Symmetry

17 pages, 6843 KiB

Open AccessArticle

Optimal Flexibility Dispatching of Multi-Pumped Hydro Storage Stations Considering the Uncertainty of Renewable Energy

by Xinyi Chen, Pan Wu, Hongyu He, Bingbing Song, Kangping Qin, Xiaobi Teng, Fan Yang and Dongdong Li

Symmetry 2024, 16(10), 1404; https://doi.org/10.3390/sym16101404 - 21 Oct 2024

Viewed by 577

Abstract

With the continuous increase in the penetration rate of renewable energy, the randomness and flexibility demand in the power system continues to increase. The main grid side of the power system vigorously develops pumped hydro storage (PHS) resources. However, the current PHS station [...] Read more.

With the continuous increase in the penetration rate of renewable energy, the randomness and flexibility demand in the power system continues to increase. The main grid side of the power system vigorously develops pumped hydro storage (PHS) resources. However, the current PHS station scheduling method of a fixed time period and fixed power has lost a certain flexibility supply. In this paper, an optimal dispatching model of multi-pumped hydro storage stations is proposed to supply flexibility for different regions of the state grid in east China. Firstly, the credible predictable power (CPP) of renewable energy is calculated and the definition of flexibility demand of a power system is given. The calculation model for flexibility demand is established. Secondly, considering the regional allocation constraint in the state grid in east China, a non-centralized model of multi-PHS within the dispatch scope is established. In the model, the constraints of storage capacity of different hydropower conversion coefficients of each PHS station is considered. The flexibility supply model of PHS stations to each region of the state grid in east China is established to realize reasonable flexibility allocation. Then, by combining the PHS station models and the flexibility demand calculation model, the optimal dispatching model for the flexibility supply of multi-PHS stations is established. Finally, based on the network dispatching example, the effectiveness and superiority of the proposed strategy are verified by a case study. Full article

(This article belongs to the Special Issue New Power System and Symmetry)

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18 pages, 417 KiB

Open AccessArticle

The Connections Between Attribute-Induced and Object-Induced Decision Rules in Incomplete Formal Contexts

by Hongwei Wang, Huilai Zhi, Yinan Li, Daxin Zhu and Jianbing Xiahou

Symmetry 2024, 16(10), 1403; https://doi.org/10.3390/sym16101403 - 21 Oct 2024

Viewed by 913

Abstract

For a given incomplete context, object-induced approximate concepts have been defined, and this type of approximate concept can induce a type of decision rule. Based on the duality principle, another set of approximate concepts can be defined from the perspective of attributes, i.e., [...] Read more.

For a given incomplete context, object-induced approximate concepts have been defined, and this type of approximate concept can induce a type of decision rule. Based on the duality principle, another set of approximate concepts can be defined from the perspective of attributes, i.e., attribute-induced approximate concepts. Although object induced approximate concepts and attribute induced approximate concepts are symmetrical by duality principle, their induced decision rules exhibit different properties and the connections between attribute induced decision rules and object induced decision rules in incomplete formal contexts are not clear. To this end, a type of attribute-induced approximate concept and a method of extracting attribute-induced decision rules are presented. More importantly, it is revealed that given a type of decision rules, there must be corresponding decision rules of the other type, and both of them can provide some useful information, but they are not equivalent to each other. In other words, each type of decision rule can provide some unique and irreplaceable information. Full article

(This article belongs to the Topic Mathematical Modeling of Complex Granular Systems)

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30 pages, 10171 KiB

Open AccessArticle

Photoacoustic Waveform Design for Optimal Parameter Estimation Based on Maximum Mutual Information

by Zuwen Sun and Natalie Baddour

Symmetry 2024, 16(10), 1402; https://doi.org/10.3390/sym16101402 - 21 Oct 2024

Viewed by 969

Abstract

Waveform design is a potentially significant approach to improve the performance of an imaging or detection system. Photoacoustic imaging is a rapidly developing field in recent years; however, photoacoustic waveform design has not been extensively investigated. This paper considers the problem of photoacoustic [...] Read more.

Waveform design is a potentially significant approach to improve the performance of an imaging or detection system. Photoacoustic imaging is a rapidly developing field in recent years; however, photoacoustic waveform design has not been extensively investigated. This paper considers the problem of photoacoustic waveform design for parameter estimation under constraints on input energy. The use of information theory is exploited to formulate and solve this optimal waveform design problem. The approach yields the optimal waveform power spectral density. Direct inverse Fourier transform of the optimal waveform frequency spectrum amplitude is proposed to obtain a real waveform in the time domain. Absorbers are assumed to be stochastic absorber ensembles with uncertain duration and location parameters. Simulation results show the relationship between absorber parameter distribution and the characteristics of optimal waveforms. Comparison of optimal waveforms for estimation, optimal waveforms for detection (signal-to-noise ratio) and other commonly used waveforms are also discussed. The symmetry properties of the forward and inverse Fourier Transforms are used to analyze the time and frequency properties and provide a heuristic view of how different goals affect the choice of waveform. Full article

(This article belongs to the Special Issue Feature Papers in Section "Engineering and Materials" 2024)

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18 pages, 285 KiB

Open AccessArticle

Chen-like Inequalities for Submanifolds in Kähler Manifolds Admitting Semi-Symmetric Non-Metric Connections

by Ion Mihai and Andreea Olteanu

Symmetry 2024, 16(10), 1401; https://doi.org/10.3390/sym16101401 - 21 Oct 2024

Viewed by 859

Abstract

The geometry of submanifolds in Kähler manifolds is an important research topic. In the present paper, we study submanifolds in complex space forms admitting a semi-symmetric non-metric connection. We prove the Chen–Ricci inequality, Chen basic inequality, and a generalized Euler inequality for such [...] Read more.

The geometry of submanifolds in Kähler manifolds is an important research topic. In the present paper, we study submanifolds in complex space forms admitting a semi-symmetric non-metric connection. We prove the Chen–Ricci inequality, Chen basic inequality, and a generalized Euler inequality for such submanifolds. These inequalities provide estimations of the mean curvature (the main extrinsic invariants) in terms of intrinsic invariants: Ricci curvature, the Chen invariant, and scalar curvature. In the proofs, we use the sectional curvature of a semi-symmetric, non-metric connection recently defined by A. Mihai and the first author, as well as its properties. Full article

(This article belongs to the Special Issue Symmetry in Metric Spaces and Topology)

18 pages, 10716 KiB

Open AccessArticle

A Novel FBG Placement Optimization Method for Tunnel Monitoring Based on WOA and Deep Q-Network

by Jiguo Liu, Ming Song, Heng Shu, Wenbo Peng, Longhai Wei and Kai Wang

Symmetry 2024, 16(10), 1400; https://doi.org/10.3390/sym16101400 - 21 Oct 2024

Viewed by 636

Abstract

By employing the whale optimization algorithm’s (WOA) capability to reduce the probability of being stuck in a locally optimal solution, this study proposed an improved WOA-DQN algorithm based on the Deep Q-Network algorithm (DQN). Firstly, the mathematical model of Fiber Bragg Grating (FBG) [...] Read more.

