Symmetry

16 pages, 461 KiB

Open AccessArticle

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 583

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

Open AccessArticle

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 550

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

C^{2}

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

Open AccessArticle

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 699

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

Open AccessArticle

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 632

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

Open AccessArticle

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 1139

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

S E (2)

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

Open AccessArticle

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 568

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

Open AccessArticle

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 621

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

(This article belongs to the Special Issue Cyber–Physical Co-regulation and Optimization Methods in Smart Power Systems from the Perspective of Cyber–Physical Symmetry)

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12 pages, 260 KiB

Open AccessArticle

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 555

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

Open AccessArticle

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 610

Abstract

A notion of generalized (two-parameterized) t-transformation of free convolution, also called

(t = (a, b))

-deformed free convolution, is introduced for

a \in R

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

a \in R

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

Open AccessArticle

The Hamilton–Waterloo Problem with C₁₆-Factors and C_m-Factors for Odd m

by Li Wang

Symmetry 2024, 16(3), 371; https://doi.org/10.3390/sym16030371 - 19 Mar 2024

Viewed by 561

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

C_{m}

-factors and

β

C_{n}

[...] 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

C_{m}

-factors and

β

C_{n}

-factors. Let

K_{v}^{*}

denote the complete graph

K_{v}

if v is odd and

K_{v}

minus a one-factor if v is even. In this paper, we completely solve the Hamilton–Waterloo problem HWP

(K_{v}^{*}; m, 16; α, β)

for odd

m \geq 9

and

α \geq 15

. Full article

(This article belongs to the Special Issue Advances in Combinatorics and Graph Theory)

22 pages, 9762 KiB

Open AccessArticle

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 684

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

Open AccessArticle

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 623

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

Open AccessArticle

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 917

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

Open AccessArticle

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 692

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-C_nH_2n+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

Open AccessReview

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 1093

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

Open AccessArticle

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 651

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

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science II)

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16 pages, 1048 KiB

Open AccessArticle

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 592

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^{\pm}

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^{\pm}

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

Open AccessArticle

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 592

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

Open AccessArticle

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 622

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

Open AccessArticle

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

Cited by 1 | Viewed by 616

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

Open AccessArticle

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 622

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

Open AccessReview

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 572

Abstract

We review the experimental status of searches for lepton-flavour violation in the charged sector. We give an overview of searches for lepton-flavour violation in purely leptonic decays, hadron decays, and decays of heavy bosons. We focus on the most stringent constraints on lepton-flavour [...] Read more.

We review the experimental status of searches for lepton-flavour violation in the charged sector. We give an overview of searches for lepton-flavour violation in purely leptonic decays, hadron decays, and decays of heavy bosons. We focus on the most stringent constraints on lepton-flavour violating processes in these areas and give prospects for ongoing and future experiments. Full article

(This article belongs to the Special Issue Symmetries and Anomalies in Flavour Physics)

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28 pages, 12037 KiB

Open AccessArticle

Improved Generative Adversarial Network for Bearing Fault Diagnosis with a Small Number of Data and Unbalanced Data

by Zhaohui Qin, Faguo Huang, Jiafang Pan, Junlin Niu and Haihua Qin

Symmetry 2024, 16(3), 358; https://doi.org/10.3390/sym16030358 - 15 Mar 2024

Viewed by 724

Abstract

Fault data under real operating conditions are often difficult to collect, making the number of trained fault data small and out of proportion to normal data. Thus, fault diagnosis symmetry (balance) is compromised. This will result in less effective fault diagnosis methods for [...] Read more.

Fault data under real operating conditions are often difficult to collect, making the number of trained fault data small and out of proportion to normal data. Thus, fault diagnosis symmetry (balance) is compromised. This will result in less effective fault diagnosis methods for cases with a small number of data and data imbalances (S&I). We present an innovative solution to overcome this problem, which is composed of two components: data augmentation and fault diagnosis. In the data augmentation section, the S&I dataset is supplemented with a deep convolutional generative adversarial network based on a gradient penalty and Wasserstein distance (WDCGAN-GP), which solve the problems of the generative adversarial network (GAN) being prone to model collapse and the gradient vanishing during the training time. The addition of self-attention allows for a better identification and generation of sample features. Finally, the addition of spectral normalization can stabilize the training of the model. In the fault diagnosis section, fault diagnosis is performed through a convolutional neural network with coordinate attention (CNN-CA). Our experiments conducted on two bearing fault datasets for comparison demonstrate that the proposed method surpasses other comparative approaches in terms of the quality of data augmentation and the accuracy of fault diagnosis. It effectively addresses S&I fault diagnosis challenges. Full article

