Symmetry

23 pages, 3487 KB

Open AccessArticle

Research and Optimization of Ultra-Short-Term Photovoltaic Power Prediction Model Based on Symmetric Parallel TCN-TST-BiGRU Architecture

by Tengjie Wang, Zian Gong, Zhiyuan Wang, Yuxi Liu, Yahong Ma, Feng Wang and Jing Li

Symmetry 2025, 17(11), 1855; https://doi.org/10.3390/sym17111855 - 3 Nov 2025

Abstract

(1) Background: Ultra-short-term photovoltaic (PV) power prediction is crucial for optimizing grid scheduling and enhancing energy utilization efficiency. Existing prediction methods face challenges of missing data, noise interference, and insufficient accuracy. (2) Methods: This study proposes a single-step hybrid neural network model integrating [...] Read more.

(1) Background: Ultra-short-term photovoltaic (PV) power prediction is crucial for optimizing grid scheduling and enhancing energy utilization efficiency. Existing prediction methods face challenges of missing data, noise interference, and insufficient accuracy. (2) Methods: This study proposes a single-step hybrid neural network model integrating Temporal Convolutional Network (TCN), Temporal Shift Transformer (TST), and Bidirectional Gated Recurrent Unit (BiGRU) to achieve high-precision 15-minute-ahead PV power prediction, with a design aligned with symmetry principles. Data preprocessing uses Variational Mode Decomposition (VMD) and random forest interpolation to suppress noise and repair missing values. A symmetric parallel dual-branch feature extraction module is built: TCN-TST extracts local dynamics and long-term dependencies, while BiGRU captures global features. This symmetric structure matches the intra-day periodic symmetry of PV power (e.g., symmetric irradiance patterns around noon) and avoids bias from single-branch models. Tensor concatenation and an adaptive attention mechanism realize feature fusion and dynamic weighted output. (3) Results: Experiments on real data from a Xinjiang PV power station, with hyperparameter optimization (BiGRU units, activation function, TCN kernels, TST parameters), show that the model outperforms comparative models in MAE and R²—e.g., the MAE is 26.53% and 18.41% lower than that of TCN and Transforme. (4) Conclusions: The proposed method achieves a balance between accuracy and computational efficiency. It provides references for PV station operation, system scheduling, and grid stability. Full article

(This article belongs to the Section Engineering and Materials)

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25 pages, 1697 KB

Open AccessArticle

Theoretical Analysis of Blood Rheology as a Non-Integer Order Nanofluid Flow with Shape-Dependent Nanoparticles and Thermal Effects

by Muhammad Shahzaib and Azhar Ali Zafar

Symmetry 2025, 17(11), 1854; https://doi.org/10.3390/sym17111854 - 3 Nov 2025

Abstract

This study theoretically investigates blood rheology in arteries by modeling blood as an Oldroyd-B nanofluid with uniformly suspended

A u

,

C u

, and

A l_{2} O_{3}

nanoparticles. A fractional order framework is employed to capture memory and hereditary effects [...] Read more.

This study theoretically investigates blood rheology in arteries by modeling blood as an Oldroyd-B nanofluid with uniformly suspended

A u

,

C u

, and

A l_{2} O_{3}

nanoparticles. A fractional order framework is employed to capture memory and hereditary effects while preserving the invariance of governing equations. The influence of nanoparticle geometry is examined by considering spherical (isotropic), cylindrical (axial), and platelet-like (planar) shapes. Using integral transform techniques, a comparative analysis highlights how particle symmetry and system parameters affect flow behavior and heat transfer. Thermal effects are further analyzed as both a contributor to flow resistance and a source of symmetry breaking in conduction, with implications for optimizing nanofluid-based blood rheology in biomedical applications such as cryosurgery. Full article

(This article belongs to the Section Mathematics)

18 pages, 5768 KB

Open AccessArticle

Nonlinear Influence of Chamber Pressure on the Asymmetric Dynamic Response of a Rifle Muzzle Under Continuous Firing Conditions

by Li Chen, Jiayi Xu, Jie Song and Zhilin Wu

Symmetry 2025, 17(11), 1853; https://doi.org/10.3390/sym17111853 - 3 Nov 2025

Abstract

The symmetry-breaking vibrational response of a gun muzzle, induced by the thermo–mechanical coupling effect under continuous firing, is a critical factor degrading shooting accuracy. This study investigates the nonlinear influence of chamber pressure variation on this asymmetric dynamic response. A thermo–mechanically coupled interaction [...] Read more.

