Symmetry

24 pages, 5378 KiB

Open AccessArticle

Assessment of the Measured Mixing Time in a Water Model of Asymmetrical Gas-Stirred Ladle with a Low Gas Flowrate Part II: Effect of the Salt Solution Tracer Volume and Concentration

by Yansong Zhao, Xin Tao, Linbo Li, Zhijie Guo, Hongyu Qi, Jia Wang, Kun Yang, Wanming Lin, Jinping Fan and Chao Chen

Symmetry 2025, 17(5), 802; https://doi.org/10.3390/sym17050802 - 21 May 2025

Viewed by 415

Abstract

Mixing time, as a key parameter for evaluating ladle refining efficiency, has long attracted extensive attention from researchers. In typical experimental studies, salt solution tracers are introduced into ladle water models to assess the degree of mixing within the ladle. Previous studies have [...] Read more.

Mixing time, as a key parameter for evaluating ladle refining efficiency, has long attracted extensive attention from researchers. In typical experimental studies, salt solution tracers are introduced into ladle water models to assess the degree of mixing within the ladle. Previous studies have demonstrated that the volume of tracer can significantly influence the measured mixing time. However, the gas flow rates employed in these studies are generally relatively high, whereas, in industrial operations, especially during final composition adjustments, lower gas flow rates are often applied. To systematically investigate the effect of the salt solution tracer volume on the mixing efficiency in a ladle water model under asymmetrical gas stirring with a low gas flow rate, a 1:3-scaled water model was developed based on a 130-ton industrial ladle. The mixing behaviors corresponding to different tracer volumes were comprehensively analyzed. The results indicate that the relationship between tracer volume and mixing time is non-monotonic. As the tracer volume increases, the mixing time first decreases and then increases, reaching a minimum at 185 mL. When the tracer volume was small, the dimensionless concentration curves at Monitoring Point 4 exhibited two distinct patterns: A parabolic profile, which was when the tracer initially moved through the left and central regions and then slowly crossed the gas plume to reach the monitoring point. A sinusoidal profile, which was when the tracer predominantly circulated along the right side of the ladle. When the tracer volume exceeded 277 mL, the concentration curves at Monitoring Point 4 consistently exhibited a sinusoidal pattern. Compared with moderate gas flow conditions (8.3 L/min), the peak concentration at Monitoring Point 3 was significantly lower under a low gas flow (2.3 L/min), and the overall mixing time was longer, indicating reduced mixing efficiency. Based on the findings, a recommended tracer volume range of 185–277 mL is proposed for low gas flow conditions (2.3 L/min) to achieve accurate and efficient mixing time measurements with minimal disturbance to the flow field. It was also observed that when the tracer concentration was relatively low, the mixing behavior throughout the ladle became more uniform. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Fluid Mechanics)

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19 pages, 38532 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 - 21 May 2025

Viewed by 262

Abstract

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)

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17 pages, 1222 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

Viewed by 480

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)

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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

Viewed by 294

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

Viewed by 323

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

Viewed by 278

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

Viewed by 470

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, 356 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

Viewed by 193

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

Viewed by 507

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

Viewed by 396

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

Viewed by 326

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

Viewed by 314

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

Viewed by 255

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

Viewed by 967

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

Viewed by 321

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

Viewed by 442

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

Viewed by 410

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

Viewed by 256

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

Viewed by 392

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

Viewed by 482

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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17 pages, 1082 KiB

Open AccessArticle

FedOPCS: An Optimized Poisoning Countermeasure for Non-IID Federated Learning with Privacy-Preserving Stability

by Fenhua Bai, Yinqi Zhao, Tao Shen, Kai Zeng, Xiaohui Zhang and Chi Zhang

Symmetry 2025, 17(5), 782; https://doi.org/10.3390/sym17050782 - 19 May 2025

Viewed by 373

Abstract

Federated learning (FL), as a distributed machine learning framework, enables multiple participants to jointly train models without sharing data, thereby ensuring data privacy and security. However, FL systems still struggle to escape the typical poisoning threat launched by Byzantine nodes. The current defence [...] Read more.

