Symmetry doi: 10.3390/sym14051024

Authors: Vladimir Vasilyev Yuri Virchenko

The theorem about equivalence of the strong hyperbolicity concept and the Friedrichs hyperbolicity concept for partial quasi-linear differential equations of the first order is proved. On the basis of this theorem, the necessary and sufficient conditions of hyperbolicity are found in terms of the matrix of the corresponding linearized first order equations system.

]]>Symmetry doi: 10.3390/sym14051027

Authors: Enhui Chai Wei Yu Tianxiang Cui Jianfeng Ren Shusheng Ding

As a key step to endow the neural network with nonlinear factors, the activation function is crucial to the performance of the network. This paper proposes an Efficient Asymmetric Nonlinear Activation Function (EANAF) for deep neural networks. Compared with existing activation functions, the proposed EANAF requires less computational effort, and it is self-regularized, asymmetric and non-monotonic. These desired characteristics facilitate the outstanding performance of the proposed EANAF. To demonstrate the effectiveness of this function in the field of object detection, the proposed activation function is compared with several state-of-the-art activation functions on the typical backbone networks such as ResNet and DSPDarkNet. The experimental results demonstrate the superior performance of the proposed EANAF.

]]>Symmetry doi: 10.3390/sym14051025

Authors: Samet Maldar

In this study, considering the advantages of parallel fixed point algorithms arising from their symmetrical behavior, new types of parallel algorithms have been defined. Strong convergence of these algorithms for certain mappings with altering points has been analyzed, and it has been observed that their convergence behavior is better than existing algorithms with non-simple samples. In addition, the concept of data dependency for these algorithms has been examined for the first time in this study. Finally, it has been proven that the solution of a variational inequality system can be obtained using newly defined parallel algorithms under suitable conditions.

]]>Symmetry doi: 10.3390/sym14051026

Authors: Ming-Tsung Kao Shang-Juh Kao Hsueh-Wen Tseng Fu-Min Chang

In reactive mode software-defined networking (SDN) networks, a new initiated flow requires back-and-forth communications between the controller and the switches along the forwarding route. As SDN is getting popularly accepted, many studies have reported on how to reduce the amount of communication traffic and to release the controller’s loading. Several techniques have been proposed, such as proactive and active mode integration, MPLS adoption, and various forwarding rule installation techniques. In this paper, we adopt the idea of the tunnel penetration technique, called the tunnel boring machine in SDN or SDN-TBM, to effectively cut down the traffic between switches and the controller as well as to speed up packet delivery. Using the TBM mechanism, the communication symmetry between the controller and the switches on the path is broken and transformed into asymmetry. Only the first and last switches of each application flow need to make forwarding queries to the controller, and all intermediate switches simply forward packets consisting of the forwarding information needed to determine the next-hop switch. An M/M/1 queueing model is developed to verify the feasibility and efficiency of the proposal. Under the simulation of more than a million flows with 3–8 intermediate switches, the packet sojourn time using SDN-TBM mechanism is less than that of adopting the conventional SDN and JumpFlow model. Additionally, by adopting SDN-TBM, both the number of packet-in and packet-out packets and the controller’s loading are significantly reduced.

]]>Symmetry doi: 10.3390/sym14051023

Authors: Solange-Odile Saliu Eugen-Mihăiţă Cioroianu Constantin Bizdadea

This paper falls under the heading of constructing consistent self-couplings in topological BF models. Our endeavor is of interest in the context of pure gravity, General Relativity, and super-gravity in Ashtekar formalism, which allow for certain economic formulations in terms of self-coupled BF theories in the presence of certain extra-constraints. More precisely, herein we address the construction of a special class of D=6 self-interactions for a collection of topological BF models with a non-standard field spectrum. Our methodology relies on a deformation method based on the relationship between antifield&ndash;BRST symmetry and the non-trivial gauge symmetries of a given field theory and implemented via the computation of certain precise spaces of the local BRST cohomology corresponding to the free limit. This cohomological BRST approach is applied to the starting free model under standard &ldquo;selection rules&rdquo; from Quantum Field Theory. Our findings are completely new and reveal a self-interacting topological BF model in D=6 with a complex gauge structure that is entirely read from the expression of the fully deformed solution to the classical master equation (the canonical generator of the antifield&ndash;BRST symmetry), and includes a generalization of the famous D=2 gravity in BF formulation.

]]>Symmetry doi: 10.3390/sym14051022

Authors: Suha Wazzan Anwar Saleh

In this paper, we introduce some new versions based on the locating vectors named locating indices. In particular, Hyper locating indices, Randi&#263; locating index, and Sambor locating index. The exact formulae for these indices of some well-known families of graphs and for the Helm graph are derived. Moreover, we determine the importance of these locating indices for 11 benzenoid hydrocarbons. Furthermore, we show that these new versions of locating indices have a reasonable correlation using linear regression with physicochemical characteristics such as molar entropy, acentric factor, boiling point, complexity, octanol&ndash;water partition coefficient, and Kovats retention index. The cases in which good correlations were obtained suggested the validity of the calculated topological indices to be further used to predict the physicochemical properties of much more complicated chemical compounds.

]]>Symmetry doi: 10.3390/sym14051021

Authors: Fahd Aldosari Laith Abualigah Khaled H. Almotairi

As data volumes have increased and difficulty in tackling vast and complicated problems has emerged, the need for innovative and intelligent solutions to handle these difficulties has become essential. Data clustering is a data mining approach that clusters a huge amount of data into a number of clusters; in other words, it finds symmetric and asymmetric objects. In this study, we developed a novel strategy that uses intelligent optimization algorithms to tackle a group of issues requiring sophisticated methods to solve. Three primary components are employed in the suggested technique, named GNDDMOA: Dwarf Mongoose Optimization Algorithm (DMOA), Generalized Normal Distribution (GNF), and Opposition-based Learning Strategy (OBL). These parts are used to organize the executions of the proposed method during the optimization process based on a unique transition mechanism to address the critical limitations of the original methods. Twenty-three test functions and eight data clustering tasks were utilized to evaluate the performance of the suggested method. The suggested method&rsquo;s findings were compared to other well-known approaches. In all of the benchmark functions examined, the suggested GNDDMOA approach produced the best results. It performed very well in data clustering applications showing promising performance.

]]>Symmetry doi: 10.3390/sym14051020

Authors: Haifeng Li Ye Chen Zhenshi Zhang Jian Peng

The deep learning method is widely used in remote sensing object detection on the premise that the training data have complete features. However, when data with a fixed class are added continuously, the trained detector is less able to adapt to new instances, impelling it to carry out incremental learning (IL). IL has two tasks with knowledge-related symmetry: continuing to learn unknown knowledge and maintaining existing knowledge. Unknown knowledge is more likely to exist in these new instances, which have features dissimilar from those of the old instances and cannot be well adapted by the detector before IL. Discarding all the old instances leads to the catastrophic forgetting of existing knowledge, which can be alleviated by relearning old instances, while different subsets represent different existing knowledge ranges and have different memory-retention effects on IL. Due to the different IL values of the data, the existing methods without appropriate distinguishing treatment preclude the efficient absorption of useful knowledge. Therefore, a rank-aware instance-incremental learning (RAIIL) method is proposed in this article, which pays attention to the difference in learning values from the aspects of the data-learning order and training loss weight. Specifically, RAIIL first designs the rank-score according to inference results and the true labels to determine the learning order and then weights the training loss according to the rank-score to balance the learning contribution. Comparative and analytical experiments conducted on two public remote sensing datasets for object detection, DOTA and DIOR, verified the superiority and effectiveness of the proposed method.

]]>Symmetry doi: 10.3390/sym14051019

Authors: Chengjing Wei Guodong Li Xiangliang Xu

The application of a memristor in chaotic circuits is increasingly becoming a popular research topic. The influence of a memristor on the dynamics of chaotic systems is worthy of further exploration. In this paper, a multi-dimensional closed-loop coupling model based on a Logistic map and Sine map (CLS) is proposed. The new chaotic model is constructed by cascade operation in which the output of the Logistic map is used as the input of the Sine map. Additionally, the one-dimensional map is extended to any dimension through the coupling modulation. In order to further increase the complexity and stability of CLS, the discrete memristor model is introduced to construct a discrete memristor-based coupling model with a Logistic map and a Sine map (MCLS). By analyzing the Lyapunov exponents, bifurcation diagram, complexity, and the 0&ndash;1 test result, the comparison result between CLS and MCLS is obtained. The dynamics performance analysis shows that the Lyapunov exponents and bifurcation diagrams present symmetrical distribution with variations of some parameters. The MCLS has parameters whose values can be set in a wider range and can generate more complex and more stable chaotic sequences. It proves that the proposed discrete memristor-based closed-loop coupling model can produce any higher dimension hyperchaotic system and the discrete memristor model can effectively improve the performance of discrete chaotic map and make this hyperchaotic system more stable.

]]>Symmetry doi: 10.3390/sym14051018

Authors: Quanjin Liu Jianlan Wu Langtao Hu Songjiao Bi Wen Ji Rui Yang

Combining Intelligent Reflecting Surface (IRS) with Non-Orthogonal Multiple Access (NOMA) technology is a viable option for increasing communication performance. Firstly, a NOMA downlink transmission system assisted by IRS is established in this study, for maximizing its energy efficiency. Then a Deep Deterministic Policy Gradient (DDPG) algorithm with symmetric properties is used to further optimize the energy efficiency of the system by intelligently adjusting the beam-forming matrix of the access point (AP) and the phase-shift matrix of the IRS. According to the simulation results, the proposed IRS-assisted NOMA downlink network based on the DDPG algorithm presented a considerably higher energy efficiency than the orthogonal multiple access network.

]]>Symmetry doi: 10.3390/sym14051017

Authors: Mohana Sundaram Muthuvalu Elayaraja Aruchunan Majid Khan Majahar Ali Jackel Vui Lung Chew Andang Sunarto Ramoshweu Lebelo Jumat Sulaiman

Initially, the concept of the complexity reduction approach was applied to solve symmetry algebraic systems that were generated from the discretization of the partial differential equations. Consequently, in this paper, the effectiveness of a complexity reduction approach based on half- and quarter-sweep iteration concepts for solving linear Fredholm integral equations of the second kind is investigated. Half- and quarter-sweep iterative methods are applied to solve dense linear systems generated from the discretization of the second kind of linear Fredholm integral equations using a repeated modified trapezoidal (RMT) scheme. The formulation and implementation of the proposed methods are presented. In addition, computational complexity analysis and numerical results of test examples are also included to verify the performance of the proposed methods.

]]>Symmetry doi: 10.3390/sym14051016

Authors: Min Wang Naeem Saleem Xiaolan Liu Arslan Hojat Ansari Mi Zhou

In this paper, we introduce some new types of extended Geraghty contractions, called (&alpha;,&beta;)-admissible generalized Geraghty F-contractions, and prove some fixed point results for such contractions in the setting of partial b-metric spaces. Moreover, based on the obtained fixed point results and the property of symmetry, we inaugurate a fixed point result for graphic generalized Geraghty F-contractions defined on partial metric spaces endowed with a directed graph. As an application, we examine the existence of a unique solution to the first-order periodic boundary value by the obtained fixed point result. Moreover, some examples are presented to illustrate the validity of the new results.

]]>Symmetry doi: 10.3390/sym14051015

Authors: Kazuhiko Sawada Shigeyoshi Saito

The asymmetric development of the cerebellum has been reported in several mammalian species. The current study quantitatively characterized cerebellar asymmetry and sexual dimorphism in cynomolgus macaques using magnetic resonance (MR) imaging-based volumetry. Three-dimensional T1W MR images at 7-tesla were acquired ex vivo from fixed adult male (n = 5) and female (n = 5) monkey brains. Five transverse domains of the cerebellar cortex, known as cerebellar compartmentation defined by the zebrin II/aldolase expression pattern, were segmented on MR images, and the left and right sides of their volumes were calculated. Asymmetry quotient (AQ) analysis revealed significant left-lateralization at the population level in the central zone posterior to the cerebellar transverse domains, which included lobule VII of the vermis with the crura I and II of ansiform lobules, in males but not females. Next, the volume of the cerebellar hemispherical lobules was calculated. Population-level leftward asymmetry was revealed in the crus II regions in males using AQ analysis. The AQ values of the other hemispherical lobules showed no left/right side differences at the population level in either sex. The present findings suggest a sexually dimorphic asymmetric aspect of the cerebellum in cynomolgus macaques, characterized by a leftward lateralization of the crus II region in males, but no left/right bias in females.

]]>Symmetry doi: 10.3390/sym14051014

Authors: Peng Jiao Shengjun Huang Bo Jiang Tao Zhang

Distributed generators and microgrids are of great importance for the stable operation of power systems when failures occur. The major work of this paper is proposing an optimal topological design model of preset connection lines, aiming at a distributed power generation network based on different nodal invulnerability requirements. Moreover, the important innovation of this paper lies in that the perspective is shifted from the system to an individual node of a different type. When a node malfunction occurs, the faulty node can be connected to its neighbor nodes by closing a switch to achieve energy exchange. The distributed generation network consists of a series of nodes that can realize self-sufficiency and can be classified into three types with different levels of importance according to their tasks. The nodes of different types must meet different requirements of destructibility. In this paper, a mixed-integer linear programming model is formulated to solve the optimal topology design problem. In addition, this paper also analyzes the influence of changing nodal power generation capacity and nodal type, and the simulation results show the practicability of the proposal.

