Symmetry

20 pages, 3433 KB

Open AccessArticle

Analysis of a Mixed Dispersion Nonlinear Hydrodynamic Model Exhibiting Single and Periodic Solitary Wave Modes with Its Invariance Under Infinitesimal Transformation

by Samrah Amjad, Ali H. Tedjani, Irfan Mahmood and Shahir Hussain

Symmetry 2026, 18(6), 1065; https://doi.org/10.3390/sym18061065 - 22 Jun 2026

Viewed by 248

Abstract

Here, we consider a nonlinear hydrodynamic model with mixed dispersion–temporal evolution as the scalar version of the generalized shallow-water wave equation, which specifically provides a comprehensive and versatile framework for studying energy propagation in nonlinear fluids of constrained depth. This equation is acknowledged [...] Read more.

Here, we consider a nonlinear hydrodynamic model with mixed dispersion–temporal evolution as the scalar version of the generalized shallow-water wave equation, which specifically provides a comprehensive and versatile framework for studying energy propagation in nonlinear fluids of constrained depth. This equation is acknowledged as an integrable model in the analysis of tidal wave dynamics and in simulations of weather variations, tsunami prediction, and irrigation flows. We also investigate a few of its singular and periodic solitary wave solutions by employing various Riccati-based ansatzes. These results highlight the necessity of studying various nonlinear wave phenomena, which may have potential applications in various domains of physics and applied mathematics. These results extend the variety of its solutions and also enrich the existing knowledge about its solutions with various profiles. To improve visual clarity and to facilitate structural understanding, the solution profiles are represented graphically using Maple software (version 2023.2) in 3D, 2D, and contour plots.We also discuss its invariance under infinitesimal transformations, which yields a one-dimensional Hamilton–Jacobi-like equation. Full article

(This article belongs to the Topic Advances in Integrable Systems: Theory, Methods and Applications)

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23 pages, 317 KB

Open AccessArticle

Structural Properties and Determinant Representations of Fubini–Fibonacci–Appell Polynomials in the Framework of Golden Calculus

by Waseem Ahmad Khan, Can Kızılateş, Khidir Shaib Mohamed and Naglaa Mohammed

Symmetry 2026, 18(6), 1064; https://doi.org/10.3390/sym18061064 - 22 Jun 2026

Viewed by 417

Abstract

In this paper, we introduce a novel class of Fubini–Fibonacci–Appell polynomials within the framework of Golden calculus. Utilizing generating function techniques and fibonomial convolution methods, we establish several structural properties, including explicit series representations, summation formulas, convolution identities, and recurrence relations involving the [...] Read more.

In this paper, we introduce a novel class of Fubini–Fibonacci–Appell polynomials within the framework of Golden calculus. Utilizing generating function techniques and fibonomial convolution methods, we establish several structural properties, including explicit series representations, summation formulas, convolution identities, and recurrence relations involving the Golden derivative. Furthermore, we construct three-dimensional extensions and derive determinant representations for these polynomials. As special cases, we identify connections with Bernoulli–Fibonacci, Euler–Fibonacci, and Genocchi–Fibonacci polynomials. The results presented herein unify and extend several known Fibonacci-type polynomial families and provide a systematic Appell-type approach in Golden calculus. Full article

(This article belongs to the Special Issue Symmetries of Difference Equations, Special Functions and Orthogonal Polynomials: 3rd Edition)

28 pages, 2535 KB

Open AccessArticle

Quantum Key Distribution Contingency in the Absence of the Classical Channel

by Naya Nagy

Symmetry 2026, 18(6), 1063; https://doi.org/10.3390/sym18061063 - 21 Jun 2026

Viewed by 309

Abstract

It is an accepted paradigm in the already matured industry of Quantum Key Distribution (QKD) implementations that when the quantum channel is attacked or unresponsive, the system reverts to classical security. Thus, in times of crises, when the quantum system is severely damaged, [...] Read more.

It is an accepted paradigm in the already matured industry of Quantum Key Distribution (QKD) implementations that when the quantum channel is attacked or unresponsive, the system reverts to classical security. Thus, in times of crises, when the quantum system is severely damaged, the saving resort is considered to be the classical solution. This paper explores the opposite approach. In the case of disaster, when parts of the classical part of the key distribution system are broken, are there any possible crisis management options to give some limited functionality? The result of this research shows that if the classical channel fails, the quantum channel can still produce and distribute keys. The experimental results of the contingency QKD show that, using positive operator-valued measurements (POVMs), keys can still be produced and shared. The scheme described in this paper uses the quantum channel only to distribute imperfect keys. Any one distributed key has a theoretical overlap of approximately

75 %

between Alice’s key and Bob’s key, respectively. The experimental POVM circuit is implemented with two different Naimark dilation approximations: one using

R_{z}

gates and the other using

R_{y}

gates. The practical implementation results are close to the theoretical analysis. As the keys have a partial overlap, the encryption/ decryption algorithm also needs to adjust to this reality. The encryption/decryption algorithm used in the experiments is a repetition algorithm that is simple but shows the resilience of the scheme. Ultimately, the classical channel is not used during the contingency QKD at all, while the quantum channel is assumed trusted under a restricted adversary model in which Eve is limited to individual attacks. Under this model, partial secrecy is retained for all non-zero channel error rates below a pre-agreed threshold. Full article

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

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26 pages, 1814 KB

Open AccessArticle

Extended Dissipative Approach for Anti-Synchronization of Delayed Inertial Valued Neural Networks via Event-Hybrid Triggered Control with Deception Attacks

by Porpattama Hammachukiattikul and Vadivel Rajarathinam

Symmetry 2026, 18(6), 1062; https://doi.org/10.3390/sym18061062 - 20 Jun 2026

Viewed by 271

Abstract

This paper investigates the problems of anti-synchronization for a class of inertial neural networks (INNs) with time-varying delays under the influence of deception attacks and hybrid triggered control. A novel dynamic hybrid-triggered control (DHTC) scheme is developed to utilize communication resources and enhance [...] Read more.

This paper investigates the problems of anti-synchronization for a class of inertial neural networks (INNs) with time-varying delays under the influence of deception attacks and hybrid triggered control. A novel dynamic hybrid-triggered control (DHTC) scheme is developed to utilize communication resources and enhance network security efficiently for the model INNs. By integrating the extended dissipative approach with Lyapunov–Krasovskii functional (LKF) techniques, new sufficient conditions are established to ensure the quadratic stability of the resulting closed-loop system. The proposed framework not only unifies the anti-synchronization problems but also extends classical passivity, (Q, S, R)-dissipative,

H_{\infty}

, and

L_{2} - L_{\infty}

results as special cases. Moreover, the DHTC mechanism dynamically switches between time-triggered and event-triggered modes, reducing unnecessary signal transmissions while maintaining system stability against deception attacks. Finally, simulation results on delayed INNs demonstrate the effectiveness and superiority of the proposed theoretical and control strategy. Full article

(This article belongs to the Special Issue Asymmetric and Symmetric Studies in Nonlinear Dynamics)

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19 pages, 3879 KB

Open AccessArticle

Biomechanical Evaluation of Sacral Load Redistribution Following Unilateral and Bilateral Sacroiliac Joint Disruption: A Three-Dimensional Finite Element Comparison of Three Fixation Strategies

by Bünyamin Arı, Melih Canlıdinç and Nafiz Yaşar

Symmetry 2026, 18(6), 1061; https://doi.org/10.3390/sym18061061 - 20 Jun 2026

Viewed by 375

Abstract

Sacroiliac joint (SIJ) disruption alters posterior pelvic ring stability and can produce abnormal sacral stress redistribution; the symmetry of sacral load transfer following different fixation strategies remains controversial. This study compared sacral stress patterns under unilateral and bilateral SIJ instability for three fixation [...] Read more.

