Symmetry doi: 10.3390/sym14102025

Authors: Svetla Stoilova

The present study aims to create groups of symmetrical autonomous metro lines that are united by common features. An integrated six-step methodology which proposes a new aggregated approach for multi-criteria evaluation of fully autonomous metro systems was proposed. The first step determines the criteria to assess the autonomous metro system. Eight criteria connected to the safety, infrastructural and technological development of the autonomous metro system were chosen. In the second step, 20 fully autonomous metro systems in European countries were selected as alternatives. The determination of the criteria weights was performed in the third step based on objective, subjective and combined approaches. For this purpose, the Shannon Entropy method and BWM (Best Worst method) were applied. The fourth step presents the ranking of the autonomous metro system by using multi-criteria methods. Three approaches were studied: distance-based, utility-based and outranking approaches. The distance-based approach includes the TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) and EDAS (Evaluation Based on Distance from Average Solution) methods; the utility-based approach includes MOORA (Multi-Objective Optimization on the Basis of Ratio Analysis) and COPRAS (COmplex PRoportional Assessment) methods; the outranking approach includes the PROMETHEE (Preference Ranking Organization METHod for Enrichment of Evaluations) method. The final ranking based on the new aggregative approach was carried out in the fifth step. Thus, Laplace&rsquo;s criterion was applied to the final ranking. The Hurwitz&rsquo;s criterion was used to verify the results. In the sixth step, the verification of the results was performed by applying cluster analysis. In was found that Line 1 in Paris is the best. Line 14 in Paris and Line D in Lyon were ranking in the second and third position, respectively. The autonomous metro in Brescia, Line C in Rome, and Line M2 in Lausanne were placed at the end of the ranking. Finally, four clearly formed groups of autonomous metro were proposed. The novelty of this study and its main advantage entails the elaboration of a new aggregated approach of multi-criteria methods, evaluation of the autonomous metro systems&rsquo; performance and determination for the groups of symmetrical autonomous lines in European countries.

]]>Symmetry doi: 10.3390/sym14102024

Authors: Micheal Mathavavisakan Nicholas GnanaSekar Indhira Kandaiyan

The concept of a single server retrial queueing system with delayed repair and feedback under a working vacation policy, along with the asymmetric transition representation, is discussed in this article. In addition, consumers are entitled to balk and renege in some situations. The steady-state probability generating function for system size and orbit size is derived by using the approach of supplementary variables. Discussions include key metrics of the system and a few significant special conditions. Moreover, the impact of system parameters is examined through the analysis of some numerical examples.

]]>Symmetry doi: 10.3390/sym14102023

Authors: Hosam Alhakami Mustafa Kamal Muhammad Sulaiman Wajdi Alhakami Abdullah Baz

It is generally observed that aquatic organisms have symmetric abilities to produce oxygen (O2) and fix carbon dioxide (CO2). A simulation model with time-dependent parameters was recently proposed to better understand the symmetric effects of accelerated climate change on coastal ecosystems. Changes in environmental elements and marine life are two examples of variables that are expected to change over time symmetrically. The sustainability of each equilibrium point is examined in addition to proving the existence and accuracy of the proposed model. To support the conclusions of this research compared to other studies, numerical simulations of the proposed model and a case study are investigated. This paper proposes an integrated bibliographical analysis of artificial neural networks (ANNs) using the Reverse-Propagation with Levenberg&ndash;Marquaradt Scheme (RP-LMS) to evaluate the main properties and applications of ANNs. The results obtained by RP-LMS show how to prevent global warming by improving the management of marine fish resources. The reference dataset for greenhouse gas emissions, environmental temperature, aquatic population, and fisheries population (GAPF) is obtained by varying parameters in the numerical Adam approach for different scenarios. The accuracy of the proposed RP-LMS neural network is demonstrated using mean square error (MSE), regression plots, and best-fit output. According to RP-LMS, the current scenario of rapid global warming will continue unabated over the next 50 years, damaging marine ecosystems, particularly fish stocks.

]]>Symmetry doi: 10.3390/sym14102022

Authors: Ayse Betul Cengiz Kokten Ulas Birant Mehmet Cengiz Derya Birant Kemal Baysari

Traditional indoor human activity recognition (HAR) has been defined as a time-series data classification problem and requires feature extraction. The current indoor HAR systems still lack transparent, interpretable, and explainable approaches that can generate human-understandable information. This paper proposes a new approach, called Human Activity Recognition on Signal Images (HARSI), which defines the HAR problem as an image classification problem to improve both explainability and recognition accuracy. The proposed HARSI method collects sensor data from the Internet of Things (IoT) environment and transforms the raw signal data into some visual understandable images to take advantage of the strengths of convolutional neural networks (CNNs) in handling image data. This study focuses on the recognition of symmetric human activities, including walking, jogging, moving downstairs, moving upstairs, standing, and sitting. The experimental results carried out on a real-world dataset showed that a significant improvement (13.72%) was achieved by the proposed HARSI model compared to the traditional machine learning models. The results also showed that our method (98%) outperformed the state-of-the-art methods (90.94%) in terms of classification accuracy.

]]>Symmetry doi: 10.3390/sym14102021

Authors: Satake Tagawa

The dynamo action, which is of importance in the study of the geomagnetism mechanism, is considered to be caused by the convection structure formed inside a rotating spherical shell. This convection structure elongated in the rotation axis is generated by the action of both heat and rotation on the fluid inside a spherical shell. In this study, we analyzed thermal convection in such a rotating spherical shell and attempted to understand the phenomenon of this convective structure. It is known that each value of the Prandtl number, the Ekman number and the Rayleigh number and their balance are important for the generation of such convective structure. We fixed these three parameters and considered the effect of centrifugal buoyancy as the Froude number additionally. To investigate how the effects of centrifugal buoyancy affect the convective structure, we carried out both three-dimensional numerical simulations and linear stability analyses. In particular, we focused on the transition from axisymmetric flow to non-axisymmetric flow having wavenumbers in the toroidal direction and investigated both growth rate and phase velocity of the disturbance. It was found that axisymmetric flow tends to be maintained as the effect of centrifugal buoyancy increases.

]]>Symmetry doi: 10.3390/sym14102020

Authors: Waikhom Henarita Chanu Sunil Panday G. Thangkhenpau

In this paper, we construct variants of Bawazir&rsquo;s iterative methods for solving nonlinear equations having simple roots. The proposed methods are two-step and three-step methods, with and without memory. The Newton method, weight function and divided differences are used to develop the optimal fourth- and eighth-order without-memory methods while the methods with memory are derivative-free and use two accelerating parameters to increase the order of convergence without any additional function evaluations. The methods without memory satisfy the Kung&ndash;Traub conjecture. The convergence properties of the proposed methods are thoroughly investigated using the main theorems that demonstrate the convergence order. We demonstrate the convergence speed of the introduced methods as compared with existing methods by applying the methods to various nonlinear functions and engineering problems. Numerical comparisons specify that the proposed methods are efficient and give tough competition to some well known existing methods.

]]>Symmetry doi: 10.3390/sym14102019

Authors: Wei Xu Ming Cheng Xiangyang Xu Cheng Chen Wei Liu

With the continuous development of engineering construction in China, more and more large-section highway tunnels have emerged. Different geological engineering environments determine the diversity of construction plans. The determination of construction plans and the prediction of tunnel deformations have always been the key points of engineering construction. In this paper, we use numerical simulations to determine specific construction parameters in the context of actual highway tunnel projects, and then use deep learning methods to predict deformation during tunnel construction, thus providing guidance for construction. We have found that: (i) Different excavation sequences and excavation depths have different effects on the surrounding rock deformation around the tunnel. The optimal excavation sequence through numerical simulation in this study is symmetrical excavation, and the excavation depth is 2 m. (ii) Numerical simulation based on Long Short-Term Memory (LSTM) algorithm is used to predict the tunnel deformation. It is found that the prediction results of the LSTM algorithm are more consistent with the actual monitoring data. (iii) Multi-step prediction is more important for engineering guidance, and three-step prediction can be considered during the process of engineering construction. Therefore, the machine learning algorithm provides a new method for engineering prediction.

]]>Symmetry doi: 10.3390/sym14102017

Authors: Luming Zou Chao Zheng Zhi Zheng Feng Hu Yichuan Shao Xin Xue

A horizontally symmetric all-metallic vibration isolator (AM-VI) is proposed to further investigate the dynamic mechanical performance. The novel AM-VI was constructed by combining hat-shaped metal rubber and oblique springs, which were connected in parallel. The springs were arranged symmetrically relative to the support. The elliptic method and the frequency sweeping method were used to compare the dynamic stiffness and the loss factor of the AM-VI. The results demonstrated that the dynamic stiffness and the loss factor calculated by two distinct test methodologies were considerably different, indicating that the inertial force effect of the dynamic testing equipment should be taken into count when adopting the elliptic method. Furthermore, when the vibration isolation performance was evaluated by utilizing mechanical impedance and force transmissibility, the AM-VI achieved excellent vibration isolation performance within a broad frequency range.

]]>Symmetry doi: 10.3390/sym14102018

Authors: Hari M. Srivastava Firdous A. Shah Waseem Z. Lone

Wavelet transform is a powerful tool for analysing the problems arising in harmonic analysis, signal and image processing, sampling, filtering, and so on. However, they seem to be inadequate for representing those signals whose energy is not well concentrated in the frequency domain. In pursuit of representations of such signals, we propose a novel time-frequency transform coined as quadratic-phase wave packet transform in L2(R). The proposed transform is aimed at rectifying the conventional wavelet transform by employing a quadratic-phase Fourier transform with extra degrees of freedom. Besides the formulation of all the fundamental results, including the orthogonality relation, reconstruction formula and the characterization of range, we also derive a direct relationship between the well-known Wigner-Ville distribution and the proposed transform. In addition, we study the quadratic-phase wave-packet transform in the framework of almost periodic functions. Finally, we extend the scope of the present work by investigating the composition of quadratic-phase wave packet transforms.

]]>Symmetry doi: 10.3390/sym14102016

Authors: Aleksey Yu. Varaksin Sergei V. Ryzhkov

Single-phase vortices are a classic example of objects characterized by symmetry in the distribution of all main parameters. The presence of inertial particles (or droplets) in such objects, even with their initial uniform distribution in space, leads to symmetry breaking due to the inverse effect of the dispersed phase on the characteristics of carrier vortices. A review of calculation-theoretical and experimental works devoted to the study of the motion of particles (or droplets) in various concentrated vortex structures, as well as their inverse effect on vortex characteristics, is conducted. The main characteristics (inertia, concentration) as well as dimensionless parameters (Reynolds, Stokes, Froude, Tachikawa numbers) determining the interaction between the dispersed phase and vortices are described. The results of available studies are analyzed in order to establish the peculiarities of particle (or droplet) behavior and stability of different vortex structures, including natural ones. The works analyzed in the review cover a wide range of inertia of the dispersed phase (Stkf = 0.002 &minus; 14.7) and vortex intensities (Re&Gamma; = 200 &minus; 5000).

]]>Symmetry doi: 10.3390/sym14102015

Authors: Ghulam Muhiuddin Mohamed E. Elnair Deena Al-Kadi

The study of symmetry is one of the most important and beautiful themes uniting various areas of contemporary arithmetic. Algebraic structures are useful structures in pure mathematics for learning a geometrical object&rsquo;s symmetries. In order to provide a mathematical tool for dealing with negative information, a negative-valued function came into existence along with N-structures. In the present analysis, the notion of N-structures is applied to the ideals, especially the commutative ideals of BCI-algebras. Firstly, several properties of N-subalgebras and N-ideals in BCI-algebras are investigated. Furthermore, the notion of a commutative N-ideal is defined, and related properties are investigated. In addition, useful characterizations of commutative N-ideals are established. A condition for a closed N-ideal to be a commutative N-ideal is provided. Finally, it is proved that in a commutative BCI-algebra, every closed N-ideal is a commutative N-ideal.

]]>Symmetry doi: 10.3390/sym14102014

Authors: Kazuhiko Sawada

The brain is lateralized morphologically and functionally, with unique species-related specifications [...]

]]>Symmetry doi: 10.3390/sym14102012

Authors: Pier Remigio Salvi Cristina Gellini

Symmetry plays a fundamental role in molecular spectroscopy [...]

]]>Symmetry doi: 10.3390/sym14102013

Authors: Numan Naeem Dumitru Vieru Noor Muhammad Najma Ahmed

Axisymmetric granular flows in vertical cylindrical pipes under action of gravity are studied using mathematical particle&ndash;particle models based on the Hertz&ndash;Mindlin theory. By and large, in granular flows, the density field and the pressure are unknown scalar functions. A well-known relationship between these fields gives the pressure field a power law of the density. The aim of this paper was to study unsteady, axisymmetric, fully developed granular flow under gravity action in a vertical cylindrical pipe, under the assumptions that the density field is constant and the velocity on the pipe&rsquo;s wall is time-dependent. Using integral transforms method and appropriate initial-boundary conditions, the analytical solution for axial velocity is determined. The obtained analytical solution is used to determine the steady-state solution (the solution for large values of the time). The properties of the flow in some particular cases of the velocity on the pipe&rsquo;s surface are analyzed and the transient flow is compared with the stationary one.