The symmetry-breaking vibrational response of a gun muzzle, induced by the thermo–mechanical coupling effect under continuous firing, is a critical factor degrading shooting accuracy. This study investigates the nonlinear influence of chamber pressure variation on this asymmetric dynamic response. A thermo–mechanically coupled interaction model between a 5.8 mm bullet and its barrel is established using nonlinear finite element methods, incorporating experimentally measured pressure data. The kinematic state of the muzzle under a heated barrel condition (after 90 rounds) is systematically analyzed across five chamber pressure levels (90% to 110% of standard). The results reveal a highly nonlinear relationship between chamber pressure and muzzle vibration. Surprisingly, the maximum values for comprehensive radial displacement (10.601 × 10⁻³ mm), velocity (0.327 m/s), acceleration (11.083 m/s²), swing angle (0.192 mrad), and swing angular velocity (9.166 rad/s) occurred at the 100% standard pressure, not the highest pressure. Reducing the pressure to 90% of the standard effectively suppressed these asymmetric vibrations, with magnitudes declining by 84.28% to 95.49%. This indicates that the symmetry of the muzzle’s dynamic state is disrupted under thermal effects, and strategically lowering chamber pressure can restore a more symmetric and stable launch attitude, thereby enhancing accuracy. This study elucidates the nonlinear correlation mechanism between pressure and thermally induced asymmetric vibration, providing a novel perspective for optimizing the accuracy of rapid-fire weapons based on symmetry principles. Full article

(This article belongs to the Section Engineering and Materials)

25 pages, 368 KB

Open AccessArticle

Stability Analysis of Bidirectional Associative Memory Neural Networks with Time-Varying Delays via Second-Order Reciprocally Convex Approach

by Kalaivani Chandran, Renuga Kuppusamy and Vembarasan Vaitheeswaran

Symmetry 2025, 17(11), 1852; https://doi.org/10.3390/sym17111852 - 3 Nov 2025

Abstract

This research examines the Lyapunov-based criterion for global asymptotic stability of Bidirectional Associative Memory (BAM) neural networks that have mixed-interval time-varying delays. Using a second-order reciprocally convex approach, this paper introduces a novel stability criterion for BAM neural networks with time delays. The [...] Read more.

This research examines the Lyapunov-based criterion for global asymptotic stability of Bidirectional Associative Memory (BAM) neural networks that have mixed-interval time-varying delays. Using a second-order reciprocally convex approach, this paper introduces a novel stability criterion for BAM neural networks with time delays. The literature has recently incorporated a few triple integral expressions in the Lyapunov–Krasovskii functional to lessen conservatism in the analysis of system stability with interval time-varying delays using a second-order reciprocally convex combination strategy. This research work establishes the negative definiteness of the Lyapunov–Krasovskii functional derivative and is formulated using Linear Matrix Inequalities (LMIs). The effectiveness of the proposed result is demonstrated through numerical examples. Full article

(This article belongs to the Section Mathematics)

28 pages, 2340 KB

Open AccessArticle

An Intelligent Playbook Recommendation Algorithm Based on Dynamic Interest Modeling for SOAR

by Hangyu Hu, Liangrui Zhang, Zhaoyu Zhang, Xingmiao Yao and Xia Wu

Symmetry 2025, 17(11), 1851; https://doi.org/10.3390/sym17111851 - 3 Nov 2025

Abstract

With the growing demand for refined security operations, Security Orchestration, Automation, and Response (SOAR) technologies have undergone rapid advancement. By leveraging intelligent orchestration capabilities in conjunction with core playbooks, SOAR facilitates both automated and semi-automated responses to security incidents. Nevertheless, the continuous evolution [...] Read more.