By employing the whale optimization algorithm’s (WOA) capability to reduce the probability of being stuck in a locally optimal solution, this study proposed an improved WOA-DQN algorithm based on the Deep Q-Network algorithm (DQN). Firstly, the mathematical model of Fiber Bragg Grating (FBG) sensor placement was established to calculate the reward of DQN. Secondly, the effectiveness and applicability of WOA-DQN were validated through experiments in nine cases. It indicated that the algorithm is far superior to other methods (Noisy DQN, Prioritized DQN, DQN, WOA), especially with the learning rate of 0.001, the initial noise 0.4, the hidden layer 3–512, and the updated frequency of 20. Finally, the FBG sensors were placed at [0°, 27°, 30°, 47°, 51°, 111°, 126°, 219°, 221°, 289°] to detect the accurate deformation of the tunnel with the maximum error 8.66 mm, which is better than the traditional placement. In conclusion, the algorithm provides a theoretical foundation for sensor placement and improves monitoring accuracy. It further shows great promise for deformation monitoring in tunnels. Full article

(This article belongs to the Section Computer)

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15 pages, 343 KiB

Open AccessArticle

New Results Regarding Positive Periodic Solutions of Generalized Leslie–Gower-Type Population Models

by Axiu Shu, Xiaoliang Li and Bo Du

Symmetry 2024, 16(10), 1399; https://doi.org/10.3390/sym16101399 - 21 Oct 2024

Viewed by 849

Abstract

In this paper, we focus on the existence of positive periodic solutions of generalized Leslie–Gower-type population models. Using the topological degree, we provide sufficient conditions to demonstrate the existence of positive periodic solutions to the considered models. It is interesting that the positive [...] Read more.

In this paper, we focus on the existence of positive periodic solutions of generalized Leslie–Gower-type population models. Using the topological degree, we provide sufficient conditions to demonstrate the existence of positive periodic solutions to the considered models. It is interesting that the positive periodic solutions in this paper are general positive functions, not e exponential functions, which generalizes and improves the existing results. We note that due to the symmetrical property of periodic solutions, the results of this paper provide a deeper understanding of the periodic behavior of biological populations. Two numerical examples show the effectiveness of our main results. Full article

(This article belongs to the Special Issue The Advances of Nonlinear Equations: Mathematical Models, Symmetry and Applications)

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14 pages, 255 KiB

Open AccessArticle

A New Hybrid Generalization of Balancing Polynomials

by Dorota Bród, Mariola Rubajczyk and Anetta Szynal-Liana

Symmetry 2024, 16(10), 1397; https://doi.org/10.3390/sym16101397 - 21 Oct 2024

Viewed by 939

Abstract

In this paper, we introduce and study balancing hybrinomials, i.e., polynomials being a generalization of balancing hybrid numbers. We provide some properties of the balancing hybrinomials, including Catalan, Cassini, d’Ocagne, and Vajda identities, among others. Moreover, we present a matrix representation of the [...] Read more.

In this paper, we introduce and study balancing hybrinomials, i.e., polynomials being a generalization of balancing hybrid numbers. We provide some properties of the balancing hybrinomials, including Catalan, Cassini, d’Ocagne, and Vajda identities, among others. Moreover, we present a matrix representation of the hybrinomials. Full article

(This article belongs to the Section Mathematics)

44 pages, 7180 KiB

Open AccessReview

Sixty Years of the Maximum Principle in Optimal Control: Historical Roots and Content Classification

by Roman Chertovskih, Vitor Miguel Ribeiro, Rui Gonçalves and António Pedro Aguiar

Symmetry 2024, 16(10), 1398; https://doi.org/10.3390/sym16101398 - 20 Oct 2024

Viewed by 815

Abstract

This study examines the scientific production focused on the Maximum Principle between 1962 and 2021. Results indicate a consistent increase in the absolute number of publications over time. In relative terms, there is a resurgence of interest in this research field after the [...] Read more.

This study examines the scientific production focused on the Maximum Principle between 1962 and 2021. Results indicate a consistent increase in the absolute number of publications over time. In relative terms, there is a resurgence of interest in this research field after the period between 2004 and 2009. Overall, these findings support the idea of strategic complementarity between the Maximum Principle and optimal control. However, there is a notable exception during the period 2010–2015, characterised by a decline in scientific production focused on the Maximum Principle and a simultaneous increase in focus on optimal control. Academic journals that play a role in promoting this research field tend to have high impact factors and interesting cite scores. Using a modified Boston Consulting Group matrix, the results reveal the persistence of two researchers labelled as stars and three as cash cows. A multiple linear regression analysis confirms that reputation significantly influences the clustering trends. A critical discussion is provided to highlight the dichotomy between popularity and effective contributions in this research field. Full article

(This article belongs to the Section Mathematics)

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21 pages, 583 KiB

Open AccessArticle

Numerical Solution of External Boundary Conditions Inverse Multilayer Diffusion Problems

by Miglena N. Koleva and Lubin G. Vulkov

Symmetry 2024, 16(10), 1396; https://doi.org/10.3390/sym16101396 - 20 Oct 2024

Viewed by 570

Abstract

The present study is concerned with the numerical solution of external boundary conditions in inverse problems for one-dimensional multilayer diffusion, using the difference method. First, we formulate multispecies parabolic problems with three types of Dirichlet–Neumann–Robin internal boundary conditions that apply at the interfaces [...] Read more.