Sacroiliac joint (SIJ) disruption alters posterior pelvic ring stability and can produce abnormal sacral stress redistribution; the symmetry of sacral load transfer following different fixation strategies remains controversial. This study compared sacral stress patterns under unilateral and bilateral SIJ instability for three fixation constructs using a three-dimensional finite element (FE) model. A lumbosacral–pelvic FE model was reconstructed from computed tomography data of a healthy adult and validated against previously published pelvic biomechanical data. SIJ instability was simulated by reducing the friction coefficient to represent ligamentous failure. Three fixation constructs were analyzed: anterior plate combined with posterior screw fixation (Model 1), spinopelvic fixation (Model 2), and hybrid fixation (Model 3). A 750 N axial compressive load was applied to simulate static standing. Peak sacral von Mises stress, stress amplification factors (SAFs), and left–right asymmetry ratios were computed and compared with the intact reference. Model 1 produced the highest sacral stress amplification (SAF = 3.46 under unilateral instability; peak stress 265.40 MPa). Model 2 reduced peak sacral stress (125.66 MPa under bilateral instability; SAF = 1.64), but values remained above the intact-model baseline. Model 3 yielded sacral stress closest to the intact condition under bilateral instability (81.64 MPa; SAF = 1.06), with near-symmetric load distribution in the bilateral injury configuration. Fixation topology strongly influenced sacral load transfer: hybrid fixation (Model 3) produced sacral stress magnitudes closest to the intact model, particularly under bilateral instability, whereas spinopelvic fixation (Model 2) showed more consistent left–right symmetry under unilateral injury. No single construct was superior across all symmetry-related outcomes. Hybrid stabilization may provide a biomechanically balanced approach to highly unstable posterior pelvic ring injuries under the simulated static axial-loading conditions. Full article

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

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61 pages, 1695 KB

Open AccessArticle

Parameter-Free Deformation Variables of the Proxy-SU(3) Symmetry in Even–Even Actinide, Superheavy, and Hyperheavy Nuclei with Z = 82–126, N = 82–258

by Dennis Bonatsos, Venkata Krishna Brahmam Kota, Andriana Martinou, Spyridon Kosmas Peroulis, Dimitrios Petrellis, Polytimos Vasileiou, Theodoros John Mertzimekis and Nikolay Minkov

Symmetry 2026, 18(6), 1060; https://doi.org/10.3390/sym18061060 - 20 Jun 2026

Cited by 1 | Viewed by 317

Abstract

Superheavy and hyperheavy nuclei are one of the frontiers of nuclear structure nowadays, while for many actinides rather limited experimental information exists. Therefore, theoretical methods providing parameter-independent predictions for these nuclei are of particular interest. Such a method is the proxy-SU(3) approximation to [...] Read more.

Superheavy and hyperheavy nuclei are one of the frontiers of nuclear structure nowadays, while for many actinides rather limited experimental information exists. Therefore, theoretical methods providing parameter-independent predictions for these nuclei are of particular interest. Such a method is the proxy-SU(3) approximation to the shell model, which has been adequately tested against experimental data in medium-mass and heavy nuclei up to the rare-earth region, and it has been found to provide reliable, parameter-independent predictions for the collective deformation variables

β

and

γ

. Within the proxy-SU(3) approach, the SU(3) symmetry of the three-dimensional harmonic oscillator, which is destroyed beyond the

s d

shell by the strong spin–orbit interaction, is restored through a unitary transformation. For each nucleus, the most symmetric irreducible representation (irrep) allowed by the Pauli principle and the short-range nature of the nucleon–nucleon interaction, called the highest-weight (hw) irrep in mathematical language, is found to suffice, except in cases in which the hw irrep turns out to be completely symmetric, so that the next highest weight (nhw) irrep has also to be included. In this article we provide a full collection of the hw and nhw irreps, as well as of the corresponding parameter-free predictions for the deformation variables

β

and

γ

, for all atomic nuclei ranging from

Z = 82

,

N = 82

to

Z = 126

,

N = 258

. Several cases exemplifying the use of the collected results for studying the prolate-to-oblate shape transition, mirror symmetries, and the evolution of the collective variables along the valley of stability are also considered. Full article

(This article belongs to the Special Issue Advances in Nuclear Physics and Symmetry)

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23 pages, 2771 KB

Open AccessArticle

Real-Time Leaf Disease Detection with Boundary-Aware and Texture-Sensitive Feature Enhancement

by Jinyang Qiu, Qiuyi Du, Yonggang Wang, Yuhan Tao, Yue Guo, Ye Zhang and Yue Gao

Symmetry 2026, 18(6), 1059; https://doi.org/10.3390/sym18061059 - 19 Jun 2026

Viewed by 303

Abstract

Accurate and robust detection of leaf diseases is a key enabler for precision agriculture and large-scale crop health monitoring. Despite the strong generalization of modern one-stage detectors (e.g., YOLOv8), two domain-specific challenges remain: (i) weak or blurry lesion boundaries hinder precise localization, and [...] Read more.

Accurate and robust detection of leaf diseases is a key enabler for precision agriculture and large-scale crop health monitoring. Despite the strong generalization of modern one-stage detectors (e.g., YOLOv8), two domain-specific challenges remain: (i) weak or blurry lesion boundaries hinder precise localization, and (ii) low color contrast between diseased and healthy tissues forces models to rely on subtle texture patterns rather than salient shapes. To tackle these challenges, we reframe the core agricultural disease detection task as the identification of “asymmetric morphological anomalies” and propose a domain-tailored enhancement framework. First, we introduce an Edge Enhancement Module (EEM) that explicitly strengthens boundary-aware representations. Inspired by the natural symmetry of healthy leaves, our EEM is specifically designed to capture symmetry-breaking boundary discontinuities and localized asymmetric edges caused by disease lesions. Our method enhances edge and texture cues that are indicative of disease lesions, which often exhibit local asymmetries and boundary discontinuities. The EEM includes a Differential Normalized Pooling Block (DNPB) that highlights edge responses through discrepancies between max pooling and average pooling, which also models cross-group edge correlations. Second, the Lightweight Texture-Sensitive Feature Enhancement (LTSFE) mechanism amplifies texture-discriminative channels under low-contrast conditions by leveraging complementary global statistics and efficient channel mixing, all with negligible computational overhead. We evaluated our method on a self-constructed dataset of 106,434 images with 225,640 annotations covering diverse crops. Experiments show that the proposed method achieves state-of-the-art accuracy (81.54% mAP@0.5:0.95) while maintaining real-time inference (142 FPS), consistently outperforming strong baselines. Ablations confirm the effectiveness and complementarity of EEM and LTSFE, demonstrating that domain-specific architectural design, inspired by biological symmetry, can substantially improve agricultural vision systems. Full article

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

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17 pages, 355 KB

Open AccessArticle

Threshold Attribute-Based Encryption Scheme Supporting Multiple Access Policies

by Vu Nam Luu, Willy Susilo and Viet Cuong Trinh

Symmetry 2026, 18(6), 1058; https://doi.org/10.3390/sym18061058 - 19 Jun 2026

Viewed by 321

Abstract

Threshold Attribute-based Encryption has attracted significant attention due to its growing importance in practical applications, such as distributed cloud storage or anonymous access control. In a threshold attribute-based encryption scheme, a sender can select a set of attributes and a corresponding threshold t [...] Read more.

