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Symmetry, Volume 16, Issue 3 (March 2024) – 126 articles

Cover Story (view full-size image): Single-shot factorization uses a general ansatz for the factorization of a single-particle Hamiltonian; here, we use a form based on confluent hypergeometric functions. By adjusting the parameters in the factorization to ensure normalizable wavefunctions, all energy eigenvalues and wavefunctions are determined at once. The approach is equivalent to Natanzon’s approach, which instead works directly with the confluent hypergeometric differential equation. This approach is halfway between the conventional Schrödinger equation approach and the Schrödinger factorization chain. Here, we depict the two bound states of a Natanzon potential that can be solved exactly with this approach. The dashed lines indicate the energies of each state, and the black line is the potential (which asymptotes to zero for large positive x). View this paper
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16 pages, 461 KiB  
Article
An Exploration of Multitasking Scheduling Considering Interruptible Job Assignments, Machine Aging Effects, the Influence of Deteriorating Maintenance, and Symmetry
by Li Zeng
Symmetry 2024, 16(3), 380; https://doi.org/10.3390/sym16030380 - 21 Mar 2024
Viewed by 526
Abstract
The unique topic of allocating and scheduling tasks on a single machine in a multitasking environment is the main emphasis of this research, which also takes into account the effects of worsening maintenance and job-dependent aging effects. In this scenario, the performance and [...] Read more.
The unique topic of allocating and scheduling tasks on a single machine in a multitasking environment is the main emphasis of this research, which also takes into account the effects of worsening maintenance and job-dependent aging effects. In this scenario, the performance and efficiency of the machine in handling different tasks should be symmetric, without significant bias due to the nature or size of the tasks. In a multitasking environment, waiting for jobs can disrupt the processing of the primary job being currently handled. As a result, the actual time required to complete a task becomes erratic and contingent upon the duration of the disruption. In addition to figuring out the best time for maintenance, where to put the due-window, and how big it should be in a multitasking environment, the primary objective is to minimize the costs associated with meeting due-window regulations. To tackle this problem, we propose two optimal algorithms. Additionally, we conduct numerical experiments to compare our approach with the classic due date assignment problem. Interestingly, we observe that in most cases, the average and minimum percentage costs tend to increase as the quantity of jobs increases. However, it is noteworthy that, when the number of jobs is relatively small, specifically when it does not exceed 20, there are instances where these costs decrease with an increase in the number of jobs. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Operations Research)
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13 pages, 405 KiB  
Article
A Symmetric Non-Stationary Loop Subdivision with Applications in Initial Point Interpolation
by Baoxing Zhang, Yunkun Zhang and Hongchan Zheng
Symmetry 2024, 16(3), 379; https://doi.org/10.3390/sym16030379 - 21 Mar 2024
Viewed by 497
Abstract
Loop subdivision is a significant surface scheme with wide applications in fields like computer graphics and wavelet. As a type of stationary scheme, Loop subdivision cannot adjust the limit surface directly. In this paper, we present a new way to solve this problem [...] Read more.
Loop subdivision is a significant surface scheme with wide applications in fields like computer graphics and wavelet. As a type of stationary scheme, Loop subdivision cannot adjust the limit surface directly. In this paper, we present a new way to solve this problem by proposing a symmetric non-stationary Loop subdivision based on a suitable iteration. This new scheme can be used to adjust the limit surfaces freely and thus can generate surfaces with different shapes. For this new scheme, we show that it is C2 convergent in the regular part of mesh and is at least tangent plane continuous at the limit positions of the extraordinary points. Additionally, we present a non-uniform generalization of this new symmetric non-stationary subdivision so as to locally control the shape of the limit surfaces. More interestingly, we present the limit positions of the initial points, both for the symmetric non-stationary Loop subdivision and its non-uniform generalization. Such limit positions can be used to interpolate the initial points with different valences, generalizing the existing result. Several numerical examples are given to illustrate the performance of the new schemes. Full article
(This article belongs to the Section Mathematics)
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22 pages, 3886 KiB  
Article
A Novel Money Laundering Prediction Model Based on a Dynamic Graph Convolutional Neural Network and Long Short-Term Memory
by Fei Wan and Ping Li
Symmetry 2024, 16(3), 378; https://doi.org/10.3390/sym16030378 - 21 Mar 2024
Viewed by 599
Abstract
Money laundering is an illicit activity that seeks to conceal the nature and origins of criminal proceeds, posing a substantial threat to the national economy, the political order, and social stability. To scientifically and reasonably predict money laundering risks, this paper focuses on [...] Read more.
