Symmetry

14 pages, 311 KiB

Open AccessArticle

Generating Bent Functions and Dynamic Filters: A Novel Equivalence-Based Approach

by Joseph Nelson, Chungath Srinivasan, Anand R. Nair and Lakshmy Koduvayur Viswanathan

Symmetry 2024, 16(11), 1501; https://doi.org/10.3390/sym16111501 (registering DOI) - 8 Nov 2024

Boolean functions are fundamental building blocks in both discrete mathematics and computer science, with applications spanning from cryptography to coding theory. Bent functions, a subset of Boolean functions with maximal nonlinearity, are particularly valuable in cryptographic applications. This study introduces a novel equivalence [...] Read more.

Boolean functions are fundamental building blocks in both discrete mathematics and computer science, with applications spanning from cryptography to coding theory. Bent functions, a subset of Boolean functions with maximal nonlinearity, are particularly valuable in cryptographic applications. This study introduces a novel equivalence relation among all Boolean functions and presents an algorithm to generate bent functions based on this relation. We systematically generated a collection of 10,000 bent functions over eight variables, all originating from the same equivalence class, and analyzed their structural complexity through rank determination. Our findings revealed the presence of at least five distinct affine classes of bent functions within this collection. By employing this construction, we devised an algorithm to generate a filter function capable of combining Boolean functions. This filter function can be dynamically adjusted based on a key, offering potential applications in symmetric cipher design, such as enhancing security or improving efficiency. Full article

(This article belongs to the Section Mathematics)

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24 pages, 697 KiB

Open AccessArticle

Enhancing Supply Chain Sustainability and Reliability Through WSM and TOPSIS: A Symmetrical Real-World Case Study

by Anshu Abhilasha, Faizan Danish and Melfi Alrasheedi

Symmetry 2024, 16(11), 1500; https://doi.org/10.3390/sym16111500 (registering DOI) - 8 Nov 2024

Abstract

Large corporations have recently demonstrated an increasing propensity to enhance the sustainability and reliability of their supply chains in order to comply with environmental regulations and improve customer satisfaction through on-time demand fulfillment. There are two phases to this study: mathematical modeling and [...] Read more.

Large corporations have recently demonstrated an increasing propensity to enhance the sustainability and reliability of their supply chains in order to comply with environmental regulations and improve customer satisfaction through on-time demand fulfillment. There are two phases to this study: mathematical modeling and model solution using precise techniques. In the first step, a mixed-integer linear programming model is developed. This model is an improvement of an existing supply chain model. Further, our suggested strategy is verified by using numerical data based on three criteria and four suppliers. The goals of the proposed model are to maximize supply chain reliability, economic profit, and social responsibilities by taking suppliers’ priorities into account. Modeled as a mixed-integer linear programming problem, the constraints on the problem include budget, emission, demand, allocation, facility, and shipping capacity. Power symmetry and information symmetry are incorporated in order to perform symmetric analysis. The weighted sum method (WSM) and the technique for order of preference by similarity to ideal solution (TOPSIS) are the two methods used in the second step of solving the model to identify the best supplier. In order to evaluate how well the proposed methodology was applied, a practical case was considered and implemented. Full article

(This article belongs to the Section Mathematics)

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30 pages, 512 KiB

Open AccessArticle

Exploring Asymmetric Gender-Based Satisfaction of Delivery Riders in Real-Time Crowdsourcing Logistics Platforms

by Dan Li and Yi Zhang

Symmetry 2024, 16(11), 1499; https://doi.org/10.3390/sym16111499 (registering DOI) - 8 Nov 2024

Abstract

This study investigates gender-based differences in the satisfaction ranking of riders on real-time crowdsourcing logistics platforms, using online reviews from the Ele.me platform. Quantitative methods, including the frequency ratio-based Analytic Hierarchy Process (AHP), probabilistic linguistic term sets (PLTS), and fuzzy comprehensive evaluation (FCE), [...] Read more.

