Symmetry

35 pages, 4901 KB

Open AccessArticle

Investigation of the Impact of Household Energy Storage on DSO Grid Load Symmetry and Photovoltaic Energy Utilization Efficiency

by Laurynas Šriupša, Mindaugas Vaitkūnas, Artūras Baronas, Gytis Svinkūnas, Julius Dosinas, Saulius Gudžius and Gytis Vilutis

Symmetry 2026, 18(5), 879; https://doi.org/10.3390/sym18050879 - 21 May 2026

Viewed by 339

Abstract

In this study, we investigate the impact of electric energy storage (EES) on phase line power flow symmetry and photovoltaic (PV) energy utilization in prosumer three-phase four-wire integrated household systems. The analysis is based on high-time-resolution (1 s) experimental data collected from a [...] Read more.

In this study, we investigate the impact of electric energy storage (EES) on phase line power flow symmetry and photovoltaic (PV) energy utilization in prosumer three-phase four-wire integrated household systems. The analysis is based on high-time-resolution (1 s) experimental data collected from a real household grid and subsequent simulations of energy flows using MATLAB/Simulink software. Two converter operation strategies were evaluated: the conventional symmetric mode and the asymmetric mode developed by the authors based on an adaptive power flow management algorithm. For both strategies, the impact of EES capacity on imbalance in the distribution system operator (DSO) grid was investigated. The methodology analyzes energy flows in each phase line separately, allowing for a detailed assessment of the imbalance between phase line phenomena and their impact on local energy consumption. Key performance parameters used for the efficiency evaluation include the self-consumption and self-sufficiency rates, which quantify the share of locally generated energy consumed within the household and the degree of independence from the DSO grid. The results show that combining adaptive asymmetric inverter control with appropriately sized energy storage allows for more efficient on-site utilization of PV energy, which, at the same time, improves the load symmetry of the phase lines in the DSO grid. Full article

(This article belongs to the Special Issue Power Supply-Demand Asymmetry and Power Quality Issues in High-Renewable Energy Power Systems)

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23 pages, 5191 KB

Open AccessArticle

WiPID: An End-to-End Deep Learning Framework for Passive Person Identification Using WiFi Signals

by Chenlu Wang, Ya Deng, Yuke Li, Shenhujing Wang and Shubin Wang

Symmetry 2026, 18(5), 878; https://doi.org/10.3390/sym18050878 - 21 May 2026

Viewed by 472

Abstract

WiFi sensing has gained widespread attention as a promising technology, owing to its non-intrusiveness, strong privacy-preserving characteristics, and cost-effective deployment, enabling diverse application scenarios. In addition, the stable spatial characteristics and symmetry-related patterns exhibited by human body postures in WiFi signal propagation provide [...] Read more.

WiFi sensing has gained widespread attention as a promising technology, owing to its non-intrusiveness, strong privacy-preserving characteristics, and cost-effective deployment, enabling diverse application scenarios. In addition, the stable spatial characteristics and symmetry-related patterns exhibited by human body postures in WiFi signal propagation provide new possibilities for robust person identification. In traditional WiFi-based person identification technologies, although gait recognition has achieved certain success, it is complex to operate and limited in application scenarios, increasing the constraints on recognition. This issue becomes more pronounced in large-scale user scenarios, where the system performance tends to degrade and exhibit instability. To overcome these challenges, we introduce a new person identification system called WiPID. The WiFi signals extracted from the static postures of users are treated as a “biometric fingerprint” for identity verification. An end-to-end deep learning framework is utilized by WiPID to process WiFi signals, and a convolutional autoencoder is adopted to preprocess the signals directly, effectively reducing redundant information and greatly simplifying the WiFi data processing. Furthermore, the integration of a multi-scale feature extraction module improves the system’s ability to capture discriminative features. The proposed system not only reduces operational complexity but also extends its applicability to a wider range of scenarios, thereby enhancing recognition performance. In an experiment involving 50 volunteers, WiPID achieved an average recognition accuracy of up to 98%, demonstrating the method’s suitability for large-scale person identification scenarios. In addition, a real-time identification experiment has been conducted on PCs and commercial WiFi devices. Experiments have proven that WiPID can achieve real-time person identification on Internet of Things devices, further validating its feasibility and stability in practical applications. Full article

(This article belongs to the Special Issue Symmetry in Computational Intelligence and Data Science)

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22 pages, 405 KB

Open AccessArticle

Multiple Points with Increasing Multiplicities on a Fixed Projective Set

by Edoardo Ballico

Symmetry 2026, 18(5), 877; https://doi.org/10.3390/sym18050877 - 21 May 2026

Viewed by 241

Abstract

Take a finite subset S of an n-dimensional projective space. We study the Hilbert function of the multiples

m S

of S, mainly when S is general or at least very general. We recall several classical conjectures on this problem, raise new [...] Read more.

Take a finite subset S of an n-dimensional projective space. We study the Hilbert function of the multiples

m S

of S, mainly when S is general or at least very general. We recall several classical conjectures on this problem, raise new open questions, and prove some particular cases. An open question is if all

m S

have the expected Hilbert function. We find cases in which there are Zariski open subsets of sets S with maximal rank for all m and pairs

(n, # S)

for which no such open set exists. We start the study of the m-Terracini sets proving when the first one is nonempty for Veronese embeddings. Full article

(This article belongs to the Special Issue Mathematics: Feature Papers 2026)

35 pages, 7455 KB

Open AccessArticle

Mixed Discrete–Continuous Constrained Optimization of Symmetric Multi-LiDAR Mount Configurations for Mapping Systems: A Physics-Based Simulation Study

by Raghad Hadi Hasan, Athraa Hashim Mohammed, Faten Mezher Radhi and Bashar Alsadik

Symmetry 2026, 18(5), 876; https://doi.org/10.3390/sym18050876 - 21 May 2026

Viewed by 343

Abstract

The configuration of a multi-LiDAR system impacts coverage, redundancy, and observability in mobile mapping. In this study, a multi-LiDAR configuration is modeled as a constrained optimization problem that considers symmetry and clearance constraints. A physics-based simulation is applied to evaluate coverage, overlap, and [...] Read more.

The configuration of a multi-LiDAR system impacts coverage, redundancy, and observability in mobile mapping. In this study, a multi-LiDAR configuration is modeled as a constrained optimization problem that considers symmetry and clearance constraints. A physics-based simulation is applied to evaluate coverage, overlap, and angular diversity for spinning LiDARs such as the Ouster OS1-64 and the Velodyne VLP-16. Three methods of Bayesian Optimization (BO), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) are used. In an indoor space, all methods find symmetric multi-sensor configurations that maximize coverage and redundancy. GA and PSO methods required thousands of evaluations, whereas BO demonstrated excellent efficiency by converging in fewer iterations. Validation using simulated, realistic trajectories and ground-truth environments shows that symmetric multi-LiDAR configuration increases surface completeness by 10–11% over single-sensor setups (up to 27% for OS1-64 and 42% for VLP-16). The results further show that bilateral symmetry is a practical mounting constraint and also a robust design principle that improves mapping completeness. Full article

(This article belongs to the Special Issue Asymmetric and Symmetric in Deep Computer Vision and Generative Modeling)

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17 pages, 3335 KB

Open AccessTechnical Note

Integrated Borehole GPR and Optical Imaging for Field Investigation of Rock Mass Structures

by Yangyang Xiong, Haijun Chen, Zengqiang Han and Chao Wang

Symmetry 2026, 18(5), 875; https://doi.org/10.3390/sym18050875 - 21 May 2026

Viewed by 461

Abstract

Conventional drilling and coring methods are inherently limited to providing one-dimensional geological data, which hinders accurate characterization of the spatial distribution of rock mass structures and properties. Mechanical disturbances during drilling often cause core breakage, further compromising the fidelity of in situ geological [...] Read more.