]]>Symmetry doi: 10.3390/sym14102011

Authors: Elvis Aponte Ponraj Vasanthakumar Narayanapillai Jayanthi

In this article, a-Browder&rsquo;s classical theorem is considered through the property (Bv), and we show that if two operators are norm equivalent, then property (Bv) holds for one if and only if it holds for the other. The necessary conditions for the difference of the spectrum and essential approximate point spectrum of the tensor product of two operators coincide with the product of differences between the spectrum and the essential approximate point spectrum of its two factors are investigated. We also discuss the necessary conditions for the tensor product of two operators to verify the property (Bv) and simultaneously give the equivalence between their various spectra with their Browder spectrum, likewise with the Drazin spectrum.

]]>Symmetry doi: 10.3390/sym14102010

Authors: Yinxia Gao Dungang Li Fan Yang Xiaoxiao Li

In this paper, we consider the inverse problem for the time-fractional Schr&ouml;dinger equation. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. We use the fractional Landweber iterative regularization method to solve this inverse problem and obtain the regularization solution. Under a priori and a posteriori regularization parameter choices, the error estimates are all obtained, respectively.

]]>Symmetry doi: 10.3390/sym14102006

Authors: Adel A. Attiya Mansour F. Yassen

In this paper, we investigate a new family of normalized analytic functions and bi-univalent functions associated with the Srivastava&ndash;Attiya operator. We use the Faber polynomial expansion to estimate the bounds for the general coefficients |an| of this family. The bounds values for the initial Taylor&ndash;Maclaurin coefficients of the functions in this family are also established.

]]>Symmetry doi: 10.3390/sym14102009

Authors: Mariano Torrisi Rita Tracinà

In this paper, we consider some reaction&ndash;advection&ndash;diffusion systems in order to obtain exact solutions via a symmetry approach. We write the determining system of a general class. Then, for particular subclasses, we obtain special forms of the arbitrary constitutive parameters that allow us to extend the principal Lie algebra. In some cases, we write the corresponding reduced system and we find special exact solutions.

]]>Symmetry doi: 10.3390/sym14102008

Authors: Vito Crincoli Roberto Cortelazzi Corrado De Biase Angela Pia Cazzolla Alessandra Campobasso Mario Dioguardi Maria Grazia Piancino Luigi Mattia Mariasevera Di Comite

Congenital syngnathia is a very rare condition of unknown etiology with multiple clinical manifestations due to different combinations of bony or soft tissue adhesions between the mandible and maxilla. It shares possible association with other congenital anomalies in the head and neck region, or with other syndromes. The aims of the present work were: (1) to perform a literature review on bony syngnathia in order to obtain a general framework on epidemiology and management protocol; (2) to describe a case of a two-year-old boy with a left unilateral bony fusion treated with a distraction protocol of three months. Original articles were searched through PubMed, Cochrane Central database and Embase with a cut-off date of June 2022. In total, 94 articles were identified through database searching. After 39 exclusions, 55 articles were included in the review process. Eighty-seven cases of bony syngnathia have been reported from 1936 to 2022, and different classifications have been suggested in terms of location, extension, functional outcomes and management protocol. Complications may range from feeding difficulty to aspiration pneumonia and respiratory arrest. Early surgery is generally required to release the ankylosis and to establish good mandible function.

]]>Symmetry doi: 10.3390/sym14102007

Authors: Ali Ahmad Ahmad Jamshed Hussain Tag El Din

Interpreting the complex interaction of nanostructured fluid flow with a dipole in a duct, with peripherally uniform temperature distribution, is the main focus of the current work. This paper also sheds light on the changes in the Nusselt number, temperature profiles, and velocity distributions for the fully developed nanofluid flow in a vertical rectangular duct due to a dipole placed near a corner of the duct. A finite volume approach has been incorporated for the numerical study of the problem. It is interesting to note the unusually lower values of the Nusselt number for the higher values of the ratio Gr/Re. Due to the nanostructure in the fluid, an enhancement in the Nusselt number has been noted, which is strongly supported by the magnetic field caused by the dipole. However, as the duct shape is transformed from rectangular to square, the Nusselt number is reduced remarkably. Further, as the dipole is brought nearer to the duct corner, the Nusselt number increases significantly. On the other hand, the flow reversal in the middle of the duct has been noted at higher values of the ratio Gr/Re. The dipole is noted to have a low impact on the reversal flow as well as on the temperature distribution.

]]>Symmetry doi: 10.3390/sym14102005

Authors: Xinjie Shi Pinhong Long Huaping Huang Fengjun Li

The purpose of this paper is to study several fixed point problems in E-metric spaces. Mainly, we show the existence and uniqueness of fixed points for two contractive mappings, including &#262;iri&#263; type contraction and &alpha;-&psi; type contraction in E-metric spaces. Furthermore, we provide examples to support the accuracy of our results and present an application of our solution to a class of differential equations.

]]>Symmetry doi: 10.3390/sym14102003

Authors: Ghoncheh Babanejad Dehaki Hamidah Ibrahim Ali A. Alwan Fatimah Sidi Nur Izura Udzir Ma’aruf Mohammed Lawal

Skyline queries, which are based on the concept of Pareto dominance, filter the objects from a potentially large multi-dimensional collection of objects by keeping the best, most favoured objects in satisfying the user&rsquo;s preferences. With today&rsquo;s advancement of technology, ad hoc meetings or impromptu gatherings involving a group of people are becoming more and more common. Intuitively, deciding on an optimal meeting point is not a straightforward task especially when conflicting criteria are involved and the number of criteria to be considered is vast. Moreover, a point that is near to a user might not meet all the various users&rsquo; preferences, while a point that meets most of the users&rsquo; preferences might be located far away from these users. The task becomes more complicated when these users are on the move. In this paper, we present the Region-based Skyline for a Group of Mobile Users (RSGMU) method, which aims to resolve the problem of continuously finding the optimal meeting points, herein called skyline objects, for a group of users while they are on the move. RSGMU assumes a centroid-based movement where users are assumed to be moving towards a centroid that is identified based on the current locations of each user in the group. Meanwhile, to limit the searching space in identifying the objects of interest, a search region is constructed. However, the changes in the users&rsquo; locations caused the search region of the group to be reconstructed. Unlike the existing methods that require users to frequently report their latest locations, RSGMU utilises a dynamic motion formula, which abides to the laws of classical physics that are fundamentally symmetrical with respect to time, in order to predict the locations of the users at a specified time interval. As a result, the skyline objects are continuously updated, and the ideal meeting points can be decided upon ahead of time. Hence, the users&rsquo; locations as well as the spatial and non-spatial attributes of the objects are used as the skyline evaluation criteria. Meanwhile, to avoid re-computation of skylines at each time interval, the objects of interest within a Single Minimum Bounding Rectangle that is formed based on the current search region are organized in a Kd-tree data structure. Several experiments have been conducted and the results show that our proposed method outperforms the previous work with respect to CPU time.

]]>Symmetry doi: 10.3390/sym14102004

Authors: Yanjiao Ji Peng Yang Tianxin Cai

In this paper, we determine all the Narayana&rsquo;s cows numbers that are factorials or double factorials. We also show that 88 is the only repdigit (i.e., a class of numbers that has reflectional symmetry across a vertical axis) that can be written as the product of consecutive Narayana&rsquo;s cows numbers.

]]>Symmetry doi: 10.3390/sym14102002

Authors: Hongping Yan Liukun He Xiangmei Song Wang Yao Chang Li Qiang Zhou

The anonymous system Tor uses an asymmetric algorithm to protect the content of communications, allowing criminals to conceal their identities and hide their tracks. This malicious usage brings serious security threats to public security and social stability. Statistical analysis of traffic flows can effectively identify and classify Tor flow. However, few features can be extracted from Tor traffic, which have a weak representational ability, making it challenging to combat cybercrime in real-time effectively. Extracting and utilizing more accurate features is the key point to improving the real-time detection performance of Tor traffic. In this paper, we design an efficient and real-time identification scheme for Tor traffic based on the time window method and bidirectional statistical characteristics. In this paper, we divide the network traffic by sliding the time window and then calculate the relative entropy of the flows in the time window to identify Tor traffic. We adopt a sequential pattern mining method to extract bidirectional statistical features and classify the application types in the Tor traffic. Finally, extensive experiments are carried out on the UNB public dataset (ISCXTor2016) to validate our proposal&rsquo;s effectiveness and real-time property. The experiment results show that the proposed method can detect Tor flow and classify Tor flow types with an accuracy of 93.5% and 91%, respectively, and the speed of processing and classifying a single flow is 0.05 s, which is superior to the state-of-the-art methods.

]]>Symmetry doi: 10.3390/sym14102001

Authors: Allan Kardec de Almeida Junior Vivian M. Gomes Antonio Fernando Bertachini de Almeida Prado

The search for life outside Earth has been a popular topic for a long time in the scientific literature, but it gained more possibilities with the discovery of planets around other stars besides our Sun. In this sense, similarly to what happens in our Solar System, moons of planets sometimes offer good conditions for life if stable orbits for those moons exist. Thus, the present paper analyzes a system composed of a moon (with the mass of the Earth) orbiting a planet (with the mass of Jupiter), which is orbiting a double star system (whose total mass is equal to the mass of the Sun). It is an important topic because there is a large proportion of double stars in the universe. The initial conditions are given by a symmetric configuration of two circular orbits. Although this symmetry is broken due to the four body dynamics, the conditions in which the moon remains bound with the planet are investigated. The stability of the system is given by the survival of the orbit of the moon for an integration time of the order of 10,000 revolutions of the satellite around its mother planet. The regions of stable, unstable, and collision orbits are mapped, and empirical linear equations that separate those regions are obtained from the maps.

]]>Symmetry doi: 10.3390/sym14102000

Authors: Siwaphorn Kanchanarat Settapat Chinviriyasit Wirawan Chinviriyasit

Diphtheria is a vaccine-preventable disease in which the outbreaks will not occur if a high enough proportion of individuals in a population are immune. Recent reports reveal that vaccinated individuals with low coverage levels of immunity may be at risk of subclinical diphtheria infection. Therefore, the development of an epidemiology model that will predict the optimal vaccine coverage level needed to prevent the spread of these diseases is crucial. In this paper, a mathematical model for diphtheria transmission with asymptomatic infection, logistic growth, and vaccination is formulated and rigorously analyzed to gain insights into its global dynamical features. The study results show that the disease is eradicated whenever the vaccination coverage is greater than the optimal vaccination coverage level needed for diphtheria eradication. The reported cases of diphtheria in Thailand are applied to estimate the appropriate parameters of the model. Sensitivity analysis reveals the rate of vaccination and the asymptomatic infection are influential factors in controlling and preventing diphtheria. Numerical simulations are illustrated in the theoretical results and show that the incubation period of asymptomatic individuals has an impact on the optimal vaccination coverage level needed for diphtheria eradication.

]]>Symmetry doi: 10.3390/sym14101999

Authors: Weihua Bai Jiaxian Zhu Jialing Zhao Wenwei Cai Keqin Li

The intelligent electrical power system is a comprehensive symmetrical system that controls the power supply and power consumption. As a basis for intelligent power supply control, load demand forecasting in power system operation management has attracted considerable research attention in energy management. In this study, we proposed a novel unsupervised multi-dimensional feature learning forecasting model, named MultiDBN-T, based on a deep belief network and transformer encoder to accurately forecast short-term power load demand and implement power generation planning and scheduling. In the model, the first layer (pre-DBN), based on a deep belief network, was designed to perform unsupervised multi-feature extraction feature learning on the data, and strongly coupled features between multiple independent observable variables were obtained. Next, the encoder layer (D-TEncoder), based on multi-head self-attention, was used to learn the coupled features between various locations, times, or time periods in historical data. The feature embedding of the original multivariate data was performed after the hidden variable relationship was determined. Finally, short-term power load forecasting was conducted. Experimental comparison and analysis of various sequence learning algorithms revealed that the forecasting results of MultiDBN-T were the best, and its mean absolute percentage error and root mean square error were improved by more than 40% on average compared with other algorithms. The effectiveness and accuracy of the model were experimentally verified.

]]>Symmetry doi: 10.3390/sym14101998

Authors: Jincheng Tan Ping Xiang Han Zhao Jian Yu Bailong Ye Delei Yang

As a type of urban life project in China, bridges need a certain capacity of trains running safely after an earthquake to ensure and guarantee transportation on railway lines, post-disaster reconstruction and relief work. Since aftershocks may occur after the main shock, the earthquake-induced irregularity and aftershock intensity are fully considered, based on the running safety index in the seismic design of bridges. However, there is a lack of research on the running safety of trains after an earthquake; it is mainly judged on experience, and lacks theoretical basis. In this paper, the established finite element model of a train bridge interaction system with symmetry was considered. The point estimation method (PEM) combined with moment expansion approximation (MEA) is used for random calculation of the Housner Intensity (HI). Furthermore, running safety indexes were analyzed and the running safety performance of a simply supported bridge with symmetry was assessed under a post-earthquake condition. Then the limit value, to ensure the traffic safety performance after an earthquake, is calculated based on stochastic analysis. The HI can be calculated with full consideration of the randomness of aftershock intensity and structural parameters. On this basis, a calculation method of the HI that considers the randomness of aftershock intensity is proposed. This study can be helpful for the performance-based design of symmetric railway structures under post-earthquake conditions.