(This article belongs to the Topic Predictive Analytics and Fault Diagnosis of Machines with Machine Learning Techniques)

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25 pages, 2100 KiB

Open AccessArticle

Special Relativity in Terms of Hyperbolic Functions with Coupled Parameters in 3+1 Dimensions

by Nikolai S. Akintsov, Artem P. Nevecheria, Gennadii F. Kopytov, Yongjie Yang and Tun Cao

Symmetry 2024, 16(3), 357; https://doi.org/10.3390/sym16030357 - 15 Mar 2024

Viewed by 653

Abstract

This paper presents a method for parameterizing new Lorentz spacetime coordinates based on coupled parameters. The role of symmetry in rapidity in special relativity is explored, and invariance is obtained for new spacetime intervals with respect to the Lorentz transformation. Using the Euler–Hamilton [...] Read more.

This paper presents a method for parameterizing new Lorentz spacetime coordinates based on coupled parameters. The role of symmetry in rapidity in special relativity is explored, and invariance is obtained for new spacetime intervals with respect to the Lorentz transformation. Using the Euler–Hamilton equations, an additional angular rapidity and perpendicular rapidity are obtained, and the Hamiltonian and Lagrangian of a relativistic particle are expanded into rapidity spectra. A so-called passage to the limit is introduced that makes it possible to decompose physical quantities into spectra in terms of elementary functions when explicit decomposition is difficult. New rapidity-dependent Lorentz spacetime coordinates are obtained. The descriptions of particle motion using the old and new Lorentz spacetime coordinates as applied to plane laser pulses are compared in terms of the particle kinetic energy. Based on a classical model of particle motion in the field of a plane monochromatic electromagnetic wave and that of a plane laser pulse, rapidity-dependent spectral decompositions into elementary functions are presented, and the Euler–Hamilton equations are derived as rapidity functions in 3+1 dimensions. The new and old Lorentz spacetime coordinates are compared with the Fermi spacetime coordinates. The proper Lorentz groups SO(1,3) with coupled parameters using the old and new Lorentz spacetime coordinates are also compared. As a special case, the application of Lorentz spacetime coordinates to a relativistic hydrodynamic system with coupled parameters in 1+1 dimensions is demonstrated. Full article

(This article belongs to the Special Issue Lorentz Symmetry and General Relativity)

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22 pages, 9020 KiB

Open AccessArticle

A Low-Latency Noise-Aware Tone Mapping Operator for Hardware Implementation with a Locally Weighted Guided Filter

by Qianwang Liang, Tianyu Yan, Nan Wang, Zhiying Zhu and Jiongyao Ye

Symmetry 2024, 16(3), 356; https://doi.org/10.3390/sym16030356 - 15 Mar 2024

Viewed by 642

Abstract

A tone mapping operator (TMO) is a module in the image signal processing pipeline that is used to convert high dynamic range images to low dynamic range images for display. Currently, state-of-the-art TMOs typically take complex algorithms and are implemented on graphics processing [...] Read more.

A tone mapping operator (TMO) is a module in the image signal processing pipeline that is used to convert high dynamic range images to low dynamic range images for display. Currently, state-of-the-art TMOs typically take complex algorithms and are implemented on graphics processing units, making it difficult to run with low latency on edge devices, and TMOs implemented in hardware circuits often lack additional noise suppression because of latency and hardware resource constraints. To address these issues, we proposed a low-latency noise-aware TMO for hardware implementation. Firstly, a locally weighted guided filter is proposed to decompose the luminance image into a base layer and a detail layer, with the weight function symmetric concerning the central pixel value of a window. Secondly, the mean and standard deviation of the basic layer and the detail layer are used to estimate the noise visibility according to the human visual characteristics. Finally, the gain for the detail layer is calculated to achieve adaptive noise suppression. In this process, luminance is first processed by the log2 function before being filtered and then symmetrically converted back to the linear domain by the exp2 function after compression. Meanwhile, the algorithms within the proposed TMO were optimized for hardware implementation to minimize latency and cache, achieving a low latency of 60.32

μ s

under video specification of 1080 P at 60 frames per second and objective metric smoothness in dark flat regions could be improved by more than 10% compared to similar methods. Full article

(This article belongs to the Special Issue Security, Communication and Privacy in Internet of Things: Symmetry and Advances — Volume II)

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27 pages, 2648 KiB

Open AccessReview

Enigma of Pyramidal Neurons: Chirality-Centric View on Biological Evolution. Congruence to Molecular, Cellular, Physiological, Cognitive, and Psychological Functions

by Victor Vasilyevich Dyakin and Nika Viktorovna Dyakina-Fagnano

Symmetry 2024, 16(3), 355; https://doi.org/10.3390/sym16030355 - 15 Mar 2024

Cited by 1 | Viewed by 1267

Abstract

The mechanism of brain information processing unfolds within spatial and temporal domains inherently linked to the concept of space–time symmetry. Biological evolution, beginning with the prevalent molecular chirality, results in the handedness of human cognitive and psychological functions (the phenomena known as biochirality). [...] Read more.