Money laundering is an illicit activity that seeks to conceal the nature and origins of criminal proceeds, posing a substantial threat to the national economy, the political order, and social stability. To scientifically and reasonably predict money laundering risks, this paper focuses on the “layering” stage of the money laundering process in the field of supervised learning for money laundering fraud prediction. A money laundering and fraud prediction model based on deep learning, referred to as MDGC-LSTM, is proposed. The model combines the use of a dynamic graph convolutional network (MDGC) and a long short-term memory (LSTM) network to efficiently identify illegal money laundering activities within financial transactions. MDGC-LSTM constructs dynamic graph snapshots with symmetrical spatiotemporal structures based on transaction information, representing transaction nodes and currency flows as graph nodes and edges, respectively, and effectively captures the relationships between temporal and spatial structures, thus achieving the dynamic prediction of fraudulent transactions. The experimental results demonstrate that compared with traditional algorithms and other deep learning models, MDGC-LSTM achieves significant advantages in comprehensive spatiotemporal feature modeling. Specifically, based on the Elliptic dataset, MDGC-LSTM improves the Macro-F1 score by 0.25 compared to that of the anti-money laundering fraud prediction model currently considered optimal. Full article
(This article belongs to the Section Computer)
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11 pages, 947 KiB  
Article
Local Muscle Oxygenation Differences between Lower Limbs according to Muscle Mass in Breath-Hold Divers
by Ognjen Uljević, Dario Vrdoljak, Ivan Drviš, Nikola Foretić and Željko Dujić
Symmetry 2024, 16(3), 377; https://doi.org/10.3390/sym16030377 - 21 Mar 2024
Viewed by 570
Abstract
Oxidative potential and anaerobic capacity could be influential to the training regimen and performance of breath-hold diving (BHD) athletes. Therefore, this study aimed to determine the differences in local muscle oxygenation between the lower limbs according to the muscle mass percentage in spearfishermen [...] Read more.
Oxidative potential and anaerobic capacity could be influential to the training regimen and performance of breath-hold diving (BHD) athletes. Therefore, this study aimed to determine the differences in local muscle oxygenation between the lower limbs according to the muscle mass percentage in spearfishermen and freedivers. The sample of participants included 21 BHD athletes (13 freedivers; 8 spearfishermen; 4 females). Their chronological age was 35.5 ± 8.6 years, body mass was 79.3 ± 9.1 kg, and height was 182.5 ± 13.0 cm. Participants’ training experience was 10.6 ± 9.5 years. The variables in this study included anthropometric indices, the Wingate anaerobic test, and muscle oxygen dynamics parameters. The results show significant differences for freedivers between the lower limbs (muscle mass percentage, p < 0.00; minimal SmO2%, p = 0.05; and maximal SmO2%, p = 0.04). However, when observing only spearfisherman, there is only one significant difference between the dominant and non-dominant lower limb (percentage of lower limb muscle mass, 85.73 ± 2.42, 85.16 ± 2.40%, respectively; p = 0.02). The results of this study demonstrate that freedivers have significant asymmetries between the lower limbs in muscle oxygenation parameters when observing the lower limb dominance in relation to the percentage of muscle mass. These findings suggest different muscular oxygenation adaptations to the load set upon athletes. Full article
(This article belongs to the Section Life Sciences)
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33 pages, 6793 KiB  
Article
Mathematical Modeling of Robotic Locomotion Systems
by Erik Prada, Ľubica Miková, Ivan Virgala, Michal Kelemen, Peter Ján Sinčák and Roman Mykhailyshyn
Symmetry 2024, 16(3), 376; https://doi.org/10.3390/sym16030376 - 20 Mar 2024
Viewed by 1020
Abstract
This article deals with the presentation of an alternative approach that uses methods of geometric mechanics, which allow one to see into the geometrical structure of the equations and can be useful not only for modeling but also during the design of symmetrical [...] Read more.