The present study is concerned with the numerical solution of external boundary conditions in inverse problems for one-dimensional multilayer diffusion, using the difference method. First, we formulate multispecies parabolic problems with three types of Dirichlet–Neumann–Robin internal boundary conditions that apply at the interfaces between adjacent layers. Then, using the symmetry of the diffusion operator, we prove the well-posedness of the direct (forward) problem in which the coefficients, the right-hand side, and the initial and boundary conditions are given. In inverse problems, instead of external boundary conditions of the first and the last layers, point observations of the solution within the entire domain are posed. Rothe’s semi-discretization of differential problems combined with a symmetric exponential finite difference solution for elliptic problems on each time layer is proposed to develop an efficient semi-analytical approach. Next, using special solution decomposition techniques, we numerically solve the inverse problems for the identification of external boundary conditions. Numerical test examples are discussed. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Models)

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14 pages, 459 KiB

Open AccessArticle

Fractional Caputo Operator and Takagi–Sugeno Fuzzy Modeling to Diabetes Analysis

by Ez-zaiym Mustapha, El Ouissari Abdellatif, El Moutaouakil Karim and Aberqi Ahmed

Symmetry 2024, 16(10), 1395; https://doi.org/10.3390/sym16101395 - 19 Oct 2024

Viewed by 1277

Abstract

Diabetes is becoming more and more dangerous, and the effects continue to grow due to the population’s ignorance of the seriousness of this phenomenon. The studies that have been carried out have not been able to follow the phenomenon more precisely, which has [...] Read more.

Diabetes is becoming more and more dangerous, and the effects continue to grow due to the population’s ignorance of the seriousness of this phenomenon. The studies that have been carried out have not been able to follow the phenomenon more precisely, which has led to the use of the fractional derivative tool, which has a very great capability to study real problems and phenomena but is somewhat limited on nonlinear models. In this work, we will develop a new fractional derivative model of a diabetic population, the Takagi–Sugeno fractional fuzzy model, which will enable us to study the phenomenon with these nonlinear terms in order to obtain greater precision in the results. We will study the existence and uniqueness of the solution using the Lipschizian theorem and then turn to the new fuzzy model, which leads us to four dynamical systems. The interpretation results show the quality of fuzzy membership in tracking the malleable phenomena of nonlinear terms existing in the system. Full article

(This article belongs to the Section Computer)

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25 pages, 1217 KiB

Open AccessArticle

Advanced Analytical Methods for Risk Mitigation in Multimodal Freight Transport

by Kwanjira Kaewfak, Chanathip Pharino and Nipa Ouppara

Symmetry 2024, 16(10), 1394; https://doi.org/10.3390/sym16101394 - 19 Oct 2024

Viewed by 1295

Abstract

Stakeholders in multimodal freight transport encounter significant challenges due to the multitude of unknowns and inherent risks that can adversely affect operations. The subjective nature of the information complicates the identification and assessment of these risks, making them particularly challenging in the context [...] Read more.

Stakeholders in multimodal freight transport encounter significant challenges due to the multitude of unknowns and inherent risks that can adversely affect operations. The subjective nature of the information complicates the identification and assessment of these risks, making them particularly challenging in the context of multimodal transport, where the potential consequences can be substantial. This research intends to provide a comprehensive understanding of the asymmetries in risks associated with multimodal freight transport by identifying and evaluating quantitative hazards. By integrating fuzzy set theory and failure mode and effects analysis (FMEA), the study offers a structured approach to statistically forecast risks, addressing imprecision in traditional risk assessments. Qualitative interviews conducted with multimodal freight transport operators in Thailand reveal critical insights, including the identification of high-priority risks such as delays from regulatory compliance, inadequate infrastructure, and inefficiencies in stakeholder communication. The findings of this study not only highlight these pressing issues but also provide actionable strategies to mitigate risks, thereby enhancing the operational resilience of multimodal freight transport systems. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Sustainable Transport and Logistics)

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14 pages, 787 KiB

Open AccessArticle

TMG Symmetry and Kinematic Analysis of the Impact of Different Plyometric Programs on Female Athletes’ Lower-Body Muscles

by Nikola Prvulović, Milena Žuža Praštalo, Ana Lilić, Saša Pantelić, Borko Katanić, Milan Čoh and Vesna Vučić

Symmetry 2024, 16(10), 1393; https://doi.org/10.3390/sym16101393 - 19 Oct 2024

Viewed by 664

Abstract

Asymmetries in sports are common and can lead to various issues; however, different training programs can facilitate change. This study aimed to assess the effects of opposing plyometric programs on tensiomyography lateral symmetry (TMG LS)/inter-limb asymmetry in female athletes’ lower-body muscles, alongside kinematic [...] Read more.

Asymmetries in sports are common and can lead to various issues; however, different training programs can facilitate change. This study aimed to assess the effects of opposing plyometric programs on tensiomyography lateral symmetry (TMG LS)/inter-limb asymmetry in female athletes’ lower-body muscles, alongside kinematic and body composition parameters. Twenty female subjects from basketball, volleyball, and track and field (sprinting disciplines) were divided into two experimental groups (n = 10 each). Two six-week plyometric programs (two sessions/week) were implemented: the first program (E1) focused on eccentric exercises, depth landings, while the second (E2) emphasized concentric exercises, squat jumps. TMG assessed LS in six muscles: vastus lateralis, vastus medialis, biceps femoris, semitendinosus, gastrocnemius lateralis, and gastrocnemius medialis. A kinematic analysis of the countermovement jump (CMJ) and body composition was conducted using “Kinovea; Version 0.9.4” software and InBody 770, respectively. The results showed significant increases in LS percentages (E1—VL 9.9%, BF 18.0%, GM 10.6% and E2—BF 22.5%, p < 0.05), and a significant large effect in E1 for VL, and in E2 for BF, p < 0.01). They also showed that E1 had a significant effect on VL, and that E2 had a significant large effect on BF (p < 0.01). E1 also led to increased lean muscle mass in both legs (left: 1.88%, right: 2.74%) and decreased BMIs (−0.4, p < 0.05). Both programs improved LS, with E1 enhancing muscle mass and lower-body positioning in CMJ. We recommend future studies use varied jump tests, incorporate 3D kinematic analysis, include male subjects, and examine more muscles to enhance TMG LS analysis. Full article

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28 pages, 24746 KiB

Open AccessArticle

Non-Periodic Quantized Model Predictive Control Method for Underwater Dynamic Docking

by Tian Ni, Can Sima, Liang Qi, Minghao Xu, Junlin Wang, Runkang Tang and Lindan Zhang

Symmetry 2024, 16(10), 1392; https://doi.org/10.3390/sym16101392 - 18 Oct 2024

Viewed by 619

Abstract

This study proposed an event-triggered quantized model predictive control (ETQMPC) method for the dynamic docking of unmanned underwater vehicles (UUVs) and human-occupied vehicles (HOVs). The proposed strategy employed a non-periodic control approach that initiated the non-linear model predictive control (NMPC) optimization and state [...] Read more.