]]>Symmetry doi: 10.3390/sym14101997

Authors: Inayatul Haq Tehseen Mazhar Qandeel Nasir Saqib Razzaq Syed Agha Hassnain Mohsan Mohammed H. Alsharif Hend Khalid Alkahtani Ayman Aljarbouh Samih M. Mostafa

Tuberculosis is curable, still the world&rsquo;s second inflectional murderous disease, and ranked 13th (in 2020) by the World Health Organization on the list of leading death causes. One of the reasons for its fatality is the unavailability of modern technology and human experts for early detection. This study represents a precise and reliable machine vision-based approach for Tuberculosis detection in the lung through Symmetry CT scan images. TB spreads irregularly, which means it might not affect both lungs equally, and it might affect only some part of the lung. That&rsquo;s why regions of interest (ROI&rsquo;s) from TB infected and normal CT scan images of lungs were selected after pre-processing i.e., selection/cropping, grayscale image conversion, and filtration, Statistical texture features were extracted, and 30 optimized features using F (Fisher) + PA (probability of error + average correlation) + MI (mutual information) were selected for final optimization and only 6 most optimized features were selected. Several supervised learning classifiers were used to classify between normal and infected TB images. Artificial Neural Network (ANN: n class) based classifier Multi-Layer Perceptron (MLP) showed comparatively better and probably best accuracy of 99% with execution time of less than a second, followed by Random Forest 98.83%, J48 98.67%, Log it Boost 98%, AdaBoostM1 97.16% and Bayes Net 96.83%.

]]>Symmetry doi: 10.3390/sym14101996

Authors: Yanlin Li Sahar H. Nazra Rashad A. Abdel-Baky

In this paper, we give the parametric equation of the Bishop frame for a timelike sweeping surface with a unit speed timelike curve in Minkowski 3-space. We introduce a new geometric invariant to explain the geometric properties and local singularities of this timelike surface. We derive the sufficient and necessary conditions for this timelike surface to be a timelike developable ruled surface. Afterwards, we take advantage of singularity theory to give the classification of singularities of this timelike developable surface. Furthermore, we give some representative examples to show the applications of the theoretical results.

]]>Symmetry doi: 10.3390/sym14101995

Authors: Isabella Schwartz Yonah Ofran Naama Karniel Martin Seyres Sigal Portnoy

Background: During the rehabilitation of individuals post stroke, evaluations are performed in order to discern the patient&rsquo;s prognosis and optimize the treatment plan. However, these tests do not focus on gait symmetry, which might be a predictor for rehabilitation outcomes. We aimed to correlate gait symmetry measures of subacute post stroke patients with rehabilitation outcome and find the symmetry measure that best predicts the variability of the rehabilitation duration. A secondary aim was to compare these measures between patients with right and left brain lesions. Methods: We recruited 30 subacute post stroke patients (14 with right side lesion). We collected the following measures: National Institutes of Health Stroke Scale (NIHSS), Functional Independence Measure (FIM), the 10 m walk test (10MWT), Functional Ambulation Categories (FAC), spatial-temporal gait measures, and gait symmetry and variability. Results: We found moderate correlations between the step length symmetry and the length of rehabilitation, NIHSS, FIM, FAC and 10MWT. The symmetry index of the step length predicted the length of the rehabilitation period as it explained 32.1% of its variance (p = 0.001). Discussion: We conclude that a simple test of the step length symmetry might be informative in predicting rehabilitation length in subacute post stroke patients.

]]>Symmetry doi: 10.3390/sym14101994

Authors: Anand Kumar Md Nishat Anwar Mikulas Huba

To maintain reliable and sustainable power supply, the frequency should be kept constant under varying load conditions. The two degrees of freedom internal model control (2DoF-IMC) scheme is a robust control technique and is efficient for load-disturbance rejection problems in industrial process control. The asymmetry of IMC compared to other methods regarding controller design is that it does not guarantee the stability of the system by itself but is based on the stability of the controlled system. For the control of less-stable and unstable systems, it is therefore usually supplemented with an additional controller, establishing two degrees of freedom in the overall design. In this manuscript, the load-frequency-regulation problem was investigated using a 2DoF-IMC scheme for a single-area as well as a multi-area power system. In the 2DoF-IMC scheme, two controllers are used to control the set-point response and load-disturbance response separately. The set-point controller is designed through the internal model control (IMC) principle, whereas the load-disturbance rejection controller is designed via the direct-synthesis (DS) approach. In the DS approach, the closed-loop transfer function of the system model is matched with the desired closed-loop transfer function of the system and the disturbance-rejection controller is approximated at a very low-frequency point to obtain the proportional&ndash;derivative (PD) controller parameter. The simulation results of the proposed method provide satisfactory performance for load-frequency control (LFC) in the single-area power system and extended to two-area and four-area power systems. The effect of non-linearity, such as generation rate constraint (GRC), was investigated in the single-area power system to establish the efficacy of the proposed method. A random step loading pattern was also considered to confirm the robustness of the proposed method. The overall performance of the proposed control scheme is comparatively better than the recently reported work.

]]>Symmetry doi: 10.3390/sym14101993

Authors: José Afonso Javier Peña Mário Sá Adam Virgile Antonio García-de-Alcaraz Chris Bishop

(1) Background: Asymmetry is ubiquitous in nature and humans have well-established bilateral asymmetries in their structures and functions. However, there are (mostly unsubstantiated) claims that bilateral asymmetries may impair sports performance or increase injury risk. (2) Objective: To critically review the evidence of the occurrence and effects of asymmetry and sports performance. (3) Development: Asymmetry is prevalent across several sports regardless of age, gender, or competitive level, and can be verified even in apparently symmetric actions (e.g., running and rowing). Assessments of bilateral asymmetries are highly task-, metric-, individual-, and sport-specific; fluctuate significantly in time (in magnitude and, more importantly, in direction); and tend to be poorly correlated among themselves, as well as with general performance measures. Assessments of sports-specific performance is mostly lacking. Most studies assessing bilateral asymmetries do not actually assess the occurrence of injuries. While injuries tend to accentuate bilateral asymmetries, there is no evidence that pre-existing asymmetries increase injury risk. While training programs reduce certain bilateral asymmetries, there is no evidence that such reductions result in increased sport-specific performance or reduced injury risk. (4) Conclusions: Bilateral asymmetries are prevalent in sports, do not seem to impair performance, and there is no evidence that suggests that they increase injury risk.

]]>Symmetry doi: 10.3390/sym14101991

Authors: Kashif Ali Wasim Jamshed Sohail Ahmad Hina Bashir Shahzad Ahmad El Sayed M. Tag El Din

Nano-fluids have considerable importance in the field of thermal development that relates to several industrial systems. There are some key applications in recent construction systems flow, as well as microscale cooling gadgets and microstructure electric gadgets for thermal migration. The current investigation concludes the study of electrically conducting nano-fluid flow and heat transfer analysis in two-dimensional boundary layer flow over a curved extending surface in the coexisting of magnetic field, heat generation and thermal radiation. The small sized particles of copper (Cu) are taken as nanoparticles and water is assumed to be the base fluid. We used quasi-linearization and central difference approximation to numerically solve the system of coupled equations obtained from the partial differential equations (PDEs) by incorporating the concept of similarity. The impacts of non-dimensional parameters on velocity, concentration and thermal profiles have been discussed with the help of suitable graphs and tables. It has been noticed that the velocity decelerated with the effect of the magnetic field interaction parameter. Thermal radiation caused an increase in temperature.

]]>Symmetry doi: 10.3390/sym14101992

Authors: Senlin Wang Dangmin Nie

In response to the problems of slow running speed and high error rates of traditional flight conflict detection algorithms, in this paper, we propose a conflict detection algorithm based on the use of a relevance vector machine. A set of symmetrical historical flight data was used as the training set of the model, and we used the SMOTE resampling method to optimize the training set. We obtained relatively symmetrical training data and trained it with the relevance vector machine, improving the kernels through an intelligent algorithm. We tested this method with new symmetrical flight data. The improved algorithm greatly improved the running speed and was able to effectively reduce the missed alarm rate of in-flight conflict detection symmetrically, thus effectively ensuring flight safety.

]]>Symmetry doi: 10.3390/sym14101990

Authors: Tahir Mahmood Zeeshan Ali Majed Albaity

Aggregation operators perform a valuable and significant role in various decision-making processes. Averaging and geometric aggregation operators are both used for capturing the interrelationships of the aggregated preferences, even if the preferences are independent. The purpose of this paper is to analyze the theory of complex linguistic fuzzy (CLF) sets and their important laws, such as algebraic laws, score values, and accuracy values, and to describe the relationship between the score and accuracy values with the help of their properties. Additionally, based on the proposed CLF information, we introduce the theory of CLF weighted averaging (CLFWA), CLF ordered weighted averaging (CLFOWA), CLF hybrid averaging (CLFHA), CLF weighted geometric (CLFWG), CLF ordered weighted geometric (CLFOWG), and CLF hybrid geometric (CLFHG) operators. The fundamental properties and some valuable results of these operators are evaluated, and their particular cases are described. Based on the presented operators, a technique for evaluating the &ldquo;multi-attribute decision-making&rdquo; (MADM) problems in the consideration of CLF sets is derived. The superiority of the derived technique is illustrated via a practical example, a set of experiments, and significant and qualitative comparisons. The illustration results indicate that the derived technique can be feasible and superior in evaluating CLF information. Further, it can be used for determining the interrelationships of attributes and the criteria of experts. Moreover, it is valuable and capable of evaluating the MADM problems using CLF numbers.

]]>Symmetry doi: 10.3390/sym14101989

Authors: Patiwat Littidej Theeraya Uttha Benjamabhorn Pumhirunroj

The main purpose of the study is to apply symmetry principles to general mathematical modelling based on multi-criteria decision making (MCDM) approach for use in development in conjunction with geographic weighted regression (GWR) model and optimize the artificial neural network-cellular automaton (ANN-CA) model for forecasting the sugarcane plot burning area of Northeast Thailand. First, to calculate the service area boundaries of sugarcane transport that caused the burning of sugarcane with a fire radiative power (FRP) values using spatial correlation analysis approach. Second, the analysis of the spatial factors influencing sugarcane burning. The study uses the approach of symmetry in the design of algorithm for finding the optimal service boundary distance (called as cut-off) in the analysis of hot-spot clustering and uses calculations with the geographic information system (GIS) approach, and the final stage is the use of screened independent variable factors to predict the plots of burned sugarcane in 2031. The results showed that the positively related factors for the percentage of cane plot sintering in the sub-area units of each sugar plant's service were the distance to transport sugarcane plots index and percentage of sugarcane plantations in service areas, while the negative coefficients were FRP differences and density of sugarcane yield factors, according to the analysis with a total of seven spatial variables. The best GWR models display local R2 values at levels of 0.902 to 0.961 in the service zones of Khonburi and Saikaw. An influential set of independent variables can increase the accuracy of the ANN-CA model in forecasting with kappa statistical estimates in the range of 0.81 to 0.85 The results of the study can be applied to other regions of Thailand, including countries with similar sugarcane harvesting industries, to formulate policies to reduce the exposure of sugarcane harvested by burning methods and to support the transportation of sugarcane within the appropriate scope of service so that particulate matter less than 2.5 microns () can be reduced.

]]>Symmetry doi: 10.3390/sym14101988

Authors: Muhammad Samad Khan Mubashir Ali Siddiqui Muhammad Idrees Afridi

Engineers and researchers are interested in the study of nonlinear convection, viscous dissipation, and Joule heating in various flow configurations due to their various applications in engineering processes. That is why the present study deals with the influence of nonlinear convection, viscous, and Joule dissipation of the temperature and velocity profile of incompressible fluid over a flat plate. In this study, the magnetic field acts perpendicular to the fluid flow and is supposed to be of uniform magnitude. Further, the Newtonian fluid, which is electrically conducting, passes over an infinite vertical flat plate under an oscillatory motion. The term representing the influence of the nonlinear convection phenomenon is integrated into the Navier&ndash;Stokes equation. The governing equations of the mentioned study were modeled in the form of non-linear PDEs and modified as non-dimensional equations via appropriate scaling analyses, which resulted in coupled and non-linear PDEs. For the numerical solution of the transformed non-linear PDEs, the finite difference method was applied. Finally, we present the effects of various flow parameters via graphical illustrations.