This study investigates gender-based differences in the satisfaction ranking of riders on real-time crowdsourcing logistics platforms, using online reviews from the Ele.me platform. Quantitative methods, including the frequency ratio-based Analytic Hierarchy Process (AHP), probabilistic linguistic term sets (PLTS), and fuzzy comprehensive evaluation (FCE), were applied to analyze satisfaction differences between men and women riders. The findings reveal an asymmetric pattern in satisfaction preferences: women riders place more emphasis on perceived value, while men riders prioritize service perceived quality. Although both groups rank platform image, product perceived quality, and rider expectations similarly, the importance of these factors varies significantly, indicating an underlying asymmetry in their expectations and values. Women riders express higher satisfaction with platform image, rider expectations, service perceived quality, and product perceived quality, with rider expectations showing the largest difference. Additionally, the multi-criteria decision-making methods used in this study offer insights for optimizing service performance in real-time crowdsourcing logistics platforms, particularly in handling uncertainty and enhancing system adaptability through fuzzy sets. These findings provide a basis for developing gender-specific strategies aimed at enhancing rider satisfaction, minimizing turnover, and improving platform adaptability—contributing to a more inclusive and sustainable logistics supply chain. Full article

(This article belongs to the Section Mathematics)

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20 pages, 2633 KiB

Open AccessArticle

A Security Situation Prediction Model for Industrial Control Network Based on Explainable Belief Rule Base

by Guoxing Li, Yuhe Wang, Jianbai Yang, Shiming Li, Xinrong Li and Huize Mo

Symmetry 2024, 16(11), 1498; https://doi.org/10.3390/sym16111498 - 8 Nov 2024

Abstract

Industrial Control Systems (ICSs) are vital components of industrial production, and their security posture significantly impacts operational safety. Given that ICSs frequently interact with external networks, cyberattacks can disrupt system symmetry, thereby affecting industrial processes. This paper aims to predict the network security [...] Read more.

Industrial Control Systems (ICSs) are vital components of industrial production, and their security posture significantly impacts operational safety. Given that ICSs frequently interact with external networks, cyberattacks can disrupt system symmetry, thereby affecting industrial processes. This paper aims to predict the network security posture of ICSs to ensure system symmetry. A prediction model for the network security posture of ICSs was established utilizing Evidence Reasoning (ER) and Explainable Belief Rule Base (BRB-e) technologies. Initially, an evaluation framework for the ICS architecture was constructed, integrating data from various layers using ER. The development of the BRB prediction model requires input from domain experts to set initial parameters; however, the subjective nature of these settings may reduce prediction accuracy. To address this issue, an ICS network security posture prediction model based on the Explainable Belief Rule Base (BRB-e) was proposed. The modeling criteria for explainability were defined based on the characteristics of the ICS network, followed by the design of the inference process for the BRB-e prediction model to enhance accuracy and precision. Additionally, a parameter optimization method for the explainable BRB-e prediction model is presented using a constrained Projection Equilibrium Optimization (P-EO) algorithm. Experiments utilizing industrial datasets were conducted to validate the reliability and effectiveness of the prediction model. Comparative analyses indicated that the BRB-e model demonstrates distinct advantages in both prediction accuracy and explainability when compared to other algorithms. Full article

(This article belongs to the Section Computer)

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15 pages, 730 KiB

Open AccessArticle

FLSAD: Defending Backdoor Attacks in Federated Learning via Self-Attention Distillation

by Lucheng Chen, Xiaoshuang Liu, Ailing Wang, Weiwei Zhai and Xiang Cheng

Symmetry 2024, 16(11), 1497; https://doi.org/10.3390/sym16111497 - 8 Nov 2024

Abstract

Federated Learning (FL), as a distributed machine learning framework, can effectively learn symmetric and asymmetric patterns from large-scale participants. However, FL is susceptible to malicious backdoor attacks through attackers injecting triggers into the backdoored model, resulting in backdoor samples being misclassified as target [...] Read more.

