Journal Description
Symmetry
Symmetry
is an international, peer-reviewed, open access journal covering research on symmetry/asymmetry phenomena wherever they occur in all aspects of natural sciences. Symmetry is published monthly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), CAPlus / SciFinder, Inspec, Astrophysics Data System, and other databases.
- Journal Rank: JCR - Q2 (Multidisciplinary Sciences) / CiteScore - Q1 (General Mathematics); Q1 (Physics and Astronomy); Q1 (Computer Science)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 16.2 days after submission; acceptance to publication is undertaken in 3.5 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Testimonials: See what our editors and authors say about Symmetry.
Impact Factor:
2.7 (2022);
5-Year Impact Factor:
2.7 (2022)
Latest Articles
Symmetric U-Net Model Tuned by FOX Metaheuristic Algorithm for Global Prediction of High Aerosol Concentrations
Symmetry 2024, 16(5), 525; https://doi.org/10.3390/sym16050525 - 26 Apr 2024
Abstract
In this study, the idea of using a fully symmetric U-Net deep learning model for forecasting a segmented image of high global aerosol concentrations is implemented. As the forecast relies on historical data, the model used a sequence of the last eight segmented
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In this study, the idea of using a fully symmetric U-Net deep learning model for forecasting a segmented image of high global aerosol concentrations is implemented. As the forecast relies on historical data, the model used a sequence of the last eight segmented images to make the prediction. For this, the classic U-Net model was modified to use ConvLSTM2D layers with MaxPooling3D and UpSampling3D layers. In order to achieve complete symmetry, the output data are given in the form of a series of eight segmented images shifted by one image in the time sequence so that the last image actually represents the forecast of the next image of high aerosol concentrations. The proposed model structure was tuned by the new FOX metaheuristic algorithm. Based on our analysis, we found that this algorithm is suitable for tuning deep learning models considering their stochastic nature. It was also found that this algorithm spends the most time in areas close to the optimal value where there is a weaker linear correlation with the required metric and vice versa. Taking into account the characteristics of the used database, we concluded that the model is capable of generating adequate data and finding patterns in the time domain based on the ddc and dtc criteria. By comparing the achieved results of this model using the AUC-PR metric with the previous results of the ResNet3D-101 model with transfer learning, we concluded that the proposed symmetric U-Net model generates data better and is more capable of finding patterns in the time domain.
Full article
(This article belongs to the Special Issue Symmetry in Mathematical Models)
Open AccessArticle
Emergency Strategies for Gushing Water of Borehole and Numerical Simulation on Circular Diaphragm Wall Excavation with Ring-Beams
by
Yi-Hao Tsai, Chia-Feng Hsu, Kuo-Hsiang Ho and Shong-Loong Chen
Symmetry 2024, 16(5), 524; https://doi.org/10.3390/sym16050524 - 26 Apr 2024
Abstract
This study explores the underground structure and soil retention capabilities of a large-scale circular diaphragm wall (93.5 m in diameter) utilized as a soil retention strategy in deep excavation projects. The symmetrical design of the wall facilitates the use of an unsupported construction
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This study explores the underground structure and soil retention capabilities of a large-scale circular diaphragm wall (93.5 m in diameter) utilized as a soil retention strategy in deep excavation projects. The symmetrical design of the wall facilitates the use of an unsupported construction method, effectively resisting soil and water pressures. Using PLAXIS 3D 2017 software, this study simulates wall deformation and ground settlement, employing three different soil models to assess behavior under standard and emergency water gushing scenarios. The results show that the hardening soil (HS) model most accurately reflects the actual deformations and settlements. This study also finds that adjusting Young’s modulus for clay significantly impacts the accuracy of soil behavior predictions, while changes in the properties of sand have minimal effects. This research highlights the challenges posed by water gushing and suggests the need for model improvements to capture better the dynamic interactions between soil and water pressure, which could lead to wall tilting. Overall, this study offers innovative and practical value, providing crucial insights for designing and mitigating strategies in large-scale circular deep excavation projects, especially in regions such as Taiwan, where such constructions are rare and face unique challenges.
