Symmetry

19 pages, 38523 KiB

Open AccessArticle

A Novel 2D Hyperchaotic Map with Homogeneous Multistability and Its Application in Image Encryption

by Xin Huang, Wenhao Yan, Wenjie Dong and Qun Ding

Symmetry 2025, 17(5), 801; https://doi.org/10.3390/sym17050801 (registering DOI) - 21 May 2025

This study proposes a novel two-dimensional hyperchaotic map model based on an orthogonal feedback mechanism, exhibiting dynamic behaviors with multistable characteristics and high complexity. By analyzing the homogeneous multistability of the system, it is revealed that the initial states determine the positions of [...] Read more.

This study proposes a novel two-dimensional hyperchaotic map model based on an orthogonal feedback mechanism, exhibiting dynamic behaviors with multistable characteristics and high complexity. By analyzing the homogeneous multistability of the system, it is revealed that the initial states determine the positions of attractors. An image encryption scheme for color images is developed by integrating confusion and diffusion strategies with this hyperchaotic map. The effectiveness of the proposed scheme in enabling secure image transmission is validated through comprehensive numerical simulations and rigorous security assessments. Full article

(This article belongs to the Section Computer)

17 pages, 1214 KiB

Open AccessArticle

The Mittag-Leffler–Caputo–Fabrizio Fractional Derivative and Its Numerical Approach

by Manal Alqhtani, Lakhlifa Sadek and Khaled Mohammed Saad

Symmetry 2025, 17(5), 800; https://doi.org/10.3390/sym17050800 - 21 May 2025

Abstract

This study introduces a novel fractional-order derivative, termed the Mittag-Leffler–Caputo–Fabrizio (MLCF) fractional derivative, which is characterized by a singular kernel. Symmetry plays a key role in the structure and behavior of fractional operators, and our formulation reflects this by incorporating symmetric properties of [...] Read more.

This study introduces a novel fractional-order derivative, termed the Mittag-Leffler–Caputo–Fabrizio (MLCF) fractional derivative, which is characterized by a singular kernel. Symmetry plays a key role in the structure and behavior of fractional operators, and our formulation reflects this by incorporating symmetric properties of the Mittag-Leffler function and its integral representation. To numerically approximate the MLCF derivative, we apply a two-point finite forward difference scheme to estimate the first-order derivative of the function

u (λ)

within the integral component of the definition. This leads to the construction of a new numerical differentiation scheme. Our analysis demonstrates that the proposed approximation exhibits first-order convergence, with absolute errors decreasing as the time step size h diminishes. These errors are quantified by comparing our numerical results with exact analytical solutions, reinforcing the accuracy of the method. Full article

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

18 pages, 312 KiB

Open AccessArticle

Lipschitz and Second-Order Regularities for Non-Homogeneous Degenerate Nonlinear Parabolic Equations in the Heisenberg Group

by Huiying Wang, Chengwei Yu, Zhiqiang Zhang and Yue Zeng

Symmetry 2025, 17(5), 799; https://doi.org/10.3390/sym17050799 - 21 May 2025

Abstract

In the Heisenberg group

H^{n}

, we establish the local regularity theory for weak solutions to non-homogeneous degenerate nonlinear parabolic equations of the form [...] Read more.

In the Heisenberg group

H^{n}

, we establish the local regularity theory for weak solutions to non-homogeneous degenerate nonlinear parabolic equations of the form

\partial_{t} u - \sum_{i = 1}^{2 n} X_{i} A_{i} (X u) = K (x, t, u, X u)

, where the nonlinear structure is modeled on non-homogeneous parabolic p-Laplacian-type operators. Specifically, we prove two main local regularities: (i) For

2 \leq p \leq 4

, we establish the local Lipschitz regularity (

u \in C_{loc}^{0, 1}

), with the horizontal gradient satisfying

X u \in L_{loc}^{\infty}

; (ii) For

2 \leq p < 3

, we establish the local second-order horizontal Sobolev regularity (

u \in H W_{loc}^{2, 2}

), with the second-order horizontal derivative satisfying

X X u \in L_{loc}^{2}

. These results solve an open problem proposed by Capogna et al. Full article

(This article belongs to the Special Issue Advances in Mathematical Models and Partial Differential Equations: 2nd Edition)

27 pages, 10202 KiB

Open AccessArticle

WIGformer: Wavelet-Based Illumination-Guided Transformer

by Wensheng Cao, Tianyu Yan, Zhile Li and Jiongyao Ye

Symmetry 2025, 17(5), 798; https://doi.org/10.3390/sym17050798 - 20 May 2025

Abstract

Low-light image enhancement remains a challenging task in computer vision due to the complex interplay of noise, asymmetrical artifacts, illumination non-uniformity, and detail preservation. Existing methods such as traditional histogram equalization, gamma correction, and Retinex-based approaches often struggle to balance contrast improvement and [...] Read more.