This study proposed an event-triggered quantized model predictive control (ETQMPC) method for the dynamic docking of unmanned underwater vehicles (UUVs) and human-occupied vehicles (HOVs). The proposed strategy employed a non-periodic control approach that initiated the non-linear model predictive control (NMPC) optimization and state sampling based on tracking errors and deviations from the predicted optimal state, thereby enhancing computing performance and system efficiency without compromising the control quality. To further conserve communication resources and improve information transfer efficiency, a quantitative feedback mechanism was employed for sampling and state quantification. The simulation experiments were performed to verify the effectiveness of the method, demonstrating excellent docking trajectory tracking performance, robustness against bounded current interference, and significant reductions in computational and communication burdens. The experimental results demonstrated that the method outperformed in the docking trajectory tracking control performance significantly improved the computational and communication performance, and comprehensively improved the system efficiency. Full article

(This article belongs to the Special Issue Symmetry in Control System Theory and Applications)

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18 pages, 21526 KiB

Open AccessArticle

Unraveling the Subsurface Damage and Material Removal Mechanism of Multi-Principal-Element Alloy FeCrNi Coatings During the Scratching Process

by Yuan Chen, Xiubo Liu, Ao Fu and Jing Peng

Symmetry 2024, 16(10), 1391; https://doi.org/10.3390/sym16101391 - 18 Oct 2024

Viewed by 599

Abstract

Multi-principal-element alloys (MPEAs) exhibit superior strength and good ductility. However, tribological properties of FeCrNi MPEAs remain unknown at nanoscale and complex environments. Here, we investigate the effects of scratching speed, depth, and temperature on microstructural and tribological characteristics of FeCrNi using molecular dynamics [...] Read more.

Multi-principal-element alloys (MPEAs) exhibit superior strength and good ductility. However, tribological properties of FeCrNi MPEAs remain unknown at nanoscale and complex environments. Here, we investigate the effects of scratching speed, depth, and temperature on microstructural and tribological characteristics of FeCrNi using molecular dynamics simulations combined with an elevated temperature tribological experiment. The scratching force experiences the increase stage, the undulated stage, and the stable stage due to chip formation. Compared to traditional alloy coatings, low force enhances the useful life. With increased speed, the friction coefficient decreases, agreeing with previous work. High speed impacting includes severe local plastic deformation, from dislocation to amorphization. As the scratching depth increases, the average scratch force and friction coefficient increases owing to material accumulation in front of the abrasive particles. The surface morphology and dislocation behavior are significantly different during the scratching process. In addition, we revealed a temperature-dependent friction mechanism. FeCrNi MPEAs have excellent wear resistance at an intermediate temperature, which is attributed to the high Cr content promoting the formation of the compact oxide layer. This work provides atomic-scale mechanistic insights into the tribological behavior of FeCrNi, and would be applied to the design of MPEAs with high performance. Full article

(This article belongs to the Section Engineering and Materials)

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11 pages, 1084 KiB

Open AccessArticle

Navicular Drop Height Asymmetry as an Intrinsic Risk Factor for Lower Limb Injury in Male Recreational Athletes

by Jarosław Domaradzki

Symmetry 2024, 16(10), 1390; https://doi.org/10.3390/sym16101390 - 18 Oct 2024

Viewed by 842

Abstract

Morphological and functional asymmetry of the lower limbs is a well-recognized factor contributing to musculoskeletal injuries among athletes across different levels. However, limited research exists on evaluating foot mobility asymmetry as a potential predictor of such injuries. This study aimed to (1) assess [...] Read more.

Morphological and functional asymmetry of the lower limbs is a well-recognized factor contributing to musculoskeletal injuries among athletes across different levels. However, limited research exists on evaluating foot mobility asymmetry as a potential predictor of such injuries. This study aimed to (1) assess the frequency of foot mobility asymmetries among amateur athletes, (2) investigate the predictive value of foot mobility asymmetry (measured via navicular height drop) for injury risk, and (3) explore the relationship between foot type and injury occurrence. A cross-sectional sampling method was employed to select 45 physically active male amateur athletes (runners and team sports practitioners) from a university. Injury history was retrospectively recorded, and a modified navicular drop test was conducted to classify foot arch height. The predictive power of navicular height drop asymmetry was analyzed using ROC curves, and the relationship between foot type (neutral and defective combinations—pronated or supinated) and injury occurrence was examined using chi-square tests for independence. Multiple logistic regression was applied to calculate injury risk odds ratios across different foot type subgroups. The results revealed a significant frequency (51.1%) of participants with at least one defective foot, including 31.1% with one neutral and one defective foot and 20% with both feet defective. Navicular height drop asymmetry emerged as a valuable predictor of injuries, with a 36% asymmetry identified as the cut-off for increased injury risk (AUC = 0.832, 95% CI: 0.691–0.973, p < 0.001). A significant relationship was found between foot type and injury occurrence. Only one out of 22 participants with neutral feet (4.55%) experienced an injury, compared to 9 out of 14 (64.29%) with one neutral and one defective foot and 5 out of 9 (55.56%) with both feet defective. These differences were statistically significant (χ² = 16.24, p < 0.001, Cramer’s V = 0.60). The odds ratio for injury risk was 37.8 (p = 0.016) for those with asymmetry (one neutral and one defective foot) and 26.3 (p = 0.102) for those with both feet defective, compared to participants with both feet neutral. In clinical practice, these findings suggest that routine screenings for physically active individuals should incorporate foot mobility asymmetry assessment. However, it is essential to integrate this factor with other risk indicators. For individuals exhibiting high asymmetry, general foot defect correction programs may be beneficial, but injury prevention strategies should adopt a more comprehensive approach, focusing on overall fitness and tailored interventions for high-risk individuals. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Life Sciences: Feature Papers 2024)

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13 pages, 1294 KiB

Open AccessArticle

Asymmetry in Galaxy Spin Directions: A Fully Reproducible Experiment Using HSC Data

by Lior Shamir

Symmetry 2024, 16(10), 1389; https://doi.org/10.3390/sym16101389 - 18 Oct 2024

Cited by 1 | Viewed by 627

Abstract

The asymmetry in the large-scale distribution of the directions in which spiral galaxies rotate has been observed by multiple telescopes, all showing a consistent asymmetry in the distribution of galaxy spin directions as observed from Earth. Here, galaxies with a redshift from HSC [...] Read more.