Threshold Attribute-based Encryption has attracted significant attention due to its growing importance in practical applications, such as distributed cloud storage or anonymous access control. In a threshold attribute-based encryption scheme, a sender can select a set of attributes and a corresponding threshold t, which is referred to as an access policy, to encrypt a message. Decryption is successful if and only if a user possesses at least t attributes from the specified attribute set. Existing threshold attribute-based encryption schemes typically consider only the setting in which a single message is encrypted under a single access policy. However, in many practical applications, more flexible encryption scenarios are needed, such as encrypting a single message under multiple access policies or encrypting multiple messages under their corresponding access policies. In this work, we first formalize the notion of threshold attribute-based encryption supporting the encryption of multiple messages under multiple access policies. We then propose the first construction of a threshold attribute-based encryption scheme based on the Key Encapsulation Mechanism paradigm that supports such functionality while achieving constant-size ciphertext. Our proposed scheme relies on bilinear pairings and is proven secure in the Generic Bilinear Group Model. As a classical pairing-based construction, it does not provide post-quantum security and is therefore unsuitable for scenarios requiring long-term confidentiality or resilience against harvest-now, decrypt-later attacks. Full article

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

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37 pages, 21339 KB

Open AccessArticle

A New Reparameterized Weibull-Type Distribution for Asymmetric Lifetime Data: Inference, Simulation, and Applications

by Ahmed Elshahhat, Heba S. Mohammed, Osama E. Abo-Kasem and Asmaa Abdel-Hakim

Symmetry 2026, 18(6), 1057; https://doi.org/10.3390/sym18061057 - 19 Jun 2026

Viewed by 311

Abstract

This article presents a comprehensive inferential and applied investigation of the newly reparameterized Z-Weibull (ZW) distribution, a flexible Weibull-type lifetime model capable of accommodating both bounded and unbounded support regimes as well as a wide variety of hazard rate shapes. Unified frequentist and [...] Read more.

This article presents a comprehensive inferential and applied investigation of the newly reparameterized Z-Weibull (ZW) distribution, a flexible Weibull-type lifetime model capable of accommodating both bounded and unbounded support regimes as well as a wide variety of hazard rate shapes. Unified frequentist and Bayesian inference procedures are developed for complete and censored samples using maximum likelihood, maximum product spacing, and Markov chain Monte Carlo methods. Theoretical properties of the estimators and their associated interval estimates are established, while extensive Monte Carlo simulations assess their finite-sample performance under diverse parameter configurations and censoring schemes. The results indicate that Bayesian spacing-based procedures generally provide more accurate estimation, lower bias, and improved interval performance than competing classical methods. Applications to biomedical survival and climatological datasets, together with comparisons against several Weibull-type and exponential-based competitors, demonstrate the superior flexibility and goodness-of-fit of the ZW model. These findings highlight the practical value of the reparameterized ZW distribution as a unified and effective tool for modeling complex lifetime and reliability data arising in survival, environmental, and engineering studies. Full article

(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications Across Disciplines, 5th Edition)

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31 pages, 495 KB

Open AccessArticle

Superelliptic Dual Quaternions and Superelliptic Screw Motion Based on Gielis Formula

by Esra Parlak and Zehra Özdemir

Symmetry 2026, 18(6), 1056; https://doi.org/10.3390/sym18061056 - 19 Jun 2026

Viewed by 295

Abstract

This paper proposes a superelliptic dual quaternion framework that extends classical dual quaternion kinematics by replacing the Euclidean metric structure with a Gielis-formula-induced superelliptic inner product and its associated vector product. Within the resulting space

R_{S_{E}}^{3}

, superelliptic dual numbers, [...] Read more.

This paper proposes a superelliptic dual quaternion framework that extends classical dual quaternion kinematics by replacing the Euclidean metric structure with a Gielis-formula-induced superelliptic inner product and its associated vector product. Within the resulting space

R_{S_{E}}^{3}

, superelliptic dual numbers, dual vectors, and an E-Study-type correspondence between unit dual vectors and directed superelliptic lines are established, yielding an algebraic model adapted to non-Euclidean geometric profiles. In contrast to the standard Euclidean dual quaternion formalism, where rotations, translations, and screw motions are governed by the ordinary inner product of

R^{3}

, the present formulation encodes these motions relative to a parameter-dependent superelliptic geometry determined by Gielis’ superformula. This distinction enables the kinematic description of motions associated with superelliptic axes and trajectories that cannot be represented naturally within the classical Euclidean setting. A superelliptic screw motion theorem is obtained, showing that a unit superelliptic dual quaternion generates simultaneous rotation about and translation along a common superelliptic axis. The framework offers a compact mathematical basis for advanced rigid-body modeling in robotics and geometric design. The proposed framework represents rotation, translation, and screw displacement by a single unit superelliptic dual quaternion, providing a compact basis for shape-dependent rigid-body modeling in robotics and geometric design. Full article

(This article belongs to the Section B: Mathematics)

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28 pages, 622 KB

Open AccessArticle

Fully Hesitant Fuzzy Bilevel Linear Programming and Its Application to Quantum Communication Resource Allocation

by Jintao Tan, Shengyue Deng, Lan Hu and Yong Zhang

Symmetry 2026, 18(6), 1055; https://doi.org/10.3390/sym18061055 - 18 Jun 2026

Viewed by 326

Abstract

The problem of bilevel decision-making under multi-expert uncertain information is addressed in this paper. Traditional fuzzy bilevel models are unable to accurately quantify expert consensus and capture evaluation hesitation. To overcome these limitations, a fully hesitant fuzzy bilevel linear programming model is proposed, [...] Read more.

The problem of bilevel decision-making under multi-expert uncertain information is addressed in this paper. Traditional fuzzy bilevel models are unable to accurately quantify expert consensus and capture evaluation hesitation. To overcome these limitations, a fully hesitant fuzzy bilevel linear programming model is proposed, in which all coefficients and decision variables are characterized by hesitant fuzzy numbers. By virtue of

(α, k)

-cuts, the original model is equivalently transformed into an interval-valued bilevel programming problem and further decomposed into best–best and worst–worst sub-models to derive the upper and lower bounds of optimal solutions. Under the Slater constraint qualification, Karush–Kuhn–Tucker (KKT) conditions are adopted to convert the two sub-models into single-level mathematical programs with complementarity constraints (MPCCs), thereby enabling efficient model solving. The proposed method is applied to the resource allocation problem in quantum communication networks. The numerical results demonstrate that the optimal solution interval converges to a unique core value as the membership-level

α

increases, while a larger consensus parameter k reduces the fuzzy support set without altering the core solution. Full article

(This article belongs to the Special Issue The Fusion of Fuzzy Sets and Optimization Using Symmetry)

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13 pages, 588 KB

Open AccessArticle

A Linearly Convergent Algorithm for the H-Spectral Radius of Index-Cyclic Symmetric Positive Tensors

by Xincun Wang and Hongbin Lyu

Symmetry 2026, 18(6), 1054; https://doi.org/10.3390/sym18061054 - 18 Jun 2026

Viewed by 247

Abstract

A class of index-cyclic symmetric positive tensors is defined, and a diagonal similarity algorithm is proposed to compute the H-spectral radius of such tensors. The linear convergence of the algorithm is rigorously proven. The computational efficiency of the proposed method is compared [...] Read more.

