Symmetry

22 pages, 3401 KB

Open AccessArticle

Theoretical Analysis of Barrow Holographic Dark Energy in Fractal Cosmology

by Hanshu Zhao and Weiqiang Yang

Symmetry 2026, 18(8), 1327; https://doi.org/10.3390/sym18081327 - 5 Aug 2026

We investigate interacting Barrow holographic dark energy (BHDE) with the Hubble horizon as the infrared cutoff in a fractal cosmological background. The fractal measure modifies the Friedmann sector and leads to the nonstandard closure relation [...] Read more.

We investigate interacting Barrow holographic dark energy (BHDE) with the Hubble horizon as the infrared cutoff in a fractal cosmological background. The fractal measure modifies the Friedmann sector and leads to the nonstandard closure relation

Ω_{dm} + Ω_{de} = 1 + γ

. Using Planck-inspired present-day normalization

Ω_{de 0} = 0.6847

and the benchmark parameters

(Δ, ω, β) = (0.8, 0.263, 0.123)

, we study four linear and nonlinear dark-sector interactions over

- 0.99 \leq z \leq 3

. The benchmark solutions remain within the physical background domain throughout this interval: the density fractions are non-negative, the relevant denominators remain positive, and the nonlinear

Q_{3}

and

Q_{4}

terms remain real. All four prescriptions exhibit a transition from decelerated to accelerated expansion. The non-interacting limit gives

z_{t} ≃ 0.86

, whereas for

ξ = 0.12

the transition redshifts are approximately

2.02

,

1.97

,

1.26

, and

1.87

for

Q_{1}

,

Q_{2}

,

Q_{3}

, and

Q_{4}

, respectively; in particular, the

Q_{4}

solution recovers a finite transition within the plotted redshift range. A stronger positive coupling generally shifts acceleration onset to a higher redshift, with the strongest response for

Q_{1}

and the weakest for

Q_{3}

. The statefinder quantities

S_{3}^{(1)}

,

S_{3}^{(2)}

, and the s–r trajectories distinguish the interaction structures through their finite-redshift evolution and present-day values. A fixed-background SN Ia comparison using 1046 selected Pantheon supernovae, diagonal FITRES uncertainties, and an analytically profiled additive nuisance parameter gives the lowest information criteria for flat

Λ

CDM. Among the BHDE benchmarks that interact,

Q_{4}

is the closest case, with

Δ AIC = Δ BIC ≃ 1.21

. This comparison is not intended as a global posterior constraint on the model parameters. Full article

(This article belongs to the Special Issue Symmetry in the Dark Sector of the Universe and Recent Astronomical Observations)

19 pages, 3169 KB

Open AccessArticle

Improving Electrical-Impedance-Tomography Reconstruction Quality by Sensitivity Matrix Transformation Using Diagonal Matrices

by Yuwei Zhao, Shihong Yue and Shiyuan Zhu

Symmetry 2026, 18(8), 1326; https://doi.org/10.3390/sym18081326 - 5 Aug 2026

Abstract

As an advanced visualization technique, electrical impedance tomography (EIT) can reconstruct the distribution of electrical parameters and thereby visually show object distribution within a detection field. The quality of EIT reconstruction greatly depends on a selected sensitivity matrix, while various matrices can lead [...] Read more.

As an advanced visualization technique, electrical impedance tomography (EIT) can reconstruct the distribution of electrical parameters and thereby visually show object distribution within a detection field. The quality of EIT reconstruction greatly depends on a selected sensitivity matrix, while various matrices can lead to very different EIT reconstruction results. A large number of efforts to improve the sensitivity matrix have been made to enhance EIT reconstruction quality, but how to construct and select a better matrix in a general and feasible way remains unsolved to date. In this paper, we use the matrix transformation method to address the issue, and two types of symmetric and diagonally dominant matrices are optimally selected to multiply the sensitivity matrix on the left and right, respectively. Therefore, EIT reconstruction quality can generally be improved. The feasibility and robustness of the proposed method have been theoretically demonstrated for both Gaussian kernel-based and power function-based matrices. Experiments validate the proposed method by EIT reconstruction quality. Full article

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

28 pages, 34686 KB

Open AccessArticle

Kinematic Symmetry-Driven Multi-Objective Collaborative Design of a Rigid Crank–Rocker Mechanism

by Changjin Liu, Dongjie Zhao, Hongkai Li, Chi Zhang and Shilun Yan

Symmetry 2026, 18(8), 1325; https://doi.org/10.3390/sym18081325 - 5 Aug 2026

Abstract

To address the persistent challenges in optimizing the transmission performance of crank-rocker mechanisms—namely, the inaccuracies of local static evaluation models, the non-linear coupling constraints among multiple objectives, and the difficulties of navigating discontinuous and restricted solution spaces—this paper proposes a multi-objective collaborative design [...] Read more.