]]>Symmetry doi: 10.3390/sym14101987

Authors: Nuno M. M. Torre Valerio A. P. Salomon Emilson Loche Shalom A. Gazale Vinicius M. Palermo

The crisis that affected Brazil as a result of the coronavirus disease 2019 (COVID-19) pandemic impacted several businesses. However, the distribution of products sold by e-commerce is one business that had increased its demand on a large scale. The Southeastern Region of Brazil has a wide territorial extension, a high number of inhabitants, and difficulties with transport logistics. Thus, this work presents a solution for choosing a location for the installation of an e-commerce warehouse, considering three possible locations, in two different Brazilian states: Rio de Janeiro and Sao Paulo. Our main objective is to identify policies that allow a balance in the trade-off between risks and service levels. Specifically, we seek to decrease logistics costs and ensure improvements in services. The choice of a location for a warehouse is a decision problem that can be solved with multiple criteria decision-making (MCDM). Three methods of MCDM have been applied: Fuzzy Decision Approach (FDA), Multi-Attribute Utility Theory (MAUT), and Multi-Attribute Value Theory (MAVT). The reasons for the application of the MAUT and MAVT methods originate from their easy understanding and use, while the concepts of FDA address the consideration of uncertainty. To maintain the simplicity of MCDM application, the FDA model is symmetric, even with symmetrical and asymmetrical fuzzy sets. Important criteria were the distance from capital cities, distance to ports, distance to airports, distance to highways, and the costs of land. Three different locations were considered for the installation of the warehouse. All three methods, FDA, MAUT, and MAVT, resulted in Location 1 as the best location for the installation of the warehouse for the distribution of e-commerce products. A discussion on conceptual qualitative divergences and the small quantitative divergence of results is also included in the conclusions.

]]>Symmetry doi: 10.3390/sym14101986

Authors: Abdumauvlen Berdyshev Rakhmatillo Aloev Dana Bliyeva Sardor Dadabayev Zharasbek Baishemirov

The paper is devoted to the construction and study of a numerical method for solving two-dimensional Saint&ndash;Venant equations. These equations have important applied significance in modern hydraulic engineering and are suitable for describing waves in the atmosphere, rivers and oceans, and for modeling tides. The issues of formulation of the mixed problems for these equations are studied. The system of equations is reduced to a symmetrical form by transforming dependent variables. Then, the matrices of coefficients are represented as the sums of two symmetric semidefinite matrices. This transformation allows constructing an upwind difference scheme in spatial directions to determine the numerical solution of the initial boundary value problem. The stability of the proposed difference scheme in energy norms is rigorously proved. The results of numerical experiments conducted for a model problem are provided to confirm the stability of the proposed method.

]]>Symmetry doi: 10.3390/sym14101985

Authors: Jaewook Shin Bum Yong Park Won Il Lee Jinwoo Yoo

This paper presents a novel variable matrix-type step-size affine projection sign algorithm (VMSS-APSA) characterized by robustness against impulsive noise. To mathematically derive a matrix-type step size, VMSS-APSA utilizes mean-square deviation (MSD) for the modified version of the original APSA. Accurately establishing the MSD of APSA is impossible. Therefore, the proposed VMSS-APSA derives the upper bound of the MSD using the upper bound of the L1-norm of the measurement noise. The optimal matrix-type step size is calculated at each iteration by minimizing the upper bound of the MSD, thereby improving the filter performance in terms of convergence rate and steady-state estimation error. Because a novel cost function of the proposed VMSS-APSA was designed to maintain a form similar to the original APSA, they have symmetric characteristics. Simulation results demonstrate that the proposed VMSS-APSA improves filter performance in a system-identification scenario in the presence of impulsive noise.

]]>Symmetry doi: 10.3390/sym14101982

Authors: Hsiu-Hui Hsu

This study explored the learning effectiveness of drawing makeup designs by computer graphic design and compared the learning differences between traditional hand-drawn and computer-assisted teaching in cosmetology students at universities. The statistical analysis methods of factor analysis, descriptive statistical analysis, and paired sample t-test are used to analyze the difference in students&rsquo; learning attitudes before and after the course. It also explored students&rsquo; learning effectiveness. The subjects were 55 students from a cosmetology department of a university in Taiwan. The results showed that using a computer tool to create makeup designs improved the overall student learning effectiveness and effectively promoted students&rsquo; interest in learning. Moreover, through focus group interviews, changes in the learning effectiveness that were brought about by the use of computer graphic design tools were obtained. Among them, the mirror function could best meet the needs of students for makeup symmetry and design drawing speed and improve their satisfaction with computer graphic makeup. The results of this study are improving the learning effectiveness, maintaining a positive attitude and increasing willingness to learn, and the systematization and digitization of makeup design, and the results could promote teachers to obtain more efficient teaching quality, improve students&rsquo; professional skills, and result in better learning results.

]]>Symmetry doi: 10.3390/sym14101984

Authors: Enrique Gaztanaga

In part I of this series, we showed that the observed Universe can be modeled as a local Black Hole of fixed mass M&#8771;6&times;1022M&#8857;, without Dark Energy: cosmic acceleration is caused by the Black Hole event horizon rS = 2GM. Here, we propose that such Black Hole Universe (together with smaller primordial Black Holes) could form from the hierarchical free-fall collapse of regular matter. We argue that the singularity could be avoided with a Big Bounce explosion, which results from neutron degeneracy pressure (Pauli exclusion principle). This happens at GeV energies, like in core collapse supernova, well before the collapse reaches Planck energies (1019 GeV). If our Universe formed this way, there is no need for Cosmic Inflation or a singular start (the Big Bang). Nucleosynthesis and recombination follow a hot expansion, as in the standard model, but cosmological measurements (which are free parameters in the standard model) could in principle be predicted from first principles. Part or all of the Dark Matter could be made up of primordial compact objects (Black Holes and Neutron Stars), remnants of the collapse and bounce. This can provide a faster start for galaxy formation. We present a simple prediction to explain the observed value of M&#8771;6&times;1022M&#8857; or equivalently &Omega;&Lambda; (the fraction of the critical energy density observed today in form of Dark Energy) and the coincidence problem &Omega;m&sim;&Omega;&Lambda;.

]]>Symmetry doi: 10.3390/sym14101983

Authors: Andrei I. Shumeiko Viktor D. Telekh Sergei V. Ryzhkov

Wave plasma sources (WPSs) were first proposed in the 1970s for electric propulsion (EP), and these research and development processes culminated in the flight test in 2021 of the WPS-based thruster REGULUS. Recently, new approaches to WPS use have emerged&mdash;multiple schemes of EPs that can generate propelling forces in multiple directions within a single thruster head, regarded as a breakthrough technology for in-space propulsion systems (PSs). One of the concepts is the bi-directional wave plasma thruster that is based on the open-ended gas discharge chamber&mdash;the symmetrical system. Up to now, the WPSs based on the open-ended chambers have not been widely studied. In this paper, the plasma flow formed by the WPS based on the open-ended chamber was axially characterized using a retarding potential analyzer (RPA), Langmuir probe (LP), and optical emission spectroscopy (OES). The presence of the double-layer (DL) was confirmed by a drastic change in the plasma potential along the axis, and a specific impulse of 1100 s was indirectly measured. The measurement results show the potential of the WPS based on the open-ended chamber for efficient operations.

]]>Symmetry doi: 10.3390/sym14101981

Authors: Shunlei Hu Yan Zhuang Yifan Wu Xidong Zhang Xiaoqiang Dong

Floating pile-supported embankment involves more complex load transfer mechanisms, and there are no clear uniform guidelines available for its design. The concepts of flexible floating, rigid floating and end-bearing pile-supported embankments were proposed in this paper. Based on three typical field cases, their pile-soil interactions and soil arching effect were examined using the three-dimensional finite element method. Due to symmetry, only a half-width embankment model was simulated here. It has been found that the flexible floating piles carry the load mainly relying on the skin friction, but end-bearing piles rely on the pile tip resistance. The rigid floating piles were somehow in between. The earth pressure coefficient (K) in the end-bearing pile-supported embankment reached a maximum of 3.28, greater than Rankine passive values of the earth pressure coefficient (KP), in which the soil arching was fully developed. The K in the embankment with rigid floating pile reached 2.21, where soil arching might be partially formed. At the bottom of the flexible floating pile-supported embankment, the K tended to equal the Rankine active values of the earth pressure coefficient (Ka), and thus soil arching was insignificant. It has also been found that using rigid floating piles might significantly improve the bearing capacity of the embankments and was cost-effective for deep soft soil areas.

]]>Symmetry doi: 10.3390/sym14101980

Authors: Celia Andreu-Sánchez Miguel Ángel Martín-Pascual Agnès Gruart José María Delgado-García

The purpose of this study is to determine if there is asymmetry in the brain activity between both hemispheres while watching cuts in movies. We presented videos with cuts to 36 participants, registered electrical brain activity through electroencephalography (EEG) and analyzed asymmetry in frontal, somatomotor, temporal, parietal and occipital areas. EEG power and alpha (8&ndash;13 Hz) asymmetry were analyzed based on 4032 epochs (112 epochs from videos &times; 36 participants) in each hemisphere. On average, we found negative asymmetry, indicating a greater alpha power in the left hemisphere and a greater activity in the right hemisphere in frontal, temporal and occipital areas. The opposite was found in somatomotor and temporal areas. However, with a high inter-subjects variability, these asymmetries did not seem to be significant. Our results suggest that cuts in audiovisuals do not provoke any specific asymmetrical brain activity in the alpha band in viewers. We conclude that brain asymmetry when decoding audiovisual content may be more related with narrative content than with formal style.

]]>Symmetry doi: 10.3390/sym14101970

Authors: Manuel J. Chinchillas-Chinchillas Horacio E. Garrafa-Gálvez Victor M. Orozco-Carmona Priscy A. Luque-Morales

Symmetry in nanomaterials is essential to know the behavior of their properties. In the present research, the photocatalytic properties of SnO2 and ZnO nanoparticles were compared for the degradation of the cationic dyes Methylene Blue (MB) and Rhodamine B (RB). The nanoparticles were obtained through a green synthesis process assisted by Randia echinocarpa extracts; they were then analyzed through Fourier transform infrared spectroscopy (FT-IR) and X-ray diffraction (XRD) to characterize their structure. Transmission electron microscopy (TEM) was used to identify the morphology and disclose nanoparticle size, and the optical properties were studied through Ultraviolet&ndash;visible spectroscopy (UV&ndash;Vis). The results show that the synthesized SnO2 and ZnO nanomaterials have quasispherical morphologies with average sizes of 8&ndash;12 and 4&ndash;6 nm, cassiterite and wurtzite crystal phases, and band gap values of 3.5 and 3.8 eV, respectively. The photocatalytic activity yielded 100% degradation of the MB and RB dyes in 210 and 150 min, respectively. ZnO performed higher photocatalytic degradation of the cationic dyes than SnO2 due to a higher content of Randia echinocarpa extracts remaining after the green synthesis process.

]]>Symmetry doi: 10.3390/sym14101979

Authors: Emmanuele Battista Giampiero Esposito

This paper builds two detailed examples of generalized normal in non-Euclidean spaces, i.e., the hyperbolic and elliptic geometries. In the hyperbolic plane we define a n-sided hyperbolic polygon P, which is the Euclidean closure of the hyperbolic plane H, bounded by n hyperbolic geodesic segments. The polygon P is built by considering the unique geodesic that connects the n+2 vertices z&tilde;,z0,z1,...,zn&minus;1,zn. The geodesics that link the vertices are Euclidean semicircles centred on the real axis. The vector normal to the geodesic linking two consecutive vertices is evaluated and turns out to be discontinuous. Within the framework of elliptic geometry, we solve the geodesic equation and construct a geodesic triangle. Additionally in this case, we obtain a discontinuous normal vector field. Last, the possible application to two-dimensional Euclidean quantum gravity is outlined.

]]>Symmetry doi: 10.3390/sym14101978

Authors: Jing Xu Chaofan Ren Yanxin Liu Xiaonan Chang

The vibration signal of the shearer is one of the important signals for coal and rock cutting mode recognition and fault diagnosis. However, the signal collected in the field contains a large amount of background noise, which is not conducive to subsequent analysis and processing. Therefore, a noise elimination method for coalcutter vibration signal based on Ensemble Empirical Mode Decomposition (EEMD) and an Improved Harris Hawks Optimization (HHO) algorithm is proposed in this paper. The vibration signal is first decomposed by EEMD to generate a series of intrinsic mode functions (IMF). The HHO algorithm was introduced to determine the optimal denoising threshold of each IMF. In addition, the original HHO has been improved to use the natural constant as the base exponential function to determine the escape energy trend line. Simulation results show that compared with the other four denoising methods, the signal waveform processed by this method is smoother. Under different types of signals and the same intensity of noise, the SNR increases by 70.9%, 6.7%, 2.6%, and 10.53% on average, respectively. The MSE decreases by 67.6%, 12.7%, 4.5%, and 5.42% on average. Under the same type of signal and different intensity of noise environment, the SNR is improved by 74.62%, 37.70%, 5.24%, and 39.72% on average, respectively. MSE decreased by 77.38%, 53.10%, 9.88%, and 54.67% on average. Finally, the method is applied to the shearer working state diagnosis system, and its actual effect is verified.

