Symmetry

31 pages, 1652 KB

Open AccessArticle

CATI: Cross-Attention-Based Task Interaction for Multi-Granular Metro Passenger Flow Forecasting

by Qiong Yang, Xianghua Xu, Juan Yu, Qifeng Gao and Cheng Zhang

Symmetry 2026, 18(5), 809; https://doi.org/10.3390/sym18050809 (registering DOI) - 8 May 2026

Accurate short-term metro passenger flow forecasting plays a key role in urban transit management, supporting train scheduling, crowd control, and operational planning. Jointly modeling station-level inflow/outflow (IO) and inter-station origin–destination flows (OD/DO) has proven effective for improving prediction accuracy, as it allows the [...] Read more.

Accurate short-term metro passenger flow forecasting plays a key role in urban transit management, supporting train scheduling, crowd control, and operational planning. Jointly modeling station-level inflow/outflow (IO) and inter-station origin–destination flows (OD/DO) has proven effective for improving prediction accuracy, as it allows the model to leverage dependencies across different flow granularities. However, effectively exploiting such dependencies remains nontrivial. Station-level intensity (IO) and inter-station migration patterns (OD/DO) differ substantially in both representation and dynamics, and the dependencies between them are inherently directional and uneven. As a result, commonly used parameter-sharing mechanisms in multi-task learning are often insufficient to capture informative cross-task interactions. To address this issue, we propose CATI (Cross-Attention-based Task Interaction), a unified framework for joint multi-granular metro flow forecasting. CATI first learns task-specific spatiotemporal representations for IO, OD, and DO flows, and then introduces directed cross-attention with Gated Residual Fusion to model selective and asymmetric interactions across tasks. In addition, an aggregation-consistency regularization is employed to maintain structural coherence between station-level and inter-station predictions. Experiments on real-world metro datasets from Hangzhou and Shanghai show that CATI consistently outperforms strong baselines across multiple prediction horizons and tasks. Further analysis indicates that the model learns adaptive attention patterns, task-dependent gating behaviors, and controlled interaction strengths, which together explain its improved performance. These results suggest that explicitly modeling asymmetric cross-task interactions is important for multi-granular spatiotemporal forecasting in metro systems. Full article

(This article belongs to the Section Computer)

21 pages, 327 KB

Open AccessArticle

Magnetic Curves in Generalized Almost Cosymplectic Manifolds

by Foued Aloui, Afshan Perween and Majid Ali Choudhary

Symmetry 2026, 18(5), 808; https://doi.org/10.3390/sym18050808 (registering DOI) - 8 May 2026

Abstract

In this paper, we study magnetic curves associated with a contact magnetic field on almost cosymplectic manifolds. In particular, we consider locally conformal almost cosymplectic manifolds and almost

α

-cosymplectic f-manifolds. The magnetic field is defined by the fundamental 2-form

Ω

, [...] Read more.

In this paper, we study magnetic curves associated with a contact magnetic field on almost cosymplectic manifolds. In particular, we consider locally conformal almost cosymplectic manifolds and almost

α

-cosymplectic f-manifolds. The magnetic field is defined by the fundamental 2-form

Ω

, with the corresponding Lorentz force determined by the structure tensor

φ

. We classify normal magnetic curves in these settings and show that they are either geodesics, Legendre

φ

-circles, or

φ

-helices of order three. We further investigate slant curves and derive conditions relating their geometry to the structure functions of the manifold. These results generalize known classifications of magnetic curves in contact and cosymplectic geometries and provide a unified treatment for the considered classes of manifolds. Full article

(This article belongs to the Topic Geometric Structures on Manifolds: Riemannian Geometry, Submanifolds, and Physical Applications)

22 pages, 14529 KB

Open AccessArticle

A Novel Two-Level Entropy-Weighted Fuzzy C-Means Algorithm and Its Application for Classifying Urban Patterns by Residential Building Characteristics

by Rosa Cafaro, Barbara Cardone and Ferdinando Di Martino

Symmetry 2026, 18(5), 807; https://doi.org/10.3390/sym18050807 (registering DOI) - 8 May 2026

Abstract

In this work, a novel entropy-weighted fuzzy c-means variation, referred to as Group-based Entropy Weighted Fuzzy C-Means (GEWFCM), is proposed. This variation introduces a semantic level of partitioning of features into groups. This approach enables the provision of optimal semantic meaning to the [...] Read more.