This article deals with the presentation of an alternative approach that uses methods of geometric mechanics, which allow one to see into the geometrical structure of the equations and can be useful not only for modeling but also during the design of symmetrical locomotion systems and their control and motion planning. These methods are based on extracting the symmetries of Lie groups from the locomotion system in order to simplify the resulting equations. In the second section, the special two-dimensional Euclidean group SE2 and its splitting into right and left actions are derived. The physical interpretation of the local group and spatial velocities is investigated, and by virtue of the fact that both of these velocities represent the same velocity from a physical point of view, the dependence between them can be found by means of the adjoint action. The third section is devoted to the modeling and analysis of the planar locomotion of the symmetrical serpentine robot; the positions and local group velocities of its links are derived, the vector fields for the local connections are given, and the trajectories of the individual variables in the lateral movement of the kinematic snake are shown. At the end of the article, the overall benefits of the scientific study are summarized, as is the comparison of the results from the simulation phase, while the most significant novelty compared to alternative publications in the field can be considered the realization of this study with a description of the relevant methodology at a detailed level; that is, the locomotion results confirm the suitability of the use of geometric mechanics for these symmetrical locomotion systems with nonholonomic constraints. Full article
(This article belongs to the Special Issue Symmetry in the Advanced Mechanics of Systems)
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22 pages, 395 KiB  
Article
Coverings of Graphoids: Existence Theorem and Decomposition Theorems
by Aleksander Malnič and Boris Zgrablić
Symmetry 2024, 16(3), 375; https://doi.org/10.3390/sym16030375 - 20 Mar 2024
Viewed by 511
Abstract
A graphoid is a mixed multigraph with multiple directed and/or undirected edges, loops, and semiedges. A covering projection of graphoids is an onto mapping between two graphoids such that at each vertex, the mapping restricts to a local bijection on incoming edges and [...] Read more.
A graphoid is a mixed multigraph with multiple directed and/or undirected edges, loops, and semiedges. A covering projection of graphoids is an onto mapping between two graphoids such that at each vertex, the mapping restricts to a local bijection on incoming edges and outgoing edges. Naturally, as it appears, this definition displays unusual behaviour since the projection of the corresponding underlying graphs is not necessarily a graph covering. Yet, it is still possible to grasp such coverings algebraically in terms of the action of the fundamental monoid and combinatorially in terms of voltage assignments on arcs. In the present paper, the existence theorem is formulated and proved in terms of the action of the fundamental monoid. A more conventional formulation in terms of the weak fundamental group is possible because the action of the fundamental monoid is permutational. The standard formulation in terms of the fundamental group holds for a restricted class of coverings, called homogeneous. Further, the existence of the universal covering and the problems related to decomposing regular coverings via regular coverings are studied in detail. It is shown that with mild adjustments in the formulation, all the analogous theorems that hold in the context of graphs are still valid in this wider setting. Full article
(This article belongs to the Section Mathematics)
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22 pages, 3961 KiB  
Article
An Equivalent-Perceptional Intertemporal Choice Heuristics Model for Electric Operation Vehicle Charging Behavior
by Yue Han, Yi Quan, Peiwen Li, Bo Fu, Mei Xie and Haiyan Zhao
Symmetry 2024, 16(3), 374; https://doi.org/10.3390/sym16030374 - 20 Mar 2024
Viewed by 565
Abstract
The inherent stochasticity of electric operation vehicle (EOV) charging poses challenges to the stability and efficiency of regional power distribution networks. Existing charging behavior decision-making models often prioritize revenue considerations, neglecting the influence of multi-time-span characteristics and the potential irrationality of EOV owners. [...] Read more.