]]>Symmetry doi: 10.3390/sym14051013

Authors: Marcin Suszyński Katarzyna Peta Vít Černohlávek Martin Svoboda

In this paper, an assembly sequence planning system, based on artificial neural networks, is developed. The problem of artificial neural network itself is largely related to symmetry at every stage of its creation. A new modeling scheme, known as artificial neural networks, takes into account selected DFA (Design for Assembly) rating factors, which allow the evaluation of assembly sequences, what are the input data to the network learning and then estimate the assembly time. The input to the assembly neural network procedure is the sequences for assembling the parts, extended by the assembly&rsquo;s connection graph that represents the parts and relations between these parts. The operation of a neural network is to predict the assembly time based on the training dataset and indicate it as an output value. The network inputs are data based on selected DFA factors influencing the assembly time. The proposed neural network model outperforms the available assembly sequence planning model in predicting the optimum assembly time for the mechanical parts. In the neural networks, the BFGS (the Broyden&ndash;Fletcher&ndash;Goldfarb&ndash;Shanno algorithm), steepest descent and gradient scaling algorithms are used. The network efficiency was checked from a set of 20,000 test networks with randomly selected parameters: activation functions (linear, logistic, tanh, exponential and sine), the number of hidden neurons, percentage set of training and test dataset. The novelty of the article is therefore the use of parts of the DFA methodology and the neural network to estimate assembly time, under specific production conditions. This approach allows, according to the authors, to estimate which mechanical assembly sequence is the most advantageous, because the simulation results suggest that the neural predictor can be used as a predictor for an assembly sequence planning system.

]]>Symmetry doi: 10.3390/sym14051012

Authors: Artur Łukaszewski Łukasz Nogal Marcin Januszewski

The recent trends in the development of power systems are focused on the Self-Healing Grid technology fusing renewable energy sources. In the event of a failure of the power system, automated distribution grids should continue to supply energy to consumers. Unfortunately, there are currently a limited number of algorithms for rebuilding a power system with renewable energy sources. This problem is possible to solve by implementing restoration algorithms based on graph theory. This article presents the new modification of Prim&rsquo;s algorithm, which has been adapted to operate on a power grid containing several power sources, including renewable energy sources. This solution is unique because Prim&rsquo;s algorithm is ultimately dedicated to single-source graph topologies, while the proposed solution is adapted to multi-source topologies. In the algorithm, the power system is modeled by the adjacency matrices. The adjacency matrixes for the considered undirected graphs are symmetric. The novel logic is based on the original method of determining weights depending on active power, reactive power and active power losses. The developed solution was verified by performing a simulation on a test model of the distribution grid powered by a renewable energy source. The control logic concept was compared with the reference algorithms, which were chosen from the ideas representing available approaches based on graph theory present in the scientific publications. The conducted research confirmed the effectiveness and validity of the novel restoration strategy. The presented algorithm may be applied as a restoration logic dedicated to power distribution systems.

]]>Symmetry doi: 10.3390/sym14051011

Authors: Zhilei Liu Mingying Li Guibing Pang Hongxiang Song Qi Yu Hui Zhang

To improve the performance of the arithmetic optimization algorithm (AOA) and solve problems in the AOA, a novel improved AOA using a multi-strategy approach is proposed. Firstly, circle chaotic mapping is used to increase the diversity of the population. Secondly, a math optimizer accelerated (MOA) function optimized by means of a composite cycloid is proposed to improve the convergence speed of the algorithm. Meanwhile, the symmetry of the composite cycloid is used to balance the global search ability in the early and late iterations. Thirdly, an optimal mutation strategy combining the sparrow elite mutation approach and Cauchy disturbances is used to increase the ability of individuals to jump out of the local optimal. The Rastrigin function is selected as the reference test function to analyze the effectiveness of the improved strategy. Twenty benchmark test functions, algorithm time complexity, the Wilcoxon rank-sum test, and the CEC2019 test set are selected to test the overall performance of the improved algorithm, and the results are then compared with those of other algorithms. The test results show that the improved algorithm has obvious advantages in terms of both its global search ability and convergence speed. Finally, the improved algorithm is applied to an engineering example to further verify its practicability.

]]>Symmetry doi: 10.3390/sym14051010

Authors: Napasool Wongvanich

Ever since the World Health Organization gave the name COVID-19 to the coronavirus pneumonia disease, much of the world has been severely impact by the pandemic socially and economically. In this paper, the mathematical modeling and stability analyses in terms of the susceptible&ndash;exposed&ndash;infected&ndash;removed (SEIR) model with a nonlinear incidence rate, along with media interaction effects, are presented. The sliding mode control methodology is used to design a robust closed loop control of the epidemiological system, where the property of symmetry in the Lyapunov function plays a vital role in achieving the global asymptotic stability in the output. Two policies are considered: the first considers only the governmental interaction, the second considers only the vaccination policy. Numerical simulations of the control algorithms are then evaluated.

]]>Symmetry doi: 10.3390/sym14051009

Authors: Evangelos Chatzaroulas Vytenis Sliogeris Pedro Victori Francesca M. Buffa Sotiris Moschoyiannis Roman Bauer

Gene regulatory networks represent collections of regulators that interact with each other and with other molecules to govern gene expression. Biological signalling networks model how signals are transmitted and how activities are coordinated in the cell. The study of the structure of such networks in complex diseases such as cancer can provide insights into how they function, and consequently, suggest suitable treatment approaches. Here, we explored such topological characteristics in the example of a mitogen-activated protein kinase (MAPK) signalling network derived from published studies in cancer. We employed well-established techniques to conduct network analyses, and collected information on gene function as obtained from large-scale public databases. This allowed us to map topological and functional relationships, and build hypotheses on this network&rsquo;s functional consequences. In particular, we find that the topology of this MAPK network is highly non-random, modular and robust. Moreover, analysis of the network&rsquo;s structure indicates the presence of organisational features of cancer hallmarks, expressed in an asymmetrical manner across communities of the network. Finally, our results indicate that the organisation of this network renders it problematic to use treatment approaches that focus on a single target. Our analysis suggests that multi-target attacks in a well-orchestrated manner are required to alter how the network functions. Overall, we propose that complex network analyses combined with pharmacological insights will help inform on future treatment strategies, exploiting structural vulnerabilities of signalling and regulatory networks in cancer.

]]>Symmetry doi: 10.3390/sym14051008

Authors: Van-Tsai Liu Home-Young Wing

In engineering applications, where we demand more and more precision, the modeling of systems with hysteretic nonlinearity has received considerable attention. The classical Preisach model (CPM) is currently the most popular for characterizing systems with hysteresis, and this model can represent the hysteresis with an infinite but countable first-order inversion curve (FORC). The table method is a method used to realize CPM in practice. The data in the table corresponds to a limited number of FORC samples. There are two problems with this approach: First, in order to reflect the timing effects of elements with hysteresis, it needs to consume a lot of memory space to obtain accurate data table. Second, it is difficult to come up with an efficient way to modify the data table to reflect the timing effects of elements with hysteresis. To overcome these shortcomings, this paper proposes to use a set of polynomials instead of the table method to implement the CPM. The proposed method only needs to store a small number of polynomial coefficients, and thus it reduces the required memory usage. In addition, to obtain polynomial coefficients, we can use least squares approximation or adaptive identification algorithms, which can track hysteresis model parameters. We developed an adaptive algorithm for the identification of polynomial coefficients of micro-piezoelectric actuators by applying the least mean method, which not only reduces the required memory size compared to the table method implementation, but also achieves a significantly improved model accuracy, and the proposed method was successfully verified for displacement prediction and tracking control of micro-piezoelectric actuators.

]]>Symmetry doi: 10.3390/sym14051007

Authors: Saiful R. Mondal

The functions 1+z, ez, 1+Az, A&isin;(0,1] map the unit disc D to a domain which is symmetric about the x-axis. The Regular Coulomb wave function (RCWF) FL,&eta; is a function involving two parameters L and &eta;, and FL,&eta; is symmetric about these. In this article, we derive conditions on the parameter L and &eta; for which the normalized form fL of FL,&eta; are subordinated by 1+z. We also consider the subordination by ez and 1+Az, A&isin;(0,1]. A few more subordination properties involving RCWF are discussed, which leads to the star-likeness of normalized Regular Coulomb wave functions.

]]>Symmetry doi: 10.3390/sym14051006

Authors: Hong-Qiang You Zheng-Zhe Qu Ren-Hang Wu Hao-Ze Su Xiao-Tao He

We build and train an artificial neural network (ANN) model based on experimental &alpha;-decay energy (Q&alpha;) data. In addition to decays between the ground states of parent and daughter nuclei, decays from the ground states of parent nuclei to the excited states of daughter nuclei are also included. In this way, the number of samples is increased dramatically. The &alpha; particle is assumed to have a spherical symmetric shape. The root-mean-square deviation between the calculated results obtained from the ANN model and the experimental data is 0.105 MeV. It shows a good predictive power for &alpha;-decay energy with the ANN model. The influence of different inputs is investigated. It is found that both the shell effect and the pairing effect result in an obvious improvement of the predictive power of the ANN model, and the shell effect plays a more important role. The optimal result can be obtained when both the shell and pairing effects are considered simultaneously. The application of the ANN model in predicting &alpha;-decay energy indicates a neutron magic number at N=184 in the superheavy nuclei mass region.

]]>Symmetry doi: 10.3390/sym14051005

Authors: Chen-Wei Huang Jian-Jiun Ding

The motivation of this paper is to address the limitations of the conventional keypoint-based disparity estimation methods. Conventionally, disparity estimation is usually based on the local information of keypoints. However, keypoints may distribute sparsely in the smooth region, and keypoints with the same descriptors may appear in a symmetric pattern. Therefore, conventional keypoint-based disparity estimation methods may have limited performance in smooth and symmetric regions. The proposed algorithm is superpixel-based. Instead of performing keypoint matching, both keypoint and semiglobal information are applied to determine the disparity in the proposed algorithm. Since the local information of keypoints and the semi-global information of the superpixel are both applied, the accuracy of disparity estimation can be improved, especially for smooth and symmetric regions. Moreover, to address the non-uniform distribution problem of keypoints, a disparity refining mechanism based on the similarity and the distance of neighboring superpixels is applied to correct the disparity of the superpixel with no or few keypoints. The experiments show that the disparity map generated by the proposed algorithm has a lower matching error rate than that generated by other methods.

]]>Symmetry doi: 10.3390/sym14051004

Authors: Junhua Hu Wanying Cao Pei Liang

In the sequential three-way decision model (S3WD), conditional probability and decision threshold pair are two key elements affecting the classification results. The classical model calculates the conditional probability based on the strict equivalence relationship, which limits its application in reality. In addition, little research has studied the relationship between the threshold change and its cause at different granularity levels. To deal with these deficiencies, we propose a novel sequential three-way decision model and apply it to medical diagnosis. Firstly, we propose two methods of calculating conditional probability based on similarity relation, which satisfies the property of symmetry. Then, we construct an S3WD model for a medical information system and use three different kinds of cost functions as the basis for modifying the threshold pair at each level. Subsequently, the rule of the decision threshold pair change is explored. Furthermore, two algorithms used for implementing the proposed S3WD model are introduced. Finally, extensive experiments are carried out to validate the feasibility and effectiveness of the proposed model, and the results show that the model can achieve better classification performance.

]]>Symmetry doi: 10.3390/sym14051003

Authors: Ahmad Mozaffer Karim Hilal Kaya Veysel Alcan Baha Sen Ismail Alihan Hadimlioglu

Due to false negative results of the real-time Reverse Transcriptase-Polymerase Chain Reaction (RT-PCR) test, the complemental practices such as computed tomography (CT) and X-ray in combination with RT-PCR are discussed to achieve a more accurate diagnosis of COVID-19 in clinical practice. Since radiology includes visual understanding as well as decision making under limited conditions such as uncertainty, urgency, patient burden, and hospital facilities, mistakes are inevitable. Therefore, there is an immediate requirement to carry out further investigation and develop new accurate detection and identification methods to provide automatically quantitative evaluation of COVID-19. In this paper, we propose a new computer-aided diagnosis application for COVID-19 detection using deep learning techniques. A new technique, which receives symmetric X-ray data as the input, is presented in this study by combining Convolutional Neural Networks (CNN) with Ant Lion Optimization Algorithm (ALO) and Multiclass Na&iuml;ve Bayes Classifier (NB). Moreover, several other classifiers such as Softmax, Support Vector Machines (SVM), K-Nearest Neighbors (KNN) and Decision Tree (DT) are combined with CNN. The promising results of these classifiers are evaluated and presented for accuracy, precision, and F1-score metrics. NB classifier with Ant Lion Optimization Algorithm and CNN produced the best results with 98.31% accuracy, 100% precision and 98.25% F1-score and with the lowest execution time.