Full article
(This article belongs to the Special Issue Symmetry, Finite Element Analysis, and Intelligent Sensing and Monitoring: Applications in Engineering)
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Open AccessArticle
Utilizing Multiple Regression Analysis and Entropy Method for Automated Aesthetic Evaluation of Interface Layouts
by
Xinyue Wang, Mu Tong, Yukun Song and Chengqi Xue
Symmetry 2024, 16(5), 523; https://doi.org/10.3390/sym16050523 - 26 Apr 2024
Abstract
Aesthetic evaluation of increasingly complex and personalized human–computer interaction interfaces serves as a critical bridge between humans and machines, fundamentally enhancing various interaction factors. This study addresses the challenges in aesthetic evaluation by adjusting existing methodologies to incorporate seven aesthetic metrics: density, symmetry,
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Aesthetic evaluation of increasingly complex and personalized human–computer interaction interfaces serves as a critical bridge between humans and machines, fundamentally enhancing various interaction factors. This study addresses the challenges in aesthetic evaluation by adjusting existing methodologies to incorporate seven aesthetic metrics: density, symmetry, balance, proportionality, uniformity, simplicity, and sequence. These metrics were effectively integrated into a composite evaluation metric through both multiple regression analysis and entropy methods, with the efficacy of both fitting methods validated. Leveraging automatic segmentation and recognition technology for interface screenshots, this research enables rapid, automated acquisition of evaluations for the seven metrics and the composite index, leading to the development of a prototype system for interface layout aesthetic assessment. Aimed at reducing the time, manpower, and resources required for interface evaluation, this study enhances the universality, compatibility, and flexibility of layout assessments. It promotes integration at any stage of the design process, significantly benefiting lightweight rapid evaluation and iterative design cycles, thereby advancing the field of interface aesthetic evaluation.
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(This article belongs to the Section Computer)
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Open AccessArticle
A Deterministic Calibration Method for the Thermodynamic Model of Gas Turbines
by
Zhen Jiang, Xi Wang, Shubo Yang and Meiyin Zhu
Symmetry 2024, 16(5), 522; https://doi.org/10.3390/sym16050522 - 26 Apr 2024
Abstract
Performance adaptation is an effective way to improve the accuracy of gas turbine performance models. Although current performance adaptation methods, such as those using genetic algorithms or evolutionary computation to modify component characteristic maps, are useful for finding good solutions, they are essentially
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Performance adaptation is an effective way to improve the accuracy of gas turbine performance models. Although current performance adaptation methods, such as those using genetic algorithms or evolutionary computation to modify component characteristic maps, are useful for finding good solutions, they are essentially searching methods and suffer from long computation time. This paper presents a novel approach that can achieve good performance adaptation with low time complexity and without using any searching method. In this method, the actual component performance parameters are first estimated using engine measurements at different operating conditions. For each operating condition, some scaling factors are introduced and calculated to indicate the difference between the actual and predicted component performance parameters. Afterward, an interpolating algorithm is adopted to synthesize the scaling factors for modifying all major component maps. The adapted component maps are then able to make the engine model match all the gas path measurements and achieve the required accuracy of the engine performance model. The proposed approach has been tested with a model high-bypass turbofan engine using simulated data. The results show that the proposed performance adaptation approach can effectively improve the model’s accuracy. Specifically, the prediction errors can be reduced from about 9% to about 0.6%. In addition, this approach has much less computational complexity compared to other optimization-based counterparts.
Full article
(This article belongs to the Special Issue Carbon Neutrality and Symmetry in Power Engineering and Engineering Thermophysics)
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Open AccessArticle
Pinching Results for Doubly Warped Products’ Pointwise Bi-Slant Submanifolds in Locally Conformal Almost Cosymplectic Manifolds with a Quarter-Symmetric Connection
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Md Aquib, Ibrahim Al-Dayel, Mohd Aslam, Meraj Ali Khan and Mohammad Shuaib
Symmetry 2024, 16(5), 521; https://doi.org/10.3390/sym16050521 - 25 Apr 2024
Abstract
In this research paper, we establish geometric inequalities that characterize the relationship between the squared mean curvature and the warping functions of a doubly warped product pointwise bi-slant submanifold. Our investigation takes place in the context of locally conformal almost cosymplectic manifolds, which
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In this research paper, we establish geometric inequalities that characterize the relationship between the squared mean curvature and the warping functions of a doubly warped product pointwise bi-slant submanifold. Our investigation takes place in the context of locally conformal almost cosymplectic manifolds, which are equipped with a quarter-symmetric metric connection. We also consider the cases of equality in these inequalities. Additionally, we derive some geometric applications of our obtained results.
Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology III)
Open AccessArticle
Distilling Knowledge from a Transformer-Based Crack Segmentation Model to a Light-Weighted Symmetry Model with Mixed Loss Function for Portable Crack Detection Equipment
by
Xiaohu Zhang and Haifeng Huang
Symmetry 2024, 16(5), 520; https://doi.org/10.3390/sym16050520 - 25 Apr 2024
Abstract
The detection of cracks is extremely important for maintenance of concrete structures. Deep learning-based segmentation models have achieved high accuracy in crack segmentation. However, mainstream crack segmentation models have very high computational complexity, and therefore cannot be used in portable crack detection equipment.
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The detection of cracks is extremely important for maintenance of concrete structures. Deep learning-based segmentation models have achieved high accuracy in crack segmentation. However, mainstream crack segmentation models have very high computational complexity, and therefore cannot be used in portable crack detection equipment. To address this problem, a knowledge distilling structure is designed by us. In this structure, a large teacher model named TBUNet is proposed to transfer crack knowledge to a student model with symmetry structure named ULNet. In the TBUNet, stacked transformer modules are used to capture dependency relationships between different crack positions in feature maps and achieve contextual awareness. In the ULNet, only a tiny U-Net with light-weighted parameters is used to maintain very low computational complexity. In addition, a mixed loss function is designed to ensure detail and global features extracted by the teacher model are consistent with those of the student model. Our designed experiments demonstrate that the ULNet can achieve accuracies of 96.2%, 87.6%, and 75.3%, and recall of 97.1%, 88.5%, and 76.2% on the Cracktree200, CRACK500, and MICrack datasets, respectively, which is 4–6% higher than most crack segmentation models. However, the ULNet only has a model size of 1 M, which is suitable for use in portable crack detection equipment.
Full article
(This article belongs to the Section Engineering and Materials)
Open AccessArticle
Hawking Radiation as a Manifestation of Spontaneous Symmetry Breaking
by
Ivan Arraut
Symmetry 2024, 16(5), 519; https://doi.org/10.3390/sym16050519 - 25 Apr 2024
Abstract
We demonstrate that black hole evaporation can be modeled as a process where one symmetry of the system is spontaneously broken continuously. We then identify three free parameters of the system. The sign of one of the free parameters governs whether the particles
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We demonstrate that black hole evaporation can be modeled as a process where one symmetry of the system is spontaneously broken continuously. We then identify three free parameters of the system. The sign of one of the free parameters governs whether the particles emitted by the black hole are fermions or bosons. The present model explains why the black hole evaporation process is so universal. Interestingly, this universality emerges naturally inside certain modifications of gravity.
