Symmetry

13 pages, 294 KiB

Open AccessArticle

Dissipation Functions and Brownian Oscillators

by Matteo Colangeli, Lamberto Rondoni and Pasquale Vozza

Symmetry 2025, 17(8), 1297; https://doi.org/10.3390/sym17081297 - 11 Aug 2025

We develop a general framework for response theory in Markovian diffusion processes governed by Fokker–Planck equations. Our formalism, based on the notion of the dissipation function, is capable of handling dynamics that are driven by an external perturbation arbitrarily far from a given [...] Read more.

We develop a general framework for response theory in Markovian diffusion processes governed by Fokker–Planck equations. Our formalism, based on the notion of the dissipation function, is capable of handling dynamics that are driven by an external perturbation arbitrarily far from a given reference process. Using the analytically solvable Brownian oscillator model, we derive exact response formulae for both overdamped and underdamped dynamics of harmonically bound Brownian particles. We also demonstrate that for certain observables and under suitable time scaling, the operations of model reduction and response formula extraction commute, which highlights a relevant symmetry of the adopted mathematical formalism. Notably, the time reversal invariance symmetry, which is manifested as detailed balance in stochastic processes and is often required in statistical mechanics, is not necessary in our response framework. Full article

(This article belongs to the Section Mathematics)

33 pages, 21500 KiB

Open AccessArticle

Lorenz and Chua Chaotic Key-Based Dynamic Substitution Box for Efficient Image Encryption

by Sarala Boobalan and Sathish Kumar Gurunathan Arthanari

Symmetry 2025, 17(8), 1296; https://doi.org/10.3390/sym17081296 - 11 Aug 2025

Abstract

With the growing demand for secure image communication, effective encryption solutions are critical for safeguarding visual data from unauthorized access. The substitution box (S-box) in AES (Advanced Encryption Standard) is critical for ensuring nonlinearity and security. However, the static S-box used in AES [...] Read more.

With the growing demand for secure image communication, effective encryption solutions are critical for safeguarding visual data from unauthorized access. The substitution box (S-box) in AES (Advanced Encryption Standard) is critical for ensuring nonlinearity and security. However, the static S-box used in AES is vulnerable to algebraic attacks, side-channel attacks, and so on. This study offers a novel Lorenz key and Chua key-based Reversible Substitution Box (LCK-SB) for image encryption, which takes advantage of the chaotic behavior of the Lorenz and Chua key systems to improve security due to nonlinear jumps and mixed chaotic behavior while maintaining optimal quantum cost, area, and power. The suggested method uses a hybrid Lorenz and Chua key generator to create a highly nonlinear and reversible S-box, which ensures strong confusion and diffusion features. The performance of the LCK-SB approach is examined on field-programmable gate array (FPGA) and application-specific integrated circuit (ASIC) platforms, and the findings show that quantum cost, delay, and power are decreased by 97%, 74.6%, and 35%, respectively. Furthermore, the formal security analysis shows that the suggested technique efficiently resists threats. The theoretical analysis and experimental assessment show that the suggested system is more secure for picture encryption, making it suitable for real-time and high-security applications. Full article

(This article belongs to the Section Engineering and Materials)

48 pages, 15203 KiB

Open AccessArticle

MRBMO: An Enhanced Red-Billed Blue Magpie Optimization Algorithm for Solving Numerical Optimization Challenges

by Baili Lu, Zhanxi Xie, Junhao Wei, Yanzhao Gu, Yuzheng Yan, Zikun Li, Shirou Pan, Ngai Cheong, Ying Chen and Ruishen Zhou

Symmetry 2025, 17(8), 1295; https://doi.org/10.3390/sym17081295 - 11 Aug 2025

Abstract

To address the limitations of the Red-billed Blue Magpie Optimization algorithm (RBMO), such as its tendency to get trapped in local optima and its slow convergence rate, an enhanced version called MRBMO was proposed. MRBMO was improved by integrating Good Nodes Set Initialization, [...] Read more.