]]>Symmetry doi: 10.3390/sym14051002

Authors: Łukasz Warguła Agnieszka Marciniak

Innovative wheelchair designs require new means of controlling the drive units or the propulsion transmission systems. The article proposes a signal to control the gear ratio or the amount of additional propulsion torque coming from an electric motor. The innovative control signal in this application is the signal generated by the maximum voluntary contraction (MVC) of the muscles of the upper limbs, transformed by the central processing unit (CPU) into muscle activity (MA) when using a wheelchair. The paper includes research on eight muscles of the upper limbs that are active when propelling a wheelchair. Asymmetry in the value for MVC was found between the left and right limbs, while the belly of the long radial extensor muscle of the wrist was determined to be the muscle with the least asymmetry for the users under study. This pilot research demonstrates that the difference in mean MVCmax values between the left and the right limbs can range from 20% to 49%, depending on the muscle being tested. The finding that some muscle groups demonstrate less difference in MVC values suggests that it is possible to design systems for regulating the gear ratio or additional propelling force based on the MVC signal from the muscle of one limb, as described in the patent application from 2022, no. P.440187.

]]>Symmetry doi: 10.3390/sym14051001

Authors: Sachin Kumar Srivastava Fatemah Mofarreh Anuj Kumar Akram Ali

In this article, we study the properties of PR-pseudo-slant submanifold of para-Kenmotsu manifold and obtain the integrability conditions for the slant distribution and anti-invariant distribution of such submanifold. We derived the necessary and sufficient conditions for a PR-pseudo-slant submanifold of para-Kenmotsu manifold to be a PR-pseudo-slant warped product which are in terms of warping functions and shape operator. Some examples of PR-pseudo-slant warped products of para-Kenmotsu manifold are also illustrated in the article.

]]>Symmetry doi: 10.3390/sym14051000

Authors: Ali M. Mubaraki Maha M. Helmi Rahmatullah Ibrahim Nuruddeen

The current study examines the propagation of surface waves in an asymmetric rotating doubly coated nonhomogeneous half space. The coating layers are assumed to be made of different homogeneous isotropic materials, while the overlaying nonhomogeneous half space layer is considered to be of exponentially varying material properties. The consequential exact vibrational displacements and dispersion relation are determined analytically, in addition to the approximate validation of the dispersion relation via the application of an asymptotic procedure within the long wave limit. Two cases of unloaded and loaded end surface scenarios are analyzed by examining the posed fundamental modes. More precisely, an elastic Winkler foundation was considered in the case of a mechanically loaded end surface condition and was found to proliferate the transition between having a fundamental mode over the frequency axis to the wave number axis as the angular velocity increased. Moreover, the rotational effect was found to have a direct impact on the surface wave propagation with a long wave and low frequency. Aside from that, an increase in the nonhomogeneity parameter resulted in propagation with a relatively long frequency.

]]>Symmetry doi: 10.3390/sym14050999

Authors: Pearanat Chuchard Nattakarn Numpanviwat

Electroosmotic force has been used extensively to manipulate fluid flow in a microfluidic system with various channel shapes, especially an elliptic cylinder. However, developing a computational domain and simulating fluid flow for a system involving an elliptic channel consumes a large amount of time. Moreover, the mathematical expression for the fluid velocity of electroosmotic flow in an elliptic channel may be given in the form of the Mathieu functions that have difficulty in achieving the numerical result. In addition, there is clear scientific evidence that confirms the slippage of fluid at the solid-fluid interface in a microscale system. In this study, we present the mathematical model of combined pressure-driven and electroosmotic flow through elliptic microchannels under the slip-fluid condition. From the practical point of view in fluidics, the effect of the eccentricity of the channel cross-section is investigated on the volumetric flow rate to overcome the difficulty. The results show that the substitution of the equivalent circular channel for an elliptic channel provides a valid flow rate under the situation that the areas of both channel cross-sections are equal and the eccentricity of the elliptic cross-section is less than 0.5. Additionally, the flow rate obtained from the substitution is more accurate when the slip length increases or the pressure-gradient-to-external-electric-field ratio decreases.

]]>Symmetry doi: 10.3390/sym14050998

Authors: Atiqah Azhari Andrea Bizzego Jan Paolo Macapinlac Balagtas Kelly Sng Hwee Leng Gianluca Esposito

Mother&ndash;child shared play provides rich opportunities for mutual symmetrical interactions that serve to foster bond formation in dyads. Mutual gaze, a symmetrical behaviour that occurs during direct eye contact between two partners, conveys important cues of social engagement, affect and attention. However, it is not known whether the prefrontal cortical areas responsible for higher-order social cognition of mothers and children likewise exhibit neural symmetry; that is, similarity in direction of neural activation in mothers and children. This study used functional Near-infrared Spectroscopy (fNIRS) hyperscanning on 22 pairs of mothers and their preschool-aged children as they engaged in a 10-min free-play session together. The play interaction was video recorded and instances of mutual gaze were coded for after the experiment. Multivariate linear regression analyses revealed that neural asymmetry occurred during mother&ndash;child mutual gaze, where mothers showed a deactivation of prefrontal activity whereas children showed an activation instead. Findings suggest that mothers and children may employ divergent prefrontal mechanisms when engaged in symmetrical behaviours such as mutual gaze. Future studies could ascertain whether the asymmetric nature of a parent&ndash;child relationship, or potential neurodevelopmental differences in social processing between adults and children, significantly contribute to this observation.

]]>Symmetry doi: 10.3390/sym14050997

Authors: Hao Wu Xu Liu Hang Zhang Xinchao Ruan Ying Guo

Continuous variable quantum teleportation (CVQT) is one of the technologies currently explored to implement global quantum networks. Entanglement source is an indispensable resource to realize CVQT, and its distribution process has natural symmetry. Though there are many results for CVQT over optical fiber or atmospheric channel, little attention is paid to seawater channel. In this paper, a model based on seawater chlorophyll concentration is used to study the attenuation effect of seawater on light. In our scheme, a noiseless linear amplifier is utilized for enhancing the performance of CVQT under seawater channel. Simulation results show that the proposed scheme has an improvement in terms of fidelity and maximum transmission distance compared with the original scheme.

]]>Symmetry doi: 10.3390/sym14050996

Authors: Daniel Sacco Shaikh Maura Sassetti Niccolò Traverso Ziani

Phase transitions&mdash;both classical and quantum types&mdash;are the perfect playground for appreciating universality at work. Indeed, the fine details become unimportant and a classification in very few universality classes is possible. Very recently, a striking deviation from this picture has been discovered: some antiferromagnetic spin chains with competing interactions show a different set of phase transitions depending on the parity of number of spins in the chain. The aim of this article is to demonstrate that the same behavior also characterizes the most simple quantum spin chain: the Ising model in a transverse field. By means of an exact solution based on a Wigner&ndash;Jordan transformation, we show that a first-order quantum phase transition appears at the zero applied field in the odd spin case, while it is not present in the even case. A hint of a possible physical interpretation is given by the combination of two facts: at the point of the phase transition, the degeneracy of the ground state in the even and the odd case substantially differs, being respectively 2 and 2N, with N being the number of spins; the spin of the most favorable kink shows changes at that point.

]]>Symmetry doi: 10.3390/sym14050995

Authors: Florin Avram Rim Adenane Andrei Halanay

Our paper presents three new classes of models: SIR-PH, SIR-PH-FA, and SIR-PH-IA, and states two problems we would like to solve about them. Recall that deterministic mathematical epidemiology has one basic general law, the &ldquo;R0 alternative&rdquo; of Van den Driessche and Watmough, which states that the local stability condition of the disease-free equilibrium may be expressed as R0&lt;1, where R0 is the famous basic reproduction number, which also plays a major role in the theory of branching processes. The literature suggests that it is impossible to find general laws concerning the endemic points. However, it is quite common that 1. When R0&gt;1, there exists a unique fixed endemic point, and 2. the endemic point is locally stable when R0&gt;1. One would like to establish these properties for a large class of realistic epidemic models (and we do not include here epidemics without casualties). We have introduced recently a &ldquo;simple&rdquo; but broad class of &ldquo;SIR-PH models&rdquo; with varying populations, with the express purpose of establishing for these processes the two properties above. Since that seemed still hard, we have introduced a further class of &ldquo;SIR-PH-FA&rdquo; models, which may be interpreted as approximations for the SIR-PH models, and which include simpler models typically studied in the literature (with constant population, without loss of immunity, etc.). For this class, the first &ldquo;endemic law&rdquo; above is &ldquo;almost established&rdquo;, as explicit formulas for a unique endemic point are available, independently of the number of infectious compartments, and it only remains to check its belonging to the invariant domain. This may yet turn out to be always verified, but we have not been able to establish that. However, the second property, the sufficiency of R0&gt;1 for the local stability of an endemic point, remains open even for SIR-PH-FA models, despite the numerous particular cases in which it was checked to hold (via Routh&ndash;Hurwitz time-onerous computations, or Lyapunov functions). The goal of our paper is to draw attention to the two open problems above, for the SIR-PH and SIR-PH-FA, and also for a second, more refined &ldquo;intermediate approximation&rdquo; SIR-PH-IA. We illustrate the current status-quo by presenting new results on a generalization of the SAIRS epidemic model.

]]>Symmetry doi: 10.3390/sym14050994

Authors: Mannque Rho

We describe the mapping at high density of topological structure of baryonic matter to a nuclear effective field theory that implements hidden symmetries emergent from strong nuclear correlations. The theory constructed is found to be consistent with no conflicts with the presently available observations in both normal nuclear matter and compact-star matter. The hidden symmetries involved are &ldquo;local flavor symmetry&rdquo; of the vector mesons identified to be (Seiberg-)dual to the gluons of QCD and hidden &ldquo;quantum scale symmetry&rdquo; with an IR fixed point with a &ldquo;genuine dilaton (GD)&rdquo; characterized by non-vanishing pion and dilaton decay constants. Both the skyrmion topology for Nf&ge;2 baryons and the fractional quantum Hall (FQH) droplet topology for Nf=1 baryons are unified in the &ldquo;homogeneous/hidden&rdquo; Wess&ndash;Zumino term in the hidden local symmetry (HLS) Lagrangian. The possible indispensable role of the FQH droplets in going beyond the density regime of compact stars approaching scale-chiral restoration is explored by moving toward the limit where both the dilaton and the pion go massless.

]]>Symmetry doi: 10.3390/sym14050993

Authors: Azali Saudi A’qilah Ahmad Dahalan

This paper presents the extended variants to the established two-stage Arithmetic Mean (AM) method known as the Modified Accelerated Arithmetic Mean (MAAM) and Skewed Modified Accelerated Arithmetic Mean (SkMAAM) methods to solve the two-dimensional elliptic problem. The existing two-stage AM and its skewed variants apply one weighted parameter for the computation of nodes in Levels 1 and 2. The suggested MAAM and SkMAAM methods employ red&ndash;black ordering with two different weighted parameters and an additional two distinct accelerated parameters for red and black nodes, respectively. By carefully choosing optimum parameter values, the proposed MAAM and SkMAAM improve the computational execution of the algorithm. With red&ndash;black ordering, the computational molecules of red and black nodes are symmetrical, in which the computation of red nodes applies the updated values of their four neighbouring black nodes and vice versa. These symmetrical computational molecules of red and black nodes can be seen for the modified variants MAM and MAAM, and their corresponding skewed variants SkMAM and SkMAAM. The proposed MAAM and SkMAAM methods are compared to the existing AM and Modified AM (MAM) and their corresponding skewed variants, namely the Skewed AM (SkAM) and Skewed MAM (SkMAM) methods. The performance of the newly proposed MAAM and SkMAAM methods is compared against the existing methods in terms of computational complexity and actual execution time. It is shown in the simulation results that the skewed variants are superior to their corresponding regular variants, in which the SkMAAM method gives the best performance.

]]>Symmetry doi: 10.3390/sym14050992

Authors: Porntip Promsinchai Nimit Nimana

In this paper, we consider the solving of an equilibrium problem over the common fixed set of cutter mappings in a real Hilbert space. To this end, we present a subgradient-type extrapolation cyclic method. The proposed method is generated based on the ideas of a subgradient method and an extrapolated cyclic cutter method. We prove a strong convergence of the method provided that some suitable assumptions of step-size sequences are assumed. We finally show the numerical behavior of the proposed method.

]]>Symmetry doi: 10.3390/sym14050991

Authors: Salma Haque Fatima Azmi Nabil Mlaiki

In this article, we present an extension of the controlled rectangular b-metric spaces, so-called controlled rectangular metric-like spaces, where we keep the symmetry condition and we only change the condition [D(s,r)=0&hArr;s=r]to[D(s,r)=0&rArr;s=r], which means we may have a non-zero self distance; also, D(s,s) is not necessarily less than D(s,r). This new type of metric space is a generalization of controlled rectangular b-metric spaces and partial rectangular metric spaces.