Federated learning (FL), as a distributed machine learning framework, enables multiple participants to jointly train models without sharing data, thereby ensuring data privacy and security. However, FL systems still struggle to escape the typical poisoning threat launched by Byzantine nodes. The current defence measures almost all rely on the anomaly detection of local gradients in a plaintext state, which not only weakens privacy protection but also allows malicious clients to upload malicious ciphertext gradients once they are encrypted, which thus easily evade existing screenings. At the same time, mainstream aggregation algorithms are generally based on the premise that “each client’s data satisfy an independent and identically distributed (IID)”, which is obviously difficult to achieve in real scenarios where large-scale terminal devices hold their own data. Symmetry in data distribution and model updates across clients is crucial for achieving robust and fair aggregation, yet non-IID data and adversarial attacks disrupt this balance. To address these challenges, we propose FedOPCS, an optimized poisoning countermeasure for non-IID FL algorithms with privacy-preserving stability by introducing three key innovations: Conditional Generative Adversarial Network (CGAN)-based data augmentation with conditional variables to simulate global distribution, a dynamic weight adjustment mechanism with homomorphic encryption, and two-stage anomaly detection combining gradient analysis and model performance evaluation. Extensive experiments on MNIST and CIFAR-10 show that, in the model poisoning and mixed poisoning environments, FedOPCS outperforms the baseline methods by 11.4% and 4.7%, respectively, while maintaining the same efficiency as FedAvg. FedOPCS therefore offers a privacy-preserving, Byzantine-robust, and communication-efficient solution for future heterogeneous FL deployments. Full article

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19 pages, 289 KiB

Open AccessArticle

The Radial Symmetry and Monotonicity of Solutions of Fractional Parabolic Equations in the Unit Ball

by Xingyu Liu

Symmetry 2025, 17(5), 781; https://doi.org/10.3390/sym17050781 - 19 May 2025

Cited by 1 | Viewed by 283

Abstract

We use the method of moving planes to prove the radial symmetry and monotonicity of solutions of fractional parabolic equations in the unit ball. Since the fractional Laplacian operator is a linear operator, we investigate the maximal regularity of nonlocal parabolic fractional Laplacian [...] Read more.

We use the method of moving planes to prove the radial symmetry and monotonicity of solutions of fractional parabolic equations in the unit ball. Since the fractional Laplacian operator is a linear operator, we investigate the maximal regularity of nonlocal parabolic fractional Laplacian equations in the unit ball. The maximal regularity of nonlocal parabolic fractional Laplacian equations guarantees the existence of solutions in the unit ball. Based on these conditions, we first establish a maximum principle in a parabolic cylinder, and the principles provide a starting position to apply the method of moving planes. Then, we consider the fractional parabolic equations and derive the radial symmetry and monotonicity of solutions in the unit ball. Full article

(This article belongs to the Special Issue Symmetry and Applications of Differential Geometry to the Differential Equations of Mathematical Physics)

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31 pages, 6017 KiB

Open AccessArticle

LGNet: A Symmetric Dual-Branch Lightweight Model for Remote Sensing Scene Classification Based on Lie Group Feature Extraction and Cross-Attention Mechanism

by Haoyang Zeng, Shaopu Zou, Chunlian Yao and Chengjun Xu

Symmetry 2025, 17(5), 780; https://doi.org/10.3390/sym17050780 - 18 May 2025

Viewed by 454

Abstract

Existing remote sensing scene classification (RSSC) models mainly rely on convolutional neural networks (CNNs) to extract high-level features from remote sensing images, while neglecting the importance of low-level features. To address this, we propose a novel RSSC framework, LGNet, a lightweight model with [...] Read more.

Existing remote sensing scene classification (RSSC) models mainly rely on convolutional neural networks (CNNs) to extract high-level features from remote sensing images, while neglecting the importance of low-level features. To address this, we propose a novel RSSC framework, LGNet, a lightweight model with a symmetric dual-branch architecture that combines Lie group-based feature extraction with an innovative multi-dimensional cross-attention mechanism. By utilizing the Lie group feature covariance matrix in one branch, the model captures the low-level features of the image while extracting the high-level semantic information using CNNs in the parallel branch. The dynamic fusion of these multi-scale features using the attention mechanism optimizes the classification accuracy and computational efficiency. Extensive experiments on three standard datasets (AID, UC Merced, and NWPU-RESISC45) show that LGNet outperforms current state-of-the-art models, providing superior classification performance with significantly fewer parameters. Verified on publicly available challenging datasets, LGNet achieves a classification accuracy of 96.50% with 4.71M parameters on AID. Compared with other state-of-the-art models, it has certain advantages regarding classification accuracy and parameter count. These results highlight the efficiency and effectiveness of LGNet in complex remote sensing scenarios, making it a promising solution for large-scale high-resolution remote sensing images (HRSSI) tasks. Full article