]]>Symmetry doi: 10.3390/sym14101977

Authors: Wenbo Wang Muhammad Yousaf Ding Liu Ayesha Sohail

Medical optical imaging, with the aid of the &ldquo;terahertz tomography&rdquo;, is a novel medical imaging technique based on the electromagnetic waves. Such advanced imaging techniques strive for the detailed theoretical and computational analysis for better verification and validation. Two important aspects, the analytic approach for the understanding of the Schrodinger transforms and machine learning approaches for the understanding of the medical images segmentation, are presented in this manuscript. While developing an AI algorithm for complex datasets, the computational speed and accuracy cannot be overlooked. With the passage of time, machine learning approaches have been further modified using the Bayesian, genetic and quantum approaches. These strategies have boosted the efficiency of the machine learning, and specifically the deep learning tools, by taking into account the probabilistic, evolutionary and quantum qubits hypothesis and operations, respectively. The current research encompasses the detailed analysis of image segmentation algorithms based on the evolutionary approach. The image segmentation algorithm that converts the color model from RGB to HSI and the image segmentation algorithm that uses the clustering technique are discussed in detail, and further extensions of these genetic algorithms to quantum algorithms are proposed. Based on the genetic algorithm, the optimal selection of parameters is realized so as to achieve a better segmentation effect.

]]>Symmetry doi: 10.3390/sym14101976

Authors: Wisal Khan Kislay Raj Teerath Kumar Arunabha M. Roy Bin Luo

In the present work, we propose a novel method utilizing only a decoder for generation of pseudo-examples, which has shown great success in image classification tasks. The proposed method is particularly constructive when the data are in a limited quantity used for semi-supervised learning (SSL) or few-shot learning (FSL). While most of the previous works have used an autoencoder to improve the classification performance for SSL, using a single autoencoder may generate confusing pseudo-examples that could degrade the classifier&rsquo;s performance. On the other hand, various models that utilize encoder&ndash;decoder architecture for sample generation can significantly increase computational overhead. To address the issues mentioned above, we propose an efficient means of generating pseudo-examples by using only the generator (decoder) network separately for each class that has shown to be effective for both SSL and FSL. In our approach, the decoder is trained for each class sample using random noise, and multiple samples are generated using the trained decoder. Our generator-based approach outperforms previous state-of-the-art SSL and FSL approaches. In addition, we released the Urdu digits dataset consisting of 10,000 images, including 8000 training and 2000 test images collected through three different methods for purposes of diversity. Furthermore, we explored the effectiveness of our proposed method on the Urdu digits dataset by using both SSL and FSL, which demonstrated improvement of 3.04% and 1.50% in terms of average accuracy, respectively, illustrating the superiority of the proposed method compared to the current state-of-the-art models.

]]>Symmetry doi: 10.3390/sym14101975

Authors: Sakthi Prakash Murugu A. R. Srikrishnan Bharath Kumar Krishnaraj. Anguraj Jayaraj Akram Mohammad Ratna Kishore Velamati

Chevron nozzles, which are characterized by the serrations at the nozzle exit, are widely used for suppressing jet noise in aircraft engines. The noise suppression is accomplished by the enhanced mixing of the exhaust streams, which, in turn, is a result of the streamwise vorticity induced by the serrations. The present study focuses on the numerical modeling of the acoustic field in a compressible jet issuing from a chevron nozzle at a Mach number of 0.8. The study evaluates the effectiveness of turbulence modeling approaches of Large Eddy Simulation and Detached Eddy Simulation methods and compares them with the less computationally intensive Unsteady Reynolds Averaged Navier&ndash;Stokes (URANS) formulation. The Ffowcs Williams&ndash;Hawkings noise model was used to predict the overall sound pressure level in the far field. The LES predictions of the acoustic signature were found to match well with the experimental data, whereas the URANS model grossly underpredicted the sound pressure levels in the compressible jet flow field.

]]>Symmetry doi: 10.3390/sym14101974

Authors: Andronikos Paliathanasis

We investigate exact and analytic solutions for the field equations in the teleparallel dark energy model, where the physical space is described by the locally rotational symmetric Bianchi I, Bianchi III and Kantowski-Sachs geometries. We make use of the property that a point-like Lagrangian exists for the description of the field equations, and variational symmetries are applied for the construction of invariant functions and conservation laws. The latter are used for the derivation of new analytic solutions for the classical field equations and exact function forms for the wavefunction in the quantum limit.

]]>Symmetry doi: 10.3390/sym14101973

Authors: Saeed Roshani Salah I. Yahya Jamal Rastad Yaqeen Sabah Mezaal Louis W. Y. Liu Sobhan Roshani

A power divider (PD) with a wide stopband and simple symmetric structure using open- and short-ended stubs is analyzed and implemented in this paper. In the proposed power divider, for the first time, the output resistor is divided into two sections and open- and short-ended stubs are used between the resistors. The incorporated open- and short-ended stubs have resulted in a controllable bandwidth for the proposed PD, which resulted in 40% of the fractional bandwidth considering 3 dB attenuation of insertion loss. The proposed PD operates at 2 GHz, which shows more than 20 dB attenuation for the return and isolation losses. In addition, the obtained insertion loss at the operating frequency is approximately 0.3 dB, which shows a minor loss, and also, high isolation is achieved in the device. Moreover, 20 dB and 30 dB attenuation levels have been achieved for second and third harmonics. The results show high performance for the proposed power divider.

]]>Symmetry doi: 10.3390/sym14101972

Authors: Sondekola Rudra Swamy Luminiţa-Ioana Cotîrlă

The object of this article is to explore a &tau;-pseudo-&nu;-convex &kappa;-fold symmetric bi-univalent function family satisfying subordinations condition generalizing certain previously examined families. We originate the initial Taylor&ndash;Maclaurin coefficient estimates of functions in the defined family. The classical Fekete&ndash;Szeg&ouml; inequalities for functions in the defined &tau;-pseudo-&nu;-convex family is also estimated. Furthermore, we present some of the special cases of the main results. Relevant connections with those in several earlier works are also pointed out. Our study in this paper is also motivated by the symmetry nature of &kappa;-fold symmetric bi-univalent functions in the defined class.

]]>Symmetry doi: 10.3390/sym14101971

Authors: Djihane Benmorsli Zine El Abiddine Fellah Djema Belgroune Nicholas O. Ongwen Erick Ogam Claude Depollier Mohamed Fellah

In this paper, the influence of the transverse wave on sound propagation in a porous medium with a flexible structure is considered. The study is carried out in the time domain using the modified Biot theory obtained by the symmetry of the Lagrangian (invariance by translation and rotation). The viscous exchanges between the fluid and the structure are described by fractional calculus. When a sound pulse arrives at normal incidence on a porous material with a flexible structure, the transverse waves interfere with the longitudinal waves during propagation because of the viscous interactions that appear between the fluid and the structure. By performing a calculation in the Laplace domain, the reflection and transmission operators are derived. Their time domain expressions depend on the Green functions of the longitudinal and transverse waves. In order to study the effects of the transverse wave on the transmitted longitudinal waves, numerical simulations of the transmitted waves in the time domain by varying the characteristic parameters of the medium are realized whether the transverse wave is considered or not.

]]>Symmetry doi: 10.3390/sym14101969

Authors: Lei Wang Liangxin Dong Yiyang Chen Keqing Wang Feng Gao

An iterative learning fault-tolerant control method is designed for an actuator fault intermittent process with simultaneous uncertainties for the system parameters. First, an intermittent fault tolerance controller is designed using 2D system theory, and the iterative learning control (ILC) intermittent process is transformed into a 2D Roesser model. Secondly, sufficient conditions for the controller&rsquo;s existence are analyzed using the linear matrix inequality (LMI) technique, and the control gain matrices are obtained by convex optimization with LMI constraints. Under these conditions for all additive uncertainties for the system parameters and admissible failures, the controller can ensure closed-loop fault-tolerant performance in both the time and batch directions, and it can also meet the H&infin; robust performance level against outside disturbances. Eventually, the algorithm&rsquo;s computational complexity is analyzed, and the effectiveness of the algorithm is verified by simulation with respect to an injection molding machine model. Compared with traditional ILC laws, which do not consider actuator faults, the proposed algorithm has a better convergence speed and stability when the time-invariant and time-variant actuator faults occur during implementation.

]]>Symmetry doi: 10.3390/sym14101968

Authors: Aleksei Boikov Vladimir Payor

This article is a review of current scientific problems in the field of automation of the electromagnetic levitation melting process control of non-ferrous metals and potential solutions using modern digital technologies. The article describes the technological process of electromagnetic levitation melting as a method of obtaining ultrapure metals and the main problems of the automation of this process taking into account domestic and international experience. Promising approaches to control the position of the melt in the inductor in real time on the basis of vision systems are considered. The main problems and factors preventing the mass introduction of levitation melting in the electromagnetic field to the industry are highlighted. The problem of passing the Curie point by the heated billet and the effect of the billet&rsquo;s loss of magnetism on the vibrational circuit of the installation and the temperature of the inductor are also considered. The article also reflects key areas of research development in the field of levitation melting, including: optimization of energy costs, stabilization of the position of the melt in the inductor, predictive process control, and scaling of levitation melting units. The concept of a digital twin based on a numerical model as a component of an automatic process control system for the implementation of inductor control and prediction of process parameters of the melt is presented. The possibility of using vision for visual control of the melt position in the inductor based on video images for its further stabilization in the inductor and increasing the accuracy of numerical simulation results by specifying the real geometry of the melt in parallel with the calculation of the model itself is considered.

]]>Symmetry doi: 10.3390/sym14101967

Authors: Piotr Nowak Łukasz Kubaszewski

Asymmetry in the degenerative lumbar spine may eventually evolve to debilitating scoliosis. The point where it starts to accelerate in some individuals is obscure. Discreet preclinical asymmetry may be a prognostic feature of the condition. The aim of this study was to assess the asymmetry of the intervertebral foramina of lower lumbar motion segments of the spine based on morphometric measurements using novel techniques of three-dimensional imaging. Computed tomography scans of 19 subjects with axial low back pain aged 50 to 78 of both sexes were digitally processed, and 3D reconstruction of L4/L5 and L5/S1 motion segments were obtained. The planes of intervertebral foramina were defined in reference to the axis of the pedicles bordering the intervertebral canal and the measurements were performed yielding absolute values in millimeters. The circumference ranged from 33.4 mm to 63.86 mm on the left side and from 33.01 mm to 73.54 mm on the right side. The horizontal dimension ranged from 6.86 mm to 17.84 mm on the left side and from 5.41 mm to 17.63 mm on the right side. The vertical dimension ranged from 10.17 mm to 23.65 mm on the left side and from 9.04 mm to 29.69 mm on the right side. All the measurements were combined to assess the asymmetry. Only in three cases (15%), symmetry in both segments was confirmed. No defined lateralization of asymmetry was found, as well as no significant link between the sex and age could be confirmed. This is the first study confirming the asymmetry among the intervertebral foramina. It seems that it is the dominant phenotype for intervertebral foramina. As the observed asymmetry lacks the dominant lateralization, it may be linked with the same trait of degenerative scoliosis. Though no direct link between the age and sex was confirmed in this study, it suggests other factors should be considered in prediction of the progress and magnitude of the deformity.

]]>Symmetry doi: 10.3390/sym14101966

Authors: Tudor Bînzar Flavius Pater Sorin Nădăban

The aim of this paper is to provide new ways of dealing with dynamic programming using a context of newly proven results about fixed-point problems in linear spaces endowed with a fuzzy norm. In our paper, the general framework is set to fuzzy normed linear spaces as they are defined by N&#259;d&#259;ban and Dzitac. When completeness is required, we will use the George and Veeramani (G-V) setup, which, for our purposes, we consider to be more suitable than Grabiec-completeness. As an important result of our work, we give an original proof for a version of Banach&rsquo;s fixed-point principle on this particular setup of fuzzy normed spaces, a variant of Jungck&rsquo;s fixed-point theorem in the same setup, and they are proved in G-V-complete fuzzy normed spaces, paving the way for future developments in various fields within this framework, where our application of dynamic programming makes a proper example. As the uniqueness of almost every dynamic programming problem is necessary, the fixed-point theorems represent an important tool in achieving that goal.

]]>Symmetry doi: 10.3390/sym14101965

Authors: Teerawat Simmachan Wikanda Phaphan

The notion of length-biased distribution can be used to develop adequate models. Length-biased distribution was known as a special case of weighted distribution. In this work, a new class of length-biased distribution, namely the two-sided length-biased inverse Gaussian distribution (TS-LBIG), was introduced. The physical phenomenon of this scenario was described in a case of cracks developing from two sides. Since the probability density function of the original TS-LBIG distribution cannot be written in a closed-form expression, its generalization form was further introduced. Important properties such as the moment-generating function and survival function cannot be provided. We offered a different approach to solving this problem. Some distributional properties were investigated. The parameters were estimated by the method of the moment. Monte Carlo simulation studies were carried out to appraise the performance of the suggested estimators using bias, variance, and mean square error. An application of a real dataset was presented for illustration. The results showed that the suggested estimators performed better than the original study. The proposed distribution provided a more appropriate model than other candidate distributions for fitting based on Akaike information criterion.