Federated Learning (FL), as a distributed machine learning framework, can effectively learn symmetric and asymmetric patterns from large-scale participants. However, FL is susceptible to malicious backdoor attacks through attackers injecting triggers into the backdoored model, resulting in backdoor samples being misclassified as target classes. Due to the stealthy nature of backdoor attacks in FL, it is difficult for users to discover the symmetric and asymmetric backdoor properties. Currently, backdoor defense methods in FL cause model performance degradation while reducing backdoors. In addition, some methods will assume the existence of clean samples, which does not match the realistic scenarios. To address such issues, we propose FLSAD, an effective backdoor defense method in FL via self-attention distillation. FLSAD can recover the triggers using an entropy maximization estimator. Based on the recovered triggers, we leverage the self-attention distillation to eliminate the backdoor. Compared with the baseline backdoor defense methods, FLSAD can reduce the success rates of different state-of-the-art backdoor attacks to 2% on four real-world datasets through extensive evaluation. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Cybersecurity)

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16 pages, 7088 KiB

Open AccessArticle

An Efficient Dense Reconstruction Algorithm from LiDAR and Monocular Camera

by Siyi Xiang, Zepeng Zeng, Jiantao Jiang, Dabo Zhang and Nannan Liu

Symmetry 2024, 16(11), 1496; https://doi.org/10.3390/sym16111496 - 8 Nov 2024

Abstract

Dense reconstruction have been studied for decades in the fields of computer vision and robotics, in which LiDAR and camera are widely used. However, vision-based methods are sensitive to illumination variation and lack direct depth, and LiDAR-based methods are limited by sparse LiDAR [...] Read more.

Dense reconstruction have been studied for decades in the fields of computer vision and robotics, in which LiDAR and camera are widely used. However, vision-based methods are sensitive to illumination variation and lack direct depth, and LiDAR-based methods are limited by sparse LiDAR measurement and lacking color and texture information. In this paper, we propose a novel 3D reconstruction algorithm based on LiDAR and a monocular camera, which realizes dense reconstruction. In the algorithm, a LiDAR odometry is used to get accurate poses and poses calculated by the odometry module are used in the calculation of depth maps and fusion of depth maps, and then mesh and texture mapping are implemented. In addition, a semantic segmentation network and a depth completion network are used to obtain dense and accurate depth maps. The concept of symmetry is utilized to generate 3D models of objects or scenes; that is, the reconstruction and camera imaging of these objects or scenes are symmetrical. Experimental results on public dataset show that the proposed algorithm achieves higher accuracy, efficiency and completeness than existing methods. Full article

(This article belongs to the Section Computer)

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14 pages, 7171 KiB

Open AccessArticle

Quantitative Analysis of Magnetic Force of Axial Symmetry Permanent Magnet Structure Using Hybrid Boundary Element Method

by Ana Vučković, Dušan Vučković, Mirjana Perić and Branislav M. Ranđelović

Symmetry 2024, 16(11), 1495; https://doi.org/10.3390/sym16111495 - 8 Nov 2024

Abstract

This paper investigates the forces generated by axially magnetized ring permanent magnets with trapezoidal cross-sections when placed near a soft magnetic cylinder. Utilizing the Hybrid Boundary Element Method (HBEM), this study models interactions in magnetic configurations, aiming to improve force calculation efficiency and [...] Read more.

This paper investigates the forces generated by axially magnetized ring permanent magnets with trapezoidal cross-sections when placed near a soft magnetic cylinder. Utilizing the Hybrid Boundary Element Method (HBEM), this study models interactions in magnetic configurations, aiming to improve force calculation efficiency and accuracy compared to traditional finite element methods (FEMM 4.2 software program). The influence of the permanent magnet and the soft magnetic cylinder is approximated with a system of thin toroidal sources on the surfaces of the magnet and the cylinder, which significantly reduces the computation time for the force calculation. The approach is validated by comparing results with FEM solutions, revealing high precision with a much faster computation. Additionally, this study explores the influence of various parameters, including magnet size, separation distance, and magnetic permeability of the cylinder, on the magnetic force. The results demonstrate that the HBEM approach is effective for analyzing complex magnetic configurations, particularly in applications requiring efficient parametric studies. This approach can be adapted for other geometries, such as truncated cones or rectangular cross-section ring magnets. The findings contribute valuable insights into designing efficient magnetic systems and optimizing force calculations for varied magnet geometries and configurations, including the atypical ones. Full article