Conventional drilling and coring methods are inherently limited to providing one-dimensional geological data, which hinders accurate characterization of the spatial distribution of rock mass structures and properties. Mechanical disturbances during drilling often cause core breakage, further compromising the fidelity of in situ geological representation. This study proposes an integrated approach combining borehole optical imaging and GPR to enhance the characterization of rock mass structures. A dynamic exploration method is introduced, defined as an adaptive drilling layout workflow based on phased information feedback. The fundamental concept, key assumptions, boundary conditions, and field implementation procedures of this dynamic survey are systematically described. The integrated method is applied to a high-speed railway investigation project in the Tengzhou section, Shandong Province, China, where six boreholes were surveyed using both techniques. Results demonstrate that fused analysis of borehole optical images and GPR data effectively reveals rock morphology, fracture distribution, joint systems, and fractured zones. Optical imaging provides high-resolution orientation data at the borehole wall. Borehole GPR extends detection radially into the surrounding rock mass. Together, the two methods enable spatially enhanced characterization and partially mitigate the azimuthal ambiguity inherent in single-borehole radar measurements. A triangular borehole survey scheme is shown to be feasible for locating subsurface anomalies. The proposed method effectively reduces borehole requirements compared to conventional grid layouts. Through the integrated analysis of optical imaging and GPR data, common anomalous features can be successfully identified. The method demonstrates practical applicability for detecting fractures with apertures greater than 1 cm and meter-scale cavities. Good consistency between the two techniques validates the feasibility of this integrated approach. The method’s limitations, including resolution constraints and detection omission risks, are explicitly acknowledged, and risk control strategies are proposed. Overall, the dynamic exploration approach reduces investigation costs and accelerates project timelines. It also provides a practical framework for the spatial characterization of rock mass discontinuities with minimal borehole requirements. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Rock Mechanics and Geotechnical Engineering)

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23 pages, 14104 KB

Open AccessArticle

Symbol Recognition of Station Signal Layout Drawings Using a Fusion Design of Generalized Focal Loss and Dilated Residual Segmentation

by Qi Sun, Weizhi Deng, Mengxin Zhu, Wentong Fan and Tianyu Li

Symmetry 2026, 18(5), 874; https://doi.org/10.3390/sym18050874 - 21 May 2026

Viewed by 512

Abstract

Station Signal Layout Plans (SSLPs) are pivotal engineering drawings used in the design of railway signaling systems. Accurate recognition of such drawings is essential for enabling intelligent railway operations and supporting digital management. However, the inherent complexity of engineering drawings—characterized by diverse object [...] Read more.

Station Signal Layout Plans (SSLPs) are pivotal engineering drawings used in the design of railway signaling systems. Accurate recognition of such drawings is essential for enabling intelligent railway operations and supporting digital management. However, the inherent complexity of engineering drawings—characterized by diverse object categories and significant scale variations—substantially increases the difficulty of detection tasks. To address these challenges, this paper proposes an improved YOLOv8-based algorithm for rapid and accurate object detection. First, to enhance the detection of small objects in engineering drawings, a cross-scale attention mechanism is introduced into the mid-scale detection head. During prediction, this mechanism leverages fine-grained details from lower-level features to improve small-object detection. In addition, to suppress noise and blurred edges in drawings, the YOLOv8 neck network is enhanced with a DWRSeg-based design. This structure enlarges the receptive field while preserving local details, thereby effectively reducing the impact of noise on localization. To evaluate the proposed method, a complex dataset was constructed from station signal layout plans provided by a railway bureau, featuring substantial variations in target scale, diverse categories, and densely distributed objects. Experimental results demonstrate that, compared with YOLOv8n, the proposed DCS-YOLO model improves precision, recall, and mAP@0.5 by 3.1%, 0.8%, and 2.1%, respectively, while maintaining a comparable mAP@0.5:0.95. Comparative experiments with representative object detection methods demonstrate that the proposed algorithm achieves competitive detection accuracy and real-time performance for SSLP symbol recognition, providing a practical technical solution for the intelligent analysis of engineering drawings in the railway industry. Full article

(This article belongs to the Section A: Computer Science)

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23 pages, 3868 KB

Open AccessArticle

Evaluating the Performance of Multiple Machine Learning and Deep Learning Models on Glacier Mass Balance Estimation

by Yu Liao, Lin Liu and Xueyu Zhang

Symmetry 2026, 18(5), 873; https://doi.org/10.3390/sym18050873 - 21 May 2026

Cited by 1 | Viewed by 504

Abstract

Glacier mass balance estimation is important for understanding glacier responses to climate change and for assessing mountain water resources. Data-driven methods are widely used, but their cross-regional transferability remains unclear, especially in High Mountain Asia (HMA), where observations are limited. This study develops [...] Read more.

Glacier mass balance estimation is important for understanding glacier responses to climate change and for assessing mountain water resources. Data-driven methods are widely used, but their cross-regional transferability remains unclear, especially in High Mountain Asia (HMA), where observations are limited. This study develops a unified framework to compare 16 machine learning and deep learning models across the European Alps and HMA. A degree-day-based monthly decomposition scheme is used to generate physically constrained monthly mass balance estimates. These are used as intermediate supervision signals. All models are trained at the monthly scale, and the outputs are aggregated to annual values for evaluation against observations. In transfer experiments, models are trained on Alpine data and tested in HMA. In joint-training experiments, different proportions of HMA samples are gradually added to the training set to assess the role of target-region information. Results show that machine learning models outperform deep learning models in cross-regional settings. Random Forest and K-Nearest Neighbors remain relatively stable under limited HMA data, while deep learning models are more sensitive to distribution shifts. Adding a small amount of HMA data improves annual prediction performance, highlighting the value of region-specific information. Overall, this study provides guidance for modeling glacier mass balance in data-scarce regions. Full article

(This article belongs to the Section A: Computer Science)

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20 pages, 2240 KB

Open AccessArticle

Reliability Analysis and Component Importance Assessment for k-out-of-n Systems with Uncertain Continuous States and Uncertain Weights

by Haiyan Shi, Chun Wei, Guoqing Wang and Zhiqiang Zhang

Symmetry 2026, 18(5), 872; https://doi.org/10.3390/sym18050872 - 21 May 2026

Viewed by 497

Abstract

Engineering systems generally exhibit continuous state degradation in practical operation, and reliability evaluation is often challenged by data scarcity and uncertain component weights. Existing studies on weighted k-out-of-n systems mainly focus on deterministic or discrete-state models, while rarely addressing reliability modeling and component [...] Read more.

