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
Numerical Investigations on the Jet Dynamics during Cavitation Bubble Collapsing between Dual Particles
Symmetry 2024, 16(5), 535; https://doi.org/10.3390/sym16050535 (registering DOI) - 29 Apr 2024
Abstract
The jet dynamics during cavitation bubble collapsing between unequal-sized dual particles are investigated utilizing a numerical model that combines the finite volume approach alongside the volume of fluid approach. The model incorporates the compressibility of the two-phase fluid and accounts for mass and
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The jet dynamics during cavitation bubble collapsing between unequal-sized dual particles are investigated utilizing a numerical model that combines the finite volume approach alongside the volume of fluid approach. The model incorporates the compressibility of the two-phase fluid and accounts for mass and heat transfer between two phases. The computational model utilizes an axisymmetric model, where the axis of symmetry is defined as the line that connects the centers of the particles and the bubble. A comprehensive analysis is presented on the influence of the particle radius and bubble–particle distance on the jet behavior. Furthermore, the variations of surface pressure on the particles induced by jet impingement are quantitatively analyzed. Four distinct jet behaviors are categorized, depending on the formation mechanism, as well as the number and the direction of the jets. For case 1, the bubble produces a single jet directed toward a small particle; for case 2, the bubble fragments produces double jets receding from each other; for case 3, the bubble produces double jets approaching each other; and for case 4, the bubble produces a single jet directed toward a large particle. The pressure perturbations induced by jet impingement upon the particles exceed those caused by shock wave impacts. The larger the bubble volume at the moment of jet formation, the longer the duration of the pressure variation caused by the jet impinging on the particles.
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(This article belongs to the Section Physics)
Open AccessArticle
Coplanar Waveguide (CPW) Loaded with Symmetric Circular and Polygonal Split-Ring Resonator (SRR) Shapes
by
Supakorn Harnsoongnoen, Saksun Srisai and Pongsathorn Kongkeaw
Symmetry 2024, 16(5), 534; https://doi.org/10.3390/sym16050534 (registering DOI) - 29 Apr 2024
Abstract
This paper investigates the performance of coplanar waveguide (CPW) structures loaded with symmetric circular and polygonal split-ring resonators (SRRs) for microwave and RF applications, leveraging their unique electromagnetic properties. These properties make them suitable for metamaterials, sensors, filters, resonators, antennas, and communication systems.
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This paper investigates the performance of coplanar waveguide (CPW) structures loaded with symmetric circular and polygonal split-ring resonators (SRRs) for microwave and RF applications, leveraging their unique electromagnetic properties. These properties make them suitable for metamaterials, sensors, filters, resonators, antennas, and communication systems. The objectives of this study are to analyze the impact of different SRR shapes on the transmission characteristics of CPWs and to explore their potential for realizing compact and efficient microwave components. The CPW-SRR structures are fabricated on a dielectric substrate, and their transmission properties and spectrogram are experimentally characterized in the frequency range of 4 GHz to 10 GHz with the rotation angles of the SRR gap. The simulation results demonstrate that the resonant frequencies and magnitude of the transmission coefficient of the CPW-SRR structures are influenced by the geometry of the SRR shapes and the rotation angles of the SRR gap, with certain shapes exhibiting enhanced performance characteristics compared to others. Moreover, the symmetric circular and polygonal SRRs offer design flexibility and enable the realization of miniaturized microwave components with improved performance metrics. Overall, this study provides valuable insights into the design and optimization of CPW-based microwave circuits utilizing symmetric SRR shapes, paving the way for advancements in the miniaturization and integration of RF systems.