The asymmetry in the large-scale distribution of the directions in which spiral galaxies rotate has been observed by multiple telescopes, all showing a consistent asymmetry in the distribution of galaxy spin directions as observed from Earth. Here, galaxies with a redshift from HSC DR3 are annotated by their direction of rotation, and their distribution is analyzed. The results show that galaxies that rotate in the opposite direction relative to the Milky Way as observed from Earth are significantly more prevalent compared to galaxies that rotate in the same direction relative to the Milky Way. The asymmetry also forms a dipole axis that becomes stronger when the redshift gets higher. These results are aligned with observations from virtually all premier digital sky surveys, as well as space telescopes such as the HST and the JWST. This shows that the distribution of galaxy spin directions as observed from Earth is not symmetrical, and has a possible link to the rotational velocity of the Milky Way. This experiment provides data, code, and a full protocol that allows the results to be easily reproduced in a transparent manner. This practice is used to overcome the “reproducibility crisis” in science. Full article

(This article belongs to the Special Issue Global and Local Scale Symmetry in Gravitation and Cosmology)

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15 pages, 5216 KiB

Open AccessArticle

Deep Learning Evidence for Global Optimality of Gerver’s Sofa

by Kuangdai Leng, Jia Bi, Jaehoon Cha, Samuel Pinilla and Jeyan Thiyagalingam

Symmetry 2024, 16(10), 1388; https://doi.org/10.3390/sym16101388 - 18 Oct 2024

Viewed by 875

Abstract

The moving sofa problem, introduced by Leo Moser in 1966, seeks to determine the maximal area of a 2D shape that can navigate an L-shaped corridor of unit width. Joseph Gerver’s 1992 solution, providing a lower bound of approximately 2.2195, is the [...] Read more.

The moving sofa problem, introduced by Leo Moser in 1966, seeks to determine the maximal area of a 2D shape that can navigate an L-shaped corridor of unit width. Joseph Gerver’s 1992 solution, providing a lower bound of approximately 2.2195, is the best known, though its global optimality remains unproven. This paper leverages neural networks’ approximation power and recent advances in invexity optimization to explore global optimality. We propose two approaches supporting Gerver’s conjecture that his sofa is the unique global maximum. The first approach uses continuous function learning, discarding assumptions about the monotonicity, symmetry, and differentiability of sofa movements. The sofa area is computed as a differentiable function using our “waterfall” algorithm, with the loss function incorporating both differential terms and initial conditions based on physics-informed machine learning. Extensive training with diverse network initialization consistently converges to Gerver’s solution. The second approach applies discrete optimization to the Kallus–Romik upper bound, improving it from 2.37 to 2.3337 for five rotation angles. As the number of angles increases, our model asymptotically converges to Gerver’s area from above, indicating that no larger sofa exists. Full article

(This article belongs to the Section Computer)

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15 pages, 302 KiB

Open AccessArticle

Rapid Assessment of Morphological Asymmetries Using 3D Body Scanner and Bioelectrical Impedance Technologies in Sports: A Case of Comparative Analysis Among Age Groups in Judo

by Jožef Šimenko, Hrvoje Sertić, Ivan Segedi and Ivan Čuk

Symmetry 2024, 16(10), 1387; https://doi.org/10.3390/sym16101387 - 18 Oct 2024

Viewed by 613

Abstract

(1) Background: The advancement of technologies has made morphological assessment rapid and reliable. A combination of 3D body scanning (3D-BS) and bioelectrical impedance (BIA) could be essential in monitoring the morphological status of athletes and the general population and their symmetries for coaches, [...] Read more.

(1) Background: The advancement of technologies has made morphological assessment rapid and reliable. A combination of 3D body scanning (3D-BS) and bioelectrical impedance (BIA) could be essential in monitoring the morphological status of athletes and the general population and their symmetries for coaches, researchers and medical professionals. (2) Methods: The current study presents the use of Inbody-720 BIA and 3D-BS NX-16 for analyzing the asymmetry profile of an athlete in 2 min on a sample of 106 male judo competitors from the following age categories: older boys—U14 (N = 24), younger cadets—U16 (N = 31), cadets—U18 (N = 17), juniors—U21 (N = 19) and seniors (N = 15). Variables observed were arm lean mass, upper arm, elbow, forearm and wrist girth, leg lean mass, thigh length, thigh, knee and calf girth. The paired sample t-test, asymmetry index (AI) and Kruskal–Wallis analysis were used at p ≤ 0.05; (3) Results: Morphological asymmetries were detected in all age categories: seniors—three, U21—four, U18—three, U16—five and U14—four. The most common asymmetrical variable in all categories was the forearm girth, while thigh length, knee girth and upper arm girth presented symmetrical variables in all age categories. AI showed that the size of the asymmetries did not differentiate between the age groups. (4) Conclusions: The current study demonstrated great potential for combining BIA and 3D-BS for rapid asymmetry detection that would allow for monitoring and quick adjustments to the training process in youth to senior age categories. Full article

(This article belongs to the Special Issue Application of Symmetry in Biomechanics)

15 pages, 425 KiB

Open AccessArticle

Sequence of Bounds for Spectral Radius and Energy of Digraph

by Jietong Zhao, Saira Hameed, Uzma Ahmad, Ayesha Tabassum and Leila Asgharsharghi

Symmetry 2024, 16(10), 1386; https://doi.org/10.3390/sym16101386 - 18 Oct 2024

Viewed by 849

Abstract

The graph spectra analyze the structure of the graph using eigenspectra. The spectral graph theory deals with the investigation of graphs in terms of the eigenspectrum. In this paper, the sequence of lower bounds for the spectral radius of digraph

D

having at [...] Read more.

The graph spectra analyze the structure of the graph using eigenspectra. The spectral graph theory deals with the investigation of graphs in terms of the eigenspectrum. In this paper, the sequence of lower bounds for the spectral radius of digraph

D

having at least one doubly adjacent vertex in terms of indegree is proposed. Particularly, it is exhibited that

ρ (D) \geq α^{j} = \sqrt{\frac{\sum_{p = 1}^{m} {(χ_{j + 1}^{(p)})}^{2}}{\sum_{p = 1}^{m} {(χ_{j}^{(p)})}^{2}}}

, such that equality is attained iff

D = \overset{\leftrightarrow}{G} +

{

DE \notin

Cycle}, where each component of associated graph is a k-regular or

(k_{1}, k_{2})

semiregular bipartite. By utilizing the sequence of lower bounds of the spectral radius of

D

, the sequence of upper bounds of energy of

D

, where the sequence decreases when

\sqrt{\frac{e}{U}} \leq α^{j}

and increases when

\sqrt{\frac{e}{U}} > α^{j}

, are also proposed. All of the obtained inequalities are elaborated using examples. We also discuss the monotonicity of these sequences. Full article

(This article belongs to the Special Issue Symmetry in Combinatorics and Discrete Mathematics)

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25 pages, 323 KiB

Open AccessArticle

Classification of Petrov Homogeneous Spaces

by V. V. Obukhov

Symmetry 2024, 16(10), 1385; https://doi.org/10.3390/sym16101385 - 17 Oct 2024

Viewed by 383

Abstract

In this paper, the final stage of the Petrov classification is carried out. As it is known, the Killing vector fields specify infinitesimal transformations of the group of motions of space

V_{4}

. In the case where the group of motions [...] Read more.

