Symmetry

37 pages, 636 KB

Open AccessArticle

Protocol-Dependent Critical Exponents in Random Composites: Beyond Universality

by Simon Gluzman, Zhanat Zhunussova, Akylkerey Sarvarov and Vladimir Mityushev

Symmetry 2026, 18(4), 700; https://doi.org/10.3390/sym18040700 - 21 Apr 2026

Viewed by 269

Classical homogenization theory treats critical exponents as universal quantities depending only on spatial dimension, but recent evidence shows that this assumption fails for continuum composites once the mechanism of randomness generation is taken into account. We synthesize three complementary frameworks—structural approximation, structural sums, [...] Read more.

Classical homogenization theory treats critical exponents as universal quantities depending only on spatial dimension, but recent evidence shows that this assumption fails for continuum composites once the mechanism of randomness generation is taken into account. We synthesize three complementary frameworks—structural approximation, structural sums, and self-similar renormalization—to develop a unified geometric theory of criticality in random composites. Dilute-regime expansions for the effective conductivity and shear modulus are expressed in terms of structural sums whose ensemble statistics depend sensitively on the randomness protocol. To bridge the dilute and critical regimes, we employ self-similar factor approximants, iterated-root approximants, additive approximants, and renormalization schemes based on minimal-difference and minimal-sensitivity conditions, combined with Borel summation. For maximally disordered protocols

P (τ)

, the conductivity index s and the elasticity index S fall within comparable numerical ranges, indicating a shared geometric origin and spectral response to the continuous breaking of translational symmetry. A regular periodic arrangement of inclusions (

τ = 0

) possesses full discrete translational symmetry; as a stochastic protocol

P (τ)

is applied (

τ

increases), this symmetry is gradually degraded until statistical chaos is reached. For instance, the parameter

τ

can be considered as a time of stirring. During this evolution, the system traverses a continuous spectrum of critical indices,

s = s [P (τ)],

which encodes the geometric and topological memory of the initial ordered state. It is established that the classical “universality” of percolation corresponds to a fixed point

τ

within a broader manifold of protocol-dependent critical behaviors. The framework developed here provides a coherent basis for inverse design, diagnostics, and classification of random composites by their disorder history, offering a geometric alternative to the universality paradigm. Full article

(This article belongs to the Section Mathematics)

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16 pages, 3178 KB

Open AccessArticle

Investigation of Self-Disproportionation of Enantiomers via Column Chromatography (SDEvCC) Using 3-(ortho-Substituted-phenyl)quinazolin-4-one Derivatives

by Tomomi Imai, Shumpei Terada, Osamu Kitagawa, Magdalena Kwiatkowska, Alicja Wzorek and Vadim A. Soloshonok

Symmetry 2026, 18(4), 699; https://doi.org/10.3390/sym18040699 - 21 Apr 2026

Viewed by 287

Abstract

In this study, the applicability of achiral column chromatography—including both medium-pressure liquid chromatography (MPLC) and classical gravity-driven techniques—was evaluated as a laboratory method for enantiomeric enrichment of scalemic (non-racemic) samples of axially chiral compounds. As model substrates, 3-(ortho-substituted-phenyl)quinazolin-4-one derivatives were employed. [...] Read more.

In this study, the applicability of achiral column chromatography—including both medium-pressure liquid chromatography (MPLC) and classical gravity-driven techniques—was evaluated as a laboratory method for enantiomeric enrichment of scalemic (non-racemic) samples of axially chiral compounds. As model substrates, 3-(ortho-substituted-phenyl)quinazolin-4-one derivatives were employed. The results confirmed that self-disproportionation of enantiomers (SDE), occurring during column chromatography (SDEvCC), enabled the efficient isolation of enantiomerically pure fractions, with MPLC demonstrating particularly high effectiveness. Additionally, the parameters governing gravity-driven column chromatography were systematically optimized, with particular attention to variables such as eluent type and concentration, stationary phase composition, sample preparation protocol, and solvent purity. Furthermore, leveraging known crystallographic data and quantum chemical calculations based on Density Functional Theory (DFT), a molecular association mechanism was proposed to elucidate the physicochemical basis of the SDE phenomenon. Full article

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

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26 pages, 7247 KB

Open AccessArticle

Fast Unconstraint Convex Symmetric Matrix for Semi-Supervised Learning

by Wenhao Wang, Kaiwen Chen, Wenjun Luo, Nan Zhou and Yanyi Cao

Symmetry 2026, 18(4), 698; https://doi.org/10.3390/sym18040698 - 21 Apr 2026

Viewed by 291

Abstract

Symmetric matrix factorization (SMF) plays an important role in clustering and representation learning. Nevertheless, most existing SMF-based approaches are formulated as non-convex optimization problems, which often leads to unstable convergence and high computational costs. In this paper, we develop a fast unconstrained convex [...] Read more.

Symmetric matrix factorization (SMF) plays an important role in clustering and representation learning. Nevertheless, most existing SMF-based approaches are formulated as non-convex optimization problems, which often leads to unstable convergence and high computational costs. In this paper, we develop a fast unconstrained convex symmetric matrix factorization framework, termed FUCSMF, for semi-supervised learning. By incorporating label information into the symmetric factorization formulation, the proposed model is transformed into a convex objective, which guarantees global optimality and enables efficient optimization using standard unconstrained solvers. To further improve scalability, a bipartite graph structure is introduced into SMF from a hypergraph-inspired perspective, significantly reducing the computational burden. The resulting computational complexity is reduced to

O (n m d)

, which is substantially lower than the

O (n m d + m^{2} n + m^{3})

complexity required by existing bipartite graph-based methods, where n, m, and d denote the numbers of samples, anchor points, and feature dimensions, respectively. In addition, we propose a correntropy-based graph construction strategy to alleviate the sensitivity of conventional adaptive neighbor bipartite graph methods. Extensive experiments on six benchmark datasets, involving comparisons with eleven state-of-the-art methods, demonstrate that FUCSMF achieves superior clustering performance while requiring significantly less computational time. Empirical results further show that the proposed method converges rapidly, typically within ten iterations. Full article

(This article belongs to the Section Computer)

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22 pages, 1189 KB

Open AccessArticle

Oscillatory Behaviors of Two-Component Genetic Networks

by Yuanhao Wu, Renbao Li and Chunyan Gao

Symmetry 2026, 18(4), 697; https://doi.org/10.3390/sym18040697 - 21 Apr 2026

Viewed by 272

Abstract

Transcriptional and translational inhibition are fundamental regulatory mechanisms in gene networks, governing diverse processes from viral replication to neuroplasticity. Two-component genetic oscillators based on the “activator–repressor” motif serve as ideal models for studying biological rhythms due to their simplicity and rich dynamics. However, [...] Read more.

