Symmetry

15 pages, 6690 KiB

Open AccessArticle

Computed Mass-Fragmentation Energy Profiles of Some Acetalized Monosaccharides for Identification in Mass Spectrometry

by Mihai-Cosmin Pascariu, Nicolae Dinca, Carolina Cojocariu, Eugen Sisu, Alina Serb, Romina Birza and Marius Georgescu

Symmetry 2022, 14(5), 1074; https://doi.org/10.3390/sym14051074 - 23 May 2022

Cited by 2 | Viewed by 2129

Abstract

Our study found that quantum calculations can differentiate fragmentation energies into isomeric structures with asymmetric carbon atoms, such as those of acetalized monosaccharides. It was justified by the good results that have been published in recent years on the discrimination of structural isomers [...] Read more.

Our study found that quantum calculations can differentiate fragmentation energies into isomeric structures with asymmetric carbon atoms, such as those of acetalized monosaccharides. It was justified by the good results that have been published in recent years on the discrimination of structural isomers and diastereomers by correlating the calculated mass energy fragmentation profiles with their mass spectra. Based on the quantitative structure–fragmentation relationship (QSFR), this technique compares the intensities of primary ions from the experimental spectrum using the mass energy profiles calculated for the candidate structures. Maximum fit is obtained for the true structure. For a preliminary assessment of the accuracy of the identification of some di-O-isopropylidene monosaccharide diastereomers, we used fragmentation enthalpies (Δ_fH) and Gibbs energies (Δ_fG) as the energetic descriptors of fragmentation. Four quantum chemical methods were used: RM1, PM7, DFT Δ_fH and DFT Δ_fG. The mass energy database shows that the differences between the profiles of the isomeric candidate structures could be large enough to be distinguished from each other. This database allows the optimization of energy descriptors and quantum computing methods that can ensure the correct identification of these isomers. Full article

(This article belongs to the Topic Molecular Topology and Computation)

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12 pages, 292 KiB

Open AccessArticle

Certain Generalizations of Quadratic Transformations of Hypergeometric and Generalized Hypergeometric Functions

by Mohd Idris Qureshi, Junesang Choi and Tafaz Rahman Shah

Symmetry 2022, 14(5), 1073; https://doi.org/10.3390/sym14051073 - 23 May 2022

Cited by 3 | Viewed by 1690

Abstract

There have been numerous investigations on the hypergeometric series

_{2} F_{1}

and the generalized hypergeometric series

_{p} F_{q}

such as differential equations, integral representations, analytic continuations, asymptotic expansions, reduction cases, extensions of one and several variables, continued fractions, Riemann’s equation, group [...] Read more.

There have been numerous investigations on the hypergeometric series

_{2} F_{1}

and the generalized hypergeometric series

_{p} F_{q}

such as differential equations, integral representations, analytic continuations, asymptotic expansions, reduction cases, extensions of one and several variables, continued fractions, Riemann’s equation, group of the hypergeometric equation, summation, and transformation formulae. Among the various approaches to these functions, the transformation formulae for the hypergeometric series

_{2} F_{1}

and the generalized hypergeometric series

_{p} F_{q}

are significant, both in terms of applications and theory. The purpose of this paper is to establish a number of transformation formulae for

_{p} F_{q}

, whose particular cases would include Gauss’s and Kummer’s quadratic transformation formulae for

_{2} F_{1}

, as well as their two extensions for

_{3} F_{2}

, by making advantageous use of a recently introduced sequence and some techniques commonly used in dealing with

_{p} F_{q}

theory. The

_{p} F_{q}

function, which is the most significant function investigated in this study, exhibits natural symmetry. Full article

(This article belongs to the Special Issue Recent Advances in Special Functions and Their Applications)

13 pages, 953 KiB

Open AccessArticle

Research on Aspect-Level Sentiment Analysis Based on Text Comments

by Jing Tian, Wushour Slamu, Miaomiao Xu, Chunbo Xu and Xue Wang

Symmetry 2022, 14(5), 1072; https://doi.org/10.3390/sym14051072 - 23 May 2022

Cited by 6 | Viewed by 2415

Abstract

Sentiment analysis is the processing of textual data and giving positive or negative opinions to sentences. In the ABSA dataset, most sentences contain one aspect of sentiment polarity, or sentences of one aspect have multiple identical sentiment polarities, which weakens the sentiment polarity [...] Read more.

Sentiment analysis is the processing of textual data and giving positive or negative opinions to sentences. In the ABSA dataset, most sentences contain one aspect of sentiment polarity, or sentences of one aspect have multiple identical sentiment polarities, which weakens the sentiment polarity of the ABSA dataset. Therefore, this paper uses the SemEval 14 Restaurant Review dataset, in which each document is symmetrically divided into individual sentences, and two versions of the datasets ATSA and ACSA are created. ATSA: Aspect Term Sentiment Analysis Dataset. ACSA: Aspect Category Sentiment Analysis Dataset. In order to symmetrically simulate the complex relationship between aspect contexts and accurately extract the polarity of emotional features, this paper combines the latest development trend of NLP, combines capsule network and BRET, and proposes the baseline model CapsNet-BERT. The experimental results verify the effectiveness of the model. Full article

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14 pages, 3078 KiB

Open AccessArticle

Sombor Index over the Tensor and Cartesian Products of Monogenic Semigroup Graphs

by Seda Oğuz Ünal

Symmetry 2022, 14(5), 1071; https://doi.org/10.3390/sym14051071 - 23 May 2022

Cited by 7 | Viewed by 2237

Abstract

Consider a simple graph G with vertex set

V (G)

and edge set

E (G)

. A graph invariant for G is a number related to the structure of G, which is invariant under the symmetry of G [...] Read more.