To address the persistent challenges in optimizing the transmission performance of crank-rocker mechanisms—namely, the inaccuracies of local static evaluation models, the non-linear coupling constraints among multiple objectives, and the difficulties of navigating discontinuous and restricted solution spaces—this paper proposes a multi-objective collaborative design methodology grounded in kinematic and dynamic analysis. First, full-cycle mathematical models for transmission efficiency and transmission inertia are established, explicitly quantifying the impact of quick-return characteristics on inertial forces. Second, targeting the maximization of transmission efficiency alongside the minimization of transmission inertia and kinematic asymmetry, an adaptive multi-objective genetic algorithm is developed. Using a bearing life testing machine as the engineering baseline, virtual prototype simulations and multi-load physical bench tests are conducted to validate the proposed approach. Post-optimization results indicate that the full-cycle average transmission efficiency of the mechanism surges significantly from 73.6% to 91.96%, while the transmission inertial force is drastically curtailed by 72.28%. Concurrently, the advance-to-return time ratio, an indicator of kinematic asymmetry, is reduced to 1.0229. Additionally, the torque fluctuations at the output shaft are notably mitigated, and the overall operational noise level is reduced by 4 to 6 dB. This research provides a highly effective theoretical and engineering paradigm for achieving the globally collaborative optimum of planar mechanisms under complex physical constraints. Full article

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

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26 pages, 7945 KB

Open AccessArticle

Baseline Response Characterization and Relative Vertical Displacement Reconstruction of Multi-Layer Asphalt Pavements Based on Quasi-Distributed FBG Monitoring Information

by Jing-Cheng Zhou, Jia Rui, Xiao-Wei Feng, Ke-Wei Xiao-Yan, Jin-Kui Zhang, Hua-Ping Wang and Ping Xiang

Symmetry 2026, 18(8), 1324; https://doi.org/10.3390/sym18081324 - 5 Aug 2026

Abstract

Internal responses of multilayer pavement structures are difficult to characterize using surface-based inspection alone. This study investigates a scaled multilayer pavement model instrumented with embedded quasi-distributed fiber Bragg grating (FBG) sensing lines to obtain baseline internal strain responses and FBG-derived relative vertical displacement [...] Read more.

Internal responses of multilayer pavement structures are difficult to characterize using surface-based inspection alone. This study investigates a scaled multilayer pavement model instrumented with embedded quasi-distributed fiber Bragg grating (FBG) sensing lines to obtain baseline internal strain responses and FBG-derived relative vertical displacement distributions under controlled loading. Central single-point stepwise loading, symmetric two-point loading, and asymmetric two-point loading were applied, and FBG wavelength responses were converted into temperature-compensated strain and then into line-wise relative vertical displacement through strain–curvature conversion, curvature integration, and linear baseline correction. During loading, the ambient temperature ranged from 22.70 to 23.40 °C, and the maximum relative shift of the T-sensor was 0.008297 nm. Under 686 N central loading, SAL1 reached a maximum temperature-compensated strain of 1459.39 με and a maximum relative vertical displacement of 1.079 mm, whereas SAL2 reached 793.13 με and 0.583 mm. Under approximately 490 N asymmetric two-point loading, SAT2 reached 1699.48 με and 0.761 mm. Soil-base responses were substantially lower. Because no independent displacement measurement was acquired, the reconstructed quantity is interpreted as an FBG-derived relative deformation measure rather than an absolute displacement. The results establish intact baseline data for future, separately validated comparisons with abnormal conditions. Full article

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

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14 pages, 2456 KB

Open AccessArticle

Spectral Analysis of Epidemic Dynamics via the Kirchhoff Index

by Fawzy A. Bukhari and Mohamed A. Sohaly

Symmetry 2026, 18(8), 1323; https://doi.org/10.3390/sym18081323 - 5 Aug 2026

Abstract

This paper develops a spectral framework for analyzing epidemic dynamics on weighted networks through the Kirchhoff index and the Laplacian spectrum. Starting from a nonlinear network-based SIS model, we investigate the disease-free and endemic equilibria and establish their local stability conditions in terms [...] Read more.

