencies and detailed local spatial information. Meanwhile, the WTED module employs a dual-branch design to fuse spatial and frequency domain features, improving the richness of feature representations. Comparative experiments were conducted on the DCASE2021 Task 3 and DCASE2022 Task 3 datasets. The results demonstrate that the proposed FFMamba model outperforms recent approaches in capturing long-range temporal dependencies and effectively integrating multi-scale audio features. In addition, ablation studies confirmed the effectiveness of the MSFVSS and WTED modules. Full article
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16 pages, 2536 KB  
Article
Research on Optimization of Tourism Spatial Structure of Linear Cultural Heritage: A Case Study of the Beijing–Hangzhou Grand Canal
by Shuying Zhang, Wenting Yu and Jiasheng Cui
Heritage 2025, 8(10), 408; https://doi.org/10.3390/heritage8100408 - 29 Sep 2025
Abstract
Linear cultural heritage poses significant challenges in tourism development, primarily due to the complexities involved in implementing scientific zoning and differentiated management strategies. Systematic optimization of its tourism spatial structure has thus become crucial for achieving sustainable utilization. This study adopts a case [...] Read more.
Linear cultural heritage poses significant challenges in tourism development, primarily due to the complexities involved in implementing scientific zoning and differentiated management strategies. Systematic optimization of its tourism spatial structure has thus become crucial for achieving sustainable utilization. This study adopts a case study approach based on deductive reasoning to examine the morphological characteristics and evolutionary patterns of the tourism space along linear cultural heritage. Taking the Beijing–Hangzhou Grand Canal as an example, it proposes a targeted optimization pathway from a spatial positioning perspective. The findings indicate that the tourism value of linear cultural heritage exhibits a “vine-shaped structure” spatially, and the development process of the tourism space structure follows the “growth pole” evolution law. Moreover, spatial optimization can be achieved through the dual dimensions of spatial form and utilization intensity. Based on this pathway, a three-level tourism zone system is constructed for the Beijing–Hangzhou Grand Canal: the primary tourism zone, located in southern sections, such as Yangzhou and Hangzhou, serves as leading regions that play a pivotal and driving role; the secondary tourism zone, encompassing Beijing, Tianjin, Langfang, and Cangzhou, requires focused enhancement and functional upgrading; and the tertiary tourism zone, mainly including Shandong Province and Xuzhou, Suqian, in Jiangsu Province, necessitate comprehensive and integrated development to achieve overall improvement. This classification not only facilitates coordinated tourism development along the entire canal from a holistic perspective but also provides a basis for formulating targeted strategies for segments with varying tourism values and utilization intensities. Full article
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35 pages, 70837 KB  
Article
CAM3D: Cross-Domain 3D Adversarial Attacks from a Single-View Image via Mamba-Enhanced Reconstruction
by Ziqi Liu, Wei Luo, Sixu Guo, Jingnan Zhang and Zhipan Wang
Electronics 2025, 14(19), 3868; https://doi.org/10.3390/electronics14193868 - 29 Sep 2025
Abstract
With the widespread deployment of deep neural networks in real-world physical environments, assessing their robustness against adversarial attacks has become a central issue in AI safety. However, the existing two-dimensional adversarial methods often lack robustness in the physical world, while three-dimensional adversarial camouflage [...] Read more.