Low-light image enhancement remains a challenging task in computer vision due to the complex interplay of noise, asymmetrical artifacts, illumination non-uniformity, and detail preservation. Existing methods such as traditional histogram equalization, gamma correction, and Retinex-based approaches often struggle to balance contrast improvement and naturalness preservation. Deep learning methods such as CNNs and transformers have shown promise, but face limitations in modeling multi-scale illumination and long-range dependencies. To address these issues, we propose WIGformer, a novel wavelet-based illumination-guided transformer framework for low-light image enhancement. The proposed method extends the single-stage Retinex theory to explicitly model noise in both reflectance and illumination components. It introduces a wavelet illumination estimator with a Wavelet Feature Enhancement Convolution (WFEConv) module to capture multi-scale illumination features and an illumination feature-guided corruption restorer with an Illumination-Guided Enhanced Multihead Self-Attention (IGEMSA) mechanism. WIGformer leverages the symmetry properties of wavelet transforms to achieve multi-scale illumination estimation, ensuring balanced feature extraction across different frequency bands. The IGEMSA mechanism integrates adaptive feature refinement and illumination guidance to suppress noise and artifacts while preserving fine details. The same mechanism allows us to further exploit symmetrical dependencies between illumination and reflectance components, enabling robust and natural enhancement of low-light images. Extensive experiments on the LOL-V1, LOL-V2-Real, and LOL-V2-Synthetic datasets demonstrate that WIGformer achieves state-of-the-art performance and outperforms existing methods, with PSNR improvements of up to 26.12 dB and an SSIM score of 0.935. The qualitative results demonstrate WIGformer’s superior capability to not only restore natural illumination but also maintain structural symmetry in challenging conditions, preserving balanced luminance distributions and geometric regularities that are characteristic of properly exposed natural scenes. Full article

(This article belongs to the Section Computer)

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19 pages, 758 KiB

Open AccessArticle

Closed Forms and Structural Properties of Lucas Matrices Derived from Tridiagonal Toeplitz Matrices

by Fikri Koken and Muaz Aksoy

Symmetry 2025, 17(5), 797; https://doi.org/10.3390/sym17050797 - 20 May 2025

Abstract

This study investigates the closed forms of Lucas matrices, with a particular emphasis on the

n^{t h}

powers of the tridiagonal symmetric Toeplitz matrix

S_{4} (x, y)

, whose entries are associated with Lucas numbers

L_{n}

. [...] Read more.

This study investigates the closed forms of Lucas matrices, with a particular emphasis on the

n^{t h}

powers of the tridiagonal symmetric Toeplitz matrix

S_{4} (x, y)

, whose entries are associated with Lucas numbers

L_{n}

. The analysis extends Filipponi’s foundational work by examining distinct cases of ordered pairs

(x, y)

, thereby determining the precise conditions under which

S_{4} (x, y)

qualifies as a Fibonacci–Lucas matrix. Furthermore, it identifies specific conditions under which

S_{4} (x, y)

can be classified as any Fibonacci–Lucas matrix. These findings contribute to the theoretical framework of Fibonacci–Lucas matrices and provide novel insights into their structural properties. Full article

(This article belongs to the Section Mathematics)

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24 pages, 1736 KiB

Open AccessArticle

ProFusion: Multimodal Prototypical Networks for Few-Shot Learning with Feature Fusion

by Jia Zhao, Ziyang Cao, Huiling Wang, Xu Wang and Yingzhou Chen

Symmetry 2025, 17(5), 796; https://doi.org/10.3390/sym17050796 - 20 May 2025

Abstract

Existing few-shot learning models leverage vision-language pre-trained models to alleviate the data scarcity problem. However, such models usually process visual and text information separately, which causes still inherent disparities between cross-modal features. Therefore, we propose the ProFusion model, which leverages multimodal pre-trained models [...] Read more.

