Symmetry

37 pages, 5564 KiB

Open AccessArticle

Improved Weighted Chimp Optimization Algorithm Based on Fitness–Distance Balance for Multilevel Thresholding Image Segmentation

by Asuman Günay Yılmaz and Samoua Alsamoua

Symmetry 2025, 17(7), 1066; https://doi.org/10.3390/sym17071066 - 4 Jul 2025

Abstract

Multilevel thresholding image segmentation plays a crucial role in various image processing applications. However, achieving optimal segmentation results often poses challenges due to the intricate nature of images. In this study, a novel metaheuristic search algorithm named Weighted Chimp Optimization Algorithm with Fitness–Distance [...] Read more.

Multilevel thresholding image segmentation plays a crucial role in various image processing applications. However, achieving optimal segmentation results often poses challenges due to the intricate nature of images. In this study, a novel metaheuristic search algorithm named Weighted Chimp Optimization Algorithm with Fitness–Distance Balance (WChOA-FDB) is developed. The algorithm integrates the concept of Fitness–Distance Balance (FDB) to ensure balanced exploration and exploitation of the solution space, thus enhancing convergence speed and solution quality. Moreover, WChOA-FDB incorporates weighted Chimp Optimization Algorithm techniques to further improve its performance in handling multilevel thresholding challenges. Experimental studies were conducted to test and verify the developed method. The algorithm’s performance was evaluated using 10 benchmark functions (IEEE_CEC_2020) of different types and complexity levels. The search performance of the algorithm was analyzed using the Friedman and Wilcoxon statistical test methods. According to the analysis results, the WChOA-FDB variants consistently outperform the base algorithm across all tested dimensions, with Friedman score improvements ranging from 17.3% (Case-6) to 25.2% (Case-4), indicating that the FDB methodology provides significant optimization enhancement regardless of problem complexity. Additionally, experimental evaluations conducted on color image segmentation tasks demonstrate the effectiveness of the proposed algorithm in achieving accurate and efficient segmentation results. The WChOA-FDB method demonstrates significant improvements in Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), and Feature Similarity Index (FSIM) metrics with average enhancements of 0.121348 dB, 0.012688, and 0.003676, respectively, across different threshold levels (m = 2 to 12), objective functions, and termination criteria. Full article

(This article belongs to the Section Mathematics)

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23 pages, 639 KiB

Open AccessArticle

Reusable Fuzzy Extractor from Isogeny-Based Assumptions

by Yunhua Wen, Tianlong Jin and Wei Li

Symmetry 2025, 17(7), 1065; https://doi.org/10.3390/sym17071065 - 4 Jul 2025

Abstract

A fuzzy extractor is a foundational cryptographic component that enables the extraction of reproducible and uniformly random strings from sources with inherent noise, such as biometric traits. Reusable fuzzy extractor guarantees the security of multiple extractions from the same noisy source. In addition, [...] Read more.

A fuzzy extractor is a foundational cryptographic component that enables the extraction of reproducible and uniformly random strings from sources with inherent noise, such as biometric traits. Reusable fuzzy extractor guarantees the security of multiple extractions from the same noisy source. In addition, although isogeny-based cryptography has become an important branch in post-quantum cryptography, the study of fuzzy extractors based on isogeny assumptions is still in its early stages and holds much room for improvement. In this paper, we give two reusable fuzzy extractor schemes derived from isogeny-based assumptions: one is based on the linear hidden shift assumption over group actions, while the other is built upon the group-action decisional Diffie–Hellman assumption within the isogeny framework. Both proposed constructions achieve post-quantum security and are capable of correcting a linear proportion of errors. They rely solely on fundamental cryptographic primitives, which ensure simplicity and efficiency. Additionally, the second construction is based on restricted effective group action, which is weaker than the effective group action used in the first construction, thereby offering greater practical applicability. Full article

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28 pages, 10581 KiB

Open AccessArticle

A Textual Semantic Analysis Framework Integrating Geographic Metaphors and GIS-Based Spatial Analysis Methods

by Yu Liu, Zhen Ren, Kaifeng Wang, Qin Tian, Xi Kuai and Sheng Li

Symmetry 2025, 17(7), 1064; https://doi.org/10.3390/sym17071064 - 4 Jul 2025

Abstract

Geographic information systems (GISs) have shown considerable promise in enhancing textual semantic analysis. Current textual semantic analysis methods face significant limitations in accurately delineating semantic boundaries, identifying semantic clustering patterns, and representing knowledge evolution. To address these issues, this study proposes a framework [...] Read more.