With the growing demand for refined security operations, Security Orchestration, Automation, and Response (SOAR) technologies have undergone rapid advancement. By leveraging intelligent orchestration capabilities in conjunction with core playbooks, SOAR facilitates both automated and semi-automated responses to security incidents. Nevertheless, the continuous evolution of network-attack techniques and the explosive growth of security alerts have rendered traditional static rule-based playbook matching and recommendation approaches increasingly inadequate in addressing the high frequency of alerts and the emergence of novel attack patterns. In this study, we propose an intelligent playbook recommendation algorithm for SOAR, developed under the paradigm of dynamic interest modeling. Specifically, the algorithm integrates a Transformer encoder, which captures long-term dynamic characteristics of alert signals in real time, with an LSTM network designed to extract short-term behavioral patterns. This hybrid architecture not only enables accurate playbook recommendations in high-volume alert scenarios, but also supports the reconstruction and optimization of playbooks, thereby offering valuable guidance for the mitigation of emerging threats. Experimental evaluations demonstrate that the proposed dynamic interest modeling-based algorithm exhibits high feasibility. It achieves improved performance in terms of both recommendation accuracy and efficiency, thus providing a robust technical foundation for enhancing the effectiveness of network security incident response and offering practical support for real-world security operations. Full article

(This article belongs to the Special Issue Applications Based on Symmetry in Adversarial Machine Learning)

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17 pages, 362 KB

Open AccessArticle

A Generalized Nonlinear Extension of Quantum Mechanics

by Alan Chodos and Fred Cooper

Symmetry 2025, 17(11), 1850; https://doi.org/10.3390/sym17111850 - 3 Nov 2025

Abstract

We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying Hamiltonian structure. We analyze a particular solution [...] Read more.

We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying Hamiltonian structure. We analyze a particular solution in detail, and we used a natural extension of the Born rule to compute particle trajectories. We find that closed particle orbits are possible. Full article

(This article belongs to the Section Physics)

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24 pages, 7059 KB

Open AccessArticle

A High-Precision Verifiable Watermarking Scheme for Vector Geographic Data Using Difference Expansion and Metadata Restoration

by Li-Ming Gao, Qian Wang and Li Zhang

Symmetry 2025, 17(11), 1849; https://doi.org/10.3390/sym17111849 - 3 Nov 2025

Abstract

Vector geographic data require strict preservation of coordinate precision and topological integrity. However, their open transmission poses simultaneous challenges for copyright protection and data security. To address these issues, this study proposes a reversible watermarking framework that integrates difference expansion (DE) for lossless [...] Read more.

Vector geographic data require strict preservation of coordinate precision and topological integrity. However, their open transmission poses simultaneous challenges for copyright protection and data security. To address these issues, this study proposes a reversible watermarking framework that integrates difference expansion (DE) for lossless coordinate recovery, the Arnold transform for watermark encryption, and a metadata-assisted dual restoration mechanism to ensure geometric and topological consistency after embedding. Experimental evaluations on multiple vector datasets—including administrative boundaries, hydrographic networks, and road layers—demonstrate that the proposed method achieves near-zero distortion (RMSE ≈ 10⁻¹⁶), complete reversibility, and strong robustness against geometric and noise attacks, outperforming conventional DFT- and QIM-based schemes in terms of imperceptibility and restoration accuracy. The approach provides an efficient and verifiable solution for secure sharing and copyright protection of vector geographic data, contributing to reliable data provenance and trustworthy spatial information management. Full article

(This article belongs to the Special Issue Symmetries and Symmetry-Breaking in Data Security)

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33 pages, 603 KB

Open AccessReview

Remarks on Multivalued Variants of Ekeland Principle with Applications

by Irina Meghea

Symmetry 2025, 17(11), 1848; https://doi.org/10.3390/sym17111848 - 3 Nov 2025

Abstract

This review provides an extended discussion on multivalued variants of Ekeland’s variational principle, with the aim of highlighting the importance of this special type of result. After a presentation of the background containing general problems which appear in relation to this extended and [...] Read more.