With the widespread deployment of deep neural networks in real-world physical environments, assessing their robustness against adversarial attacks has become a central issue in AI safety. However, the existing two-dimensional adversarial methods often lack robustness in the physical world, while three-dimensional adversarial camouflage generation typically relies on high-fidelity 3D models, limiting practicality. To address these limitations, we propose CAM3D, a cross-domain 3D adversarial camouflage generation framework based on single-view image input. The framework establishes an inverse graphics network based on the Mamba architecture, integrating a hybrid non-causal state-space-duality module and a wavelet-enhanced dual-branch local perception module. This design preserves global dependency modeling while strengthening high-frequency detail representation, enabling high-precision recovery of 3D geometry and texture from a single image and providing a high-quality structural prior for subsequent adversarial camouflage optimization. On this basis, CAM3D employs a progressive three-stage optimization strategy that sequentially performs multi-view pseudo-supervised reconstruction, real-image detail refinement, and cross-domain adversarial camouflage generation, thereby systematically improving the attack effectiveness of adversarial camouflage in both the digital and physical domains. The experimental results demonstrate that CAM3D substantially reduces the detection performance of mainstream object detectors, and comparative as well as ablation studies further confirm its advantages in geometric consistency, texture fidelity, and physical transferability. Overall, CAM3D offers an effective paradigm for adversarial attack research in real-world physical settings, characterized by low data dependency and strong physical generalization. Full article
(This article belongs to the Special Issue Adversarial Attacks and Defenses in AI Safety/Reliability)
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10 pages, 1952 KB  
Article
Three-Dimensional Volumetric Iodine Mapping of the Liver Segment Derived from Contrast-Enhanced Dual-Energy CT for the Assessment of Hepatic Cirrhosis
by Yosuke Kawano, Masahiro Tanabe, Mayumi Higashi, Haruka Kiyoyama, Naohiko Kamamura, Jo Ishii, Haruki Furutani and Katsuyoshi Ito
Tomography 2025, 11(10), 109; https://doi.org/10.3390/tomography11100109 - 29 Sep 2025
Abstract
Objective: This study aimed to evaluate the hepatic volume, iodine concentration, and extracellular volume (ECV) of each hepatic segment in cirrhotic patients using three-dimensional (3D) volumetric iodine mapping of the liver segment derived from contrast-enhanced dual-energy CT (DECT) superimposed on extracted color-coded [...] Read more.
Objective: This study aimed to evaluate the hepatic volume, iodine concentration, and extracellular volume (ECV) of each hepatic segment in cirrhotic patients using three-dimensional (3D) volumetric iodine mapping of the liver segment derived from contrast-enhanced dual-energy CT (DECT) superimposed on extracted color-coded CT liver segments in comparison with non-cirrhotic patients. Methods: The study population consisted of 66 patients, 34 with cirrhosis and 32 without cirrhosis. Using 3D volumetric iodine mapping of the liver segment derived from contrast-enhanced DECT superimposed on extracted color-coded CT liver segments, the volume and iodine concentration of each hepatic segment in the portal venous phase (PVP) and equilibrium phase (EP), the difference in iodine concentration between PVP and EP (ICPVP-liver—ICEP-liver), and ECV fractions were compared between cirrhotic and non-cirrhotic groups. Results: The iodine concentration was not significantly different in all hepatic segments between the cirrhotic and non-cirrhotic groups. Conversely, the difference in iodine concentration between PVP and EP (ICPVP-liver—ICEP-liver) was significantly smaller in the cirrhosis group than in the non-cirrhosis group for all hepatic segments (p < 0.001). The ECV fraction of the left medial segment was significantly higher in the cirrhosis group than in the non-cirrhotic group ([26.4 ± 7.6] vs. [23.1 ± 5.1]; p < 0.05). Conclusions: The decreased difference in iodine concentration between PVP and EP calculated from 3D volumetric iodine mapping of the liver segment using DECT may be a clinically useful indicator for evaluating patients with compensated cirrhosis, suggesting a combined effect of a reduced portal venous flow and increased interstitial space associated with fibrosis. Full article
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28 pages, 3341 KB  
Article
Research on Dynamic Energy Management Optimization of Park Integrated Energy System Based on Deep Reinforcement Learning
by Xinjian Jiang, Lei Zhang, Fuwang Li, Zhiru Li, Zhijian Ling and Zhenghui Zhao
Energies 2025, 18(19), 5172; https://doi.org/10.3390/en18195172 - 29 Sep 2025
Abstract
Under the background of energy transition, the Integrated Energy System (IES) of the park has become a key carrier for enhancing the consumption capacity of renewable energy due to its multi-energy complementary characteristics. However, the high proportion of wind and solar resource access [...] Read more.