]]>Symmetry doi: 10.3390/sym14050990

Authors: Pavel Michal Jana Hudecová Radek Čelechovský Milan Vůjtek Michal Dudka Josef Kapitán

The optical purity of a chiral sample is of particular importance to the analytical chemistry and pharmaceutical industries. In recent years, the vibrational optical activity (VOA) has become established as a sensitive and nondestructive technique for the analysis of chiral molecules in solution. However, the relatively limited accuracy in the range of about 1&ndash;2% reported in published papers and the relatively small spread of experimental facilities to date have meant that vibrational spectroscopy has not been considered a common method for determining enantiomeric excess. In this paper, we attempt to describe, in detail, a methodology for the determination of enantiomeric excess using Raman optical activity (ROA). This method achieved an accuracy of 0.05% for neat &alpha;-pinene and 0.22% for alanine aqueous solution, after less than 6 h of signal accumulation for each enantiomeric mixture, which we believe is the best result achieved to date using vibrational optical activity techniques. An algorithm for the elimination of systematic errors (polarization artifacts) is proposed, and the importance of normalizing ROA spectra to correct for fluctuations in excitation power is established. Results comparable to those obtained with routinely used chemometric analysis by the partial least squares (PLS) method were obtained. These findings show the great potential of ROA spectroscopy for the quantitative analysis of enantiomeric mixtures.

]]>Symmetry doi: 10.3390/sym14050989

Authors: Fotini Moschona Christina Misirlaki Nikolaos Karadimas Maria Koutiva Ioanna Savvopoulou Gerasimos Rassias

The intramolecular halocyclization of alkenes possessing an internal heteroatom nucleophile leads to multifunctional heterocycles which are useful versatile intermediates in organic synthesis. The asymmetric chlorocyclisation of 2-substituted allylic amides gives access to chiral oxazolines bearing a chloromethyl moiety for further synthetic manipulation. The literature reports on this transformation involve complex syntheses of the 2-substituted allylic amides and cryogenic temperatures for achieving high enantioselectivities in the organocatalyzed halocyclization step. Based on the Heck reaction of aryl bromides and Boc-protected allylamine or allylamine benzamides, we developed a practical synthesis of 2-substituted allylic amides that does not require chromatography and accomplished their asymmetric halocyclization reaction with 24&ndash;92%ee under practical conditions (5 &deg;C, CpME) catalyzed by (S)-(+)-DTBM-SEGPHOS. In addition, using appropriately substituted substrates, we generated Hammett plots and formulated a consistent mechanism for the halocyclization reaction which involves two competing modes of formation of the haliranium intermediate whose relative kinetics are governed by the electronic properties of the substrate.

]]>Symmetry doi: 10.3390/sym14050988

Authors: Zhigang Wu Yajiu Zhang Zhuhong Liu Xingqiao Ma

Fully compensated ferrimagnets do not create any magnetic stray field and allow for a completely polarized current of charges. As a result, these alloys show promising prospects for applications as spintronic devices. In this paper, we investigated the phase stability, the site preference, the tetragonal distortion and the influence of symmetry from the crystal structure and chemical environments of magnetic ions on the magnetic properties of Cr2YZ and Mn2YZ (Y = void, Ni, Cu, and Zn; Z = Ga, Ge, and As) full Heusler alloys by first-principles calculations. We found that the selected Cr2-based alloys, except for Cr2NiGa and Cr2NiGe, prefer to crystallize in the centrosymmetric L21-type structure, while the selected Mn2-based alloys, except for Mn2CuAs, Mn2ZnGe and Mn2ZnAs, tend to crystallize in the non-centrosymmetric XA-type structure. Due to the symmetry, the antiferromagnetism of the selected L21-type alloys is very stable, and no spin-polarized density of states could be generated. In contrast, the magnetic moment of the selected XA-type alloys depends heavily on the number of valence electrons and tetragonal distortion, and spin-polarized density of states is generated. Therefore, the selected alloys with L21-type structures and their tetragonal-distorted structure are potential candidates for conventional antiferromagnets, while those with XA-type structure and their tetragonal-distorted structure are promising candidates for (fully) compensated ferrimagnets.

]]>Symmetry doi: 10.3390/sym14050987

Authors: Jun Fu Yujia Xu Yumeng Shi

This article introduces a new type of on-site non-destructive testing instrument for the impermeability measurement of walls. The research and development of this instrument is based on the water drenching method. The influence of symmetry is mainly considered in the design process, and it has on-site testing functions such as water pressure adjustment and wind pressure simulation. The water seepage of the four types of masonry walls under the combined working conditions of three levels of spray strength and wind pressure strength was tested by using instruments. The results show that the weak location regarding the impermeability of the masonry wall is the junction of mortar joints. Parameters such as wall leakage time, seepage area and water seepage amount are significantly affected by wind pressure. Furthermore, during on-site inspection, the influence of wind pressure on water seepage conditions must be considered when simulating the real wind-driven rain conditions. The testing instrument will be promoted and used according to the compiled industry regulations.

]]>Symmetry doi: 10.3390/sym14050986

Authors: Nehad Ali Shah Yasser S. Hamed Khadijah M. Abualnaja Jae-Dong Chung Rasool Shah Adnan Khan

In this paper, we find the solution of the fractional-order Kaup&ndash;Kupershmidt (KK) equation by implementing the natural decomposition method with the aid of two different fractional derivatives, namely the Atangana&ndash;Baleanu derivative in Caputo manner (ABC) and Caputo&ndash;Fabrizio (CF). When investigating capillary gravity waves and nonlinear dispersive waves, the KK equation is extremely important. To demonstrate the accuracy and efficiency of the proposed technique, we study the nonlinear fractional KK equation in three distinct cases. The results are given in the form of a series, which converges quickly. The numerical simulations are presented through tables to illustrate the validity of the suggested technique. Numerical simulations in terms of absolute error are performed to ensure that the proposed methodologies are trustworthy and accurate. The resulting solutions are graphically shown to ensure the applicability and validity of the algorithms under consideration. The results that we obtain confirm that the proposed method is the best tool for handling any nonlinear problems arising in science and technology.

]]>Symmetry doi: 10.3390/sym14050985

Authors: Jiting Gu Zhibo Liu

In the context of energy transformation, new energy technologies are developing rapidly, the penetration rate of new energy is increasing, and the energy structure tends to be low-carbon, which leads to the asymmetry between traditional energy and new energy. At present, the smart power grid can be conceived as a complex cyber-physical system, and its resilience assessment in the face of extreme disasters needs more holistic consideration. Therefore, considering the impact of massive access to new energy on the resilience of the power grid main network, the resilience evaluation index system of the power grid main network under the background of the energy transition is established. It is proposed to use the priority comparison method and CRITIC (Criteria Importance Through Intercriteria Correlation) to determine the subjective weight and subjective and objective weight of the index, respectively, and combine the influence of the two weights to obtain the comprehensive weight. Then, TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) is used to evaluate the regional power grid restoring force. The results of an example show that the proposed method can effectively evaluate the resilience level of the power grid under the background of the energy transition, which has a certain guiding significance for improving the power grid&rsquo;s resilience under the environment of energy transformation.

]]>Symmetry doi: 10.3390/sym14050984

Authors: Miran B. M. Amin Shazad Shawki Ahmad

This study is the first to use Laplace transform methods to solve a system of Caputo fractional Volterra integro-differential equations with variable coefficients and a constant multi-time delay. This technique is based on different types of kernels, which we will explain in this paper. Symmetry kernels, which have properties of difference kernels or simple degenerate kernels, are able to compute analytical work. These are demonstrated by solving certain examples and analyzing the effectiveness and precision of cause techniques.

]]>Symmetry doi: 10.3390/sym14050983

Authors: László Pokorádi

Temporal networks and network-structured systems are gaining ground in daily life. Such net-works are Vehicular Ad-hoc NETworks (VANET) and Mobile Ad-hoc NETworks (MANET), in fact, Industry 4.0 requires similar local networks. During mathematical model-based analysis of real temporal systems, it is vital to determine the existence and frequency of accessibility between components. Graph theory is a well-known mathematical tool used for studying accessibility of network components. In previous publications, the author proposed an easy-usable algorithm for determining the existence of interconnection between system-components. The Monte-Carlo Simulation can model the temporality of systems. The aim of this paper is to propose a Monte-Carlo Simulation-based method that estimates symmetry or asymmetry and the frequency of accessibilities between the components of temporal network-structured systems.

]]>Symmetry doi: 10.3390/sym14050982

Authors: Haiming Liu Jiajing Miao

In this paper, we find some new information on Legendrian dualities and extend them to the case of Legendrian dualities for continuous families of pseudo-spheres in general semi-Euclidean space. In particular, we construct all contact diffeomorphic mappings between the contact manifolds and display them in a table that contains all information about Legendrian dualities.

]]>Symmetry doi: 10.3390/sym14050981

Authors: Welvis Felipe Fernandes Castilheiro Francesc Muñoz-Muñoz Jacint Ventura Manoel dos Santos-Filho Maria da Luz Mathias Sofia Isabel Gabriel

(1) Background: Southern Amazonia encompasses some of the most human-impacted and deforested regions of South America, resulting in a hyper-fragmented landscape. In this context, by using a geometric morphometrics approach, we aimed to examine the effect of forest fragmentation on developmental instability (DI) of the mandible, assessed by variation of fluctuating asymmetry (FA), in four neotropical small mammal species inhabiting the municipality of Alta Floresta (Brazil). (2) Methods: The impact of fragment area, fragment shape, isolation, and edge length on DI were assessed by measuring variation in mandibular FA in the long-tailed spiny rat (Proechimys longicaudatus), the hairy-tailed bolo mouse (Necromys lasiurus), the woolly mouse opossum (Marmosa demerarae), and the Amazonian red-sided opossum (Monodelphis glirina). Mandibles from a total of 304 specimens originating from different-sized fragments (ranging from 5 to 900 ha) were used. Twelve homologous landmarks were digitized in photographs of the mesial view of each hemi-mandible. (3) Results: The two largest species, P. longicaudatus and M. demerarae, exhibited significantly higher levels of FA in mandibular shape in small fragments (5&ndash;26 ha) in comparison to large ones (189&ndash;900 ha). Edge length negatively impacted M. demerarae, the only arboreal species, reinforcing its strongest dependence on core forest habitats. (4) Conclusions: For small mammal communities, we propose that fragments &gt;~200 ha should be the focus of conservation efforts, as both resilient and more sensitive species would benefit from their more preserved biotic and abiotic conditions. Conversely, fragments &lt;~25 ha seem to lead to a significant increase in stress during developmental stages.

]]>Symmetry doi: 10.3390/sym14050980

Authors: Radu Mircea Morariu-Gligor

The paper presents a mechanical and a mathematical model, developed by the author for the study of the dynamical behavior of a tamping rammer. At first, some aspects related to the compaction of soil for construction works are presented. In this study, the soil was modeled using the Kelvin&ndash;Voigt model. To validate the mathematical model, a program written in C language, that allows to analyze the parameters that influence the operation of the tamping rammer, was developed. Three constructive variants of tamping rammers, following the variation of the displacements of the frame and the sole and the variation of the impact force were analyzed. In the final part, the variation of the studied parameters is illustrated by means of graphical representations. The variation of the studied parameters becomes symmetrical, related to an equilibrium position. Using the application, developed by the author, the variation of the sole and frame displacements, and the variation of the impact force can be traced. The numerical results obtained by running the application, (using three sets of input data), demonstrate the accuracy and the correctness of the proposed mathematical model by analogy with the values provided by the manufacturers. Finally, further research in this field is presented.

]]>Symmetry doi: 10.3390/sym14050979

Authors: Dan Peng Jie Wang Donghai Liu Zaiming Liu

The improved evaluation based on the distance from average solution (EDAS) of the interval-valued intuitionistic trapezoidal fuzzy set is proposed. At first, we propose a new distance between interval-valued intuitionistic trapezoidal fuzzy numbers according to their interval endpoints and centroid point, and its properties are also discussed. Furthermore, we apply the proposed distance measure to calculate the expectation level of the emergency plan, and the optimal dynamic expectation level of the emergency plan is obtained by solving the programming model. Then, we improve the EDAS method based on the dynamic expectation level of the decision makers and apply it to calculate the optimal emergency plan. Finally, a numerical example about flood disaster rescue is given to verify the feasibility and effectiveness of the proposed method, which is also compared with the existing methods.

]]>Symmetry doi: 10.3390/sym14050978

Authors: Arunkumar Arulappan Gunasekaran Raja Kalpdrum Passi Aniket Mahanti

Network Function Virtualization (NFV) is an enabling technology that brings together automated network service management and corresponding virtualized network functions that use an NFV Infrastructure (NFVI) framework. The Virtual Network Function Manager (VNFM) placement in a large-scale distributed NFV deployment is therefore a challenging task due to the potential negative impact on performance and operating expense cost. The VNFM assigns Virtual Network Functions (VNFs) and operates efficiently based on network demands with resilient performance through efficient placement techniques. The degradation in performance and a tremendous increase in capital expenditure and operating expenses indicated this chaotic problem. This article proposed a method for VNFM placement using information on the resources of each nodes&rsquo; Element Manager (EM), which is an efficient method to assign VNFs to each node of element management systems. In addition, this paper proposed an Optimized Element Manager (OEM) method for looking at appropriate EMs for the placement of VNF through periodic information on available resources. It also overcomes challenges such as delays and variations in VNFs workload for edge computing and distributed cloud regions. The performance is measured based on computations performed on various optimization algorithms such as linear programming and tabu search algorithms. The advent of the new service provisioning model of BGP-EVPN for VXLAN is materialized by integrating VTS with OpenStack. The numerical analysis shows that the proposed OEM algorithm gives an optimal solution with an average gap of 8%.