A class of index-cyclic symmetric positive tensors is defined, and a diagonal similarity algorithm is proposed to compute the H-spectral radius of such tensors. The linear convergence of the algorithm is rigorously proven. The computational efficiency of the proposed method is compared with that of the classical power method by numerical examples. The results indicate that the proposed algorithm achieves reliable linear convergence and offers competitive computational performance for index-cyclic symmetric positive tensors. Full article

(This article belongs to the Section B: Mathematics)

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29 pages, 3769 KB

Open AccessArticle

A Joint Event Extraction Method Based on Curriculum Adversarial Learning and Adaptive Enhancement

by Hongyong An, Tonghui An, Haoran Jiang and Yujie Yang

Symmetry 2026, 18(6), 1053; https://doi.org/10.3390/sym18061053 - 18 Jun 2026

Viewed by 345

Abstract

Event extraction is a core NLP task that aims to identify triggers and arguments in unstructured text. In the financial domain, dense events, overlapping arguments, and ambiguous semantics pose significant challenges. This paper proposes CADAEE, a joint extraction framework that integrates curriculum adversarial [...] Read more.

Event extraction is a core NLP task that aims to identify triggers and arguments in unstructured text. In the financial domain, dense events, overlapping arguments, and ambiguous semantics pose significant challenges. This paper proposes CADAEE, a joint extraction framework that integrates curriculum adversarial learning and an enhanced adaptive layer. Curriculum adversarial learning dynamically adjusts training difficulty, thereby improving robustness and generalization on complex samples. The enhanced adaptive layer introduces learnable role-bias embeddings to model semantic dependencies between triggers and arguments, while a multi-head attention mechanism captures diverse feature interactions. Extensive experiments on the FewFC and DuEE-Fin datasets demonstrate the superiority of CADAEE. The model achieves highly competitive F1-scores in both trigger and argument classification, reaching 80.1% and 73.5% on FewFC, and 88.8% and 71.8% on DuEE-Fin, respectively. Ablation studies validate the synergistic contributions of the proposed modules. These results demonstrate that CADAEE provides robust and accurate extraction in complex, overlapping event scenarios, highlighting the value of combining curriculum learning with adaptive, role-aware enhancements for financial event extraction. Full article

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

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26 pages, 5499 KB

Open AccessArticle

PC-LossGNN: A Physics-Consistent Spatiotemporal Graph Neural Network for Line Loss Anomaly Classification

by Xiaojing Zhu, Li Huang, Gan Zhou, Junyang Yang and Chengge Duan

Symmetry 2026, 18(6), 1052; https://doi.org/10.3390/sym18061052 - 18 Jun 2026

Viewed by 410

Abstract

Modern distribution networks undergo frequent topology reconfiguration, volatile bi-directional flows, and noisy measurements, making five-class line-loss anomaly classification both valuable and challenging. In this study, PC-LossGNN is proposed—a physics-consistent spatiotemporal graph neural network for edge-level classification into Normal, Infrastructure, Documentation, Metering, and Theft. [...] Read more.

Modern distribution networks undergo frequent topology reconfiguration, volatile bi-directional flows, and noisy measurements, making five-class line-loss anomaly classification both valuable and challenging. In this study, PC-LossGNN is proposed—a physics-consistent spatiotemporal graph neural network for edge-level classification into Normal, Infrastructure, Documentation, Metering, and Theft. A static topology prior is fused with a measurement-adaptive graph and confidence-aware multi-source features; power-flow physics is injected via residual-guided attention using active/reactive balance, voltage-drop, and ohmic-loss residuals. A dual-path decoder is employed to yield calibrated probabilities and interpretable class evidence, trained under an uncertainty-weighted curriculum objective. On six months of real utility data, macro-F1 of 0.8503 and accuracy of 0.9915 are achieved, surpassing XGBoost, LSTM, GCN, STGCN, and two recent physics-aware spatiotemporal GNN baselines including ST-RGNN and PA-STGCN. Ablation indicates that physics-consistent regularization is pivotal, while adaptive topology and interactive temporal encoding further improve performance. Robustness tests with injected Gaussian noise show more graceful degradation than baselines. These results suggest that PC-LossGNN provides accurate, physically plausible, and interpretable five-way line-loss diagnostics suitable for real-world operations. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Data Analysis)

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22 pages, 663 KB

Open AccessArticle

State-Dependent Asymmetry in Soft-Pity Gacha Waiting-Time Models: Exact Recurrences, Tail Risk, and Featured-Target Extensions

by Saisai Hou, Yunzhi Zhu and Sen Zhang

Symmetry 2026, 18(6), 1051; https://doi.org/10.3390/sym18061051 - 18 Jun 2026

Viewed by 363

Abstract

Randomized reward mechanisms are often described as repeated trials with a fixed success probability. This constant-hazard reference case is symmetric in the limited finite-state sense that, conditional on non-absorption, the next-draw success probability is invariant with respect to the current draw count. Pity [...] Read more.

Randomized reward mechanisms are often described as repeated trials with a fixed success probability. This constant-hazard reference case is symmetric in the limited finite-state sense that, conditional on non-absorption, the next-draw success probability is invariant with respect to the current draw count. Pity and guarantee rules break this draw-count homogeneity by making the hazard depend on the current state. This paper studies that state-dependent asymmetry for a finite soft-pity waiting-time model. The waiting time for one rare item is represented as an absorption time of a Markov chain whose transient state is the pity counter. We write the corresponding absorbing transition matrix explicitly and then derive the equivalent first-step recurrences for the expectation, variance, and full probability mass function. A simple stochastic-ordering proposition shows how increasing the statewise success probabilities decreases the waiting-time distribution in the usual tail order. Repeated convolution then yields the distribution for multiple independent stages. The numerical section reports quantiles, tail probabilities, VaR/CVaR-type summaries, expected excess values, sensitivity analyses, normal-approximation diagnostics, and distributional asymmetry indicators. A featured-target variant with a binary guarantee state is also included. Throughout, the reported quantities are consequences of the stated transition rule; Monte Carlo simulation is used only as a numerical check. Full article

(This article belongs to the Section B: Mathematics)

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17 pages, 614 KB

Open AccessReview

Probing the Tau Anomalous Magnetic Moment at Colliders: From Ultra-Peripheral Collisions to the Precision Frontier

by Natascia Vignaroli

Symmetry 2026, 18(6), 1050; https://doi.org/10.3390/sym18061050 - 18 Jun 2026

Viewed by 384

Abstract

The anomalous magnetic moment of the tau lepton,

a_{τ}

, represents a fundamental test of the Standard Model (SM) and a high-sensitivity probe for New Physics in the third generation of leptons. Due to the tau’s extremely short lifetime, traditional spin-precession measurements [...] Read more.