]]>Symmetry doi: 10.3390/sym14101964

Authors: Soubhagya Kumar Sahoo Pshtiwan Othman Mohammed Donal O’Regan Muhammad Tariq Kamsing Nonlaopon

As is known, integral inequalities related to convexity have a close relationship with symmetry. In this paper, we introduce a new notion of interval-valued harmonically m,h1,h2-Godunova&ndash;Levin functions, and we establish some new Hermite&ndash;Hadamard inequalities. Moreover, we show how this new notion of interval-valued convexity has a close relationship with many existing definitions in the literature. As a result, our theory generalizes many published results. Several interesting examples are provided to illustrate our results.

]]>Symmetry doi: 10.3390/sym14101963

Authors: Yang Yang Xiaokun Tan Huicheng Lu Shangling Xue Ruiqiong Wang Yao Zhang

The indirect method of using a passing vehicle to identify modal properties of a girder bridge has become attractive recently. Compared to the direct method, which requires a lot of sensors installed directly on the bridge itself, the indirect method only requires a single sensor installed on the vehicle to indirectly measure the response of the bridge. However, it is difficult to eliminate the adverse effect of road surface roughness. An indirect approach based on blind source separation is proposed for the first time in this study to identify the bridge element stiffness where two movable vehicles are used. Two identical vehicles stay at rest at the designated measurement points and their vertical accelerations are collected. After one measurement, the two vehicles move to other designated measurement points and the accelerations are collected again. The same procedure is repeated until the two vehicles have moved over all the designated measurement points. Then the blind source separation technique is employed to extract the fundamental mode shape of the bridge and the improved direct stiffness method is adopted to estimate the bridge element stiffness based on the collected data, which are used to monitor the health of the bridge structure and to maintain structure safety and natural symmetry. The proposed method only requires the output response of the vehicle due to the involvement of the blind separation technique. In addition, the proposed method can overcome the adverse effect of road surface roughness because the vehicles only move between two measurements and they stay at rest during one measurement. Numerical simulation was conducted to validate the proposed method, and the effect of various factors such as bridge damping ratio and measurement noise was investigated. Field measurement on Min-Xie bridge in Chongqing city was also carried out to further investigate the feasibility of the proposed method and showed that it can perform well in extracting the fundamental mode shape and evaluating bridge element stiffness.

]]>Symmetry doi: 10.3390/sym14101962

Authors: Vishal Midya Jiangang Liao Chris Gennings Elena Colicino Susan L. Teitelbaum Robert O. Wright Damaskini Valvi

Epidemiologists often study the associations between a set of exposures and multiple biologically relevant outcomes. However, the frequently used scale-and-context-dependent regression coefficients may not offer meaningful comparisons and could further complicate the interpretation if these outcomes do not have similar units. Additionally, when scaling up a hypothesis-driven study based on preliminary data, knowing how large to make the sample size is a major uncertainty for epidemiologists. Conventional p-value-based sample size calculations emphasize precision and might lead to a large sample size for small- to moderate-effect sizes. This asymmetry between precision and utility is costly and might lead to the detection of irrelevant effects. Here, we introduce the &ldquo;&delta;-score&rdquo; concept, by modifying Cohen&rsquo;s f2. &delta;-score is scale independent and circumvents the challenges of regression coefficients. Further, under a new hypothesis testing framework, it quantifies the maximum Cohen&rsquo;s f2 with certain optimal properties. We also introduced &ldquo;Sufficient sample size&rdquo;, which is the minimum sample size required to attain a &delta;-score. Finally, we used data on adults from a 2017&ndash;2018 U.S. National Health and Nutrition Examination Survey to demonstrate how the &delta;-score and sufficient sample size reduced the asymmetry between precision and utility by finding associations between mixtures of per-and polyfluoroalkyl substances and metals with serum high-density and low-density lipoprotein cholesterol.

]]>Symmetry doi: 10.3390/sym14101959

Authors: Yun-Xian Chen Ping-Hui Mou Guo-Ping Li

The study of black hole shadows by considering the surrounding kinds of matter has attracted interest in recent years. In this paper, we use the ray-tracing method to study shadows and photon spheres of renormalization group improved (RGI) black holes, taking into account the different thin spherical accretion models. We find that an increase in the parameters &Omega; and &gamma;, which are excited by renormalization group theory, can decrease the event horizon and the radius of the photon sphere while increasing the effective potential. For static and infalling accretions, these results indicate that black hole shadows are related to the geometry of spacetime, and are nearly unaffected by spherical accretions. However, due to the Doppler effect, the shadow in the infalling case is darker than the static one, and the intensities of the photon sphere decay more slowly from the photon sphere to infinity. In addition, the peak intensities out of the shadow increase with the parameters &Omega; and &gamma;. Finally, it can be seen that the effect of &Omega; on the shadow is more distinct by comparing it with that of &gamma; at the same parameter level.

]]>Symmetry doi: 10.3390/sym14101961

Authors: Oleksandr Sushchov Piotr Homola Marcin Piekarczyk Ophir Ruimi Kévin Almeida Cheminant Olaf Bar Łukasz Bibrzycki Bohdan Hnatyk Péter Kovács Bartosz Łozowski Michał Niedźwiecki Sławomir Stuglik Arman Tursunov Tadeusz Wibig

Cosmic rays interact with fields and background radiation as they propagate in space, producing particle cascades of various sizes, shapes and constituents. The potential observation of at least parts of such phenomena, referred to as cosmic-ray ensembles (CRE), from Earth would open a new channel of cosmic-ray investigation, since it might be a manifestation of fundamental symmetries of nature. Research dedicated to CRE is one of the main scientific objectives of the Cosmic-Ray Extremely Distributed Observatory (CREDO) Collaboration, and with this article we address one of the cornerstones of the relevant scientific program: the simulation method dedicated to CRE studies. Here we focus on CRE resulting from synchrotron radiation by high energy electrons as one of the most prevalent energy loss processes. Providing the example of simulation output analysis, we demonstrate the advantages of our approach as well as discuss the possibility of generalization of current research.

]]>Symmetry doi: 10.3390/sym14101960

Authors: Carlo Bianca

The recent developments in dynamical systems theory and non-equilibrium statistical mechanics have allowed the birth of new challenges and research perspectives. In particular, different frameworks have been proposed for the modeling of complex emerging phenomena occurring in nature and society. This editorial article introduces the topic and the contributions of this Special Issue. This Special Issue focuses, on the one hand, on the development of new methods, frameworks and models coming from dynamical system theory and the equilibrium/non-equilibrium statistical mechanics and, on the other hand, opens problems related to the existing frameworks. The Special Issue also includes applications to physical, biological and engineering systems.

]]>Symmetry doi: 10.3390/sym14101958

Authors: Ghada AlNemer Mohammed R. Kenawy Haytham M. Rezk Ahmed A. El-Deeb Mohammed Zakarya

In this paper, some fractional Leindler and Hardy-type inequalities and their reversed will be proved by using integration by parts and H&ouml;lder inequality on conformable fractional calculus. As a special case, some classical integral inequalities will be obtained. Symmetrical properties play an essential role in determining the correct methods to solve inequalities. The new fractional inequalities in special cases yield some recent relevance, which also provide new estimates on inequalities of these type.

]]>Symmetry doi: 10.3390/sym14101957

Authors: Muhammad Tariq Soubhagya Kumar Sahoo Sotiris K. Ntouyas Omar Mutab Alsalami Asif Ali Shaikh Kamsing Nonlaopon

Fractional derivative and integral operators are often employed to present new generalizations of mathematical inequalities. The introduction of new fractional operators has prompted another direction in different branches of mathematics and applied sciences. First, we investigate and prove new fractional equality. Considering this equality as the auxiliary result, we attain some estimations of a Hermite&ndash;Hadamard type inequality involving s-preinvex, s-Godunova&ndash;Levin preinvex, and prequasi invex functions. In addition, we investigate a fractional order Hadamard&ndash;Fej&eacute;r inequality and some of its refinements pertaining to h-preinvexity via a non-conformable fractional integral operator. Finally, we present a Pachpatte type inequality for the product of two preinvex functions. The findings as well as the special cases presented in this research are new and applications of our main results.

]]>Symmetry doi: 10.3390/sym14101956

Authors: Liu Wang Ji Wang Hou

In this work, a novel driver abnormal behavior analysis system based on practical facial landmark detection (PFLD) and you only look once version 5 (YOLOv5) were developed to solve the recognition and analysis of driver abnormal behaviors. First, a library for analyzing the abnormal behavior of vehicle drivers was designed, in which the factors that cause an abnormal behavior of drivers were divided into three categories according to the behavioral characteristics including natural behavioral factors, unnatural behavioral factors, and passive behavioral factors. Then, different neural network models were established through the representation of the actual scene of the three behaviors. Specifically, the abnormal driver behavior caused by natural behavioral factors was identified by a PFLD neural network model based on facial key point detection, and the abnormal driver behavior caused by unnatural behavioral factors and passive behavioral factors were identified by a YOLOv5 neural network model based on target detection. In addition, in a test of the driver abnormal behavior analysis system in an actual vehicle, the precision rate was greater than 95%, which meets the requirements of practical application.

]]>Symmetry doi: 10.3390/sym14101955

Authors: Nursabillilah Mohd Ali Rosli Besar Nor Azlina Ab. Aziz

Breast cancer (BC) remains the most dominant cancer among women worldwide. Numerous BC gene expression microarray-based studies have been employed in cancer classification and prognosis. The availability of gene expression microarray data together with advanced classification methods has enabled accurate and precise classification. Nevertheless, the microarray datasets suffer from a large number of gene expression levels, limited sample size, and irrelevant features. Additionally, datasets are often asymmetrical, where the number of samples from different classes is not balanced. These limitations make it difficult to determine the actual features that contribute to the existence of cancer classification in the gene expression profiles. Various accurate feature selection methods exist, and they are being widely applied. The objective of feature selection is to search for a relevant, discriminant feature subset from the basic feature space. In this review, we aim to compile and review the latest hybrid feature selection methods based on bio-inspired metaheuristic methods and wrapper methods for the classification of BC and other types of cancer.

]]>Symmetry doi: 10.3390/sym14101954

Authors: Amjad Ali Aftab Hussain Muhammad Arshad Hamed Al Sulami Muhammad Tariq

In this study, inspired by the concept of B-metric-like space (BMLS), we introduce the concept of orthogonal B-metric-like space (OBMLS) via a hybrid pair of operators. Additionally, we establish the concept of orthogonal dynamic system (ODS) as a generalization of the dynamic system (DS), which improves the existing results for analysies such as those presented here. By applying this, some new refinements of the F&perp;-Suzuki-type (F&perp;-ST) fixed-point results are presented. These include some tangible instances, and applications in the field of nonlinear analysis are given to highlight the usability and validity of the theoretical results.

]]>Symmetry doi: 10.3390/sym14091953

Authors: Vladislav Golubkov Maxim Khlopov Anastasia Kirichenko Alexandra Kravtsova Andrey Mayorov Rustam Yulbarisov

Several candidates for antihelium events have been found in the AMS-02 experiment. They cannot be created by natural astrophysical sources and, if confirmed, imply the existence of antimatter stars in our galaxy. This immediately reduces the class of inflationary models with baryosynthesis to those that can provide the creation of an antimatter domain of surviving size together with the general baryon asymmetry of the Universe. To confront the future results of experimental searches for cosmic antihelium with predictions of this hypothesis, we develop numerical studies of the creation and propagation of antihelium flux from antimatter globular clusters in the Galaxy. This article presents the results of such a simulation: a function of the magnetic cut-off for the penetration of antihelium nuclei into the Galaxy disk and an estimate of the energy range in which the search and detection of antihelium is most optimal.

]]>Symmetry doi: 10.3390/sym14091952

Authors: Renáta-Ildikó Száva Ioan Száva Sorin Vlase Pál-Botond Gálfi Károly Jármai Teofil Gălățeanu Gabriel Popa Zsolt Asztalos

In order to foresee the response during the fire of a real symmetrical structure (prototype), nowadays engineers apply methods which involve the associated reduced-scale model&rsquo;s behaviors, mainly dimensional analysis behaviors. Between the dimensional analysis methods, the so-called Modern Dimensional Analysis (MDA), developed by Szirtes, fulfills all engineering requirements compared with the classical one. The authors used this new proposed method to describe their original electric fire simulation testing bench, as well as the Model Law (using MDA) for the heat transfer in tubular rectangular bars. So, a validation of the Model Law was performed based on several scrupulous experimental investigations both on a real column&rsquo;s segment and its associated reduced-scale models manufactured at 1:2; 1:4, as well as 1:10 scales. The original heating system, the elaborated protocol, the deduced Model Law, and the results of the experimental investigations represent the contributions of the authors in the field of metallic structures subject to fires. The results validate the possibility of using MDA in the case of heat transmission.