In this work, a novel entropy-weighted fuzzy c-means variation, referred to as Group-based Entropy Weighted Fuzzy C-Means (GEWFCM), is proposed. This variation introduces a semantic level of partitioning of features into groups. This approach enables the provision of optimal semantic meaning to the clusters, thereby capturing the intrinsic structure of the features, which are naturally grouped into homogeneous semantic sets; the weights are independent of the clusters. The cluster weights provide a direct measure of the importance of each group, determining which dimensions of the phenomenon are relevant, and the intragroup weights determine the most relevant features within a group. Additionally, GEWFCM is computationally more efficient than other cluster-specific weighted fuzzy clustering algorithms, due to the independence of the weights from the clusters. The efficacy of the method was assessed by evaluating census data from 16 Italian cities, with the objective of partitioning urban settlements based on characteristics of residential buildings, including construction technique, period, number of floors, and state of conservation. The findings suggest that the proposed algorithm effectively captures the semantic meaning of clusters. In addition, a comparative analysis between GEWFCM and the well-known Entropy Weighted Fuzzy C-Means (EWFCM) algorithm showed that, although both algorithms provide high similarity of results for all case studies, GEWFCM is significantly faster. Full article

(This article belongs to the Special Issue Symmetries in Machine Learning and Artificial Intelligence)

23 pages, 2753 KB

Open AccessArticle

Branch-Priority Exploration for Mobile Robots in Restricted Industrial Corridors

by Wenjie Yu and Wangzhe Du

Symmetry 2026, 18(5), 806; https://doi.org/10.3390/sym18050806 (registering DOI) - 8 May 2026

Abstract

This paper proposes the Branch-Priority Exploration (BPE) framework for autonomous coverage in confined industrial corridor environments. BPE integrates three components: (1) a symmetry-aware LiDAR branch detector; (2) a hierarchical BFS/DFS mode-switching policy; and (3) a barrier-based branch memory. Frontier-based methods often struggle in [...] Read more.

This paper proposes the Branch-Priority Exploration (BPE) framework for autonomous coverage in confined industrial corridor environments. BPE integrates three components: (1) a symmetry-aware LiDAR branch detector; (2) a hierarchical BFS/DFS mode-switching policy; and (3) a barrier-based branch memory. Frontier-based methods often struggle in industrial corridors where branches split off from the main corridor. The symmetric layout of such environments, featuring T-shaped junctions and L-shaped turns, creates recurring geometric patterns that conventional frontier scoring fails to exploit. When the robot reaches a junction, nearby frontier candidates often receive similar scores, causing repeated target switching as the local map changes. Meanwhile, frontier cells inside a branch tend to score lower than those along the main corridor; so, the robot often bypasses the branch and continues forward, which leads to additional backtracking later. Even when the robot eventually returns, residual frontier cells near the entrance may attract the planner repeatedly, causing redundant re-entry into already-covered branches. To address these issues, a branch-priority exploration framework is developed. A symmetry-aware branch detection module uses LiDAR range measurements from multiple directions to identify T-shaped junctions and lateral openings, applying identical geometric criteria to lateral openings on either side of the robot. This allows branch entry to be triggered by explicit geometric evidence, rather than frontier score comparisons that tend to be unreliable near intersections. When a branch is detected, the robot transitions from BFS mode to DFS mode for systematic branch coverage. Entry and post-return locks prevent mode reversal before the robot commits to the new heading. Once a branch is completed, a permanent virtual barrier is placed at its entrance; so, the planner no longer routes the robot back into that branch. The framework is formalized as a constrained coverage problem on occupancy grids, and monotonic coverage progress and finite branch completion under barrier memory are established theoretically. A fully reproducible ROS implementation on a wheeled platform with differential drive is validated. Experiments span several corridor environments of increasing topological complexity. Compared to a nearest-frontier baseline, the proposed method substantially reduces both exploration time and goal cancellations while achieving complete coverage across all trials. The cancellation count matches the number of T-branches per environment, with near-zero variance across repeated runs. Full article

(This article belongs to the Topic Artificial Intelligence in Intelligent Control, Robotics, and Manufacturing)

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34 pages, 647 KB

Open AccessArticle

Advances in Bayesian and Non-Bayesian Approaches Under Progressive Type-II Censoring with Applications

by Neama T. AL-Sayed, Asmaa M. Abd AL-Fattah, Hebatalla H. Mohammad, Gannat R. AL-Dayian and Abeer A. EL-Helbawy

Symmetry 2026, 18(5), 805; https://doi.org/10.3390/sym18050805 (registering DOI) - 8 May 2026

Abstract

Recent advances in lifetime modeling have led to several extensions of classical distributions, among which the extended inverted Kumaraswamy lifetime model, known as the exponentiated generalized inverted Kumaraswamy model, represents a significant innovation. In parallel, progressive Type-II censoring frameworks have garnered growing attention [...] Read more.