Engineering systems generally exhibit continuous state degradation in practical operation, and reliability evaluation is often challenged by data scarcity and uncertain component weights. Existing studies on weighted k-out-of-n systems mainly focus on deterministic or discrete-state models, while rarely addressing reliability modeling and component importance assessment for continuous-state systems with uncertain information under data shortage, which constitutes a clear research gap. This paper first defines the connotation of uncertain continuous state as the continuous degradation process of system performance affected by ambiguous parameter information and insufficient historical data. On this basis, a reliability modeling framework is established for a weighted k-out-of-n system with uncertain continuous states. Adopting stochastic reliability theory, this paper comparatively investigates system reliability under constant component weights and uncertain variable component weights, and further adopts the Birnbaum importance measure to quantify component importance under variable weight uncertainty. To reduce computational complexity and improve solution efficiency, a binary search-based numerical algorithm is developed to solve the established model. A distributed solar power generation system is employed as a practical case to validate the feasibility and applicability of the proposed model and algorithm. The presented approach effectively fills the limitation of existing discrete and deterministic models, and provides a novel theoretical reference for reliability analysis and key component identification of continuous degradation engineering systems. Full article

(This article belongs to the Section B: Mathematics)

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24 pages, 3324 KB

Open AccessCommunication

An Edge-Preserving Hybrid Filter Based on UFIR Filters for Reducing Gaussian Noise in Digital Images

by Erika Mendoza-Salvador, Luis J. Morales-Mendoza, Mario Gonzalez-Lee, Eli G. Pale-Ramon, Hector Vazquez-Leal, Hector Perez-Meana and Rene F. Vazquez-Bautista

Symmetry 2026, 18(5), 871; https://doi.org/10.3390/sym18050871 - 21 May 2026

Viewed by 825

Abstract

In this paper, we propose a new digital filtering approach based on the FIR-Median Hybrid (FMH) structure, which incorporates an Unbiased Finite Impulse Response (UFIR) filter as its core component. The proposed filter employs spatially symmetric window configurations to reduce Gaussian noise while [...] Read more.

In this paper, we propose a new digital filtering approach based on the FIR-Median Hybrid (FMH) structure, which incorporates an Unbiased Finite Impulse Response (UFIR) filter as its core component. The proposed filter employs spatially symmetric window configurations to reduce Gaussian noise while preserving edges in images. Although the scientific community is rapidly adopting machine-learning- and deep-learning-based filters, there are several reasons to continue developing filters based on traditional methods. For example, these methods are well understood and rely on a strong mathematical foundation. Moreover, the structure of the proposed filter is simple; thus, this type of filter may be appealing to engineers unfamiliar with the machine-learning field. The performance of the proposed filter was assessed using two datasets: the first consisted of a set of artificial binary images, and the second comprised a subset of the BOWS image dataset. We conducted three main experiments. In the first experiment, we fine-tuned the filter considering three window-shape configurations. In the second experiment, Gaussian noise was added to the images, and the proposed filter was compared against other filters using edge-preservation-oriented metrics such as the Structural Similarity Index Measure (SSIM), the Normalized Step Edge Response (NSER), and the Gradient Conduction Mean Square Error (GcMSE), among others. The third experiment evaluated the performance of the best-performing window-shape configurations. This final test was assessed quantitatively using the Friedman test to identify the best-performing structure, whereas qualitative assessment was conducted using a Mean Opinion Score (MOS) test. The results show that the proposed filter achieved improved performance according to the PSNR, SNR, RMSE, and GcMSE metrics. These findings suggest that the proposed filter can be used in practical applications such as image enhancement, computer vision, and edge-detection-based preprocessing. Full article

(This article belongs to the Special Issue Symmetry in Image Processing: Current Advances and Applications)

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13 pages, 294 KB

Open AccessArticle

Blow-Up Profiles and Dynamics in Negative Time for the Semilinear Heat Equation

by Rubayyi T. Alqahtani, Nadiyah Hussain Alharthi and Younes Abouelhanoune

Symmetry 2026, 18(5), 870; https://doi.org/10.3390/sym18050870 - 21 May 2026

Viewed by 369

Abstract

We investigate the blow-up behavior of solutions to the semilinear heat equation

u_{t} = u_{x x} + {| u |}^{p - 1} u, x \in R, u \in R,

for exponents [...] Read more.

We investigate the blow-up behavior of solutions to the semilinear heat equation

u_{t} = u_{x x} + {| u |}^{p - 1} u, x \in R, u \in R,

for exponents

1 < p < 1 + \frac{2}{m}

, where

m \in N

denotes the number of positive eigenvalues of the linearized operator in similarity variables, equivalently the dimension of the associated unstable manifold, which determines both the admissible exponent range and the structure of the blow-up profiles. We construct solutions that exist on the interval

- 1 < t < T

and become unbounded both as

t \to - 1

(backward blow-up) and as

t \to T

(forward blow-up). At blow-up time, the solution profile exhibits a finite number of critical values, which can be prescribed in advance, and possesses a structure with

m + 1

monotonicity intervals. By introducing similarity variables, we reduce the problem to an evolution equation in weighted spaces and identify the role of unstable manifolds. Our results establish a classification of blow-up dynamics in terms of spectral properties and provide a systematic framework for constructing solutions with prescribed spatial patterns of singularity. Full article

(This article belongs to the Section B: Mathematics)

31 pages, 4178 KB

Open AccessArticle

MSCB-DualAttn Network for sEMG-Based Gesture Recognition in Transradial Amputees with Varying Residual Limb Lengths

by Xinwei Shi, Zuxiang He, Liangdong Zheng, Yu Chen, Wenxia Bai, Menglei Xu and Rui Zhu

Symmetry 2026, 18(5), 869; https://doi.org/10.3390/sym18050869 - 20 May 2026

Viewed by 390

Abstract

Transradial amputation severely impairs hand function, and myoelectric control offers a promising solution. However, due to the heterogeneity of neuromuscular compensation, existing methods often struggle to generalize across populations with varying residual limb lengths. In this study, we collected an EMG dataset from [...] Read more.

Transradial amputation severely impairs hand function, and myoelectric control offers a promising solution. However, due to the heterogeneity of neuromuscular compensation, existing methods often struggle to generalize across populations with varying residual limb lengths. In this study, we collected an EMG dataset from 41 participants, including healthy individuals and amputees with long, medium, and short residual limbs, performing 15 gestures, and proposed a Multi-Scale Convolutional Block with Dual Attention Network (MSCB-DualAttn) that integrates parallel multi-scale convolutions (kernel sizes 3, 5, and 7) with channel and temporal attention mechanisms. The model achieved recognition accuracies of 93.79%, 86.13%, and 78.10% in the healthy, long-stump, and middle-stump groups, respectively, and 62.69% in the short-stump group, representing a 13.83 percentage point improvement over the baseline model. Ablation studies and interpretability analyses confirmed the complementary roles of the multi-scale and attention modules, while the performance degradation in the short-stump group suggested a potential limitation of existing models when neuromuscular control shifts from fine synergy to coarse compensation. This study proposes a model framework that enhances gesture recognition accuracy in amputees and highlights the potential of physiology-driven architectures for myoelectric control. Full article

(This article belongs to the Section E: Life Sciences)

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42 pages, 15988 KB

Open AccessArticle

Emergency Logistics Distribution Center Location Model Based on ISG-IAGNES Clustering and Symmetrical IDFS Spatial Decision Tree Algorithm

by Xiao Zhou, Wenbing Liu, Jun Wang and Fan Jiang

Symmetry 2026, 18(5), 868; https://doi.org/10.3390/sym18050868 - 20 May 2026

Viewed by 375

Abstract

Taking emergency logistics scenarios under urban public emergencies as the research background, this paper analyzes the current research status and existing problems of distribution center location methods. It constructs an emergency logistics distribution center location model based on ISG-IAGNES clustering and a symmetrical [...] Read more.