This paper develops a spectral framework for analyzing epidemic dynamics on weighted networks through the Kirchhoff index and the Laplacian spectrum. Starting from a nonlinear network-based SIS model, we investigate the disease-free and endemic equilibria and establish their local stability conditions in terms of the spectral radius of the adjacency matrix. We then introduce a spectral criterion based on the Kirchhoff index, deriving bounds that connect the total effective resistance of the network with the algebraic connectivity and the characteristic relaxation time. A dimensionless parameter combining epidemic transmission and network topology is proposed, leading to a critical Kirchhoff threshold that separates highly resilient networks from weakly connected and more sensitive structures. These results are summarized in the Kirchhoff Stability Principle, which provides a unified relationship between the Kirchhoff index, algebraic connectivity, relaxation time, and dynamical robustness. Numerical illustrations on several canonical graph topologies, including complete, star, cycle, and path graphs, validate the theoretical findings and demonstrate that networks with smaller Kirchhoff indices exhibit faster convergence and stronger resilience against perturbations. The proposed framework offers a simple spectral approach for understanding the interplay between graph topology and epidemic dynamics and can be extended to more general epidemic and network models. Full article

(This article belongs to the Section B: Mathematics)

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28 pages, 4843 KB

Open AccessArticle

Vibration Activates Pre-Existing Supramolecular Control over Molecular Symmetry

by Sergey A. Tarasov, Anastasia O. Petrova, Ekaterina O. Khimich, Evgenia S. Nechaeva, Galina V. Yarmoschuk, Olesya M. Gizitdinova, Olga V. Fartushnaia, Angelina A. Boriskina, Anastasia D. Zatykina, Irina V. Molodtsova, Kseniya S. Peshketova, Liudmila E. Samsonova, Maria A. Vershinina, Alexey V. Smirnov, Polina N. Borisoglebskaya, Evgeniy A. Gorbunov, Alexander L. Kovalchuk and Oleg I. Epstein

Symmetry 2026, 18(8), 1322; https://doi.org/10.3390/sym18081322 - 4 Aug 2026

Abstract

For many years, our research group has been studying a phenomenon initially discovered in biological models: a solution of a substance subjected to vibration treatment exerts a modifying effect on an intact sample of the same substance, altering its physicochemical and biological properties. [...] Read more.

For many years, our research group has been studying a phenomenon initially discovered in biological models: a solution of a substance subjected to vibration treatment exerts a modifying effect on an intact sample of the same substance, altering its physicochemical and biological properties. This effect also occurs without direct contact, when the vibration-treated and intact substances are kept in separate vials. Since the emergence of this modifying effect requires minimal energy input, we suggest that it is mediated by pre-existing supramolecular mechanisms. During vibration, the molecules deviate from a specific axis of symmetry (a local stationary state), which likely activates an evolutionarily developed supramolecular control over the molecular spatial structure. While testing this hypothesis, we observed that the modifying effect can be detected at a significant distance. This finding indicates that the phenomenon cannot be explained solely by the direct electromagnetic radiation of the vibrating molecules. Instead, the vibration treatment remotely alters the electromagnetic environment of the intact substance, thereby inducing the modifying effect. While non-trivial quantum effects might underlie this process, we favor the assumption that other fundamental interactions influence the electromagnetic field. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2026)

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21 pages, 295 KB

Open AccessArticle

Computation of H-Basis and Syzygies via QR Decomposition

by Sibel Cansu and Özlem Altunbezel

Symmetry 2026, 18(8), 1321; https://doi.org/10.3390/sym18081321 - 4 Aug 2026

Abstract

H-bases provide an attractive alternative to Gröbner bases for the study of polynomial ideals because they are independent of monomial orderings and therefore preserve structural properties that may be obscured in Gröbner basis computations. However, the practical use of H-bases has been limited [...] Read more.

H-bases provide an attractive alternative to Gröbner bases for the study of polynomial ideals because they are independent of monomial orderings and therefore preserve structural properties that may be obscured in Gröbner basis computations. However, the practical use of H-bases has been limited by the lack of efficient algorithms for their construction, particularly due to the difficulty of computing syzygy modules and eliminating redundant generators. In this paper, we present a new algorithm for computing syzygies and H-bases based on numerical linear algebraic techniques. The proposed approach utilizes QR decomposition to construct syzygies directly from coefficient matrices, avoiding the need for monomial orderings and Gröbner basis computations. A recursive framework derived from QR factorization is developed to compute both syzygy modules and H-bases while simultaneously defining an associated reduction process. In contrast to existing methods based on Gröbner bases, Schreyer’s theorem, or singular value decomposition, the proposed algorithm requires fewer matrix reductions and relies on computationally less demanding operations. Furthermore, its termination criterion is determined by an upper bound independent of Gröbner basis theory. Consequently, the method provides a more streamlined and conceptually simpler framework for the computation of syzygies and H-bases of polynomial ideals. Full article

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

24 pages, 404 KB

Open AccessArticle

Anti-Holomorphic Involutions and Langlands Duality on the Moduli Space of Principal G₂-Bundles

by Álvaro Antón-Sancho and Samer R. Yaseen

Symmetry 2026, 18(8), 1320; https://doi.org/10.3390/sym18081320 - 4 Aug 2026

Abstract

Let X be a compact Riemann surface of genus

g \geq 2

equipped with an anti-holomorphic involution

τ

, and let

M (G_{2})

denote the moduli space of stable principal

G_{2}

-bundles over X. We study the fixed-point [...] Read more.