(This article belongs to the Section Engineering and Materials)

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17 pages, 1472 KiB

Open AccessArticle

Clean-Label Backdoor Watermarking for Dataset Copyright Protection via Trigger Optimization

by Weitong Chen, Gaoyang Wei, Xin Xu, Yanyan Xu, Haibo Peng and Yingchen She

Symmetry 2024, 16(11), 1494; https://doi.org/10.3390/sym16111494 - 8 Nov 2024

Abstract

High-quality datasets are essential for training high-performance models, while the process of collection, cleaning, and labeling is costly. As a result, datasets are considered valuable intellectual property. However, when security mechanisms are symmetry-breaking, creating exploitable vulnerabilities, unauthorized use or data leakage can infringe [...] Read more.

High-quality datasets are essential for training high-performance models, while the process of collection, cleaning, and labeling is costly. As a result, datasets are considered valuable intellectual property. However, when security mechanisms are symmetry-breaking, creating exploitable vulnerabilities, unauthorized use or data leakage can infringe on the copyright of dataset owners. In this study, we design a method to mount clean-label dataset watermarking based on trigger optimization, aiming to protect the copyright of the dataset from infringement. We first perform iterative optimization of the trigger based on a surrogate model, with targets class samples guiding the updates. The process ensures that the optimized triggers contain robust feature representations of the watermark target class. A watermarked dataset is obtained by embedding optimized triggers into randomly selected samples from the watermark target class. If an adversary trains a model with the watermarked dataset, our watermark will manipulate the model’s output. By observing the output of the suspect model on samples with triggers, it can be determined whether the model was trained on the watermarked dataset. The experimental results demonstrate that the proposed method exhibits high imperceptibility and strong robustness against pruning and fine-tuning attacks. Compared to existing methods, the proposed method significantly improves effectiveness at very low watermarking rates. Full article

(This article belongs to the Special Issue Symmetries and Symmetry-Breaking in Data Security)

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8 pages, 234 KiB

Open AccessArticle

Some New Graph Interpretations of Padovan Numbers

by Mateusz Pirga, Andrzej Włoch and Iwona Włoch

Symmetry 2024, 16(11), 1493; https://doi.org/10.3390/sym16111493 - 8 Nov 2024

Abstract

Padovan numbers and Perrin numbers belong to the family of numbers of the Fibonacci type and they are well described in the literature. In this paper, by studying independent (1,2)-dominating sets in paths and cycles, we obtain new binomial formulas for Padovan and [...] Read more.

Padovan numbers and Perrin numbers belong to the family of numbers of the Fibonacci type and they are well described in the literature. In this paper, by studying independent (1,2)-dominating sets in paths and cycles, we obtain new binomial formulas for Padovan and Perrin numbers. As a consequence of graph interpretation, we propose a new dependence between Padovan and Perrin numbers. By studying special independent (1,2)-dominating sets in a composition of two graphs, we define Padovan polynomials of graphs. By the fact that every independent (1,2)-dominating set includes the set of leaves as a subset, in some cases a symmetric structure of the independent (1,2)-dominating set can be used. Full article

(This article belongs to the Section Mathematics)

17 pages, 599 KiB

Open AccessArticle

Centroid-Induced Ranking of Triangular Picture Fuzzy Numbers and Applications in Decision-Making

by Lorena Popa

Symmetry 2024, 16(11), 1492; https://doi.org/10.3390/sym16111492 - 7 Nov 2024

Abstract

This paper proposes the concept of a centroid for picture fuzzy numbers and particularly for triangular picture fuzzy numbers. The concept allows the implementation of a ranking function for the triangular picture fuzzy numbers, which has the advantage of reuniting the symmetry and [...] Read more.