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(This article belongs to the Special Issue Topological Aspects of Quantum Gravity and Quantum Information Theory)
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Ordered Patterns of (3+1)-Dimensional Hadronic Gauged Solitons in the Low-Energy Limit of Quantum Chromodynamics at a Finite Baryon Density, Their Magnetic Fields and Novel BPS Bounds
by
Fabrizio Canfora, Evangelo Delgado and Luis Urrutia
Symmetry 2024, 16(5), 518; https://doi.org/10.3390/sym16050518 - 25 Apr 2024
Abstract
In this paper, we will review two analytical approaches to the construction of non-homogeneous Baryonic condensates in the low-energy limit of QCD in (3+1) dimensions. In both cases, the minimal coupling with the Maxwell gauge field can be taken
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In this paper, we will review two analytical approaches to the construction of non-homogeneous Baryonic condensates in the low-energy limit of QCD in (3+1) dimensions. In both cases, the minimal coupling with the Maxwell gauge field can be taken explicitly into account. The first approach (which is related to the generalization of the usual spherical hedgehog ansatz to situations without spherical symmetry at a finite Baryon density) allows for the construction of ordered arrays of Baryonic tubes and layers. When the minimal coupling of the Pions to the Maxwell gauge field is taken into account, one can show that the electromagnetic field generated by these inhomogeneous Baryonic condensates is of a force-free type (in which the electric and magnetic components have the same size). Thus, it is natural to wonder whether it is also possible to analytically describe magnetized hadronic condensates (namely, Hadronic distributions generating only a magnetic field). The idea of the second approach is to construct a novel BPS bound in the low-energy limit of QCD using the theory of the Hamilton–Jacobi equation. Such an approach allows us to derive a new topological bound which (unlike the usual one in the Skyrme model in terms of the Baryonic charge) can actually be saturated. The nicest example of this phenomenon is a BPS magnetized Baryonic layer. However, the topological charge appearing naturally in the BPS bound is a non-linear function of the Baryonic charge. Such an approach allows us to derive important physical quantities (which would be very difficult to compute with other methods), such as how much one should increase the magnetic flux in order to increase the Baryonic charge by one unit. The novel results of this work include an analysis of the extension of the Hamilton–Jacobi approach to the case in which Skyrme coupling is not negligible. We also discuss some relevant properties of the Dirac operator for quarks coupled to magnetized BPS layers.
Full article
(This article belongs to the Special Issue The Advances of Nonlinear Equations: Mathematical Models, Symmetry and Applications)
Open AccessArticle
Research on a Capsule Network Text Classification Method with a Self-Attention Mechanism
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Xiaodong Yu, Shun-Nain Luo, Yujia Wu, Zhufei Cai, Ta-Wen Kuan and Shih-Pang Tseng
Symmetry 2024, 16(5), 517; https://doi.org/10.3390/sym16050517 - 24 Apr 2024
Abstract
Convolutional neural networks (CNNs) need to replicate feature detectors when modeling spatial information, which reduces their efficiency. The number of replicated feature detectors or labeled training data required for such methods grows exponentially with the dimensionality of the data being used. On the
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Convolutional neural networks (CNNs) need to replicate feature detectors when modeling spatial information, which reduces their efficiency. The number of replicated feature detectors or labeled training data required for such methods grows exponentially with the dimensionality of the data being used. On the other hand, space-insensitive methods are difficult to encode and express effectively due to the limitation of their rich text structures. In response to the above problems, this paper proposes a capsule network (self-attention capsule network, or SA-CapsNet) with a self-attention mechanism for text classification tasks, wherein the capsule network itself, given the feature with the symmetry hint on two ends, acts as both encoder and decoder. In order to learn long-distance dependent features in sentences and encode text information more efficiently, SA-CapsNet maps the self-attention module to the feature extraction layer of the capsule network, thereby increasing its feature extraction ability and overcoming the limitations of convolutional neural networks. In addition, in this study, in order to improve the accuracy of the model, the capsule was improved by reducing its dimension and an intermediate layer was added, enabling the model to obtain more expressive instantiation features in a given sentence. Finally, experiments were carried out on three general datasets of different sizes, namely the IMDB, MPQA, and MR datasets. The accuracy of the model on these three datasets was 84.72%, 80.31%, and 75.38%, respectively. Furthermore, compared with the benchmark algorithm, the model’s performance on these datasets was promising, with an increase in accuracy of 1.08%, 0.39%, and 1.43%, respectively. This study focused on reducing the parameters of the model for various applications, such as edge and mobile applications. The experimental results show that the accuracy is still not apparently decreased by the reduced parameters. The experimental results therefore verify the effective performance of the proposed SA-CapsNet model.