The inherent stochasticity of electric operation vehicle (EOV) charging poses challenges to the stability and efficiency of regional power distribution networks. Existing charging behavior decision-making models often prioritize revenue considerations, neglecting the influence of multi-time-span characteristics and the potential irrationality of EOV owners. To address these limitations, this study proposes a comprehensive framework encompassing three aspects. First, operational data are statistically analyzed to reconstruct EOV operation scenarios, establishing a dynamic charging scheme tailored to multi-time-span characteristics. Second, an improved ITCH model is developed using operational equivalent change to incorporate both gains and losses. Third, a WFL framework is employed to integrate the perceptual attenuation of revenue into the ITCH model. Simulation results show that decision-makers (DMs) demonstrate a preference for charging schemes with high equivalent perceived revenues and low time costs. Moreover, when the charging price is doubled, revenue perception attenuation leads decision-makers to postpone their charging behavior. Compared to other models, the equivalent perception intertemporal choice heuristics (EP-ITCH) charging model results in reduced load peaks, valleys, and variances on the grid side. This study highlights the model’s effectiveness and accuracy in optimizing EOV charging infrastructure. Full article
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12 pages, 260 KiB  
Article
On Some Combinatorial Properties of Balancing Split Quaternions
by Dorota Bród
Symmetry 2024, 16(3), 373; https://doi.org/10.3390/sym16030373 - 19 Mar 2024
Viewed by 502
Abstract
Quaternions and split quaternions are used in quantum physics, computer science, and in many areas of mathematics. In this paper, we define and study two new classes of split quaternions, namely balancing split quaternions and Lucas-balancing split quaternions. Moreover, well-known properties, e.g., Catalan, [...] Read more.
Quaternions and split quaternions are used in quantum physics, computer science, and in many areas of mathematics. In this paper, we define and study two new classes of split quaternions, namely balancing split quaternions and Lucas-balancing split quaternions. Moreover, well-known properties, e.g., Catalan, d’Ocagne, and Vajda identities, for these quaternions are also presented. We give matrix generators for balancing split quaternions and Lucas-balancing split quaternions, too. Full article
(This article belongs to the Section Mathematics)
14 pages, 288 KiB  
Article
On Generalized t-Transformation of Free Convolution
by Ayed. R. A. Alanzi, Raouf Fakhfakh and Fatimah Alshahrani
Symmetry 2024, 16(3), 372; https://doi.org/10.3390/sym16030372 - 19 Mar 2024
Viewed by 561
Abstract
A notion of generalized (two-parameterized) t-transformation of free convolution, also called (t=(a,b))-deformed free convolution, is introduced for aR and b>0. In this article, some results of t-deformed [...] Read more.
A notion of generalized (two-parameterized) t-transformation of free convolution, also called (t=(a,b))-deformed free convolution, is introduced for aR and b>0. In this article, some results of t-deformed free convolution are given within the theory of Cauchy-Stieltjes Kernel (CSK) families. The variance function is a fundamental concept in CSK families. An expression is provided for the variance function under t-deformed free convolution power. In addition, through the use of the variance function, an approximation is provided for members of the t-deformed free Gaussian CSK family and members of the t-deformed free Poisson CSK family respectively. Furthermore, by involving the free multiplicative convolution, a new limit theorem is provided with respect to t-deformed free convolution. Full article
(This article belongs to the Section Mathematics)
10 pages, 265 KiB  
Article
The Hamilton–Waterloo Problem with C16-Factors and Cm-Factors for Odd m
by Li Wang
Symmetry 2024, 16(3), 371; https://doi.org/10.3390/sym16030371 - 19 Mar 2024
Viewed by 515
Abstract
The Hamilton–Waterloo problem is a problem of graph factorization. The Hamilton–Waterloo problem HWP(H;m,n;α,β) asks for a two-factorization of a graph H containing α Cm-factors and β Cn [...] Read more.
The Hamilton–Waterloo problem is a problem of graph factorization. The Hamilton–Waterloo problem HWP(H;m,n;α,β) asks for a two-factorization of a graph H containing α Cm-factors and β Cn-factors. Let Kv* denote the complete graph Kv if v is odd and Kv minus a one-factor if v is even. In this paper, we completely solve the Hamilton–Waterloo problem HWP(Kv*;m,16;α,β) for odd m9 and α15. Full article
(This article belongs to the Special Issue Advances in Combinatorics and Graph Theory)
22 pages, 9762 KiB  
Article
Influence of the Plan Structural Symmetry on the Non-Linear Seismic Response of Framed Reinforced Concrete Buildings
by Juan Carlos Vielma-Quintero, Edgar Giovanny Diaz-Segura and Juan Carlos Vielma
Symmetry 2024, 16(3), 370; https://doi.org/10.3390/sym16030370 - 19 Mar 2024
Viewed by 598
Abstract
Seismic-resistant design incorporates measures to ensure that structures perform adequately under specific limit states, focusing on seismic forces derived from both the equivalent static and spectral modal methods. This study examined buildings on slopes in densely built urban areas, a common scenario in [...] Read more.