This paper proposes the concept of a centroid for picture fuzzy numbers and particularly for triangular picture fuzzy numbers. The concept allows the implementation of a ranking function for the triangular picture fuzzy numbers, which has the advantage of reuniting the symmetry and asymmetry of the information. Then, empirical applications are considered for the picture fuzzy numbers. Specifically, multiple TPFNs are considered. The ranked, A comparison study is conducted for said ranked TPFNs relative to other methodologies in the specialized literature, illustrating that these methods exhibit limitations in specific scenarios. An additional compelling example is provided: before elections, opinion surveys are extensively utilised to assess voter intentions about candidates. The survey findings can be analysed through PFNs and the ranking mechanism proposed in this study. Another contribution of this paper is the development an algorithm meant to solve decision making problems in an uncertain environment. This is applied in the practical context of comparing the performance of several standards in two successive evaluations. Full article

(This article belongs to the Special Issue Fuzzy Set Theory and Uncertainty Theory—3rd Edition)

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26 pages, 357 KiB

Open AccessArticle

Exploring Symmetry in Industrial Decision-Making: A New Framework Based on Cubic Type-2 Fuzzy Soft Sets

by Kholood Mohammad Alsager and Hajar Abdullah Alharbi

Symmetry 2024, 16(11), 1491; https://doi.org/10.3390/sym16111491 - 7 Nov 2024

Abstract

Industry 4.0 supply chains, characterized by dynamic environments, uncertainty, and intricate interdependencies, necessitate robust decision-making tools. While existing models have made strides in addressing these complexities, they often struggle to effectively handle the high degree of uncertainty inherent in such systems. To bridge [...] Read more.

Industry 4.0 supply chains, characterized by dynamic environments, uncertainty, and intricate interdependencies, necessitate robust decision-making tools. While existing models have made strides in addressing these complexities, they often struggle to effectively handle the high degree of uncertainty inherent in such systems. To bridge this gap, this research introduces a novel framework grounded in the axioms of Cubic Type-2 Fuzzy Soft Sets (CT2FSSs). By leveraging the enhanced flexibility and uncertainty-handling capabilities of CT2FSSs, our proposed framework empowers decision-makers to navigate complexities, optimize supply chain processes, and mitigate risks while maintaining symmetry in decision-making. Through rigorous theoretical analysis and practical applications, this study not only advances fuzzy set theory but also demonstrates its efficacy in the context of Industry 4.0. The unique contribution of this research lies in the development of a CT2FSS-based framework that offers superior adaptability to uncertain and complex environments, thereby enhancing the resilience and performance of supply chains in symmetrical scenarios. Full article

(This article belongs to the Section Mathematics)

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19 pages, 2502 KiB

Open AccessArticle

Piecewise Neural Network Method for Solving Large Interval Solutions to Initial Value Problems of Ordinary Differential Equations

by Dongpeng Han and Chaolu Temuer

Symmetry 2024, 16(11), 1490; https://doi.org/10.3390/sym16111490 - 7 Nov 2024

Abstract

Traditional numerical methods often provide local solutions for initial value problems of differential equations, even though these problems may have solutions over larger intervals. Current neural network algorithms and deep learning methods also struggle to ensure solutions across these broader intervals. This paper [...] Read more.