Geographic information systems (GISs) have shown considerable promise in enhancing textual semantic analysis. Current textual semantic analysis methods face significant limitations in accurately delineating semantic boundaries, identifying semantic clustering patterns, and representing knowledge evolution. To address these issues, this study proposes a framework that innovatively introduces GIS methods into textual semantic analysis and aligns them with the conceptual foundation of geographical metaphor theory. Specifically, word embedding models are employed to endow semantic primitives with comprehensive, high-dimensional semantic representations. GIS methods and geographical metaphors are subsequently utilized to project both semantic primitives and their relationships into a low-dimensional geospatial analog, thereby constructing a semantic space model that facilitates accurate delineation of semantic boundaries. On the basis of this model, spatial correlation measurements are adopted to reveal underlying semantic patterns, while knowledge evolution is represented using ArcGIS 10.7-based visualization techniques. Experiments on social media data validate the effectiveness of the framework in semantic boundary delineation and clustering pattern identification. Moreover, the framework supports dynamic three-dimensional visualization of topic evolution. Importantly, by employing specialized visualization methods, the proposed framework enables the intuitive representation of semantic symmetry and asymmetry within semantic spaces. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Data Mining)

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33 pages, 2533 KiB

Open AccessArticle

VBTCKN: A Time Series Forecasting Model Based on Variational Mode Decomposition with Two-Channel Cross-Attention Network

by Zhiguo Xiao, Changgen Li, Huihui Hao, Siwen Liang, Qi Shen and Dongni Li

Symmetry 2025, 17(7), 1063; https://doi.org/10.3390/sym17071063 - 4 Jul 2025

Abstract

Time series forecasting serves a critical function in domains such as energy, meteorology, and power systems by leveraging historical data to predict future trends. However, existing methods often prioritize long-term dependencies while neglecting the integration of local features and global patterns, resulting in [...] Read more.

Time series forecasting serves a critical function in domains such as energy, meteorology, and power systems by leveraging historical data to predict future trends. However, existing methods often prioritize long-term dependencies while neglecting the integration of local features and global patterns, resulting in limited accuracy for short-term predictions of non-stationary multivariate sequences. To address these challenges, this paper proposes a time series forecasting model named VBTCKN based on variational mode decomposition and a dual-channel cross-attention network. First, the model employs variational mode decomposition (VMD) to decompose the time series into multiple frequency-complementary modal components, thereby reducing sequence volatility. Subsequently, the BiLSTM channel extracts temporal dependencies between sequences, while the transformer channel captures dynamic correlations between local features and global patterns. The cross-attention mechanism dynamically fuses features from both channels, enhancing complementary information integration. Finally, prediction results are generated through Kolmogorov–Arnold networks (KAN). Experiments conducted on four public datasets demonstrated that VBTCKN outperformed other state-of-the-art methods in both accuracy and robustness. Compared with BiLSTM, VBTCKN reduced RMSE by 63.32%, 68.31%, 57.98%, and 90.76%, respectively. Full article

(This article belongs to the Special Issue Applications Based on Symmetry and Asymmetry in Deep Learning and Artificial Intelligence Methods)

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16 pages, 1229 KiB

Open AccessArticle

Nonlinear Hydrogen Bond Network in Small Water Clusters: Combining NMR, DFT, FT-IR, and EIS Research

by Ignat Ignatov, Yordan G. Marinov, Paunka Vassileva, Georgi Gluhchev, Ludmila A. Pesotskaya, Ivan P. Jordanov and Mario T. Iliev

Symmetry 2025, 17(7), 1062; https://doi.org/10.3390/sym17071062 - 4 Jul 2025

Abstract

Water’s unique physicochemical properties arise from its dynamic hydrogen-bonding network, yet the precise molecular threshold at which these cooperative behaviors emerge remains a key question. This study employed nuclear magnetic resonance (NMR) spectroscopy and density functional theory (DFT) calculations to investigate the evolution [...] Read more.

Water’s unique physicochemical properties arise from its dynamic hydrogen-bonding network, yet the precise molecular threshold at which these cooperative behaviors emerge remains a key question. This study employed nuclear magnetic resonance (NMR) spectroscopy and density functional theory (DFT) calculations to investigate the evolution of hydrogen bonding strength in small water clusters, ranging from dimers to pentamers. The observed exponential increase in NMR chemical shift up to the pentamer reflects growing hydrogen bond cooperativity, identifying the (H₂O)₅ cluster as a critical structural and energetic threshold. At this size, the network achieves sufficient connectivity to support key bulk-like phenomena such as proton transfer and dielectric relaxation. These conclusions were corroborated by complementary FT-IR and electrochemical impedance spectroscopy (EIS) measurements of bulk water. Our results position the water pentamer as the molecular onset of emergent solvent behavior, effectively bridging the divide between discrete clusters and the macroscopic properties of liquid water. Full article