Seismic-resistant design incorporates measures to ensure that structures perform adequately under specific limit states, focusing on seismic forces derived from both the equivalent static and spectral modal methods. This study examined buildings on slopes in densely built urban areas, a common scenario in Latin American cities with high seismic risks. The adjustment of high-rise buildings to sloping terrains induces structural asymmetry, leading to plan and elevation irregularities that significantly impact their seismic response. This paper explores the asymmetry in medium-height reinforced concrete frame buildings on variable inclines (0°, 15°, 30°, and 45°) and its effect on their nonlinear response, assessed via displacements, rotations, and damage. Synthetic accelerograms matched with Chile’s high seismic hazard design spectrum, scaled for different performance states and seismic records from the Chilean subduction zone, were applied. The findings highlight structural asymmetry’s role in influencing nonlinear response parameters such as ductility, transient interstory drifts, and roof rotations, and uncover element demand distributions surpassing conventional analysis and in earthquake-resistant design expectations. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos II)
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17 pages, 5327 KiB  
Article
Control and Analysis of a Hybrid-Rotor Bearingless Switched Reluctance Motor with One-Phase Full-Period Suspension
by Zeyuan Liu, Xingcheng Wu, Wenfeng Zhang, Yan Yang and Chengzi Liu
Symmetry 2024, 16(3), 369; https://doi.org/10.3390/sym16030369 - 18 Mar 2024
Viewed by 584
Abstract
In the traditional control scheme of a 12/8-pole bearingless switched reluctance motor (BSRM), radial force and torque are usually controlled as a compromise due to the conflict between their effective output areas. Additionally, each phase requires individual power circuits and is excited in [...] Read more.
In the traditional control scheme of a 12/8-pole bearingless switched reluctance motor (BSRM), radial force and torque are usually controlled as a compromise due to the conflict between their effective output areas. Additionally, each phase requires individual power circuits and is excited in turn to produce a continuous levitation force, resulting in high power device requirements and high controller costs. This paper discusses a 12/8-pole single-winding hybrid-rotor bearingless switched reluctance motor (HBSRM) with a hybrid rotor consisting of cylindrical and salient-pole lamination segments. The asymmetric rotor of the HBSRM slightly increases the complexity of its structure and magnetic circuit, but makes it possible to generate the desired radial force at any rotor angular position. A control scheme for the HBSRM is developed to utilize the independent excitation of the four windings in one phase to generate the desired levitation force at any rotor angular position, and it requires only half the number of power circuits used in the conventional control scheme of a 12/8-pole single-winding BSRM. Different from the average torque chosen to be controlled in traditional methods, this scheme directly regulates the instantaneous total torque produced by all excited phases together and presents a current algorithm to optimize the torque contribution of each phase so as to reduce torque pulsation, and the improved performance of this bearingless motor is finally validated by simulation analysis. Full article
(This article belongs to the Special Issue Research on Motor and Special Electromagnetic Device of Symmetry II)
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16 pages, 673 KiB  
Article
Recent Developments in Iterative Algorithms for Digital Metrics
by Aasma Shaheen, Afshan Batool, Amjad Ali, Hamed Al Sulami and Aftab Hussain
Symmetry 2024, 16(3), 368; https://doi.org/10.3390/sym16030368 - 18 Mar 2024
Viewed by 864
Abstract
This paper aims to provide a comprehensive analysis of the advancements made in understanding Iterative Fixed-Point Schemes, which builds upon the concept of digital contraction mappings. Additionally, we introduce the notion of an Iterative Fixed-Point Schemes in digital metric spaces. In this study, [...] Read more.