Consider a simple graph G with vertex set

V (G)

and edge set

E (G)

. A graph invariant for G is a number related to the structure of G, which is invariant under the symmetry of G. The Sombor index of G is a new graph invariant defined as

S O (G) = \sum_{u v \in E (G)} \sqrt{{(d_{u})}^{2} + {(d_{v})}^{2}}

. In this work, we connected the theory of the Sombor index with abstract algebra. We computed this topological index over the tensor and Cartesian products of a monogenic semigroup graph by presenting two different algorithms; the obtained results are illustrated by examples. Full article

(This article belongs to the Topic Molecular Topology and Computation)

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19 pages, 3546 KiB

Open AccessArticle

Optimizing Multi-Objective Federated Learning on Non-IID Data with Improved NSGA-III and Hierarchical Clustering

by Jialin Zhong, Yahui Wu, Wubin Ma, Su Deng and Haohao Zhou

Symmetry 2022, 14(5), 1070; https://doi.org/10.3390/sym14051070 - 23 May 2022

Cited by 8 | Viewed by 3342

Abstract

Federated learning (FL) can tackle the problem of data silos of asymmetric information and privacy leakage; however, it still has shortcomings, such as data heterogeneity, high communication cost and uneven distribution of performance. To overcome these issues and achieve parameter optimization of FL [...] Read more.

Federated learning (FL) can tackle the problem of data silos of asymmetric information and privacy leakage; however, it still has shortcomings, such as data heterogeneity, high communication cost and uneven distribution of performance. To overcome these issues and achieve parameter optimization of FL on non-Independent Identically Distributed (non-IID) data, a multi-objective FL parameter optimization method based on hierarchical clustering and the third-generation non-dominated sorted genetic algorithm III (NSGA-III) algorithm is proposed, which aims to simultaneously minimize the global model error rate, global model accuracy distribution variance and communication cost. The introduction of a hierarchical clustering algorithm on non-IID data can accelerate convergence so that FL can employ an evolutionary algorithm with a low FL client participation ratio, reducing the overall communication cost of the NSGA-III algorithm. Meanwhile, the NSGA-III algorithm, with fast greedy initialization and a strategy of discarding low-quality individuals (named NSGA-III-FD), is proposed to improve the convergence efficiency and the quality of Pareto-optimal solutions. Under two non-IID data settings, the CNN experiments on both MNIST and CIFAR-10 datasets show that our approach can obtain better Pareto-optimal solutions than classical evolutionary algorithms, and the selected solutions with an optimized model can achieve better multi-objective equilibrium than the standard federated averaging (FedAvg) algorithm and the Clustering-based FedAvg algorithm. Full article

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10 pages, 809 KiB

Open AccessArticle

Does Sex, Skeletal Class and Mandibular Asymmetry Affect Tooth Length and Asymmetry in Tooth Length?

by Maciej Warnecki, Małgorzata Żak, Klaudia Szkoda-Poliszuk, Beata Kawala and Michał Sarul

Symmetry 2022, 14(5), 1069; https://doi.org/10.3390/sym14051069 - 23 May 2022

Cited by 1 | Viewed by 1754

Abstract

Introduction: The aim of our cross-sectional study is to determine whether there is a link between sex, skeletal class and mandibular asymmetry in orthodontic patients, with tooth length and asymmetry in tooth length on contralateral sides of the mandible. Methods: As the source [...] Read more.

Introduction: The aim of our cross-sectional study is to determine whether there is a link between sex, skeletal class and mandibular asymmetry in orthodontic patients, with tooth length and asymmetry in tooth length on contralateral sides of the mandible. Methods: As the source for relevant data to answer this question, 3D cone-beam tomography (CBCT) images of a total of 95 future orthodontic patients were retrospectively selected from private practice records and were analyzed. The CBCT images were part of routine orthodontic diagnosis. Patients were divided into three groups (Class I, Class III with asymmetry and Class III without asymmetry) based on skeletal variables assessed on orthodontic cephalometric images and frontal photos of the face. Three null hypotheses were developed, and a series of statistical tests was performed in order to support or reject them. Results: We have established that there exists a sexual dimorphism in some of the teeth’s lengths in our sample. Furthermore, we failed to find a link between mandibular asymmetry and asymmetry in tooth length. We have also found a link between skeletal class and tooth length differences in some of the analyzed measurements. Conclusions: Computational models used to design orthodontic appliances and to plan orthodontic treatment should be more individualized to consider a patient’s sex and skeletal class. Full article

(This article belongs to the Special Issue Dentofacial Asymmetry — Challenges and Perspectives)

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12 pages, 299 KiB

Open AccessArticle

New Conditions for Testing the Oscillation of Fourth-Order Differential Equations with Several Delays

by Ali Muhib, Osama Moaaz, Clemente Cesarano and Sameh S. Askar

Symmetry 2022, 14(5), 1068; https://doi.org/10.3390/sym14051068 - 23 May 2022

Cited by 4 | Viewed by 1686

Abstract

In this paper, we establish oscillation theorems for all solutions to fourth-order neutral differential equations using the Riccati transformation approach and some inequalities. Some new criteria are established that can be used in cases where known theorems fail to apply. The approach followed [...] Read more.

In this paper, we establish oscillation theorems for all solutions to fourth-order neutral differential equations using the Riccati transformation approach and some inequalities. Some new criteria are established that can be used in cases where known theorems fail to apply. The approach followed depends on finding conditions that guarantee the exclusion of positive solutions, and as a result of the symmetry between the positive and negative solutions of the studied equation, we therefore exclude negative solutions. An illustrative example is given. Full article

(This article belongs to the Special Issue Ordinary and Partial Differential Equations: Theory and Applications II)

15 pages, 2158 KiB

Open AccessArticle

Numerical Modeling and Symmetry Analysis of a Pine Wilt Disease Model Using the Mittag–Leffler Kernel

by V. Padmavathi, N. Magesh, K. Alagesan, M. Ijaz Khan, Samia Elattar, Mamdooh Alwetaishi and Ahmed M. Galal

Symmetry 2022, 14(5), 1067; https://doi.org/10.3390/sym14051067 - 23 May 2022

Cited by 7 | Viewed by 1980

Abstract

The existence of man is dependent on nature, and this existence can be disturbed by either man-made devastations or by natural disasters. As a universal phenomenon in nature, symmetry has attracted the attention of scholars. The study of symmetry provides insights into physics, [...] Read more.