Taking emergency logistics scenarios under urban public emergencies as the research background, this paper analyzes the current research status and existing problems of distribution center location methods. It constructs an emergency logistics distribution center location model based on ISG-IAGNES clustering and a symmetrical IDFS spatial decision tree algorithm. Firstly, the ISG spatial model is constructed to divide urban geographic space into cellular units and then topologically generate the cellular space. Secondly, the IAGNES algorithm is established to achieve cellular space clustering, realizing the dimensionality reduction operation of the urban emergency space. Thirdly, the symmetrical characteristic of the pathway is taken as the core condition to construct the DFS algorithm to build the graph global searching model, and then the logistics distribution center location model based on the symmetrical IDFS spatial decision tree algorithm is constructed. The experiment proves that the optimization rate of the distribution center selected by the proposed algorithm in terms of route distance cost and time cost is 9.82% compared to the centroid method and analytic hierarchy process, 14.41% compared to the Dijkstra algorithm, and 17.21% compared to the Prim algorithm. It proves that the proposed algorithm has advantages over traditional algorithms in reducing the distance cost and time cost of logistics routes. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Data Mining and Machine Learning)

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24 pages, 9903 KB

Open AccessArticle

A Symmetric Multistable Chaotic System Optimized by Chaotic Particle Swarm for Secure Electric Vehicle Communication

by Mohamed Fadi Kethiri, Faiza Zaamoune and Christos Volos

Symmetry 2026, 18(5), 867; https://doi.org/10.3390/sym18050867 - 20 May 2026

Cited by 2 | Viewed by 449

Abstract

Secure real-time communication is a critical requirement in modern electric vehicle (EV) networks. These networks transmit safety-critical control commands through vulnerable in-vehicle communication channels. This study proposes a novel three-dimensional symmetric chaotic system for high-security EV communication. The system exhibits extensive multistability and [...] Read more.

Secure real-time communication is a critical requirement in modern electric vehicle (EV) networks. These networks transmit safety-critical control commands through vulnerable in-vehicle communication channels. This study proposes a novel three-dimensional symmetric chaotic system for high-security EV communication. The system exhibits extensive multistability and symmetric double-wing attractors. To enhance dynamical complexity, its parameters are optimized using chaotic-enhanced particle swarm optimization (C-PSO). The largest Lyapunov exponent is used as the optimization objective. A fixed-time nonlinear controller is designed for rapid drive–response synchronization. The settling-time bound is independent of the initial conditions. The proposed method is evaluated through realistic Controller Area Network (CAN) bus simulations. These simulations include 12-bit quantization and a 1 ms sampling period. The experimental results show synchronization within 0.057 s. The recovered signal achieves an MSE of

1.202 \times 10^{- 4}

. The encrypted signal reaches a Shannon entropy of 7.9904. These results confirm accurate recovery, strong randomness, and improved resistance to cryptographic attacks. Full article

(This article belongs to the Section F: Engineering and Materials)

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23 pages, 2289 KB

Open AccessArticle

Symmetry-Guided Distributed Control Strategy for Source–Load Coordination in Active Distribution Networks with Electric Heating Loads

by Shoudong Li, Jinhang Song and Guangqing Bao

Symmetry 2026, 18(5), 866; https://doi.org/10.3390/sym18050866 - 20 May 2026

Viewed by 267

Abstract

As a clean heating solution, electric heating loads (EHLs) have become a critical flexible load resource on the demand side in recent years. To enhance the power grid’s frequency regulation capability and mitigate the impacts of both EHLs and high-penetration renewable energy on [...] Read more.

As a clean heating solution, electric heating loads (EHLs) have become a critical flexible load resource on the demand side in recent years. To enhance the power grid’s frequency regulation capability and mitigate the impacts of both EHLs and high-penetration renewable energy on the power grid, a symmetry-guided distributed control strategy for active distribution networks (ADNs) considering demand response (DR) of EHLs is proposed from the perspective of source–load bilateral coordination. Based on the symmetry of information interaction and control structure between distributed generators (DGs) and EHLs, a thermodynamic dynamic model of EHLs and a source–load coordinated response control framework are established. An improved consensus-based distributed control algorithm and a temperature queue sorting-based distributed response strategy are designed to maintain symmetrical power allocation and symmetrical response coordination between DGs and EHLs, achieving rapid and stable source–load coordination. Finally, comprehensive simulations verify the effectiveness of the proposed strategy. The results show that the proposed strategy improved the convergence speed by 27.5%, achieved fast and effective control of DGs and EHLs, maintained the steady-state frequency above 49.95 Hz under various interferences, effectively eliminated frequency deviation caused by source–load interference, and significantly improved the stability and frequency support capability of ADNs. Full article

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25 pages, 27185 KB

Open AccessReview

A Review of Symmetrical and Asymmetrical Research Outputs on Wastewater Treatment and Water Purification Through Sorption-Based Technologies

by Abhijit Debnath, Anurag Mishra, Archana Pandey, Prabhat Kumar Singh, Yogesh Chandra Sharma and Rajnish Kaur Calay

Symmetry 2026, 18(5), 865; https://doi.org/10.3390/sym18050865 - 20 May 2026

Viewed by 962

Abstract

This review focuses on research outputs of water purification, wastewater treatment, metallic remediation, and sorption-based experimental studies. It aims to identify the leading nations contributing to these areas and identify the journals that have published the highest number of papers from 2010 to [...] Read more.