This review provides an extended discussion on multivalued variants of Ekeland’s variational principle, with the aim of highlighting the importance of this special type of result. After a presentation of the background containing general problems which appear in relation to this extended and current subject, three series of results are developed to describe three multiple-valued versions of this important principle. In this part of the work, some different or improved proofs have been given, along with several special remarks from the author, together with their demonstrations. The discussion section contains an overview of many applications of such multivalued variants in solving problems issuing from real phenomena modeling. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis: 3rd Edition)

30 pages, 7664 KB

Open AccessArticle

Symmetry-Preserving 4D Gaussian Splatting and Mapping for Motion-Aware Dynamic Scene Reconstruction

by Rui Zhao, Mingrui Li and Zunjie Zhu

Symmetry 2025, 17(11), 1847; https://doi.org/10.3390/sym17111847 - 3 Nov 2025

Abstract

This paper introduces a novel and efficient approach for Gaussian Splatting in dynamic scenes that leverages symmetry principles for enhanced computational efficiency and visual fidelity. First, we diverge from conventional methods that process static and dynamic regions uniformly by implementing an adaptive separation [...] Read more.

This paper introduces a novel and efficient approach for Gaussian Splatting in dynamic scenes that leverages symmetry principles for enhanced computational efficiency and visual fidelity. First, we diverge from conventional methods that process static and dynamic regions uniformly by implementing an adaptive separation mechanism. This approach exploits the inherent symmetry-breaking properties between static and dynamic Gaussian points, utilizing motion differentials to identify and isolate dynamic elements. This symmetry-aware partitioning allows for the application of specialized processing techniques to each region type, with static regions benefiting from their temporal symmetry while dynamic regions receive targeted deformation modeling. Second, through this fine-grained partitioning of static and dynamic components guided by symmetry analysis, we achieve more judicious allocation of computational resources. The symmetric treatment of spatially coherent static regions and the focused processing of symmetry-breaking dynamic elements substantially reduce memory requirements and training time while preserving reconstruction quality. This optimization effectively conserves valuable computational resources without compromising visual fidelity. Third, we introduce a sophisticated deformation modeling framework that learns the transformational characteristics of grids composed of multiple Gaussian points. By incorporating radial basis function principles, which inherently preserve local rotational and translational symmetries, our method efficiently encodes complex motion information of dynamic Gaussian points. This symmetry-preserving deformation approach not only enables high-fidelity reconstruction of dynamic regions but also significantly improves the rendering of continuously evolving shadow interactions by maintaining physical consistency. The result is a marked reduction in visual distortion and rendering outputs that demonstrate exceptional correspondence to ground truth imagery across diverse dynamic scenes. Full article

(This article belongs to the Section Engineering and Materials)

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27 pages, 3340 KB

Open AccessArticle

A Comparative Study of CNN-sLSTM-Attention-Based Time Series Forecasting: Performance Evaluation on Data with Symmetry and Asymmetry Phenomena

by Haopeng Liu and Lufeng Yang

Symmetry 2025, 17(11), 1846; https://doi.org/10.3390/sym17111846 (registering DOI) - 3 Nov 2025

Abstract

This paper proposes a hierarchical CNN-sLSTM-Attention model for long-sequence time series forecasting. It enhances efficiency by replacing traditional LSTMs with a stable LSTM (sLSTM) variant, which incorporates exponential gating and memory mixing. The architecture integrates CNN for local feature extraction, sLSTM blocks for [...] Read more.

This paper proposes a hierarchical CNN-sLSTM-Attention model for long-sequence time series forecasting. It enhances efficiency by replacing traditional LSTMs with a stable LSTM (sLSTM) variant, which incorporates exponential gating and memory mixing. The architecture integrates CNN for local feature extraction, sLSTM blocks for temporal modeling, and an attention mechanism for dynamic weighting. This integrated design enables the effective processing of data with symmetric patterns or asymmetric patterns, which are prevalent in real-world time series. Experimental results on six datasets—encompassing scenarios with symmetry/asymmetry characteristics, such as temperature cycles and traffic flow fluctuations—demonstrate the model’s superior performance. Key findings include a 33% reduction in RMSE over standard LSTM on temperature prediction; 10× faster convergence with stability achieved within 12 epochs for traffic flow prediction; a 15–47% reduction in long-sequence error attributable to the sLSTM component; and a 35% improvement in trend fitting due to the attention mechanism. Although the model outperforms baseline methods in handling periodic (often symmetric) and noisy data, its performance is limited on multimodal cases. These findings suggest that future work should focus on lightweight optimization, which has the potential to improve the model’s adaptability to a broader spectrum of symmetry and asymmetry patterns in time series. Full article