(This article belongs to the Section Chemistry: Symmetry/Asymmetry)

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18 pages, 3039 KiB

Open AccessArticle

Security Symmetry in Embedded Systems: Using Microsoft Defender for IoT to Detect Firmware Downgrade Attacks

by Marian Hristov, Maria Nenova and Viktoria Dimitrova

Symmetry 2025, 17(7), 1061; https://doi.org/10.3390/sym17071061 - 4 Jul 2025

Abstract

Nowadays, the world witnesses cyber attacks daily, and these threats are becoming exponentially sophisticated due to advances in Artificial Intelligence (AI). This progress allows adversaries to accelerate malware development and streamline the exploitation process. The motives vary, and so do the consequences. Unlike [...] Read more.

Nowadays, the world witnesses cyber attacks daily, and these threats are becoming exponentially sophisticated due to advances in Artificial Intelligence (AI). This progress allows adversaries to accelerate malware development and streamline the exploitation process. The motives vary, and so do the consequences. Unlike Information Technology (IT) breaches, Operational Technology (OT)—such as manufacturing plants, electric grids, or water and wastewater facilities—compromises can have life-threatening or environmentally hazardous consequences. For that reason, this article explores a potential cyber attack against an OT environment—firmware downgrade—and proposes a solution for detection and response by implementing Microsoft Defender for IoT (D4IoT), one of the leading products on the market for OT monitoring. To detect the malicious firmware downgrade activity, D4IoT was implemented in a pre-commissioning (non-production) environment. The solution passively monitored the network, identified the deviation, and generated alerts for response actions. Testing showed that D4IoT effectively detected the firmware downgrade attempts based on a protocol analysis and asset behavior profiling. These findings demonstrate that D4IoT provides valuable detection capabilities against an intentional firmware downgrade designed to exploit known vulnerabilities in the older, less secure version, thereby strengthening the cybersecurity posture of OT environments. The explored attack scenario leverages the symmetry between genuine and malicious firmware flows, where the downgrade mimics the upgrade process, aiming to create challenges in detection. The proposed solution discerns adversarial actions from legitimate firmware changes by breaking this functional symmetry through behavioral profiling. Full article

(This article belongs to the Topic Application of IoT on Manufacturing, Communication and Engineering)

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19 pages, 793 KiB

Open AccessArticle

Lateral Asymmetries and Their Predictive Ability for Maximal Incremental Cycle Ergometer Performance in Road Cyclists

by Mario Iglesias-Caamaño, Jose Manuel Abalo-Rey, Tania Álvarez-Yates, Diego Fernández-Redondo, Jose Angel López-Campos, Fábio Yuzo Nakamura, Alba Cuba-Dorado and Oscar García-García

Symmetry 2025, 17(7), 1060; https://doi.org/10.3390/sym17071060 - 4 Jul 2025

Abstract

This study aimed to (1) determine and compare the magnitude and direction of asymmetry in lower limbs neuromuscular properties, range of motion, strength and muscle electrical activity (EMG) in well-trained male road cyclist across categories (elite, under-23 and junior); (2) establish test- and [...] Read more.

This study aimed to (1) determine and compare the magnitude and direction of asymmetry in lower limbs neuromuscular properties, range of motion, strength and muscle electrical activity (EMG) in well-trained male road cyclist across categories (elite, under-23 and junior); (2) establish test- and age-specific asymmetry thresholds for these variables to enable individualized classification; and (3) examine the relationship between these lateral asymmetries and performance in a maximal incremental cycle ergometer test. Fifty-five well-trained road cyclists were assessed through tensiomyography (TMG), active knee extension test (AKE), leg press and EMG of vastus lateralis (VL-EMG) during a maximal incremental cycling test. Junior cyclists showed lower asymmetry in VM than elite cyclists, but greater asymmetry in AKE. No significant differences were found in strength or VL-EMG during the maximal incremental cycle ergometer test. The magnitude and direction of lateral asymmetry differs between tests (TMG: 11.3–21.3%; AKE: 2.3%; leg-press: 9.8–31.9%; VL-EMG: 20.8–22.7%). Multiple linear regression revealed a significant predictive model for maximal incremental cycling ergometer performance based on lateral asymmetry in AKE, leg press and VL and rectus femoris contraction time (R²_a = 0.23). These reference data can support trainers in monitoring and managing lateral asymmetry throughout the cyclists’ season. Full article