Under the background of energy transition, the Integrated Energy System (IES) of the park has become a key carrier for enhancing the consumption capacity of renewable energy due to its multi-energy complementary characteristics. However, the high proportion of wind and solar resource access and the fluctuation of diverse loads have led to the system facing dual uncertainty challenges, and traditional optimization methods are difficult to adapt to the dynamic and complex dispatching requirements. To this end, this paper proposes a new dynamic energy management method based on Deep Reinforcement Learning (DRL) and constructs an IES hybrid integer nonlinear programming model including wind power, photovoltaic, combined heat and power generation, and storage of electric heat energy, with the goal of minimizing the operating cost of the system. By expressing the dispatching process as a Markov decision process, a state space covering wind and solar output, multiple loads and energy storage states is defined, a continuous action space for unit output and energy storage control is constructed, and a reward function integrating economic cost and the penalty for renewable energy consumption is designed. The Deep Deterministic Policy Gradient (DDPG) and Deep Q-Network (DQN) algorithms were adopted to achieve policy optimization. This study is based on simulation rather than experimental validation, which aligns with the exploratory scope of this research. The simulation results show that the DDPG algorithm achieves an average weekly operating cost of 532,424 yuan in the continuous action space scheduling, which is 8.6% lower than that of the DQN algorithm, and the standard deviation of the cost is reduced by 19.5%, indicating better robustness. Under the fluctuation of 10% to 30% on the source-load side, the DQN algorithm still maintains a cost fluctuation of less than 4.5%, highlighting the strong adaptability of DRL to uncertain environments. Therefore, this method has significant theoretical and practical value for promoting the intelligent transformation of the energy system. Full article
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20 pages, 5249 KB  
Article
Research on Anomaly Detection in Wastewater Treatment Systems Based on a VAE-LSTM Fusion Model
by Xin Liu, Zhengxuan Gong and Xing Zhang
Water 2025, 17(19), 2842; https://doi.org/10.3390/w17192842 - 28 Sep 2025
Abstract
This study addresses the problem of anomaly detection in water treatment systems by proposing a hybrid VAE–LSTM model with a combined loss function that integrates reconstruction and prediction errors. Following the signal flow of wastewater treatment systems, data acquisition, transmission, and cyberattack scenarios [...] Read more.
This study addresses the problem of anomaly detection in water treatment systems by proposing a hybrid VAE–LSTM model with a combined loss function that integrates reconstruction and prediction errors. Following the signal flow of wastewater treatment systems, data acquisition, transmission, and cyberattack scenarios were simulated, and a dual-dimensional learning framework of “feature space—temporal space” was designed: the VAE learns latent data distributions and computes reconstruction errors, while the LSTM models temporal dependencies and computes prediction errors. Anomaly decisions are made through feature extraction and weighted scoring. Experimental comparisons show that the proposed fusion model achieves an accuracy of approximately 0.99 and an F1-Score of about 0.75, significantly outperforming single models such as Isolation Forest and One-Class SVM. It can accurately identify attack anomalies in devices such as the LIT101 sensor and MV101 actuator, e.g., water tank overflow and state transitions, with reconstruction errors primarily beneath 0.08 ensuring detection reliability. In terms of time efficiency, Isolation Forest is suitable for real-time preliminary screening, while VAE-LSTM adapts to high-precision detection scenarios with an “offline training (423 s) + online detection (1.39 s)” mode. This model provides a practical solution for intelligent monitoring of industrial water treatment systems. Future research will focus on model lightweighting, enhanced data generalization, and integration with edge computing to improve system applicability and robustness. The proposed approach breaks through the limitations of traditional single models, demonstrating superior performance in detection accuracy and scenario adaptability. It offers technical support for improving the operational efficiency and security of water treatment systems and serves as a paradigm reference for anomaly detection in similar industrial systems. Full article
(This article belongs to the Section Wastewater Treatment and Reuse)
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30 pages, 1770 KB  
Article
A Hybrid Numerical–Semantic Clustering Algorithm Based on Scalarized Optimization
by Ana-Maria Ifrim and Ionica Oncioiu
Algorithms 2025, 18(10), 607; https://doi.org/10.3390/a18100607 - 27 Sep 2025
Abstract
This paper addresses the challenge of segmenting consumer behavior in contexts characterized by both numerical regularities and semantic variability. Traditional models, such as RFM-based segmentation, capture the transactional dimension but neglect the implicit meanings expressed through product descriptions, reviews, and linguistic diversity. To [...] Read more.