(This article belongs to the Section Computer)

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21 pages, 11005 KiB

Open AccessArticle

Shape-Aware Dynamic Alignment Network for Oriented Object Detection in Aerial Images

by Linsen Zhu, Donglin Jing, Baiyu Lu, Dong Zheng, Shuaixing Ren and Zhili Chen

Symmetry 2025, 17(5), 779; https://doi.org/10.3390/sym17050779 - 17 May 2025

Viewed by 314

Abstract

The field of remote sensing target detection has experienced rapid development in recent years, demonstrating significant value in various applications. However, general detection algorithms still face many key challenges when dealing with directional target detection: firstly, conventional networks struggle to accurately represent features [...] Read more.

The field of remote sensing target detection has experienced rapid development in recent years, demonstrating significant value in various applications. However, general detection algorithms still face many key challenges when dealing with directional target detection: firstly, conventional networks struggle to accurately represent features of rotated targets, particularly in modeling the slender shape characteristics of high-aspect-ratio targets; secondly, the mismatch between the static label allocation strategy and the feature space of dynamic rotating targets leads to bias in training sample selection under extreme-aspect-ratio scenarios. To address these issues, this paper proposes a single-stage Shape-Aware Dynamic Alignment Network (SADA-Net) that collaboratively enhances detection accuracy through feature representation optimization and adaptive label matching. The network’s design philosophy demonstrates greater flexibility and complementarity than that of previous models. Specifically, a Dynamic Refined Rotated Convolution Module (DRRCM) is designed to achieve rotation-adaptive feature alignment. An Anchor-Refined Feature Alignment Module (ARFAM) is further constructed to correct feature-to-spatial misalignment. In addition, a Shape-Aware Quality Assessment (SAQA) strategy is proposed to optimize sample matching quality based on target shape information. Experiment results demonstrate that SADA-Net achieves excellent performance comparable to state-of-the-art methods on three widely used remote sensing datasets (i.e., HRSC2016, DOTA, and UCAS-AOD). Full article

(This article belongs to the Section Mathematics)

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26 pages, 6013 KiB

Open AccessArticle

Dynamic Responseof Complex Defect near Anisotropic Bi-Material Interface by Incident Out-Plane Wave

by Huanan Xu, Caizhu Yang, Yonghui Wang, Guoguan Lan and Faqiang Qiu

Symmetry 2025, 17(5), 778; https://doi.org/10.3390/sym17050778 - 17 May 2025

Viewed by 253

Abstract

The Dynamic response of two cavities, an elliptical inclusion and a linear crack near anisotropic bi-material interface, was explored analytically by incident out-plane waves in the current work. Firstly, the media is divided into two half spaces (an elastic anisotropic half space with [...] Read more.

The Dynamic response of two cavities, an elliptical inclusion and a linear crack near anisotropic bi-material interface, was explored analytically by incident out-plane waves in the current work. Firstly, the media is divided into two half spaces (an elastic anisotropic half space with a circular cavity and a linear crack, and an elastic isotropic half space containing an elliptical cavity and an elliptical inclusion). With the help of the image principle, the complex function method is then used to derive the wave fields in each half space. Combined with Green’s functions approach, the relevant Green’s functions developed in the “crack creation” and “conjunction of two half spaces” procedures are derived sequentially. Subsequently, based on the “conjunction” technique, undetermined anti-plane forces are applied to the horizontal surfaces of two half spaces to maintain the continuity criteria of the interface. A series of Fredholm integral equations isobtained and then solved by utilizing the direct discrete technique. Dynamic stress concentration of two elliptical cavities and an elliptical inclusion is mainly considered graphically to discuss the interaction between two half spaces. Finally, a parametric study on the dynamic stress concentration factor (DSCF) was given to show the influence of different parameters on the interaction. Full article

(This article belongs to the Section Mathematics)

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46 pages, 846 KiB

Open AccessArticle

Advancing Tensor Theories

by Pierros Ntelis

Symmetry 2025, 17(5), 777; https://doi.org/10.3390/sym17050777 - 16 May 2025

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Abstract

This paper advances the foundations of tensor and category theories by introducing novel concepts and rigorous constructive proofs. We generalize tensor theory through the innovative notion of a generalised tensor index, a versatile framework that unifies diverse tensor indices, and explore its transformation [...] Read more.