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(This article belongs to the Section Engineering and Materials)
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Open AccessArticle
A Hybrid Swarming Algorithm for Adaptive Enhancement of Low-Illumination Images
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Yi Zhang, Xinyu Liu and Yang Lv
Symmetry 2024, 16(5), 533; https://doi.org/10.3390/sym16050533 (registering DOI) - 29 Apr 2024
Abstract
This paper presents an improved swarming algorithm that enhances low-illumination images. The algorithm combines a hybrid Harris Eagle algorithm with double gamma (IHHO-BIGA) and incomplete beta (IHHO-NBeta) functions. This paper integrates the concept of symmetry into the improvement steps of the image adaptive
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This paper presents an improved swarming algorithm that enhances low-illumination images. The algorithm combines a hybrid Harris Eagle algorithm with double gamma (IHHO-BIGA) and incomplete beta (IHHO-NBeta) functions. This paper integrates the concept of symmetry into the improvement steps of the image adaptive enhancement algorithm. The enhanced algorithm integrates chaotic mapping for population initialization, a nonlinear formula for prey energy calculation, spiral motion from the black widow algorithm for global search enhancement, a nonlinear inertia weight factor inspired by particle swarm optimization, and a modified Levy flight strategy to prevent premature convergence to local optima. This paper compares the algorithm’s performance with other swarm intelligence algorithms using commonly used test functions. The algorithm’s performance is compared against several emerging swarm intelligence algorithms using commonly used test functions, with results demonstrating its superior performance. The improved Harris Eagle algorithm is then applied for image adaptive enhancement, and its effectiveness is evaluated on five low-illumination images from the LOL dataset. The proposed method is compared to three common image enhancement techniques and the IHHO-BIGA and IHHO-NBeta methods. The experimental results reveal that the proposed approach achieves optimal visual perception and enhanced image evaluation metrics, outperforming the existing techniques. Notably, the standard deviation data of the first image show that the IHHO-NBeta method enhances the image by 8.26%, 120.91%, 126.85%, and 164.02% compared with IHHO-BIGA, the single-scale Retinex enhancement method, the homomorphic filtering method, and the limited contrast adaptive histogram equalization method, respectively. The processing time of the improved method is also better than the previous heuristic algorithm.
Full article
(This article belongs to the Special Issue Asymmetric and Symmetric Study on Image Processing and Statistical Data Analysis)
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Open AccessArticle
Product Quality Anomaly Recognition and Diagnosis Based on DRSN-SVM-SHAP
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Yong Liu, Zhuo Wang, Dong Zhang, Mingshun Yang, Xinqin Gao and Li Ba
Symmetry 2024, 16(5), 532; https://doi.org/10.3390/sym16050532 (registering DOI) - 29 Apr 2024
Abstract
Conventional quality control methodologies are inadequate for fully elucidating the aberrant patterns of product quality. A multitude of factors influence product quality, yet the limited number of controlled quality characteristics is insufficient for accurately diagnosing quality abnormalities. Additionally, there are asymmetries in data
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Conventional quality control methodologies are inadequate for fully elucidating the aberrant patterns of product quality. A multitude of factors influence product quality, yet the limited number of controlled quality characteristics is insufficient for accurately diagnosing quality abnormalities. Additionally, there are asymmetries in data collection, data pre-processing, and model interpretation. In this context, a quality anomaly recognition and diagnosis model for the complex product manufacturing process is constructed based on a deep residual network, support vector machine (SVM), and Shapley additive explanation (SHAP). Given the numerous complex product quality characteristic indexes and unpredictable accidental factors in the production process, it is necessary to mine the deep relationship between quality characteristic data and quality state. This mining is achieved by utilizing the strong feature extraction ability of the deep residual shrinkage network (DRSN) through self-learning. The symmetry of the data within the model has also been taken into account to ensure a more balanced and comprehensive analysis. The excellent binary classification ability of the support vector machine is combined with the DRSN to identify the quality anomaly state. The SHAP interpretable model is employed to diagnose the quality anomaly problem of a single product and to identify and diagnose quality anomalies in the manufacturing process of complex products. The effectiveness of the model is validated through case analysis. The accuracy of the DRSN-SVM quality anomaly recognition model reaches 99%, as demonstrated by example analysis, and the model exhibits faster convergence and significantly higher accuracy compared with the naive Bayesian model classification and support vector machine classification models.
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(This article belongs to the Topic Predictive Analytics and Fault Diagnosis of Machines with Machine Learning Techniques)
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Open AccessArticle
Attached Flows for Reaction–Diffusion Processes Described by a Generalized Dodd–Bullough–Mikhailov Equation
by
Carmen Ionescu and Iulian Petrisor
Symmetry 2024, 16(5), 531; https://doi.org/10.3390/sym16050531 (registering DOI) - 28 Apr 2024
Abstract
This paper uses the attached flow method for solving nonlinear second-order differential equations of the reaction–diffusion type. The key steps of the method consist of the following: (i) reducing the differentiability order by defining the first derivative of the variable as a new
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This paper uses the attached flow method for solving nonlinear second-order differential equations of the reaction–diffusion type. The key steps of the method consist of the following: (i) reducing the differentiability order by defining the first derivative of the variable as a new variable called the flow and (ii) a forced decomposition of the derivative-free term so that the flow appears explicitly in it. The resulting reduced equation is solved using specific balancing rules. Only step (i) would lead to an Abel-type equation with complicated integral solutions. Completed with (ii) and with the graduation procedure, the attached flow method used in the paper, without requiring such a great effort, allows for the obtaining of accurate analytical solutions. The method is applied here to a subclass of reaction–diffusion equations, the generalized Dodd–Bulough–Mikhailov equation, which includes a translation of the variable and nonlinearities up to order five. The equation is solved for each order of nonlinearity, and the solutions are discussed following the values of the parameters involved in the equation.