To address the limitations of the Red-billed Blue Magpie Optimization algorithm (RBMO), such as its tendency to get trapped in local optima and its slow convergence rate, an enhanced version called MRBMO was proposed. MRBMO was improved by integrating Good Nodes Set Initialization, an Enhanced Search-for-food Strategy, a newly designed Siege-style Attacking-prey Strategy, and Lens-Imaging Opposition-Based Learning (LIOBL). The experimental results showed that MRBMO demonstrated strong competitiveness on the CEC2005 benchmark. Among a series of advanced metaheuristic algorithms, MRBMO exhibited significant advantages in terms of convergence speed and solution accuracy. On benchmark functions with 30, 50, and 100 dimensions, the average Friedman values of MRBMO were 1.6029, 1.6601, and 1.8775, respectively, significantly outperforming other algorithms. The overall effectiveness of MRBMO on benchmark functions with 30, 50, and 100 dimensions was 95.65%, which confirmed the effectiveness of MRBMO in handling problems of different dimensions. This paper designed two types of simulation experiments to test the practicability of MRBMO. First, MRBMO was used along with other heuristic algorithms to solve four engineering design optimization problems, aiming to verify the applicability of MRBMO in engineering design optimization. Then, to overcome the shortcomings of metaheuristic algorithms in antenna S-parameter optimization problems—such as time-consuming verification processes, cumbersome operations, and complex modes—this paper adopted a test suite specifically designed for antenna S-parameter optimization, with the goal of efficiently validating the effectiveness of metaheuristic algorithms in this domain. The results demonstrated that MRBMO had significant advantages in both engineering design optimization and antenna S-parameter optimization. Full article

(This article belongs to the Section Engineering and Materials)

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19 pages, 8749 KiB

Open AccessArticle

Applying Computer Vision for the Detection and Analysis of the Condition and Operation of Street Lighting

by Sunggat Aiymbay, Ainur Zhumadillayeva, Eric T. Matson, Bakhyt Matkarimov and Bigul Mukhametzhanova

Symmetry 2025, 17(8), 1294; https://doi.org/10.3390/sym17081294 - 11 Aug 2025

Abstract

Urban safety critically depends on effective street lighting systems; however, rapidly expanding cities, such as Astana, face considerable challenges in maintaining these systems due to the inefficiency, high labor intensity, and error-prone nature of conventional manual inspection methods. This necessitates an urgent shift [...] Read more.

Urban safety critically depends on effective street lighting systems; however, rapidly expanding cities, such as Astana, face considerable challenges in maintaining these systems due to the inefficiency, high labor intensity, and error-prone nature of conventional manual inspection methods. This necessitates an urgent shift toward automated, accurate, and scalable monitoring systems capable of quickly identifying malfunctioning streetlights. In response, this study introduces an advanced computer vision-based approach for automated detection and analysis of street lighting conditions. Leveraging high-resolution dashcam footage collected under diverse nighttime weather conditions, we constructed a robust dataset of 4260 carefully annotated frames highlighting streetlight poles and lamps. To significantly enhance detection accuracy, we propose the novel YOLO-CSE model, which integrates a Channel Squeeze-and-Excitation (CSE) module into the YOLO (You Only Look Once) detection architecture. The CSE module leverages the inherent symmetry of streetlight structures, such as the bilateral symmetry of poles and the radial symmetry of lamps, to dynamically recalibrate feature channels, emphasizing spatially repetitive and geometrically uniform patterns. By modifying the bottleneck layer through the addition of an extra convolutional layer and the SE block, the model learns richer, more discriminative feature representations, particularly for small or distant lamps under partial occlusion or low illumination. A comprehensive comparative analysis demonstrates that YOLO-CSE outperforms conventional YOLO variants and state-of-the-art models, achieving a mean average precision (mAP) of 0.798, recall of 0.794, precision of 0.824, and an F1 score of 0.808. The model’s symmetry-aware design enhances robustness to urban clutter (e.g., asymmetric noise from headlights or signage) while maintaining real-time efficiency. These results validate YOLO-CSE as a scalable solution for smart cities, where symmetry principles bridge geometric priors with computational efficiency in infrastructure monitoring. Full article

(This article belongs to the Special Issue Symmetry in Advancing Digital Signal and Image Processing)

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18 pages, 400 KiB

Open AccessArticle

Symmetry in the Algebra of Learning: Dual Numbers and the Jacobian in K-Nets

by Agustin Solis-Winkler, J. Raymundo Marcial-Romero and J. A. Hernández-Servín

Symmetry 2025, 17(8), 1293; https://doi.org/10.3390/sym17081293 - 11 Aug 2025

Abstract

The black-box nature of deep machine learning hinders the extraction of knowledge in science. To address this issue, a proposal for a neural network (k-net) based on the Kolmogorov–Arnold Representation Theorem is presented, pursuing to be an alternative to the traditional Multilayer Perceptron. [...] Read more.