The anomalous magnetic moment of the tau lepton,

a_{τ}

, represents a fundamental test of the Standard Model (SM) and a high-sensitivity probe for New Physics in the third generation of leptons. Due to the tau’s extremely short lifetime, traditional spin-precession measurements remain inaccessible, necessitating innovative experimental strategies at high-energy colliders. This review provides a comprehensive overview of the current experimental landscape, highlighting the recent paradigm shift from LEP-era constraints to the unprecedented precision reached at the LHC. We emphasize the importance of Ultra-Peripheral Heavy-Ion Collisions (UPCs), which act as a “photon-photon collider” of extreme intensity. By leveraging the

Z^{4}

enhancement of the coherent photon flux in Lead–Lead (

P b P b

) interactions, these collisions provide a theoretically robust “quasi-static” environment. To interpret these developments, we first establish the general theoretical framework within the Standard Model Effective Field Theory (SMEFT). This allows us to critically compare the UPC results with the latest measurements from proton–proton collisions—including the recent CMS observation of the

γ γ \to τ τ

process and the ATLAS constraints from the high-mass Drell–Yan tail—evaluating their complementarity and the challenges related to Effective Field Theory validity at the TeV scale. Finally, we outline the future prospects for

a_{τ}

at Belle II and the Future Circular Collider (FCC) stages. While FCC-hh in

P b P b

mode provides a theoretically clean environment, its sensitivity remains limited to

O (10^{- 2})

. Conversely, the next generation of lepton facilities, specifically Belle II and FCC-ee, aims for the

O (10^{- 5})

level, required to probe SM electroweak loop corrections. Long-term projections for a high-energy Muon Collider suggest a potential reach of

O (10^{- 6})

. Full article

(This article belongs to the Special Issue Symmetry and Relativistic Heavy-Ion Collisions)

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29 pages, 12339 KB

Open AccessArticle

Soliton Solutions to a Nonisospectral mKdV-sG Equation with Self-Consistent Sources and Reductions

by Han Wang, Wei Feng and Song-Lin Zhao

Symmetry 2026, 18(6), 1049; https://doi.org/10.3390/sym18061049 - 17 Jun 2026

Viewed by 381

Abstract

We derive multisoliton solutions for a nonisospectral mKdV-sG equation with self-consistent sources by means of the bilinear approach. This nonisospectral equation is a generic one which is related to a time-dependent spectral parameter with time evolution [...] Read more.

We derive multisoliton solutions for a nonisospectral mKdV-sG equation with self-consistent sources by means of the bilinear approach. This nonisospectral equation is a generic one which is related to a time-dependent spectral parameter with time evolution

λ_{t} = μ_{2} λ + 4 μ_{3} λ^{3} + ν_{2} / (4 λ)

. Reductions to some soliton equations with self-consistent sources are investigated. One- and two-soliton solutions for the reduced equations are presented and dynamical behaviors are illustrated. Full article

(This article belongs to the Special Issue Symmetry in Integrable Systems: Topics and Advances (Second Edition))

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30 pages, 2505 KB

Open AccessArticle

A Knowledge Graph Multi-Hop Question Answering Method Based on Adaptive Graph Convolutional Neural Networks

by Cheng Gan, Yuhang Cai, Shenyi Qian, Songhe Jin, Bowen Fu, Tongxin Zhao and Daiyi Li

Symmetry 2026, 18(6), 1048; https://doi.org/10.3390/sym18061048 - 17 Jun 2026

Viewed by 447

Abstract

Multi-hop question answering (MQA) requires models to perform multi-step reasoning and integrate multiple knowledge sources. However, existing methods combining pre-trained language models (PLMs) and graph neural networks (GNNs) often suffer from low computational efficiency, insufficient deep semantic fusion, and imbalanced modeling of heterogeneous [...] Read more.

Multi-hop question answering (MQA) requires models to perform multi-step reasoning and integrate multiple knowledge sources. However, existing methods combining pre-trained language models (PLMs) and graph neural networks (GNNs) often suffer from low computational efficiency, insufficient deep semantic fusion, and imbalanced modeling of heterogeneous relations. To solve these problems, we propose a Dynamic Hierarchical Adaptive Graph Convolution Network (DHACNet). First, to deal with the issues of insufficient computational efficiency and feature interpretability, we introduce Dynamic Sparse Activation (DSA). A trainable gate unit is used to generate importance masks for the encoder outputs, keeping only the task-relevant neurons. This greatly decreases the computational burden and enhances the interpretability of the model’s decisions. Second, to alleviate insufficient deep semantic fusion, we design a Hierarchical Feature Fusion (HFF) mechanism. It adaptively weights and fuses hidden states from different layers, enhancing the extraction and representation of deep textual semantics. Furthermore, for graph structure modeling, we present Adaptive Graph Convolution (AGC), which assigns learnable weights to different edge types in the graph, thereby improving heterogeneous relation modeling. Finally, hierarchical graph pooling is introduced, which integrates attention mechanism and Top-

K

selection to achieve efficient and robust graph-level representation. The experimental results show that our proposed model maintains the symmetry between the text representation and graph representation through adaptive layered fusion and relational perceptual graph propagation. This symmetry-aware reasoning process encourages semantic consistency during multi-hop inference and makes knowledge integration more robust. Full article

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

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20 pages, 403 KB

Open AccessArticle

Exactly Solvable Quantum Model with Spin-Dependent Coulomb Interaction

by Jiang-Lin Zhou, Yu-Xuan Zhang, Choo Hiap Oh and Jing-Ling Chen

Symmetry 2026, 18(6), 1047; https://doi.org/10.3390/sym18061047 - 17 Jun 2026

Viewed by 314

Abstract

In this work, we report an exactly solvable quantum model featuring a spin-dependent Coulomb interaction, described by the spin vector potential

\vec{A} = k (\vec{r} \times \vec{S}) / r^{2}

together with a Coulomb-type scalar potential [...] Read more.

In this work, we report an exactly solvable quantum model featuring a spin-dependent Coulomb interaction, described by the spin vector potential

\vec{A} = k (\vec{r} \times \vec{S}) / r^{2}

together with a Coulomb-type scalar potential

φ = κ / r

. The model is governed by the Schrödinger-type Hamiltonian

H_{S} = {\vec{Π}}^{2} / (2 M) + q φ

in nonrelativistic quantum mechanics and by the Dirac-type Hamiltonian

H_{D} = c \vec{α} \cdot \vec{Π} + β M c^{2} + q φ

in relativistic quantum mechanics, where

\vec{Π} = \vec{p} - (q / c) \vec{A}

is the canonical momentum. We demonstrate two main results: (i) Just as the Coulomb-type scalar potential

S_{Maxwell} = {\vec{A} = 0, φ = κ / r}

is a local exact solution of Maxwell’s equations on

r \neq 0

, the gauge potential

S_{YM} = {\vec{A} = k (\vec{r} \times \vec{S}) / r^{2}, φ = κ / r}

constitutes a local exact solution of the Yang–Mills equations on the punctured region

r \neq 0

. (ii) Both Hamiltonians

H_{S}

and

H_{D}

can be solved exactly in the presence of this spin-dependent Coulomb interaction. The resulting energy spectra are derived, and they naturally reduce to those of the ordinary hydrogen atom when the spin-dependent terms are neglected. Finally, we clarify the quantization conditions and the fixed-background interpretation of the model. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Quantum Models)

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26 pages, 4164 KB

Open AccessArticle

Dynamic Pricing for Perishable Fresh Produce with Attention-Augmented PPO Algorithm

by Wenya Zhang, Xuetong Zhang and Gendao Li

Symmetry 2026, 18(6), 1046; https://doi.org/10.3390/sym18061046 - 17 Jun 2026

Viewed by 445

Abstract

Perishable products are usually priced in real-time to volatile market environments, thereby optimizing inventory control, minimizing resource wastage, and maximizing corporate profitability. Based on the public dataset from the 2023 Higher Education Press Cup National College Students Mathematical Modeling Competition, this paper addresses [...] Read more.