(This article belongs to the Section Computer)

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13 pages, 914 KB

Open AccessArticle

Variational Analysis and Integration of the (2 + 1) Fourth-Order Time-Dependent Biharmonic Equation via Energy and Momentum Conservation

by Yasir Masood, A. H. Kara, F. D. Zaman and Ali Raza

Symmetry 2025, 17(11), 1845; https://doi.org/10.3390/sym17111845 - 3 Nov 2025

Abstract

We consider the fourth-order PDE

u_{x x x x} + 2 u_{x x y y} + u_{y y y y} - u_{t t} = h (u)

. The Lie and Noether symmetry generators are constructed, and we [...] Read more.

We consider the fourth-order PDE

u_{x x x x} + 2 u_{x x y y} + u_{y y y y} - u_{t t} = h (u)

. The Lie and Noether symmetry generators are constructed, and we reduce the PDE to simpler ODEs. Furthermore, we use some well-known methods to compute the conserved vectors associated with the PDE. An analysis of reduced ordinary differential equations (ODEs), invariant solutions, and their physical interpretations is presented. Full article

(This article belongs to the Special Issue Symmetry in Functional Equations: Methods, Applications and Mathematical Models)

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Graphical abstract

19 pages, 21004 KB

Open AccessArticle

The Symmetry-Preserving Rosenbrock Approach: Application to Solve the Chaotic Lorenz System

by Lakhlifa Sadek and Ibtisam Aldawish

Symmetry 2025, 17(11), 1844; https://doi.org/10.3390/sym17111844 - 3 Nov 2025

Abstract

This extensive study introduces the Rosenbrock method (RosM) for numerically integrating the chaotic Lorenz system, with a focus on its ability to preserve the system’s intrinsic dynamical and structural symmetries. The Lorenz system exhibits significant symmetry, most notably an inversion symmetry [...] Read more.

This extensive study introduces the Rosenbrock method (RosM) for numerically integrating the chaotic Lorenz system, with a focus on its ability to preserve the system’s intrinsic dynamical and structural symmetries. The Lorenz system exhibits significant symmetry, most notably an inversion symmetry

(x, y, z) ⟶ (- x, - y, z)

, which is a fundamental feature of its chaotic attractor. We lay forth the algorithm and, after systematic comparisons to explicit Runge–Kutta higher-order schemes and semi-analytically obtained solutions, show that the second-order Rosenbrock method performs with excellent accuracy and stability. Crucially, we demonstrate that RosM reliably preserves the system’s symmetry over long-term integration, a property where some explicit methods can exhibit subtle drift. We give a formal error characterization, assess the computational efficiency, and verify the method via bifurcation analysis to support that RosM is a robust and symmetry-aware tool for simulating chaotic systems. Full article

(This article belongs to the Special Issue Symmetries and Fractional Differential Equations: Theory and Applications)

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10 pages, 1439 KB

Open AccessArticle

Positron Production by Runaway Electrons in Lorentzian Plasmas

by Erik O. Shalenov, Murat A. Myrzali, Yeldos S. Seitkozhanov, Karlygash N. Dzhumagulova, Ranna U. Masheyeva and Murat N. Jumagulov

Symmetry 2025, 17(11), 1843; https://doi.org/10.3390/sym17111843 - 3 Nov 2025

Abstract

We study electron–positron pair production by runaway electrons in fusion plasmas. The analysis uses a Coulomb logarithm derived for a Lorentzian plasma, which captures the high-energy “tail” in the non-Maxwellian runaway-electron distribution (κ-distribution). The Coulomb logarithm decreases as the distribution departs [...] Read more.