The black-box nature of deep machine learning hinders the extraction of knowledge in science. To address this issue, a proposal for a neural network (k-net) based on the Kolmogorov–Arnold Representation Theorem is presented, pursuing to be an alternative to the traditional Multilayer Perceptron. In its core, the algorithmic nature of neural networks lies in the fundamental symmetry between forward-mode and reverse-mode accumulation techniques, both of which rely on the chain rule of partial derivatives. These methods are essential for computing gradients of functions, an operation that is at the core of the training process of neural networks. Automatic differentiation addresses the need for accurate and efficient calculation of derivative values in scientific computing; procedural programs are thus transformed into the computation of the required derivatives at the same numerical arguments. This work formalizes the algebraic structure of neural network computations by framing the training process within the domain of hyperdual numbers. Specifically, it defines a Kolmogorov–Arnold-inspired neural network (k-net) using dual numbers by extending the univariate functions and their compositions that appear in the representation theorem. This approach focuses on computation of the Jacobian and the ability to implement such procedures algorithmically, without sacrificing accuracy and mathematical rigor, while exploiting the inherent symmetry of the dual number formalism. Full article

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

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21 pages, 1549 KiB

Open AccessArticle

Reinforcement Learning-Guided Particle Swarm Optimization for Multi-Objective Unmanned Aerial Vehicle Path Planning

by Wuke Li, Ying Xiong and Qi Xiong

Symmetry 2025, 17(8), 1292; https://doi.org/10.3390/sym17081292 - 11 Aug 2025

Abstract

Multi-objective Unmanned Aerial Vehicle (UAV) path planning in complex 3D environments presents a fundamental challenge requiring the simultaneous optimization of conflicting objectives such as path length, safety, altitude constraints, and smoothness. This study proposes a novel hybrid framework, termed QL-MOPSO, that integrates reinforcement [...] Read more.

Multi-objective Unmanned Aerial Vehicle (UAV) path planning in complex 3D environments presents a fundamental challenge requiring the simultaneous optimization of conflicting objectives such as path length, safety, altitude constraints, and smoothness. This study proposes a novel hybrid framework, termed QL-MOPSO, that integrates reinforcement learning with metaheuristic optimization through a three-stage hierarchical architecture. The framework employs Q-learning to generate a global guidance path in a discretized 2D grid environment using an eight-directional symmetric action space that embodies rotational symmetry at π/4 intervals, ensuring uniform exploration capabilities and unbiased path planning. A crucial intermediate stage transforms the discrete 2D path into a 3D initial trajectory, bridging the gap between discrete learning and continuous optimization domains. The MOPSO algorithm then performs fine-grained refinement in continuous 3D space, guided by a novel Q-learning path deviation objective that ensures continuous knowledge transfer throughout the optimization process. Experimental results demonstrate that the symmetric action space design yields 20.6% shorter paths compared to asymmetric alternatives, while the complete QL-MOPSO framework achieves 5% path length reduction and significantly faster convergence compared to standard MOPSO. The proposed method successfully generates Pareto-optimal solutions that balance multiple objectives while leveraging the symmetry-aware guidance mechanism to avoid local optima and accelerate convergence, offering a robust solution for complex multi-objective UAV path planning problems. Full article

(This article belongs to the Special Issue Symmetry in Chaos Theory and Applications)

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17 pages, 2642 KiB

Open AccessArticle

Exploiting Semantic-Visual Symmetry for Goal-Oriented Zero-Shot Recognition

by Haixia Zheng, Yu Zhou and Mingjie Jiang

Symmetry 2025, 17(8), 1291; https://doi.org/10.3390/sym17081291 - 11 Aug 2025

Abstract

Traditional machine learning methods only classify the instances whose classes are seen during training. In practice, many applications require to recognize the classes unknown in the training stage. In order to tackle this kind of challenging task, zero-shot learning is introduced, which incorporates [...] Read more.