Existing few-shot learning models leverage vision-language pre-trained models to alleviate the data scarcity problem. However, such models usually process visual and text information separately, which causes still inherent disparities between cross-modal features. Therefore, we propose the ProFusion model, which leverages multimodal pre-trained models and prototypical networks to construct multiple prototypes. Specifically, ProFusion generates image and text prototypes symmetrically using the visual encoder and text encoder, while integrating visual and text information through the fusion module to create more expressive multimodal feature fusion prototypes. Additionally, we introduce the alignment module to ensure consistency between image and text prototypes. During inference, ProFusion calculates the similarity of test images to the three types of prototypes separately and applies a weighted sum to generate the final prediction. Experiments demonstrate that ProFusion performs outstanding classification tasks on 15 benchmark datasets. Full article

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

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34 pages, 589 KiB

Open AccessArticle

Anisotropic Four-Dimensional Spaces of Real Numbers

by Maksut M. Abenov, Mars B. Gabbassov, Tolybay Z. Kuanov and Berik I. Tuleuov

Symmetry 2025, 17(5), 795; https://doi.org/10.3390/sym17050795 - 20 May 2025

Abstract

This article constructs all the anisotropic spaces of four-dimensional numbers in which the commutative and associative operations of addition and multiplication are defined. In this case, so-called “zero divisors” appear in these spaces. The structures of zero divisors in each space are described [...] Read more.

This article constructs all the anisotropic spaces of four-dimensional numbers in which the commutative and associative operations of addition and multiplication are defined. In this case, so-called “zero divisors” appear in these spaces. The structures of zero divisors in each space are described and their properties are investigated. It is shown that there are two types of zero divisors and they form a two-dimensional subspace of the four-dimensional space. A space of 4 × 4 matrices is constructed that is isomorphic to the space of four-dimensional numbers. The concept of the spectrum of a four-dimensional number is introduced and a bijective mapping between four-dimensional numbers and their spectra is constructed. Thanks to this, methods for solving linear and quadratic equations in four-dimensional spaces are developed. It is proven that a quadratic equation in a four-dimensional space generally has four roots. The concept of the spectral norm is introduced in the space of four-dimensional numbers and the equivalence of the spectral norm to the Euclidean norm is proved. Full article

(This article belongs to the Section Mathematics)

16 pages, 1509 KiB

Open AccessArticle

A Reliable Deep Learning Model for ECG Interpretation: Mitigating Overconfidence and Direct Uncertainty Quantification

by Xuedong Li, Qingxiao Zheng, Shibin Zhang, Shipeng Fu, Yingke Chen and Ke Ye

Symmetry 2025, 17(5), 794; https://doi.org/10.3390/sym17050794 - 20 May 2025

Abstract

Electrocardiogram (ECG) interpretation using deep learning models holds immense potential for improving cardiac diagnosis. However, existing models often suffer from overconfident predictions and lack the capability to directly quantify uncertainty, leading to unreliable clinical guidance. To address this challenge, we propose a model [...] Read more.

Electrocardiogram (ECG) interpretation using deep learning models holds immense potential for improving cardiac diagnosis. However, existing models often suffer from overconfident predictions and lack the capability to directly quantify uncertainty, leading to unreliable clinical guidance. To address this challenge, we propose a model for uncertainty-aware ECG interpretation. The model employs a deep convolutional architecture with max-pooling residual modules to capture both local and global spatiotemporal features from raw ECG signals. The architectural design respects the symmetry inherent in ECG waveforms—such as periodicity and morphological consistency across cardiac cycles—enabling the network to extract clinically relevant features more effectively. Then, unlike conventional models that rely on softmax-based probability outputs, our approach parameterizes class distributions using the Dirichlet distribution, while Subjective Logic translates these parameters into interpretable belief masses and uncertainty scores. We evaluate the model on the PhysioNet Challenge 2017 dataset, our model achieves an accuracy of 86.12%, an F1 score of 83.14%, a Precision-Recall Area Under the Curve (PR-AUC) of 85.25%, and a Receiver Operating Characteristic Area Under the Curve (ROC-AUC) of 92.87%—outperforming baseline models in three out of four metrics. Critically, the model reduces overconfidence to 0.59% (compared to 12–22% in softmax-based baselines), aligning prediction confidence with true accuracy. By progressively increasing the uncertainty threshold u, the model dynamically filters low-confidence predictions, leading to consistently improved performance—reaching up to 93.59% accuracy, 93.22% F1 score, 89.17% PR-AUC, and 95.10% ROC-AUC at u = 0.1. These results validate the model’s capacity for reliable ECG interpretation while leveraging physiological signal symmetry for enhanced feature extraction. Full article