We study electron–positron pair production by runaway electrons in fusion plasmas. The analysis uses a Coulomb logarithm derived for a Lorentzian plasma, which captures the high-energy “tail” in the non-Maxwellian runaway-electron distribution (κ-distribution). The Coulomb logarithm decreases as the distribution departs further from a Maxwellian. A lower kappa (κ) therefore reduces the Coulomb logarithm and yields a faster decline of the differential positron generation rate with increasing electron energy. Future work will explore how the electron–positron charge asymmetry manifests in their synchrotron radiation. Full article

(This article belongs to the Section Physics)

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16 pages, 3542 KB

Open AccessArticle

A Framework Designed with Perceptual Symmetry and Interactive Asymmetry for XR Collaboration

by Gustavo Adolfo Murillo Gutierrez, Rong Jin, Juan-Pablo I. Ramirez-Paredes and Uriel Haile Hernandez Belmonte

Symmetry 2025, 17(11), 1842; https://doi.org/10.3390/sym17111842 - 3 Nov 2025

Abstract

Collaborative experiences are enriched through cross-platform interactions in the context of eXtended Reality (XR) systems. In this paper, we introduce SRVS-C (Spatially Referenced Virtual Synchronization for Collaboration), a centralized framework designed to support co-located, real-time AR (on smartphone) and VR (in headset) interactions [...] Read more.

Collaborative experiences are enriched through cross-platform interactions in the context of eXtended Reality (XR) systems. In this paper, we introduce SRVS-C (Spatially Referenced Virtual Synchronization for Collaboration), a centralized framework designed to support co-located, real-time AR (on smartphone) and VR (in headset) interactions over local networks. The framework adopts an architecture of interactive asymmetry, where the interaction roles, input modalities, and rendering responsibilities are adapted to the unique capabilities and constraints of each device. Concurrently, the framework maintains perceptual symmetry, guaranteeing a coherent spatial and semantic experience for all users. This is achieved through anchor-based spatial registration and unified data representations. Compared to prior work that relies on cloud services or symmetric platforms (e.g., VR–VR, AR–AR, and PC–PC pairings), SRVS-C supports seamless communication between AR and VR endpoints, operating entirely over TCP sockets using serialization-agnostic message formats. We evaluated SRVS-C in a dual-user scenario involving a mobile AR and a VR headset, using shared freehand drawing tasks. These tasks include simple linear strokes and geometry-rich drawing content to assess how varying interaction complexity—ranging from low-density sketches to intricate, high-vertex structures— impacted the end-to-end latency, state replication timing, and collaborative fluency. The results show that the system sustains latency between 35 ms and 175 ms, even during rapid, continuous drawing actions that generate a high number of stroke updates per second, and when handling drawings composed of numerous vertices and complex shapes. Throughout these conditions, the system maintains perceptual continuity and spatial alignment across users by applying platform-specific interactive asymmetry. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Image Processing and Computer Vision Using Embedded Systems)

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25 pages, 1661 KB

Open AccessArticle

DdONN-PINNs: Complex Optical Wavefield Reconstruction by Domain Decomposition of Optical Neural Networks and Physics-Informed Information

by Xiaoyu Miao, Xiaoyue Zhuang and Lipu Zhang

Symmetry 2025, 17(11), 1841; https://doi.org/10.3390/sym17111841 - 3 Nov 2025

Abstract

To address the challenges of poor adaptability to spatial heterogeneity, easy breakage of amplitude–phase coupling relationships, and insufficient physical consistency in complex optical wavefield reconstruction, this paper proposes the DdONN-PINNs hybrid framework. Focused on preserving the intrinsic symmetries of wave physics, the framework [...] Read more.

To address the challenges of poor adaptability to spatial heterogeneity, easy breakage of amplitude–phase coupling relationships, and insufficient physical consistency in complex optical wavefield reconstruction, this paper proposes the DdONN-PINNs hybrid framework. Focused on preserving the intrinsic symmetries of wave physics, the framework achieves deep integration of optical neural networks and physics-informed information. Centered on an architecture of “SIREN shared encoding–domain-specific output”, it utilizes the periodic activation property of SIREN encoders to maintain the spatial symmetry of wavefield distribution, incorporates learnable Fourier diffraction layers to model physical propagation processes, and adopts native complex-domain modeling to avoid splitting the real and imaginary parts of complex amplitudes—effectively adapting to spatial heterogeneity while fully preserving amplitude-phase coupling in wavefields. Validated on rogue wavefields governed by the Nonlinear Schrödinger Equation (NLSE), experimental results demonstrate that DdONN-PINNs achieve an amplitude Mean Squared Error (MSE) of