]]>Symmetry doi: 10.3390/sym14050977

Authors: Yuhan Wei Ruixian Wu Luming Zou Niuniu Liu Xin Xue

Particular attention has been given to the complexity of the elastic-porous sandwich structure with entangled metallic wire mesh (EMWM), which is a novel rigid-flexible heterogeneous and symmetrical material. The orthogonal experiment design for vacuum brazing was adopted for sensitivity analysis of the key fabrication process on the performances of an EMWM sandwich structure. The shear behaviors of the sandwich structures with different vacuum brazing parameters (e.g., heating rate, brazing temperature, and holding time) were analyzed by mechanical experiments and an interfacial microstructure. The results indicated that the failure behavior of the sandwich structure could be divided into four stages in the mode-I experiment. In addition, the joint quality of the different vacuum brazing process could be shown by the mode-II experiment, and the failure behaviors involves three stages. Additionally, the failure behaviors of the sandwich structure were mainly associated with the deformation of the EMWM core and the strength of the brazing joint. In addition, the relationship between the joint strength and the shear performance of the sandwich structure was revealed through the interfacial microstructure. Furthermore, the importance of the optimized vacuum brazing parameters to fabricate the novel sandwich structure with the best joint performance was demonstrated in this work.

]]>Symmetry doi: 10.3390/sym14050976

Authors: Collins Okon Edet Emmanuel Benjamin Ettah Syed Alwee Aljunid Rosdisham Endut Norshamsuri Ali Akpan Ndem Ikot Muhammad Asjad

The global quantum information-theoretical analysis of the class of Yukawa potential (CYP) in the presence of magnetic and Aharonov&ndash;Bohm (AB) fields has been examined both analytically and numerically in this research piece. The energy equation and wave function for the CYP are obtained by solving the Schrodinger equation in the presence of external magnetic and AB fields using the functional analysis technique. The probability density is used to calculate the Tsallis, R&eacute;nyi, and Onicescu information energy entropies numerically. The influence of the screening parameter (&beta;), magnetic (B&rarr;), and AB (&xi;) fields on the global information-theoretical measurements for the CYP is explored. Atomic and molecular physics, quantum chemistry, and physics are specific areas where these research findings will find application.

]]>Symmetry doi: 10.3390/sym14050975

Authors: Qiming Zhao Lin Yang Yongqiao Wang

In this paper, we consider Frenet type framed base curves that may have singular points and define one-parameter developable surfaces associated with such curves. By using the singularity theory, we classify the generic singularities of the developable surfaces, which are cuspidal edges and swallowtails. In order to characterize these singularities, two geometric invariants are discovered. At last, an example is given to demonstrate the main results.

]]>Symmetry doi: 10.3390/sym14050973

Authors: Tong Jiao Chuhong Pu Wenjing Xing Tao Lv Yuan Li Huaping Wang Jianping He

Glass fiber-reinforced polymer- (GFRP-) packaged optical fiber (OF) sensors are considered a promising engineering-suitable sensor for structural health monitoring. To date, some critical characteristics of the GFRP-packaged OF (GFRP-OF) sensors have not yet been thoroughly studied. This study aimed to systematically characterize the properties of the GFRP-OF sensors. Firstly, we proposed a dimension optimization method for GFRP-OF sensors by strain transfer theory, which is based on a symmetrical three-layered cylindrical model. Then, we experimentally investigated the properties of the GFRP-packaged fiber Bragg grating sensor and GFRP-packaged distributed optical fiber sensor, including their mechanical properties, strain/temperature sensing performance, fatigue resistance, and corrosion resistance. The experimental results showed that the shear bearing capacity of GFRP-OF sensors was more than 120 times larger than that of the other three coated OF sensors, indicating that GFRP dramatically enhanced the robustness of the OF sensor. The GFRP&ndash;OF sensors also feature excellent strain and temperature sensing performance with high linearity and repeatability. The results also demonstrated that the GFRP&ndash;OF sensors have good fatigue properties with absolute fluctuations of strain sensitivity coefficients throughout the fatigue cycles within 0.02 pm/&mu;&epsilon;; repeatability error did not exceed 0.5%, and nonlinear errors were less than 2%. A case study presented in the last section also illustrates the effectiveness of the GFRP-OF sensor in a field application.

]]>Symmetry doi: 10.3390/sym14050974

Authors: Nianqing Zhu Xinxing Gao Jilei Liang Yan Wang Rongjie Hou Zhongbing Ni

Melt blending is an effective way to prepare new composite materials, but most polymers are incompatible. In order to reduce the interfacial tension and obtain fine and stable morphology with internal symmetric micro-textures, suitable compatibilizers should be added to the blend. The two immiscible polymers, low-density polyethylene (LDPE) and polystyrene (PS), were compatibilized by styrene/ethylene/butylene/styrene block copolymers grafted with maleic anhydride (SEBS-g-MAH) and organomontmorillonite (OMMT). The scanning electron microscope results indicated that the size of the PS phase decreased with increasing the content of SEBS-g-MAH. By introducing OMMT into LDPE/PS/SEBS-g-MAH composites, the compatibility of composites was further improved. The rheological analysis and Cole&ndash;Cole plot analysis indicated that the addition of SEBS-g-MAH and OMMT increased the interaction between the two phases. The tensile strength, elongation at break, and impact strength of the LDPE/PS/SEBS-g-MAH (70/30/7, wt%) composite increased by 64%, 255%, and 380%, respectively, compared with the LDPE/PS (70/30, wt%) composite. A small amount of OMMT could synergistically compatibilize the LDPE/PS composite with SEBS-g-MAH. After adding 0.3% OMMT into the LDPE/PS/SEBS-g-MAH system, the tensile strength, elongation at break, and impact strength of the composite were further increased to 18.57 MPa, 71.87%, and 33.28 kJ/m2, respectively.

]]>Symmetry doi: 10.3390/sym14050972

Authors: Petr Karpov Serguei Brazovskii

Broken symmetries of quasi one-dimensional electronic systems give rise to microscopic solitons taking roles of carriers of the charge or spin. The double degeneracy gives rise to solitons as kinks of the scalar order parameter A; the continuous degeneracy for the complex order parameter Aexp(i&theta;) gives rise to phase vortices, amplitudes solitons, and their combinations. These degrees of freedom can be controlled or accessed independently via either the spin polarization or the charge doping. The long-range ordering in dimensions above one imposes super-long-range confinement forces upon the solitons, leading to a sequence of phase transitions in their ensembles. The higher-temperature T transition enforces the confinement of solitons into topologically bound complexes: pairs of kinks or the amplitude solitons dressed by exotic half-integer vortices. At a second lower T transition, the solitons aggregate into rods of bi-kinks or into walls of amplitude solitons terminated by rings of half-integer vortices. With lowering T, the walls multiply, passing sequentially across the sample. Here, we summarize results of a numerical modeling for different symmetries, for charged and neutral soliton, in two and three dimensions. The efficient Monte Carlo algorithm, preserving the number of solitons, was employed which substantially facilitates the calculations, allowing to extend them to the three-dimensional case and to include the long-range Coulomb interactions.

]]>Symmetry doi: 10.3390/sym14050971

Authors: Sebastian Ocklenburg Onur Güntürkün

Asymmetry is an inherent characteristic of brain organization in both humans and other vertebrate species, and is evident at the behavioral, neurophysiological, and structural levels. Brain asymmetry underlies the organization of several cognitive systems, such as emotion, communication, and spatial processing. Despite this ubiquity of asymmetries in the vertebrate brain, we are only beginning to understand the complex neuronal mechanisms underlying the interaction between hemispheric asymmetries and cognitive systems. Unfortunately, despite the vast number of empirical studies on brain asymmetries, theoretical models that aim to provide mechanistic explanations of hemispheric asymmetries are sparse in the field. Therefore, this Special Issue aims to highlight empirically based mechanistic models of brain asymmetry. Overall, six theoretical and four empirical articles were published in the Special Issue, covering a wide range of topics, from human handedness to auditory laterality in bats. Two key challenges for theoretical models of brain asymmetry are the integration of increasingly complex molecular data into testable models, and the creation of theoretical models that are robust and testable across different species.

]]>Symmetry doi: 10.3390/sym14050970

Authors: Raúl Alejandro Morán-Vásquez Duván Humberto Cataño Salazar Daya K. Nagar

The multivariate skew-normal distribution is useful for modeling departures from normality in data through parameters controlling skewness. Recently, several extensions of this distribution have been proposed in the statistical literature, among which the truncated multivariate skew-normal distribution is the foremost. Truncated distributions appear frequently in various theoretical and applied statistical problems. In this article, we study several properties of the truncated multivariate skew-normal distribution. We obtain distributional results through affine transformations, marginalization, and conditioning. Furthermore, the log-concavity of the joint probability density function is established.

]]>Symmetry doi: 10.3390/sym14050969

Authors: Ireneusz Wróbel Adam Skowronek Adam Grajcar

The production of ultra-high strength automotive components requires a multi-directional approach. Hot stamping combines both forming and heat treatment processes to obtain a usually martensitic structure of complicated shaped automotive parts. The preparation for production using hot stamping must involve the latest methods of numerical analysis of both temperature changes and forming, which are applied for an increasing range of materials used. In this paper, the current state of knowledge about the basics of hot stamping, used technological lines, and the current state of material used with applied heat treatments and possible coatings have been reviewed. Moreover, the numerical modeling process has been described. The most important aspects of process automation, including the use of digital twins for simulation and optimization of operational kinetics of the robots accomplishing the production process, analysis and minimization of time of production cycles, and searching for weak operational points of the control systems and for real time visualization of operation of complete line, are considered. The digital twins and corresponding numerical models enable the symmetrical design of real production lines. The details of heat treatment profiles with so called tailored zone heat treatment are provided. Hot stamping is a dynamically developing technology as evidenced by the increasing range of materials used, also from the 3rd generation of advanced high strength (AHSS) steels. It starts to combine forming of symmetric or asymmetric elements with more complex heat treatment processes as required for dual phase (DP) stainless steels or the newest generation of high-strength and ductile medium-manganese steels.

]]>Symmetry doi: 10.3390/sym14050968

Authors: Jihong Pang Jinkun Dai Chaohui Zhang Hongyong Zhou Yong Li

Product fault diagnosis has always been the focus of quality and reliability research. However, a failure&ndash;rate curve of some products is a symmetrical function, the fault analysis result is not true because the failure period of the products cannot be judged accurately. In order to solve the problem of fault diagnosis, this paper proposes a new Takagi-Sugeno (T-S) dynamic fault tree analysis method based on a Bayesian network accompanying the Wiener process. Firstly, the top event, middle event, and bottom event of the product failure mode are determined, and the T-S dynamic fault tree is constructed. Secondly, in order to form the Bayesian network diagram of the T-S dynamic fault tree, the events in the fault tree are transformed into nodes, and the T-S dynamic gate is also transformed into directed edges. Then, the Wiener process is used to model the performance degradation process of the stationary independent increment of the symmetric function distribution, and the maximum likelihood estimation method is applied to estimate the unknown parameters of the degradation model. Next, the product residual life prediction model is established based on the concept of first arrival time, and a symmetric function of failure&ndash;rate curve is obtained by using the product failure probability density function. According to the fault density function derived from the Wiener process, the reverse reasoning algorithm of the Bayesian network is established. Combined with the prior probability of the bottom event, the posterior probability of the root node is calculated and sorted as well. Finally, taking the insufficient braking force of electromagnetic brakes as an example, the practicability and objectivity of the new method are proved.

]]>Symmetry doi: 10.3390/sym14050967

Authors: Zhicheng Yan Qibing Jin Yang Zhang Zeyu Wang Ziming Li

Aiming at the problems of low precision, low search efficiency, and being easy to fall into local optimization of the multi-objective harris hawk optimization algorithm (MOHHO) based on grid method, a MOHHO based on blank angle region enhanced search (BARESMOHHO) is proposed. The main changes of the algorithm are as follows: firstly, chaotic mapping is used to initialize the population, which is beneficial to speed up the search. Then, in order to find low-density regions faster, the algorithm adjusts the classification level according to the number of individuals in the external archive. In order to make the distribution of individuals in the target space more uniform, inspired by the idea of symmetrical segmentation, the number of archives at different levels are symmetrically distributed. Finally, it strengthens the search for the non-individual region (blank angle region) in the process of division. The effectiveness of the proposed algorithm is verified by comparing it with some known classical functions on test functions.

]]>Symmetry doi: 10.3390/sym14050966

Authors: Weiguo Qiao Zhong’an Li

Squaraines (SQs) are unusual cyanine dyes with a unique resonance-stabilized zwitterionic structure. These dyes have attracted significant attention in the fields of organic electronics and organic photonics, due to their facile synthesis, intense and narrow visible and near-infrared absorption/emission, high photostability, low biotoxicity, etc. In this review, we summarize the recent progress of SQ-based fluorescent materials and their biomedical applications. After a brief introduction to SQs, general synthetic routes and design principles of SQ-based fluorescent materials, as well as their aggregation-induced luminescence behaviors, are discussed. Subsequently, their biomedical applications for cell imaging and as fluorescent sensors and therapeutic agents are introduced. Finally, a summary and perspective are given for promoting the development of SQs-based fluorescent materials.