(This article belongs to the Section Computer)

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19 pages, 6004 KiB

Open AccessArticle

Remote Sensing Image Change Detection Based on Dynamic Adaptive Context Attention

by Yong Xie, Yixuan Wang, Xin Wang, Yin Tan and Qin Qin

Symmetry 2025, 17(5), 793; https://doi.org/10.3390/sym17050793 - 20 May 2025

Abstract

Although some progress has been made in deep learning-based remote sensing image change detection, the complexity of scenes and the diversity of changes in remote sensing images lead to challenges related to background interference. For instance, remote sensing images typically contain numerous background [...] Read more.

Although some progress has been made in deep learning-based remote sensing image change detection, the complexity of scenes and the diversity of changes in remote sensing images lead to challenges related to background interference. For instance, remote sensing images typically contain numerous background regions, while the actual change regions constitute only a small proportion of the overall image. To address these challenges in remote sensing image change detection, this paper proposes a Dynamic Adaptive Context Attention Network (DACA-Net) based on an exchanging dual encoder–decoder (EDED) architecture. The core innovation of DACA-Net is the development of a novel Dynamic Adaptive Context Attention Module (DACAM), which learns attention weights and automatically adjusts the appropriate scale according to the features present in remote sensing images. By fusing multi-scale contextual features, DACAM effectively captures information regarding changes within these images. In addition, DACA-Net adopts an EDED architectural design, where the conventional convolutional modules in the EDED framework are replaced by DACAM modules. Unlike the original EDED architecture, DACAM modules are embedded after each encoder unit, enabling dynamic recalibration of T1/T2 features and cross-temporal information interaction. This design facilitates the capture of fine-grained change features at multiple scales. This architecture not only facilitates the extraction of discriminative features but also promotes a form of structural symmetry in the processing pipeline, contributing to more balanced and consistent feature representations. To validate the applicability of our proposed method in real-world scenarios, we constructed an Unmanned Aerial Vehicle (UAV) remote sensing dataset named the Guangxi Beihai Coast Nature Reserves (GBCNR). Extensive experiments conducted on three public datasets and our GBCNR dataset demonstrate that the proposed DACA-Net achieves strong performance across various evaluation metrics. For example, it attains an F1 score (F1) of 72.04% and a precision(P) of 66.59% on the GBCNR dataset, representing improvements of 3.94% and 4.72% over state-of-the-art methods such as semantic guidance and spatial localization network (SGSLN) and bi-temporal image Transformer (BIT), respectively. These results verify that the proposed network significantly enhances the ability to detect critical change regions and improves generalization performance. Full article

(This article belongs to the Section Computer)

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18 pages, 1890 KiB

Open AccessArticle

Symmetry-Entropy-Constrained Matrix Fusion for Dynamic Dam-Break Emergency Planning

by Shuai Liu, Dewei Yang, Hao Hu and Junping Wang

Symmetry 2025, 17(5), 792; https://doi.org/10.3390/sym17050792 - 20 May 2025

Abstract

Existing studies on ontology evolution lack automated mechanisms to balance semantic coherence and adaptability under real-time uncertainties, particularly in resolving spatiotemporal asymmetry and multidimensional coupling imbalances in dam-break scenarios. Traditional methods such as WordNet’s tree symmetry and FrameNet’s frame symmetry fail to formalize [...] Read more.

Existing studies on ontology evolution lack automated mechanisms to balance semantic coherence and adaptability under real-time uncertainties, particularly in resolving spatiotemporal asymmetry and multidimensional coupling imbalances in dam-break scenarios. Traditional methods such as WordNet’s tree symmetry and FrameNet’s frame symmetry fail to formalize dynamic adjustments through quantitative metrics, leading to path dependency and delayed responses. This study addresses this gap by introducing a novel symmetry-entropy-constrained matrix fusion algorithm, which integrates algebraic direct sum operations and Hadamard product with entropy-driven adaptive weighting. The original contribution lies in the symmetry entropy metric, which quantifies structural deviations during fusion to systematically balance semantic stability and adaptability. This work formalizes ontology evolution as a symmetry-driven optimization process. Experimental results demonstrate that shared concepts between ontologies (s = 3) reduce structural asymmetry by 25% compared to ontologies (s = 1), while case studies validate the algorithm’s ability to reconcile discrepancies between theoretical models and practical challenges in evacuation efficiency and crowd dynamics. This advancement promotes the evolution of traditional emergency management systems towards an adaptive intelligent form. Full article