The existence of man is dependent on nature, and this existence can be disturbed by either man-made devastations or by natural disasters. As a universal phenomenon in nature, symmetry has attracted the attention of scholars. The study of symmetry provides insights into physics, chemistry, biology, and mathematics. One of the most important characteristics in the expressive assessment and development of computational design techniques is symmetry. Yet, mathematical models are an important method of studying real-world systems. The symmetry reflected by such a mathematical model reveals the inherent symmetry of real-world systems. This study focuses on the contagious model of pine wilt disease and symmetry, employing the q-HATM (q-Homotopy Analysis Transform Method) to the leading fractional operator Atangana–Baleanu (AB) to arrive at better understanding. The outgrowths are exhibited in the forms of figures and tables. Finally, the paper helps to analyze the practical theory, assisting the prediction of its manner that corresponds to the guidelines when contemplating the replica. Full article

(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)

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10 pages, 330 KiB

Open AccessArticle

Classification of Arc-Transitive Elementary Abelian Covers of the C13 Graph

by Qianru Xiao, Aysha Khan, Narges Mehdipoor and Ali Asghar Talebi

Symmetry 2022, 14(5), 1066; https://doi.org/10.3390/sym14051066 - 23 May 2022

Cited by 1 | Viewed by 1695

Abstract

Let

Γ

be a graph and

G ⩽ A u t (Γ)

. A graph

Γ

can be called G-arc-transitive (GAT) if G acts transitively on its arc set. A regular covering projection

p : \bar{Γ} \to Γ

is [...] Read more.

Let

Γ

be a graph and

G ⩽ A u t (Γ)

. A graph

Γ

can be called G-arc-transitive (GAT) if G acts transitively on its arc set. A regular covering projection

p : \bar{Γ} \to Γ

is arc-transitive (AT) if an AT subgroup of

A u t (Γ)

lifts under p. In this study, by applying a number of concepts in linear algebra such as invariant subspaces (IVs) of matrix groups (MGs), we discuss regular AT elementary abelian covers (R-AT-EA-covers) of the

C 13

graph. Full article

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13 pages, 3259 KiB

Open AccessArticle

T-Stress Evaluation Based Cracking of Pipes Using an Extended Isogeometric Analysis (X-IGA)

by Khadija Yakoubi, Soufiane Montassir, Hassane Moustabchir, Ahmed Elkhalfi, Maria Luminita Scutaru and Sorin Vlase

Symmetry 2022, 14(5), 1065; https://doi.org/10.3390/sym14051065 - 23 May 2022

Cited by 3 | Viewed by 2079

Abstract

The aim of this study is to investigate the problem of pipe cracking based on T-stress analysis and the influence of other parameters, using a numerical computation performed by extended isogeometric analysis (X-IGA). This article examines the T-stress, which defines the [...] Read more.

The aim of this study is to investigate the problem of pipe cracking based on T-stress analysis and the influence of other parameters, using a numerical computation performed by extended isogeometric analysis (X-IGA). This article examines the T-stress, which defines the second term of the Williams’ series expansion. T-stress provides effective elastic modeling at the crack tip. Using the extended iso-geometric analysis (X-IGA), we determined the distribution of T-stress at the crack tip in a pipe under internal pressure as a function of internal pressure, crack size, and Poisson’s ratio. To validate the promising findings, the results are expanded with a comparison to the extended finite element (X-FEM) method and existing research in this field, and we obtained an error between 0.2% and 4.6%. This work demonstrated the significance of T-stress in fracture description, the effect of Poisson’s ratio and size on T-stress, and that X-IGA provided accurate numerical results by precisely describing the geometry of the crack and enriching it. Full article

(This article belongs to the Section Mathematics)

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20 pages, 4569 KiB

Open AccessArticle

Prediction of Spread Trend of Epidemic Based on Spatial-Temporal Sequence

by Qian Li, Qiao Pan and Liying Xie

Symmetry 2022, 14(5), 1064; https://doi.org/10.3390/sym14051064 - 23 May 2022

Cited by 2 | Viewed by 2126

Abstract

Coronavirus Disease 2019 (COVID-19) continues to spread throughout the world, and it is necessary for us to implement effective methods to prevent and control the spread of the epidemic. In this paper, we propose a new model called Spatial–Temporal Attention Graph Convolutional Networks [...] Read more.

Coronavirus Disease 2019 (COVID-19) continues to spread throughout the world, and it is necessary for us to implement effective methods to prevent and control the spread of the epidemic. In this paper, we propose a new model called Spatial–Temporal Attention Graph Convolutional Networks (STAGCN) that can analyze the long-term trend of the COVID-19 epidemic with high accuracy. The STAGCN employs a spatial graph attention network layer and a temporal gated attention convolutional network layer to capture the spatial and temporal features of infectious disease data, respectively. While the new model inherits the symmetric “space-time space” structure of Spatial–Temporal Graph Convolutional Networks (STGCN), it enhances its ability to identify infectious diseases using spatial–temporal correlation features by replacing the graph convolutional network layer with a graph attention network layer that can pay more attention to important features based on adaptively adjusted feature weights at different time points. The experimental results show that our model has the lowest error rate compared to other models. The paper also analyzes the prediction results of the model using interpretable analysis methods to provide a more reliable guide for the decision-making process during epidemic prevention and control. Full article

(This article belongs to the Special Issue Recent Advances in Social Data and Artificial Intelligence II)

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13 pages, 3751 KiB

Open AccessEditor’s ChoiceArticle

Heat Flow Characteristics of Ferrofluid in Magnetic Field Patterns for Electric Vehicle Power Electronics Cooling

by Seong-Guk Hwang, Kunal Sandip Garud, Jae-Hyeong Seo and Moo-Yeon Lee

Symmetry 2022, 14(5), 1063; https://doi.org/10.3390/sym14051063 - 22 May 2022

Cited by 7 | Viewed by 3672

Abstract

The ferrofluid is a kind of nanofluid that has magnetization properties in addition to excellent thermophysical properties, which has resulted in an effective performance trend in cooling applications. In the present study, experiments are conducted to investigate the heat flow characteristics of ferrofluid [...] Read more.