In this paper, the final stage of the Petrov classification is carried out. As it is known, the Killing vector fields specify infinitesimal transformations of the group of motions of space

V_{4}

. In the case where the group of motions

G_{3}

acts in a simply transitive way in the homogeneous space

V_{4}

, the geometry of the non-isotropic hypersurface is determined by the geometry of the transitivity space

V_{3}

of the group

G_{3}

. In this case, the metric tensor of the space

V_{3}

can be given by a nonholonomic reper consisting of three independent vectors

ℓ_{(a)}^{α}

, which define the generators of the group

G_{3}

of finite transformations in the space

V_{3}

. The representation of the metric tensor of

V_{4}

spaces by means of vector fields

ℓ_{(a)}^{α}

has a great physical meaning and makes it possible to substantially simplify the equations of mathematical physics in such spaces. Therefore, the Petrov classification should be complemented by the classification of vector fields

ℓ_{(a)}^{α}

connected to Killing vector fields. For homogeneous spaces, this problem has been largely solved. A complete solution of this problem is presented in the present paper, where I refine the Petrov classification for homogeneous spaces in which the group

G_{3}

, which belongs to type

V I I I

according to the Petrov classification, acts simply transitively. In addition, this paper provides the complete classification of vector fields

ℓ_{(a)}^{α}

for space

V_{4}

in which the group

G_{3}

acts simply transitivity on isotropic hypersurfaces. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2024)

18 pages, 317 KiB

Open AccessArticle

Foliation-Generating Observers Under Lorentz Transformations

by Daniel Blixt, Alejandro Jiménez Cano and Aneta Wojnar

Symmetry 2024, 16(10), 1384; https://doi.org/10.3390/sym16101384 - 17 Oct 2024

Cited by 1 | Viewed by 947

Abstract

In this work, we revise the concept of foliation and related aspects that are crucial when formulating the Hamiltonian evolution for various theories beyond General Relativity. In particular, we show the relation between the kinematic characteristics of timelike congruences (observers) and the existence [...] Read more.

In this work, we revise the concept of foliation and related aspects that are crucial when formulating the Hamiltonian evolution for various theories beyond General Relativity. In particular, we show the relation between the kinematic characteristics of timelike congruences (observers) and the existence of foliations orthogonal to them. We then explore how local Lorentz transformations acting on observers affect the existence of transversal foliations, provide examples, and discuss the implications of these results for the

3 + 1

formulation of tetrad modified theories of gravity. Full article

(This article belongs to the Special Issue Aspects of Particle Physics and High Energy Physics- Dedicated to Zhengdao Li's 95 Anniversary)

19 pages, 1413 KiB

Open AccessArticle

In Silico Comparison of Quantum and Bioactivity Parameters of a Series of Natural Diphenyl Acetone Analogues, and In Vitro Caco-2 Studies on Three Main Chalcone Derivatives

by Amalia Stefaniu, Georgeta Neagu, Adrian Albulescu, Nicoleta Radu and Lucia Camelia Pirvu

Symmetry 2024, 16(10), 1383; https://doi.org/10.3390/sym16101383 - 17 Oct 2024

Viewed by 1000

Abstract

This paper aims to compare the in silico and in vitro properties of a series of diphenyl acetone derivatives, specifically six chalcone analogues, namely benzophenone, chalcone, phloretin, phloridzin, nothofagin and 4-methylchalcone. The in silico studies were conducted using the Spartan’14 mechanistic program to [...] Read more.

This paper aims to compare the in silico and in vitro properties of a series of diphenyl acetone derivatives, specifically six chalcone analogues, namely benzophenone, chalcone, phloretin, phloridzin, nothofagin and 4-methylchalcone. The in silico studies were conducted using the Spartan’14 mechanistic program to perform a comparative analysis of the molecular, quantum and bioactivity parameters of the six analogues under study. The in vitro MTS studies were designed to investigate the cytotoxic and anti-proliferative effect of the reference substances (r.s.) of three main chalcone derivatives in nature, namely phloretin, phloridzin and 4-methylchalcone, on the Caco-2 cell line. Overall, the in silico results foremost suggested the potential of phloretin to traverse the blood–brain barrier, and the abilities of phloridzin and nothofagin to act as broad cell enzyme inhibitors; the in vitro results demonstrated that phloretin and 4-methylchalcone have the potential to induce both cytotoxic and anti-proliferative effects, depending on their concentration level: the antiproliferative effects were noticed in the interval from 1 to 50 µg of r.s. per sample, while the cytotoxic effects were noticed from 1 to 50 µg of r.s. per sample in the case of 4-methychalcone, and at 50 µg of r.s. per sample in the case of phloretin. Phloridzin did not affect the viability of the Caco-2 line. Full article

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

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17 pages, 4709 KiB

Open AccessArticle

Top-Oil Temperature Prediction of Power Transformer Based on Long Short-Term Memory Neural Network with Self-Attention Mechanism Optimized by Improved Whale Optimization Algorithm

by Dexu Zou, He Xu, Hao Quan, Jianhua Yin, Qingjun Peng, Shan Wang, Weiju Dai and Zhihu Hong

Symmetry 2024, 16(10), 1382; https://doi.org/10.3390/sym16101382 - 17 Oct 2024

Viewed by 1016

Abstract

The operational stability of the power transformer is essential for maintaining the symmetry, balance, and security of power systems. Once the power transformer fails, it will lead to heightened instability within grid operations. Accurate prediction of oil temperature is crucial for efficient transformer [...] Read more.