Let X be a compact Riemann surface of genus

g \geq 2

equipped with an anti-holomorphic involution

τ

, and let

M (G_{2})

denote the moduli space of stable principal

G_{2}

-bundles over X. We study the fixed-point loci

M {(G_{2})}^{σ}

of the involutions

σ = θ^{*} \circ τ^{*}

on

M (G_{2})

, where

θ

is a Cartan involution of

G_{2}

corresponding to one of its two real forms: the compact form

G_{2}^{c}

and the split form

G_{2}^{2, 2}

. We prove that

M {(G_{2})}^{σ_{c}}

is connected with Euler characteristic 1, and that

M {(G_{2})}^{σ_{s}}

has exactly

2^{c}

connected components, where c is the number of connected components of the fixed-point set

X^{τ}

. Each component is shown to be a compact, real-analytic, totally real submanifold of

M (G_{2})

of real dimension

14 (g - 1)

. For the split form, we establish that

χ (M {(G_{2})}^{σ_{s}}) = 3^{g - 1}

when

c = 0

, where the factor

3 = | W (G_{2}) | / | W (SO (4)) |

arises from the Borel–Hirzebruch formula applied to the symmetric space

G_{2}^{2, 2} / SO (4)

. We further analyse the monodromy element

k_{0} \in SO (4)

associated to the non-trivial topological type over the ovals, proving that its centraliser in

G_{2}^{2, 2}

is exactly

SO (4)

and that its conjugacy class coincides with

G_{2}^{2, 2} / SO (4)

, with

e (O (k_{0})) = 3

. This supports a conjecture asserting

χ (C_{(w_{1}, \dots, w_{c})}) = 3^{g - 1}

for each component when

c \geq 1

. Finally, exploiting the Langlands self-duality

G_{2}^{\lor} ≅ G_{2}

, we show that

M {(G_{2})}^{σ}

is a

(B, B, B)

-brane in the hyperkähler manifold

T^{*} M (G_{2})

, and that it is self-specular: it is preserved by the derived Fourier–Mukai autoequivalence

Φ : D^{b} (Coh (M (G_{2}))) \tilde{\to} D^{b} (Coh (M (G_{2})))

induced by the Langlands self-duality, which restricts to a self-equivalence of

D^{b} (Coh (M {(G_{2})}^{σ}))

. Full article

(This article belongs to the Section B: Mathematics)

34 pages, 6337 KB

Open AccessArticle

FGOGNN: An Energy-Efficient and Intelligent Cluster-Based Routing Protocol for Wireless Sensor Networks

by Huangshui Hu, Shuo Liu, Qier Kang, Suli Zhang and Chengshuo Tian

Symmetry 2026, 18(8), 1319; https://doi.org/10.3390/sym18081319 - 4 Aug 2026

Abstract

Energy-efficient and robust routing remains a critical problem in wireless sensor networks (WSNs), where limited energy resources and dynamic topologies hinder performance. To address this challenge, a novel cluster-based routing protocol FGOGNN is proposed in this paper, which integrates a Fungal Growth Optimizer [...] Read more.

Energy-efficient and robust routing remains a critical problem in wireless sensor networks (WSNs), where limited energy resources and dynamic topologies hinder performance. To address this challenge, a novel cluster-based routing protocol FGOGNN is proposed in this paper, which integrates a Fungal Growth Optimizer (FGO) for adaptive cluster head (CH) selection and a Graph Neural Network (GNN) for inter-cluster routing. The FGO simulates fungal growth processes, ensuring balanced and energy-efficient CH selection while preventing premature convergence. In the routing phase, the GNN dynamically adapts routing paths by leveraging node energy, connectivity, and directional edge features, offering low computational overhead while maintaining accuracy. Extensive simulations show that FGOGNN outperforms existing routing protocols, extending network lifetime by up to 75% and improving throughput by 38%, with a reduction in end-to-end delay. These results demonstrate FGOGNN’s potential for deployment in real-time WSN applications, where energy efficiency and dynamic adaptability are paramount. Full article

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

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14 pages, 305 KB

Open AccessArticle

Generalizations of Certain Summation Formulas Involving the Generalized Hypergeometric Function Due to Eslahchi and Masjed-Jamei

by Prathima Jayarama, Insuk Kim, Arjun K. Rathie and Sunil D. Purohit

Symmetry 2026, 18(8), 1318; https://doi.org/10.3390/sym18081318 - 4 Aug 2026

Abstract

Classical summation theorems for generalized hypergeometric series constitute an important tool in the study of special functions. Motivated by earlier generalizations of these theorems, this paper derives several new summation formulas for generalized hypergeometric functions by employing the generalized classical summation theorems of [...] Read more.