Traditional numerical methods often provide local solutions for initial value problems of differential equations, even though these problems may have solutions over larger intervals. Current neural network algorithms and deep learning methods also struggle to ensure solutions across these broader intervals. This paper introduces a novel approach employing piecewise neural networks to address this issue. The method involves dividing the solution interval into smaller segments and utilizing neural networks with a uniform structure to solve sub-problems within each segment. These solutions are then combined to form a piecewise expression representing the overall solution. The approach guarantees continuous differentiability of the obtained solution over the entire interval, except for finite end points of those sub-intervals.To enhance accuracy, parameter transfer and multiple rounds of pre-training are employed. Importantly, this method maintains a consistent network size and training data scale across sub-domains, unlike existing neural network algorithms. Numerical experiments validate the efficiency of the proposed algorithm. Full article

(This article belongs to the Section Mathematics)

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22 pages, 7141 KiB

Open AccessArticle

A Numerical Analysis on Gradient Coils in Nuclear Magnetic Resonance for Imaging

by Gabriele Barbaraci

Symmetry 2024, 16(11), 1489; https://doi.org/10.3390/sym16111489 - 7 Nov 2024

Abstract

A mathematical discussion is introduced to describe the gradient coils characterizing the NMRI system. A comparison between the physical laws characterizing the magnetic field of winding coils and a magnetohydrodynamic analysis is built up. The requirements for gradient coil performance are described and [...] Read more.

A mathematical discussion is introduced to describe the gradient coils characterizing the NMRI system. A comparison between the physical laws characterizing the magnetic field of winding coils and a magnetohydrodynamic analysis is built up. The requirements for gradient coil performance are described and analyzed. Design methods are characterized by mathematical manipulation to reduce the nonlinearities that make the magnetic field not suitable for image extraction. A mathematical study has been shown to represent the Golay’s pairs as generators of linear magnetic fields. The entire study shows how the choice of the magnetic field pattern inside the NMRI can occur by choosing the proper geometrical parameters that are a function of the nonlinearities involved in the gradient coils design. Full article

(This article belongs to the Section Mathematics)

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13 pages, 1302 KiB

Open AccessArticle

Confidence Intervals for the Coefficient of Variation in Delta Inverse Gaussian Distributions

by Wasurat Khumpasee, Sa-Aat Niwitpong and Suparat Niwitpong

Symmetry 2024, 16(11), 1488; https://doi.org/10.3390/sym16111488 - 7 Nov 2024

Abstract

The inverse Gaussian distribution is characterized by its asymmetry and right-skewed shape, indicating a longer tail on the right side. This distribution represents extreme values in one direction, such as waiting times, stochastic processes, and accident counts. Moreover, depending on if the accident [...] Read more.

The inverse Gaussian distribution is characterized by its asymmetry and right-skewed shape, indicating a longer tail on the right side. This distribution represents extreme values in one direction, such as waiting times, stochastic processes, and accident counts. Moreover, depending on if the accident counts data can occur or not and may have zero value, the Delta Inverse Gaussian (Delta-IG) distribution is more suitable. The confidence interval (CI) for the coefficient of variation (CV) of the Delta-IG distribution in accident counts is essential for risk assessment, resource allocation, and the creation of transportation safety policies. Our objective is to establish CIs of CV for the Delta-IG population using various methods. We considered seven CI construction methods, namely Generalized Confidence Interval (GCI), Adjusted Generalized Confidence Interval (AGCI), Parametric Bootstrap Percentile Confidence Interval (PBPCI), Fiducial Confidence Interval (FCI), Fiducial Highest Posterior Density Confidence Interval (F-HPDCI), Bayesian Credible Interval (BCI), and Bayesian Highest Posterior Density Credible Interval (B-HPDCI). We utilized Monte Carlo simulations to assess the proposed CI technique for average widths (AWs) and coverage probability (CP). Our findings revealed that F-HPDCI and AGCI exhibited the most effective coverage probability and average widths. We applied these methods to generate CIs of CV for accident counts in India. Full article

(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines Fourth Edition)

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22 pages, 1205 KiB

Open AccessReview

Primordial Black Hole Messenger of Dark Universe

by Maxim Khlopov

Symmetry 2024, 16(11), 1487; https://doi.org/10.3390/sym16111487 - 7 Nov 2024

Abstract

Primordial black holes (PBH), if survive to the present time, can be a fraction, or even the dominant form of dark matter of the Universe. If PBH evaporate before the present time, rare forms of dark matter like superweakly interacting or supermassive particles [...] Read more.