(This article belongs to the Section Life Sciences)

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17 pages, 2314 KiB

Open AccessArticle

Characteristics of Foot Pressure Distribution During Standing and Walking with Anatomical Leg Length Discrepancy—A Comparative Analysis of Patients with and Without Low Back Pain

by Krzysztof Konior, Aleksandra Bitenc-Jasiejko, Anna Lubkowska, Ewa Stachowska, Anna Walińska, Kinga Gonta, Piotr Skomro and Danuta Lietz-Kijak

Symmetry 2025, 17(7), 1059; https://doi.org/10.3390/sym17071059 - 4 Jul 2025

Abstract

Body asymmetry is often analysed in the context of low back pain (LBP). To date, research has mainly focused on the general relationships between asymmetry and pain, with less attention paid to issues related to pressure distribution and its potential impact on the [...] Read more.

Body asymmetry is often analysed in the context of low back pain (LBP). To date, research has mainly focused on the general relationships between asymmetry and pain, with less attention paid to issues related to pressure distribution and its potential impact on the occurrence of LBP. The aim of this study was to compare biomechanical parameters in people with anatomical leg length discrepancy with and without LBP to identify overloads that may lead to pain. Early detection of common abnormalities in these parameters in both groups may influence the early prevention of 0LBP in the course of LLD. Materials and methods: This study included 60 patients with diagnosed LLD, of whom 30 had LBP (group 1, NP) and 30 were pain-free (group 2, NwP). Body weight distribution during standing and walking was analysed using pedobarography. The analysis was carried out in two stages, the first being the analysis of the biomechanical parameters for the whole study population, for group 1 with LBP and group 2 without LBP, while the second stage focused on the main issue, i.e., the comparison of the group with LBP with the group without LBP. The study included standing and walking tests. Left–right pressure distribution and ground contact time were analysed. In addition, the angle of foot abduction was analysed to indirectly assess compensatory mechanisms resulting from the asymmetry. Results: The standing test showed significantly greater pressure on the longer limb (p = 0.022) in the whole study population (N = 60). When divided into groups, it was found that in those with LBP (NP = 30), the difference was not statistically significant (p = 0.359), whereas in those without pain (NwP = 30), the pressure on the longer limb was significantly greater (p = 0.002). No differences were found between the groups in the comparative analysis. The angle of foot abduction was greater than normal across the study population (N = 60), with greater values in the shorter limb (12.83° vs. 11.04°), which was close to significance (p = 0.065). The group with LBP (NP = 30) showed a similar trend, also close to statistical significance (p = 0.054), with significantly higher values of abduction angle in both legs compared to the group without LBP (NwP = 30). In the walking test, the left–right load distributions were significantly dispersed. The mean pressure on the longer limb was significantly higher in group 1 (NP = 30) (p = 0.031), whereas this difference was not statistically significant in group 2 (NwP = 30). For mean peak pressure, there were no significant differences in any of the groups tested. In addition, the mean ground contact time during gait was longer for the longer limb in the whole study population (N = 60) (938.8 ms vs. 915 ms), but again, this difference did not reach statistical significance (p = 0.305). Comparative analysis showed no differences between the groups. Conclusions: This study showed that in people with anatomical LLD, both with and without LBP, most parameters reflected marked asymmetries in peak and mean pressures and abduction angles. A prolongation of ground contact time has also been shown, and even though some parameters were not statistically significant, it is important to note the high dispersion of left–right loading, which provides information on body load asymmetries in patients with anatomical LLD. Given that there were no differences between the groups for most of the parameters, it is important for both clinical practice and further research that the abnormalities observed in both groups (NP = 30, NwP = 30) may have been a significant predictor of the development of LBP, as the abnormalities preceded the onset of pain. This should be taken into account in diagnostic and preventive measures. Full article

(This article belongs to the Section Life Sciences)

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21 pages, 9849 KiB

Open AccessArticle

A Motion Control Strategy for a Blind Hexapod Robot Based on Reinforcement Learning and Central Pattern Generator

by Lei Wang, Ruiwen Li, Xiaoxiao Wang, Weidong Gao and Yiyang Chen

Symmetry 2025, 17(7), 1058; https://doi.org/10.3390/sym17071058 - 4 Jul 2025

Abstract

Hexapod robots that use external sensors to sense the environment are susceptible to factors such as light intensity or foggy weather. This effect leads to a drastic decrease in the motility of the hexapod robot. This paper proposes a motion control strategy for [...] Read more.