2.94 \times 10^{- 3}

and a phase MSE of

5.86 \times 10^{- 4}

, outperforming non-domain-decomposed models and ReLU-activated variants significantly. Robustness analysis shows stable reconstruction performance even at a noise level of

σ = 0.1

. This framework provides a balanced solution for wavefield reconstruction that integrates precision, physical interpretability, and robustness, with potential applications in fiber-optic communication and ocean optics. Full article

(This article belongs to the Section Computer)

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16 pages, 1582 KB

Open AccessArticle

A New Method Based on the Symmetrical Calculus of GEFS and SEFS of Fuzzy Relations to Assess the Effectiveness of Local Policies for Increasing the Well-Being of Citizens

by Barbara Cardone and Ferdinando Di Martino

Symmetry 2025, 17(11), 1840; https://doi.org/10.3390/sym17111840 - 2 Nov 2025

Abstract

This research proposes a method based on the greatest and shortest eigen fuzzy sets of fuzzy relations to evaluate the effectiveness of policies and strategies implemented in urban settlements aimed at increasing the livability and well-being of citizens. This assessment is performed by [...] Read more.

This research proposes a method based on the greatest and shortest eigen fuzzy sets of fuzzy relations to evaluate the effectiveness of policies and strategies implemented in urban settlements aimed at increasing the livability and well-being of citizens. This assessment is performed by extracting population census data collected at the beginning and end of the analyzed period and grouping them by subzone, that is, for each of the urban areas into which the urban settlement is divided. The greatest eigen fuzzy set (GEFS) and the smallest eigen fuzzy set (SEFS) are determined symmetrically as min-max and max-min solutions of fuzzy relations; they are calculated to estimate the average impact of urban strategies on generating symptoms of growth in citizen well-being during the investigated period. The method is implemented on a GIS (Geographic Information System) platform and was tested to assess the effectiveness of local policies applied between 2011 and 2021 on the growth of employment rates and educational attainment in the city of Naples (Italy), partitioned by neighborhood. Our model, unlike other fuzzy-based models for evaluating the effectiveness of actions and strategies to improve the quality of life in urban settlements, does not allow for subjective interpretations based on the knowledge or experience of different stakeholders, but relies solely on measurements over time of characteristics collected during census activities. Furthermore, it is integrated into a GIS-based platform, providing additional capabilities for identifying the urban areas where the impact of local strategies and policies has been most significant and those most critical. The test results show that the proposed framework can be a valuable tool for supporting decision makers in evaluating the effectiveness of local actions and policies aimed at improving the livability and well-being of citizens. Full article

(This article belongs to the Special Issue Computing with Words with Symmetry)

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23 pages, 1737 KB

Open AccessArticle

Arc Flow Formulation for Efficient Uniform Parallel Machine Scheduling

by Khaled Bamatraf and Anis Gharbi

Symmetry 2025, 17(11), 1839; https://doi.org/10.3390/sym17111839 - 2 Nov 2025

Abstract

This paper considers the scheduling problem of uniform parallel machines. The objective is to minimize the makespan. This problem holds practical significance and is inherently NP-hard. Therefore, solutions of the exact formulation are limited to small-sized instances. As the problem size increases, the [...] Read more.

This paper considers the scheduling problem of uniform parallel machines. The objective is to minimize the makespan. This problem holds practical significance and is inherently NP-hard. Therefore, solutions of the exact formulation are limited to small-sized instances. As the problem size increases, the exact formulation struggles to find optimal solutions within a reasonable time. To address this challenge, an arc flow formulation is proposed, aiming to solve larger instances. The arc flow formulation creates a pseudo-polynomial number of variables, with its size being significantly influenced by the problem’s bounds. Therefore, bounds from the literature are utilized, and symmetry-breaking rules are applied to reduce the size of the arc flow graph. To test the effectiveness of the proposed arc flow formulation, it was compared with a mathematical formulation from the literature on small instances with up to 30 jobs. Computational results showed that the arc flow formulation outperforms the mathematical formulation from the literature, solving all cases within a few seconds. Additionally, on larger benchmark instances, the arc flow formulation solved 84.27% of the cases to optimality. The maximum optimality gap does not exceed 0.072% for the instances not solved to optimality. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Operations Research)