Primordial black holes (PBH), if survive to the present time, can be a fraction, or even the dominant form of dark matter of the Universe. If PBH evaporate before the present time, rare forms of dark matter like superweakly interacting or supermassive particles can be produced in the course of their evaporation. Stable remnants of PBH evaporation can also play the role of dark matter candidates. In the context of the modern standard cosmology, based on inflationary models with baryosynthesis and dark matter, which find their physical grounds beyond the Standard models of elementary particles (BSM), primordial black holes acquire the important role of sensitive probes for BSM models and their parameters. It makes PBHs a profound messenger of physics of Dark Universe. Full article

(This article belongs to the Special Issue The Dark Universe: The Harbinger of a Major Discovery)

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11 pages, 2967 KiB

Open AccessArticle

Does Presentation Duration Modulate the Effect of Task on Perceptual Organization?

by Ned Buckley and Alexis D. J. Makin

Symmetry 2024, 16(11), 1486; https://doi.org/10.3390/sym16111486 - 7 Nov 2024

Abstract

Visual symmetry activates the extrastriate cortex. This symmetry activation generates an Event Related Potential (ERP) named the Sustained Posterior Negativity (SPN). The SPN is larger when participants engage in regularity discrimination tasks than luminance discrimination tasks. Two recent studies suggest that the type [...] Read more.

Visual symmetry activates the extrastriate cortex. This symmetry activation generates an Event Related Potential (ERP) named the Sustained Posterior Negativity (SPN). The SPN is larger when participants engage in regularity discrimination tasks than luminance discrimination tasks. Two recent studies suggest that the type of task matters more when the stimulus is presented briefly. We tested this claim with a new sample of 52 participants in a within-subjects design. As predicted, the SPNs were larger in Regularity tasks than Luminance tasks. However, contrary to predictions, the effect of the task was very similar in long and short presentation duration blocks. It remains unclear what factors modulate the task effect. However, presentation duration is not as important as previous results suggest. Full article

(This article belongs to the Section Life Sciences)

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13 pages, 266 KiB

Open AccessReview

Motor Asymmetry in Football: Implications for Muscular Power, Balance, and Injury Prevention

by Monoem Haddad

Symmetry 2024, 16(11), 1485; https://doi.org/10.3390/sym16111485 - 7 Nov 2024

Abstract

This review explores the prevalence and impacts of muscular power and dynamic balance motor asymmetry among football players, emphasizing its impact on performance and injury risk. Motor asymmetry frequently occurs in football, largely due to the sport’s specific demands, including the frequent use [...] Read more.

This review explores the prevalence and impacts of muscular power and dynamic balance motor asymmetry among football players, emphasizing its impact on performance and injury risk. Motor asymmetry frequently occurs in football, largely due to the sport’s specific demands, including the frequent use of one leg for kicking and passing. While some motor asymmetry may lead to functional specialization and does not always hinder performance, significant imbalances are often linked to an increased risk of injuries, particularly to the lower extremities. Dynamic balance motor asymmetry is also associated with a higher risk of non-contact injuries, underscoring the importance of joint stability in preventing such injuries. However, the direct impact of balance motor asymmetry on performance metrics like sprint speed and agility is less definitive, suggesting that compensatory mechanisms or training adaptations could mitigate potential negative effects. Technological advances in assessment, such as motion capture systems and wearable devices, have enhanced the precision of asymmetry evaluations, enabling more targeted interventions. In addition, personalized training interventions, informed by real-time data from these technologies, allow for tailored rehabilitation and performance optimization, addressing asymmetry-related risks early. Despite these technological advancements, there is a significant gap in understanding how motor asymmetry affects underrepresented groups, such as female football players and youth athletes. Further research is needed to investigate motor asymmetry in these populations, particularly to assess the long-term impact on injury risk and performance. Addressing these gaps will provide valuable insights into the development of gender- and age-specific training interventions. This review recommends a multidisciplinary approach, integrating biomechanics, sports medicine, and coaching insights, to develop comprehensive strategies for managing motor asymmetry in football. Such strategies, supported by real-time monitoring and tailored interventions, will be crucial for optimizing player performance, minimizing injury risk, and improving training and rehabilitation programs tailored to the diverse needs of football players. Full article