The mechanism of brain information processing unfolds within spatial and temporal domains inherently linked to the concept of space–time symmetry. Biological evolution, beginning with the prevalent molecular chirality, results in the handedness of human cognitive and psychological functions (the phenomena known as biochirality). The key element in the chain of chirality transfer from the downstream to upstream processes is the pyramidal neuron (PyrN) morphology–function paradigm (archetype). The most apparent landmark of PyrNs is the geometry of the cell soma. However, “why/how PyrN’s soma gains the shape of quasi-tetrahedral symmetry” has never been explicitly articulated. Resolving the above inquiry is only possible based on the broad-view assumption that encoding 3D space requires specific 3D geometry of the neuronal detector and corresponding network. Accordingly, our hypothesis states that if the primary function of PyrNs, at the organism level, is sensory space symmetry perception, then the pyramidal shape of soma is the best evolutionary-selected geometry to support sensory-motor coupling. The biological system’s non-equilibrium (NE) state is fundamentally linked to an asymmetric, non-racemic, steady state of molecular constituents. The chiral theory of pyramidal soma shape conceptually agrees that living systems have evolved as non-equilibrium systems that exchange energy with the environment. The molecular mechanism involved in developing PyrN’s soma is studied in detail. However, the crucial missing element—the reference to the fundamental link between molecular chirality and the function of spatial navigation—is the main obstacle to resolving the question in demand: why did PyrNs’ soma gain the shape of quasi-tetrahedral symmetry? Full article

(This article belongs to the Section Life Sciences)

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24 pages, 515 KiB

Open AccessArticle

Hidden-Charm Pentaquarks with Strangeness in a Chiral Quark Model

by Gang Yang, Jialun Ping and Jorge Segovia

Symmetry 2024, 16(3), 354; https://doi.org/10.3390/sym16030354 - 14 Mar 2024

Cited by 4 | Viewed by 598

Abstract

The LHCb collaboration has recently announced the discovery of two hidden-charm pentaquark states with strange quark content,

P_{c s} (4338)

and

P_{c s} (4459)

; its analysis points towards having both hadrons’ isospins equal to zero and [...] Read more.

The LHCb collaboration has recently announced the discovery of two hidden-charm pentaquark states with strange quark content,

P_{c s} (4338)

and

P_{c s} (4459)

; its analysis points towards having both hadrons’ isospins equal to zero and spin-parity quantum numbers

{\frac{1}{2}}^{-}

and

{\frac{3}{2}}^{-}

, respectively. Herein, we perform a systematical investigation of the

q q s c \bar{c}

(q = u, d)

system by means of a chiral quark model, along with a highly accurate computational method, the Gaussian expansion approach combined with the complex scaling technique. baryon-meson configurations in both singlet- and hidden-color channels are considered. The

P_{c s} (4338)

and

P_{c s} (4459)

signals can be well identified as molecular bound states with dominant components

Λ J / ψ

(60 %)

and

Ξ_{c} D

(23 %)

for the lowest-energy case and

Ξ_{c} D^{*}

(72 %)

for the highest-energy one. In addition, it seems that some narrow resonances can also be found in each allowed

I (J^{P})

channel in the energy region of

4.6

–

5.5

GeV, except for the

1 ({\frac{1}{2}}^{-})

channel where a shallow bound state with dominant

Ξ_{c}^{*} D^{*}

structure is obtained at 4673 MeV with binding energy

E_{B} = - 3

MeV. These exotic states are expected to be confirmed in future high-energy experiments. Full article

(This article belongs to the Section Physics)

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22 pages, 375 KiB

Open AccessArticle

Anisotropy and Asymptotic Degeneracy of the Physical-Hilbert-Space Inner-Product Metrics in an Exactly Solvable Unitary Quantum Model

by Miloslav Znojil

Symmetry 2024, 16(3), 353; https://doi.org/10.3390/sym16030353 - 14 Mar 2024

Cited by 1 | Viewed by 557

Abstract

A unitary-evolution process leading to an ultimate collapse and to a complete loss of observability alias quantum phase transition is studied. A specific solvable

N -

state model is considered, characterized by a non-stationary non-Hermitian Hamiltonian. Our analysis uses quantum mechanics formulated in [...] Read more.