Transcriptional and translational inhibition are fundamental regulatory mechanisms in gene networks, governing diverse processes from viral replication to neuroplasticity. Two-component genetic oscillators based on the “activator–repressor” motif serve as ideal models for studying biological rhythms due to their simplicity and rich dynamics. However, systematic theoretical comparisons of distinct inhibitory mechanisms—particularly using inhibition strength as a control variable—remain lacking. Addressing this gap, we present a comprehensive bifurcation analysis of the post-translational repression model, proving the existence and uniqueness of its positive equilibrium, deriving Hopf bifurcation conditions, and identifying critical parameter ranges for sustained oscillations. Using inhibition strength as a key comparator, we systematically contrast transcriptional and post-translational repression, elucidating how different inhibitory mechanisms modulate oscillation initiation and amplitude. We further reveal distinct symmetry–asymmetry patterns in their bifurcation dynamics: transcriptional repression exhibits asymmetric bistable regimes, while post-translational repression manifests narrow, nearly symmetric oscillatory intervals. This unified analytical framework not only advances the theoretical understanding of two-component genetic oscillators but also provides a generalizable paradigm for dissecting complex gene regulatory dynamics. Full article

(This article belongs to the Section Computer)

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17 pages, 1608 KB

Open AccessArticle

Two Operations of a “Symmetric Difference” Type on Three-Dimensional Index Matrices

by Krassimir Atanassov, Veselina Bureva and Tania Pencheva

Symmetry 2026, 18(4), 696; https://doi.org/10.3390/sym18040696 - 21 Apr 2026

Viewed by 172

Abstract

In the current research, we introduce two operations of a “symmetric difference” type over three-dimensional extended index matrices, and investigate some of their basic properties. An example of the implementation of symmetric difference-type operations is presented in the field of relational databases, aiming [...] Read more.

In the current research, we introduce two operations of a “symmetric difference” type over three-dimensional extended index matrices, and investigate some of their basic properties. An example of the implementation of symmetric difference-type operations is presented in the field of relational databases, aiming to demonstrate the operations’ efficiency by comparing sets with dissimilar attributes. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Control)

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15 pages, 272 KB

Open AccessArticle

Smash Products of Multiplier Left Hopf Algebras

by Chunxiao Yan and Shuanhong Wang

Symmetry 2026, 18(4), 695; https://doi.org/10.3390/sym18040695 - 21 Apr 2026

Viewed by 193

Abstract

Firstly, we define and study the notions of a smash product for actions of multiplier left Hopf algebras on algebras and of an integral on such smash products. Then we construct an analogue of Radford’s biproduct in the framework of multiplier left Hopf [...] Read more.

Firstly, we define and study the notions of a smash product for actions of multiplier left Hopf algebras on algebras and of an integral on such smash products. Then we construct an analogue of Radford’s biproduct in the framework of multiplier left Hopf algebras under assumption of a multiplier left Hopf algebra having an anti-bialgebra homomorphic left antipode. Finally, we study a duality theorem for smash products of a left Hopf algebra of dimension n which is a special multiplier left Hopf algebra. Full article

(This article belongs to the Section Mathematics)

16 pages, 1828 KB

Open AccessArticle

Recognition of Electricity Meter Digits Based on Improved YOLOv10n and Cascaded Visual-Semantic Processing

by Yan Li and Yanfei Bai

Symmetry 2026, 18(4), 694; https://doi.org/10.3390/sym18040694 - 21 Apr 2026

Viewed by 203

Abstract

Digital electricity meters display readings via digits, but accurate image-based recognition faces a key challenge: the frequent omission of decimal points creates a critical asymmetry between the visual image and its true semantic meaning. To address this visual-semantic asymmetry, we propose an improved [...] Read more.

Digital electricity meters display readings via digits, but accurate image-based recognition faces a key challenge: the frequent omission of decimal points creates a critical asymmetry between the visual image and its true semantic meaning. To address this visual-semantic asymmetry, we propose an improved YOLOv10n approach incorporating cascaded Visual-Semantic processing. We introduce a Reparameterized Convolution Single-Shot Aggregation (RCSOSA) module and a SimAM attention mechanism to enhance feature extraction, and employ Normalized Wasserstein Distance (NWD) Loss to boost small-target detection. To rectify the visual-semantic asymmetry, we introduce domain-specific format rules based on power industry standards (taking GB/T 17215-2018 as an example) to provide structural constraints for digit recognition. Experimental results show superior performance with 0.870 precision, 0.932 mAP50, and 116 FPS inference speed, outperforming reference models in both precision and efficiency for real-time meter inspection. Full article

(This article belongs to the Special Issue The Impact of Multivariate Information Symmetry on the State of Electrical Equipment)

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11 pages, 5740 KB

Open AccessReview

Recent Progress in Antimatter Research with Heavy-Ion Collisions

by Tan Lu, Junlin Wu and Hao Qiu

Symmetry 2026, 18(4), 693; https://doi.org/10.3390/sym18040693 - 21 Apr 2026

Viewed by 591

Abstract

Matter–antimatter asymmetry is a fundamental question in both astronomy and particle physics. Investigating antimatter is of great interest for testing the potential explanations of matter–antimatter asymmetry in our Universe. In relativistic heavy-ion collisions, the extremely high energy density and temperature are similar to [...] Read more.

Matter–antimatter asymmetry is a fundamental question in both astronomy and particle physics. Investigating antimatter is of great interest for testing the potential explanations of matter–antimatter asymmetry in our Universe. In relativistic heavy-ion collisions, the extremely high energy density and temperature are similar to the early Universe shortly after the Big Bang. In this paper, we review the recent progress in antimatter search and study heavy-ion collisions, with a focus on the RHIC-STAR and LHC-ALICE experiments, particularly the newly observed antimatter hypernuclei

{}_{\bar{Λ}}^{4}{\bar{H}}

and

{}_{\bar{Λ}}^{4}{\bar{He}}

. The statistical thermal model and the coalescence production model can quantitatively describe the production yields and yield ratios, and the yield measurements of

{}_{\bar{Λ}}^{4}{\bar{H}}

,

{}_{\bar{Λ}}^{4}{\bar{He}}

and their matter counterparts indicate the existence of spin-excited states of these (anti)hypernuclei. Furthermore, new measurements of the lifetimes of

{}_{\bar{Λ}}^{3}{\bar{H}}

,

{}_{\bar{Λ}}^{4}{\bar{H}}

and their matter counterparts reveal no difference between a particle and its corresponding antiparticle, which validates the CPT theorem. Full article

(This article belongs to the Collection Symmetry/Asymmetry in Baryon Decay: Polarization, Hyperon Asymmetry Parameters and CP Violation)

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51 pages, 10042 KB

Open AccessArticle

A Symmetry-Guided Multi-Strategy Differential Hybrid Slime Mold Algorithm for Sustainable Microgrid Dispatch Under Refined Battery Degradation Models

by Xingyu Lai, Minjie Dai, Yuhang Luo and Xin Song

Symmetry 2026, 18(4), 692; https://doi.org/10.3390/sym18040692 - 21 Apr 2026

Viewed by 245

Abstract

Optimized dispatch of microgrids is crucial for improving the economic performance and long-term sustainability of modern low-carbon power systems. In particular, accurate economic dispatch modeling for battery energy storage systems (BESSs) is essential for properly evaluating the operational benefits and lifetime costs of [...] Read more.