Perishable products are usually priced in real-time to volatile market environments, thereby optimizing inventory control, minimizing resource wastage, and maximizing corporate profitability. Based on the public dataset from the 2023 Higher Education Press Cup National College Students Mathematical Modeling Competition, this paper addresses the challenge of multi-product joint pricing for perishable fresh produce and proposes an attention-augmented proximal policy optimization algorithm (termed ATT-PPO), which embeds an attention mechanism into the proximal policy optimization (PPO) framework. The integrated attention mechanism confers three core advantages to the model: first, it dynamically captures inter-product interdependencies, enabling an accurate reflection of cross-price elasticity and demand correlations; second, it reduces feature redundancy and computational overhead in multi-product collaborative pricing strategies; third, it enhances both the interpretability and computational efficiency of the model. Experimental results demonstrate that in the scenario of multi-product pricing, the ATT-PPO algorithm achieves competitive performance compared to PPO, DDPG (Deep Deterministic Policy Gradient), SAC (Soft Actor-Critic), and TD3 (Twin Delayed Deep Deterministic Policy Gradient), with the key advantage lying in its ability to provide interpretable attention weights that reveal dynamic cross-product dependencies in pricing decisions. This study not only expands the applicability of DRL (Deep Reinforcement Learning) to practical economic problems in the fresh produce sector but also provides valuable theoretical insights that can be generalized to other short-lifecycle product domains, including fashion apparel and consumer electronics. Full article

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

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94 pages, 33281 KB

Open AccessReview

Higgs Sector Prospects at Future Particle Colliders in Europe

by Aleandro Nisati

Symmetry 2026, 18(6), 1045; https://doi.org/10.3390/sym18061045 - 17 Jun 2026

Viewed by 604

Abstract

The discovery of the Higgs boson in 2012 at the Large Hadron Collider marked a major milestone in our understanding of electroweak symmetry breaking. Since then, increasingly precise measurements by the ATLAS and CMS Collaborations, based primarily on proton–proton collision data at [...] Read more.

The discovery of the Higgs boson in 2012 at the Large Hadron Collider marked a major milestone in our understanding of electroweak symmetry breaking. Since then, increasingly precise measurements by the ATLAS and CMS Collaborations, based primarily on proton–proton collision data at

\sqrt{s} = 13 TeV

corresponding to about

140 {fb}^{- 1}

per experiment, have confirmed its compatibility with Standard Model predictions within current uncertainties. The Higgs boson mass is now measured with a precision of about 0.08%, while its couplings to fermions and bosons are determined at the 7–20% level. The completion of the LHC programme and the High-Luminosity LHC, will probe Higgs boson couplings at the few-percent level. However, sub-percent precision is required for stringent tests of the Standard Model, as any deviation would signal new physics beyond it. This strongly motivates future collider facilities, designed both as high-precision Higgs factories and, in many cases, as energy-frontier machines. Within the framework of the update of the European Strategy for Particle Physics, we discuss the physics case and main characteristics of the proposed particle collider options, highlighting their complementarity, technological challenges, and expected performance. The 2026 Strategy Update identifies the FCC-ee collider as the preferred next flagship project at CERN. Operating at the Z pole and at centre-of-mass energies between 240 and 365 GeV, it would enable model-independent, per-mille-level precision on Higgs boson couplings, while providing a pathway to a future high-energy hadron collider. The Higgs sector thus constitutes a central laboratory for precision tests of the Standard Model and for exploring the fundamental structure of our universe. Full article

(This article belongs to the Special Issue Symmetries/Asymmetries in Particle Physics)

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1 pages, 125 KB

Open AccessRetraction

RETRACTED: Chen et al. Airspace Operation Effectiveness Evaluation Based on q-Rung Orthopair Probabilistic Hesitant Fuzzy GRA and TOPSIS. Symmetry 2022, 14, 242

by Zhiyuan Chen, Di Shen, Yaojun Ren, Fuping Yu and Xiujiu Yuan

Symmetry 2026, 18(6), 1044; https://doi.org/10.3390/sym18061044 - 17 Jun 2026

Viewed by 354

Abstract

The journal retracts the article “Airspace Operation Effectiveness Evaluation Based on q-Rung Orthopair Probabilistic Hesitant Fuzzy GRA and TOPSIS” [...] Full article

39 pages, 2631 KB

Open AccessArticle

Active Circuit Discovery: A Multi-Action POMDP Agent for Causal Feature Identification in Transformer Attribution Graphs

by Sharath Sathish, Mominul Ahsan and Majid Latifi

Symmetry 2026, 18(6), 1043; https://doi.org/10.3390/sym18061043 - 16 Jun 2026

Viewed by 976

Abstract

Mechanistic interpretability seeks to reverse-engineer the computational circuits within large language models, but current methods rely on exhaustive or heuristic search over exponentially many feature interactions. This paper introduces Active Circuit Discovery (ACD), a framework that combines attribution-graph analysis with active inference to [...] Read more.

Mechanistic interpretability seeks to reverse-engineer the computational circuits within large language models, but current methods rely on exhaustive or heuristic search over exponentially many feature interactions. This paper introduces Active Circuit Discovery (ACD), a framework that combines attribution-graph analysis with active inference to select interventions efficiently. ACD uses Anthropic’s circuit-tracer library as its attributiongraph backend, applying Edge Attribution Patching with transcoders to identify the active transcoder features for each prompt. A partially observable Markov decision process (POMDP) agent, implemented with pymdp, maintains a multi-factor generative model of feature importance, layer role, and causal influence. At each step, the agent selects both a target feature and an intervention type (ablation, activation patching, or feature steering) by minimising Expected Free Energy over the joint feature–action space, and it learns its observation model online through Dirichlet parameter updates. ACD is an interventionselection layer over existing attribution-graph tools; it is not a whole-circuit discovery method, and no claim of state-of-the-art circuit discovery is made. The framework is evaluated on Gemma-2-2B (26 layers) and Llama-3.2-1B (16 layers) across four settings: Indirect Object Identification (IOI), multi-step reasoning, feature steering, and a multidomain benchmark spanning geography, mathematics, science, logic, and history. With a budget of 20 interventions per prompt, an ablation-only agent scored by bounded oracle efficiency against the ablation oracle reaches 82.0% efficiency on Gemma IOI and 73.0% on Gemma multi-step. It exceeds random selection by 43.5% (relative) on Gemma IOI (paired permutation p = 0.031) and is competitive with greedy ranking, a heuristic UCB bandit, and a plain UCB baseline. A direct Edge-Attribution-Patching ranking is itself a strong baseline that the agent does not consistently surpass, and on Llama multi-step the agent reaches 9.3% efficiency (37.8% with finer layer-role bins). All comparisons report bootstrap 95% confidence intervals. The full multi-action agent is characterised separately by a Relative Cumulative KL, a steering-driven amplification factor reported apart from the bounded efficiency. Feature steering changes the top-1 prediction in a dose-dependent manner, but a matched random-feature control shows that circuit-selected features are only marginally, and not significantly, more steerable than random active features at large multipliers, indicating that part of the effect is generic activation scaling. Multi-domain analysis shows task-dependent circuit structure, with IOI circuits concentrated in late layers and reasoning and scientific knowledge recruiting early and middle layers. Code, notebooks (free T4), AMD64/aarch64 Docker images, and raw results are publicly available. Full article