Hexapod robots that use external sensors to sense the environment are susceptible to factors such as light intensity or foggy weather. This effect leads to a drastic decrease in the motility of the hexapod robot. This paper proposes a motion control strategy for a blind hexapod robot. The hexapod robot is symmetrical and its environmental sensing capability is obtained by collecting proprioceptive signals from internal sensors, allowing it to pass through rugged terrain without the need for external sensors. The motion gait of the hexapod robot is generated by a central pattern generator (CPG) network constructed by Hopf oscillators. This gait is a periodic gait controlled by specific parameters given in advance. A policy network is trained in the target terrain using deep reinforcement learning (DRL). The trained policy network is able to fine-tune specific parameters by acquiring information about the current terrain. Thus, an adaptive gait is obtained. The experimental results show that the adaptive gait enables the hexapod robot to stably traverse various complex terrains. Full article

(This article belongs to the Section Engineering and Materials)

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14 pages, 6545 KiB

Open AccessArticle

Dynamics and Confinement Characteristics of the Last Closed Surface in a Levitated Dipole Configuration

by Zhao Wang, Teng Liu, Shuyi Liu, Junjie Du and Guoshu Zhang

Symmetry 2025, 17(7), 1057; https://doi.org/10.3390/sym17071057 - 4 Jul 2025

Abstract

Based on the magnetic configuration of the China Astro-Torus-1 (CAT-1) levitated dipole device, this study investigated the confinement performance of common discharge gas ions under E × B transverse transport conditions induced by electric fields. By adjusting L-coil parameters to shift the inject [...] Read more.

Based on the magnetic configuration of the China Astro-Torus-1 (CAT-1) levitated dipole device, this study investigated the confinement performance of common discharge gas ions under E × B transverse transport conditions induced by electric fields. By adjusting L-coil parameters to shift the inject location, it was found that when the loss boundary is in the outer weak-field region, most particles with large Larmor radii are lost after colliding with the wall, for particles with large pitch angles, the strongly anisotropic magnetic field causes particles across a broad range of energies to be lost through the X-point into the divertor. The study demonstrates that for particle kinetic energies between 100 and 300 eV, the CAT-1 device exhibits a loss cone angle θ_loss of approximately 58°, indicating favorable confinement performance. Full article

(This article belongs to the Section Physics)

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23 pages, 5294 KiB

Open AccessArticle

CMB Parity Asymmetry from Unitary Quantum Gravitational Physics

by Enrique Gaztañaga and K. Sravan Kumar

Symmetry 2025, 17(7), 1056; https://doi.org/10.3390/sym17071056 - 4 Jul 2025

Abstract

Longstanding anomalies in the Cosmic Microwave Background (CMB), including the low quadrupole moment and hemispherical power asymmetry, have recently been linked to an underlying parity asymmetry. We show here how this parity asymmetry naturally arises within a quantum framework that explicitly incorporates the [...] Read more.

Longstanding anomalies in the Cosmic Microwave Background (CMB), including the low quadrupole moment and hemispherical power asymmetry, have recently been linked to an underlying parity asymmetry. We show here how this parity asymmetry naturally arises within a quantum framework that explicitly incorporates the construction of a geometric quantum vacuum based on parity (

P

) and time-reversal (

T

) transformations. This framework restores unitarity in quantum field theory in curved spacetime (QFTCS). When applied to inflationary quantum fluctuations, this unitary QFTCS formalism predicts parity asymmetry as a natural consequence of cosmic expansion, which inherently breaks time-reversal symmetry. Observational data strongly favor this unitary QFTCS approach, with a Bayes factor, the ratio of marginal likelihoods associated with the model given the data

p (M | D)

, exceeding 650 times that of predictions from the standard inflationary framework. This Bayesian approach contrasts with the standard practice in the CMB community, which evaluates

p (D | M)

, the likelihood of the data under the model, which undermines the importance of low-ℓ physics. Our results, for the first time, provide compelling evidence for the quantum gravitational origins of CMB parity asymmetry on large scales. Full article

(This article belongs to the Special Issue Quantum Gravity and Cosmology: Exploring the Astroparticle Interface)

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14 pages, 5672 KiB

Open AccessArticle

Numerical Study of the Combustion-Flow-Thermo-Pyrolysis Process in an Innovative Externally Heated Oil Shale Retort

by Lixin Zhao, Yingxue Mei and Luwei Pan

Symmetry 2025, 17(7), 1055; https://doi.org/10.3390/sym17071055 - 3 Jul 2025

Abstract

A novel externally heated retort for Jimsar oil shale resources is proposed, and the symmetrical mathematical model of the transport process in the retort is established through intensively studying the mechanisms of shale gas flows, heat transfer, and pyrolysis reactions in the retort. [...] Read more.