Classical summation theorems for generalized hypergeometric series constitute an important tool in the study of special functions. Motivated by earlier generalizations of these theorems, this paper derives several new summation formulas for generalized hypergeometric functions by employing the generalized classical summation theorems of Lavoie et al. within a well-known hypergeometric identity. The proposed formulas extend previously reported results, including those of Eslahchi and Masjed-Jamei, which arise as special cases of the present work. The obtained identities provide a unified framework for deriving summation formulas and may be useful in further investigations involving generalized hypergeometric functions and related identities. Full article

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

29 pages, 20928 KB

Open AccessArticle

Thermal Stress Distribution Characteristics and Axial Segmentation Design of the Epoxy Resin Insulation Layer in Arm Reactors Under Combined AC–DC Operating Conditions

by Liang Zou, Cheng Chang, Zhiyun Han, Kejie Huang, Hanwen Ren, Rongzhao Jia and Zhen Li

Symmetry 2026, 18(8), 1317; https://doi.org/10.3390/sym18081317 - 4 Aug 2026

Abstract

Bridge-arm reactors subjected to long-term AC–DC composite currents with multiple harmonics may develop non-uniform winding temperature rise and thermal-expansion mismatch, leading to localized thermal stress concentrations and potential insulation cracking. Unlike previous studies focused mainly on purely AC conditions, this study investigates a [...] Read more.

Bridge-arm reactors subjected to long-term AC–DC composite currents with multiple harmonics may develop non-uniform winding temperature rise and thermal-expansion mismatch, leading to localized thermal stress concentrations and potential insulation cracking. Unlike previous studies focused mainly on purely AC conditions, this study investigates a ±800 kV dry-type air-core bridge-arm reactor and develops a thermo-mechanical model incorporating AC–DC composite currents and harmonic losses. To mitigate thermal stress concentration, an axially segmented configuration is proposed to relieve the restraint associated with cumulative axial thermal expansion. The results show that a 65% axial segmentation ratio provides the best stress-regulation performance among the investigated cases. Under AC–DC composite conditions containing second- and fifth-order harmonics, the maximum Von Mises stress and maximum first-principal stress decrease by 33.42% and 38.11%, respectively, while the stress distribution becomes more uniform. The analysis is based on a two-dimensional axisymmetric model with one-way thermo-mechanical coupling and excludes long-term cyclic thermal aging and interfacial slip between winding and insulation layers. These findings provide theoretical support for the stress-oriented structural design and reliability assessment of high-capacity bridge-arm reactors. Full article

(This article belongs to the Topic Advanced Electromagnetic Modeling and Simulation for Multidisciplinary Engineering Systems)

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19 pages, 332 KB

Open AccessArticle

A Novel l₁ Exact Penalty Function Method and Its Application

by Yu Lv

Symmetry 2026, 18(8), 1316; https://doi.org/10.3390/sym18081316 - 4 Aug 2026

Abstract

Penalty function methods are fundamental for solving constrained optimization problems, yet the widely used

l_{1}

exact penalty function is non-differentiable and therefore incompatible with gradient-based algorithms. This paper proposes a continuously differentiable smoothing approximation that preserves the exactness of the original penalty [...] Read more.

Penalty function methods are fundamental for solving constrained optimization problems, yet the widely used

l_{1}

exact penalty function is non-differentiable and therefore incompatible with gradient-based algorithms. This paper proposes a continuously differentiable smoothing approximation that preserves the exactness of the original penalty while enabling efficient numerical solution. The proposed smoothing function is shown to be

C^{1}

on

R

, with explicit error bounds and a computable lower bound for the penalty parameter that guarantees exactness under standard constraint qualifications. An iterative algorithm is developed and its convergence is proved. Numerical experiments on benchmark problems validate the effectiveness of the approach. The method is then applied to a policy-driven university financial risk management model with twelve decision variables, three conflicting objectives, and multiple regulatory constraints. Results demonstrate faster convergence and improved objective values compared with the traditional non-smooth penalty method, confirming the practical utility of the proposed smoothing technique. Full article

(This article belongs to the Section B: Mathematics)

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21 pages, 2898 KB

Open AccessArticle

Multi-Parameter Analysis of PCM-Based Thermal Management Performance and Thermophysical Characteristics of Lithium-Ion Battery Packs

by Yong Ding, Wenjie Hou, Fan Yang and Zhoujian An

Symmetry 2026, 18(8), 1315; https://doi.org/10.3390/sym18081315 - 4 Aug 2026

Abstract

A three-dimensional structural model of a cylindrical lithium-ion battery pack incorporating composite phase change material (PCM) is developed in this study, and numerical simulations are conducted using CFD software to investigate the heat dissipation characteristics of the battery pack. The results show that [...] Read more.