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(This article belongs to the Special Issue Advances in Computer Vision, Pattern Recognition, Machine Learning and Symmetry)
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Algebraic Nexus of Fibonacci Forms and Two-Simplex Topology in Multicellular Morphogenesis
by
William E. Butler Hoyos, Héctor Andrade Loarca, Kristopher T. Kahle, Ziv Williams, Elizabeth G. Lamb, Julio Alcántara, Thomas Bernard Kinane and Luis J. Turcio Cuevas
Symmetry 2024, 16(5), 516; https://doi.org/10.3390/sym16050516 - 24 Apr 2024
Abstract
Background: Fibonacci patterns and tubular forms both arose early in the phylogeny of multicellular organisms. Tubular forms offer the advantage of a regulated internal milieu, and Fibonacci forms may offer packing efficiencies. The underlying mechanisms behind the cellular genesis of Fibonacci and tubular
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Background: Fibonacci patterns and tubular forms both arose early in the phylogeny of multicellular organisms. Tubular forms offer the advantage of a regulated internal milieu, and Fibonacci forms may offer packing efficiencies. The underlying mechanisms behind the cellular genesis of Fibonacci and tubular forms remain unknown. Methods: In a multicellular organism, cells adhere to form a macrostructure and to coordinate further replication. We propose and prove simple theorems connecting cell replication and adhesion to Fibonacci forms and simplicial topology. Results: We identify some cellular and molecular properties whereby the contact inhibition of replication by adhered cells may approximate Fibonacci growth patterns. We further identify how a component cellular multiplication step may generate a multicellular structure with some properties of a two-simplex. Tracking the homotopy of a two-simplex to a circle and to a tube, we identify some molecular and cellular growth properties consistent with the morphogenesis of tubes. We further find that circular and tubular cellular aggregates may be combinatorially favored in multicellular adhesion over flat shapes. Conclusions: We propose a correspondence between the cellular and molecular mechanisms that generate Fibonacci cell counts and those that enable tubular forms. This implies molecular and cellular arrangements that are candidates for experimental testing and may provide guidance for the synthetic biology of hollow morphologies.
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(This article belongs to the Special Issue Fibonacci and Lucas Numbers and the Golden Ratio in Physics and Biology)
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(Non-Symmetric) Yetter–Drinfel’d Module Category and Invariant Coinvariant Jacobians
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Zhongwei Wang and Yong Wang
Symmetry 2024, 16(5), 515; https://doi.org/10.3390/sym16050515 - 24 Apr 2024
Abstract
In this paper, we generalize the homomorphisms of modules over groups and Lie algebras as being morphisms in the category of (non-symmetric) Yetter–Drinfel’d modules. These module homomorphisms play a key role in the conjecture of Yau.
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(This article belongs to the Special Issue Symmetry/Asymmetry Study in Hopf-Type Algebras and Groups)
Open AccessArticle
YOLOv7-SN: Underwater Target Detection Algorithm Based on Improved YOLOv7
by
Ming Zhao, Huibo Zhou and Xue Li
Symmetry 2024, 16(5), 514; https://doi.org/10.3390/sym16050514 - 24 Apr 2024
Abstract
Exploring the ocean’s resources requires finding underwater objects, which is a challenging task due to blurry images and small, densely packed targets. To improve the accuracy of underwater target detection, we propose an enhanced version of the YOLOv7 network called YOLOv7-SN. Our goal
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Exploring the ocean’s resources requires finding underwater objects, which is a challenging task due to blurry images and small, densely packed targets. To improve the accuracy of underwater target detection, we propose an enhanced version of the YOLOv7 network called YOLOv7-SN. Our goal is to optimize the effectiveness and accuracy of underwater target detection by introducing a series of innovations. We incorporate the channel attention module SE into the network’s key part to improve the extraction of relevant features for underwater targets. We also introduce the RFE module with dilated convolution behind the backbone network to capture multi-scale information. Additionally, we use the Wasserstein distance as a new metric to replace the traditional loss function and address the challenge of small target detection. Finally, we employ probe heads carrying implicit knowledge to further enhance the model’s accuracy. These methods aim to optimize the efficacy of underwater target detection and improve its ability to deal with the complexity and challenges of underwater environments. We conducted experiments on the URPC2020, and RUIE datasets. The results show that the mean accuracy (mAP) is improved by 5.9% and 3.9%, respectively, compared to the baseline model.