This paper advances the foundations of tensor and category theories by introducing novel concepts and rigorous constructive proofs. We generalize tensor theory through the innovative notion of a generalised tensor index, a versatile framework that unifies diverse tensor indices, and explore its transformation properties. Using fractional derivatives, we provide a geometrical interpretation of these generalised tensors, revealing new insights into its structure. Additionally, we forge a deep connection between tensor and category theories, integrating sets, tensors, categories, and functors with extensions like partial differentiation and integration. This synthesis yields original constructs—setorial tensors, categorial tensors, and functorial tensors—which open uncharted pathways in mathematical analysis. Our contributions not only extend prior research but also significantly enhance tensor theory, category theory, set theory, logic, topology, algebraic geometry, foundations, and philosophy, with potential applications spanning physics, geometry, and beyond. Full article

(This article belongs to the Special Issue Advances in Topology and Algebraic Geometry)

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21 pages, 911 KiB

Open AccessArticle

Competition in Bike-Sharing: Effects of Discount Incentives and Comfort Level

by Lishuang Bian, Qizhou Hu, Xiaoyu Wu, Xin Zhang and Minjia Tan

Symmetry 2025, 17(5), 776; https://doi.org/10.3390/sym17050776 - 16 May 2025

Viewed by 335

Abstract

This paper investigates the competition between two types of bike-sharing services, particularly at bus stops, subway stations, and residential areas. Two types of shared bicycle travel choice models are constructed. A shared bicycle operator attracts users by implementing discount incentives, and the comfort [...] Read more.

This paper investigates the competition between two types of bike-sharing services, particularly at bus stops, subway stations, and residential areas. Two types of shared bicycle travel choice models are constructed. A shared bicycle operator attracts users by implementing discount incentives, and the comfort levels of riding the two types of shared bicycles are different. The equilibrium fares, potential user demand, and operator profits under joint profit maximization, price competition, and potential user demand competition scenarios are derived, and the competitive results under the three scenarios are compared. The results show that, in the potential user demand competition, the difference in potential demand between the two operators is largest; in the joint profit maximization scenario involving shared bicycle operators, the difference in potential user demand is smallest. In all competitive scenarios, higher operating costs and costs in lowering comfort loss for the shared bicycle operators will increase fares; the substitution level between the two types of shared bicycles has a positive impact on potential user demand, and the higher the substitution level, the better the effect of discounts in attracting users. Full article

(This article belongs to the Section Engineering and Materials)

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22 pages, 3105 KiB

Open AccessArticle

High Impedance Fault Line Detection Based on Current Traveling Wave Spectrum Symmetry Driving for New Distribution Network

by Maner Xiao, Jupeng Zeng, Zehua Zhou, Qiming Zhang, Li Deng and Feiyu Peng

Symmetry 2025, 17(5), 775; https://doi.org/10.3390/sym17050775 - 16 May 2025

Viewed by 345

Abstract

Challenges are brought to high impedance fault (HIF) line selection in traditional distribution networks by the fault signals with short windows and weak characteristics provided by new energy power sources. A new method driven by the symmetry of current traveling wave spectrum is [...] Read more.

Challenges are brought to high impedance fault (HIF) line selection in traditional distribution networks by the fault signals with short windows and weak characteristics provided by new energy power sources. A new method driven by the symmetry of current traveling wave spectrum is proposed in this paper. Frequency-domain features are extracted by using Pisarenko spectral decomposition, and the differences in amplitude, frequency, and polarity between faulted and healthy feeders are analyzed. A similarity matrix is constructed with the help of Manhattan distance, and an improved density-based spatial clustering of application with noise (DBSCAN) clustering is adopted to achieve intelligent fault line selection. Experimental results show that compared with the steady state component method and the transient component method, the accuracy of this method is increased to 97.5%, with an improvement of more than 12.5%. Quantitative thresholds are replaced by qualitative spectrum differences, and this method is not affected by weak signals, thus solving the problem of threshold setting caused by the access of new energy. The accuracy of this method under different fault types, phases, and resistances is verified by simulation, ensuring easy engineering implementation. Full article

(This article belongs to the Section Engineering and Materials)

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19 pages, 933 KiB

Open AccessArticle

Revisiting the Contact Model with Diffusion Beyond the Conventional Methods

by Roberto da Silva, Eliseu Venites Filho, Henrique A. Fernandes and Paulo F. Gomes

Symmetry 2025, 17(5), 774; https://doi.org/10.3390/sym17050774 - 16 May 2025

Viewed by 230

Abstract

The contact process is a nonequilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the effects of particle mobility and diffusion on criticality have [...] Read more.