Optimized dispatch of microgrids is crucial for improving the economic performance and long-term sustainability of modern low-carbon power systems. In particular, accurate economic dispatch modeling for battery energy storage systems (BESSs) is essential for properly evaluating the operational benefits and lifetime costs of microgrids. However, when both battery cycle aging and calendar aging are considered, the resulting scheduling model becomes highly nonlinear, high-dimensional, non-convex, and multimodal, which poses substantial challenges to conventional optimization methods. To alleviate the above problem, a symmetry-guided multi-strategy differential hybrid slime mold algorithm (MDHSMA) is introduced for the day-ahead economic dispatch of microgrids under a refined battery degradation framework. First, a chaotic bimodal mirrored Latin hypercube sampling strategy is designed to exploit symmetry during population initialization, thereby enhancing diversity and improving structured coverage of the search space. Second, a history-driven adaptive differential evolution mechanism is integrated to balance global exploration and local exploitation more effectively during the iterative search process. Third, a state-aware stagnation handling framework is incorporated to maintain population vitality and further improve convergence accuracy and robustness. MDHSMA is evaluated against 12 state-of-the-art optimizers on the CEC2017 and CEC2022 benchmark suites and two representative engineering optimization problems to verify its overall performance. In addition, it is applied to a microgrid case study with refined BESS degradation modeling. The results show that MDHSMA achieves the lowest comprehensive operating cost by effectively coordinating electricity arbitrage and battery life consumption. Moreover, it guides the energy storage system toward shallow charge–-discharge patterns, thereby mitigating accelerated degradation caused by excessive cycling. These results confirm the effectiveness and practical value of the proposed method for sustainable microgrid dispatch in complex nonconvex optimization scenarios. Full article

(This article belongs to the Special Issue Symmetry and Metaheuristic Algorithms)

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21 pages, 2215 KB

Open AccessArticle

Optimal Consensus Tracking Control for Nonlinear Multi-Agent Systems via Actor–Critic Reinforcement Learning

by Yi Mo, Xinsuo Li, Kunyu Xiang and Dengguo Xu

Symmetry 2026, 18(4), 691; https://doi.org/10.3390/sym18040691 - 21 Apr 2026

Viewed by 311

Abstract

This paper presents an adaptive optimal consensus tracking control scheme for canonical nonlinear multi-agent systems (MASs) with unknown dynamics, employing an actor–critic reinforcement learning (RL) framework. The scheme integrates a sliding mode mechanism to suppress tracking errors and ensure consensus tracking between the [...] Read more.

This paper presents an adaptive optimal consensus tracking control scheme for canonical nonlinear multi-agent systems (MASs) with unknown dynamics, employing an actor–critic reinforcement learning (RL) framework. The scheme integrates a sliding mode mechanism to suppress tracking errors and ensure consensus tracking between the followers and the leader. Additionally, optimal control is designed to find a Nash equilibrium in a graphical game. To address the intractability of obtaining an analytical solution for the coupled Hamilton–Jacobi–Bellman (HJB) equation, a policy iteration algorithm is utilized. Within this algorithm, a critic neural network (NN) approximates the gradient of the optimal value function, while an actor NN approximates the optimal control policy. Together, these networks form a compact actor–critic (AC) architecture that achieves optimal consensus tracking. Furthermore, the proposed method guarantees the boundedness of all closed-loop signals while ensuring consensus tracking. Finally, two simulations are conducted to verify the effectiveness and advantages of the proposed method. Full article

(This article belongs to the Special Issue Symmetry in Control Systems: Theory, Design, and Application)

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35 pages, 6273 KB

Open AccessArticle

Location-Robust Cost-Preserving Blended Pricing in Multi-Campus AI Data Centers

by Qi He

Symmetry 2026, 18(4), 690; https://doi.org/10.3390/sym18040690 - 21 Apr 2026

Viewed by 215

Abstract

Multi-campus AI data centers procure identical hardware and service SKUs across geographically heterogeneous locations, yet finance and operations require a single system-level benchmark (“world price”) per SKU for budgeting, chargeback, and capacity planning. Naive deployment-weighted aggregation preserves total cost but can induce Simpson-type [...] Read more.

Multi-campus AI data centers procure identical hardware and service SKUs across geographically heterogeneous locations, yet finance and operations require a single system-level benchmark (“world price”) per SKU for budgeting, chargeback, and capacity planning. Naive deployment-weighted aggregation preserves total cost but can induce Simpson-type aggregation bias, where heterogeneous location mixes reverse global SKU rankings and weaken managerial decision signals. This study formalizes the problem of location-robust, cost-preserving aggregation and develops two mathematically structured operators for production cost pipelines. The first operator applies a two-way fixed-effects decomposition to separate global SKU effects from campus-specific premia, followed by normalization to guarantee exact cost preservation. This yields an interpretable benchmark that performs well when campus coverage is sufficiently broad and location effects remain approximately additive. The second operator solves a constrained convex common-weight optimization, producing a unified set of non-negative campus weights that preserves total cost while providing the strongest protection against dominance reversals in the ordered setting. Simulation experiments and a semi-real calibrated AI datacenter OPEX illustration show that both operators substantially improve ranking stability relative to naive blending, while the convex operator serves as the more conservative safeguard under adverse heterogeneity. The resulting detect–correct–validate workflow provides a scalable decision-support framework for robust cost aggregation in distributed AI infrastructure and illustrates how symmetry-preserving aggregation operators can stabilize benchmarking in large heterogeneous systems. Full article

(This article belongs to the Section Mathematics)

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33 pages, 1352 KB

Open AccessArticle

Criticality-Aware Adaptive Local Differential Privacy for Privacy-Preserving Decentralized Graph Data

by Zongwen Liang, Chongchen Xue and Yongcai Ao

Symmetry 2026, 18(4), 689; https://doi.org/10.3390/sym18040689 - 21 Apr 2026

Viewed by 292

Abstract

The collection of graph data in decentralized environments raises critical privacy concerns. Local differential privacy (LDP) provides a strong privacy model but applying uniform noise to all graph elements often destroys utility. To address this, we propose the Criticality-Aware Adaptive Local Differential Privacy [...] Read more.

The collection of graph data in decentralized environments raises critical privacy concerns. Local differential privacy (LDP) provides a strong privacy model but applying uniform noise to all graph elements often destroys utility. To address this, we propose the Criticality-Aware Adaptive Local Differential Privacy (CA-LDP) framework. CA-LDP quantifies the structural importance of nodes and edges, then dynamically allocates privacy budgets: stronger protection for critical structures, and weaker protection for non-critical ones. Users report a low-dimensional criticality-weighted vector and, for a subset of critical edges, a precise randomized response. The server reconstructs a synthetic graph using an enhanced graph structure learning model that integrates these criticality signals. A theoretical analysis proves CA-LDP satisfies

ε

-LDP. Experiments on real-world datasets show that CA-LDP outperforms state-of-the-art baselines in preserving critical edges and node classification accuracy, while effectively reducing the success rate of link inference attacks on critical structures. Full article

(This article belongs to the Section Computer)

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34 pages, 22620 KB

Open AccessArticle

Improved Secretary Bird Optimization Algorithm Based on Financial Investment Strategy for Global Optimization and Real Application Problems

by Yiming Liu, Bingchun Yuan and Shuqi Yuan

Symmetry 2026, 18(4), 688; https://doi.org/10.3390/sym18040688 - 21 Apr 2026

Viewed by 313

Abstract

This paper proposes a multi-strategy Secretary Bird Optimization Algorithm (MS-SBOA) for solving global optimization problems and 3D wireless sensor network deployment. While preserving the original two-phase search framework of SBOA, the proposed algorithm achieves a dynamic balance between global exploration and local exploitation [...] Read more.