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(This article belongs to the Special Issue Artificial Intelligence, Adaptation and Symmetry/Asymmetry)
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Pursuit and Evasion Linear Differential Game Problems with Generalized Integral Constraints
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Bashir Mai Umar, Jewaidu Rilwan, Maggie Aphane and Kanikar Muangchoo
Symmetry 2024, 16(5), 513; https://doi.org/10.3390/sym16050513 - 24 Apr 2024
Abstract
In this paper, we study pursuit and evasion differential game problems of one pursuer/one evader and many pursuers/one evader, respectively, in the space . In both problems, we obtain sufficient conditions that guarantee the completion of a pursuit and an evasion.
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In this paper, we study pursuit and evasion differential game problems of one pursuer/one evader and many pursuers/one evader, respectively, in the space . In both problems, we obtain sufficient conditions that guarantee the completion of a pursuit and an evasion. We construct the players’ optimal strategies in both problems, and we estimate the possible distance that an evader can preserve from pursuers. Lastly, we illustrate our results via some numerical examples.
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(This article belongs to the Special Issue Symmetry in Fractional Calculus: Advances and Applications)
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Image Enhancement Based on Dual-Branch Generative Adversarial Network Combining Spatial and Frequency Domain Information for Imbalanced Fault Diagnosis of Rolling Bearing
by
Yuguang Huang, Bin Wen, Weiqing Liao, Yahui Shan, Wenlong Fu and Renming Wang
Symmetry 2024, 16(5), 512; https://doi.org/10.3390/sym16050512 - 24 Apr 2024
Abstract
To address the problems of existing 2D image-based imbalanced fault diagnosis methods for rolling bearings, which generate images with inadequate texture details and color degradation, this paper proposes a novel image enhancement model based on a dual-branch generative adversarial network (GAN) combining spatial
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To address the problems of existing 2D image-based imbalanced fault diagnosis methods for rolling bearings, which generate images with inadequate texture details and color degradation, this paper proposes a novel image enhancement model based on a dual-branch generative adversarial network (GAN) combining spatial and frequency domain information for an imbalanced fault diagnosis of rolling bearing. Firstly, the original vibration signals are converted into 2D time–frequency (TF) images by a continuous wavelet transform, and a dual-branch GAN model with a symmetric structure is constructed. One branch utilizes an auxiliary classification GAN (ACGAN) to process the spatial information of the TF images, while the other employs a GAN with a frequency generator and a frequency discriminator to handle the frequency information of the input images after a fast Fourier transform. Then, a shuffle attention (SA) module based on an attention mechanism is integrated into the proposed model to improve the network’s expression ability and reduce the computational burden. Simultaneously, mean square error (MSE) is integrated into the loss functions of both generators to enhance the consistency of frequency information for the generated images. Additionally, a Wasserstein distance and gradient penalty are also incorporated into the losses of the two discriminators to prevent gradient vanishing and mode collapse. Under the supervision of the frequency WGAN-GP branch, an ACWGAN-GP can generate high-quality fault samples to balance the dataset. Finally, the balanced dataset is utilized to train the auxiliary classifier to achieve fault diagnosis. The effectiveness of the proposed method is validated by two rolling bearing datasets. When the imbalanced ratios of the four datasets are 0.5, 0.2, 0.1, and 0.05, respectively, their average classification accuracy reaches 99.35% on the CWRU bearing dataset. Meanwhile, the average classification accuracy reaches 96.62% on the MFS bearing dataset.