]]>Symmetry doi: 10.3390/sym14050964

Authors: Dolores García-Toral Raúl Mendoza-Báez Ernesto Chigo-Anota Antonio Flores-Riveros Víctor M. Vázquez-Báez Gregorio Hernández Cocoletzi Juan Francisco Rivas-Silva

Based on the Density Functional Theory (DFT) calculations, we analyze the structural and electronic properties of boron phosphide nanotubes (BPNTs) as functions of chirality. The DFT calculations are performed using the M06-2X method in conjunction with the 6-31G(d) divided valence basis set. All nanostructures, (n,0) BPNT (n = 5&ndash;8, 10, 12, 14) and (n,n) BPNT (n = 3&ndash;11), were optimized minimizing the total energy, assuming a non-magnetic nature and a total charge neutrality. Results show that the BPNT diameter size increases linearly with the chiral index &ldquo;n&rdquo; for both chiralities. According to the global molecular descriptors, the (3,3) BPNT is the most stable structure provided that it shows the largest global hardness value. The low chirality (5,0) BPNT has a strong electrophilic character, and it is the most conductive system due to the small |HOMO-LUMO| energy gap. The chemical potential and electrophilicity index in the zigzag-type BPNTs show remarkable chirality-dependent behavior. The increase in diameter/chirality causes a gradual decrease in the |HOMO-LUMO| energy gap for the zigzag BPNTs; however, in the armchair-type BPNTs, a phase transition is generated from a semiconductor to a conductor system. Therefore, the nanostructures investigated in this work may be suggested for both electrical and biophysical applications.

]]>Symmetry doi: 10.3390/sym14050965

Authors: Haixiao Zhang Xiaoli Liu Yu Bao Yiwei Zhang Jinyu Zhao

The pursuit of artificial structures exhibiting unusual acoustic properties is a major scientific endeavor, in which anti-parity-time (PT) symmetry has been coming into view recent years. At the same time, with the emergence of new acoustic metamaterials, the classical Fabry&ndash;Perot resonance mode also exhibits fascinating scattering features similar to those of the anti-PT-symmetric system. We derive the generalized relation for the scattering parameters of an acoustic anti-PT-symmetric system with a transfer matrix, including conjugate bidirectional reflection coefficients and pure real feature of transmission coefficient. In the absence of the real or the imaginary (representing gain/loss) part of the refractive index, the anti-PT-symmetric system degrades into a pair of complementary media, resulting in the bidirectional total transmission. Moreover, a Fabry&ndash;Perot resonance mode exhibiting conjugate bidirectional reflection coefficients and a pure imaginary transmission coefficient has been demonstrated. Our results are meaningful for guiding the experimental test of an acoustic anti-PT-symmetric system and the design of associated bidirectional response prototype devices.

]]>Symmetry doi: 10.3390/sym14050963

Authors: Maitri R. Pathak Ajay Nath

In the paper, we introduce a new model that addresses the generation of quantum droplets (QDs) in the binary Bose&ndash;Einstein condensate (BEC) mixture with mutually symmetric spinor components loaded in multi-color optical lattices (MOLs) of commensurate wavelengths and tunable intensities. The considered MOL confinement is the combination of the four-color optical lattice with an exponential periodic trap, which includes the complete set of the Fourier harmonics. Employing the one-dimensional (1D) extended Gross&ndash;Pit&auml;evskii equation (eGPE), we calculate the exact analytical form of the wavefunction, MF/BMF nonlinearities, and MOL trap parameters. Utilizing the exact solutions, the formation of supersolid-like spatially periodic matter-wave droplet lattices and superlattices is illustrated under the space-periodic nonlinearity management. The precise positioning of the density maxima/minima of the droplet patterns at the center of the trap and tunable Anderson-like localization are observed by tuning the symmetry and amplitude of the considered MOL trap. The stability of the obtained solution is confirmed using the Vakhitov&ndash;Kolokolov (VK) criterion.

]]>Symmetry doi: 10.3390/sym14050962

Authors: Francesco Caroccia Ludovica Passanello Rossana Pipitone Francesco Moscagiuri Paolo Asperio Alessandra Lucchese Luciana Breda Michele D’Attilio

The aim of this study was to evaluate the effect of juvenile idiopathic arthritis (JIA) on the activity of masticatory muscles using surface electromyography (sEMG). Forty-one JIA subjects (ten males, thirty-one females; average age 13 years &plusmn; 3) and thirty-two healthy control subjects (twenty-seven females, five males; average age 14 years &plusmn; 2) were recruited. sEMG of anterior temporalis (TA), masseter (MM), and sternocleidomastoid (SCM) muscles was performed by using the occlusal contact analyzer software called Teethan (BTS S.p.A., Garbagnate Milanese, Milan, Italy). Comparisons between groups were assessed with unpaired t-tests for non-normally distributed data and with Mann&ndash;Whitney U tests for normally distributed parameters. The JIA group showed a significant increased percentage overlapping coefficient of TA (POC TA) (p = 0.01) and impact index (IMP) (p = 0.003). No significant differences were observed for the POC MM, POC SCM, percentage overlapping coefficient between posterior and anterior teeth contact (BAR), the torsion index (TORS), and the asymmetry index (ASIM). Masticatory muscles seemed to be slightly affected by JIA. sEMG could be an effective aid in the early clinical detection of TMJ involvement in JIA. Further research is needed to confirm its validity.

]]>Symmetry doi: 10.3390/sym14050961

Authors: Esperanza Navarro-Pardo

The first article is &ldquo;Spectral Clustering Reveals Different Profiles of Central Sensitization in Women with Carpal Tunnel Syndrome (CTS)&rdquo; [...]

]]>Symmetry doi: 10.3390/sym14050960

Authors: Vishal Verma Deepali Gupta Sheifali Gupta Mudita Uppal Divya Anand Arturo Ortega-Mansilla Fahd S. Alharithi Jasem Almotiri Nitin Goyal

A population explosion has resulted in garbage generation on a large scale. The process of proper and automatic garbage collection is a challenging and tedious task for developing countries. This paper proposes a deep learning-based intelligent garbage detection system using an Unmanned Aerial Vehicle (UAV). The main aim of this paper is to provide a low-cost, accurate and easy-to-use solution for handling the garbage effectively. It also helps municipal corporations to detect the garbage areas in remote locations automatically. This automation was derived using two Convolutional Neural Network (CNN) models and images of solid waste were captured by the drone. Both models were trained on the collected image dataset at different learning rates, optimizers and epochs. This research uses symmetry during the sampling of garbage images. Homogeneity regarding resizing of images is generated due to the application of symmetry to extract their characteristics. The performance of two CNN models was evaluated with the state-of-the-art models using different performance evaluation metrics such as precision, recall, F1-score, and accuracy. The CNN1 model achieved better performance for automatic solid waste detection with 94% accuracy.

]]>Symmetry doi: 10.3390/sym14050958

Authors: Yuanyuan Liu Fan Jia

The properties of fuzzy relations have been extensively studied, and the preservation of their properties plays a fundamental role in the various applications. However, either sufficient or necessity conditions for the preservation requires the aggregated functions of fuzzy relations to dominate or to be dominated by the corresponding operations, which constructs a significant limitation on applicable functions. This work concentrates on the preservation of transitivities and Ferrers property for the aggregation of comonotone or countermonotone fuzzy relations. Firstly, definitions of comonotonicity and countermonotonicity for binary functions are initially proposed. On the foundation of that, the relations of commuting and bisymmetry between min/max and commonly used increasing/decreasing functions are found. Afterwards, with the condition that underlying fuzzy relations are pair-wisely comonotone or countermonotone, theorems on the aggregation functions which can preserve the transitivities and the Ferrers property are proposed. Moreover, an interesting conclusion that the equivalent condition for the min-Ferrers property of fuzzy relations is clarified.

]]>Symmetry doi: 10.3390/sym14050959

Authors: Shih-Shen Chen Ken Hung Chien-Shu Tsai

This paper incorporates more general cases with a new class of constantly adjusted concavity demand curves and includes three types of taxes. To verify the output symmetry under various forms of taxation, we simulate both linear and constant elasticity demand functions under the unit, demand ad valorem, and cost ad valorem taxes. If all the demand functions in the submarkets are linear, the total outputs are identical under both uniform pricing and third-degree price discrimination. Furthermore, if all the weak market demand curves are strictly &ldquo;Robinson-concave&rdquo; and all the strong market demand curves are strictly &ldquo;Robinson-convex&rdquo; or linear, then the total output under price discrimination exceeds that under uniform pricing, and vice versa. While different taxes lead to higher costs, the cost pass-through changes the prices of the products, and the change of total output still depends on the curvature of the demand curve. Therefore, the curvature of the demand curve remains the main determinant of changes in output. Our study provides a theoretical basis for market intervention in price discrimination.

]]>Symmetry doi: 10.3390/sym14050957

Authors: Le Ngoc Truc Le Anh Vu Tran Van Thoan Bui Trung Thanh Tung Lam Nguyen

The paper focuses on faulty actuator problems in an industrial robot using servomotors, and provides an adaptive sliding mode control law to overcome this circumstance. Because of multifarious reasons, robot actuators can undergo a variety of failures, such as locked or stuck joints, free-swinging joints, and partial or total loss of actuation effectiveness. The robot behavior will become worsen if the system controller has not been designed with adequate faulty tolerance. The proportional degradation of actuator torque at unknown degrees of loss, which is one type of partial loss of actuation effectiveness, is considered in this study to design a suitable controller. The robot model is constructed with uncertain parameters and unknown friction, whereas the controller uses only the approximate parameters. Symmetry and skew-symmetry give important contributions in robot modeling and transformation, as well as in the process of proving the system stability. An adjustable coefficient vector of the proposed controller can adaptively reach the upper bounds of an uncertain parametric vector, which guarantees the criterion of Lyapunov stability. In the numerical simulation stage, the selected industrial robot is a Serpent 1 robot with three degrees of freedom. A quasi-physical model based on MATLAB/Simscape Multibody for the robot is built and used in order to increase the reliability of the simulation performance closer to reality. Simulation results illustrate the efficiency of the proposal control methodology in the presence of the mentioned failure. The controller can still deliver satisfactory responses to the robot system under reasonable levels of actuator torque degradation.

]]>Symmetry doi: 10.3390/sym14050956

Authors: Rashad M. EL-Sagheer Muqrin A. Almuqrin Mahmoud El-Morshedy Mohamed S. Eliwa Fathy H. Eissa Doaa A. Abdo

This paper deals with the estimation of the parameters for asymmetric distribution and some lifetime indices such as reliability and hazard rate functions based on progressive first-failure censoring. Maximum likelihood, bootstrap and Bayesian approaches of the distribution parameters and reliability characteristics are investigated. Furthermore, the approximate confidence intervals and highest posterior density credible intervals of the parameters are constructed based on the asymptotic distribution of the maximum likelihood estimators and Markov chain Monte Carlo technique, respectively. In addition, the delta method is implemented to obtain the variances of the reliability and hazard functions. Moreover, we apply two methods of bootstrap to construct the confidence intervals. The Bayes inference based on the squared error and LINEX loss functions is obtained. Extensive simulation studies are conducted to evaluate the behavior of the proposed methods. Finally, a real data set of the COVID-19 mortality rate is analyzed to illustrate the estimation methods developed here.

]]>Symmetry doi: 10.3390/sym14050955

Authors: Bhukya Ramadevi Kishore Bingi

Traditional statistical, physical, and correlation models for chaotic time series prediction have problems, such as low forecasting accuracy, computational time, and difficulty determining the neural network&rsquo;s topologies. Over a decade, various researchers have been working with these issues; however, it remains a challenge. Therefore, this review paper presents a comprehensive review of significant research conducted on various approaches for chaotic time series forecasting, using machine learning techniques such as convolutional neural network (CNN), wavelet neural network (WNN), fuzzy neural network (FNN), and long short-term memory (LSTM) in the nonlinear systems aforementioned above. The paper also aims to provide issues of individual forecasting approaches for better understanding and up-to-date knowledge for chaotic time series forecasting. The comprehensive review table summarizes the works closely associated with the mentioned issues. It includes published year, research country, forecasting approach, application, forecasting parameters, performance measures, and collected data area in this sector. Future improvements and current studies in this field are broadly examined. In addition, possible future scopes and limitations are closely discussed.

]]>Symmetry doi: 10.3390/sym14050954

Authors: Guihong Liu Qiang Guan Yincai Tang Yunhuei Tzeng

In this paper, we proposed an interval degradation model to improve the reliability of the classical single point degradation model. The interval degradation model is very flexible when model parameters follows different distributions. Twenty-five types of interval Gamma degradation models are considered and discussed under different conditions. The reliabilities of interval Gamma degradation models are obtained. The Monte Carlo method has been studied to compute the reliability and lifetime of interval Gamma degradation model. The numerical examples are conducted to compare the interval degradation model with the classical single point degradation model. Simulation results reveal that the performance of reliability and mean lifetime of interval Gamma degradation model are much better than those of the single Gamma degradation model. Finally, we applied our model to a real data example and demonstrated the effectiveness and feasibility of the interval Gamma degradation model.