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28 pages, 883 KB

Open AccessArticle

Evaluation of Adaptive Management Strategies for Agricultural Production to Climate Change Using Interval Type-2 Fuzzy Sets with Symmetric Fuzzy Numbers

by Timea Juhász-Hallai, Radivoj Prodanović, Zoran Mastilo, Vladica Ristić, Vladimir Tomašević, Biljana Carić, Zoran Ovcin and Adis Puška

Symmetry 2026, 18(6), 1042; https://doi.org/10.3390/sym18061042 - 16 Jun 2026

Viewed by 410

Abstract

Climate change affects all sectors, with a particularly significant impact on agricultural production. Therefore, agricultural production must adapt to these changes, and adaptive strategies for managing agricultural production should be applied. This research evaluates which adaptive strategies yield the best results in agricultural [...] Read more.

Climate change affects all sectors, with a particularly significant impact on agricultural production. Therefore, agricultural production must adapt to these changes, and adaptive strategies for managing agricultural production should be applied. This research evaluates which adaptive strategies yield the best results in agricultural production in Bosnia and Herzegovina and Serbia through expert decision-making. In doing so, the interval type-2 fuzzy set (IF2S) is applied, using symmetric fuzzy numbers through the membership function. The results obtained by applying IF2S M-SiWeC (Modified Simple Weight Calculation) show that the criteria of the greatest importance are yield stability and climate risk reduction. The ranking of the six selected adaptive strategies is carried out using the IF2S MABAC (Multi-Attributive Border Approximation area Comparison) method, which indicates that agricultural production diversification and adaptive water management strategies provide the best results according to expert assessments. These results are confirmed by additional analyses, including comparative analysis and sensitivity analysis. The contribution of this research is reflected in proposing guidelines on the adaptive strategies that should be applied in practice in agricultural production in order to reduce the negative effects of climate change. Full article

(This article belongs to the Special Issue Symmetry in Algorithm and Decision-Making)

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22 pages, 2036 KB

Open AccessArticle

Ramsey Approach to Symmetry

by Edward Bormashenko

Symmetry 2026, 18(6), 1041; https://doi.org/10.3390/sym18061041 - 16 Jun 2026

Viewed by 639

Abstract

Symmetry operations are usually studied within the frameworks of group theory, geometry, and operator algebra. In the present work, a Ramsey-theoretic approach to symmetry is developed. Symmetry operations are treated as operators serving as vertices of complete bi-colored graphs, called symmetry graphs (SGs). [...] Read more.

Symmetry operations are usually studied within the frameworks of group theory, geometry, and operator algebra. In the present work, a Ramsey-theoretic approach to symmetry is developed. Symmetry operations are treated as operators serving as vertices of complete bi-colored graphs, called symmetry graphs (SGs). Two symmetry operators are connected by a maroon edge when they commute and by a teal edge when they do not commute. Thus, the commutation structure of a symmetry group is transformed into a combinatorial object suitable for Ramsey-theoretic analysis. The introduced coloring is generally non-transitive, leading naturally to nontrivial complete bi-colored graphs constrained simultaneously by group-theoretical and combinatorial principles. It is shown that every symmetry graph containing six vertices necessarily contains either a monochromatic commuting triangle or a monochromatic non-commuting triangle as a direct consequence of the classical Ramsey theorem

R (3,3) = 6

. The framework is illustrated for the symmetry groups of the equilateral triangle, regular tetrahedron, crystallographic point groups, infinite Cairo pentagonal tilings, and the triangular Ising ferromagnet. Higher-order structures, including teal quadrangles, second-order graph symmetries, infinite monochromatic cliques, and Lie-algebraic constraints arising from the Jacobi identity, are discussed. The proposed framework establishes a new connection between symmetry theory, Ramsey theory, graph theory, crystallography, and operator algebra. Full article

(This article belongs to the Section C: Physics)

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27 pages, 2516 KB

Open AccessArticle

DCM-YOLO: Robust Electric Bicycle Detection in Confined Indoor Environments Under Occlusion and Image Degradation

by Guanfang Zuo, Yuxuan Wang, Yanyou Sha, Yuchen Xia, Mohan Tang, Hengkuo Jia and Ronghua Chi

Symmetry 2026, 18(6), 1040; https://doi.org/10.3390/sym18061040 - 16 Jun 2026

Viewed by 418

Abstract

To address electric bicycle detection in confined indoor environments affected by occlusion and image degradation, this study proposes DCM-YOLO, a robustness-oriented detection framework designed to improve detection accuracy under complex indoor visual conditions. First, the Dual-branch Adaptive Fusion (DAF) module combines lightweight feature [...] Read more.

To address electric bicycle detection in confined indoor environments affected by occlusion and image degradation, this study proposes DCM-YOLO, a robustness-oriented detection framework designed to improve detection accuracy under complex indoor visual conditions. First, the Dual-branch Adaptive Fusion (DAF) module combines lightweight feature generation with adaptive modulation to preserve local structures and channel diversity when target appearances are incomplete. Second, the Spatial–Channel Synergistic Attention (SCSA) mechanism sequentially refines informative regions and semantic channels, allowing the detector to suppress background interference more effectively. Third, the Multi-Scale Group-Aware Head (MSGA-Head) introduces multi-branch receptive-field modeling and grouped refinement to improve scale-sensitive classification and localization. These components form a coordinated backbone–attention–head design, reducing detection ambiguity caused by partial visibility and degraded image quality, including underexposure, overexposure, low contrast, and blur. Experimental results on a public dataset collected from representative indoor environments indicate that DCM-YOLO achieves 87.6% Precision, 83.7% Recall, 86.2% mAP50, and 65.1% mAP50-95, exceeding the baseline model by 2.5, 2.9, 2.8, and 1.7 percentage points, respectively. Additional evaluations on public benchmark datasets further verify the effectiveness and robustness of DCM-YOLO. Full article

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

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36 pages, 4327 KB

Open AccessArticle

PetriLink: A Web-Based Platform for Control of Discrete-Event and Hybrid Systems Using Hybrid Colored Petri Nets and OPC UA

by Ondrej Kolimár, Erik Kučera, Oto Haffner and Kamil Kušnirák

Symmetry 2026, 18(6), 1039; https://doi.org/10.3390/sym18061039 - 16 Jun 2026

Viewed by 390

Abstract

Petri nets represent a highly versatile mathematical formalism for modeling discrete event and hybrid systems. For the development of modern complex production processes for Industry 4.0, integrating these formal models with industrial communication standards is an appropriate and effective option. The main aim [...] Read more.