Recent advances in lifetime modeling have led to several extensions of classical distributions, among which the extended inverted Kumaraswamy lifetime model, known as the exponentiated generalized inverted Kumaraswamy model, represents a significant innovation. In parallel, progressive Type-II censoring frameworks have garnered growing attention for their adaptability and relevance across various applied disciplines, including medical, engineering, and social sciences. Driven by this motivation, the present study focuses on the problem of parameter estimation for the proposed lifetime model under a progressive Type-II censoring scheme. Both Bayesian and non-Bayesian frameworks are utilized to estimate the model parameters, reliability function, and hazard rate. Furthermore, interval estimation is conducted by constructing confidence and Bayesian credible intervals for these measures. Assuming independent gamma priors, Bayes estimators are derived under both symmetric and asymmetric loss functions to account for different decision-making perspectives. In addition, conditional and Bayesian predictive analyses are developed within a two-sample prediction framework, and their associated prediction intervals are constructed. The efficiency and robustness of the proposed estimation and prediction methodologies are thoroughly evaluated through an extensive simulation study conducted under various sample sizes and censoring schemes. To further demonstrate the model’s practical relevance, real-world medical and engineering datasets are analyzed, highlighting the applicability and effectiveness of the proposed distribution in empirical contexts. Full article

(This article belongs to the Section Mathematics)

32 pages, 4545 KB

Open AccessArticle

Interest-Aware Cooperative Caching for Symmetric Space–Air–Ground Integrated Networks

by Rui Xu, Jinhui Cao, Shuge Li and Jiping Jiang

Symmetry 2026, 18(5), 804; https://doi.org/10.3390/sym18050804 (registering DOI) - 8 May 2026

Abstract

The space–air–ground integrated network (SAGIN) is a key 6G architecture that provides seamless three-dimensional connectivity, exhibiting hierarchical structural symmetry between LEO satellite and HAP layers. Integrating information-centric networking (ICN) with caching on Low Earth Orbit (LEO) satellites and high-altitude platforms (HAPs) significantly enhances [...] Read more.

The space–air–ground integrated network (SAGIN) is a key 6G architecture that provides seamless three-dimensional connectivity, exhibiting hierarchical structural symmetry between LEO satellite and HAP layers. Integrating information-centric networking (ICN) with caching on Low Earth Orbit (LEO) satellites and high-altitude platforms (HAPs) significantly enhances content distribution efficiency. Existing studies on caching mechanisms have made progress but lack optimized cache resource allocation and accurate popular content identification. Thus, an interest-aware caching scheme (ICRL) based on reinforcement learning is proposed to optimize the SAGIN’s popular content caching decisions, aiming to achieve rational symmetric allocation of cache resources across LEO and HAP layers. Different from existing RL-based caching methods, the proposed ICRL scheme considers the LEO-HAP hierarchical architecture and designs an improved reinforcement learning mechanism to adapt to the dynamic characteristics of the SAGIN. First, an air–space two-tier caching architecture is constructed to enable collaborative caching between LEO satellites and HAPs. Second, to select high-value nodes intelligently, the proposed scheme leverages a comprehensive importance model that quantitatively analyzes HAP and LEO indicators such as topology, transmission capacity, and location. Finally, a reinforcement learning-based dynamic cache mechanism is developed. It captures real-time network requests and cache states to select optimal actions and adapt to network dynamics for better content popularity matching. Extensive evaluations based on NDNSIM demonstrate that ICRL outperforms baseline schemes in terms of cache hit ratio, server load, and request latency and achieves a symmetric balance of network load and service performance in the whole SAGIN. Full article

(This article belongs to the Section Computer)

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23 pages, 3143 KB

Open AccessReview

Recent Advances in Phase Change Materials for Thermal Management of Lithium-Ion and Emerging X-Ion Batteries: A Review

by Ya-Chu Chang

Symmetry 2026, 18(5), 803; https://doi.org/10.3390/sym18050803 (registering DOI) - 8 May 2026

Abstract

The rapid global transition toward electric vehicles (EVs) demands lithium-ion battery (LIB) systems that ensure both extreme performance and uncompromising safety. However, the inherent thermal asymmetry within battery packs—driven by non-uniform heat generation and localized hotspots—remains a critical bottleneck, accelerating degradation and triggering [...] Read more.

The rapid global transition toward electric vehicles (EVs) demands lithium-ion battery (LIB) systems that ensure both extreme performance and uncompromising safety. However, the inherent thermal asymmetry within battery packs—driven by non-uniform heat generation and localized hotspots—remains a critical bottleneck, accelerating degradation and triggering thermal runaway. Phase change materials (PCMs) have emerged as pivotal thermal buffers due to their high latent heat capacity and ability to maintain passive thermal symmetry. This review provides a comprehensive analysis of recent advancements in PCM-based battery thermal management systems (BTMSs), transitioning from material-level nanostructural enhancements to system-level hybrid architectures. Unlike traditional reviews, we critically evaluate how the integration of multidimensional conductive fillers and advanced encapsulation technologies resolves the trade-offs between energy density and thermal response rates. Furthermore, the synergistic coordination between PCMs and active cooling strategies (liquid, air, and heat pipes) is synthesized to provide a roadmap for achieving global thermal equilibrium under extreme fast-charging (XFC) conditions. Full article