A novel externally heated retort for Jimsar oil shale resources is proposed, and the symmetrical mathematical model of the transport process in the retort is established through intensively studying the mechanisms of shale gas flows, heat transfer, and pyrolysis reactions in the retort. The descriptions of axial and radial movements and temperature of oil shale and gases, and the distribution of pyrolysis reaction and yielding of gaseous products and semi-coke in various regions of the retort are simulated. The results show that oil shale can pyrolyze gradually from the region near the wall to the core region of the retorting chamber and pyrolyze completely at the bottom of the retorting zone through receiving the heat flux transferring from the combustion channels. The final pyrolysis temperature of oil shale is 821.05 K, and the outlet temperature of semi-coke cooled by cold recycled gas is 676.35 K, which are in agreement with the design requirements. In total, 75 toil shales can be retorted in one retorting chamber per day, and the productivity of the retort can be increased by increasing the number of retorting chambers. The fuel self-sufficiency rate of this externally heated oil shale retort can reach 82.83%. Full article

(This article belongs to the Section Engineering and Materials)

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21 pages, 2725 KiB

Open AccessArticle

A Strategy for Improving Millimeter Wave Communication Reliability by Hybrid Network Considering Rainfall Attenuation

by Jiaqing Sun, Chunxiao Li, Junfeng Wei and Jiajun Shen

Symmetry 2025, 17(7), 1054; https://doi.org/10.3390/sym17071054 - 3 Jul 2025

Abstract

With the rapid development of smart connected vehicles, vehicle network communications demand high-speed data transmission to support advanced automotive services. Millimeter Wave (mmWave) communication offers fast data rates, strong anti-interference capabilities, high precision localization and low-latency, making it suitable for high-speed in-vehicle communications. [...] Read more.

With the rapid development of smart connected vehicles, vehicle network communications demand high-speed data transmission to support advanced automotive services. Millimeter Wave (mmWave) communication offers fast data rates, strong anti-interference capabilities, high precision localization and low-latency, making it suitable for high-speed in-vehicle communications. However, mmWave communication performance in vehicular networks is hindered by high path loss and frequent beam alignment updates, significantly degrading the coverage and connectivity of vehicle nodes (VNs). In addition, atmospheric propagation attenuation further deteriorates signal quality and limits system performance due to raindrop absorption and scattering. Therefore, the pure mmWave networks cannot meet the high requirements of highway vehicular communications. To address these challenges, this paper proposes a hybrid mmWave and microwave network architecture to improve VNs’ coverage and connectivity performances through the strategic deployment of Roadside Units (RSUs). Using Radio Access Technology (RAT), mmWave and microwave RSUs are symmetrically deployed on both sides of the road to communicate with VNs located at the road center. This symmetric RSUs deployment significantly improves the network reliability. Analytical expressions for coverage and connectivity in the proposed hybrid networks are derived and compared with the pure mmWave networks, accounting for rainfall attenuation. The study results show that the proposed hybrid network shows better performance than the pure mmWave network in both coverage and connectivity. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Future Wireless Networks)

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18 pages, 1717 KiB

Open AccessArticle

Symmetries, Conservation Laws, and Exact Solutions of a Potential Kadomtsev–Petviashvili Equation with Power-Law Nonlinearity

by Dimpho Millicent Mothibi

Symmetry 2025, 17(7), 1053; https://doi.org/10.3390/sym17071053 - 3 Jul 2025

Abstract

This study investigates the potential Kadomtsev–Petviashvili equation incorporating a power-type nonlinearity (PKPp), a model that features prominently in various nonlinear phenomena encountered in physics and applied mathematics. A complete Noether symmetry classification of the PKPp equation is conducted, revealing four distinct scenarios based [...] Read more.

This study investigates the potential Kadomtsev–Petviashvili equation incorporating a power-type nonlinearity (PKPp), a model that features prominently in various nonlinear phenomena encountered in physics and applied mathematics. A complete Noether symmetry classification of the PKPp equation is conducted, revealing four distinct scenarios based on different values of the exponent

p

, namely, the general case where

p \neq 1, - 1, - 2,

and three special cases where

p = 1,

p = - 1,

and

p = - 2 .