This review focuses on research outputs of water purification, wastewater treatment, metallic remediation, and sorption-based experimental studies. It aims to identify the leading nations contributing to these areas and identify the journals that have published the highest number of papers from 2010 to 2025, and centers on yearly publication trends. A thorough quantitative analysis was carried out to examine key characteristics of adsorbents derived from various materials, as well as symmetry and asymmetry of wastewater treatment for the removal of metallic pollutants. Key adsorption mechanisms—including ion exchange, surface complexation, electrostatic attraction, and pore filling—are discussed alongside the structural roles of symmetric (ordered) and asymmetric (heterogeneous) adsorbent architectures. Data was collected from the Scopus database, focusing on specific keywords like “metal,” “water,” “removal,” “adsorption,” “purification,” “drinking water,” “nano adsorbent,” etc. Among approximately 29,598 publications encompassing research papers, reviews, short communications, conference papers, and book chapters, China emerged as the leading publisher with 11,957 papers, trailed by India (4324 papers), the USA (1825 papers), Iran (1739 papers), Saudi Arabia (1484 papers), Egypt (1318 papers), and Republic of Korea (1194 papers). The bibliometric mapping of conventional adsorbents and nanomaterials used in sorption-based technologies was analyzed using VOSviewer, revealing major research clusters, research hotspots, networks, and evolutionary patterns in wastewater treatment and sorption-based water purification. This study indicates that several journals from Elsevier Ltd. and Springer Nature are leading the field with a large number of publications per year. The analysis reveals a consistent upward trend in the number of research publications in recent years. In sum, the bibliometric data provided highlights the growing relevance of these areas among academicians and acts as a catalyst for further research, motivating researchers to investigate new adsorbents or modifications that could improve adsorption performance while maintaining economic viability and efficiency. Full article

(This article belongs to the Special Issue Symmetry in Chemical and Systems Engineering: From Resource Recovery to Sustainable Design)

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15 pages, 868 KB

Open AccessArticle

Approximate Analysis of a Viscoelastic Plate Floating on a Fluid of Finite Depth

by Yuanzhi Qi and Ping Wang

Symmetry 2026, 18(5), 864; https://doi.org/10.3390/sym18050864 - 20 May 2026

Viewed by 411

Abstract

The responses of a very large floating structure (VLFS), which is modeled as a thin viscoelastic plate floating on a fluid of finite depth, are analytically studied within the framework of the nonlinear potential flow theory. We use the Laplace equation with the [...] Read more.

The responses of a very large floating structure (VLFS), which is modeled as a thin viscoelastic plate floating on a fluid of finite depth, are analytically studied within the framework of the nonlinear potential flow theory. We use the Laplace equation with the dynamical boundary condition to express a balance among the hydrodynamic, inertial, and viscoelastic forces. For the case of steady-state incident waves, we obtain convergent series solutions for plate deflection and velocity potential by choosing the optimal convergence-control parameter

C_{0}

and proper auxiliary linear operators in the homotopy analysis method (HAM). The strain relaxation time for the viscoelastic plate is studied, and the result shows that the plate deflection decreases when the retardation time increases. The influences of other physical parameters on the viscoelastic plate are also discussed. The nonlinearity of dispersion relation and the retardation time of the plate have important and non-negligible effects on the responses of the VLFS. The results obtained here may be helpful in understanding the different physical parameters to model hydroelastic responses of a VLFS in the real ocean. Full article

(This article belongs to the Special Issue Advances in Mathematical Models and Partial Differential Equations: 2nd Edition)

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19 pages, 12389 KB

Open AccessArticle

Tensor Completion via Linear Combination of Nuclear Norms

by Xihong Yan, Shibo Gong and Kai Wang

Symmetry 2026, 18(5), 863; https://doi.org/10.3390/sym18050863 - 19 May 2026

Viewed by 451

Abstract

Tensor completion is commonly formulated by minimizing a convex combination of nuclear norms of mode-wise unfolding matrices. Although effective, the non-negative weight constraint can limit the flexibility of mode balancing, especially when different modes contribute unequally to the reconstruction. In this paper, we [...] Read more.

Tensor completion is commonly formulated by minimizing a convex combination of nuclear norms of mode-wise unfolding matrices. Although effective, the non-negative weight constraint can limit the flexibility of mode balancing, especially when different modes contribute unequally to the reconstruction. In this paper, we propose a tensor completion model based on a linear combination of nuclear norms, where the weights are allowed to take signed values under a normalization constraint. To implement this model, we develop an ADMM-based algorithm, termed FlexHaLRTC, which extends the standard singular value thresholding update to handle both shrinkage for positive weights and expansion for negative weights. Experiments on color image inpainting and video completion show that the proposed method achieves competitive PSNR, SSIM, and RSE results, with more noticeable gains in high-missing-rate settings. Full article

(This article belongs to the Section B: Mathematics)

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16 pages, 34018 KB

Open AccessArticle

On Some Incommensurate Fractional-Order Reaction–Diffusion Systems: The Degn–Harrison and Its Stability

by Omar Kahouli, Amel Hioual, Adel Ouannas, Waleed Mohammed Abdelfattah, Younès Bahou, Ilyes Abidi, Sameir Hamed, Mohamed Chaabane and Sarra Elgharbi

Symmetry 2026, 18(5), 862; https://doi.org/10.3390/sym18050862 - 19 May 2026

Viewed by 341

Abstract

In this paper, we consider a reaction–diffusion system governed by incommensurate fractional time derivatives based on the Degn–Harrison model. Its formulation incorporates various memory effects on axial position through Caputo derivatives of variable orders, producing a more realistic modeling of the temporal dynamics. [...] Read more.

In this paper, we consider a reaction–diffusion system governed by incommensurate fractional time derivatives based on the Degn–Harrison model. Its formulation incorporates various memory effects on axial position through Caputo derivatives of variable orders, producing a more realistic modeling of the temporal dynamics. This paper starts with a study of the spatially homogeneous system and establishes conditions for local stability by using the Matignon criterion. The spectral decomposition method under Neumann boundary condition is then applied to study the complete reaction–diffusion system and describe diffusion-induced instabilities. Our results indicate that the noninteger fractional orders lead to significant changes in stability regions, as well as the initiation of pattern formation. Specifically, the orders of fractions induced as a control variable are regarded to be effective in controlling the stability of the system, thus they are global (or positive) control variables when their values achieved at some levels apply to the entire saturation, etc. Our numerical simulations are in excellent agreement with the theoretical predictions and show that memory asymmetry induces complex spatiotemporal dynamics not seen for classical integer-order systems. Full article

(This article belongs to the Special Issue Symmetry in Mathematical and Statistical Sciences: Theory, Methods, and Applications)

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18 pages, 1331 KB

Open AccessArticle

Approximation of RCI Set Under p-Norm Ball Constraints for Linear Discrete-Time Systems

by Hongli Yang, Longfei Yang and Ivan Ganchev Ivanov

Symmetry 2026, 18(5), 861; https://doi.org/10.3390/sym18050861 - 19 May 2026

Viewed by 299

Abstract

This paper investigates the approximation of robust control invariant (RCI) sets for linear discrete-time systems subject to p-norm ball constraints (

p \geq 1

). Unlike classical results focusing on specific cases like polytope or ellipsoid constraints, we propose a unified framework [...] Read more.

This paper investigates the approximation of robust control invariant (RCI) sets for linear discrete-time systems subject to p-norm ball constraints (

p \geq 1

). Unlike classical results focusing on specific cases like polytope or ellipsoid constraints, we propose a unified framework for arbitrary p-norm ball constraints. Sufficient conditions for a non-empty set to be contained within a p-norm ball are established, revealing the geometric insight that the set is essentially contained within the inscribed 2-norm ball. Utilizing these results, the approximation problem of the RCI set is formulated as a standard linear programming problem that requires verifying constraints at only n standard basis vectors, significantly reducing computational complexity. Specific optimization models are derived, and numerical experiments demonstrate the effectiveness and competitive accuracy of the proposed method. Full article

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38 pages, 476 KB

Open AccessArticle

On the Cohomological Understanding of Interactions Between Weyl Graviton and Photon

by Eugen-Mihaita Cioroianu and Stefan-Sabin Manolescu

Symmetry 2026, 18(5), 860; https://doi.org/10.3390/sym18050860 - 19 May 2026

Viewed by 266

Abstract

The problem of constructing consistent interactions between a Weyl graviton—with its free limit expressed by the linearized Weyl action—and a photon—with its free dynamics generated from the standard Maxwell action—is analyzed as a deformation problem for the antifield-BRST generator associated with the non-interacting [...] Read more.