A three-dimensional structural model of a cylindrical lithium-ion battery pack incorporating composite phase change material (PCM) is developed in this study, and numerical simulations are conducted using CFD software to investigate the heat dissipation characteristics of the battery pack. The results show that the composite PCM effectively suppresses the temperature rise within the battery pack, maintaining both the temperature and the temperature difference in the battery pack within acceptable ranges. Parameter analysis reveals that increasing the radial thermal conductivity of the battery reduces the heating rate and improves the temperature uniformity of the overall system. Within the investigated parameter range, increasing the thermal conductivity of the composite PCM beyond approximately 1 W/(m·K) results in a region of diminishing improvement in thermal performance. Beyond this range, further increases in thermal conductivity result in only marginal reductions in the maximum temperature, indicating that excessive enhancement of thermal conductivity provides limited thermal benefits and should be balanced with latent heat capacity. An increase in the latent heat of the composite PCM lowers both the maximum temperature and the maximum temperature difference at the end of discharge, thereby enhancing system temperature uniformity. Conversely, enlarging the external air convection heat transfer coefficient yields a limited cooling effect while deteriorating the temperature uniformity within the system. Therefore, on the principle of fully utilizing latent heat and minimizing energy consumption, the external convection heat transfer coefficient should be set as low as possible. This study provides theoretical guidance for the parametric design of PCM-based thermal management systems. Full article

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

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21 pages, 11743 KB

Open AccessArticle

Validation-Generalization Asymmetry in Metaheuristic CNN Forecasting: An Extremely Small Time-Series Case

by Baidong Zhao, Hao Yu, Laixing Jing, Aman Mussa, Chenghan Yang, Dingkun Zheng, Sholpan Jomartova and Huannian Meng

Symmetry 2026, 18(8), 1314; https://doi.org/10.3390/sym18081314 - 4 Aug 2026

Abstract

Hyperparameter optimization can reduce validation error while worsening future performance when data are extremely scarce. This study examines that risk in a public railway-mileage implementation workbook containing 17 ordered five-lag input-target rows, of which 14 form the development set and three form a [...] Read more.

Hyperparameter optimization can reduce validation error while worsening future performance when data are extremely scarce. This study examines that risk in a public railway-mileage implementation workbook containing 17 ordered five-lag input-target rows, of which 14 form the development set and three form a locked outer test. No independently verified 22-point raw series was available; exact archived rows are therefore the primary data, while an overlap-consistent inferred chronology is used only for sensitivity analysis. WOA-CNN and BWO-CNN were evaluated through 10 complete HPO searches under shuffled and rolling-origin validation. Five-search purged runs were used as a stress-test sensitivity, while a fixed Manual CNN served as the matched reference. Median locked-test MAPE was 3.75% for WOA-Random, 2.56% for BWO-Random, 4.16% for WOA-Rolling, and 4.51% for BWO-Rolling, compared with a matched Manual CNN reference mean of 2.54%. The four HPO procedures beat that reference in only 3/10, 5/10, 2/10, and 1/10 searches, respectively. A mean-increment baseline obtained 0.63% MAPE. A separate benchmark of 160 independent simulated series examines sample-size and validation-selection mechanisms under four pre-specified data-generating processes. Taken together, the two analyses characterize how validation design and data availability affect model-selection stability in extremely small time-series settings. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Neural Networks)

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22 pages, 18443 KB

Open AccessArticle

PCMTRefer: Symmetry-Aware Text-Guided Point Mamba for Referring Segmentation in Indoor 3D Point Clouds

by Li Yuan, Bo Kong, Chenhao Li, Anting Guo and Wenjiang Huang

Symmetry 2026, 18(8), 1313; https://doi.org/10.3390/sym18081313 - 3 Aug 2026

Abstract

Indoor 3D referring segmentation aims to identify and segment the target object in a point cloud according to a natural language expression. Although recent advances in multimodal feature fusion have markedly improved this task, existing methods do not jointly model the structural regularities [...] Read more.