The ferrofluid is a kind of nanofluid that has magnetization properties in addition to excellent thermophysical properties, which has resulted in an effective performance trend in cooling applications. In the present study, experiments are conducted to investigate the heat flow characteristics of ferrofluid based on thermomagnetic convection under the influence of different magnetic field patterns. The temperature and heat dissipation characteristics are compared for ferrofluid under the influence of no-magnet, I, L, and T magnetic field patterns. The results reveal that the heat gets accumulated within ferrofluid near the heating part in the case of no magnet, whereas the heat flows through ferrofluid under the influence of different magnetic field patterns without any external force. Owing to the thermomagnetic convection characteristic of ferrofluid, the heat dissipates from the heating block and reaches the cooling block by following the path of the I magnetic field pattern. However, in the case of the L and T magnetic field patterns, the thermomagnetic convection characteristic of ferrofluid drives the heat from the heating block to the endpoint location of the pattern instead of the cooling block. The asymmetrical heat dissipation in the case of the L magnetic field pattern and the symmetrical heat dissipation in the case of the T magnetic field pattern are observed following the magnetization path of ferrofluid in the respective cases. The results confirm that the direction of heat flow could be controlled based on the type of magnetic field pattern and its path by utilizing the thermomagnetic behavior of ferrofluid. The proposed lab-scale experimental set-up and results database could be utilized to design an automatic energy transport system for the cooling of power conversion devices in electric vehicles. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Advanced Research for Efficient Electric Vehicles)

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24 pages, 1362 KiB

Open AccessArticle

The Dual Expression of Parallel Equidistant Ruled Surfaces in Euclidean 3-Space

by Sümeyye Gür Mazlum, Süleyman Şenyurt and Luca Grilli

Symmetry 2022, 14(5), 1062; https://doi.org/10.3390/sym14051062 - 22 May 2022

Cited by 28 | Viewed by 2578

Abstract

In this study, we examine the dual expression of Valeontis’ concept of parallel p-equidistant ruled surfaces well known in Euclidean 3-space, according to the Study mapping. Furthermore, we show that the dual part of the dual angle on the unit dual sphere [...] Read more.

In this study, we examine the dual expression of Valeontis’ concept of parallel p-equidistant ruled surfaces well known in Euclidean 3-space, according to the Study mapping. Furthermore, we show that the dual part of the dual angle on the unit dual sphere corresponds to the p-distance. We call these ruled surfaces we obtained “dual parallel equidistant ruled surfaces” and we briefly denote them with “DPERS”. Furthermore, we find the Blaschke vectors, the Blaschke invariants and the striction curves of these DPERS and we give the relationships between these elements. Moreover, we show the relationships between the Darboux screws, the instantaneous screw axes, the instantaneous dual Pfaff vectors and dual Steiner rotation vectors of these surfaces. Finally, we give an example, which we reinforce this article, and we explain all of these features with the figures on the example. Furthermore, we see that the corresponding dual curves on the dual unit sphere to these DPERS are such that one of them is symmetric with respect to the imaginary symmetry axis of the other. Full article

(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology)

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14 pages, 1222 KiB

Open AccessArticle

Spin-Dependent Scattering of Scalar and Vector Dark Matter on the Electron

by Ke-Yun Wu and Zhao-Hua Xiong

Symmetry 2022, 14(5), 1061; https://doi.org/10.3390/sym14051061 - 22 May 2022

Cited by 3 | Viewed by 1813

Abstract

The property of dark matter remains to date unknown. However, a model-independent classification of dark matter candidates can be achieved by using various symmetries, as performed in the standard model. Fermionic dark matter has been extensively researched, and one favored candidate is the [...] Read more.

The property of dark matter remains to date unknown. However, a model-independent classification of dark matter candidates can be achieved by using various symmetries, as performed in the standard model. Fermionic dark matter has been extensively researched, and one favored candidate is the neutralino in the Minimal Supersymmetric Standard Model, which is required by fermion–boson symmetry and the preservation of R-parity. Bosonic dark matter has not been sufficiently studied, especially the scenario of dark matter with a mass of sub-GeV. In this paper, we consider the effect of spin-dependent (SD) on scalar and vector dark matter, which are mediated by pseudoscalar and axial-vector, and evaluate the effect on the dark matter–electron scattering cross-section. We list all the interactions and form factor of dark matter–electron SD scattering, and use XENON10/100/1T experiment data to derive the exclusion limit of the SD cross-section. We find that the SD scattering of scalar and vector dark matter can be three orders of magnitude stronger than spin-independent (SI) scattering due to the p-wave scattering. Full article

(This article belongs to the Special Issue Supersymmetry in Particle Physics)

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21 pages, 3055 KiB

Open AccessArticle

A Hierarchical Universal Algorithm for Geometric Objects’ Reflection Symmetry Detection

by Borut Žalik, Damjan Strnad, Štefan Kohek, Ivana Kolingerová, Andrej Nerat, Niko Lukač and David Podgorelec

Symmetry 2022, 14(5), 1060; https://doi.org/10.3390/sym14051060 - 21 May 2022

Cited by 6 | Viewed by 2413

Abstract

A new algorithm is presented for detecting the global reflection symmetry of geometric objects. The algorithm works for 2D and 3D objects which may be open or closed and may or may not contain holes. The algorithm accepts a point cloud obtained by [...] Read more.