Traditional machine learning methods only classify the instances whose classes are seen during training. In practice, many applications require to recognize the classes unknown in the training stage. In order to tackle this kind of challenging task, zero-shot learning is introduced, which incorporates additional semantic information to establish a semantic-visual symmetry, thereby facilitating the transfer of knowledge from known to unknown classes. Although user-defined attributes are commonly utilized to provide prior semantic information for zero-shot recognition, their importance for discrimination is not always consistent. Motivated by the observation that there exist both latent discriminative features and attributes in the images, this paper proposes a goal-oriented joint learning architecture to establish the symmetric relationships between images, attributes and categories for zero-shot learning. To be more specific, we model the latent feature and attribute spaces using the dictionary learning architecture. To learn the symmetric relationships between latent features and latent attributes, a linear transformation is applied while maintaining the semantic information. Moreover, seen-class classifiers are trained to enhance the discriminability of latent features. Extensive experiments on three representative benchmark datasets show that the proposed algorithm outperforms existing methods, highlighting the effectiveness of modeling explicit symmetry in the semantic-visual space for robust zero-shot knowledge transfer. Full article

(This article belongs to the Special Issue Asymmetry in Machine Learning)

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23 pages, 6919 KiB

Open AccessArticle

Addressing the Information Asymmetry of Fake News Detection Using Large Language Models and Emotion Embeddings

by Kirishnni Prabagar, Kogul Srikandabala, Nilaan Loganathan, Shalinka Jayatilleke, Gihan Gamage and Daswin De Silva

Symmetry 2025, 17(8), 1290; https://doi.org/10.3390/sym17081290 - 11 Aug 2025

Abstract

Fake news generation and propagation occurs in large volumes, at high speed, in diverse formats, while also being short-lived to evade detection and counteraction. Despite its role as an enabler, Artificial Intelligence (AI) has been effective at fake news detection and prediction through [...] Read more.

Fake news generation and propagation occurs in large volumes, at high speed, in diverse formats, while also being short-lived to evade detection and counteraction. Despite its role as an enabler, Artificial Intelligence (AI) has been effective at fake news detection and prediction through diverse techniques of both supervised and unsupervised machine learning. In this article, we propose a novel Artificial Intelligence (AI) approach that addresses the underexplored attribution of information asymmetry in fake news detection. This approach demonstrates how fine-tuned language models and emotion embeddings can be used to detect information asymmetry in intent, emotional framing, and linguistic complexity between content creators and content consumers. The intensity and temperature of emotion, selection of words, and the structure and relationship between words contribute to detecting this asymmetry. An empirical evaluation conducted on five benchmark datasets demonstrates the generalizability and real-time detection capabilities of the proposed AI approach. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Large Language Models-Based Natural Language Processing)

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16 pages, 5796 KiB

Open AccessArticle

Microstructural Evolution and Mechanical Properties of an Additively Manufactured AlSi10Mg Alloy Post-Processed by Twist Equal Channel Angular Pressing

by Przemysław Snopiński, Augustine Appiah, Ondřej Hilšer and Jiři Hajnyš

Symmetry 2025, 17(8), 1289; https://doi.org/10.3390/sym17081289 - 11 Aug 2025

Abstract

This study investigates the microstructural evolution and mechanical response of an additively manufactured (PBF-LB/M) AlSi10Mg alloy subjected to severe plastic deformation via two passes of twist channel angular pressing (TCAP). Processing was conducted using Route Bc, with the first pass at 150 °C [...] Read more.

This study investigates the microstructural evolution and mechanical response of an additively manufactured (PBF-LB/M) AlSi10Mg alloy subjected to severe plastic deformation via two passes of twist channel angular pressing (TCAP). Processing was conducted using Route Bc, with the first pass at 150 °C and the second at 250 °C. For the first time, the evolution from the initial hierarchical AM structure to a refined state was characterized in high-fidelity detail using a novel EBSD detector. The two-pass process transformed the initial structure into a heterogeneous, bimodal microstructure existing in a non-equilibrium state, characterized by a high fraction of low-angle grain boundaries (63%) and significant internal lattice distortion. The mechanical properties were dictated by the processing temperature: a single pass at 150 °C induced work hardening, increasing the yield strength from 450 MPa to 482 MPa. Conversely, the second pass at an elevated temperature of 250 °C promoted significant dynamic recovery. This led to a decrease in yield strength to 422 MPa but concurrently resulted in a substantial increase in ultimate compressive strength to 731 MPa. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry and Novel Nanomaterials: Preparation, Characterizations, and Applications)

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4 pages, 171 KiB

Open AccessEditorial

Special Issue: Electron Diffraction and Structural Imaging—Volume I

by Partha Pratim Das, Arturo Ponce-Pedraza, Enrico Mugnaioli and Stavros Nicolopoulos

Symmetry 2025, 17(8), 1288; https://doi.org/10.3390/sym17081288 - 11 Aug 2025

Abstract

In recent years, electron diffraction (ED) and structural imaging have undergone a major resurgence in the scientific community, driven by continuous advancements in transmission electron microscopy (TEM) instrumentation, such as Cs correctors, direct detection cameras and automation, and the development or expansion of [...] Read more.