Corresponding to each case, conservation laws are derived through a second-order Lagrangian framework. Furthermore, Lie group analysis is employed to reduce the nonlinear partial differential Equation (NLPDE) to ordinary differential Equations (ODEs), thereby enabling the effective application of the Kudryashov method and direct integration techniques to construct exact solutions. In particular, exact solutions of of the considered nonlinear partial differential equation are obtained for the cases

p = 1

and

p = 2,

illustrating the practical implementation of the proposed approach. The solutions obtained include solitary wave, periodic, and rational-type solutions. These results enhance the analytical understanding of the PKPp equation and contribute to the broader theory of nonlinear dispersive equations. Full article

(This article belongs to the Special Issue Symmetries in Differential Equations and Application—2nd Edition)

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25 pages, 3011 KiB

Open AccessArticle

An Enhanced YOLOv8 Model with Symmetry-Aware Feature Extraction for High-Accuracy Solar Panel Defect Detection

by Xiaoxia Lin, Xinyue Xiao, Lin Sun, Xiaodong Yang, Chunwei Leng, Yan Li, Zhenyu Niu, Yingzhou Meng and Weihao Gong

Symmetry 2025, 17(7), 1052; https://doi.org/10.3390/sym17071052 - 3 Jul 2025

Abstract

The growing popularity of solar panels is crucial for global decarbonization, but harsh environmental conditions can lead to defects such as cracks, fingerprints, and short circuits. Existing methods face the challenge of detecting multi-scale defects while maintaining real-time performance. This paper proposes a [...] Read more.

The growing popularity of solar panels is crucial for global decarbonization, but harsh environmental conditions can lead to defects such as cracks, fingerprints, and short circuits. Existing methods face the challenge of detecting multi-scale defects while maintaining real-time performance. This paper proposes a solar panel defect detection model, DCE-YOLO, based on YOLOv8. The model incorporates a C2f-DWR-DRB module for multi-scale feature extraction, where the parallel DRB branch models spatial symmetry through symmetric-rate dilated convolutions, improving robustness and consistency. The COT attention module strengthens long-range dependencies and fuses local and global contexts to achieve symmetric feature representation. The lightweight and efficient detection head improves detection speed and accuracy. The CIoU loss function is replaced with WIoU, and a non-monotonic dynamic focusing mechanism is used to mitigate the effect of low-quality samples. Experimental results show that compared with the YOLOv8 benchmark, DCE-YOLO achieves a 2.1% performance improvement on mAP@50 and a 4.9% performance improvement on mAP@50-95. Compared with recent methods, DCE-YOLO exhibits broader defect coverage, stronger robustness, and a better performance-efficiency balance, making it highly suitable for edge deployment. The synergistic interaction between the C2f-DWR-DRB module and COT attention enhances the detection of symmetric and multi-scale defects under real-world conditions. Full article

(This article belongs to the Section Engineering and Materials)

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24 pages, 601 KiB

Open AccessArticle

Algebraic Properties of the Category of Involutive m-Semilattices and Its Limits

by Shaohui Liang

Symmetry 2025, 17(7), 1051; https://doi.org/10.3390/sym17071051 - 3 Jul 2025

Abstract

An involutive m-semilattice is a kind of algebraic structure with symmetry. Symmetry is reflected from partial-order relations to algebraic operations and even categorical properties. In this study, firstly, the concepts of the nucleus and congruence in involutive m-semilattices are introduced, and their interrelationships [...] Read more.

An involutive m-semilattice is a kind of algebraic structure with symmetry. Symmetry is reflected from partial-order relations to algebraic operations and even categorical properties. In this study, firstly, the concepts of the nucleus and congruence in involutive m-semilattices are introduced, and their interrelationships are discussed. On this basis, the concrete structure of a coequalizer in the category of involutive m-semilattices is obtained. We introduce the definition of free involutive m-semilattices, and the concrete structure of involutive m-semilattices is discussed. In addition, It is shown that the category of involutive m-semilattices is algebraic. Secondly, the colimit in the category of involutive m-semilattices is shown to be a very difficult problem. We obtain the concrete structure of the colimit for a full subcategory of the category of involutive m-semilattices. Thirdly, we introduce the definition of an inverse system in the category of involutive m-semilattices and give the concrete structure of the inverse limit of an inverse system. We establish the concept of a mapping between two inverse systems. The properties of inverse limits are discussed. Finally, we study the direct limit of the category of involutive m-semilattices and give its concrete structure. Full article

(This article belongs to the Special Issue Symmetric Ordered Algebraic Structures and Lattice Theory)

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20 pages, 1455 KiB

Open AccessArticle

Dynamic Adaptation for Class-Imbalanced Streams: An Imbalanced Continuous Test-Time Framework

by Wuxi Ma and Hao Yang

Symmetry 2025, 17(7), 1050; https://doi.org/10.3390/sym17071050 - 3 Jul 2025

Abstract

Test-time adaptation (TTA) enhances model performance in target domains by dynamically adjusting parameters using unlabeled test data. However, existing TTA methods typically assume balanced data distributions, whereas real-world test data is often imbalanced and continuously evolving. This persistent imbalance significantly degrades the effectiveness [...] Read more.