This paper proposes a multi-strategy Secretary Bird Optimization Algorithm (MS-SBOA) for solving global optimization problems and 3D wireless sensor network deployment. While preserving the original two-phase search framework of SBOA, the proposed algorithm achieves a dynamic balance between global exploration and local exploitation through the synergistic integration of multiple enhancement strategies, including a hybrid initialization scheme combining Latin hypercube sampling and quasi-opposition-based learning, a success-history-based adaptive parameter learning mechanism, a finance-inspired market-state trading operator, and an elite-guided population regulation strategy. Experimental results on the IEEE CEC2020 and CEC2022 benchmark test suites demonstrate that MS-SBOA significantly outperforms nine comparative algorithms, including VPPSO, IAGWO, and QHSBOA, under both 10-dimensional and 20-dimensional settings. The proposed algorithm exhibits superior optimization accuracy, faster convergence speed, and stronger robustness. Statistical analyses using the Wilcoxon rank-sum test and the Friedman mean rank test further confirm that the observed performance improvements are statistically significant. Moreover, MS-SBOA is applied to three-dimensional wireless sensor network (3D WSN) deployment optimization problems, where the average coverage rates reach 76.22% and 82.32% for 30-node and 50-node deployment scenarios, respectively. The resulting node distributions are more uniform, and the computational efficiency is improved compared with competing algorithms. Full article

(This article belongs to the Special Issue Symmetry in Optimization Algorithms and Applications)

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18 pages, 2599 KB

Open AccessArticle

Collaborative Scheme for Speed Limit and Illumination at Rural Highway Intersection Based on Drivers’ Ability to Visually Recognize VRUs

by Mengyuan Huang, Ying Hu, Jiaming Liu, Jinjun Sun and Ayinigeer Wumaierjiang

Symmetry 2026, 18(4), 687; https://doi.org/10.3390/sym18040687 - 21 Apr 2026

Viewed by 258

Abstract

Poor visibility contributes to nighttime accidents at highway intersections, especially in developing countries where vehicles mix with vulnerable road users (VRUs) such as pedestrians and cyclists. Unlike downtown intersections with traffic signals and ambient lighting, rural intersections have no signals and minimal ambient [...] Read more.

Poor visibility contributes to nighttime accidents at highway intersections, especially in developing countries where vehicles mix with vulnerable road users (VRUs) such as pedestrians and cyclists. Unlike downtown intersections with traffic signals and ambient lighting, rural intersections have no signals and minimal ambient light, forcing drivers to rely on roadway lighting for hazard recognition. Improving illumination arrangements can significantly reduce the likelihood of crashes. However, there are significant differences in the effects of illumination on drivers’ visual search ability at different vehicle speeds. Therefore, the collaborative matching of illumination and speed limits can effectively improve traffic efficiency and reduce the probability of nighttime accidents. In this paper, we establish a collaborative optimization model of illumination and speed limits at rural highway intersections that considers drivers’ visual recognition of VRUs. We then design an experiment with illuminance, vehicle speed, and VRU type/location as control variables to collect recognition distances, and finally analyze their effects to calculate speed limits under different illuminances. Results indicate that pedestrians and cyclists appearing from the left side are recognized 24.73% and 15.79% earlier than those from the right, suggesting that VRUs from the right side are more vulnerable. Additionally, the safety benefit of improving illumination on increasing speed limits gradually diminishes as illuminance rises. Therefore, determining the most suitable illumination and speed limit configuration requires a comprehensive evaluation of the cost–benefit relationship between lighting investments and the gains resulting from higher speed limits. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Intelligent Transportation System)

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10 pages, 235 KB

Open AccessArticle

Property (A) of Third-Order Differential Equations as a Consequence of Comparison Theorems

by Blanka Baculikova

Symmetry 2026, 18(4), 686; https://doi.org/10.3390/sym18040686 - 20 Apr 2026

Viewed by 263

Abstract

The aim of this paper is to provide a general method for extending the criteria known for a simple canonical equation

x''' (t) + q (t) x (σ (t)) = 0

to a noncanonical equation of the form

{(r_{2} (t) {(r_{1} (t) y^{'} (t))}^{'})}^{'} + p (t) y (τ (t)) = 0

. Full article

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

12 pages, 261 KB

Open AccessArticle

Beyond the Standard Model of Cosmology: Testing New Paradigms with a Multiprobe Exploration of the Dark Universe

by Juan García-Bellido

Symmetry 2026, 18(4), 685; https://doi.org/10.3390/sym18040685 - 20 Apr 2026

Viewed by 564

Abstract

Cosmology is living through fascinating times, where new observations from ground and space telescopes are questioning the established paradigm, the so-called

Λ

Cold Dark Matter model. The particle nature of Dark Matter is severely constrained by underground experiments, while recent observations by galaxy [...] Read more.

Cosmology is living through fascinating times, where new observations from ground and space telescopes are questioning the established paradigm, the so-called

Λ

Cold Dark Matter model. The particle nature of Dark Matter is severely constrained by underground experiments, while recent observations by galaxy surveys indicate that the cosmological constant (

Λ

) may not be constant after all. Furthermore, observations at high redshift of fully formed galaxies with massive black holes at their centers by the James Webb Space Telescope, as well as black holes with unexpected properties observed by the LIGO-Virgo gravitational wave detectors, are driving an in-depth revision of our assumptions in models of structure formation and the evolution of the Universe. I propose exploring two new paradigms to account for Dark Matter and Dark Energy, based on known physics, without introducing new particles into the Standard Model of Particle Physics. I will extend the primordial spectrum of fluctuations to small scales with new statistical properties to provide a viable Primordial Black Hole scenario for Dark Matter, and will include non-equilibrium thermodynamics in the expanding Universe, in the form of General Relativistic Entropic Acceleration, to explain Dark Energy. My proposal could provide a unified explanation for a plethora of interrelated multi-epoch, multi-scale, and multi-probe observations from present and future Gravitational Wave detectors, Large Scale Structure observatories, and Cosmic Microwave Background experiments. It emphasizes the need to develop new theoretical ideas hand-in-hand with observations to acquire a deeper understanding of our universe. If these ideas are correct, they will open a new window into the early universe and a new fundamental understanding of gravity in the late universe. Full article

(This article belongs to the Special Issue Nature and Origin of Dark Matter and Dark Energy, 2nd Edition)

33 pages, 2134 KB

Open AccessArticle

Symmetry and Symmetry Breaking in Pulsar Spin-Down Dynamics: Fractional Calculus, Non-Integer Braking Indices, and the Resolution of the Crab Pulsar Puzzle

by Farrukh Ahmed Chishtie and Sree Ram Valluri

Symmetry 2026, 18(4), 684; https://doi.org/10.3390/sym18040684 - 20 Apr 2026

Viewed by 387

Abstract

The rotational evolution of pulsars is governed by torque mechanisms whose mathematical structure encodes fundamental symmetries of the underlying physics. We demonstrate that the standard spin-down equation

\dot{f} = - s f - r f^{3} - g f^{5}

derives from [...] Read more.