A new algorithm is presented for detecting the global reflection symmetry of geometric objects. The algorithm works for 2D and 3D objects which may be open or closed and may or may not contain holes. The algorithm accepts a point cloud obtained by sampling the object’s surface at the input. The points are inserted into a uniform grid and so-called boundary cells are identified. The centroid of the boundary cells is determined, and a testing symmetry axis/plane is set through it. In this way, the boundary cells are split into two parts and they are faced with the symmetry estimation function. If the function estimates the symmetric case, the boundary cells are further split until a given threshold is reached or a non-symmetric result is obtained. The new testing axis/plane is then derived and tested by rotation around the centroid. This paper introduces three techniques to accelerate the computation. Competitive results were obtained when the algorithm was compared against the state of the art. Full article

(This article belongs to the Section Computer)

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13 pages, 296 KiB

Open AccessArticle

A New Accelerated Fixed-Point Algorithm for Classification and Convex Minimization Problems in Hilbert Spaces with Directed Graphs

by Kobkoon Janngam and Rattanakorn Wattanataweekul

Symmetry 2022, 14(5), 1059; https://doi.org/10.3390/sym14051059 - 21 May 2022

Cited by 3 | Viewed by 1660

Abstract

A new accelerated algorithm for approximating the common fixed points of a countable family of G-nonexpansive mappings is proposed, and the weak convergence theorem based on our main results is established in the setting of Hilbert spaces with a symmetric directed graph [...] Read more.

A new accelerated algorithm for approximating the common fixed points of a countable family of G-nonexpansive mappings is proposed, and the weak convergence theorem based on our main results is established in the setting of Hilbert spaces with a symmetric directed graph G. As an application, we apply our results for solving classification and convex minimization problems. We also apply our proposed algorithm to estimate the weight connecting the hidden layer and output layer in a regularized extreme learning machine. For numerical experiments, the proposed algorithm gives a higher performance of accuracy of the testing set than that of FISTA-S, FISTA, and nAGA. Full article

(This article belongs to the Special Issue Functional Equations and Inequalities 2021)

16 pages, 1366 KiB

Open AccessArticle

Fitting Non-Parametric Mixture of Regressions: Introducing an EM-Type Algorithm to Address the Label-Switching Problem

by Sphiwe B. Skhosana, Frans H. J. Kanfer and Salomon M. Millard

Symmetry 2022, 14(5), 1058; https://doi.org/10.3390/sym14051058 - 21 May 2022

Cited by 2 | Viewed by 1816

Abstract

The non-parametric Gaussian mixture of regressions (NPGMRs) model serves as a flexible approach for the determination of latent heterogeneous regression relationships. This model assumes that the component means, variances and mixing proportions are smooth unknown functions of the covariates where the error distribution [...] Read more.

The non-parametric Gaussian mixture of regressions (NPGMRs) model serves as a flexible approach for the determination of latent heterogeneous regression relationships. This model assumes that the component means, variances and mixing proportions are smooth unknown functions of the covariates where the error distribution of each component is assumed to be Gaussian and hence symmetric. These functions are estimated over a set of grid points using the Expectation-Maximization (EM) algorithm to maximise the local-likelihood functions. However, maximizing each local-likelihood function separately does not guarantee that the local responsibilities and corresponding labels, obtained at the E-step of the EM algorithm, align at each grid point leading to a label-switching problem. This results in non-smooth estimated component regression functions. In this paper, we propose an estimation procedure to account for label switching by tracking the roughness of the estimated component regression functions. We use the local responsibilities to obtain a global estimate of the responsibilities which are then used to maximize each local-likelihood function. The performance of the proposed procedure is demonstrated using a simulation study and through an application using real world data. In the case of well-separated mixture regression components, the procedure gives similar results to competitive methods. However, in the case of poorly separated mixture regression components, the procedure outperforms competitive methods. Full article

(This article belongs to the Special Issue Symmetry in Multivariate Analysis)

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18 pages, 3707 KiB

Open AccessArticle

Experimental and Numerical Simulation of a Symmetrical Three-Cylinder Buoy

by Yun Pan, Fengting Yang, Huanhuan Tong, Xiao Zuo, Liangduo Shen, Dawen Xue and Can Liu

Symmetry 2022, 14(5), 1057; https://doi.org/10.3390/sym14051057 - 21 May 2022

Cited by 2 | Viewed by 1882

Abstract

The wave resistance of a buoy is affected by the mode of anchorage and the buoy structure. Combining the structures and the mode of anchorage of the existing buoys, designing a buoy with significantly improved wave resistance is a major challenge for marine [...] Read more.

The wave resistance of a buoy is affected by the mode of anchorage and the buoy structure. Combining the structures and the mode of anchorage of the existing buoys, designing a buoy with significantly improved wave resistance is a major challenge for marine environment monitoring. This work carried out experimental and numerical simulation studies on the hydrodynamic properties of a self-designed symmetrical three-cylinder buoy. The wave resistance of the buoy was analyzed using different wave conditions, and a full-scale simulation of the buoy was performed using the finite element method and lumped mass method. Experimentally, it was found that the symmetrical three-cylinder buoy stability was less affected by the wave height, but mainly by the wave period. Additionally, the effects of wave height and wave period on mooring tension were also studied, and the results showed that mooring tension was mainly affected by wave period, which was explained by the rate of change of the buoy momentum. Finally, a numerical model was proposed for the interpretation of these experiments. Results from numerical simulations for the trajectory of the buoy and the tension of the mooring cable correlated well with the experimental data. Full article

(This article belongs to the Special Issue Test and Measurement Technology in Ocean Engineering)

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21 pages, 327 KiB

Open AccessArticle

Solving a System of Sylvester-like Quaternion Matrix Equations

by Ruo-Nan Wang, Qing-Wen Wang and Long-Sheng Liu

Symmetry 2022, 14(5), 1056; https://doi.org/10.3390/sym14051056 - 20 May 2022

Cited by 12 | Viewed by 2160

Abstract

Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary and sufficient solvability conditions for a system of Sylvester-type quaternion matrix equations, and give an expression of the general solution to the system when it is solvable. [...] Read more.