The operational stability of the power transformer is essential for maintaining the symmetry, balance, and security of power systems. Once the power transformer fails, it will lead to heightened instability within grid operations. Accurate prediction of oil temperature is crucial for efficient transformer operation. To address challenges such as the difficulty in selecting model hyperparameters and incomplete consideration of temporal information in transformer oil temperature prediction, a novel model is constructed based on the improved whale optimization algorithm (IWOA) and long short-term memory (LSTM) neural network with self-attention (SA) mechanism. To incorporate holistic and local information, the SA is integrated with the LSTM model. Furthermore, the IWOA is employed in the optimization of the hyper-parameters for the LSTM-SA model. The standard IWOA is improved by incorporating adaptive parameters, thresholds, and a Latin hypercube sampling initialization strategy. The proposed method was applied and tested using real operational data from two transformers within a practical power grid. The results of the single-step prediction experiments demonstrate that the proposed method significantly improves the accuracy of oil temperature prediction for power transformers, with enhancements ranging from 1.06% to 18.85% compared to benchmark models. Additionally, the proposed model performs effectively across various prediction steps, consistently outperforming benchmark models. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry Studies in Modern Power Systems)

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21 pages, 1156 KiB

Open AccessArticle

EDSCVD: Enhanced Dual-Channel Smart Contract Vulnerability Detection Method

by Huaiguang Wu, Yibo Peng, Yaqiong He and Siqi Lu

Symmetry 2024, 16(10), 1381; https://doi.org/10.3390/sym16101381 - 17 Oct 2024

Viewed by 570

Abstract

Ensuring the absence of vulnerabilities or flaws in smart contracts before their deployment is crucial for the smooth progress of subsequent work. Existing detection methods heavily rely on expert rules, resulting in low robustness and accuracy. Therefore, we propose EDSCVD, an enhanced deep [...] Read more.

Ensuring the absence of vulnerabilities or flaws in smart contracts before their deployment is crucial for the smooth progress of subsequent work. Existing detection methods heavily rely on expert rules, resulting in low robustness and accuracy. Therefore, we propose EDSCVD, an enhanced deep learning vulnerability detection model based on dual-channel networks. Firstly, the contract fragments are preprocessed by BERT into the required word embeddings. Next, we utilized adversarial training FGM to the word embeddings to generate perturbations, thereby producing symmetric adversarial samples and enhancing the robustness of the model. Then, the dual-channel model combining BiLSTM and CNN is utilized for feature training to obtain more comprehensive and symmetric information on temporal and local contract features.Finally, the combined output features are passed through a classifier to classify and detect contract vulnerabilities. Experimental results show that our EDSCVD exhibits excellent detection performance in the detection of classical reentrancy vulnerabilities, timestamp dependencies, and integer overflow vulnerabilities. Full article

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27 pages, 14949 KiB

Open AccessArticle

Experimental Study on Strength and Deformation Moduli of Columnar Jointed Rock Mass—Uniaxial Compression as an Example

by Zhenbo Xu, Zhende Zhu, Chao Jiang and Xiaobin Hu

Symmetry 2024, 16(10), 1380; https://doi.org/10.3390/sym16101380 - 17 Oct 2024

Viewed by 1031

Abstract

The irregular joint network unique to columnar joints separates the rock mass into several irregular polygonal prisms. Similar physical model specimens of columnar jointed rock mass (CJRM) were fabricated using a rock-like material. The effect of the irregularity of the joint network was [...] Read more.

The irregular joint network unique to columnar joints separates the rock mass into several irregular polygonal prisms. Similar physical model specimens of columnar jointed rock mass (CJRM) were fabricated using a rock-like material. The effect of the irregularity of the joint network was considered in the horizontal plane, and the effect of the dip angle of the joint network was considered in the vertical plane. The strength and deformation moduli of the specimen were investigated using uniaxial compression tests. A total of four failure modes of regular columnar jointed rock mass (RCJRM) and irregular columnar jointed rock mass (ICJRM) were identified through the tests. The peak stress of the irregular columnar jointed rock mass specimen is reduced by 56.65%. The strength and deformation moduli of RCJRM were greater than those of ICJRM, while the anisotropic characteristics of ICJRM were stronger. The failure mode of CJRM was determined by the dip angle. With the increase in the dip angle, the strength and deformation moduli of irregular columnar jointed rock mass are a symmetrical “V” type distribution, 45° corresponds to the minimum strength, and 30° obtains the minimum deformation modulus. With the increase in the irregularity coefficient, the strength and deformation moduli of CJRM decreased first and then increased gradually. When the irregularity coefficient is 0.1, the linear deformation modulus reaches the minimum value. When the irregularity coefficient is 0.7, the median deformation modulus reaches the minimum value. The fitting function proposed in the form of the cosine function managed to predict the strength value of CJRM and showed the strength of the anisotropic characteristics caused by the change in the dip angle. Compared with the existing physical model test results, it is determined that the strength of the specimen is positively correlated with the addition amount of rock-like material and the loading rate, and negatively correlated with the water consumption. Full article

(This article belongs to the Section Engineering and Materials)

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23 pages, 365 KiB

Open AccessArticle

Is the Wavefunction Already an Object on Space?

by Ovidiu Cristinel Stoica

Symmetry 2024, 16(10), 1379; https://doi.org/10.3390/sym16101379 - 16 Oct 2024

Cited by 4 | Viewed by 1002

Abstract

Since the discovery of quantum mechanics, the fact that the wavefunction is defined on the

3 n

-dimensional configuration space rather than on the 3-dimensional space has seemed uncanny to many, including Schrödinger, Lorentz, and Einstein. Even today, this continues to be seen [...] Read more.

Since the discovery of quantum mechanics, the fact that the wavefunction is defined on the

3 n

-dimensional configuration space rather than on the 3-dimensional space has seemed uncanny to many, including Schrödinger, Lorentz, and Einstein. Even today, this continues to be seen as a significant issue in the foundations of quantum mechanics. In this article, it will be shown that the wavefunction is, in fact, a genuine object on space. While this may seem surprising, the wavefunction does not possess qualitatively new features that were not previously encountered in objects known from Euclidean geometry and classical physics. The methodology used involves finding equivalent reinterpretations of the wavefunction exclusively in terms of objects from the geometry of space. The result is that we will find the wavefunction to be equivalent to geometric objects on space in the same way as was always the case in geometry and physics. This will be demonstrated to hold true from the perspective of Euclidean geometry, but also within Felix Klein’s Erlangen Program, which naturally fits into the classification of quantum particles by the representations of spacetime isometries, as realized by Wigner and Bargmann, adding another layer of confirmation. These results lead to clarifications in the debates about the ontology of the wavefunction. From an empirical perspective, we already take for granted that all quantum experiments take place in space. I suggest that the reason why this works is that they can be interpreted naturally and consistently with the results presented here, showing that the wavefunction is an object on space. Full article

(This article belongs to the Special Issue Symmetry and Chaos in Quantum Mechanics)

19 pages, 13601 KiB

Open AccessArticle

ETLSH-YOLO: An Edge–Real-Time Transmission Line Safety Hazard Detection Method

by Liangliang Zhao, Yu Zhang, Yinke Dou, Yangyang Jiao and Qiang Liu

Symmetry 2024, 16(10), 1378; https://doi.org/10.3390/sym16101378 - 16 Oct 2024

Viewed by 565

Abstract

Using deep learning methods to detect potential safety hazards in transmission lines is the mainstream method for power grid security monitoring. However, the existing model is too complex to adapt to edge device deployment and real-time detection. Therefore, an edge–real-time transmission line safety [...] Read more.