In recent years, electron diffraction (ED) and structural imaging have undergone a major resurgence in the scientific community, driven by continuous advancements in transmission electron microscopy (TEM) instrumentation, such as Cs correctors, direct detection cameras and automation, and the development or expansion of analytical methods, such as cryo-EM, beam precession, 4D Scanning Electron Diffraction, 3D electron diffraction, 4D-STEM, and ptychography [...] Full article

(This article belongs to the Special Issue Electron Diffraction and Structural Imaging)

4 pages, 172 KiB

Open AccessEditorial

Special Issue: Electron Diffraction and Structural Imaging—Volume II

by Partha Pratim Das, Arturo Ponce-Pedraza, Enrico Mugnaioli and Stavros Nicolopoulos

Symmetry 2025, 17(8), 1287; https://doi.org/10.3390/sym17081287 - 11 Aug 2025

Abstract

Following the success of the first edition of our Special Issue “Electron Diffraction and Structural Imaging”, we present Volume II, featuring new and innovative contributions that further expand the scope and depth of this rapidly evolving field [...] Full article

(This article belongs to the Special Issue Electron Diffraction and Structural Imaging II)

25 pages, 4087 KiB

Open AccessReview

Progress in High-Entropy Alloy-Based Microwave Absorbing Materials

by Chengkun Ma and Yuying Zhang

Symmetry 2025, 17(8), 1286; https://doi.org/10.3390/sym17081286 - 10 Aug 2025

Abstract

The rational design of high-performance microwave absorbers with broadband coverage, superior attenuation, and environmental durability is critical for addressing challenges in both defense and civilian technologies. High-entropy alloys (HEAs) exhibit atomic-scale asymmetric arrangements, demonstrating exceptional potential for microwave absorption through their unique lattice [...] Read more.

The rational design of high-performance microwave absorbers with broadband coverage, superior attenuation, and environmental durability is critical for addressing challenges in both defense and civilian technologies. High-entropy alloys (HEAs) exhibit atomic-scale asymmetric arrangements, demonstrating exceptional potential for microwave absorption through their unique lattice distortion, high entropy, sluggish diffusion, and “cocktail effect”. This critical review article provides an overview of the progress made in the development and understanding of HEA-based microwave absorbing materials. Initially, the microwave dissipation mechanisms for HEAs were analyzed, where atomic-scale distortions enhance polarization loss and broaden resonance bandwidth. Subsequently, key synthesis techniques like mechanical alloying and carbothermal shock are discussed, highlighting non-equilibrium processing for phase engineering. Building on these foundations, the discussion then progresses to evaluate four principal material design approaches: (1) compositionally-tuned powders, (2) multifunctional core–shell structures, (3) phase-controlled architectures, and (4) two-dimensional/porous configurations, each demonstrating distinct performance advantages. Finally, the discussion concludes by addressing current challenges in quantitative property modeling and industrial scalability while outlining future directions, including machine learning-assisted design and flexible integration, providing comprehensive guidance for developing next-generation high-performance microwave absorbing materials. Full article

(This article belongs to the Section Engineering and Materials)

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18 pages, 7574 KiB

Open AccessArticle

Compact Four-Port Axial Symmetry UWB MIMO Antenna Array with Bandwidth Enhancement Using Reactive Stub Loading

by José Alfredo Tirado-Méndez, Hildeberto Jardón-Aguilar, Roberto Linares-Miranda, Ruben Flores-Leal, Alberto Vasquez-Toledo, Ricardo Gomez-Villanueva and Angel Perez-Miguel

Symmetry 2025, 17(8), 1285; https://doi.org/10.3390/sym17081285 - 10 Aug 2025

Abstract

This work presents the use of a novel impedance coupling technique and electrical length increase by using stub loading placed from the radiator to the ground plane. This method is applied to the design of a small four-element ultrawideband (UWB) MIMO antenna arranged [...] Read more.