The rotational evolution of pulsars is governed by torque mechanisms whose mathematical structure encodes fundamental symmetries of the underlying physics. We demonstrate that the standard spin-down equation

\dot{f} = - s f - r f^{3} - g f^{5}

derives from a discrete antisymmetry requirement, namely invariance of the torque under reversal of rotation sense, which restricts the frequency dependence to odd integer powers. We show that physically motivated plasma processes systematically break this symmetry, introducing fractional frequency exponents: viscous Ekman pumping at the crust–superfluid boundary layer (

f^{3 / 2}

), magnetohydrodynamic turbulent dissipation via Kolmogorov and Sweet–Parker cascades (

f^{10 / 3}

,

f^{11 / 3}

), non-linear superfluid vortex dynamics (

f^{5 / 2}

), and saturated r-mode oscillations (

f^{7 - 2 β}

). The central result is an exact analytical resolution of the long-standing Crab pulsar braking index puzzle: the observed

n = 2.51 \pm 0.01

, which has defied explanation for nearly four decades, emerges naturally from the superposition of magnetic dipole radiation (

\dot{f} \propto f^{3}

) and boundary layer Ekman pumping (

\dot{f} \propto f^{3 / 2}

), with analytically derived coefficients yielding a dipole-component surface field

B_{p} = 6.2 \times 10^{12}

G—higher than the standard

\sqrt{P \dot{P}}

estimate of

3.8 \times 10^{12}

G, because that formula conflates dipole and non-dipole torques, but lower than applying the Larmor formula to the full spin-down rate (

7.6 \times 10^{12}

G), since

32.7 %

of the total torque is non-radiative boundary-layer dissipation. We develop the Riemann–Liouville fractional calculus formalism for these equations, showing that fractional derivatives break time-translation symmetry through intrinsic memory effects, with solutions expressed in terms of Mittag-Leffler and Fox H-functions that interpolate continuously between exponential (fully symmetric) and power-law (scale-free symmetric) relaxation. Lambert–Tsallis

W_{q}

functions with non-extensive parameter q encoding broken statistical symmetry enable equation-of-state-independent inference of neutron star compactness and tidal deformability. Our framework establishes a unified symmetry-based classification of pulsar spin-down mechanisms and predicts frequency-dependent braking indices evolving at rate

d n / d t \sim 2 \times 10^{- 4}

yr⁻¹, yielding

Δ n \approx 0.01

over 50 years—testable with current pulsar timing programmes. The formalism provides a coherent theoretical foundation connecting plasma microphysics at the neutron star interior to macroscopic observables in electromagnetic and gravitational wave channels. Full article

(This article belongs to the Special Issue Symmetry in Plasma Astrophysics)

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53 pages, 1196 KB

Open AccessArticle

Parameter-Free Deformation Variables of the Proxy-SU(3) Symmetry in Even–Even Atomic Nuclei with Z = 28–82, N = 28–126

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

Symmetry 2026, 18(4), 683; https://doi.org/10.3390/sym18040683 - 20 Apr 2026

Viewed by 214

Abstract

The proxy-SU(3) approximation to the shell model, which restores the SU(3) symmetry of the 3-dimensional harmonic oscillator beyond the

s d

shell, predicts the collective deformation variables

β

and

γ

of even–even atomic nuclei in a parameter-free way based on the most symmetric [...] Read more.

The proxy-SU(3) approximation to the shell model, which restores the SU(3) symmetry of the 3-dimensional harmonic oscillator beyond the

s d

shell, predicts the collective deformation variables

β

and

γ

of even–even atomic nuclei in a parameter-free way based on the most symmetric irreducible representation (irrep) of SU(3) allowed by the Pauli principle and the short-range nature of the nucleon–nucleon interaction, which in group theoretical language is the highest-weight (hw) irrep. In the few cases in which the hw irrep turns out to be completely symmetric, thus being able to accommodate only the ground-state band, the next hw (nhw) irrep becomes indispensable. In the present article, complete tables of the hw and nhw irreps are given for all atomic nuclei ranging from

Z = 28

,

N = 28

to

Z = 82

,

N = 126

, along with the corresponding parameter-free predictions for the deformation variables

β

and

γ

. A few examples using the tabulated results to provide microscopic insight for specific effects in various regions of the nuclear chart are also given. Full article

(This article belongs to the Special Issue Nuclear Physics and Symmetry/Asymmetry: Advances and Prospects)

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25 pages, 735 KB

Open AccessArticle

Tachyonic AdS/QCD, Determining the Strong Running Coupling and β-Function in Both UV and IR Regions of AdS Space

by Adamu Issifu, Elijah Anertey Abbey and Francisco A. Brito

Symmetry 2026, 18(4), 682; https://doi.org/10.3390/sym18040682 - 20 Apr 2026

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Abstract

In this paper, we investigate the Quantum Chromodynamics (QCD)-like running coupling,

α_{s}^{A d S} (Q^{2})

, and its associated

β

-function within a tachyonic Anti-de Sitter (AdS)/QCD framework. The

{AdS}_{5}

bulk geometry is deformed through the introduction [...] Read more.

In this paper, we investigate the Quantum Chromodynamics (QCD)-like running coupling,

α_{s}^{A d S} (Q^{2})

, and its associated

β

-function within a tachyonic Anti-de Sitter (AdS)/QCD framework. The

{AdS}_{5}

bulk geometry is deformed through the introduction of a color dielectric function

G (ϕ (z))

, associated with a tachyon field

ϕ (z)

. This function governs the behavior of

α_{s}^{A d S} (Q^{2})

across all momentum scales by modifying the AdS background at both small and large values of the holographic coordinate z. In the ultraviolet (UV) regime (small z), the deformation is driven by free tachyons and reproduces features consistent with perturbative QCD. In contrast, in the infrared (IR) regime (large z), tachyon condensation dominates, yielding behavior characteristic of nonperturbative QCD. This construction enables a unified description of the running coupling and its

β

-function over the full range of momentum transfer

Q^{2}

, where

Q^{2}

denotes the space-like momentum scale. Full article

(This article belongs to the Special Issue Gravitational Physics and Symmetry)

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26 pages, 17603 KB

Open AccessArticle

SICABI: Symmetry-Informed Stochastic Modeling via Dominant-Period Stationarity and Recursive Adaptive Parametric Density Estimation

by Daniel Canton-Enriquez, Jorge-Luis Perez-Ramos, Selene Ramirez-Rosales, Luis-Antonio Diaz-Jimenez, Ana-Marcela Herrera-Navarro and Hugo Jimenez-Hernandez

Symmetry 2026, 18(4), 681; https://doi.org/10.3390/sym18040681 - 20 Apr 2026

Viewed by 272

Abstract

Wind dynamics in urban environments exhibit non-stationarity and marked spatial variability, complicating stochastic modeling when a single global distribution is assumed. This article discusses the estimation of wind density under quasi-stationary regimes at the local level using SICABI, a two-phase framework: (i) Stationary [...] Read more.