Using the ranks and Moore-Penrose inverses of involved matrices, in this paper we establish some necessary and sufficient solvability conditions for a system of Sylvester-type quaternion matrix equations, and give an expression of the general solution to the system when it is solvable. As an application of the system, we consider a special symmetry solution, named the

η

-Hermitian solution, for a system of quaternion matrix equations. Moreover, we present an algorithm and a numerical example to verify the main results of this paper. Full article

(This article belongs to the Section Mathematics)

18 pages, 3903 KiB

Open AccessArticle

A Method for Solving Approximate Partition Boundaries of Spatial Big Data Based on Histogram Bucket Sampling

by Ruijie Tian, Tiansheng Chen, Huawei Zhai, Weishi Zhang and Fei Wang

Symmetry 2022, 14(5), 1055; https://doi.org/10.3390/sym14051055 - 20 May 2022

Viewed by 1737

Abstract

In recent years, the volume of spatial data has rapidly grown, so it is crucial to process them in an efficient manner. The level of parallel processing in big data platforms such as Hadoop and Spark is determined by partitioning the dataset. A [...] Read more.

In recent years, the volume of spatial data has rapidly grown, so it is crucial to process them in an efficient manner. The level of parallel processing in big data platforms such as Hadoop and Spark is determined by partitioning the dataset. A common approach is to split the data into chunks based on the number of bytes. While this approach works well for text-based batch processing, in many cases, it is preferable to take advantage of the structured information contained in the dataset (e.g., spatial coordinates) to plan data partitioning. In view of the huge amount of data and the impossibility of quickly establishing partitions, this paper designs a method for approximate partition boundary solving, which divides the data space into multiple non-overlapping symmetric bins and samples each bin, making the probability density of the sampling set bounded by the deviation of the probability density of the original data. The sampling set is read into the memory at one time for calculation, and the established partition boundary satisfies the partition threshold-setting. Only a few boundary adjustment operations are required, which greatly shortens the partition time. In this paper, the method proposed in the paper is tested on the synthetic dataset, the bus trajectory dataset, and six common spatial partitioning methods (Grid, Z-curve, H-curve, STR, Kd-tree, and R*-Grove) are selected for comparison. The results show that the symmetric bin sampling method can describe the spatial data distribution well and can be directly used for partition boundary division. Full article

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13 pages, 342 KiB

Open AccessArticle

Kantorovich Type Generalization of Bernstein Type Rational Functions Based on (p,q)-Integers

by Hayatem Hamal and Pembe Sabancigil

Symmetry 2022, 14(5), 1054; https://doi.org/10.3390/sym14051054 - 20 May 2022

Cited by 3 | Viewed by 1520

Abstract

In this paper, we define a new Kantorovich-type

(p, q)

-generalization of the Balázs–Szabados operators. We derive a recurrence formula, and with the help of this formula, we give explicit formulas for the first and second-order moments, which follow a [...] Read more.

In this paper, we define a new Kantorovich-type

(p, q)

-generalization of the Balázs–Szabados operators. We derive a recurrence formula, and with the help of this formula, we give explicit formulas for the first and second-order moments, which follow a symmetric pattern. We estimate the second and fourth-order central moments. We examine the local approximation properties in terms of modulus of continuity, we give a Voronovskaja type theorem, and we give the weighted approximation properties of the operators. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Functional Analysis and Optimization Theory II)

17 pages, 341 KiB

Open AccessArticle

Certain Subclasses of Analytic Functions Associated with Generalized Telephone Numbers

by Gangadharan Murugusundaramoorthy and Kaliappan Vijaya

Symmetry 2022, 14(5), 1053; https://doi.org/10.3390/sym14051053 - 20 May 2022

Cited by 14 | Viewed by 1902

Abstract

The goal of this article is to contemplate coefficient estimates for a new class of analytic functions f associated with generalized telephone numbers to originate certain initial Taylor coefficient estimates and Fekete–Szegö inequality for f in the new function class. Comparable results have [...] Read more.

The goal of this article is to contemplate coefficient estimates for a new class of analytic functions f associated with generalized telephone numbers to originate certain initial Taylor coefficient estimates and Fekete–Szegö inequality for f in the new function class. Comparable results have been attained for the function

f^{- 1} .

Further application of our outcomes to certain functions demarcated by convolution products with certain normalized analytic functions in the open unit disk are specified, and we obtain Fekete–Szegö variations for this new function class defined over Poisson and Borel distribution series. Full article

(This article belongs to the Special Issue Symmetry in Pure Mathematics and Real and Complex Analysis)

12 pages, 378 KiB

Open AccessArticle

Petri-Net-Based Scheduling of Flexible Manufacturing Systems Using an Estimate Function

by Gongdan Xu and Yufeng Chen

Symmetry 2022, 14(5), 1052; https://doi.org/10.3390/sym14051052 - 20 May 2022

Cited by 7 | Viewed by 2005

Abstract

In this paper, a novel admissible estimate function is proposed to schedule flexible manufacturing systems (FMSs) by using heuristic search. The FMSs to be scheduled are modeled by P-timed Petri nets. The problem is to make the system evolve from the initial marking [...] Read more.