Using deep learning methods to detect potential safety hazards in transmission lines is the mainstream method for power grid security monitoring. However, the existing model is too complex to adapt to edge device deployment and real-time detection. Therefore, an edge–real-time transmission line safety hazard detection method (ETLSH-YOLO) was proposed to reduce the model’s complexity and improve the model’s robustness. Firstly, a re-parameterized Ghost efficient layer aggregation network (RepGhostCSPELAN) was designed to effectively fuse the feature information of different layers while enhancing the model’s expression ability and reducing the number of model parameters and floating-point operations. Then, a spatial channel decoupled downsampling block (CSDovn) was designed to reduce computational redundancy and improve the computational efficiency of the model. Then, coordinate attention (CA) was added in the process of multi-scale feature fusion to suppress the interference of complex background and improve the global perception ability of the model object. Finally, the Mish activation function was used to improve the network’s training speed, convergence, and generalization ability. The experimental results show that the mAP50 of this model improved by 1.73% compared with the baseline model, and the number of parameters and floating-point operations were reduced by 33.96% and 22.22%, respectively. This model lays the foundation for solving the dilemma of edge device deployment. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry Study in Object Detection)

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19 pages, 22914 KiB

Open AccessReview

Multilevel Diffractive Lenses: Recent Advances and Applications

by Chenyu Shi, Weipeng Zhao, Sai Chen and Wenli Li

Symmetry 2024, 16(10), 1377; https://doi.org/10.3390/sym16101377 - 16 Oct 2024

Viewed by 2460

Abstract

Multilevel diffractive lenses (MDLs) has undergone considerable advancements, marked by their exceptional efficiency and diverse focusing capabilities, resulting in their widespread use in optical systems. In recent times, MDLs have consistently been juxtaposed with metalenses, which have experienced swift progress over the last [...] Read more.

Multilevel diffractive lenses (MDLs) has undergone considerable advancements, marked by their exceptional efficiency and diverse focusing capabilities, resulting in their widespread use in optical systems. In recent times, MDLs have consistently been juxtaposed with metalenses, which have experienced swift progress over the last decade. Concurrently, MDLs have continued to evolve, propelled by their distinct advantages, such as cost-effective production and adaptability for mass manufacturing. This article explores the evolution and foundational concepts of MDLs, highlighting the advantages of their circular symmetry in enhancing simulation and optimization efficiency. Furthermore, we present several innovative fabrication methods for MDLs that capitalize on the latest advancements in 3D printing technology. We also show the practical applications and potential future developments of MDLs. Full article

(This article belongs to the Special Issue Metamaterials and Symmetry: Recent Advances and Applications)

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15 pages, 4238 KiB

Open AccessArticle

An Improved PINN Algorithm for Shallow Water Equations Driven by Deep Learning

by Yanling Li, Qianxing Sun, Junfang Wei and Chunyan Huang

Symmetry 2024, 16(10), 1376; https://doi.org/10.3390/sym16101376 - 16 Oct 2024

Viewed by 771

Abstract

Solving shallow water equations is crucial in science and engineering for understanding and predicting natural phenomena. To address the limitations of Physics-Informed Neural Network (PINN) in solving shallow water equations, we propose an improved PINN algorithm integrated with a deep learning framework. This [...] Read more.

Solving shallow water equations is crucial in science and engineering for understanding and predicting natural phenomena. To address the limitations of Physics-Informed Neural Network (PINN) in solving shallow water equations, we propose an improved PINN algorithm integrated with a deep learning framework. This algorithm introduces a regularization term as a penalty in the loss function, based on the PINN and Long Short-Term Memory (LSTM) models, and incorporates an attention mechanism to solve the original equation across the entire domain. Simulation experiments were conducted on one-dimensional and two-dimensional shallow water equations. The results indicate that, compared to the classical PINN algorithm, the improved algorithm shows significant advantages in handling discontinuities, such as sparse waves, in one-dimensional problems. It accurately captures sparse waves and avoids smoothing effects. In two-dimensional problems, the improved algorithm demonstrates good symmetry and effectively reduces non-physical oscillations. It also shows significant advantages in capturing details and handling complex phenomena, offering higher reliability and accuracy. The improved PINNs algorithm, which combines neural networks with physical mechanisms, can provide robust solutions and effectively avoid some of the shortcomings of classical PINNs methods. It also possesses high resolution and strong generalization capabilities, enabling accurate predictions at any given moment. Full article

(This article belongs to the Section Computer)

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20 pages, 1849 KiB

Open AccessArticle

Diffusion Augmented Complex Inverse Square Root for Adaptive Frequency Estimation over Distributed Networks

by Pucha Song, Jinghua Ye, Kang Yan and Zhengyan Luo

Symmetry 2024, 16(10), 1375; https://doi.org/10.3390/sym16101375 - 16 Oct 2024

Viewed by 956

Abstract

Using adaptive filtering to estimate the frequency of power systems has become a popular trend. In recent years, however, few studies have been performed on adaptive frequency estimations in non-stationary noise environments. In this paper, we propose the distributed complex inverse square root [...] Read more.

Using adaptive filtering to estimate the frequency of power systems has become a popular trend. In recent years, however, few studies have been performed on adaptive frequency estimations in non-stationary noise environments. In this paper, we propose the distributed complex inverse square root algorithm and distributed augmented complex inverse square root algorithm for the frequency estimation of power systems based on the widely linear model and the inverse square root cost function, where the function can restrain both positive and negative large errors, based on its symmetry. Moreover, the wireless sensor networks support monitoring and adaptation for the frequency estimation in the distributed networks, and the proposed approach can ensure good robustness of the balanced or unbalanced three-phase power system with the help of a local complex-value voltage signal generated by Clark’s transformation. In addition, the bound of step size is driven by the global vectors, and that low computation complexity do not hinder those performances. The results of several experiments demonstrate that our algorithms can effectively estimate the frequency in impulsive noise environments. Full article

(This article belongs to the Section Computer)

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