(This article belongs to the Section Engineering and Materials)

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24 pages, 8097 KB

Open AccessArticle

A Symmetric XOR-Based Dynamic Multiple Secret Sharing Visual Cryptography Framework

by Sona G and Purusothaman T

Symmetry 2026, 18(5), 802; https://doi.org/10.3390/sym18050802 (registering DOI) - 7 May 2026

Abstract

The increasing trend in the transmission of image-based data across various ecosystems like telemedicine, multimedia communication, Internet of Things (IoT), and cloud storage demands a strong security system that can withstand both classical and emerging computational threats. Classical cryptographic solutions require complex processing, [...] Read more.

The increasing trend in the transmission of image-based data across various ecosystems like telemedicine, multimedia communication, Internet of Things (IoT), and cloud storage demands a strong security system that can withstand both classical and emerging computational threats. Classical cryptographic solutions require complex processing, and hence, meeting the real-time processing requirements is challenging. In contrast, visual cryptography (VC) provides a lightweight security solution. This study proposes a new XOR-based Dynamic Multiple Secret Sharing Visual Cryptography Scheme (XDMSSVCS) designed to share multiple binary image secrets with resistance to emerging computational threats. This work introduces a novel base share creation algorithm designed to generate statistically independent shares while maintaining the symmetric reconstruction property inherent in XOR-based visual cryptography. Also, a lightweight chaotic scrambling mechanism is integrated to address the information leakage problem during transmission. The experimental results indicate pixel-perfect reconstruction (MSE = 0, PSNR = ∞, SSIM = 1), near-ideal entropy, near-zero correlation between shares, high key sensitivity (10⁻¹⁴ variation leading to decorrelated outputs), and a large key space exceeding 2¹²⁸, ensuring resistance against brute-force attacks. The framework also exhibits low computational overhead (XOR: ~0.90 ms, scrambling: ~383.72 ms, memory: ~15.58 MB), and strong resistance to attacks, establishing the XDMSSVCS as a secure and scalable framework for dynamic multi-secret sharing. Full article

(This article belongs to the Section Computer)

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28 pages, 477 KB

Open AccessArticle

Effective Potentials for de Sitter and Anti-de Sitter Quantum Fields

by Alfio Bonanno, Sergio Luigi Cacciatori and Ugo Moschella

Symmetry 2026, 18(5), 801; https://doi.org/10.3390/sym18050801 - 7 May 2026

Abstract

We derive a systematic treatment of one-loop effective potentials for interacting scalar fields in curved spacetimes, providing a general formula valid in arbitrary geometries and explicit results for de Sitter and anti-de Sitter backgrounds. We then compute the effective potential for a scalar [...] Read more.

We derive a systematic treatment of one-loop effective potentials for interacting scalar fields in curved spacetimes, providing a general formula valid in arbitrary geometries and explicit results for de Sitter and anti-de Sitter backgrounds. We then compute the effective potential for a scalar

O (N)

theory on a de Sitter space in any integer dimension. In

d = 3

and dimensional regularization, we extend the calculation up to two-loops and compute the

β

-function and the anomalous mass dimension. They coincide exactly with flat-space results, despite dramatic curvature modifications to physical masses/couplings. The flat limit

R \to \infty

recovers Coleman–Weinberg, confirming consistency. Working in

d = 3

dimension, we repeat the calculation for

A d S_{3}

by using point-splitting regularization, obtaining analogue results for the

β

-function and anomalous mass dimension (Dedicated to Jean Pierre Gazeau on his 80th Birthday). Full article

(This article belongs to the Special Issue Symmetry in Mathematical Physics: Current Topics and Recent Advances—in Honour of Professor Jean-Pierre Gazeau on the Occasion of His 80th Birthday)

22 pages, 5605 KB

Open AccessArticle

Topology-Aware Multi-Objective Swarm Optimization for Bond ETF Allocation Under Credit-Risk Constraints

by Ziyi Tang, Jingming Li, Jingjing Jiang, Mu-Jiang-Shan Wang, Wentao Zhu and Yue Zhu

Symmetry 2026, 18(5), 800; https://doi.org/10.3390/sym18050800 - 7 May 2026

Abstract

Bond ETF rebalancing is difficult to describe with return and risk objectives alone, because a portfolio that looks attractive on paper may still be impractical if it requires large and unstable trades. This paper proposes a topology-aware multi-objective particle swarm optimization framework for [...] Read more.