In this paper, a novel admissible estimate function is proposed to schedule flexible manufacturing systems (FMSs) by using heuristic search. The FMSs to be scheduled are modeled by P-timed Petri nets. The problem is to make the system evolve from the initial marking to a given final marking by firing a sequence of transitions. The structure of jobs in an FMS is always symmetrical to utilize the shared resources, but the processing time of each job is asymmetrical to reduce the global process time. By utilizing the structural symmetry of a Petri net model of an FMS, a partial reachability graph is generated such that the notorious state explosion problem is mitigated. For each generated marking, the proposed estimate function is used to provide an estimated cost for firing the transition sequence. Then, we can select the marking with the smallest cost from the generated markings and compute its successors. This process is continued until the system reaches the final marking. With the proposed method, the performance is evaluated in terms of the cost of the obtained transition firing sequence and the number of the expanded markings. The cost provided by the proposed estimate function is closer to the optimal cost than the previous work, i.e., the proposed method can find a transition firing sequence with less expanded markings and minimal process time from a marking to the final marking. Experimental results are used to demonstrate and evaluate the proposed approach. Full article

(This article belongs to the Special Issue Advanced Materials, Structures, Symmetrical Design and Mechanism in Mechanical Engineering)

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16 pages, 363 KiB

Open AccessReview

Advances in Quasi-Symmetry for Square Contingency Tables

by Kouji Tahata

Symmetry 2022, 14(5), 1051; https://doi.org/10.3390/sym14051051 - 20 May 2022

Cited by 5 | Viewed by 1677

Abstract

Contingency tables highlight relationships between categorical variables. Typically, the symmetry or marginal homogeneity of a square contingency table is evaluated. The original symmetry model often does not accurately fit a dataset due to its restrictions. Caussinus proposed a quasi-symmetry model which served as [...] Read more.

Contingency tables highlight relationships between categorical variables. Typically, the symmetry or marginal homogeneity of a square contingency table is evaluated. The original symmetry model often does not accurately fit a dataset due to its restrictions. Caussinus proposed a quasi-symmetry model which served as a bridge between symmetry and marginal homogeneity in square contingency tables. This study significantly influenced methodological developments in the statistical analysis of categorical data. Herein recent advances in quasi-symmetry are reviewed with an emphasis on four topics related to the author’s results: (1) modeling based on the f-divergence, (2) the necessary and sufficient condition of symmetry, (3) partition of test statistics for symmetry, and (4) measure of the departure from symmetry. The asymmetry model based on f-divergence enables us to express various asymmetries. Additionally, these models are useful to derive the necessary and sufficient conditions of symmetry with desirable properties. This review may be useful to consider the statistical modeling and the measure of symmetry for contingency tables with the same classifications. Full article

(This article belongs to the Section Mathematics)

16 pages, 1966 KiB

Open AccessArticle

Ab Initio Computations of O and AO as well as ReO₂, WO₂ and BO₂-Terminated ReO₃, WO₃, BaTiO₃, SrTiO₃ and BaZrO₃ (001) Surfaces

by Roberts I. Eglitis, Juris Purans, Anatoli I. Popov, Dmitry Bocharov, Anastasiia Chekhovska and Ran Jia

Symmetry 2022, 14(5), 1050; https://doi.org/10.3390/sym14051050 - 20 May 2022

Cited by 31 | Viewed by 2562

Abstract

We present and discuss the results of surface relaxation and rumpling computations for ReO₃, WO₃, SrTiO₃, BaTiO₃ and BaZrO₃ (001) surfaces employing a hybrid B3LYP or B3PW description of exchange and correlation. In particular, we [...] Read more.

We present and discuss the results of surface relaxation and rumpling computations for ReO₃, WO₃, SrTiO₃, BaTiO₃ and BaZrO₃ (001) surfaces employing a hybrid B3LYP or B3PW description of exchange and correlation. In particular, we perform the first B3LYP computations for O-terminated ReO₃ and WO₃ (001) surfaces. In most cases, according to our B3LYP or B3PW computations for both surface terminations BO₂- and O, AO-terminated ReO₃, WO₃, BaTiO₃, SrTiO₃ and BaZrO₃ (001) surface upper layer atoms shift downwards, towards the bulk, the second layer atoms shift upwards and the third layer atoms, again, shift downwards. Our ab initio computes that ReO₃, WO₃, BaTiO₃, SrTiO₃ and BaZrO₃ (001) surface Γ-Γ bandgaps are always smaller than their respective bulk Γ-Γ bandgaps. Our first principles compute that B-O atom chemical bond populations in the BaTiO₃, SrTiO₃ and BaZrO₃ perovskite bulk are always smaller than near their BO₂-terminated (001) surfaces. Just opposite, the Re-O and W-O chemical bond populations in the ReO₃ (0.212e) and WO₃ (0.142e) bulk are slightly larger than near the ReO₂ and WO₂-terminated ReO₃ as well as WO₃ (001) surfaces (0.170e and 0.108e, respectively). Full article

(This article belongs to the Special Issue Applied Surface Science)

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21 pages, 1547 KiB

Open AccessArticle

Research on Detent Force Characteristics of Winding Segmented Permanent Magnet Linear Synchronous Motor Based on Analytical Model

by Tuanshan Zhang and Xuesong Mei

Symmetry 2022, 14(5), 1049; https://doi.org/10.3390/sym14051049 - 20 May 2022

Cited by 4 | Viewed by 2001

Abstract

The winding segmented permanent magnet linear synchronous motor (WS-PMLSM) has not only a general slotting effect but also a unique two-end effect caused by the segmented stator and the finite length passive mover, which makes the detent force of WS-PMLSM possess the qualities [...] Read more.

The winding segmented permanent magnet linear synchronous motor (WS-PMLSM) has not only a general slotting effect but also a unique two-end effect caused by the segmented stator and the finite length passive mover, which makes the detent force of WS-PMLSM possess the qualities of all types of linear motors. This paper adopts a physics-based multiple analytical method to study the detent force properties. First, an accurate sub-domain model is used to obtain the magnetic field distribution of the tooth slot, and the results of the analytical solution and the graph of the tooth slot effect are obtained using the scalar magnetic potential. Subsequently, the effect of the end unenergized core on the magnetic field is analyzed using Maxwell’s theory for the stator end effect, revealing that the end effect causes pulsating and reversing magnetic fields in the motor, which in turn creates mutual inductance with unequal phases, and generates thrust fluctuations. Finally, a complex relative air-gap permeability is introduced on the basis of the conformal mapping to equate the end effect generated by the permanent magnet. The accuracy of the proposed multiple analytical models was verified by the results of the finite element method (FEM) and experimental model. Full article

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7 pages, 678 KiB

Open AccessArticle

Crossover in Extended Newtonian Gravity Emerging from Thermodynamics

by Sumiyoshi Abe and Peter Ván

Symmetry 2022, 14(5), 1048; https://doi.org/10.3390/sym14051048 - 20 May 2022

Cited by 3 | Viewed by 1636

Abstract

Recently, it has been discovered that a scalar field coupled to a fluid and allowed to be a thermodynamic variable in consistency with the second law of thermodynamics is only of gravity, and, accordingly, the emergence of extended Newtonian gravity has been predicted. [...] Read more.