Wind dynamics in urban environments exhibit non-stationarity and marked spatial variability, complicating stochastic modeling when a single global distribution is assumed. This article discusses the estimation of wind density under quasi-stationary regimes at the local level using SICABI, a two-phase framework: (i) Stationary Region Identification (ISR) estimates, through spectral power analysis, a specific dominant period for each location and validates the induced subsampling using the Augmented Dickey–Fuller (ADF) test, and (ii) RAPID adjusts an adaptive parametric density by recursively updating the mixture parameters and creating new components when a normalized membership distance exceeds a threshold. The analysis uses wind speed records collected from eight stations in the Metropolitan Area of Queretaro, Mexico, during the period from 1 January 2023 to 31 December 2023, aggregated at a 10 min resolution, from which

X_{δ, s}

is constructed for each site. RAPID is compared against Gaussian Kernel Density Estimation (KDE) with Silverman bandwidth and EM-fitted Gaussian mixtures with BIC-based selection (

K_{max} = 12

). The resulting densities were compared with an empirical density estimated from a histogram over a fixed grid (

m = 50

) using the MISE and RMSE metrics. The results reveal marked site-dependent differences in dominant periodicity and residual behavior, including asymmetry and heavy tails. ISR identified dominant periods ranging from 37 to 166 days, and RAPID adapted its complexity with

K_{s} \in [5, 10]

without fixing the number of mixture components in advance. Quantitatively, RAPID achieved the lowest RMSE at 6/8 sites and the lowest MISE at 5/8 sites, while also exhibiting shorter execution times than KDE and MoG under the same input

X_{δ, s}

. The results support RAPID as a competitive adaptive method for site-specific density estimation in non-stationary urban climate signals. In this context, local regimes can be viewed as approximate invariants under time translation in the weak stochastic sense, while deviations from this assumption are reflected in increased distributional complexity across sites. Full article

(This article belongs to the Special Issue Symmetry in Stochastic Models for Machine Learning Applications: Theoretical Insights and Applications)

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14 pages, 4755 KB

Open AccessArticle

New Soliton-Type Solutions of the (2 + 1)-Dimensional Variable-Coefficient Boussinesq Equation

by Jing Li and Zhiyi Cao

Symmetry 2026, 18(4), 680; https://doi.org/10.3390/sym18040680 - 20 Apr 2026

Viewed by 211

Abstract

The

(2 + 1)

-dimensional Boussinesq equation plays an important role in mathematical physics. In this paper, we investigate some exact solutions of the

(2 + 1)

-dimensional variable-coefficient Boussinesq equation. Firstly, the Painlevé analysis is carried out, and [...] Read more.

The

(2 + 1)

-dimensional Boussinesq equation plays an important role in mathematical physics. In this paper, we investigate some exact solutions of the

(2 + 1)

-dimensional variable-coefficient Boussinesq equation. Firstly, the Painlevé analysis is carried out, and an auto-Bäcklund transformation is constructed by means of a truncated Painlevé expansion combined with symbolic computation. Then, a class of new soliton-type solutions is derived. By selecting appropriate parameter values, detailed simulations are presented to illustrate the dynamical behavior of water wave propagation. Finally, the Lie point symmetries of the equation are studied, and several similarity reductions are derived by solving the corresponding characteristic equations. Full article

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

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21 pages, 16717 KB

Open AccessArticle

Supramolecular Diversity in Metal–Organic Hybrids with [VO₂(2,6-pydc)]⁻ Anion and Piperazine and Its Derivatives

by Mišel Hozjan and Franc Perdih

Symmetry 2026, 18(4), 679; https://doi.org/10.3390/sym18040679 - 19 Apr 2026

Viewed by 337

Abstract

Ten compounds have been prepared among them six different dioxido(pyridine-2,6-dicarboxylato)vanadate(V) compounds with piperazinium (H₂pip²⁺) (1·6H₂O), methylpiperazinium (H₂mepip²⁺) (2·5H₂O), ethylpiperazinium (H₂etpip²⁺) (3·3H [...] Read more.

Ten compounds have been prepared among them six different dioxido(pyridine-2,6-dicarboxylato)vanadate(V) compounds with piperazinium (H₂pip²⁺) (1·6H₂O), methylpiperazinium (H₂mepip²⁺) (2·5H₂O), ethylpiperazinium (H₂etpip²⁺) (3·3H₂O), isopropylpiperazinium (H₂isopip²⁺) (4·H₂O), phenylpiperazinium (Hphepip⁺) (5∙H₂O) and thiomorpholinium 1-oxide (HtmorO⁺) (6·2,6-H₂pydc·2H₂O) cations as counterions as well as methylpiperazinium (H₂mepip²⁺) salt of a mixed valence vanadium [VO(2,6-pydc)-(μ-O)-VO(H₂O)(2,6-pydc)]⁻ complex (7), thiomorpholin-4-ium vanadate (Htmor)VO₃ (8), hexa(thiomorpholin-4-ium) decavanadate hexahydrate (Htmor)₆[V₁₀O₂₈]·6H₂O (9·6H₂O) and organic salt cocrystal thiomorpholin-4-ium 6-carboxypicolinate pyridine-2,6-dicarboxylic acid (Htmor)⁺(2,6-Hpydc)⁻∙(2,6-H₂pydc)·2H₂O (10·2H₂O) via different pathways starting either from pyridine-2,6-dicarboxylic acid or its esters, and were structurally characterized by single-crystal X-ray diffraction. Extended hydrogen bonding interactions are present due to the presence of organic cations as well as due to the diverse roles of water molecules in the hydrogen bonding network. Centrosymmetric hydrogen bonding was found to be an important motif, and diverse supramolecular patterns were also observed due to a wide variety of C–H···O and π···π interactions stabilizing the crystal lattices. Full article

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

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22 pages, 4182 KB

Open AccessArticle

Model-Free Non-Singular Fast Terminal Sliding Mode Control Based on Agricultural Unmanned Aerial Vehicle Electrical Control System

by Mingyuan Hu, Longhui Qi, Changning Wei, Lei Zhang, Yaqing Gu, Bo Gao, Yang Liu and Dongjun Zhang

Symmetry 2026, 18(4), 678; https://doi.org/10.3390/sym18040678 - 18 Apr 2026

Viewed by 212

Abstract

Permanent magnet synchronous motors (PMSMs) are widely used in agricultural unmanned aerial vehicle (UAV) electromechanical systems for their high efficiency and power density. While sliding mode control (SMC) offers robustness for PMSM drives, conventional designs face challenges like slow convergence, singularity, and chattering. [...] Read more.