]]>Symmetry doi: 10.3390/sym14091951

Authors: Ziqiu Zhang Xi Jiang Shiqing Tang

The cross fusion of quantum mechanics and information science forms quantum information science. Quantum logic gates and quantum entanglement are very important building blocks in quantum information processing. In this paper, we propose one-step schemes for realizing quantum swap gates and generating two-mode entangled coherent states via circuit QED. In our scheme, due to the adiabatic elimination of the excited state of the qutrit under the condition of large detuning, the decoherence of the spontaneous emission of the qutrit can be ignored. The fidelity of the quantum swap gate remains at a very high level. In addition, we also explore the nonclassical properties of two-mode entangled coherent states prepared in our scheme by addressing the second-order correlation function and intermodal squeezing. In particular, two classes of entangled coherent states demonstrate distinct entanglement and nonclassical behavior.

]]>Symmetry doi: 10.3390/sym14091950

Authors: Gregory Fedotenkov Lev Rabinskiy Sergey Lurie

The paper presents the solution of the spatial transient problem of the impact of a moving heat flux source induced by the laser radiation on the surface of a half-space using the superposition principle and the method of transient functions. The hyperbolic equation of transient thermal conductivity accounting for the relaxation time is used to model the laser heating process. It is assumed that the heat flux is distributed symmetrically with respect to the center of the heating spot. The combined numerical and analytical algorithm has been developed and implemented, which allows one to determine the temperature distribution both on the surface and on the depth of the half-space. In this case, the principle of superposition is used with the use of a special symmetric Gaussian distribution to describe the model of a source of high-intensity heat flux. The use of such a symmetric distribution made it possible to calculate the integrals over the spatial variables analytically. The results of the work could be used to estimate the contribution of the conductive component in the overall heat transfer of materials exposed to intense heat flows (laser surface treatment, laser additive technologies, streamlining and heating of materials by high-enthalpy gases, etc.).

]]>Symmetry doi: 10.3390/sym14091949

Authors: Shuiyan Wu Han Liu Xiaobo Li

This paper studies the event-triggered adaptive tracking control problem of a class of pure-feedback systems. Via the backstepping method and the neural network approximation with the central symmetric distribution, an event-triggered adaptive neural network controller is designed. In particular, a dynamic gain driven by the tracking error is introduced into the event-triggering mechanism. Then, by using the Lyapunov stability theory, the boundedness of all the closed-loop signals is proved, and the tracking error falls into a prespecified &#1013;-neighbourhood of zero. Meanwhile, the Zeno behaviour is avoided. Finally, two simulations verify the effectiveness of the proposed control scheme.

]]>Symmetry doi: 10.3390/sym14091948

Authors: Sunisa Theswan Sotiris K. Ntouyas Bashir Ahmad Jessada Tariboon

We introduce and study a new class of nonlinear coupled Hilfer differential equations with nonlocal boundary conditions involving Riemann&ndash;Liouville and Hadamard-type iterated fractional integral operators. By applying the Leray&ndash;Schauder alternative and Krasnosel&rsquo;ski&#301;&rsquo;s fixed point theorem, two results presenting different criteria for the existence of solutions to the given problem are proven. The third result provides a sufficient criterion for the existence of a unique solution to the problem at hand. Numerical examples are constructed to demonstrate the application of the results obtained. Two graphs show asymmetric solutions when a Hilfer parameter is varied. The work presented in this paper is novel and significantly enriches the literature on the topic.

]]>Symmetry doi: 10.3390/sym14091946

Authors: S. Nanda Kumar Nalin Kant Mohanty

Frequency regulation of low inertia symmetric micro grids with the incorporation of asymmetric renewable sources such as solar and wind is a challenging task. Virtual Inertia Control (VIC) is the idea of increasing micro grids&rsquo; inertia by energy storage systems. In the current study, an adaptive fuzzy PID structure with a derivative filter (AFPIDF) controller is suggested for VIC of a micro grid with renewable sources. To optimize the proposed controllers, a modified Golden Jackal Optimization (mGJO) has been proposed, where variable Sine Cosine adopted Scaling Factor (SCaSF) is employed to adjust the Jackal&rsquo;s location in the course of search process to improve the exploration and exploitation capability of the original Golden Jackal Optimization (GJO) algorithm. The performance of the mGJO algorithm is verified by equating it with original GJO, as well as Grey Wolf Optimization (GWO), Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), Teaching Learning Based Optimization (TLBO) and Ant Lion Optimizer (ALO), considering various standard benchmark test functions. In the next stage, conventional PID and proposed FPIDF controller parameters are optimized using the proposed mGJO technique and the superiority of mGJO over other symmetric optimization algorithms is demonstrated. The robustness of the controller is also investigated under intermittent load disturbances, as well as different levels of asymmetric RESs integration.

]]>Symmetry doi: 10.3390/sym14091947

Authors: Alan Chodos

We introduce a new symmetry, light-cone reflection (LCR), which interchanges timelike and spacelike intervals. Our motivation is to provide a reason, based on symmetry, why tachyons might exist, with emphasis on application to neutrinos. We show that LCR, combined with translations, leads to a much larger symmetry. We construct an LCR-invariant Lagrangian and discuss some of its properties. In a simple example, we find complete symmetry in the spectrum between tachyons and ordinary particles. We also show that the theory allows for the introduction of a further gauge invariance related to chiral symmetry.

]]>Symmetry doi: 10.3390/sym14091943

Authors: Moh Yaseen Sawan Kumar Rawat Anum Shafiq Manoj Kumar Kamsing Nonlaopon

In the last two decades, academicians have concentrated on the nanofluid squeezing flow between parallel plates. The increasing energy demands and their applications have seen the focus shifted to the hybrid nanofluid flows, but so much is still left to be investigated. This analysis is executed to explore the symmetry of the MHD squeezing nanofluid (MoS2/H2O) flow and the hybrid nanofluid (MoS2&ndash;SiO2/H2O&ndash;C2H6O2) flow between the parallel plates and their heat transport property. The heat transport phenomenon is analyzed with the magnetic field, thermal radiation, heat source/sink, suction/injection effect, and porous medium. In the present model, the plate situated above is in the movement towards the lower plate, and the latter is stretching with a linear velocity. The prevailing PDEs depicting the modeled problem with the aforementioned effects are transformed via similarity transformations and solved via the &ldquo;bvp4c&rdquo; function, which is an inbuilt function in MATLAB software. The control of the factors on the fields of velocity and temperature, heat transfer rate, velocity boundary layer patterns, and streamlines is investigated. The solution profiles are visually shown and explained. Furthermore, the Nusselt number at the bottom plate is larger for the (MoS2&ndash;SiO2/H2O&ndash;C2H6O2) hybrid nanofluid than for the (MoS2/H2O) nanofluid flow. In the presence of suction/injection, the streamlines appear to be denser. In addition, the magnetic field has a thinning consequence on the velocity boundary layer region. The results of this study apply to several thermal systems, engineering, and industrial processes, which utilize nanofluid and hybrid nanofluid for cooling and heating processes.

]]>Symmetry doi: 10.3390/sym14091944

Authors: Aisha Abdullah Alderremy Rasool Shah Naveed Iqbal Shaban Aly Kamsing Nonlaopon

This article investigates different nonlinear systems of fractional partial differential equations analytically using an attractive modified method known as the Laplace residual power series technique. Based on a combination of the Laplace transformation and the residual power series technique, we achieve analytic and approximation results in rapid convergent series form by employing the notion of the limit, with less time and effort than the residual power series method. Three challenges are evaluated and simulated to validate the suggested method&rsquo;s practicability, efficiency, and simplicity. The analysis of the acquired findings demonstrates that the method mentioned above is simple, accurate, and appropriate for investigating the solutions to nonlinear applied sciences models.

]]>Symmetry doi: 10.3390/sym14091945

Authors: Marcin Kamiński

This paper aims at certain theoretical studies and additional computational analysis on symmetry and its lack in Kullback-Leibler and Jeffreys probabilistic divergences related to some engineering applications. As it is known, the Kullback-Leibler distance in between two different uncertainty sources exhibits a lack of symmetry, while the Jeffreys model represents its symmetrization. The basic probabilistic computational implementation has been delivered in the computer algebra system MAPLE 2019&reg;, whereas engineering illustrations have been prepared with the use of the Finite Element Method systems Autodesk ROBOT&reg; &amp; ABAQUS&reg;. Determination of the first two probabilistic moments fundamental in the calculation of both relative entropies has been made (i) analytically, using a semi-analytical approach (based upon the series of the FEM experiments), and (ii) the iterative generalized stochastic perturbation technique, where some reference solutions have been delivered using (iii) Monte-Carlo simulation. Numerical analysis proves the fundamental role of computer algebra systems in probabilistic entropy determination and shows remarkable differences obtained with the two aforementioned relative entropy models, which, in some specific cases, may be neglected. As it is demonstrated in this work, a lack of symmetry in probabilistic divergence may have a decisive role in engineering reliability, where extreme and admissible responses cannot be simply replaced with each other in any case.

]]>Symmetry doi: 10.3390/sym14091942

Authors: Wen-Chao Bai Hui Hu Ben-Hu Zhou Gui-Xiang Liu Ge Tang Yang-Yu Huang Yan Cao Han Zhang Han-Zhuang Zhang

We designed magneto-electro-elastic piezoelectric, electromagnetic (EM) metamaterials (MEEPEM) by using a square lattice of the periodic arrays of conducting wires, piezoelectric photonic crystal (PPC), and split-ring resonators (SRRs). We analyzed the mechanism for multi-field coupling in MEEPEM. The magnetic field of the EM wave excites an attractive Amp&egrave;re force in SRRs, which periodically compress MEEPEM, and this can create electric polarization due to the piezoelectric effect. The electric field of the EM wave can excite a longitudinal superlattice vibration in the PPC, which can also create electric polarization. The electric polarization can couple to the electric field of the periodic arrays of conducting wires. The coupled electric field will couple to the EM wave. These interactions result in multi-field coupling in MEEPEM. The coupling creates a type of polariton, called multi-field coupling polaritons, corresponding to a photonic band gap, namely, the multi-field coupling photonic band gap. We calculated the dielectric functions, the reflection coefficients, and the effective magnetic permeability of MEEPEM. By using them, we analyzed the transmission properties of EM waves in the MEEPEM. We analyzed the possibility of MEEPEM as left-handed metamaterials and zero refractive index material.

]]>Symmetry doi: 10.3390/sym14091941

Authors: Abdelkader Rahmani Wei-Shih Du Mohammed Taha Khalladi Marko Kostić Daniel Velinov

In this work, we introduce the notion of a (weak) proportional Caputo fractional derivative of order &alpha;&isin;(0,1) for a continuous (locally integrable) function u:[0,&infin;)&rarr;E, where E is a complex Banach space. In our definition, we do not require that the function u(&middot;) is continuously differentiable, which enables us to consider the wellposedness of the corresponding fractional relaxation problems in a much better theoretical way. More precisely, we systematically investigate several new classes of (degenerate) fractional solution operator families connected with the use of this type of fractional derivatives, obeying the multivalued linear approach to the abstract Volterra integro-differential inclusions. The quasi-periodic properties of the proportional fractional integrals as well as the existence and uniqueness of almost periodic-type solutions for various classes of proportional Caputo fractional differential inclusions in Banach spaces are also considered.

]]>Symmetry doi: 10.3390/sym14091940

Authors: Kashif Ali Aftab Ahmed Faridi Sohail Ahmad Wasim Jamshed Syed M. Hussain El Sayed M. Tag-Eldin

Thermal performance of magnetically driven Casson nanofluid over a nonlinear stretching sheet under the influence of entropy, activation energy and convective boundary conditions was analyzed numerically, employing the quasi-linearization method (QLM). The collective behavior of thermophoretic diffusion and Brownian motion along with special effects of viscous dissipation, thermal radiation, heat generation and joule heating are considered in the energy equation for the flow problem. The addition of nanoparticles helps to stabilize the flowing of a nanofluid and maintain the symmetry of the flowing structure. The governing highly nonlinear coupled differential equations of velocity, temperature, concentration and entropy are simulated through an iterative scheme encoded with MATLAB programming language. The geometric model is, therefore, described using a symmetry technique. A comparative analysis of linear and nonlinear stretching in sheets is presented via graphs and tables regarding pertinent dimensionless parameters. It is worth noting that the Nusselt number and Sherwood number decrease at relatively higher rates with growing values of activation energy in the case of nonlinear stretching. Moreover, the entropy generation rate near the stretching surface decreases due to the strong effects of Brownian motion and thermophoretic diffusion while it goes on improving far off the stretching surface.