This paper addresses the challenge of segmenting consumer behavior in contexts characterized by both numerical regularities and semantic variability. Traditional models, such as RFM-based segmentation, capture the transactional dimension but neglect the implicit meanings expressed through product descriptions, reviews, and linguistic diversity. To overcome this gap, we propose a hybrid clustering algorithm that integrates numerical and semantic distances within a unified scalar framework. The central element is a scalar objective function that combines Euclidean distance in the RFM space with cosine dissimilarity in the semantic embedding space. A continuous parameter λ regulates the relative influence of each component, allowing the model to adapt granularity and balance interpretability across heterogeneous data. Optimization is performed through a dual strategy: gradient descent ensures convergence in the numerical subspace, while genetic operators enable a broader exploration of semantic structures. This combination supports both computational stability and semantic coherence. The method is validated on a large-scale multilingual dataset of transactional records, covering five culturally distinct markets. Results indicate systematic improvements over classical approaches, with higher Silhouette scores, lower Davies–Bouldin values, and stronger intra-cluster semantic consistency. Beyond numerical performance, the proposed framework produces intelligible and culturally adaptable clusters, confirming its relevance for personalized decision-making. The contribution lies in advancing a scalarized formulation and hybrid optimization strategy with wide applicability in scenarios where numerical and textual signals must be analyzed jointly. Full article
(This article belongs to the Special Issue Recent Advances in Numerical Algorithms and Their Applications)
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20 pages, 1837 KB  
Article
Unlabeled Insight, Labeled Boost: Contrastive Learning and Class-Adaptive Pseudo-Labeling for Semi-Supervised Medical Image Classification
by Jing Yang, Mingliang Chen, Qinhao Jia and Shuxian Liu
Entropy 2025, 27(10), 1015; https://doi.org/10.3390/e27101015 - 27 Sep 2025
Abstract
The medical imaging domain frequently encounters the dual challenges of annotation scarcity and class imbalance. A critical issue lies in effectively extracting information from limited labeled data while mitigating the dominance of head classes. The existing approaches often overlook in-depth modeling of sample [...] Read more.
The medical imaging domain frequently encounters the dual challenges of annotation scarcity and class imbalance. A critical issue lies in effectively extracting information from limited labeled data while mitigating the dominance of head classes. The existing approaches often overlook in-depth modeling of sample relationships in low-dimensional spaces, while rigid or suboptimal dynamic thresholding strategies in pseudo-label generation are susceptible to noisy label interference, leading to cumulative bias amplification during the early training phases. To address these issues, we propose a semi-supervised medical image classification framework combining labeled data-contrastive learning with class-adaptive pseudo-labeling (CLCP-MT), comprising two key components: the semantic discrimination enhancement (SDE) module and the class-adaptive pseudo-label refinement (CAPR) module. The former incorporates supervised contrastive learning on limited labeled data to fully exploit discriminative information in latent structural spaces, thereby significantly amplifying the value of sparse annotations. The latter dynamically calibrates pseudo-label confidence thresholds according to real-time learning progress across different classes, effectively reducing head-class dominance while enhancing tail-class recognition performance. These synergistic modules collectively achieve breakthroughs in both information utilization efficiency and model robustness, demonstrating superior performance in class-imbalanced scenarios. Extensive experiments on the ISIC2018 skin lesion dataset and Chest X-ray14 thoracic disease dataset validate CLCP-MT’s efficacy. With only 20% labeled and 80% unlabeled data, our framework achieves a 10.38% F1-score improvement on ISIC2018 and a 2.64% AUC increase on Chest X-ray14 compared to the baselines, confirming its effectiveness and superiority under annotation-deficient and class-imbalanced conditions. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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