This paper aims to provide a comprehensive analysis of the advancements made in understanding Iterative Fixed-Point Schemes, which builds upon the concept of digital contraction mappings. Additionally, we introduce the notion of an Iterative Fixed-Point Schemes in digital metric spaces. In this study, we extend the idea of Iteration process Mann, Ishikawa, Agarwal, and Thakur based on the ϝ-Stable Iterative Scheme in digital metric space. We also design some fractal images, which frame the compression of Fixed-Point Iterative Schemes and contractive mappings. Furthermore, we present a concrete example that exemplifies the motivation behind our investigations. Moreover, we provide an application of the proposed Fractal image and Sierpinski triangle that compress the works by storing images as a collection of digital contractions, which addresses the issue of storing images with less storage memory in this paper. Full article
(This article belongs to the Special Issue New Trends in Fixed Point Theory with Emphasis on Symmetry)
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23 pages, 24085 KiB  
Article
An ONIOM-Based High-Level Thermochemistry Study on Hydrogen Abstraction Reactions of Large Straight-Chain Alkanes by Hydrogen, Hydroxyl, and Hydroperoxyl Radicals
by Yicheng Chi, Hao Pan, Qinghui Meng, Lidong Zhang and Peng Zhang
Symmetry 2024, 16(3), 367; https://doi.org/10.3390/sym16030367 - 18 Mar 2024
Viewed by 631
Abstract
Accurate thermochemical data are of great importance in developing quantitatively predictive reaction mechanisms for transportation fuels, such as diesel and jet fuels, which are primarily composed of large hydrocarbon molecules, especially large straight-chain alkanes containing more than 10 carbon atoms. This paper presents [...] Read more.
Accurate thermochemical data are of great importance in developing quantitatively predictive reaction mechanisms for transportation fuels, such as diesel and jet fuels, which are primarily composed of large hydrocarbon molecules, especially large straight-chain alkanes containing more than 10 carbon atoms. This paper presents an ONIOM[QCISD(T)/CBS:DFT]-based theoretical thermochemistry study on the hydrogen abstraction reactions of straight-chain alkanes, n-CnH2n+2, (n = 1–16) by hydrogen (H), hydroxyl (OH), and hydroperoxyl (HO2) radicals. These reactions, with n ≥ 10, pose significant computational challenges for prevalent high-level ab initio methods. However, they are effectively addressed using the ONIOM-based method. One notable aspect of this study is the consideration of the high symmetry of straight-chain alkanes. This symmetry allows us to study half of the reactions, employing a generalized approach. Therefore, a total of 216 reactions are systematically studied for the three reaction systems. Our results align very well with those from the widely accepted high-level QCISD(T)/CBS method, with discrepancies between the two generally less than 0.10 kcal/mol. Furthermore, we compared large straight-chain alkanes (n-C16H34 and n-C18H38) with large methyl ester molecules (C15H31COOCH3 and C17H33COOCH3) to elucidate the impact of functional groups (ester group and C=C double bond) on the reactivity of the long-chain structure. These findings underscore the accuracy and efficiency of the ONIOM-based method in computational thermochemistry, particularly for large straight-chain hydrocarbons in transportation fuels. Full article
(This article belongs to the Special Issue Symmetry in Aerospace Sciences and Applications)
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25 pages, 2118 KiB  
Review
An Extensive Investigation into the Use of Machine Learning Tools and Deep Neural Networks for the Recognition of Skin Cancer: Challenges, Future Directions, and a Comprehensive Review
by Syed Ibrar Hussain and Elena Toscano
Symmetry 2024, 16(3), 366; https://doi.org/10.3390/sym16030366 - 18 Mar 2024
Viewed by 926
Abstract
Skin cancer poses a serious risk to one’s health and can only be effectively treated with early detection. Early identification is critical since skin cancer has a higher fatality rate, and it expands gradually to different areas of the body. The rapid growth [...] Read more.
Skin cancer poses a serious risk to one’s health and can only be effectively treated with early detection. Early identification is critical since skin cancer has a higher fatality rate, and it expands gradually to different areas of the body. The rapid growth of automated diagnosis frameworks has led to the combination of diverse machine learning, deep learning, and computer vision algorithms for detecting clinical samples and atypical skin lesion specimens. Automated methods for recognizing skin cancer that use deep learning techniques are discussed in this article: convolutional neural networks, and, in general, artificial neural networks. The recognition of symmetries is a key point in dealing with the skin cancer image datasets; hence, in developing the appropriate architecture of neural networks, as it can improve the performance and release capacities of the network. The current study emphasizes the need for an automated method to identify skin lesions to reduce the amount of time and effort required for the diagnostic process, as well as the novel aspect of using algorithms based on deep learning for skin lesion detection. The analysis concludes with underlying research directions for the future, which will assist in better addressing the difficulties encountered in human skin cancer recognition. By highlighting the drawbacks and advantages of prior techniques, the authors hope to establish a standard for future analysis in the domain of human skin lesion diagnostics. Full article
(This article belongs to the Special Issue Feature Papers in Mathematics Section)
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20 pages, 545 KiB  
Article
Statistical Inference and Application of Asymmetrical Generalized Pareto Distribution Based on Peaks-Over-Threshold Model
by Wenru Chen, Xu Zhao, Mi Zhou, Haiqing Chen, Qingqing Ji and Weihu Cheng
Symmetry 2024, 16(3), 365; https://doi.org/10.3390/sym16030365 - 18 Mar 2024
Viewed by 606
Abstract
Generalized Pareto distribution (GPD), an asymmetrical distribution, primarily models exceedances over a high threshold in many applications. Within the peaks-over-threshold (POT) framework, we consider a new GPD parameter estimation method to estimate a common tail risk measure, the value at risk (VaR). The [...] Read more.