(This article belongs to the Section Mathematics)

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10 pages, 1543 KiB

Open AccessArticle

Synthesis, Structural Characterization, EPR Analysis and Antimicrobial Activity of a Copper(II) Thiocyanate Complex Based on 3,7-Di(3-pyridyl)-1,5-dioxa-3,7-diazacyclooctane

by Wei Qian, Zibo Wang, Jingfeng Xia, Hongxia Wang, Shuling Dong, Shuai Lou, Ping Ding and Li Li

Symmetry 2025, 17(5), 791; https://doi.org/10.3390/sym17050791 - 20 May 2025

Abstract

The reaction of bipyridine 3,7-di(3-pyridyl)-1,5-dioxa-3,7-diazacyclooctane (L) with copper thiocyanate produces a discrete metallamacrocycle [Cu(L)(SCN)₂(DMF)]₂ (1). In complex 1, two cis-coordinated ligands combine with two copper ions to form an unabridged 24-membered macrocycle. Each copper ion is five-coordinated [...] Read more.

The reaction of bipyridine 3,7-di(3-pyridyl)-1,5-dioxa-3,7-diazacyclooctane (L) with copper thiocyanate produces a discrete metallamacrocycle [Cu(L)(SCN)₂(DMF)]₂ (1). In complex 1, two cis-coordinated ligands combine with two copper ions to form an unabridged 24-membered macrocycle. Each copper ion is five-coordinated with two nitrogens from separate ligands, two nitrogens from thiocyanates and one oxygen from the dimethylformamide (DMF) solvent. Complex 1 has been characterized using single-crystal X-ray diffraction, optical and thermal analyses and antimicrobial activity measurements. The solid electron paramagnetic resonance (EPR) analysis of complex 1 yielded a characteristic structural g factor value of 2.147. In addition, the thermal analysis established that the complex is thermally stable at up to 176 °C. The antimicrobial activity measurements demonstrated that both the ligand and complex 1 exhibit an inhibitory effect on two strains, where the complex exhibits a significantly greater inhibition relative to that of the free ligand (p < 0.05). Full article

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

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10 pages, 222 KiB

Open AccessArticle

Maximum Colored Cuts in Edge-Colored Complete k-Partite Graphs and Complete Graphs

by Huawen Ma

Symmetry 2025, 17(5), 790; https://doi.org/10.3390/sym17050790 - 20 May 2025

Abstract

The Maximum Colored Cut problem aims to seek a bipartition of the vertex set of a graph, maximizing the number of colors in the crossing edges. It is a classical Max-Cut problem if the host graph is rainbow. Let [...] Read more.

The Maximum Colored Cut problem aims to seek a bipartition of the vertex set of a graph, maximizing the number of colors in the crossing edges. It is a classical Max-Cut problem if the host graph is rainbow. Let

m c c (G)

denote the maximum number of colors in a cut of an edge-colored graph G. Let

C_{k}

be a cycle of length k; we say G is PC-

C_{k}

-free if G contains no properly colored

C_{k}

. We say G is a p-edge-colored graph if there exist p colors in G. In this paper, we first show that if G is a PC-

C_{3}

-free p-edge-colored complete 4-partite graph, then

m c c (G) = p

. Let

k \geq 3

be an integer. Then, we show that if G is a PC-

C_{4}

-free p-edge-colored complete k-partite graph, then

m c c (G) \geq min {p - 1, 15 p / 16}

. Finally, for a p-edge-colored complete graph G, we prove that

m c c (G) \geq p - 1

if G is PC-

C_{4}

-free, and

m c c (G) \geq min {p - 6, 7 p / 8}

if G is PC-

C_{5}

-free and

p \geq 7

. Full article

(This article belongs to the Special Issue Advances in Graph Theory Ⅱ)

22 pages, 5367 KiB

Open AccessArticle

An Improved Bee Colony Optimization Algorithm Using a Sugeno–Takagi Interval Type-2 Fuzzy Logic System for the Optimal Design of Stable Autonomous Mobile Robot Controllers

by Leticia Amador-Angulo, Patricia Melin and Oscar Castillo

Symmetry 2025, 17(5), 789; https://doi.org/10.3390/sym17050789 - 20 May 2025

Abstract

This study proposes an enhanced Sugeno–Takagi interval type-2 fuzzy logic system (SIT2FLS) to find the best values for two important parameters in Bee Colony Optimization (BCO). The aim of this study was to develop a stable controller for a mobile robot utilizing BCO [...] Read more.