Test-time adaptation (TTA) enhances model performance in target domains by dynamically adjusting parameters using unlabeled test data. However, existing TTA methods typically assume balanced data distributions, whereas real-world test data is often imbalanced and continuously evolving. This persistent imbalance significantly degrades the effectiveness of conventional TTA techniques. To address this challenge, we introduce imbalanced continuous test-time adaptation (ICTTA), a novel framework explicitly designed to handle class imbalance in dynamically evolving test data streams. We construct an imbalanced perturbation dataset to simulate real-world scenarios and empirically demonstrate the limitations of existing methods. To overcome these limitations, we propose a dynamic adaptive imbalanced loss function that assigns adaptive weights during network optimisation, enabling effective learning from minority classes while preserving performance on majority classes. Theoretical analysis shows the superiority of our approach in handling imbalanced continuous TTA. Extensive experiments conducted on the CIFAR and ImageNet datasets demonstrate that our proposed method significantly outperforms state-of-the-art TTA approaches. It achieves a mean classification error rate of 16.5% on CIFAR10-C and 68.1% on ImageNet-C. These results underscore the critical need to address real-world data imbalances and represent a significant advancement toward more adaptive and robust test-time learning paradigms. Full article

(This article belongs to the Section Computer)

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22 pages, 3237 KiB

Open AccessArticle

Local Polar Coordinate Feature Representation and Heterogeneous Fusion Framework for Accurate Leaf Image Retrieval

by Mengjie Ye, Yong Cheng, Yongqi Yuan, De Yu and Ge Jin

Symmetry 2025, 17(7), 1049; https://doi.org/10.3390/sym17071049 - 3 Jul 2025

Abstract

Leaf shape is a crucial visual cue for plant recognition. However, distinguishing among plants with high inter-class shape similarity remains a significant challenge, especially among cultivars within the same species where shape differences can be extremely subtle. To address this issue, we propose [...] Read more.

Leaf shape is a crucial visual cue for plant recognition. However, distinguishing among plants with high inter-class shape similarity remains a significant challenge, especially among cultivars within the same species where shape differences can be extremely subtle. To address this issue, we propose a novel shape representation and an advanced heterogeneous fusion framework for accurate leaf image retrieval. Specifically, based on the local polar coordinate system, multiscale analysis, and statistical histograms, we first propose local polar coordinate feature representation (LPCFR), which captures spatial distribution from two orthogonal directions while encoding local curvature characteristics. Next, we present heterogeneous feature fusion with exponential weighting and Ranking (HFER), which enhances the compatibility and robustness of fused features by applying exponential weighted normalization and ranking-based encoding within neighborhood distance measures. Extensive experiments on both species-level and cultivar-level leaf datasets demonstrate that the proposed representation effectively captures shape features, and the fusion framework successfully integrates heterogeneous features, outperforming state-of-the-art (SOTA) methods. Full article

(This article belongs to the Section Computer)

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17 pages, 572 KiB

Open AccessArticle

Statistical Analysis Under a Random Censoring Scheme with Applications

by Mustafa M. Hasaballah and Mahmoud M. Abdelwahab

Symmetry 2025, 17(7), 1048; https://doi.org/10.3390/sym17071048 - 3 Jul 2025

Abstract

The Gumbel Type-II distribution is a widely recognized and frequently utilized lifetime distribution, playing a crucial role in reliability engineering. This paper focuses on the statistical inference of the Gumbel Type-II distribution under a random censoring scheme. From a frequentist perspective, point estimates [...] Read more.

The Gumbel Type-II distribution is a widely recognized and frequently utilized lifetime distribution, playing a crucial role in reliability engineering. This paper focuses on the statistical inference of the Gumbel Type-II distribution under a random censoring scheme. From a frequentist perspective, point estimates for the unknown parameters are derived using the maximum likelihood estimation method, and confidence intervals are constructed based on the Fisher information matrix. From a Bayesian perspective, Bayes estimates of the parameters are obtained using the Markov Chain Monte Carlo method, and the average lengths of credible intervals are calculated. The Bayesian inference is performed under both the squared error loss function and the general entropy loss function. Additionally, a numerical simulation is conducted to evaluate the performance of the proposed methods. To demonstrate their practical applicability, a real world example is provided, illustrating the application and development of these inference techniques. In conclusion, the Bayesian method appears to outperform other approaches, although each method offers unique advantages. Full article

(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines, Fourth Edition)

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