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

29 pages, 1679 KiB

Open AccessArticle

Symmetrical Generalized Pareto Dominance and Adjusted Reference Vector Cooperative Evolutionary Algorithm for Many-Objective Optimization

by Shuwei Zhu, Liusheng Zeng and Meiji Cui

Symmetry 2024, 16(11), 1484; https://doi.org/10.3390/sym16111484 - 6 Nov 2024

Abstract

In Pareto-based many-objective evolutionary algorithms, performance usually degrades drastically as the number of objectives increases due to the poor discriminability of Pareto optimality. Although some relaxed Pareto domination relations have been proposed to relieve the loss of selection pressure, it is hard to [...] Read more.

In Pareto-based many-objective evolutionary algorithms, performance usually degrades drastically as the number of objectives increases due to the poor discriminability of Pareto optimality. Although some relaxed Pareto domination relations have been proposed to relieve the loss of selection pressure, it is hard to maintain good population diversity, especially in the late phase of evolution. To solve this problem, we propose a symmetrical Generalized Pareto Dominance and Adjusted Reference Vectors Cooperative (GPDARVC) evolutionary algorithm to deal with many-objective optimization problems. The symmetric version of generalized Pareto dominance (GPD), as an efficient framework, provides sufficient selection pressure without degrading diversity, no matter of the number of objectives. Then, reference vectors (RVs), initially generated evenly in the objective space, guide the selection with good diversity. The cooperation of GPD and RVs in environmental selection in part ensures a good balance of convergence and diversity. Also, to further enhance the effectiveness of RV-guided selection, we regenerate more RVs according to the proportion of valid RVs; thereafter, we select the most valid RVs for adjustment after the association operation. To validate the performance of GPDARVC, we compare it with seven representative algorithms on commonly used sets of problems. This comprehensive analysis results in 26 test problems with different objective numbers and 6 practical problems, which show that GPDARVC outperforms other algorithms in most cases, indicating its great potential to solve many-objective optimization problems. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Evolutionary Algorithms)

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21 pages, 419 KiB

Open AccessArticle

Martínez–Kaabar Fractal–Fractional Laplace Transformation with Applications to Integral Equations

by Francisco Martínez and Mohammed K. A. Kaabar

Symmetry 2024, 16(11), 1483; https://doi.org/10.3390/sym16111483 (registering DOI) - 6 Nov 2024

Abstract

This paper addresses the extension of Martinez–Kaabar (MK) fractal–fractional calculus (for simplicity, in this research work, it is referred to as MK calculus) to the field of integral transformations, with applications to some solutions to integral equations. A new notion of Laplace transformation, [...] Read more.

This paper addresses the extension of Martinez–Kaabar (MK) fractal–fractional calculus (for simplicity, in this research work, it is referred to as MK calculus) to the field of integral transformations, with applications to some solutions to integral equations. A new notion of Laplace transformation, named MK Laplace transformation, is proposed, which incorporates the MK

α, γ

-integral operator into classical Laplace transformation. Laplace transformation is very applicable in mathematical physics problems, especially symmetrical problems in physics, which are frequently seen in quantum mechanics. Symmetrical systems and properties can be helpful in applications of Laplace transformations, which can help in providing an effective computational tool for solving such problems. The main properties and results of this transformation are discussed. In addition, the MK Laplace transformation method is constructed and applied to the non-integer-order first- and second-kind Volterra integral equations, which exhibit a fractal effect. Finally, the MK Abel integral equation’s solution is also investigated via this technique. Full article

(This article belongs to the Section Mathematics)

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