This study proposes an enhanced Sugeno–Takagi interval type-2 fuzzy logic system (SIT2FLS) to find the best values for two important parameters in Bee Colony Optimization (BCO). The aim of this study was to develop a stable controller for a mobile robot utilizing BCO in the fuzzy controller and to determine the best membership functions (MFs) in a type-1 fuzzy logic system (T1FLS) for control. Another objective was to use an SIT2FLS to find the best

α

and

β

parameters for BCO to enhance the robot trajectory, which was evaluated through an analysis of the mean squared errors. Three types of perturbations were analyzed and simulated. The performance of the SIT2FLS-FBCO was evaluated and compared to that of the T1FLS-FBCO. In addition, a comparative study was performed to demonstrate that the improved BCO works well when there are disturbances affecting the controller. Finally, it was compared with the Mamdani approach, and an FBCO with an interval type-3 FLS was also developed. Full article

(This article belongs to the Special Issue Theory and Applications on the Recent Extensions of Ordinary Fuzzy Sets)

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29 pages, 2593 KiB

Open AccessArticle

Symmetry and Time-Delay-Driven Dynamics of Rumor Dissemination

by Cunlin Li, Zhuanting Ma, Lufeng Yang and Tajul Ariffin Masron

Symmetry 2025, 17(5), 788; https://doi.org/10.3390/sym17050788 - 19 May 2025

Abstract

The dissemination of rumors can lead to significant economic damage and pose a grave threat to social harmony and the stability of people’s livelihoods. Consequently, curbing the dissemination of rumors is of paramount importance. The model in the text assumes that the population [...] Read more.

The dissemination of rumors can lead to significant economic damage and pose a grave threat to social harmony and the stability of people’s livelihoods. Consequently, curbing the dissemination of rumors is of paramount importance. The model in the text assumes that the population is homogeneous in terms of transmission behavior. This homogeneity is essentially a manifestation of translational symmetry. This paper undertakes a thorough examination of the impact of time delay on the dissemination of rumors within social networking services. We have developed a model for rumor dissemination, establishing the positivity and boundedness of its solutions, and identified the existence of an equilibrium point. The study further involved determining the critical threshold of the proposed model, accompanied by a comprehensive examination of its Hopf bifurcation characteristics. In the expression of the threshold

R_{0}

, the parameters appear in a symmetric form, reflecting the balance between dissemination and suppression mechanisms. Furthermore, detailed investigations were carried out to assess both the localized and global stability properties of the system’s equilibrium states. In stability analysis, the symmetry in the distribution of characteristic equation roots determines the system’s dynamic behavior. Through numerical simulations, we analyzed the potential impacts and theoretically examined the factors influencing rumor dissemination, thereby validating our theoretical analysis. An optimal control strategy was formulated, and three control variables were incorporated to describe the strategy. The optimization framework incorporates a specifically designed cost function that simultaneously accounts for infection reduction and resource allocation efficiency in control strategy implementation. The optimal control strategy proposed in the study involves a comparison between symmetric and asymmetric interventions. Symmetric control measures may prove inefficient, whereas asymmetric control demonstrates higher efficacy—highlighting a trade-off in symmetry considerations for optimization problems. Full article

(This article belongs to the Special Issue Advances in Mathematical Models and Partial Differential Equations: 2nd Edition)

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57 pages, 2571 KiB

Open AccessReview

Heavy–Heavy and Heavy–Light Mesons in Cold Nuclear Matter

by J. J. Cobos-Martínez, Guilherme N. Zeminiani and Kazuo Tsushima

Symmetry 2025, 17(5), 787; https://doi.org/10.3390/sym17050787 - 19 May 2025

Abstract

We review the in-medium modifications of effective masses (Lorentz scalar potentials or phenomenon of mass shift) of the heavy–heavy and heavy–light mesons in symmetric nuclear matter and their nuclear bound states. We use a combined approach with the quark–meson coupling (QMC) model and [...] Read more.