This work presents the use of a novel impedance coupling technique and electrical length increase by using stub loading placed from the radiator to the ground plane. This method is applied to the design of a small four-element ultrawideband (UWB) MIMO antenna arranged in axial symmetry to achieve a compact array size while obtaining a bandwidth starting from a very low cutoff frequency compared to a conventional radiator operating at the same frequency. The four-element MIMO antenna, with an operational bandwidth of 1.9 GHz to 30 GHz, is based on a wideband monopole with a semicircular geometry, fed by a coplanar structure and an L-shaped half-ground plane section. To increase the electrical length of the structure and achieve a compact antenna design, reactive stub loading is introduced, placing it on the backside of the substrate, located orthogonally between the radiator and the L-shaped ground plane, obtaining a small-sized configuration. The axial symmetry is employed to increase the antennas’ isolation by taking advantage of the orthogonal positioning and making the radiated fields have a low correlation. The antenna array footprint measures 48 mm × 48 mm, corresponding to 0.3λ₀ × 0.3λ₀ at the lower cutoff frequency. The array exhibits a low envelope correlation coefficient (ECC) of around 0.033 at 2 GHz, and less than 0.001 at the rest of the bandwidth; a diversity gain (DG) of approximately 10; a stable total active reflection coefficient (TARC) below −10 dB; interport isolation between 20 and 40 dB; and an average gain of 2.8 dBi. Full article

(This article belongs to the Special Issue Innovations in Passive and Active Microwave Circuits for Advanced Communication and Sensing Systems: Exploiting Symmetry for Enhanced Performance)

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13 pages, 1900 KiB

Open AccessArticle

Symmetric Taper Fiber Cleaving for Centered Waist-Inserted FPI: Temperature-Compensated High-Sensitivity Strain Sensor

by Xuntao Yu, Weijie Kong, Yunfeng Zhang, Hongqi Yuan, Jingwei Lv, Chao Liu, Miao Liu and Paul K. Chu

Symmetry 2025, 17(8), 1284; https://doi.org/10.3390/sym17081284 - 10 Aug 2025

Abstract

A highly sensitive Fabry–Pérot interferometer (FPI) is fabricated via symmetric taper fiber cleaving and centered waist-inserted assembly, a design where geometric symmetry is fundamental to the sensor’s performance. The FPI is fabricated by simple and cost-effective techniques, including fiber cleaving, splicing, and tapering. [...] Read more.

A highly sensitive Fabry–Pérot interferometer (FPI) is fabricated via symmetric taper fiber cleaving and centered waist-inserted assembly, a design where geometric symmetry is fundamental to the sensor’s performance. The FPI is fabricated by simple and cost-effective techniques, including fiber cleaving, splicing, and tapering. Due to the ultra-long cantilever beam with an effective length of 2.33 mm and the ultra-short Fabry–Pérot (FP) cavity with an actual length of 13.98 μm, the sensor exhibits an ultra-high strain sensitivity of 544.57 pm/με in experimental results. The sensor boasts a small temperature sensitivity of 1.02 pm/°C and a cross-temperature sensitivity of 0.0019 µε/°C in the temperature range of 25–200 °C. Furthermore, the sensor has good stability and repeatability. Owing to the symmetry-enhanced design, simple fabrication process, high strain sensitivity, as well as a stable, linearly proportional response over an extensive strain regime, the device has large potential in various sensing applications. Full article

(This article belongs to the Section Engineering and Materials)

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31 pages, 8113 KiB

Open AccessArticle

An Autoencoder-like Non-Negative Matrix Factorization with Structure Regularization Algorithm for Clustering

by Haiyan Gao and Ling Zhong

Symmetry 2025, 17(8), 1283; https://doi.org/10.3390/sym17081283 - 10 Aug 2025

Abstract

Clustering plays a crucial role in data mining and knowledge discovery, where non-negative matrix factorization (NMF) has attracted widespread attention due to its effective data representation and dimensionality reduction capabilities. However, standard NMF has inherent limitations when processing sampled data embedded in low-dimensional [...] Read more.