Full article
(This article belongs to the Topic Nonlinear Phenomena, Chaos, Control and Applications to Engineering and Science and Experimental Aspects of Complex Systems)
Open AccessArticle
Second Hankel Determinant and Fekete–Szegö Problem for a New Class of Bi-Univalent Functions Involving Euler Polynomials
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Semh Kadhim Gebur and Waggas Galib Atshan
Symmetry 2024, 16(5), 530; https://doi.org/10.3390/sym16050530 (registering DOI) - 28 Apr 2024
Abstract
Orthogonal polynomials have been widely employed by renowned authors within the context of geometric function theory. This study is driven by prior research and aims to address the —Fekete-Szegö problem. Additionally, we provide bound estimates for the coefficients and an upper bound estimate
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Orthogonal polynomials have been widely employed by renowned authors within the context of geometric function theory. This study is driven by prior research and aims to address the —Fekete-Szegö problem. Additionally, we provide bound estimates for the coefficients and an upper bound estimate for the second Hankel determinant for functions belonging to the category of analytical and bi-univalent functions. This investigation incorporates the utilization of Euler polynomials.
Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions II)
Open AccessArticle
Flexible Techniques to Detect Typical Hidden Errors in Large Longitudinal Datasets
by
Renato Bruni, Cinzia Daraio and Simone Di Leo
Symmetry 2024, 16(5), 529; https://doi.org/10.3390/sym16050529 (registering DOI) - 28 Apr 2024
Abstract
The increasing availability of longitudinal data (repeated numerical observations of the same units at different times) requires the development of flexible techniques to automatically detect errors in such data. Besides standard types of errors, which can be treated with generic error correction techniques,
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The increasing availability of longitudinal data (repeated numerical observations of the same units at different times) requires the development of flexible techniques to automatically detect errors in such data. Besides standard types of errors, which can be treated with generic error correction techniques, large longitudinal datasets may present specific problems not easily traceable by the generic techniques. In particular, after applying those generic techniques, time series in the data may contain trends, natural fluctuations and possible surviving errors. To study the data evolution, one main issue is distinguishing those elusive errors from the rest, which should be kept as they are and not flattened or altered. This work responds to this need by identifying some types of elusive errors and by proposing a statistical-mathematical approach to capture their complexity that can be applied after the above generic techniques. The proposed approach is based on a system of indicators and works at the formal level by studying the differences between consecutive values of data series and the symmetries and asymmetries of these differences. It operates regardless of the specific meaning of the data and is thus applicable in a variety of contexts. We implement this approach in a relevant database of European Higher Education institutions (ETER) by analyzing two key variables: “Total academic staff” and “Total number of enrolled students”, which are two of the most important variables, often used in empirical analysis as a proxy for size, and are considered by policymakers at the European level. The results are very promising.
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(This article belongs to the Topic Decision-Making and Data Mining for Sustainable Computing)
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In Pursuit of BRST Symmetry and Observables in 4D Topological Gauge-Affine Gravity
by
Oussama Abdelghafour Belarbi and Ahmed Meziane
Symmetry 2024, 16(5), 528; https://doi.org/10.3390/sym16050528 (registering DOI) - 28 Apr 2024
Abstract
The realization of a BRST cohomology of the 4D topological gauge-affine gravity is established in terms of a superconnection formalism. The identification of fields in the quantized theory occurs directly as is usual in terms of superconnection and its supercurvature components with the
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The realization of a BRST cohomology of the 4D topological gauge-affine gravity is established in terms of a superconnection formalism. The identification of fields in the quantized theory occurs directly as is usual in terms of superconnection and its supercurvature components with the double covering of the general affine group . Then, by means of an appropriate decomposition of the metalinear double-covering group with respect to the general linear double-covering group , one can easily obtain the enlargements of the fields while remaining consistent with the BRST algebra. This leads to the descent equations, allowing us to build the observables of the theory by means of the BRST algebra constructed using a algebra-valued superconnection. In particular, we discuss the construction of topological invariants with torsion.