We review the in-medium modifications of effective masses (Lorentz scalar potentials or phenomenon of mass shift) of the heavy–heavy and heavy–light mesons in symmetric nuclear matter and their nuclear bound states. We use a combined approach with the quark–meson coupling (QMC) model and an effective Lagrangian. As demonstrated by the cases of pionic and kaonic atoms, studies of the meson–nucleus bound state can provide us with important information on chiral symmetry in a dense nuclear medium. In this review, we examine the mesons,

K, K^{*}, D, D^{*}, B, B^{*}, η, η^{'}, ϕ, η_{c}, J / ψ, η_{b}, Υ

, and

B_{c}

, where our emphasis is on the heavy mesons. In addition, we also present some new results for the

B_{c}

-nucleus bound states. Full article

(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)

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28 pages, 2804 KiB

Open AccessArticle

Adaptive Network-Based Fuzzy Inference System Training Using Nine Different Metaheuristic Optimization Algorithms for Time-Series Analysis of Brent Oil Price and Detailed Performance Analysis

by Ebubekir Kaya, Ahmet Kaya and Ceren Baştemur Kaya

Symmetry 2025, 17(5), 786; https://doi.org/10.3390/sym17050786 - 19 May 2025

Abstract

Brent oil holds a significant position in the global energy market, as oil prices in many regions are indexed to it. Therefore, forecasting the future price of Brent oil is of great importance. In recent years, artificial intelligence techniques have been widely applied [...] Read more.

Brent oil holds a significant position in the global energy market, as oil prices in many regions are indexed to it. Therefore, forecasting the future price of Brent oil is of great importance. In recent years, artificial intelligence techniques have been widely applied in modeling and prediction tasks. In this study, an Adaptive Neuro-Fuzzy Inference System (ANFIS), a well-established AI approach, was employed for the time-series forecasting of Brent oil prices. To ensure effective learning and improve prediction accuracy, ANFIS was trained using nine different metaheuristic algorithms: Artificial Bee Colony (ABC), Selfish Herd Optimizer (SHO), Biogeography-Based Optimization (BBO), Multi-Verse Optimizer (MVO), Teaching–Learning-Based Optimization (TLBO), Cuckoo Search (CS), Moth Flame Optimization (MFO), Marine Predator Algorithm (MPA), and Flower Pollination Algorithm (FPA). Symmetric training procedures were applied across all algorithms to ensure fair and consistent evaluation. The analyses were conducted on the lowest and highest daily, weekly, and monthly Brent oil prices. Mean squared error (MSE) was used as the primary performance metric. The results showed that all algorithms achieved effective prediction performance. Among them, BBO and TLBO demonstrated superior accuracy and stability, particularly in handling the complexities of Brent oil forecasting. This study contributes to the literature by combining ANFIS and metaheuristics within a symmetric framework of experimentation and evaluation. Full article

(This article belongs to the Special Issue Evolutionary Computation, Metaheuristics, Nature-Inspired Algorithms, and Symmetry)

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25 pages, 2909 KiB

Open AccessArticle

Modeling Academic Social Networks Using Covering and Matching in Intuitionistic Fuzzy Influence Graphs

by Waheed Ahmad Khan, Yusra Arooj and Hai Van Pham

Symmetry 2025, 17(5), 785; https://doi.org/10.3390/sym17050785 - 19 May 2025

Abstract

Influence graphs are essential tools for analyzing interactions and relationships in social networks. However, real-world networks often involve uncertainty due to incomplete, vague, or dynamic information. The structure of influence graphs often exhibits natural symmetries, which play a crucial role in optimizing covering [...] Read more.