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(This article belongs to the Section Engineering and Materials)
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SwinDPSR: Dual-Path Face Super-Resolution Network Integrating Swin Transformer
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Xing Liu, Yan Li, Miao Gu, Hailong Zhang, Xiaoguang Zhang, Junzhu Wang, Xindong Lv and Hongxia Deng
Symmetry 2024, 16(5), 511; https://doi.org/10.3390/sym16050511 - 23 Apr 2024
Abstract
Whether to use face priors in the face super-resolution (FSR) methods is a symmetry problem.Various face priors are used to describe the overall and local face features, making the generation of super-resolution face images expensive and laborious. FSR methods that do not require
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Whether to use face priors in the face super-resolution (FSR) methods is a symmetry problem.Various face priors are used to describe the overall and local face features, making the generation of super-resolution face images expensive and laborious. FSR methods that do not require any prior information tend to focus too much on the local features of the face, ignoring the modeling of global information. To solve this problem, we propose a dual-path facial image super-resolution network (SwinDPSR) fused with Swin Transformer. The network does not require additional face priors, and it learns global face shape and local face components through two independent branches. In addition, the channel attention ECA module is used to aggregate the global and local face information in the above dual-path sub-networks, which can generate corresponding high-quality face images. The results of face super-resolution reconstruction experiments on public face datasets and a real-scene face dataset show that SwinDPSR is superior to previous advanced methods both in terms of visual effects and objective indicators. The reconstruction results are evaluated with four evaluation metrics: peak signal-to-noise ratio (PSNR), structural similarity (SSIM), learned perceptual image patch similarity (LPIPS), and mean perceptual score (MPS).
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(This article belongs to the Section Computer)
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On Maximum Guaranteed Payoff in a Fuzzy Matrix Decision-Making Problem with a Fuzzy Set of States
by
Svajone Bekesiene and Serhii Mashchenko
Symmetry 2024, 16(5), 510; https://doi.org/10.3390/sym16050510 - 23 Apr 2024
Abstract
The current study delves into a fuzzy matrix decision-making problem involving fuzzy sets of states. It establishes that a maximum guaranteed payoff constitutes a type-2 fuzzy set defined on the real line. Additionally, it provides the associated type-2 membership function. Moreover, the paper
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The current study delves into a fuzzy matrix decision-making problem involving fuzzy sets of states. It establishes that a maximum guaranteed payoff constitutes a type-2 fuzzy set defined on the real line. Additionally, it provides the associated type-2 membership function. Moreover, the paper illustrates that the maximum guaranteed payoff type-2 fuzzy set of the decision-making problem can be broken down, based on the secondary membership grades, into a finite collection of fuzzy numbers. Each of these fuzzy numbers represents the maximum guaranteed payoff of the corresponding decision-making problem with a crisp set of states. This set corresponds to a specific cut of the original fuzzy set of states. Some properties of the maximum guaranteed payoff type-2 fuzzy set are investigated, and illustrative examples are provided. Since the problem formulation is symmetrical with respect to alternatives and states of nature, the results obtained can be used in the case of a fuzzy set of alternatives.
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(This article belongs to the Special Issue Symmetry in Process Optimization)
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Construction of Ruled Surfaces from the W-Curves and Their Characterizations in
by
Samah Gaber, Adel H. Sorour and A. A. Abdel-Salam
Symmetry 2024, 16(5), 509; https://doi.org/10.3390/sym16050509 - 23 Apr 2024
Abstract
Ruled surfaces are considered one of the significant aspects of differential geometry. These surfaces are formed by the motion of a straight line called a generator, and every curve that intersects all the generators is called a directrix. In the present research paper,
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Ruled surfaces are considered one of the significant aspects of differential geometry. These surfaces are formed by the motion of a straight line called a generator, and every curve that intersects all the generators is called a directrix. In the present research paper, we explore a family of ruled surfaces constructed from circular helices (W-curve) using the Frenet frame in the Euclidean space . We derive the explicit formulas for the second mean curvature and second Gaussian curvature. We present some ruled surfaces, and we describe their properties. In addition, we determine the sufficient conditions for these surfaces to be minimal, flat, II-minimal, and II-flat. Also, we obtain sufficient conditions for the base curve for these ruled surfaces to be a geodesic curve, an asymptotic line, and a principal line. Furthermore, we present an application for a ruled surface whose base curve is a circular helix, we compute some quantities for this surface such as the mean curvature and Gaussian curvatures and we plot the ruled surface with its base curve, and at symmetric points and along a symmetry axis.