]]>Symmetry doi: 10.3390/sym14050952

Authors: Yuchen Liu Gang Shi Yanxiang Li Ziyu Zhao

Traffic signs can be seen everywhere in daily life. Traffic signs are symmetrical, and traffic sign detection is easily affected by distortion, distance, light intensity and other factors, which also increases the potential safety hazards of assisted driving in practical application. In order to solve this problem, a symmetrical traffic sign detection algorithm M-YOLO for complex scenes is proposed. The algorithm optimizes the delay problem by reducing the computational overhead of the network, and speeds up the speed of feature extraction. While improving the detection efficiency, it ensures a certain degree of generalization and robustness, and enhances the detection performance of traffic signs in complex environments, such as scale and illumination changes. Experimental results on CCTSDB dataset containing traffic signs in complex scenes and HRRSD small target dataset show that M-YOLO algorithm has good detection performance. Compared with other algorithms, it has higher detection accuracy and detection speed. The test results in real complex scenes show that the detection effect of this algorithm is better than that of YOLOv5l algorithm, and M-YOLO algorithm can accurately detect the traffic signs that cannot be detected by YOLOv5l algorithm. Therefore, the algorithm proposed in this article can effectively improve the detection accuracy of traffic signs, is suitable for complex scenes, and has a good detection effect on small targets.

]]>Symmetry doi: 10.3390/sym14050953

Authors: Li Chen Munawwar Ali Abbas Wissam Sadiq Khudair Bo Sun

This paper deals with the MHD peristaltic flow of Williamson fluids through a porous medium between two joint cylinders. The fluid flow was considered to be that of a non-Newtonian fluid, i.e., a Williamson fluid. The inner tube was uniform, while the flexible outer tube had a Sine wave moving down its wall. The analytical solutions for velocity and temperature were obtained as functions (Bessell functions of the first and second types). The solution for velocity profile, temperature, and concentration distribution were obtained as functions of the physical parameters of the problem (Darcy number, magnetic parameter, Grasoff thermal number, Reynolds number, Prantl number, and Schmidt number) along with other physical parameters. The effect of the physical parameters was discussed graphically. A comparison with previously published graphical results was also carried out. The ambition of the present paper is to contribute to practical applications in geographical and physiological fluid dynamics, such as on sandstone, in the human lungs, on beach sand, on limestone, and in the bile duct. This study is based on theoretical research and can be helpful in the fields of fluid mechanics and mathematics.

]]>Symmetry doi: 10.3390/sym14050951

Authors: Yajun Zhou You Gao

The synchronous genetic regulatory networks model includes the drive system and response system, and the drive-response system is symmetric. From a biological point of view, this model illustrates the dynamic behaviors in gene-to-protein processes, in terms of transcription and translation. This paper introduces a model of genetic regulatory networks with time delay. The fixed-time synchronization control problem of the proposed model is studied based on fixed-time stability theory and the Lyapunov method. Concretely, the authors first propose a way to switch from the given model to matrix form. Then, two types of novel controllers are designed and the corresponding sufficient conditions are investigated respectively to ensure the fixed-time synchronization goal. Moreover, the settling times of fixed-time synchronization are estimated for the addressed discontinuous controllers, which are not dependent on the initial or delayed states of the model. Finally, numerical simulations are presented and compared to illustrate the benefits of the theoretical results.

]]>Symmetry doi: 10.3390/sym14050950

Authors: Yang Zhang Rui Li Jun Chen

In the field of civil engineering and architecture, the concept of symmetry has been widely accepted. The bridge can be treated as a typical symmetrical structure of civil engineering buildings. Among them, the Subgrade can be identified as an important part to bear the vehicle loads. Severe pavement problems and bridge service capabilities will be caused by problems of the bridge&ndash;subgrade transition section. Therefore, setting the rigid&ndash;flexible transition is an important method to solve this problem. The bridge&ndash;subgrade transition section has been set at both ends of the bridge, which can be regarded as a typical symmetrical structure. Based on nonlinear finite element numerical simulation and synergistic theory, the cooperative control problems of the bridge&ndash;subgrade transition section were studied in this work. The change rule of the stiffness of the transition section was discussed and the influence of stiffness variation of the bridge&ndash;subgrade transition section on the stress state of the structure was also analyzed. Furthermore, the influence of subgrade stiffness change on the stress and strain field was analyzed. A permanent strain prediction model was established and stiffness or subsidence difference coordination control was also discussed.

]]>Symmetry doi: 10.3390/sym14050949

Authors: Yuan Zeng Kun Liu Jingbo Wei Zhizhou Zhang

To realize the hyperstatic performance index of a magnetically suspended flywheel and simultaneously suppress the vibration force caused by mass imbalance and sensor runout, a compound control method based on a repetitive controller and displacement force compensation of the synchronous force is proposed. First, the mechanism of different interference vibration forces is analyzed by establishing a model of the magnetically suspended flywheel. The analysis shows that the x&ndash;y direction is symmetric, and the flywheel structure has symmetry. Second, considering the symmetry of the x- and y-directions, the x-direction is taken as an example for analysis, the parameter design and stability analysis are carried out, and the range of parameters of the compound repetitive control method is obtained. Finally, a flywheel with different speeds is simulated. It was found that the vibration force of each frequency can be suppressed by the compound control method, and the inhibition rate of the vibration force can reach as much as 95%. The results show that the unbalanced vibration and vibration force caused by the sensor runout can be effectively suppressed by using the compound repetitive control method.

]]>Symmetry doi: 10.3390/sym14050948

Authors: Shi-Zheng Yang Jian-Hua Gao Zuo-Tang Liang

The fluid in global equilibrium must fulfill some constraints. These constraints can be derived from quantum statistical theory or kinetic theory. In this work, we show how these constraints can be applied to determine the non-dissipative transport coefficients for chiral systems along with the energy-momentum conservation, chiral anomaly for charge current and trace anomaly in the energy-momentum tensor.

]]>Symmetry doi: 10.3390/sym14050947

Authors: Hui Wang Haoyu Li Yuan Zhao

High mobility and the complexity of mobile behavior are the main characteristics of nodes in Vehicle to Everything (V2X). Furthermore, these characteristics entail that resource deployment cannot effectively meet the demands of users for differentiated service quality. Due to this significance, the main objective of this study is to propose an intelligent congestion control strategy based on deep reinforcement learning (ICCDRL) in heterogeneous V2X, which can meet the diverse service needs of vehicles to some extent, so as to solve the problem of network congestion effectively. The proposal is implemented through three aspects: Firstly, the paper establishes a congestion control model based on DRL. Secondly, a large amount of QoS data is used as the training set to optimize the model. Finally, the congestion sensitivity factor is used to select the size of the congestion window for the next moment, resulting in an intelligent congestion control strategy based on QoS on-demand drive. For verification, a series of simulation experiments are designed on the ns-3 simulation platform. The results show that the proposed ICCDRL outperforms the traditional algorithm in terms of throughput, convergence, friendliness and fairness, and can effectively guarantee real-time, reliable information interaction in V2X.

]]>Symmetry doi: 10.3390/sym14050946

Authors: Barakah Almarri Fahd Masood Ali Muhib Osama Moaaz

In this paper, we obtain new monotonic properties for positive solutions of even-order delay differential equations in the non-canonical case. Using these properties, we establish a new oscillation criterion for solutions by comparison with an equation of the first order. The approach adopted is based on the use of symmetry between positive and negative solutions.

]]>Symmetry doi: 10.3390/sym14050945

Authors: Huaping Yang Jing Li Changjiang Shao Yongjiu Qian Qiming Qi Jianxian He

An innovative symmetrical hysteresis model for reinforced concrete (RC) rectangular hollow columns is presented. The Bouc&ndash;Wen&ndash;Baber&ndash;Noori (BWBN) model was selected to depict the inelastic restoring forces and was improved by introducing a coefficient to describe the relationship between stiffness degradation and peak displacement. Sensitivity analysis was conducted at the local and global levels to clarify the importance of each parameter in the improved BWBN model. As such, a hybrid intelligence algorithm named PSOGSA was employed to identify the parameters of the BWBN model utilizing quasi-static tests of 16 hollow columns. The empirical formulas were regressed to bridge the connection between the BWBN model and design parameters of hollow columns. The results showed that the hysteresis curves of the improved BWBN model calibrated by the PSOGSA agreed well with the measured loops. In addition, the accuracy of the empirical prediction method of hysteretic parameters was checked through comparison with other hollow members. The calibrated improved BWBN model produced more precise hysteretic responses for RC hollow columns, since the peak and residual performance levels were simultaneously considered.

]]>Symmetry doi: 10.3390/sym14050944

Authors: María Teresa de Bustos Zouhair Diab Juan Luis G. Guirao Miguel A. López Raquel Martínez

We study analytically the existence of periodic solutions of the generalized Li&eacute;nard differential equations of the form x&uml;+fx,x&#729;x&#729;+n2x+gx=&epsilon;2p1t+&epsilon;3p2t, where n&isin;N*, the functions f,g are of class C3,C4 in a neighborhood of the origin, respectively, the functions pi are of class C0, 2&pi;&minus;periodic in the variable t, with i=1,2, and &epsilon; is a small parameter as usual. The mathematical tool that we have used is the averaging theory of dynamical systems of second order.

]]>Symmetry doi: 10.3390/sym14050943

Authors: Georg Walther Christian Martin Amelie Haase Ulf Nestler Stefan Schob

Intracranial aneurysms represent a potentially life-threatening condition and occur in 3&ndash;5% of the population. They are increasingly diagnosed due to the broad application of cranial magnetic resonance imaging and computed tomography in the context of headaches, vertigo, and other unspecific symptoms. For each affected individual, it is utterly important to estimate the rupture risk of the respective aneurysm. However, clinically applied decision tools, such as the PHASES score, remain insufficient. Therefore, a machine learning approach assessing the rupture risk of intracranial aneurysms is proposed in our study. For training and evaluation of the algorithm, data from a single neurovascular center was used, comprising 446 aneurysms (221 ruptured, 225 unruptured). The machine learning model was then compared with the PHASES score and proved superior in accuracy (0.7825), F1-score (0.7975), sensitivity (0.8643), specificity (0.7022), positive predictive value (0.7403), negative predictive value (0.8404), and area under the curve (0.8639). The frequency distributions of the predicted rupture probabilities and the PHASES score were analyzed. A symmetry can be observed between the rupture probabilities, with a symmetry axis at 0.5. A feature importance analysis reveals that the body mass index, consumption of anticoagulants, and harboring vessel are regarded as the most important features when assessing the rupture risk. On the other hand, the size of the aneurysm, which is weighted most in the PHASES score, is regarded as less important. Based on our findings we discuss the potential role of the model for clinical practice in geographically confined aneurysm patients.

]]>Symmetry doi: 10.3390/sym14050942

Authors: Ivan V. Stepanyan Michail Y. Lednev

Coronaviruses are viruses that infect the respiratory system of humans. Besides high mortality rates among the population, they brought about several economic crises on a global scale. Methods. To study and identify features in the genetic composition of the nucleotide sequences of various coronaviruses, we applied copyright algorithms and visualization, which allowed us to compare the biochemical parameters of diverse RNA coronaviruses in a visual form. Results. The article provides examples of different approaches to imaging coronaviruses. We have provided examples of coronavirus RNA structure visualization in various parametric spaces (1-D and 2-D). We employed various visualization types, including structural, integral, and frequency. The research discussed methods of visualization. Our team developed visualization and comparative analysis of coronavirus serotypes and visualization of SARS-CoV-2 coronavirus datasets. Discussion followed on the visualization results. The presented techniques and the results allowed for displaying the structure of RNA sequences of coronaviruses in spaces of various dimensions. Conclusions. According to our findings, the proposed method contributes to the visualization of the genetic coding of coronaviruses. We discussed the issues of machine learning and neural network technology concerning the analysis of coronaviruses based on the presented approach. The described line of research is essential for the study and control of complex quantum mechanical systems, such as RNA or DNA.

]]>Symmetry doi: 10.3390/sym14050941

Authors: Minglei Xiong Guangming Xie

Division of labor in self-organized groups is a problem of both theoretical significance and application value. Many application problems in the real world require efficient task allocation. We propose a model combining bio-inspiration and evolutionary game theory. This research model theoretically analyzes the problem of target search in unknown areas for multi-robot systems. If the robot&rsquo;s operating area is underwater, the problem becomes more complicated due to its information sharing restrictions. Additionally, it drives strategy updates and calculates the fixed probability of relevant strategies, using evolutionary game theory and the commonly used Fermi function. Our study estimates the fixed probability under arbitrary selection intensity and the fixed probability and time under weak selection for the two-player game model. In the multi-player game, we get these results for weak selection, which is conducive to the coexistence of the two strategies. Moreover, the conducted simulations confirm our analysis. These results help to understand and design effective mechanisms in which self-organizing collective dynamics appears in the form of maximizing the benefits of multi-agent systems in the case of the asymmetric game.