Bond ETF rebalancing is difficult to describe with return and risk objectives alone, because a portfolio that looks attractive on paper may still be impractical if it requires large and unstable trades. This paper proposes a topology-aware multi-objective particle swarm optimization framework for bond ETF allocation under credit-risk-related constraints. The method jointly considers annualized return, CVaR, and diversification, while enforcing long-only, exposure, and hard maximum-step turnover constraints. The central idea is to treat the swarm as a communication graph: particles exchange information through an explicit topology, and this topology affects how feasible regions are explored and how leaders are selected. When a candidate portfolio update violates the turnover budget, it is repaired toward the feasible set before evaluation, so that the search remains tied to tradable rebalancing decisions. We test the framework in a walk-forward out-of-sample backtest on U.S. bond ETFs from 2008 to 2024. The empirical analysis compares stronger classical and evolutionary baselines, four communication topologies, hard-versus-soft turnover control, stress-period behavior, and a synthetic scalability proxy. The results suggest that hard turnover repair is effective in truncating extreme rebalancing events, while communication topology changes the return–risk–turnover profile. In our experiments, the ring topology gives the most stable default behavior. Overall, the evidence suggests that topology is not just an implementation detail in swarm-based portfolio search, but a design choice that affects constrained multi-objective allocation. Full article

(This article belongs to the Section Computer)

22 pages, 30006 KB

Open AccessArticle

Depth-Guided Cross-Modal Fusion Network for Underwater Salient Instance Segmentation

by Shijie Zheng, Xiaofei Zhou, Liuxin Bao, Xiaoxi Hu and Jiyong Zhang

Symmetry 2026, 18(5), 799; https://doi.org/10.3390/sym18050799 - 7 May 2026

Abstract

Underwater salient instance segmentation (USIS) remains challenging because color distortion, low contrast, and scattering often weaken appearance cues, while reliable geometric measurements are usually unavailable. Existing methods mainly rely on red–green–blue (RGB) information, which can be insufficient in visually degraded underwater scenes. We [...] Read more.

Underwater salient instance segmentation (USIS) remains challenging because color distortion, low contrast, and scattering often weaken appearance cues, while reliable geometric measurements are usually unavailable. Existing methods mainly rely on red–green–blue (RGB) information, which can be insufficient in visually degraded underwater scenes. We propose the Depth-guided Cross-modal Fusion Network (DCFNet), a depth-guided fusion framework that leverages pseudo-depth estimated from RGB images as an auxiliary structural prior. DCFNet contains a dual-branch encoder, a cross-modal fusion branch, a refinement decoder, and an instance branch. In the fusion branch, the proposed Depth-Aware Modality Injection (DAMI) module selectively exchanges information between RGB and pseudo-depth features to reduce the influence of noisy depth estimates. The decoder further combines Inverted Residual Transformer (IRT) blocks and Bidirectional Attention Gate (BiAG) modules for contextual modeling and boundary refinement. Finally, the instance branch integrates positional cues to generate dynamic kernels for proposal-free mask prediction. Experiments on USIS10K and USIS16K show that DCFNet achieves competitive performance against several relevant baselines. Ablation studies further indicate that both the pseudo-depth prior and the proposed fusion architecture contribute to the final performance. Full article

(This article belongs to the Section Computer)

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17 pages, 2335 KB

Open AccessArticle

Cavitation Bubble Collapse Dynamics near a Wall with a Spherical Cap Protrusion

by Jiang Zhao, Miaomiao Qiu, Xiaoyu Wang, Jian Zhou, Yuning Zhang, Yuning Zhang, Jinsen Hu and Xu Qiu

Symmetry 2026, 18(5), 798; https://doi.org/10.3390/sym18050798 - 7 May 2026

Abstract

Protrusions on the flow-passing surfaces of hydraulic machinery readily induce localized cavitation and exacerbate cavitation erosion damage. This study investigates the influence of a spherical cap protrusion on a flat wall on the collapse dynamics of cavitation bubbles. By integrating high-speed photography experiments [...] Read more.

Protrusions on the flow-passing surfaces of hydraulic machinery readily induce localized cavitation and exacerbate cavitation erosion damage. This study investigates the influence of a spherical cap protrusion on a flat wall on the collapse dynamics of cavitation bubbles. By integrating high-speed photography experiments with Kelvin impulse theory, an impulse model is constructed based on boundary treatment and potential flow superposition. The dynamic evolution characteristics of cavitation bubbles at both symmetric and asymmetric positions are systematically analyzed, with emphasis on the effects of the spherical cap angle and bubble azimuthal angle on bubble morphology evolution, bubble wall collapse velocity, and the magnitude and direction of the Kelvin impulse. The results indicate that as the spherical cap angle increases, the non-spherical collapse of bubbles at symmetric positions becomes substantially more pronounced, and the collapse mode transitions from flat wall-dominated to protrusion-dominated behavior. At asymmetric positions, a larger spherical cap angle intensifies the non-uniformity of the bubble wall collapse velocity: the minimum velocity continues to decrease, and the location of this extremum shifts toward the side adjacent to the protrusion. Meanwhile, the Kelvin impulse magnitude exhibits accelerating growth, and its direction reorients from perpendicular to the wall toward the protrusion structure. Full article