Petri nets represent a highly versatile mathematical formalism for modeling discrete event and hybrid systems. For the development of modern complex production processes for Industry 4.0, integrating these formal models with industrial communication standards is an appropriate and effective option. The main aim of the proposed article is to design a new web-based software tool for the modeling, simulation, and control of mechatronic systems with OPC Unified Architecture support. To accomplish this task, an original software solution called PetriLink is proposed. This platform leverages an intuitive graphical interface and significantly expands the formalism by combining hybrid Petri nets with Colored Petri Nets (CPN) data extensions and a reactive OPC UA subscription model. These new features greatly expand the area of systems that can be modeled and controlled, bridging the gap between theoretical academic tools and practical industrial automation. Furthermore, the structural flexibility of the implemented Petri net models enables the explicit representation of symmetric cyber-physical architectures, as well as the design of asymmetric, event-driven control strategies (e.g., using inhibitor and reset arcs) for enhanced system robustness. The platform was evaluated on a reference net of 5000 places and 2500 transitions, where an incremental dirty-flag evaluation mechanism keeps the per-step engine cost below 1 ms for sparse industrial markings and at about 350 µs for a moderate workload of one hundred concurrent tokens, yielding a speed-up of up to roughly three orders of magnitude over naive full re-evaluation and confirming consistent soft real-time behavior on commodity hardware. Offering a graphical environment for the design of discrete event and hybrid system control algorithms, it can be used for education, research and practice in cyber-physical systems (Industry 4.0). Full article

(This article belongs to the Special Issue Symmetry-Inspired Approaches in Control, Robotics, and Intelligent Systems)

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31 pages, 9491 KB

Open AccessArticle

Transportation-Integrated Flexible Job Shop Scheduling with a Shared Buffer

by Xin Liu, Yuangang Wang, Hongli Liu, Haocheng Zhao and Lin Zhang

Symmetry 2026, 18(6), 1038; https://doi.org/10.3390/sym18061038 - 16 Jun 2026

Viewed by 365

Abstract

In flexible job shop scheduling, industrial robots undertake both workpiece transportation and loading/unloading operations. Equipping each machine with dedicated buffers tends to increase transportation workload and further intensify transport bottlenecks. Shared buffers are therefore introduced to temporarily store workpieces and relieve congestion in [...] Read more.

In flexible job shop scheduling, industrial robots undertake both workpiece transportation and loading/unloading operations. Equipping each machine with dedicated buffers tends to increase transportation workload and further intensify transport bottlenecks. Shared buffers are therefore introduced to temporarily store workpieces and relieve congestion in the production process. This paper establishes a transport-integrated flexible job shop scheduling model with shared buffer constraints, which minimizes makespan, total energy consumption, and machine load range simultaneously. Correspondingly, an enhanced non-dominated sorting genetic algorithm II (ENSGA-II) is developed to achieve better solution performance. A time-window-based path-planning decoding scheme is constructed to address buffer constraints and transportation conflicts in the coordinated production and transportation process. In parallel, four initialization rules are designed to improve the quality and diversity of the initial population, and a variable neighborhood search algorithm (VNS) is embedded to enhance the local exploitation ability of the proposed algorithm. The performance of the presented method is evaluated through two groups of numerical experiments. The first group is carried out on extended benchmark instances. Comparisons with the conventional Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-Objective Particle Swarm Optimization algorithms (MOPSO) validate the efficacy of the proposed strategies and demonstrate the superiority of ENSGA-II in both solution quality and computational efficiency. Experimental results on real-world cases further illustrate that the proposed method can effectively solve the integrated scheduling problem in flexible manufacturing systems where industrial robots are employed as the main transport resources. Full article

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

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39 pages, 4349 KB

Open AccessArticle

Verification-Gated Persona State Transitions for Memory-Augmented Language Agents

by Fan Li, Jia Li, Siyuan Ma and Yang Liu

Symmetry 2026, 18(6), 1037; https://doi.org/10.3390/sym18061037 - 16 Jun 2026

Viewed by 688

Abstract

Memory-augmented language agents are increasingly used for long-horizon personalized interaction, but they still struggle to adapt to user-specific evidence without gradually drifting away from a stable and reliable persona. In this paper, we study how to maintain long-term persona invariance while preserving the [...] Read more.

Memory-augmented language agents are increasingly used for long-horizon personalized interaction, but they still struggle to adapt to user-specific evidence without gradually drifting away from a stable and reliable persona. In this paper, we study how to maintain long-term persona invariance while preserving the utility of memory-based personalization. We propose a verification-aware memory framework that separates fast-changing episodic memory from a slow persona state and treats persona evolution as a controlled state transition rather than an unconstrained memory write. At a high level, retrieved evidence can only induce a bounded tentative persona update, and the update is committed only if an external verifier confirms that the resulting symbolic trace satisfies explicit persona specifications. Across long-term memory, personalized dialogue, persona consistency, and over-personalization benchmarks, our method achieves the best overall performance, improving utility metrics on LongMemEval, LoCoMo, and PersonaMem-v2 while reducing hard violation rate from 6.9 to 3.2 and increasing repair success rate from 67.5 to 74.9 on reliability benchmarks. These results show that explicit verification can make memory-augmented agents both more adaptive and more dependable, offering a practical path toward safer long-term personalization. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Human-Computer Interaction)

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33 pages, 5582 KB

Open AccessArticle

Symmetric and Asymmetric Stress Redistribution in Corrugated Steel–Concrete Composite Tunnel Linings Under Non-Uniform External Pressure

by Beibei Dong

Symmetry 2026, 18(6), 1036; https://doi.org/10.3390/sym18061036 - 16 Jun 2026

Viewed by 320

Abstract

Circular tunnel linings are geometrically symmetric structures, whereas non-uniform external pressure and different steel–concrete layer arrangements may induce asymmetric stress redistribution. To distinguish the axisymmetric response from the asymmetric harmonic response, this study develops an analytical solution for a two-layer corrugated steel–concrete composite [...] Read more.

Circular tunnel linings are geometrically symmetric structures, whereas non-uniform external pressure and different steel–concrete layer arrangements may induce asymmetric stress redistribution. To distinguish the axisymmetric response from the asymmetric harmonic response, this study develops an analytical solution for a two-layer corrugated steel–concrete composite tunnel lining subjected to equivalent external pressure. The concrete layer is modeled as an isotropic elastic material, while the corrugated steel layer is represented as an equivalent cylindrically orthotropic material. The governing equations are formulated in polar coordinates under plane-strain conditions, and the solution is obtained by superposing the axisymmetric component and the harmonic component. Perfect bonding is assumed at the steel–concrete interface, where displacement, radial stress, and shear stress are continuous. The proposed analytical solution is verified using finite element models for three cases: a single-layer homogeneous lining under uniform pressure, a two-layer composite lining under uniform pressure, and a two-layer composite lining under non-uniform pressure. The analytical and finite element results show good agreement, confirming the mathematical consistency and implementation accuracy of the proposed formulation. Based on the verified solution, the effects of layer arrangement, corrugated steel stiffness ratio, and burial depth are investigated. The results show that the corrugated steel layer carries the dominant hoop stress in both layer arrangements. The inner corrugated steel arrangement may be more relevant to internal strengthening of existing tunnels, whereas the outer corrugated steel arrangement provides a useful reference for new composite linings dominated by external ground pressure. Increasing the stiffness ratio transfers more hoop stress to the steel layer and reduces the elastic stress and displacement responses of the concrete layer, although improvement becomes less significant at large stiffness ratios. Increasing burial depth mainly amplifies the response magnitude without changing the overall symmetry pattern. The proposed solution provides a closed-form benchmark for evaluating symmetry-related stress redistribution in corrugated steel–concrete composite tunnel linings within the linear-elastic range. Full article

(This article belongs to the Special Issue Applications Based on Symmetry and Asymmetry in Structural and Geotechnical Engineering)

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