The problem of constructing consistent interactions between a Weyl graviton—with its free limit expressed by the linearized Weyl action—and a photon—with its free dynamics generated from the standard Maxwell action—is analyzed as a deformation problem for the antifield-BRST generator associated with the non-interacting free model. By relaxing the standard working hypotheses to allow at most four spacetime derivatives in the interaction vertices, while not restricting the number of derivatives on the photon potentials, the most general cross-couplings are derived. This proves the uniqueness of the previously geometrically prescribed, overall fourth-order Lagrangian dynamics of the electromagnetic field in the presence of dynamical-type full Weyl gravity. Full article

(This article belongs to the Special Issue Gravitational Physics and Symmetry)

26 pages, 2609 KB

Open AccessArticle

Perceiving Symmetry and Variability: A Probabilistic Vision–Language Framework for Medical Image Segmentation

by Jiu Jiang, Qi Zhou and Chu He

Symmetry 2026, 18(5), 859; https://doi.org/10.3390/sym18050859 - 19 May 2026

Viewed by 339

Abstract

Medical image segmentation is challenging due to subtle pathological patterns and the inherent ambiguity of clinical descriptions. Although vision–language models have shown promise, they frequently lack fine-grained perception of structural variability. To address these limitations, we propose the Symmetry- and Variability-Perceiving Conditional Variational [...] Read more.

Medical image segmentation is challenging due to subtle pathological patterns and the inherent ambiguity of clinical descriptions. Although vision–language models have shown promise, they frequently lack fine-grained perception of structural variability. To address these limitations, we propose the Symmetry- and Variability-Perceiving Conditional Variational Autoencoder (SVP-CVAE). The proposed method integrates a clinical attribute encoder with a morphology-aware enhancement module that incorporates a cross-bilateral symmetry mechanism to explicitly capture symmetry-related variations. By reformulating the segmentation task as a probabilistic prior-to-posterior inference process, SVP-CVAE models the one-to-many mapping between textual attributes and visual realizations. Furthermore, we introduce an attribute-latent contrastive objective to ensure that the latent space encodes discriminative morphological information. Extensive experiments demonstrate that the proposed framework achieves superior segmentation accuracy compared to state-of-the-art methods. Results indicate that SVP-CVAE effectively captures diverse yet anatomically plausible structural variations while maintaining high sensitivity to bilateral symmetry. Comprehensive ablation studies confirm that the performance gains are synergistically driven by the proposed symmetry-perceiving module and the contrastive semantic alignment objective, rather than relying solely on the probabilistic formulation. In conclusion, integrating explicit symmetry perception with probabilistic modeling significantly enhances the reliability and interpretability of multimodal medical image segmentation in complex clinical scenarios. Full article

(This article belongs to the Special Issue Hybrid Deep Learning and Explainable AI for Symmetry-Aware and Multiscale Medical Image Analysis)

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27 pages, 6695 KB

Open AccessArticle

UAV Flight Path Planning Based on HPSOCAOA Optimization Algorithm

by Kaijun Xu, Hongda Luo, Yilin Hong, Yong Yang and Weiqi Feng

Symmetry 2026, 18(5), 858; https://doi.org/10.3390/sym18050858 - 18 May 2026

Viewed by 349

Abstract

To address the issues with the Crocodile Ambush Optimization Algorithm (CAOA) in UAV trajectory planning—such as its tendency to get stuck in local optima, the difficulty in balancing global search and local exploration, and low convergence accuracy—this study proposes a three-dimensional trajectory planning [...] Read more.

To address the issues with the Crocodile Ambush Optimization Algorithm (CAOA) in UAV trajectory planning—such as its tendency to get stuck in local optima, the difficulty in balancing global search and local exploration, and low convergence accuracy—this study proposes a three-dimensional trajectory planning method based on the Hybrid Particle Swarm and Crocodile Ambush Optimization Algorithm (HPSOCAOA). First, a collaborative search structure combining the Particle Swarm Optimization (PSO) algorithm and the Crocodile Ambush Optimization Algorithm (CAOA) is established; second, an adaptive energy consumption coefficient is designed to address the issues of premature individual elimination in the early stages and insufficient convergence momentum in the later stages, thereby further balancing global exploration and local exploitation; finally, crossover learning is introduced. Using a cross-group replacement mechanism for superior individuals, PSO’s fine-tuning identifies high-quality individuals, which are then substituted for lower-quality individuals in CAOA. This resolves the problems of redundant low-quality individuals within the population and low search efficiency, and enhances overall optimization performance. Standard test functions demonstrate that HPSOCAOA outperforms the comparison algorithms in terms of optimization accuracy and stability. In simulation experiments for path planning in complex 3D mountainous environments, HPSOCAOA was compared with classical intelligent algorithms, verifying its superiority and practicality in complex 3D scenarios. Full article

(This article belongs to the Section B: Mathematics)

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28 pages, 9544 KB

Open AccessArticle

A Symmetric Fault Diagnosis Method for Power Batteries Based on Digital Battery Passport and Knowledge Graph-Fuzzy Bayesian Network

by Tongzhou Ji and Jie Li

Symmetry 2026, 18(5), 857; https://doi.org/10.3390/sym18050857 - 18 May 2026

Cited by 2 | Viewed by 471

Abstract

The safe operation of power battery systems relies on the dynamic symmetric equilibrium of electrochemical distribution and thermal management states, whereas fault occurrence is often accompanied by symmetry breaking. To achieve accurate fault diagnosis and symmetry restoration, this study proposes a symmetrical closed-loop [...] Read more.

The safe operation of power battery systems relies on the dynamic symmetric equilibrium of electrochemical distribution and thermal management states, whereas fault occurrence is often accompanied by symmetry breaking. To achieve accurate fault diagnosis and symmetry restoration, this study proposes a symmetrical closed-loop framework (DBP-KG-FBN) that integrates digital battery passport (DBP) text mining, knowledge graph (KG), and fuzzy Bayesian network (FBN). Power battery fault diagnosis is critical to new energy vehicle (NEV) safety; however, conventional methods face two key limitations: (1) they inadequately exploit multi-source heterogeneous textual data in DBPs; and (2) they fail to handle uncertainty in fault propagation. The methodology proceeds as follows. First, a BERT-BiLSTM-CRF model extracts fault-related entities and relations from unstructured DBP text, which are structured into a Neo4j-based knowledge graph. Second, via rule-based topological mapping, the KG topology is transformed into a Bayesian network through structurally symmetric transformation between the semantic and probabilistic layers, with cyclic dependencies resolved by introducing latent variables. Third, network parameters are determined by integrating fuzzy set theory with game theory-based weighting to quantify uncertainty and subjectivity in expert evaluations, thereby achieving symmetric utilization of subjective and objective information. This enables bidirectional symmetric reasoning for forward fault prediction and backward fault traceability. Experimental results demonstrate that while maintaining symmetric stability of the diagnostic knowledge topology, the proposed DBP-KG-FBN method achieves a diagnostic accuracy of 0.92 (Top-3). This symmetrical closed-loop framework significantly outperforms fault tree analysis (FTA) and event tree analysis (ETA) in diagnostic accuracy and reasoning efficiency. It transforms unstructured DBP data into computable knowledge for intelligent battery diagnosis. Future work will expand the corpus via transfer learning and optimize adaptive weighting algorithms for expert evaluations. Full article