]]>Symmetry doi: 10.3390/sym14050940

Authors: Abrar Hussain Kifayat Ullah Mohammed Nasser Alshahrani Miin-Shen Yang Dragan Pamucar

Multi-attribute decision-making (MADM) is usually used to aggregate fuzzy data successfully. Choosing the best option regarding data is not generally symmetric on the grounds that it does not provide complete information. Since Aczel-Alsina aggregation operators (AOs) have great impact due to their parameter variableness, they have been well applied in MADM under fuzzy construction. Recently, the Aczel-Alsina AOs on intuitionistic fuzzy sets (IFSs), interval-valued IFSs and T-spherical fuzzy sets have been proposed in the literature. In this article, we develop new types of Pythagorean fuzzy AOs by using Aczel-Alsina t-norm and Aczel-Alsina t-conorm. Thus, we give these new operations Aczel-Alsina sum and Aczel-Alsina product on Pythagorean fuzzy sets based on Aczel-Alsina t-norm and Aczel-Alsina t-conorm. We also develop new types of Pythagorean fuzzy AOs including Pythagorean fuzzy Aczel-Alsina weighted averaging and Pythagorean fuzzy Aczel-Alsina weighted geometric operators. We elaborate some characteristics of these proposed Aczel-Alsina AOs on Pythagorean fuzzy sets, such as idempotency, monotonicity, and boundedness. By utilizing the proposed works, we solve an example of MADM in the information of the multinational company under the evaluation of impacts in MADM. We also illustrate the comparisons of the proposed works with previously existing AOs in different fuzzy environments. These comparison results demonstrate the effectiveness of the proposed Aczel-Alsina AOs on Pythagorean fuzzy sets.

]]>Symmetry doi: 10.3390/sym14050938

Authors: Jianxia Zhang Jianxin Zhang Qiang Zhang Xiaopeng Wei

In order to meet security requirements of space on orbit service, an obstacle avoidance trajectory planning method using improved particle swarm optimization had been presented in this paper. On the basis of the actual overall structure of 7 degrees of freedom redundant space manipulator and the characteristics of obstacles, the envelope method was used to model the arm and obstacles, respectively. The limit conditions to avoid the collision between them were analyzed. Then, the fitness function under the symmetrical conditions of avoiding the collision and searching for the shortest trajectory was constructed. In addition, the obstacle avoidance trajectory planning was solved based on improved particle swarm optimization (IPSO). Finally, simulation experiments were carried out to prove its effectiveness and rationality, where there were symmetrical advantages in two aspects. It can be concluded that the presented method based on IPSO has strong robustness.

]]>Symmetry doi: 10.3390/sym14050939

Authors: Zhiming Xia Tong Qiao Ming Xu Xiaoshuai Wu Li Han Yunzhi Chen

With the development of computer hardware and deep learning, face manipulation videos represented by Deepfake have been widely spread on social media. From the perspective of symmetry, many forensics methods have been raised, while most detection performance might drop under compression attacks. To solve this robustness issue, this paper proposes a Deepfake video detection method based on MesoNet with preprocessing module. First, the preprocessing module is established to preprocess the cropped face images, which increases the discrimination among multi-color channels. Next, the preprocessed images are fed into the classic MesoNet. The detection performance of proposed method is verified on two datasets; the AUC on FaceForensics++ can reach 0.974, and it can reach 0.943 on Celeb-DF which is better than the current methods. More importantly, even in the case of heavy compression, the detection rate can still be more than 88%.

]]>Symmetry doi: 10.3390/sym14050937

Authors: Huichao Han Shanzhong Zhang Yibin Wu Yi Cui Xin Liu Shengli Li

As a new method for structural wind engineering research, the transiting test has good application prospects. However, in the road environment, the experimental results will inevitably be influenced by other vehicles (especially larger vehicles). In this paper, a large vehicle was set as an interference vehicle to drive in specific conditions, and the symmetrical CAARC standard model was used to investigate the large vehicle&rsquo;s interference on the transiting test method for measuring building wind pressure coefficient. The results indicate that the wind pressure coefficient time history will appear as a clear up and down undulation phenomenon during the overtaking interference period instead of the single convex phenomenon. The mean wind pressure coefficient in the negative pressure area during the overtaking interference period is lower than that in the no-interference situation. The overtaking interference features are clear and easy to distinguish, and the interference duration is long (more than 6 s). In contrast, the overtaking interference when the test vehicle is overtaken is greater. For following driving, the wake of the large vehicle no longer interferes with the transiting test results after the vehicle spacing exceeds 70 m.

]]>Symmetry doi: 10.3390/sym14050936

Authors: Jamilu Sabi’u Kazeem Olalekan Aremu Ali Althobaiti Abdullah Shah

In this paper, we derived a modified conjugate gradient (CG) parameter by adopting the Birgin and Marti&acute;nez strategy using the descent three-term CG direction and the Newton direction. The proposed CG parameter is applied and suggests a robust algorithm for solving constrained monotone equations with an application to image restoration problems. The global convergence of this algorithm is established using some proper assumptions. Lastly, the numerical comparison with some existing algorithms shows that the proposed algorithm is a robust approach for solving large-scale systems of monotone equations. Additionally, the proposed CG parameter can be used to solve the symmetric system of nonlinear equations as well as other relevant classes of nonlinear equations.

]]>Symmetry doi: 10.3390/sym14050935

Authors: Maojun Duan Xiaocan Suo Fenghui Dong Jianhui Li Guofen Li

Most existing methods for the determination of the reasonable finished state of self-anchored symmetry suspension bridges were based on the stress state of the stiffening girders used in the construction. A simple and practical control method for the reasonable completion state of stiffened beam based on double control indexes of deformation and stress was proposed. In this paper, the long-term effects of shrinkage and creep were taken into consideration, and a finite element model was built to study the change in the stiffening girder stress during operation. The mid-span deflection of the middle span sustained increasing and the compression stress in the bottom slab of the stiffening girder consistently decreased under the effects of shrinkage and creep. The speed changes from fast to slow and tends to become stable in 50 years. Furthermore, stiffening girders under the action of hanger force, dead weight, cable force, and pre-stress were investigated to study the mechanism of the stress change during operation. Based on the safety stress state of stiffening girders after 50 years, a new control method for the reasonable finished state was proposed. Moreover, the total cross-section of stiffening girders maintained the compression stress state during the developing processes of shrinkage and creep in 50 years. Finally, the utilization in the Hunan Road self-anchored symmetry suspension bridge verified the simplicity and practicality of this new control method and confirms that the method can be implemented to guide the design and construction of the similar bridges.

]]>Symmetry doi: 10.3390/sym14050934

Authors: Lior Shamir

Spiral galaxies can spin clockwise or counterclockwise, and the spin direction of a spiral galaxy is a clear visual characteristic. Since in a sufficiently large universe the Universe is expected to be symmetric, the spin direction of a galaxy is merely the perception of the observer, and therefore, galaxies that spin clockwise are expected to have the same characteristics of galaxies spinning counterclockwise. Here, machine learning is applied to study the possible morphological differences between galaxies that spin in opposite directions. The dataset used in this study is a dataset of 77,840 spiral galaxies classified by their spin direction, as well as a smaller dataset of galaxies classified manually. A machine learning algorithm was applied to classify between images of clockwise galaxies and counterclockwise galaxies. The results show that the classifier was able to predict the spin direction of the galaxy by its image in accuracy higher than mere chance, even when the images in one of the classes were mirrored to create a dataset with consistent spin directions. That suggests that galaxies that seem to spin clockwise to an Earth-based observer are not necessarily fully symmetric to galaxies that spin counterclockwise; while further research is required, these results are aligned with previous observations of differences between galaxies based on their spin directions.

]]>Symmetry doi: 10.3390/sym14050933

Authors: Fukiat Nualsri Khamron Mekchay

Contingent claims, such as bonds, swaps, and options, are financial derivatives whose payoffs depend on uncertain future real values of underlying assets which emphasize various real-world applications. In general, valuations for contingent claims can be derived from the conditional expectations of underlying assets. For a simple process, the moments are usually directly obtained from its transition probability density function (PDF). However, if the transition PDF is unavailable in simple form, the derivations of the moments and the contingent claim prices will not be accessible in closed forms. This paper provides a closed-form formula for pricing contingent claims with nonlinear payoff under a no-arbitrage principle when underlying assets follow the extended Cox&ndash;Ingersoll&ndash;Ross (ECIR) process with the symmetry properties of the Brownian motion. The formula proposed here is a consequence of successfully solving an explicit solution for a system of recurrence partial differential equations in which its solution subtly depends on the conditional moments. For the particular CIR process, we obtain simple closed-form formulas by solving the Riccati differential equation. Furthermore, we carry out a complete investigation of the convergent case for those formulas. In case such as that of the unsolvable Riccati differential equation, ECIR case, a numerical method for numerically evaluating the mentioned analytical formulas and numerical validations for the formulas are examined. The validity and efficiency of the formulas are numerically demonstrated by comparison with results from Monte Carlo simulations for various modeling parameters. Finally, the proposed formula is applied to the value contingent claims such as coupon bonds, interest rate swaps, and arrears swaps.

]]>Symmetry doi: 10.3390/sym14050932

Authors: Ismail Zahed

We briefly review some essential aspects of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry, the spontaneous breaking of chiral symmetry, and the axial U(1) anomaly. The anomaly causes the intrinsic nucleon spin to transmute to the vacuum topological charge by quantum tunneling. We use Ji&prime;s invariant spin decomposition to discuss the spin budget of the nucleon as a quark&ndash;diquark state in the QCD instanton vacuum. A measure of the intrinsic quark spin of the nucleon is a measure of the quenched topological susceptibility of the QCD instanton vacuum.

]]>Symmetry doi: 10.3390/sym14050931

Authors: Mustafa A. Sabri Waggas Galib Atshan Essam El-Seidy

This paper is concerned with studying some results by introducing a new Hadamard product M&gamma;,b,v,&delta;C,&eta; operator for differential subordination and superordination for certain univalent functions in the open unit disc U. Firstly, we state some basic definitions and required theorems. Furthermore. Some sandwich theorems are derived. The differential subordination theory&rsquo;s features and outcomes are symmetric to those derived using the differential superordination theory.

]]>Symmetry doi: 10.3390/sym14050930

Authors: Meixi Zhang Zhiyi Wang

Fuzzy entropy has a wide range of applications in uncertainty problems. Due to the dual-complexity of its characteristics and calculation, the study on type-2 fuzzy entropy is rare, let alone the semi-ones. Given this, the paper takes the lead in proposing the credibility-based type-2 entropy and semi-entropies delivered around a specific symmetric type-2 fuzzy variable. After presenting the relevant theorems and definitions, we give the corresponding examples of linear entropy and semi-entropies to illustrate and verify the favorable property of our study. This series of formulas on type-2 entropy proposed has a strong advantage in reducing computational complexity. It can be commonly applied to measure fuzziness and solve return-oriented and cost-oriented problems in the business field. A sequence of measures on type-2 fuzzy entropy developed in this paper delivers fresh insights into this field. It also provides a new reasonable tool for the decision-making on cost and investment control in companies.

]]>Symmetry doi: 10.3390/sym14050929

Authors: Omelsaad Ahfaf Mansour Mahmoud Ahmed Talat

Symmetrical patterns exist in the nature of inequalities, which play a basic role in theoretical and applied mathematics. In several studies, inequalities present accurate approximations of functions based on their symmetry properties. In this paper, we present the following rational approximations for Bateman&rsquo;s G-function G(w)=1w+2w2+&sum;j=1n4&alpha;jw2&minus;2j&minus;1+O1w2n+2, where &alpha;1=14, and &alpha;j=(1&minus;22j+2)B2j+2j+1+&sum;&nu;=1j&minus;1(1&minus;22j&minus;2&nu;+2)B2j&minus;2&nu;+2&alpha;&nu;j&minus;&nu;+1,j&gt;1. As a consequence, we introduced some new bounds of G(w) and a completely monotonic function involving it.

]]>Symmetry doi: 10.3390/sym14050928

Authors: Xiaolong Lou Ziye Chen Preben Hansen Ren Peng

Hand motion sensing-based interaction, abbreviated as &lsquo;free-hand interaction&rsquo;, provides a natural and intuitive method for touch-less interaction on a large display. But due to inherent usability deficiencies of the unconventional size of the large display and the kinematic limitations of the user&rsquo;s arm joint movement, a large display-based free-hand interaction is suspected to have different performance across the whole areas of the large display. To verify this, a multi-directional target pointing and selection experiment was designed and conducted based on the ISO 9241-9 evaluation criteria. Results show that (1) free-hand interaction in display areas close to the center of the body had a higher accuracy than that in peripheral-body areas; (2) free-hand interaction was asymmetric at the left side and the right side of the body. More specifically, left-hand interaction in the left-sided display area was more efficient and accurate than in the right-sided display area. For the right-hand interaction, the result was converse; moreover, (3) the dominant hand generated a higher interaction accuracy than the non-dominant hand. Lessons and strategies are discussed for designing user-friendly natural user interfaces in large displays-based interactive applications.

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