Generalized Pareto distribution (GPD), an asymmetrical distribution, primarily models exceedances over a high threshold in many applications. Within the peaks-over-threshold (POT) framework, we consider a new GPD parameter estimation method to estimate a common tail risk measure, the value at risk (VaR). The proposed method is more suitable for the POT framework and makes full use of data information. Specifically, our estimation method builds upon the generalized probability weighted moments method and integrates it with the nonlinear weighted least squares method. We use exceedances for the GPD, minimizing the sum of squared differences between the sample and population moments of a function of GPD random variables. At the same time, the proposed estimator uses three iterations and assigns weight to further improving the estimated performance. Under Monte Carlo simulations and with a real heavy-tailed dataset, the simulation results show the advantage of the newly proposed estimator, particularly when VaRs are at high confidence levels. In addition, by simulating other heavy-tailed distributions, our method still exhibits good performance in estimating misjudgment distributions. Full article
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16 pages, 1048 KiB  
Article
On the Breaking of the U(1) Peccei–Quinn Symmetry and Its Implications for Neutrino and Dark Matter Physics
by Osvaldo Civitarese
Symmetry 2024, 16(3), 364; https://doi.org/10.3390/sym16030364 - 18 Mar 2024
Viewed by 532
Abstract
The Standard Model of electroweak interactions is based on the fundamental SU(2)weak × U(1)elect representation. It assumes massless neutrinos and purely left-handed massive W± and Z0 bosons to which one should add the massless photon. The existence, [...] Read more.
The Standard Model of electroweak interactions is based on the fundamental SU(2)weak × U(1)elect representation. It assumes massless neutrinos and purely left-handed massive W± and Z0 bosons to which one should add the massless photon. The existence, verified experimentally, of neutrino oscillations poses a challenge to this scheme, since the oscillations take place between at least three massive neutrinos belonging to a mass hierarchy still to be determined. One should also take into account the possible existence of sterile neutrino species. In a somehow different context, the fundamental nature of the strong interaction component of the forces in nature is described by the, until now, extremely successful representation based on the SU(3)strong group which, together with the confining rule, give a description of massive hadrons in terms of quarks and gluons. To this is added the minimal U(1) Higgs group to give mass to the otherwise massless generators. This representation may also be challenged by the existence of both dark matter and dark energy, of still unknown composition. In this note, we shall discuss a possible connection between these questions, namely the need to extend the SU(3)strong × SU(2)weak × U(1)elect to account for massive neutrinos and dark matter. The main point of it is related to the role of axions, as postulated by Roberto Peccei and Helen Quinn. The existence of neutral pseudo-scalar bosons, that is, the axions, has been proposed long ago by Peccei and Quinn to explain the suppression of the electric dipole moment of the neutron. The associated U(1)PQ symmetry breaks at very high energy, and it guarantees that the interaction of other particles with axions is very weak. We shall review the axion properties in connection with the apparently different contexts of neutrino and dark matter physics. Full article
(This article belongs to the Special Issue Role of Symmetries in Nuclear Physics)
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20 pages, 363 KiB  
Article
Modified Tseng Method for Solving Pseudomonotone Variational Inequality Problem in Banach Spaces
by Rose Maluleka, Godwin Chidi Ugwunnadi, Maggie Aphane, Hammed A. Abass and Abdul Rahim Khan
Symmetry 2024, 16(3), 363; https://doi.org/10.3390/sym16030363 - 18 Mar 2024
Viewed by 549
Abstract
This article examines the process for solving the fixed-point problem of Bregman strongly nonexpansive mapping as well as the variational inequality problem of the pseudomonotone operator. Within the context of p-uniformly convex real Banach spaces that are also uniformly smooth, we introduce [...] Read more.