Permanent magnet synchronous motors (PMSMs) are widely used in agricultural unmanned aerial vehicle (UAV) electromechanical systems for their high efficiency and power density. While sliding mode control (SMC) offers robustness for PMSM drives, conventional designs face challenges like slow convergence, singularity, and chattering. This paper proposes a model-free improved non-singular fast terminal SMC scheme with an improved adaptive super-twisting algorithm and a disturbance observer (MFINFTSMC-IADSTA-IFTSMO) for agricultural UAV applications. The designed sliding surface ensures fixed-time convergence without singularity, the adaptive reaching law reduces chattering, and the observer enables feedforward compensation of disturbances. Closed-loop stability is proven via Lyapunov theory. DSP-based experiments demonstrate that the proposed method outperforms existing SMC variants in dynamic response, steady-state accuracy, chattering suppression, and disturbance rejection. Specifically, the proposed method achieves a start-up convergence time of only 0.35 s, which is 56.25% shorter than that of the classic SMC-STA method, fully verifying its superior fast convergence performance. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Control Theory)

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25 pages, 3630 KB

Open AccessArticle

Modality-Specific Sparse Autoencoders for Efficient Multimodal ICU Alignment: A Symmetry–Asymmetry Learning Framework

by Hashim Ali and Muhammad Tahir Akhtar

Symmetry 2026, 18(4), 677; https://doi.org/10.3390/sym18040677 - 18 Apr 2026

Viewed by 233

Abstract

Intensive care units (ICUs) generate heterogeneous data streams, including structured electronic health records, physiological time series, and medical imaging, that describe the same patient state through different observational forms. Effective multimodal learning in this setting requires a principled balance between representation-level symmetry and [...] Read more.

Intensive care units (ICUs) generate heterogeneous data streams, including structured electronic health records, physiological time series, and medical imaging, that describe the same patient state through different observational forms. Effective multimodal learning in this setting requires a principled balance between representation-level symmetry and architectural asymmetry. Clinically corresponding patient states should exhibit cross-modal representational symmetry, whereas each modality retains intrinsic asymmetry in dimensionality, temporal resolution, noise characteristics, and missingness. This study proposes a modality-specific sparse autoencoder framework for efficient multimodal ICU representation learning under this symmetry–asymmetry principle. Separate sparse encoders are assigned to each modality to preserve the modality-dependent structure while suppressing redundant latent activity through adaptive gating. Representation-level symmetry is encouraged through a sparsity-aware contrastive objective that aligns paired latent embeddings across modalities only on active informative dimensions. To further model inter-patient dependencies, the framework incorporates a graph neural network (GNN) whose message-passing operations respect modality-specific sparsity patterns. Experimental results indicate that the proposed framework improves predictive performance and computational efficiency relative to conventional multimodal baselines, while also exhibiting stronger robustness under missing-modality conditions and more selective latent representations. Overall, the method provides an effective and clinically relevant multimodal learning strategy for ICU decision support while offering a measurable symmetry-aware and asymmetry-preserving formulation for heterogeneous medical data. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Machine Learning and Data Mining)

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25 pages, 816 KB

Open AccessArticle

Finite-Bit Distributed Optimization for UAV Swarms Under Communication Bandwidth Constraints

by Yingzheng Zhang and Zhenghong Jin

Symmetry 2026, 18(4), 676; https://doi.org/10.3390/sym18040676 - 18 Apr 2026

Viewed by 216

Abstract

This paper develops a unified finite-bit distributed optimization framework for UAV swarms operating over bandwidth-limited communication graphs. We consider strongly convex and smooth global objectives decomposed over local UAV cost functions and study three communication-efficient algorithmic regimes. First, we design a quantized distributed [...] Read more.

This paper develops a unified finite-bit distributed optimization framework for UAV swarms operating over bandwidth-limited communication graphs. We consider strongly convex and smooth global objectives decomposed over local UAV cost functions and study three communication-efficient algorithmic regimes. First, we design a quantized distributed gradient-tracking descent scheme with fixed finite-bit communication and show that, under bounded quantization errors, the method converges R-linearly to a quantization-dependent neighborhood of the global optimizer. Second, we introduce an adaptive quantization strategy that dynamically adjusts the number of transmitted bits according to the current convergence stage. By forcing the quantization distortion to decay proportionally to the optimization error, the proposed adaptive scheme recovers exact linear convergence to the optimal solution while substantially reducing the cumulative communication load. Third, we develop a fully distributed 1-bit communication mode in which UAVs exchange only sign information and use coordinate-wise majority voting to aggregate both descent and consensus directions. The robust linear-contraction property is proved to a small neighborhood under a sign-Polyak–Lojasiewicz condition and a probabilistic majority-correctness assumption. Full article

(This article belongs to the Section Computer)

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41 pages, 52463 KB

Open AccessArticle

A Public Management-Based Enterprise Development Optimization Algorithm Is Used for Numerical Optimization Problems and Real-World Applications

by Cheng Niu, Chun Zhou and Chengpeng Li

Symmetry 2026, 18(4), 675; https://doi.org/10.3390/sym18040675 - 17 Apr 2026

Viewed by 219

Abstract

With the rapid development of complex engineering systems, many real-world optimization problems are characterized by high dimensionality, strong nonlinearity, and variable coupling. To address these challenges, this paper proposes a Public Management–Augmented Multi-Strategy Adaptive Enterprise Development Optimization algorithm (PMAED), which integrates adaptive differential [...] Read more.

With the rapid development of complex engineering systems, many real-world optimization problems are characterized by high dimensionality, strong nonlinearity, and variable coupling. To address these challenges, this paper proposes a Public Management–Augmented Multi-Strategy Adaptive Enterprise Development Optimization algorithm (PMAED), which integrates adaptive differential evolution, an eigen-based rotated search strategy, and a hierarchical performance governance mechanism to enhance convergence efficiency and robustness. Experimental results on the CEC2020 and CEC2022 benchmark suites demonstrate that PMAED achieves superior performance across different problem types and dimensionalities. In the Friedman ranking test, PMAED consistently obtains the best average rank (1.90 and 1.60 on CEC2020; 2.00 and 1.92 on CEC2022 for 10D and 20D, respectively), outperforming all compared algorithms. The Wilcoxon rank-sum test further confirms that PMAED achieves statistically significant improvements on the majority of benchmark functions. In high-dimensional scenarios, PMAED shows remarkable optimization accuracy, for example, achieving a mean fitness value of 1.15 × 10³ on the 20-dimensional CEC2020 F1 function, significantly outperforming classical methods. In addition, PMAED is applied to a three-dimensional UAV path planning problem. The results show that the proposed method achieves the lowest average path cost (277.62) and the smallest standard deviation among all algorithms, indicating superior stability and reliability. The planned paths are smoother, safer, and more efficient compared to those generated by other methods. Overall, the proposed PMAED provides a robust and efficient solution for complex continuous optimization problems and demonstrates strong potential for real-world engineering applications. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Optimization Algorithms and Systems Control)

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16 pages, 4551 KB

Open AccessArticle

In Situ Full-Scale Uplift Tests and Three-Dimensional Numerical Analysis of Squeezed Branch Piles in Coastal Reclaimed Areas

by Yi Zeng, Zhenyuan He, Yuewei Bian, Xiaoping Li, Yue Gao and Yanbin Fu

Symmetry 2026, 18(4), 674; https://doi.org/10.3390/sym18040674 - 17 Apr 2026

Viewed by 185

Abstract

Coastal reclaimed areas are characterized by complex strata and high groundwater levels, and pile foundations in such areas often suffer from insufficient uplift resistance. Compared with conventional cast-in-place piles, squeezed branch piles exhibit superior uplift performance; however, studies on squeezed branch piles in [...] Read more.