Clustering plays a crucial role in data mining and knowledge discovery, where non-negative matrix factorization (NMF) has attracted widespread attention due to its effective data representation and dimensionality reduction capabilities. However, standard NMF has inherent limitations when processing sampled data embedded in low-dimensional manifold structures within high-dimensional ambient spaces, failing to effectively capture the complex structural information hidden in feature manifolds and sampling manifolds, and neglecting the learning of global structures. To address these issues, a novel structure regularization autoencoder-like non-negative matrix factorization for clustering (SRANMF) is proposed. Firstly, based on the non-negative symmetric encoder-decoder framework, we construct an autoencoder-like NMF model to enhance the characterization ability of latent information in data. Then, by fully considering high-order neighborhood relationships in the data, an optimal graph regularization strategy is introduced to preserve multi-order topological information structures. Additionally, principal component analysis (PCA) is employed to measure global data structures by maximizing the variance of projected data. Comparative experiments on 11 benchmark datasets demonstrate that SRANMF exhibits excellent clustering performance. Specifically, on the large-scale complex datasets MNIST and COIL100, the clustering evaluation metrics improved by an average of 35.31% and 46.17% (ACC) and 47.12% and 18.10% (NMI), respectively. Full article

(This article belongs to the Section Computer)

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16 pages, 1117 KiB

Open AccessArticle

Uncertainty-Aware Prediction of Mixing Enthalpy in Binary Alloys with Symmetry-Augmented Embeddings

by Roman Dębski, Władysław Gąsior, Wojciech Gierlotka and Adam Dębski

Symmetry 2025, 17(8), 1282; https://doi.org/10.3390/sym17081282 - 9 Aug 2025

Abstract

The modeling of the enthalpy of mixing in binary alloys is essential to thermodynamic assessments and computational alloy design, particularly in data-scarce systems where experimental measurements are limited or incomplete. In this work, we propose a machine learning framework for the prediction of [...] Read more.

The modeling of the enthalpy of mixing in binary alloys is essential to thermodynamic assessments and computational alloy design, particularly in data-scarce systems where experimental measurements are limited or incomplete. In this work, we propose a machine learning framework for the prediction of mixing enthalpy in binary alloys under conditions of limited data availability. The method integrates symmetry-augmented embeddings, which enforce physical invariances such as element permutation and compositional mirroring, ensuring consistency across chemically equivalent representations and capturing chemically meaningful similarities between elements, thereby supporting knowledge transfer across alloy systems. To account for data uncertainty and improve trust in predictions, we incorporate Bayesian neural networks, enabling the estimation of predictive confidence, especially in composition ranges lacking experimental data. The model is trained jointly across multiple binary alloy systems, allowing it to share structural insights and improve prediction quality in data-limited concentration intervals. The method achieves a reduction in mean absolute error by more than a factor of eight compared with the classical Miedema model (0.53 kJ·mol⁻¹ vs. 4.27 kJ·mol⁻¹) while maintaining consistent accuracy even when trained on only 25% of the experimental measurements, confirming its robustness thanks to cross-alloy knowledge transfer and symmetry-based data augmentation. We evaluate the method on a benchmark dataset containing both fully and partially characterized binary alloy systems and demonstrate its effectiveness in interpolating and extrapolating enthalpy values while providing reliable uncertainty estimates. The results highlight the value of incorporating domain-specific symmetries and uncertainty-aware learning in data-driven material modeling and suggest that this approach can support predictive thermodynamic assessments even in under-sampled systems. Full article

(This article belongs to the Special Issue Symmetry Application in Metals and Alloys)

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18 pages, 2337 KiB

Open AccessArticle

Foldable/Deployable Spherical Mechanisms Based on Regular Polygons

by Raffaele Di Gregorio

Symmetry 2025, 17(8), 1281; https://doi.org/10.3390/sym17081281 - 9 Aug 2025

Abstract

The possibility of satisfying special geometric conditions, either through their architecture or through their configuration, makes a mechanism acquire changeable motion characteristics (kinematotropic or metamorphic behavior, multi-mode operation capability, etc.) that are of interest. Aligning revolute (R)-pair axes is one of such special [...] Read more.