14 pages, 1162 KB

Open AccessArticle

Laguerre Parameterization and Nonlinear Disturbance Observer for PMSM Speed Control

by Luyang Miao and Keyong Shao

Symmetry 2026, 18(5), 797; https://doi.org/10.3390/sym18050797 - 7 May 2026

Abstract

Although model predictive control (MPC) has been successfully applied in permanent magnet synchronous motor (PMSM) speed control systems, its performance can degrade under high-dynamic operating conditions and uncertain load disturbances. To address these issues, a continuous-time model predictive control (CTMPC) framework is proposed [...] Read more.

Although model predictive control (MPC) has been successfully applied in permanent magnet synchronous motor (PMSM) speed control systems, its performance can degrade under high-dynamic operating conditions and uncertain load disturbances. To address these issues, a continuous-time model predictive control (CTMPC) framework is proposed to improve speed tracking accuracy and robustness. From a symmetry perspective, the proposed method leverages the orthogonal symmetry of Laguerre basis functions and the structural invariance of the continuous-time PMSM speed dynamics, enabling a compact and balanced representation of the control trajectory while preserving prediction accuracy. Specifically, a finite set of orthogonal Laguerre functions, combined with an adaptive smoothing factor and soft constraint mechanism, is employed to reduce computational complexity without compromising performance. In addition, a nonlinear disturbance observer is integrated to achieve real-time estimation and feedforward compensation of load torque variations, thereby enhancing disturbance rejection capability. Comprehensive simulation results demonstrate that the proposed approach significantly improves tracking precision, reduces overshoot, and shortens recovery time following load disturbances compared to conventional MPC methods. Full article

(This article belongs to the Special Issue Symmetry and Nonlinear Control: Theory and Applications)

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12 pages, 714 KB

Open AccessArticle

Load-Independent Hardness in Fe₇₆Mo₂Ga₂P₁₀ Metallic Glass Matrix Composites

by Danijela Radumilo, Milan Pecanac, Srdjan Rakic, Dragos Buzdugan, Viorel Aurel Serban, Milos Knezev and Sebastian Balos

Symmetry 2026, 18(5), 796; https://doi.org/10.3390/sym18050796 - 6 May 2026

Abstract

Bulk metallic glasses (BMGs) exhibit high strength and hardness due to their amorphous atomic structure; however, their wider application is often limited by intrinsic brittleness and localized shear deformation. Metallic glass matrix composites (MGMCs) represent an effective approach to overcome these limitations by [...] Read more.

Bulk metallic glasses (BMGs) exhibit high strength and hardness due to their amorphous atomic structure; however, their wider application is often limited by intrinsic brittleness and localized shear deformation. Metallic glass matrix composites (MGMCs) represent an effective approach to overcome these limitations by introducing crystalline phases into the amorphous matrix, thereby improving mechanical stability and deformation behavior. In this study, an Fe-based MGMC was produced by copper mold casting and its micro-structure and mechanical properties were investigated. Microstructural observations revealed a heterogeneous structure consisting of an amorphous matrix with dispersed crystalline phases, which was confirmed by X-ray diffraction showing a broad amorphous halo with superimposed crystalline peaks. The mechanical response was evaluated using Vickers microhardness measurements under different indentation loads, revealing a pronounced indentation size effect (ISE), where hardness decreases with increasing load and stabilizes at higher loads. The load–indentation relationship follows Meyer’s law with the empirical relation P = 0.663d^1.9245 and an excellent correlation coefficient (R² = 0.9996). The Meyer index n ＜ 2 confirms normal ISE behavior. The indentation data were further analyzed using proportional specimen resistance (PSR) and modified PSR models, enabling estimation of the load-independent hardness and providing insight into the deformation behavior of the composite material. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Smart Manufacturing)

38 pages, 19154 KB

Open AccessArticle

A Brown Bear Optimization Driven RGB–Sobel Histogram Fusion Approach for Robust Color Image Segmentation

by Dussa Sudha Mohan and Kothapelli Punnam Chandar

Symmetry 2026, 18(5), 795; https://doi.org/10.3390/sym18050795 - 6 May 2026

Abstract

Image segmentation is the first step of image processing. It allows us to comprehend and extract information from the digital image. Multilevel thresholding is one of the most commonly used image segmentation techniques because of its simplicity and effectiveness. However, with the higher [...] Read more.