Indoor 3D referring segmentation aims to identify and segment the target object in a point cloud according to a natural language expression. Although recent advances in multimodal feature fusion have markedly improved this task, existing methods do not jointly model the structural regularities commonly observed in indoor objects, such as approximate symmetry and repetitive local patterns, in conjunction with the directional constraints conveyed by referring expressions. In this work, we formulate symmetry-aware representation as the extraction of direction-consistent structural responses from both forward and backward traversals of the same spatially ordered sequence while preserving direction-sensitive variations introduced by occlusion, point cloud incompleteness, and cluttered scene layouts. Based on this formulation, we propose PCMTRefer, a symmetry-aware text-guided Point Mamba framework for indoor 3D referring segmentation. The input point cloud is first partitioned using an octree and arranged into a spatially coherent sequence via Z-order (Morton) ordering. A bidirectional state-space encoder then aggregates complementary context from both traversal directions, yielding richer representations of regular boundaries, repetitive structures, and approximately bilateral object geometries. In parallel, an asymmetric text-to-point guidance module injects semantic cues—object categories, attributes, and spatial relationships—into point-wise features, while a Background-Relaxation Token offers an auxiliary matching channel for non-target background regions. A Gumbel-Softmax-based semantic primitive learning module further extracts discriminative cues from referring expressions and integrates language semantics with point-level geometric features through a multi-scale decoder. Experimental results on the ScanRefer benchmark show that PCMTRefer achieves an Overall Acc@0.25 of 58.56%, an Overall Acc@0.5 of 54.19%, and an mIoU of 49.97%. Multi-seed validation further confirms the statistical stability of these results, with standard deviations of less than 0.2% across three independent runs. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Computer Vision and Pattern Recognition)

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21 pages, 873 KB

Open AccessArticle

Structural Properties of k-Cyclic Cutwidth Critical Graphs with a Centre

by Zhenkun Zhang

Symmetry 2026, 18(8), 1312; https://doi.org/10.3390/sym18081312 - 3 Aug 2026

Abstract

Cyclic cutwidth problem is a graph layout problem whose goal is to find an embedding

ϕ

of the vertices of a graph G with n vertices onto a cycle

C_{n}

so as to minimize the maximum cutwidth of graph G. According [...] Read more.

Cyclic cutwidth problem is a graph layout problem whose goal is to find an embedding

ϕ

of the vertices of a graph G with n vertices onto a cycle

C_{n}

so as to minimize the maximum cutwidth of graph G. According to the literature, this problem is NP-complete, and some exact results regarding cyclic cutwidth have been reported. For an integer

k > 1

, a graph G with cyclic cutwidth k is k-cyclic cutwidth critical if every proper subgraph of G has cyclic cutwidth less than k and G is homeomorphically minimal. In this paper, from the point of view of graph decomposition, we first characterize decomposable structure of some k-cyclic cutwidth critical graphs. We ascertain that a k-cyclic cutwidth critical graph G with a centre

u_{0}

has a subgraph decomposition with either two or three members, and we find that each member is a

δ

-linear cutwidth critical subgraph of G with

δ = k - 2

or

k - 1

. The result reveals the structural relation between the cyclic cutwidth and the linear cutwidth of graph G. Full article

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

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36 pages, 4717 KB

Open AccessArticle

SEAL-MAC: Symmetry-Equivariant Lyapunov Actor–Critic for Queue-Stable MEC Offloading

by Mingchuan Wu, Jian Lu and Yulin Li

Symmetry 2026, 18(8), 1311; https://doi.org/10.3390/sym18081311 - 3 Aug 2026

Abstract

Mobile edge computing (MEC) must serve rapidly growing populations of latency-critical and energy-constrained devices, yet distributed offloading faces two coupled problems: learned multi-agent policies depend on the arbitrary numerical ordering of edge servers, which wastes training samples and treats physically equivalent configurations inconsistently, [...] Read more.

Mobile edge computing (MEC) must serve rapidly growing populations of latency-critical and energy-constrained devices, yet distributed offloading faces two coupled problems: learned multi-agent policies depend on the arbitrary numerical ordering of edge servers, which wastes training samples and treats physically equivalent configurations inconsistently, while short-horizon cost minimization overloads attractive servers and destabilizes their queues. This paper presents SEAL-MAC (Symmetry-Equivariant Lyapunov Multi-Agent Actor–Critic), a distributed learning framework that addresses both problems jointly. First, a symmetric resource-set actor with a mirror consistency regularizer enforces server relabeling equivariance of each user’s policy and invariance of its value and Lyapunov critics. Second, a load-symmetric Lyapunov–potential shaping mechanism augments drift-plus-penalty rewards with normalized load-balance signals, coupling queue stability, fairness, and strategic alignment. The shaped interaction is analyzed as a Lyapunov-shaped Markov potential game: exact under orthogonal congestion-separable conditions, and a Markov