The possibility of satisfying special geometric conditions, either through their architecture or through their configuration, makes a mechanism acquire changeable motion characteristics (kinematotropic or metamorphic behavior, multi-mode operation capability, etc.) that are of interest. Aligning revolute (R)-pair axes is one of such special conditions. In spherical linkages, only R-pairs, whose axes share a common intersection (spherical motion center (SMC)), are present. Investigating how R-pair axes can become collinear in a spherical mechanism leads to the identification of those that exhibit changeable motion features. This approach is adopted here to select non-redundant spherical mechanisms coming from regular polygons that are foldable/deployable and have a wide enough workspace for performing motion tasks. This analysis shows that the ones with hexagonal architecture prevail over the others. These results are exploitable in many contexts related to field robotics (aerospace, machines for construction sites, deployable antennas, etc.) Full article

(This article belongs to the Special Issue Advances in Mechanics of Rigid and Flexible Systems: Mathematical Models, Numerical Modelling, Experiments, Symmetry and Applications)

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19 pages, 4719 KiB

Open AccessArticle

Laser Stripe Segmentation Network Based on Evidential Uncertainty Theory Modeling Fine-Tuning Optimization Symmetric Algorithm

by Chenbo Shi, Delin Wang, Xiangyu Zhang, Chun Zhang, Jia Yan, Changsheng Zhu and Xiaobing Feng

Symmetry 2025, 17(8), 1280; https://doi.org/10.3390/sym17081280 - 9 Aug 2025

Abstract

In welding applications, line-structured-light vision is widely used for seam tracking, but intense noise from arc glow, spatter, smoke, and reflections makes reliable laser-stripe segmentation difficult. To address these challenges, we propose EUFNet, an uncertainty-driven symmetrical two-stage segmentation network for precise stripe extraction [...] Read more.

In welding applications, line-structured-light vision is widely used for seam tracking, but intense noise from arc glow, spatter, smoke, and reflections makes reliable laser-stripe segmentation difficult. To address these challenges, we propose EUFNet, an uncertainty-driven symmetrical two-stage segmentation network for precise stripe extraction under real-world welding conditions. In the first stage, a lightweight backbone generates a coarse stripe mask and a pixel-wise uncertainty map; in the second stage, a functionally mirrored refinement network uses this uncertainty map to symmetrically guide fine-tuning of the same image regions, thereby preserving stripe continuity. We further employ an uncertainty-weighted loss that treats ambiguous pixels and their corresponding evidence in a one-to-one, symmetric manner. Evaluated on a large-scale dataset of 3100 annotated welding images, EUFNet achieves a mean IoU of 89.3% and a mean accuracy of 95.9% at 236.7 FPS (compared to U-Net’s 82.5% mean IoU and 90.2% mean accuracy), significantly outperforming existing approaches in both accuracy and real-time performance. Moreover, EUFNet generalizes effectively to the public WLSD benchmark, surpassing state-of-the-art baselines in both accuracy and speed. These results confirm that a structurally and functionally symmetric, uncertainty-driven two-stage refinement strategy—combined with targeted loss design and efficient feature integration—yields high-precision, real-time performance for automated welding vision. Full article

(This article belongs to the Topic Intelligent Optimization Algorithm: Theory and Applications)

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41 pages, 800 KiB

Open AccessReview

Bridging Classic Operations Research and Artificial Intelligence for Network Optimization in the 6G Era: A Review

by Pablo Adasme, Ali Dehghan Firoozabadi and Enrique San Juan

Symmetry 2025, 17(8), 1279; https://doi.org/10.3390/sym17081279 - 9 Aug 2025

Abstract

This paper comprehensively reviews how operations research and optimization procedures are applied to address challenges in wireless network communications. Key challenges such as network topology design, dynamic task scheduling, and multi-objective resource allocation are examined and systematically categorized. The revision focuses on literature [...] Read more.

This paper comprehensively reviews how operations research and optimization procedures are applied to address challenges in wireless network communications. Key challenges such as network topology design, dynamic task scheduling, and multi-objective resource allocation are examined and systematically categorized. The revision focuses on literature published between 2023 and 2025, and covers topics such as flow optimization and routing, resource allocation and scheduling, mobile and wireless network management, network resilience and robustness, and energy efficiency. The works are selected using a methodological approach ranging from the exact optimization methods, such as mixed-integer programming, to heuristic/metaheuristic strategies and machine-learning-based techniques. It is reported a comparative analysis in terms of computational efficiency, scalability, and practical applicability. The main contribution is to highlight current research gaps and open challenges, with particular emphasis on the integration of operations research and artificial intelligence, especially in problems modeled using graphs and network structures. Full article

(This article belongs to the Special Issue Navigating the Frontiers of 6G Wireless Communication Networks and Beyond)

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