The contact process is a nonequilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the effects of particle mobility and diffusion on criticality have been preliminarily explored, they remain poorly understood in many aspects. In this work, we examine how the critical rate of the model varies with the probability of particle mobility. By analyzing different stochastic evolutions of the system, we employ two modern approaches: (1) Random Matrix Theory (RMT): By building on the success of RMT, particularly Wishart-like matrices, in studying statistical physics of systems with up-down symmetry via magnetization dynamics [R. da Silva, IJMPC 2022], we demonstrate its applicability to models with an absorbing state; (2) Optimized Temporal Power Laws: By using short-time dynamics, we optimize power laws derived from ensemble-averaged evolutions of the system. Both methods consistently reveal that the critical rate decays with mobility according to a simple Belehradek function. Additionally, a straightforward mean-field analysis supports the decay of the critical parameter with mobility, although it predicts a simpler linear dependence. We also demonstrate that the more sophisticated pair approximation mean-field model developed by ben-Avraham and Köhler aligns closely with the Belehradek function, precisely matching our lattice simulation results. Full article

(This article belongs to the Section Mathematics)

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17 pages, 8321 KiB

Open AccessArticle

Flexible Piezoresistive Sensor with High Stability Based on GO@PDMS-PU Porous Structure

by Qingfang Zhang, Yi Li, Xingyu Wang, Xiaoyu Zhang, Shuyi Liu, Hengyi Yuan, Xiaodong Yang, Da Li, Zeping Jin, Yujian Zhang, Yutong Liu and Zhengmai Bian

Symmetry 2025, 17(5), 773; https://doi.org/10.3390/sym17050773 - 16 May 2025

Viewed by 480

Abstract

In recent years, flexible piezoresistive sensors based on polydimethylsiloxane (PDMS) matrix materials have developed rapidly, showing broad application prospects in fields such as human motion monitoring, electronic skin, and intelligent robotics. However, achieving a balance between structural durability and fabrication simplicity remains challenging. [...] Read more.

In recent years, flexible piezoresistive sensors based on polydimethylsiloxane (PDMS) matrix materials have developed rapidly, showing broad application prospects in fields such as human motion monitoring, electronic skin, and intelligent robotics. However, achieving a balance between structural durability and fabrication simplicity remains challenging. Traditional methods for preparing PDMS flexible substrates with high porosity and high stability often require complex, costly processes. Breaking through the constraints of conventional material systems, this study innovatively combines the high elasticity of polydimethylsiloxane (PDMS) with the stochastically distributed porous topology of a sponge-derived biotemplate through biomimetic templating replication technology, fabricating a heterogeneous composite system with an architecturally asymmetric spatial network. After 5000 loading cycles, uncoated samples experienced a thickness reduction of 7.0 mm, while PDMS-coated samples showed minimal thickness changes (2.0–3.0 mm), positively correlated with curing agent content (5:1 to 20:1). The 5:1 ratio sample demonstrated exceptional mechanical stability. As evidenced, the PDMS film-encapsulated architecturally asymmetric spatial network demonstrates superior stress dissipation efficacy, effectively mitigating stress concentration phenomena inherent to symmetric configurations that induce matrix fracture, thereby achieving optimal mechanical stability. Compared to the pre-test resistance distribution of 10–248 Ω, after 5000 cyclic loading cycles, the uncoated samples exhibited a narrowed resistance range of 10–50 Ω, while PDMS-coated samples maintained a broader resistance range (10–240 Ω) as the curing agent ratio increased (from 20:1 to 5:1), demonstrating that increasing the curing agent ratio helps maintain conductive network stability. The 5:1 ratio sample displayed the lowest resistance variation rate attenuation—only 3% after 5000 cycles (vs. 80% for uncoated samples)—and consistently minimal attenuation at all stages, validating superior electrical stability. Under 0–6 kPa pressure, the 5:1 ratio device maintained a linear sensitivity of 0.157 kPa⁻¹, outperforming some existing works. Human motion monitoring experiments further confirmed its reliable signal output. Furthermore, the architecturally asymmetric spatial network of the device enables superior conformability to complex curvilinear geometries, leveraging its structural anisotropy to achieve seamless interfacial adaptation. By synergistically optimizing material composition and structural design, this study provides a novel technical method for developing highly durable flexible electronic devices. Full article

(This article belongs to the Section Engineering and Materials)

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