Coastal reclaimed areas are characterized by complex strata and high groundwater levels, and pile foundations in such areas often suffer from insufficient uplift resistance. Compared with conventional cast-in-place piles, squeezed branch piles exhibit superior uplift performance; however, studies on squeezed branch piles in reclaimed areas remain limited. To investigate the uplift bearing performance of squeezed branch piles in the complex strata of coastal reclaimed areas, in situ full-scale uplift tests were conducted in the Shenzhen Binhai Avenue (Headquarters Base Section) traffic reconstruction project. Based on the actual physical and mechanical properties of the soil strata, a three-dimensional numerical model was established and validated against the load–displacement curves obtained from the in situ full-scale uplift tests. On this basis, the uplift bearing performance of squeezed branch piles, the differences in uplift bearing performance between branch and plate structures, and their applicable strata were analyzed. The plate structure and different branch configurations of squeezed branch piles exhibit distinct symmetric configuration characteristics, and these configuration differences influence the overall uplift bearing performance. The results show that the load–displacement curves of the uplift piles are generally smooth, without obvious abrupt rises or drops, exhibiting a gradual variation pattern, and the maximum pile-head displacements are all less than 100 mm. The mobilization of the bearing capacity of the branch and plate structures exhibits a distinct temporal and sequential pattern, with the plate structures at shallower embedment depths mobilized earlier than those at greater depths. Compared with conventional cast-in-place pile foundations, the presence of branches and plates endows squeezed branch piles with better elastic mechanical behavior and higher rebound ratios during unloading. Under identical stratum and loading conditions, the uplift bearing performance of the plate is 133% higher than that of the six-radial-branch configuration, while that of the six-radial-branch configuration is 34% higher than that of the four-radial-branch configuration. It is recommended to adopt the six-radial-branch configuration in clayey sandy gravel strata and the plate configuration in gravelly clayey soil and completely weathered coarse-grained granite strata, whereas neither branches nor plates are recommended in soil-like strongly weathered coarse-grained granite strata. Full article

(This article belongs to the Section Engineering and Materials)

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16 pages, 536 KB

Open AccessArticle

Exploring the New Exponentiated Harris-G Family of Distributions and Its Applications

by Wellington F. Charumbira, Hisham M. Almongy, Fastel Chipepa and Mavis Pararai

Symmetry 2026, 18(4), 673; https://doi.org/10.3390/sym18040673 - 17 Apr 2026

Viewed by 190

Abstract

This paper introduces a new family of distributions called exponentiated Harris-G. This new distribution is a weighted distribution of the well established exponentiated-G distributions. The model allows for easy derivation of statistical properties based on the exponentiated-G distribution. Several statistical properties for the [...] Read more.

This paper introduces a new family of distributions called exponentiated Harris-G. This new distribution is a weighted distribution of the well established exponentiated-G distributions. The model allows for easy derivation of statistical properties based on the exponentiated-G distribution. Several statistical properties for the new model were derived. The paper considered different parameter estimation techniques and the maximum likelihood estimation technique emerged as the best technique. This was evaluated via Monte Carlo simulation studies of the proposed family. Estimation techniques were ranked based on the lowest values of the root mean square error and average bias. The proposed model showed enhanced flexibility in data modeling when compared to some selected competing models. This was demonstrated through application of the special case to two real-world datasets. Full article

(This article belongs to the Section Mathematics)

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29 pages, 4275 KB

Open AccessArticle

Cooperative Trajectory Planning for Air–Ground Systems in Unstructured Mountainous Environments

by Zhen Huang, Jiping Qi and Yanfang Zheng

Symmetry 2026, 18(4), 672; https://doi.org/10.3390/sym18040672 - 17 Apr 2026

Viewed by 187

Abstract

Air–ground collaborative systems leverage the complementary strengths of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) and hold significant potential for logistics in complex, unstructured environments. However, trajectory planning in infrastructure-free mountainous regions remains challenging owing to the need for continuous tight [...] Read more.

Air–ground collaborative systems leverage the complementary strengths of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) and hold significant potential for logistics in complex, unstructured environments. However, trajectory planning in infrastructure-free mountainous regions remains challenging owing to the need for continuous tight coupling, obstacle avoidance, and reliable communication-link maintenance. To address these challenges, this study proposes a cooperative trajectory planning framework that enforces strict inter-vehicle distance constraints to maintain communication connectivity. By formulating the coordination problem in terms of relative configurations between air and ground vehicles, the proposed framework exhibits translational invariance, reflecting an underlying symmetry with respect to global position shifts. This symmetry-aware formulation reduces reliance on absolute coordinates and promotes consistent cooperative behavior under environmental variability. The trajectory planning problem is mathematically formulated as a constrained multi-objective nonlinear programming (MONLP) model that balances energy consumption and trajectory smoothness. An adaptive inertia weight particle swarm optimization (AIWPSO) algorithm is developed to efficiently solve the resulting optimization problem. Simulation results demonstrate that the proposed approach generates smooth, collision-free trajectories while maintaining stable air–ground coordination, demonstrating improved feasibility and robustness over conventional planning methods in unstructured mountainous environments. Full article

(This article belongs to the Section Computer)

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12 pages, 3224 KB

Open AccessArticle

Magnetic and Electrical Properties of La_2−xBi_xNiMnO₆ (x = 0.2, 0.5 and 1.0) Synthesized by High-Temperature and High-Pressure Method

by Lei Xing

Symmetry 2026, 18(4), 671; https://doi.org/10.3390/sym18040671 - 17 Apr 2026

Viewed by 244

Abstract

Polycrystalline La_2−xBi_xNiMnO₆ (x = 0.2, 0.5, 1.0) samples were synthesized via a high-temperature and high-pressure method, with their structural, magnetic, and electrical properties systematically characterized. X-ray diffraction (XRD) confirms a monoclinic double perovskite structure (space group P2₁ [...] Read more.

Polycrystalline La_2−xBi_xNiMnO₆ (x = 0.2, 0.5, 1.0) samples were synthesized via a high-temperature and high-pressure method, with their structural, magnetic, and electrical properties systematically characterized. X-ray diffraction (XRD) confirms a monoclinic double perovskite structure (space group P2₁/n) for all samples, while Bi³⁺ induces a lattice volume expansion trend inferred from XRD peak shifts due to its larger ionic radius than La³⁺. Magnetically, all exhibit ferromagnetism and soft magnetic features, with magnetization decreasing as Bi content increases. The x = 0.2 and 0.5 samples show two distinct Curie temperatures, both decreasing with Bi substitution, whereas the higher Curie temperature vanishes in the x = 1.0 sample, likely due to Bi-induced structural changes. Electrically, all display semiconducting behavior (resistivity: x = 0.5 > x = 0.2 > x = 1.0) and negative magnetoresistance (MR) at 200 K, peaking at 12% (x = 0.5) and 7.5% (x = 1.0). For the x = 1.0 sample, negative magnetoresistance strengthens with decreasing temperature (130–200 K), with magnetoresistance-field (MR-H) curves showing herringbone and arc shapes. Full article

(This article belongs to the Special Issue Topics in Nanocomposites and Magnetic Materials: Symmetric/Asymmetric Applications)

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