Image segmentation is the first step of image processing. It allows us to comprehend and extract information from the digital image. Multilevel thresholding is one of the most commonly used image segmentation techniques because of its simplicity and effectiveness. However, with the higher threshold level required, the more complex the process of finding the optimal threshold values becomes more complex. In this research, an effective optimization-based image segmentation technique using Otsu’s multilevel thresholding technique as the objective function to overcome the difficulties of finding the best threshold values is proposed. Instead of using the exhaustive search process, which requires more time, the best threshold values are obtained using different optimization techniques based on the nature of the image. In this study, the optimized threshold values are computed based on Otsu’s scheme, Sobel filter with Brown Bear Optimization Algorithm (BBOA), which is compared with thresholds computed based on the Artificial Bee Colony (ABC) algorithm, Jaya Algorithm (JA), Moth Flame Optimization (MFO) algorithm, Whale Optimization Algorithm (WOA) algorithm, and Particle Swarm Optimization (PSO) algorithm for segmentation. The objective function includes the sum of the variances of all four channels, namely, Red, Green, Blue, and Gray (Sobel). The superiority of the proposed method (BBOA_S) is tested on ten natural color benchmark images to verify results, and the quality of the suggested method is evaluated quantitatively by applying popular image quality assessment parameters, including PSNR, SSIM, and FSIM. The experimental results clearly show the efficiency of the suggested method of segmentation. In fact, the suggested method of segmentation has a higher PSNR value, up to 26.11, compared to other optimization methods, which have lower values. Similarly, the suggested method has a high value of structural similarity, up to 0.988, indicating that it performs a great job in terms of structural similarity. The proposed method also highly minimizes the reconstruction error, as indicated by the minimum values of the MSE, which are close to 194. This is better compared to the results of most of the other methods, which were carried out on the same images. Although the FSIM values of the proposed method are comparable to the values of the other methods, it is evident that the proposed method is good and reliable, as indicated by the overall quantitative and visual assessment. Therefore, it is clear that the use of Otsu’s multi-layer thresholding and the Sobel filter effect in combination with BBOA is effective and good. Full article

24 pages, 1950 KB

Open AccessArticle

Joint Optimization of Four-Edge Type LDPC Codes with Symmetric Decoding Structure Based on EXIT Functions

by Ying You, Guodong Su and Weiwei Lin

Symmetry 2026, 18(5), 794; https://doi.org/10.3390/sym18050794 - 6 May 2026

Abstract

Four-edge type low-density parity-check (FET-LDPC) codes, as an important subclass of multi-edge type LDPC codes, offer greater design flexibility and performance potential due to their heterogeneous edge type structure. However, their multi-dimensional degree distribution significantly increases the complexity of optimization. This paper proposes [...] Read more.

Four-edge type low-density parity-check (FET-LDPC) codes, as an important subclass of multi-edge type LDPC codes, offer greater design flexibility and performance potential due to their heterogeneous edge type structure. However, their multi-dimensional degree distribution significantly increases the complexity of optimization. This paper proposes a joint optimization framework for FET-LDPC codes leveraging the symmetric decoding structure inherent in their dual-branch architecture. The main contributions are as follows. First, an improved decoding model is established to analyze the mutual information transmission among the four edge types during iterative decoding, where the symmetry between the accumulator (ACC) and single parity-check (SPC) branches facilitates balanced information exchange. Second, a full-dimensional extrinsic information transfer (FEXIT) chart suitable for FET-LDPC codes is constructed, capturing the mutual information flow across branches. Third, a collaborative optimization model is designed by integrating the FEXIT chart with multi-constraint linear programming (LP) to perform asymmetric optimization for different edge types. The simulation results show that the proposed method achieves significant performance improvement over unoptimized codes in additive white Gaussian noise (AWGN) channels, particularly at a bit error rate (BER) of 10⁻⁶. Full article

(This article belongs to the Section Computer)

11 pages, 955 KB

Open AccessArticle

Quantum Control of Metrological Quantities in Two-Component Bose–Einstein Condensates

by Henan Wang, Qimeng Zhang, Hengyan Wang, Yixiao Huang and Hai-Jun Xing

Symmetry 2026, 18(5), 793; https://doi.org/10.3390/sym18050793 - 6 May 2026

Abstract

We investigate a two-component Bose–Einstein condensate as a platform for quantum metrology and characterize the dynamical evolution of the quantum state using two complementary metrics: the quantum Fisher information and the normalized Shannon entropy. With time-dependent control, metrological resources can be prepared and [...] Read more.