A unitary-evolution process leading to an ultimate collapse and to a complete loss of observability alias quantum phase transition is studied. A specific solvable

N -

state model is considered, characterized by a non-stationary non-Hermitian Hamiltonian. Our analysis uses quantum mechanics formulated in Schrödinger picture in which, in principle, only the knowledge of a complete set of observables (i.e., operators

Λ_{j}

) enables one to guarantee the uniqueness of the related physical Hilbert space (i.e., of its inner-product metric

Θ

). Nevertheless, for the sake of simplicity, we only assume the knowledge of just a single input observable (viz., of the energy-representing Hamiltonian

H \equiv Λ_{1}

). Then, out of all of the eligible and Hamiltonian-dependent “Hermitizing” inner-product metrics

Θ = Θ (H)

, we pick up just the simplest possible candidate. Naturally, this slightly restricts the scope of the theory, but in our present model, such a restriction is more than compensated for by the possibility of an alternative, phenomenologically better motivated constraint by which the time-dependence of the metric is required to be smooth. This opens a new model-building freedom which, in fact, enables us to force the system to reach the collapse, i.e., a genuine quantum catastrophe as a result of the mere conventional, strictly unitary evolution. Full article

(This article belongs to the Special Issue The Benefits That Physics Derives from the Concept of Symmetry)

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15 pages, 2558 KiB

Open AccessArticle

Adaptive Feedback Control of Nonminimum Phase Boost Converter with Constant Power Load

by Khalil Jouili, Monia Charfeddine and Mohammed Alqarni

Symmetry 2024, 16(3), 352; https://doi.org/10.3390/sym16030352 - 14 Mar 2024

Viewed by 637

Abstract

The inherent negative impedance characteristics of a Constant Power Load (CPL) pose a potential threat to the stability of the bus voltage in a DC microgrid consisting of a symmetrical parallel boost converter. We suggest an adaptive feedback control technique using the input–output [...] Read more.

The inherent negative impedance characteristics of a Constant Power Load (CPL) pose a potential threat to the stability of the bus voltage in a DC microgrid consisting of a symmetrical parallel boost converter. We suggest an adaptive feedback control technique using the input–output exact feedback linearization theory for a boost converter integrated into a DC microgrid to improve the stability of the DC bus voltage. This approach involves a transformation of the model into a Brunovsky canonical form, effectively addressing the nonlinear challenges arising from the CPL and the nonminimum phase characteristics of the boost converter. Subsequently, guided by the Lyapunov approach, an adaptation law is established to fine-tune the controller’s gain vector, facilitating the tracking of a predefined linearizing feedback control. We methodically create a method to choose the gains of the adaptive controller in order to guarantee an adequate output response. We validate our suggested controller’s performance using simulation. Full article

(This article belongs to the Special Issue Active Control of Asymmetrical Wake Flow in Wind Energy Systems)

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17 pages, 323 KiB

Open AccessArticle

Analytic Functions in a Complete Reinhardt Domain Having Bounded L-Index in Joint Variables

by Andriy Bandura, Tetyana Salo and Oleh Skaskiv

Symmetry 2024, 16(3), 351; https://doi.org/10.3390/sym16030351 - 14 Mar 2024

Viewed by 590

Abstract

The manuscript is an initiative to construct a full and exhaustive theory of analytical multivariate functions in any complete Reinhardt domain by introducing the concept of

L

-index in joint variables for these functions for a given continuous, non-negative, non-vanishing, vector-valued mapping

L

[...] Read more.

The manuscript is an initiative to construct a full and exhaustive theory of analytical multivariate functions in any complete Reinhardt domain by introducing the concept of

L

-index in joint variables for these functions for a given continuous, non-negative, non-vanishing, vector-valued mapping

L

defined in an interior of the domain with some behavior restrictions. The complete Reinhardt domain is an example of a domain having a circular symmetry in each complex dimension. Our results are based on the results obtained for such classes of holomorphic functions: entire multivariate functions, as well as functions which are analytical in the unit ball, in the unit polydisc, and in the Cartesian product of the complex plane and the unit disc. For a full exhaustion of the domain, polydiscs with some radii and centers are used. Estimates of the maximum modulus for partial derivatives of the functions belonging to the class are presented. The maximum is evaluated at the skeleton of some polydiscs with any center and with some radii depending on the center and the function

L

and, at most, it equals a some constant multiplied by the partial derivative modulus at the center of the polydisc. Other obtained statements are similar to the described one. Full article

(This article belongs to the Section Mathematics)

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