(This article belongs to the Section F: Engineering and Materials)

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25 pages, 4601 KB

Open AccessArticle

Key Technologies of Near-Bit Multi-Parameter MWD for Directional Drilling in Underground Engineering

by Zhiwei Chu, Shijun Hao, Quanxin Li, Long Chen, Yunhong Wang, Jun Fang, Dongdong Yang, Jiguan Zhang, Fei Liu and Guo Chen

Symmetry 2026, 18(5), 856; https://doi.org/10.3390/sym18050856 - 18 May 2026

Viewed by 463

Abstract

Near-bit multi-parameter MWD (measurement while drilling) is a key technology for achieving precise and efficient directional drilling in underground and tunnel engineering. The near-bit multi-parameter MWD method was studied, and a “center + side wall” distributed measurement scheme was proposed, based on an [...] Read more.

Near-bit multi-parameter MWD (measurement while drilling) is a key technology for achieving precise and efficient directional drilling in underground and tunnel engineering. The near-bit multi-parameter MWD method was studied, and a “center + side wall” distributed measurement scheme was proposed, based on an analysis of special application scenarios in underground and tunnel engineering. The transmission characteristics of Bluetooth wireless signals in water were investigated. An analysis of the underwater Bluetooth signal link was conducted. When the transmission distance is 100 mm, the received signal strength is −17.5 dBm, and the link margin is 69.5 dB. Wireless Bluetooth was used to transmit the near-bit data. A Bluetooth wireless communication simulation model was established using ANSYS software, and the influence of transmission power, transmission medium, and transmission distance on the Bluetooth signal strength was analyzed. The results indicate that: (1) the received signal strength increases with transmission power, and appropriately increasing the transmission power can improve the effect of Bluetooth wireless communication and extend the communication distance. (2) When the transmission medium is water, the received signal is unstable, and the echo loss curve shows a high and low oscillation form, presenting a frequency shift feature; when the transmission medium is air, the received signal is relatively stable, and the echo loss curve shows a parabolic form. The echo loss of Bluetooth wireless signal in water transmission is significantly higher than that in air transmission, indicating that the Bluetooth signal attenuates more rapidly when transmitted in water. (3) When the transmission distance increases near the optimal transmission frequency of 2.4 GHz, the echo loss increases accordingly, and the received signal strength of the wireless receiving module gradually decreases. The theoretical analysis, simulation, and indoor test results are in good agreement. The reasonable Bluetooth transmission power is 1 mW, and the transmission distance is 100 mm. After completing the overall scheme design and simulation analysis optimization, the structure, circuit, and program development were carried out, and the near-bit multi-parameter MWD device was developed. A laboratory water supply test was conducted, and the power supply, collection, and wireless transmission were all normal. A drilling test was carried out at an underground engineering of a coal mine in Wuhai City, achieving a drilling depth of 2328 m. A continuous and stable collection of various parameters such as WOB (weight on bit), torque, rotation speed, vibration, and gamma was carried out. A wireless transmission channel for near-bit data was established across the screw drilling tool. It can provide key technical support for the research and development of near-bit MWD in underground and tunnel engineering. Full article

(This article belongs to the Section F: Engineering and Materials)

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36 pages, 5057 KB

Open AccessArticle

IID-DAKD: An Incremental Intrusion Detection Method for Encrypted Traffic Based on Dual Augmentation and Fusion Knowledge Distillation

by Liangchen Chen, Deyin Fu, Shu Gao, Shuo Zhang and Baoxu Liu

Symmetry 2026, 18(5), 855; https://doi.org/10.3390/sym18050855 - 18 May 2026

Viewed by 369

Abstract

To address the pronounced degradation in detection accuracy of encrypted traffic intrusion models after incremental updates, which is primarily caused by catastrophic forgetting and task-level overfitting during incremental learning, this paper proposes a novel incremental intrusion detection method for encrypted traffic based on [...] Read more.

To address the pronounced degradation in detection accuracy of encrypted traffic intrusion models after incremental updates, which is primarily caused by catastrophic forgetting and task-level overfitting during incremental learning, this paper proposes a novel incremental intrusion detection method for encrypted traffic based on dual augmentation and fusion knowledge distillation, termed IID-DAKD. First, both known and previously unseen attacks identified during detection are leveraged to update a representative sample set. An encrypted traffic representative sample augmentation strategy based on Gaussian noise is then devised to reduce storage requirements and classifier bias, thereby effectively mitigating catastrophic forgetting. Second, a self-supervised learning framework driven by encrypted traffic class augmentation is constructed to alleviate representation bias and suppress task-level overfitting. Finally, three complementary knowledge distillation strategies are jointly employed to extract and transfer attack classification knowledge from the old model to the updated model, further improving detection accuracy and robustness while enhancing training efficiency. Extensive experimental results demonstrate that the proposed IID-DAKD approach alleviates catastrophic forgetting and task-level overfitting while maintaining symmetrical knowledge transfer during incremental learning, enabling efficient model updates and high detection accuracy for encrypted traffic intrusion detection. Full article

(This article belongs to the Section A: Computer Science)

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17 pages, 25463 KB

Open AccessArticle

Wave-DIP: Unsupervised Image Decomposition Fusing Wavelet Multi-Scale Representation and Deep Image Prior

by Zirui Mao, Liwen Feng, Quanyou Xu and Yihang Liu

Symmetry 2026, 18(5), 854; https://doi.org/10.3390/sym18050854 - 18 May 2026

Viewed by 405

Abstract

To address the issues of texture residuals and structural detail loss often encountered in traditional image decomposition methods, this paper proposes an unsupervised decomposition model that integrates the Wavelet Transform with Deep Image Prior (DIP). Leveraging the multi-scale and multi-directional characteristics of the [...] Read more.

To address the issues of texture residuals and structural detail loss often encountered in traditional image decomposition methods, this paper proposes an unsupervised decomposition model that integrates the Wavelet Transform with Deep Image Prior (DIP). Leveraging the multi-scale and multi-directional characteristics of the Wavelet Transform, the model carefully models the structural information of the cartoon component. Meanwhile, capitalizing on the unsupervised learning advantages of Deep Image Prior and incorporating low-rank constraints, it accurately extracts texture details. The model is solved via the Alternating Direction Method of Multipliers (ADMM). Experimental results on multiple test images demonstrate that, compared with existing methods, the proposed model achieves a more thorough separation of image structure and texture, yielding high-quality visual decomposition performance. Full article

(This article belongs to the Section A: Computer Science)

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23 pages, 2959 KB

Open AccessArticle

Block Cipher Generation Model: A Step Towards Generative Ciphers

by Muhammad Fahad Khan, Khalid Saleem, Ali Alshehri, Abdullah Aljuhni, Sarah Abu Ghazalah and Tehreem Sabir

Symmetry 2026, 18(5), 853; https://doi.org/10.3390/sym18050853 - 18 May 2026

Viewed by 637

Abstract

The protection of confidential information is a worldwide challenge, and block ciphers are the most reliable option by which data security is accomplished. To the best of our knowledge, this type of research is being performed for the first time, unlocking new avenues [...] Read more.