We investigate a two-component Bose–Einstein condensate as a platform for quantum metrology and characterize the dynamical evolution of the quantum state using two complementary metrics: the quantum Fisher information and the normalized Shannon entropy. With time-dependent control, metrological resources can be prepared and stabilized over a finite time window. These schemes provide a comprehensive assessment of the quantum dynamics of these resources in terms of phase sensitivity and the concentration of the state distribution, thereby offering a theoretical basis for designing robust quantum metrology protocols. Full article

(This article belongs to the Section Physics)

16 pages, 2135 KB

Open AccessArticle

EvoAgent-SQL: An Evolutionary Multi-Agent Text2SQL Framework Integrating User Feedback and Reflective Adaptation

by Bin He, Yanshu Du, Hao Meng, Shengbing Tang, Ting Zhang and Longfei Song

Symmetry 2026, 18(5), 792; https://doi.org/10.3390/sym18050792 - 6 May 2026

Abstract

Natural language to structured query language (Text2SQL) is a critical task in intelligent question answering and database interaction. A fundamental challenge lies in achieving semantic symmetry between natural language expressions and database schemas, as well as behavioral symmetry between query generation and error [...] Read more.

Natural language to structured query language (Text2SQL) is a critical task in intelligent question answering and database interaction. A fundamental challenge lies in achieving semantic symmetry between natural language expressions and database schemas, as well as behavioral symmetry between query generation and error correction. Traditional approaches often struggle with comprehending domain-specific concepts and dynamically adapting to user’s feedback, breaking the desired symmetry between system output and user intent. Thispaper presents EvoAgent-SQL as a lightweight engineering framework for private domain data querying based on low-cost lightweight models. The framework comprises three core agents: (1) the Schema Grounding Agent (SGA) establishes a symmetric mapping from natural language concepts to database fields; (2) the Execution Agent (EA) generates SQL queries; and (3) the Reflection Agent (RA) mirrors the EA’s outputs by analyzing errors and proposing corrections, forming a reflective symmetry loop. When ambiguity arises, user feedback is incorporated as a symmetry-breaking signal, which the RA uses to restore alignment through iterative evolution with a memory mechanism. We evaluate the framework on an education-domain dataset and provide a reproducibility plan for releasing sanitized schemas, natural language questions, and reference SQL while withholding confidential institutional records. Experimental results demonstrate that EvoAgent-SQL enhances query execution accuracy, achieving a

13.7 %

reduction in the relative error residual after one evolution cycle and a

17.6 %

cumulative reduction after two cycles, suggesting practical adaptability in domain-specific Text2SQL tasks. Full article

(This article belongs to the Section Computer)

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30 pages, 4289 KB

Open AccessArticle

Development of an Assembly Sequence Planning and Simulation System Based on Assembly Accuracy

by Junjuan Chen, Feng Li, Zhigang Xu, Runan Cao and Xun Duan

Symmetry 2026, 18(5), 791; https://doi.org/10.3390/sym18050791 - 6 May 2026

Abstract

Assembly represents the culminating phase in the product production cycle, accounting for over 40% of production costs. Conventional assembly sequence planning methodologies predominantly prioritize geometric feasibility, tool change frequency, and directional change frequency as primary optimization objectives. Assembly accuracy is rarely systematically considered [...] Read more.

Assembly represents the culminating phase in the product production cycle, accounting for over 40% of production costs. Conventional assembly sequence planning methodologies predominantly prioritize geometric feasibility, tool change frequency, and directional change frequency as primary optimization objectives. Assembly accuracy is rarely systematically considered during the planning phase; instead, it is typically evaluated and optimized retrospectively after the production sequence has been established, making it difficult to effectively mitigate cumulative tolerances. During physical prototyping, failure to meet accuracy standards necessitates re-planning, which delays progress and increases costs. We propose an algorithm that integrates assembly accuracy prediction directly into the assembly sequence generation process. This enables sequence planning to be driven by constraints related to both assembly accuracy and efficiency. First, assembly precedence relationships are established based on the assembly information matrix to identify the base components. During the disassembly process, disassembly feasibility checks are incorporated to prevent the creation of isolated parts with no contact points, thereby enhancing the engineering soundness of the precedence modeling. Second, we propose an improved greedy topological sorting algorithm that incorporates assembly accuracy predictions as a key constraint in the objective function; by merging symmetrical parts in the prediction model to reduce the search space, the algorithm ultimately generates an assembly sequence that balances geometric feasibility, assembly efficiency, and assembly accuracy. Finally, we developed an integrated virtual assembly simulation system that combines assembly information extraction, sequence planning, and accuracy calculation, enabling the rapid generation and closed-loop verification of high-precision assembly sequences. Utilizing a simplified model as a case study, we generate comparison sequences with and without accuracy prediction and validate them through virtual assembly simulation. The experimental results show that, compared to traditional assembly sequences that do not account for precision, the proposed method improves the assembly precision pass rate by approximately 23% while maintaining assembly efficiency and significantly reduces the risk of rework and re-assembly caused by improper sequencing. Simulation software developed using this method can accurately plan assembly sequences for 25 parts in 223.58 s. Full article

(This article belongs to the Section Engineering and Materials)

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Journal Description

Symmetry

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