Influence graphs are essential tools for analyzing interactions and relationships in social networks. However, real-world networks often involve uncertainty due to incomplete, vague, or dynamic information. The structure of influence graphs often exhibits natural symmetries, which play a crucial role in optimizing covering and matching strategies by decreasing redundancy and enhancing efficiency. Traditional influence graph models struggle to address such complexities. To address this gap, we present the novel concepts of covering and matching in intuitionistic fuzzy influence graphs (IFIGs) for modeling academic social networks. These graphs incorporate degrees of membership and non-membership to better reflect uncertainty in influence patterns. Thus, the main aim of this study is to initiate the concepts of covering and matching within the IFIG paradigm and provide its application in social networks. Initially, we establish some basic terms related to covering and matching with illustrative examples. We also investigate complete and complete bipartite IFIGs. To verify the practicality of this study, student interactions across subjects are analyzed using strong paths and strong independent sets. The proposed model is then evaluated using the TOPSIS method to rank participants based on their influence. Moreover, a comparative study is conducted to demonstrate that the proposed model not only handles uncertainty effectively but also performs better than the existing approaches. Full article

(This article belongs to the Section Mathematics)

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17 pages, 3728 KiB

Open AccessArticle

Short-Term Solar Photovoltaic Power Prediction Utilizing the VMD-BKA-BP Neural Network

by Yuanquan Sun, Zhongli Wang, Jiahui Wang and Qiuhua Li

Symmetry 2025, 17(5), 784; https://doi.org/10.3390/sym17050784 - 19 May 2025

Abstract

Photovoltaic (PV) power generation is characterized by high stochasticity, symmetry in daily power generation and low predictive accuracy. Enhancing the precision of power forecasting is crucial for improving symmetrical economic operation of the power grid. Due to Back-Propagation (BP) neural network prediction, there [...] Read more.

Photovoltaic (PV) power generation is characterized by high stochasticity, symmetry in daily power generation and low predictive accuracy. Enhancing the precision of power forecasting is crucial for improving symmetrical economic operation of the power grid. Due to Back-Propagation (BP) neural network prediction, there are problems such as difficulty in choosing network structure and high data requirements. A hybrid photovoltaic power forecasting model is introduced, utilizing the black-winged kite optimization algorithm (BKA) method to optimize the number of decompositions and maximum number of iterations in variational mode decomposition (VMD), as well as the critical parameters in the BP neural network. Initially, SHAP (Shapley Additive exPlanations) analysis identifies the primary factors used to serve as inputs for the K-means++ clustering of similar days, with the dataset segmented into samples of analogous days to reduce the asymmetric stochasticity of PV generation. Subsequently, the highly correlated features and PV power across different weather scenarios are decomposed using VMD, and a BKA-BP neural network prediction model is developed for each subcomponent. Ultimately, the predicted values are reconstructed through superimposition to yield the final prediction outcomes. The simulation findings indicate that VMD-BKA-BP neural network ensemble prediction model significantly enhances the short-term prediction accuracy of photovoltaic power relative to alternative models. This prediction model can be used in the future to optimize power dispatch and improve grid stability. Full article

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

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25 pages, 6255 KiB

Open AccessArticle

Threat Intelligence Named Entity Recognition Based on Segment-Level Information Extraction and Similar Semantic Space Construction

by Long Chen, Hongli Deng, Jun Zhang, Bochuan Zheng and Rui Jiang

Symmetry 2025, 17(5), 783; https://doi.org/10.3390/sym17050783 - 19 May 2025

Abstract

Threat intelligence is crucial for the early detection of network security threats, and named entity recognition (NER) plays a critical role in this process. However, traditional NER models based on sequence tagging primarily focus on word-level information for single-token entities, which leads to [...] Read more.

Threat intelligence is crucial for the early detection of network security threats, and named entity recognition (NER) plays a critical role in this process. However, traditional NER models based on sequence tagging primarily focus on word-level information for single-token entities, which leads to the inefficient extraction of multi-token entities in intelligence texts. Moreover, traditional NER models provide only a single semantic representation of intelligence texts, meaning that polysemous entities in intelligence texts cannot be effectively classified. To address these problems, this paper proposes a novel model based on segment-level information extraction and similar semantic space construction (SSNER). First, SSNER retrains the traditional BERT model based on a threat intelligence corpus and modifies BERT’s mask mechanism to extract the segment-level word embedding so that the ability of the SSNER to recognize multi-token entities is enhanced. Second, SSNER designs a similar semantic space construction method, which obtains compound semantic representations with symmetrical properties by filtering out the set of similar words and integrating them using self-attention to generate more accurate labels for the polysemous entities. The experimental results on two datasets, DNRTI and Bridges, indicate that SSNER outperforms both baseline and related models. In particular, SSNER achieves an F1-score of 96.02% on the Bridges dataset, exceeding the previous best model by approximately 1.46%. Full article

(This article belongs to the Section Computer)

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