This article examines the process for solving the fixed-point problem of Bregman strongly nonexpansive mapping as well as the variational inequality problem of the pseudomonotone operator. Within the context of p-uniformly convex real Banach spaces that are also uniformly smooth, we introduce a modified Halpern iterative technique combined with an inertial approach and Tseng methods for finding a common solution of the fixed-point problem of Bregman strongly nonexpansive mapping and the pseudomonotone variational inequality problem. Using our iterative approach, we develop a strong convergence result for approximating the solution of the aforementioned problems. We also discuss some consequences of our major finding. The results presented in this paper complement and build upon many relevant discoveries in the literature. Full article
(This article belongs to the Section Mathematics)
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11 pages, 279 KiB  
Article
Pseudo-Finsler Radially Symmetric Spaces
by Marianty Ionel and Miguel Ángel Javaloyes
Symmetry 2024, 16(3), 362; https://doi.org/10.3390/sym16030362 - 18 Mar 2024
Viewed by 585
Abstract
We introduce the concept of radially symmetric pseudo-Finsler spaces, which generalize the notion of symmetric Finsler spaces, and prove that this concept is equivalent to the preservation of flag curvature by parallel transport together with reversibility. As a consequence, reversible pseudo-Finsler manifolds with [...] Read more.
We introduce the concept of radially symmetric pseudo-Finsler spaces, which generalize the notion of symmetric Finsler spaces, and prove that this concept is equivalent to the preservation of flag curvature by parallel transport together with reversibility. As a consequence, reversible pseudo-Finsler manifolds with constant flag curvature are radially symmetric. Full article
(This article belongs to the Special Issue Recent Advance in Mathematical Physics II)
14 pages, 280 KiB  
Article
The Hermitian Solution to a New System of Commutative Quaternion Matrix Equations
by Yue Zhang, Qing-Wen Wang and Lv-Ming Xie
Symmetry 2024, 16(3), 361; https://doi.org/10.3390/sym16030361 - 17 Mar 2024
Viewed by 557
Abstract
This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, where we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. In addition, we also [...] Read more.
This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, where we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. In addition, we also provide the least squares Hermitian solution in cases where the system of matrix equations is not consistent. To illustrate our main findings, in this paper we present two numerical algorithms and examples. Full article
(This article belongs to the Section Mathematics)
18 pages, 1266 KiB  
Article
New Approach of Normal and Shear Stress Components for Multiple Curvilinear Holes Which Weakened a Flexible Plate
by Faizah M. Alharbi and Nafeesa G. Alhendi
Symmetry 2024, 16(3), 360; https://doi.org/10.3390/sym16030360 - 16 Mar 2024
Viewed by 566
Abstract
In this article, a thin infinite flexible plate weakened by multiple curvilinear holes is considered. The strength shapes are mapped outside a unit circle with the assistance of particular conformal mapping under certain conditions. The mathematical model that governs the rounded forces of [...] Read more.
In this article, a thin infinite flexible plate weakened by multiple curvilinear holes is considered. The strength shapes are mapped outside a unit circle with the assistance of particular conformal mapping under certain conditions. The mathematical model that governs the rounded forces of the current physical problem is the boundary value problem of elastic media. This study is applicable to many phenomena throughout nature, like tunnels, caves, and excavations in soil or rock. The Cauchy method for complex variables is used to get the closed forms of Gaursat functions and change the problem to a second-type integrodifferential equation with a Cauchy kernel, which is used for a large area of the contact problems. Then, the normal and shear stress components that act on the model are derived. Afterward, some of the physical applications are studied, and different stress components at specific values in each application are calculated and plotted using Maple 2023. Full article
(This article belongs to the Section Mathematics)
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19 pages, 3756 KiB  
Review
Charged Lepton-Flavour Violation
by Giulia Frau and Christoph Langenbruch
Symmetry 2024, 16(3), 359; https://doi.org/10.3390/sym16030359 - 16 Mar 2024
Viewed by 502