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(This article belongs to the Section Mathematics)
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Efficient Multistep Algorithms for First-Order IVPs with Oscillating Solutions: II Implicit and Predictor–Corrector Algorithms
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Theodore E. Simos
Symmetry 2024, 16(5), 508; https://doi.org/10.3390/sym16050508 - 23 Apr 2024
Abstract
This research introduces a fresh methodology for creating efficient numerical algorithms to solve first-order Initial Value Problems (IVPs). The study delves into the theoretical foundations of these methods and demonstrates their application to the Adams–Moulton technique in a five-step process. We focus on
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This research introduces a fresh methodology for creating efficient numerical algorithms to solve first-order Initial Value Problems (IVPs). The study delves into the theoretical foundations of these methods and demonstrates their application to the Adams–Moulton technique in a five-step process. We focus on developing amplification-fitted algorithms with minimal phase-lagor phase-lag equal to zero (phase-fitted). The request of amplification-fitted (zero dissipation) is to ensure behavior like symmetric multistep methods (symmetric multistep methods are methods with zero dissipation). Additionally, the stability of the innovative algorithms is examined. Comparisons between our new algorithm and traditional methods reveal its superior performance. Numerical tests corroborate that our approach is considerably more effective than standard methods for solving IVPs, especially those with oscillatory solutions.
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(This article belongs to the Section Mathematics)
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Extended Deep-Learning Network for Histopathological Image-Based Multiclass Breast Cancer Classification Using Residual Features
by
Hiren Mewada
Symmetry 2024, 16(5), 507; https://doi.org/10.3390/sym16050507 - 23 Apr 2024
Abstract
Autonomy of breast cancer classification is a challenging problem, and early diagnosis is highly important. Histopathology images provide microscopic-level details of tissue samples and play a crucial role in the accurate diagnosis and classification of breast cancer. Moreover, advancements in deep learning play
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Autonomy of breast cancer classification is a challenging problem, and early diagnosis is highly important. Histopathology images provide microscopic-level details of tissue samples and play a crucial role in the accurate diagnosis and classification of breast cancer. Moreover, advancements in deep learning play an essential role in early cancer diagnosis. However, existing techniques involve unique models for each classification based on the magnification factor and require training numerous models or using a hierarchical approach combining multiple models irrespective of the focus of the cell features. This may lead to lower performance for multiclass categorization. This paper adopts the DenseNet161 network by adding a learnable residual layer. The learnable residual layer enhances the features, providing low-level information. In addition, residual features are obtained from the convolution features of the preceding layer, which ensures that the future size is consistent with the number of channels in DenseNet’s layer. The concatenation of spatial features with residual features helps better learn texture classification without the need for an additional texture feature extraction module. The model was validated for both binary and multiclass categorization of malignant images. The proposed model’s classification accuracy ranges from 94.65% to 100% for binary and multiclass classification, and the error rate is 2.78%. Overall, the suggested model has the potential to improve the survival of breast cancer patients by allowing precise diagnosis and therapy.
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(This article belongs to the Special Issue Computational Intelligence and Soft Computing: Recent Applications—Second Volume)
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Open AccessArticle
Fixed Point Dynamics in a New Type of Contraction in b-Metric Spaces
by
María A. Navascués and Ram N. Mohapatra
Symmetry 2024, 16(4), 506; https://doi.org/10.3390/sym16040506 - 22 Apr 2024
Abstract
Since the topological properties of a b-metric space (which generalizes the concept of a metric space) seem sometimes counterintuitive due to the fact that the “open” balls may not be open sets, we review some aspects of these spaces concerning compactness, metrizability, continuity
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Since the topological properties of a b-metric space (which generalizes the concept of a metric space) seem sometimes counterintuitive due to the fact that the “open” balls may not be open sets, we review some aspects of these spaces concerning compactness, metrizability, continuity and fixed points. After doing so, we introduce new types of contractivities that extend the concept of Banach contraction. We study some of their properties, giving sufficient conditions for the existence of fixed points and common fixed points. Afterwards, we consider some iterative schemes in quasi-normed spaces for the approximation of these critical points, analyzing their convergence and stability. We apply these concepts to the resolution of a model of integral equation of Urysohn type. In the last part of the paper, we refine some results about partial contractivities in the case where the underlying set is a strong b-metric space, and we establish some relations between mutual weak contractions and quasi-contractions and the new type of contractivity.
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(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos II)
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