The protection of confidential information is a worldwide challenge, and block ciphers are the most reliable option by which data security is accomplished. To the best of our knowledge, this type of research is being performed for the first time, unlocking new avenues for block cipher design research, shifting the paradigm from cryptographer-designed ciphers to computationally generated. We propose a computational model named Block Cipher Design Generation Model (BCDGM) to generate a complete design of novel block ciphers and their primitives, such as cipher structures, S-boxes, inverse S-boxes, P-boxes, round functions, half-round functions, and derived keys, in an automated manner without the participation of cryptographers. To accomplish this goal, BCDGM only requires high-quality quantum random bits as input to generate a myriad of new block ciphers. A quantum circuit is designed over the International Business Machines Corporation (IBM) Quantum Santiago computer to generate high-quality random bits. BCDGM itself and all its generated cipher structures and primitives are invariably transparent, unreproducible, and nondeterministic due to their sole reliance on quantum random bits. Furthermore, every decision made by BCDGM is randomized. As a result, potential vulnerabilities and attacks that exist in other ciphers are bypassed in BCDGM-generated ciphers. Extensive experimentation was conducted, generating more than fifty thousand new block cipher designs tested over 107 terabytes of data. Generated ciphers are compared with twelve reputable standard block ciphers, including five AES competition finalists. The results show that the proposed block ciphers occasionally surpass standard ciphers and achieve equivalent security strength in many cases. The implementation of the proposed model is publicly available. Full article

(This article belongs to the Special Issue New Advances in Symmetric Cryptography)

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11 pages, 3523 KB

Open AccessArticle

On Generalized Criterion for the Non-Isothermic Spacelike Surfaces

by Filiz Kanbay and Burcu Yüksekdağ

Symmetry 2026, 18(5), 852; https://doi.org/10.3390/sym18050852 - 17 May 2026

Viewed by 471

Abstract

In this work, we examine the generalized criterion to determine a non-isothermic spacelike Bonnet surface in three-dimensional Lorentzian space

L^{3}

. For this aim, we generalized the criterion presented by Soyuçok in the Euclidean space to

L^{3}

. By applying the [...] Read more.

In this work, we examine the generalized criterion to determine a non-isothermic spacelike Bonnet surface in three-dimensional Lorentzian space

L^{3}

. For this aim, we generalized the criterion presented by Soyuçok in the Euclidean space to

L^{3}

. By applying the generalized criterion, we identify the non-isothermic spacelike Bonnet surfaces among the helicoid surfaces classified by Beneki et al. Full article

(This article belongs to the Section B: Mathematics)

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34 pages, 9782 KB

Open AccessArticle

An Adaptive MPA-RUN Framework for Multilevel Thresholding of Multispectral Satellite Images

by Ataberk Köşger, Arda Güneş, Enes Altındirek, İsmail Buğra Kuru and Muhammed Faruk Şahin

Symmetry 2026, 18(5), 851; https://doi.org/10.3390/sym18050851 - 17 May 2026

Cited by 2 | Viewed by 481

Abstract

Multispectral satellite image segmentation constitutes a challenging optimization problem due to high dimensionality and complex inter-band correlation structures. As the number of thresholds increases, the search space grows exponentially, causing metaheuristic methods to suffer from convergence instability by getting trapped in local optima [...] Read more.

Multispectral satellite image segmentation constitutes a challenging optimization problem due to high dimensionality and complex inter-band correlation structures. As the number of thresholds increases, the search space grows exponentially, causing metaheuristic methods to suffer from convergence instability by getting trapped in local optima on highly multimodal landscapes. In this study, a hybrid optimization method is proposed by integrating the Marine Predators Algorithm (MPA) with the Runge–Kutta (RUN) approach. The proposed framework enhances global exploration through Cauchy-based perturbation, while improving exploitation capability via a mutation-based local refinement mechanism, and reduces spectral redundancy using Principal Component Analysis (PCA). The MPA-RUN hybrid structure, combined with a Cauchy-driven exploration strategy and an adaptive local search mechanism, significantly improves the exploration–exploitation balance in multispectral image thresholding problems. Experiments are conducted on Sentinel-2 multispectral images, and the proposed method is evaluated against conventional metaheuristic algorithms over a wide threshold range (2–26), encompassing both low- and high-dimensional configurations. At high threshold levels, the proposed method achieves Peak Signal-to-Noise Ratio (PSNR) = 23.66, Structural Similarity Index Measure (SSIM) = 0.863, and Feature Similarity Index Measure (FSIM) = 0.797, while providing approximately 35% lower computational time at moderate levels, demonstrating superior efficiency. These results demonstrate that a balanced trade-off between accuracy and computational cost is achieved. The proposed approach offers a fast and reliable solution for processing high-dimensional data by effectively balancing segmentation quality and computational complexity. Full article

(This article belongs to the Special Issue Symmetry Applied in Remote Sensing Technology)

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27 pages, 3729 KB

Open AccessArticle

An Improved Hydro-Mechanical Coupling Shear Creep Model for Fully Persistent Rock Joints

by Hantao Xu, Yuhang Chen, Jiapeng Li, Haojie Wang and Qun Sui

Symmetry 2026, 18(5), 850; https://doi.org/10.3390/sym18050850 - 17 May 2026

Viewed by 350

Abstract

The model is based on the periodic translational symmetry of regular saw-toothed joint surfaces and reveals the time-dependent breaking of this symmetry under hydro-mechanical coupling through the introduction of damage evolution. Traditional creep models typically rely on static constants, which fail to capture [...] Read more.

The model is based on the periodic translational symmetry of regular saw-toothed joint surfaces and reveals the time-dependent breaking of this symmetry under hydro-mechanical coupling through the introduction of damage evolution. Traditional creep models typically rely on static constants, which fail to capture the nonlinear, time-dependent degradation of rock under complex conditions. To address this, this paper proposes a novel nonlinear shear creep model for regular saw-toothed joint surfaces under hydro-mechanical coupling. First, a calculation method for effective shear stress is established, accounting for normal stress, asperity height, and water pressure. Next, traditional static parameters are transformed into dynamic variables to accurately model the primary and steady-state creep stages. Finally, a plastic damage element is introduced to simulate the accelerated creep stage, revealing that damage accumulates with time and is exacerbated by higher seepage pressure. By integrating early-stage viscoelastic and late-stage viscoplastic characteristics, this model captures the complete nonlinear shear creep process, providing a robust theoretical basis for long-term stability evaluations. Full article

(This article belongs to the Section F: Engineering and Materials)

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