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25 pages, 5396 KB

Open AccessArticle

Cross-System Anomaly Detection in Deep-Sea Submersibles via Coupled Feature Learning

by Xing Fang, Xin Tan, Chengxi Zhang, Xiang Gao and Zhijian He

Symmetry 2025, 17(11), 1838; https://doi.org/10.3390/sym17111838 - 2 Nov 2025

Abstract

Deep-sea submersibles, often featuring a symmetrical design for hydrodynamic stability, operate as safety-critical systems in extreme environments, where the tight dynamic coupling between subsystems like hydraulics and propulsion creates complex failure modes that are challenging to diagnose. A localized fault in one system [...] Read more.

Deep-sea submersibles, often featuring a symmetrical design for hydrodynamic stability, operate as safety-critical systems in extreme environments, where the tight dynamic coupling between subsystems like hydraulics and propulsion creates complex failure modes that are challenging to diagnose. A localized fault in one system can propagate, inducing anomalous behavior in another and confounding conventional single-system monitoring approaches. This paper introduces a novel unsupervised anomaly detection framework, the Dual-Stream Coupled Autoencoder (DSC-AE), designed specifically to address this cross-system fault challenge. Our approach leverages a dual-encoder, single-decoder architecture that explicitly models the normal coupling relationship between the hydraulic and propulsion systems by forcing them into a shared latent representation. This architectural design establishes a holistic and accurate baseline of healthy, system-wide operation. Any deviation from this learned coupling manifold is robustly identified as an anomaly. We validate our model using real-world operational data from the deep-sea submersible, including curated test cases of intra-system and inter-system faults. Furthermore, we demonstrate that the proposed framework offers crucial diagnostic interpretability; by analyzing the model’s reconstruction error heatmaps, it is possible to trace fault origins and their subsequent propagation pathways, providing intuitive and actionable decision support for submersible operation and maintenance. This powerful diagnostic capability is substantiated by superior quantitative performance, where the DSC-AE significantly outperforms baseline methods in detecting propagated faults, achieving higher accuracy and recall, among other performance metrics. Full article

(This article belongs to the Section Computer)

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17 pages, 307 KB

Open AccessArticle

Generalization of the Rafid Operator and Its Symmetric Role in Meromorphic Function Theory with Electrostatic Applications

by Aya F. Elkhatib, Atef F. Hashem, Adela O. Mostafa and Mohammed M. Tharwat

Symmetry 2025, 17(11), 1837; https://doi.org/10.3390/sym17111837 - 2 Nov 2025

Abstract

This study introduces a new integral operator

I_{p, μ}^{δ}

that extends the traditional Rafid operator to meromorphic p-valent functions. Using this operator, we define and investigate two new subclasses:

Σ_{p}^{+} (δ, μ, α)

, consisting [...] Read more.

This study introduces a new integral operator

I_{p, μ}^{δ}

that extends the traditional Rafid operator to meromorphic p-valent functions. Using this operator, we define and investigate two new subclasses:

Σ_{p}^{+} (δ, μ, α)

, consisting of functions with nonnegative coefficients, and

Σ_{p}^{+} (δ, μ, α, c)

, which further fixes the second positive coefficient. For these classes, we establish a necessary and sufficient coefficient condition, which serves as the foundation for deriving a set of sharp results. These include accurate coefficient bounds, distortion theorems for functions and derivatives, and radii of starlikeness and convexity of a specific order. Furthermore, we demonstrate the closure property of the class

Σ_{p}^{+} (δ, μ, α, c)

, identify its extreme points, and then construct a neighborhood theorem. All the findings presented in this paper are sharp. To demonstrate the practical utility of our symmetric operator paradigm, we apply it to a canonical fractional electrodynamics problem. We demonstrate how sharp distortion theorems establish rigorous, time-invariant upper bounds for a solitary electrostatic potential and its accompanying electric field, resulting in a mathematically guaranteed safety buffer against dielectric breakdown. This study develops a symmetric and consistent approach to investigating the geometric characteristics of meromorphic multivalent functions and their applications in physical models. Full article

(This article belongs to the Special Issue Symmetry in Complex Analysis Operators Theory)

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