Full article
(This article belongs to the Special Issue Symmetries in Gravity Research: Classical and Quantum)
Open AccessArticle
On the Unified Concept of Generalizations of Λ-Sets
by
Emilia Przemska
Symmetry 2024, 16(5), 527; https://doi.org/10.3390/sym16050527 (registering DOI) - 27 Apr 2024
Abstract
In this paper, we propose a unified concept encompassing generalizations of two types of families defined based on Levine’s notions of generalized closed sets and Maki’s sets. The methods used in this investigation are described in my previous work, where a unified
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In this paper, we propose a unified concept encompassing generalizations of two types of families defined based on Levine’s notions of generalized closed sets and Maki’s sets. The methods used in this investigation are described in my previous work, where a unified concept of general closedness is presented. From a methodology point of view, the present concept is symmetric to the previous. In generalizing open subsets, one can use the two methods. According to the first one, the family of Levine’s generalization is used as some base to build the family of closed subsets of the new topology. In the second method, the family of open subsets is extended, in the same way, as the family of closed subsets in the classic Levine’s method. The results obtained in this general conception easily extend and imply well-known theorems of this area of investigation. In the literature on this issue, many versions of generalizations of -sets have been investigated. The tools used in this paper enabled us to prove that there exist at most 10 generalizations of these types, and we show the relationships between them in the graph. As a result, it turns out that some generalizations investigated in the literature are trivial.
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(This article belongs to the Section Mathematics)
Open AccessArticle
Analysis of the Surrounding Rock Full-Displacement Variation in Large-Span Mudstone Highway Tunnels
by
Dechao Chi, Yanbin Luo, Chengwei Chen, Shengqing Wang, Yunfei Wu and Yuhang Hu
Symmetry 2024, 16(5), 526; https://doi.org/10.3390/sym16050526 (registering DOI) - 27 Apr 2024
Abstract
Due to the increasing development of highway reconstruction and expansion projects in China, many large-span highway tunnels are being constructed near existing highway tunnels. Tunneling underneath will inevitably cause variation in the surrounding rock displacement and may even lead to collapse. In this
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Due to the increasing development of highway reconstruction and expansion projects in China, many large-span highway tunnels are being constructed near existing highway tunnels. Tunneling underneath will inevitably cause variation in the surrounding rock displacement and may even lead to collapse. In this study, based on an analysis of extensive field monitoring data from the Gucheng tunnel, the variation law for the surrounding rock full-displacement and the influence of the tunnel-face spatial effect in a large-span mudstone tunnel are analyzed. The change in the full displacement experienced the following sequence: slow pre-displacement growth → rapid increase → slow increase → gradual stability. The displacement released by the excavation of the tunnel construction accounts for 40~60% of the total displacement, and the closer to the excavation contour, the more obvious the displacement release. The final convergence value of vertical displacement is obtained by hyperbolic function regression prediction analysis. Based on this value, Lee and Hoek equations are used for parameter analysis and field-data fitting. It is concluded that the larger the proportion of the early displacement of the surrounding rock before construction to the total displacement, the smaller the influence of the tunnel-face spatial effect on the surrounding rock. The numerical simulation results are compared with actual monitoring results, and good agreement is observed. The larger the burial depth of the tunnel, the smaller the influence range in the tunnel-face spatial effect, and the more concentrated the displacement release. The variation law and the influential range for the surrounding rock full-displacement described in this paper can provide a reference for predicting and controlling the deformation during the construction of future large-span mudstone tunnels.
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(This article belongs to the Section Engineering and Materials)
Open AccessArticle
Symmetric U-Net Model Tuned by FOX Metaheuristic Algorithm for Global Prediction of High Aerosol Concentrations
by
Dušan P. Nikezić, Dušan S. Radivojević, Nikola S. Mirkov, Ivan M. Lazović and Tatjana A. Miljojčić
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.
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(This article belongs to the Special Issue Symmetry in Mathematical Models)
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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.
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(This article belongs to the Special Issue Symmetry, Finite Element Analysis, and Intelligent Sensing and Monitoring: Applications in Engineering)
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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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A Deterministic Calibration Method for the Thermodynamic Model of Gas Turbines
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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.
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(This article belongs to the Special Issue Carbon Neutrality and Symmetry in Power Engineering and Engineering Thermophysics)
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Pinching Results for Doubly Warped Products’ Pointwise Bi-Slant Submanifolds in Locally Conformal Almost Cosymplectic Manifolds with a Quarter-Symmetric Connection
by
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.
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(This article belongs to the Section Engineering and Materials)
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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.
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(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
by
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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Open AccessArticle
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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