α

-potential game under heterogeneity or interference, yielding conditional finite-time

(ϵ + α)

-Nash convergence and mean-square queue stability. Each device learns from local observations and

O (M)

queue broadcasts without exchanging gradients or policies. In simulations with up to 200 users, SEAL-MAC reduces average delay by 9.0%, 95th-percentile delay by 11.8%, energy consumption by 10.6%, and the deadline-violation rate from 3.1% to 1.8% relative to the strongest Lyapunov baseline, halves the empirical one-step deviation gain of an identically shaped Ly-PPO agent (0.048 versus 0.098), and raises the Jain fairness index from 0.88 to 0.94. Full article

(This article belongs to the Special Issue Symmetry in Artificial Intelligence and Machine Learning: Current Advances)

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31 pages, 5963 KB

Open AccessArticle

Modeling Influenza–Streptococcus pneumoniae Co-Infection: Multistage Progression and Competitive Exclusion

by Din Prathumwan, Sirawit Phakmee, Inthira Chaiya and Kamonchat Trachoo

Symmetry 2026, 18(8), 1310; https://doi.org/10.3390/sym18081310 - 3 Aug 2026

Abstract

Co-infection between influenza and Streptococcus pneumoniae is an important public health concern, since influenza can increase susceptibility to secondary bacterial invasion and enhance bacterial transmission. We develop and analyze a compartmental model of influenza–pneumococcal co-infection with eleven epidemiological compartments, incorporating imperfect vaccination, quarantine, [...] Read more.

Co-infection between influenza and Streptococcus pneumoniae is an important public health concern, since influenza can increase susceptibility to secondary bacterial invasion and enhance bacterial transmission. We develop and analyze a compartmental model of influenza–pneumococcal co-infection with eleven epidemiological compartments, incorporating imperfect vaccination, quarantine, and a three-stage pneumococcal progression from colonization to invasive disease. We establish the positivity and boundedness of solutions, determine the equilibria, and derive, via the next-generation matrix method, the sub-model reproduction numbers

R_{0}^{I}

and

R_{0}^{P}

together with the composite threshold

R_{0} = max {R_{0}^{I}, R_{0}^{P}}

. Each single infection undergoes a forward bifurcation: the disease-free equilibrium is locally asymptotically stable when the corresponding reproduction number is below unity, and a unique endemic equilibrium—globally asymptotically stable in the pneumococcal sub-model, established by a Goh–Volterra Lyapunov function—emerges above it. When both thresholds exceed unity, the two infections compete for the shared susceptible pool and undergo competitive exclusion: one infection persists while the other, together with the co-infected class, is eliminated. We show that the outcome is governed not by the disease-free reproduction numbers but by the invasion reproduction numbers evaluated at the single-infection boundary equilibria, so that even equal disease-free thresholds do not yield coexistence. Numerical simulations confirm the analytical results and quantify the effect of quarantine and vaccination, providing a framework for assessing control of interacting respiratory infections. Full article

(This article belongs to the Section B: Mathematics)

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22 pages, 5798 KB

Open AccessArticle

Adaptive Online Management of Multi-Terminal Feeder Congestion in Asymmetric MVDC Distribution Systems Under Limited Communication

by Yansong Zhao, Qian Xiao, Hong Zhu, Wenbiao Lu, Chunlei Xu, Shiwen Su, Xiaohui Pan and Kai Sun

Symmetry 2026, 18(8), 1309; https://doi.org/10.3390/sym18081309 - 3 Aug 2026

Abstract

In medium-voltage DC distribution systems (MVDC-DSs), feeder congestion may occur when multiple converter terminals sharing the same AC feeder experience fast source–load variations. Limited communication further challenges real-time converter coordination and secure system operation. To address these issues, this paper has proposed an [...] Read more.

In medium-voltage DC distribution systems (MVDC-DSs), feeder congestion may occur when multiple converter terminals sharing the same AC feeder experience fast source–load variations. Limited communication further challenges real-time converter coordination and secure system operation. To address these issues, this paper has proposed an adaptive online management strategy for multi-terminal feeder congestion in MVDC-DSs under limited communication. First, the economic operation objective and practical system constraints are formulated within a distributed optimization framework, where feeder congestion limits, voltage security, and load supply requirements are explicitly incorporated. Then, an adaptive online regulation mechanism is embedded into local converter controllers, enabling converter power to be coordinated in real time using only neighboring information. In this way, feeder congestion can be mitigated while reliable load supply and economic operation are maintained. Simulation studies and hardware-in-the-loop experimental results demonstrate the effectiveness, scalability, and real-time applicability of the proposed strategy under dynamic operating conditions. Full article

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

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