Recently, it has been discovered that a scalar field coupled to a fluid and allowed to be a thermodynamic variable in consistency with the second law of thermodynamics is only of gravity, and, accordingly, the emergence of extended Newtonian gravity has been predicted. The resulting field equation for the potential of this emergent force is nonlinear and admits the logarithmic potential as a singular solution, suggesting its relevance to the dark matter conundrum. Here, a general analysis of the nonlinear field equation is performed. It is found that the emergent force field exhibits an unsharp crossover between the

1 / r

and

1 / r^{2}

forces outside the fluid, depending on a spatial scale characteristic of the present theory to be observationally tested in the context of the dark matter conundrum. Then, the action functional is constructed for the potential of the emergent field, and the field energy is shown to be free from an infrared divergence. A comment is also made on the difference of the present theory to MOND (modified Newtonian dynamics). Full article

(This article belongs to the Special Issue Thermodynamics for Finite-Size and Time-Dependent Behavior: Small Systems, Fluctuations, Correlations, and Internal Heterogeneity)

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21 pages, 390 KiB

Open AccessArticle

Robust Optimum Life-Testing Plans under Progressive Type-I Interval Censoring Schemes with Cost Constraint

by Xiaodong Zhou, Yunjuan Wang and Rongxian Yue

Symmetry 2022, 14(5), 1047; https://doi.org/10.3390/sym14051047 - 19 May 2022

Cited by 1 | Viewed by 1608

Abstract

This paper considers optimal design problems for the Weibull distribution, which can be used to model symmetrical or asymmetrical data, in the presence of progressive interval censoring in life-testing experiments. Two robust approaches, Bayesian and minimax, are proposed to deal with the dependence [...] Read more.

This paper considers optimal design problems for the Weibull distribution, which can be used to model symmetrical or asymmetrical data, in the presence of progressive interval censoring in life-testing experiments. Two robust approaches, Bayesian and minimax, are proposed to deal with the dependence of the D-optimality and c-optimality on the unknown model parameters. Meanwhile, the compound design method is applied to ensure a compromise between the precision of estimation of the model parameters and the precision of estimation of the quantiles. Furthermore, to make the design become more practical, the cost constraints are taken into account in constructing the optimal designs. Two algorithms are provided for finding the robust optimal solutions. A simulated example and a real life example are given to illustrate the proposed methods. The sensitivity analysis is also studied. These new design methods can help the engineers to obtain robust optimal designs for the censored life-testing experiments. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Probability)

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18 pages, 3724 KiB

Open AccessArticle

Stable Difference Schemes with Interpolation for Delayed One-Dimensional Transport Equation

by Karthick Sampath, Subburayan Veerasamy and Ravi P. Agarwal

Symmetry 2022, 14(5), 1046; https://doi.org/10.3390/sym14051046 - 19 May 2022

Cited by 5 | Viewed by 1839

Abstract

In this article, we consider the one-dimensional transport equation with delay and advanced arguments. A maximum principle is proven for the problem considered. As an application of the maximum principle, the stability of the solution is established. It is also proven that the [...] Read more.

In this article, we consider the one-dimensional transport equation with delay and advanced arguments. A maximum principle is proven for the problem considered. As an application of the maximum principle, the stability of the solution is established. It is also proven that the solution’s discontinuity propagates. Finite difference methods with linear interpolation that are conditionally stable and unconditionally stable are presented. This paper presents applications of unconditionally stable numerical methods to symmetric delay arguments and differential equations with variable delays. As a consequence, the matrices of the difference schemes are asymmetric. An illustration of the unconditional stable method is provided with numerical examples. Solution graphs are drawn for all the problems. Full article

(This article belongs to the Special Issue Recent Progress in Studies of Stability of Numerical Schemes)

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22 pages, 540 KiB

Open AccessArticle

On Strengthened Extragradient Methods Non-Convex Combination with Adaptive Step Sizes Rule for Equilibrium Problems

by Meshal Shutaywi, Wiyada Kumam, Habib ur Rehman and Kamonrat Sombut

Symmetry 2022, 14(5), 1045; https://doi.org/10.3390/sym14051045 - 19 May 2022

Viewed by 1764

Abstract

Symmetries play a vital role in the study of physical phenomena in diverse areas such as dynamic systems, optimization, physics, scientific computing, engineering, mathematical biology, chemistry, and medicine, to mention a few. These phenomena specialize mostly in solving equilibria-like problems in abstract spaces. [...] Read more.

Symmetries play a vital role in the study of physical phenomena in diverse areas such as dynamic systems, optimization, physics, scientific computing, engineering, mathematical biology, chemistry, and medicine, to mention a few. These phenomena specialize mostly in solving equilibria-like problems in abstract spaces. Motivated by these facts, this research provides two innovative modifying extragradient strategies for solving pseudomonotone equilibria problems in real Hilbert space with the Lipschitz-like bifunction constraint. Such strategies make use of multiple step-size concepts that are modified after each iteration and are reliant on prior iterations. The excellence of these strategies comes from the fact that they were developed with no prior knowledge of Lipschitz-type parameters or any line search strategy. Mild assumptions are required to prove strong convergence theorems for proposed strategies. Various numerical tests have been reported to demonstrate the numerical behavior of the techniques and then contrast them with others. Full article

(This article belongs to the Section Mathematics)

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