]]>Symmetry doi: 10.3390/sym14091939

Authors: Dimitrios Z. Politis Stelios M. Potirakis Subrata Kundu Swati Chowdhury Sudipta Sasmal Masashi Hayakawa

Lithosphere&ndash;atmosphere&ndash;ionosphere coupling (LAIC) is studied through various physical or chemical quantities, obtained from different sources, which are observables of the involved complex processes. LAIC has been proposed to be achieved through three major channels: the chemical, the acoustic, and the electromagnetic. Accumulated evidence supporting the acoustic channel hypothesis has been published, while atmospheric gravity waves (AGWs) play a key role in LAIC as the leading mechanism for the transmission of energy from the lower atmosphere to the stratosphere and mesosphere, associated with atmospheric disturbances observed prior to strong earthquakes (EQs). The seismogenic AGW is the result of temperature disturbances, usually studied through stratospheric potential energy (EP). In this work, we examined 11 cases of significant EQs (M &gt; 6.7) that occurred during the last 10 years at different geographic areas by analyzing the temperature profile at the wider location of each one of the examined EQs. The &ldquo;Sounding of the Atmosphere using Broadband Emission Radiometry&rdquo; (SABER) instrument, part of the &ldquo;Thermosphere Ionosphere Mesosphere Energetics Dynamics&rdquo; (TIMED) satellite, data were employed to compute the potential energy (EP) of the AGW. Using the temperature profile, we first calculated EP and determined the altitudes&rsquo; range for which prominent pre-seismic disturbances were observed. Subsequently, the EP time series at specific altitudes, within the determined &ldquo;disturbed&rdquo; range, were for the first time analyzed using the criticality analysis method termed the &ldquo;natural time&rdquo; (NT) method in order to find any evidence of an approach to a critical state (during a phase transition from a symmetric phase to a low symmetry phase) prior to the EQ occurrence. Our results show criticality indications in the fluctuation of EP a few days (1 to 15 days) prior to the examined EQs, except from one case. In our study, we also examined all of the temperature-related extreme phenomena that have occurred near the examined geographic areas, in order to take into account any possible non-seismic influence on the obtained results.

]]>Symmetry doi: 10.3390/sym14091938

Authors: Keji Mao Jinyu Xu Xingda Yao Jiefan Qiu Kaikai Chi Guanglin Dai

Text classification is a major task of NLP (Natural Language Processing) and has been the focus of attention for years. News classification as a branch of text classification is characterized by complex structure, large amounts of information and long text length, which in turn leads to a decrease in the accuracy of classification. To improve the classification accuracy of Chinese news texts, we present a text classification model based on multi-level semantic features. First, we add the category correlation coefficient to TF-IDF (Term Frequency-Inverse Document Frequency) and the frequency concentration coefficient to CHI (Chi-Square), and extract the keyword semantic features with the improved algorithm. Then, we extract local semantic features with TextCNN with symmetric-channel and global semantic information from a BiLSTM with attention. Finally, we fuse the three semantic features for the prediction of text categories. The results of experiments on THUCNews, LTNews and MCNews show that our presented method is highly accurate, with 98.01%, 90.95% and 94.24% accuracy, respectively. With model parameters two magnitudes smaller than Bert, the improvements relative to the baseline Bert+FC are 1.27%, 1.2%, and 2.81%, respectively.

]]>Symmetry doi: 10.3390/sym14091936

Authors: Takuma Ishihara Kouji Yamamoto Kouji Tahata Sadao Tomizawa

In square contingency table analysis, we consider a partial measure that represents the degree of departure from symmetry for each of several pairs. It may be useful to pool the values of the measure into a single summary measure of partial asymmetry. We show that the estimator of partial measures is asymptotically mutually independent for a large sample size. The present paper proposes a symmetry measure in the class of weighted averages that is different from previous studies. The proposed measure is an approximation of the measure in the class of weighted averages that has the smallest variance.

]]>Symmetry doi: 10.3390/sym14091937

Authors: Saleem Khan Shariefuddin Pirzada Yilun Shang

The reciprocal distance Laplacian matrix of a connected graph G is defined as RDL(G)=RT(G)&minus;RD(G), where RT(G) is the diagonal matrix of reciprocal distance degrees and RD(G) is the Harary matrix. Clearly, RDL(G) is a real symmetric matrix, and we denote its eigenvalues as &lambda;1(RDL(G))&ge;&lambda;2(RDL(G))&ge;&hellip;&ge;&lambda;n(RDL(G)). The largest eigenvalue &lambda;1(RDL(G)) of RDL(G), denoted by &lambda;(G), is called the reciprocal distance Laplacian spectral radius. In this paper, we obtain several upper bounds for the sum of k largest reciprocal distance Laplacian eigenvalues of G in terms of various graph parameters, such as order n, maximum reciprocal distance degree RTmax, minimum reciprocal distance degree RTmin, and Harary index H(G) of G. We determine the extremal cases corresponding to these bounds. As a consequence, we obtain the upper bounds for reciprocal distance Laplacian spectral radius &lambda;(G) in terms of the parameters as mentioned above and characterize the extremal cases. Moreover, we attain several upper and lower bounds for reciprocal distance Laplacian spread RDLS(G)=&lambda;1(RDL(G))&minus;&lambda;n&minus;1(RDL(G)) in terms of various graph parameters. We determine the extremal graphs in many cases.

]]>Symmetry doi: 10.3390/sym14091935

Authors: Saad Ihsan Butt Hüseyin Budak Kamsing Nonlaopon

Recently, developments and extensions of quadrature inequalities in quantum calculus have been extensively studied. As a result, several quantum extensions of Simpson&rsquo;s and Newton&rsquo;s estimates are examined in order to explore different directions in quantum studies. The main motivation of this article is the development of variants of Simpson&ndash;Newton-like inequalities by employing Mercer&rsquo;s convexity in the context of quantum calculus. The results also give new quantum bounds for Simpson&ndash;Newton-like inequalities through H&ouml;lder&rsquo;s inequality and the power mean inequality by employing the Mercer scheme. The validity of our main results is justified by providing examples with graphical representations thereof. The obtained results recapture the discoveries of numerous authors in quantum and classical calculus. Hence, the results of these inequalities lead us to the development of new perspectives and extensions of prior results.

]]>Symmetry doi: 10.3390/sym14091934

Authors: Jamiu Hamzat Abiodun Oladipo Georgia Oros

The research presented in this paper deals with analytic p-valent functions related to the generalized probability distribution in the open unit disk U. Using the Hadamard product or convolution, function fs(z) is defined as involving an analytic p-valent function and generalized distribution expressed in terms of analytic p-valent functions. Neighborhood properties for functions fs(z) are established. Further, by applying a previously introduced linear transformation to fs(z) and using an extended Libera integral operator, a new generalized Libera-type operator is defined. Moreover, using the same linear transformation, subclasses of starlike, convex, close-to-convex and spiralike functions are defined and investigated in order to obtain geometrical properties that characterize the new generalized Libera-type operator. Symmetry properties are due to the involvement of the Libera integral operator and convolution transform.

]]>Symmetry doi: 10.3390/sym14091931

Authors: Yuetong Zhou Peng Yang Shaonan Zhang Kaiqiang Zhang

In this paper, we show that 66666 is the largest repdigit expressible as the sum of four tribonacci numbers. We used Binet&rsquo;s formula, Baker&rsquo;s theory, and a reduction method during the proving procedure. We also used the periodic properties of tribonacci number modulo 9 to deal with three individual cases.

]]>Symmetry doi: 10.3390/sym14091933

Authors: Changqing Xu Yi Liu Dongdong Chen Yintang Yang

Spiking neural networks (SNNs) can utilize spatio-temporal information and have the characteristic of energy efficiency, being a good alternative to deep neural networks (DNNs). The event-driven information processing means that SNNs can reduce the expensive computation of DNNs and save a great deal of energy consumption. However, high training and inference latency is a limitation of the development of deeper SNNs. SNNs usually need tens or even hundreds of time steps during the training and inference process, which causes not only an increase in latency but also excessive energy consumption. To overcome this problem, we propose a novel training method based on backpropagation (BP) for ultra-low-latency (1&ndash;2 time steps) SNNs with multi-threshold. In order to increase the information capacity of each spike, we introduce the multi-threshold Leaky Integrate and Fired (LIF) model. The experimental results show that our proposed method achieves average accuracy of 99.56%, 93.08%, and 87.90% on MNIST, FashionMNIST, and CIFAR10, respectively, with only two time steps. For the CIFAR10 dataset, our proposed method achieves 1.12% accuracy improvement over the previously reported directly trained SNNs with fewer time steps.

]]>Symmetry doi: 10.3390/sym14091932

Authors: Yasashvini R. Vergin Raja Sarobin M. Rukmani Panjanathan Graceline Jasmine S. Jani Anbarasi L.

Diabetic Retinopathy (DR) is an eye condition that mainly affects individuals who have diabetes and is one of the important causes of blindness in adults. As the infection progresses, it may lead to permanent loss of vision. Diagnosing diabetic retinopathy manually with the help of an ophthalmologist has been a tedious and a very laborious procedure. This paper not only focuses on diabetic retinopathy detection but also on the analysis of different DR stages, which is performed with the help of Deep Learning (DL) and transfer learning algorithms. CNN, hybrid CNN with ResNet, hybrid CNN with DenseNet are used on a huge dataset with around 3662 train images to automatically detect which stage DR has progressed. Five DR stages, which are 0 (No DR), 1 (Mild DR), 2 (Moderate), 3 (Severe) and 4 (Proliferative DR) are processed in the proposed work. The patient&rsquo;s eye images are fed as input to the model. The proposed deep learning architectures like CNN, hybrid CNN with ResNet, hybrid CNN with DenseNet 2.1 are used to extract the features of the eye for effective classification. The models achieved an accuracy of 96.22%, 93.18% and 75.61% respectively. The paper concludes with a comparative study of the CNN, hybrid CNN with ResNet, hybrid CNN with DenseNet architectures that highlights hybrid CNN with DenseNet as the perfect deep learning classification model for automated DR detection.

]]>Symmetry doi: 10.3390/sym14091930

Authors: Yanlin Li Nadia Alluhaibi Rashad A. Abdel-Baky

E. Study map is one of the most basic and powerful mathematical tools to study lines in line geometry, it has symmetry property. In this paper, based on the E. Study map, clear expressions were developed for the differential properties of one-parameter Lorentzian dual spherical movements that are coordinate systems independent. This eliminates the requirement of demanding coordinates transformations necessary in the determination of the canonical systems. With the proposed technique, new proofs for Euler&ndash;Savary, and Disteli&rsquo;s formulae were derived.

]]>Symmetry doi: 10.3390/sym14091929

Authors: Zhonggen Wang Mingqing Wang Wenyan Nie

In this paper, a monopole UWB broadband antenna is designed, fabricated, and measured for wireless communication networks. The initial radiator model of the proposed antenna has a short-sleeve shape, and to expand the impedance bandwidth, the right and left angles are subtracted symmetrically from the lower half of the radiator. The impedance matching is improved by etching slots in the feed line and adding L-shaped patches symmetrically on both sides of the feed line. The results show that the proposed miniaturized antenna system can cover WiFi 7(2.4&ndash;2.484 GHz, 5.15&ndash;5.35 GHz, 5.725&ndash;5.825 GHz, 5.925&ndash;7.125 GHz), 4G LTE (2.3&ndash;2.39 GHz, 2.555&ndash;2.655 GHz), 5G (4.8&ndash;5.0 GHz), X-band (7&ndash;12.4 GHz), Ku-band (10.7&ndash;14.59 GHz), and C-band uplink bands (5.925&ndash;6.425 GHz). Moreover, the antenna is found to be omnidirectional at low frequencies, with a maximum peak gain of 5.43 dBi. The antenna can be used for multi-frequency wireless communication applications.

]]>Symmetry doi: 10.3390/sym14091928

Authors: Hongguo Diao Ye Tian Gang Wei Xinquan Wang Xiao Li

Tunnels and foundation pits are two separate types of excavation that are frequently used in urban settings. Excavating tunnels and foundation pits sequentially around existing pile foundations is becoming more and more prevalent as urban underground space utilization rates increase. The deformation and load transfer mechanisms of the pile group foundation under two asymmetric excavation conditions of &ldquo;first tunnel, then foundation pit&rdquo; and &ldquo;first foundation pit, then tunnel&rdquo; are studied from the perspective of the relative positions of the tunnel&ndash;pile&ndash;foundation pit based on the constant gravity model test and 3D numerical simulation. The result shows: The pile settlement of the front pile (closer to the tunnel) caused by the excavation condition of the &ldquo;first foundation pit-then tunnel&rdquo; is relatively larger, while the pile settlement of the rear pile (closer to the foundation pit) caused by the excavation condition of &ldquo;first tunnel-then pit&rdquo; is larger. The transverse tilting of the pile group caused by the excavation of the &ldquo;first foundation pit-then tunnel&rdquo; is relatively larger. For the front pile, the pile tip resistance generated by &ldquo;first excavation-then tunnel&rdquo; is about 10% greater than it was before the initial excavation, which is greater than the result of &ldquo;first tunnel-then foundation pit&rdquo;. For the rear pile, the pile tip resistance generated by &ldquo;first excavation-then tunnel&rdquo; is about 85% greater than it was before the initial excavation, which is smaller than the result of &ldquo;first tunnel-then foundation pit&rdquo;. The multiple excavation sequence of &ldquo;tunnel first-then foundation pit&rdquo; leads to a larger induced bending moment for the front pile, whereas a larger induced bending moment for the rear pile results from the multiple excavation sequence &ldquo;first foundation pit-then tunnel&rdquo;.

]]>Symmetry doi: 10.3390/sym14091927

Authors: Iulia Toma Elena Amaricai Roxana Ramona Onofrei Mihai Popean

The study of the consequences of different sonata styles (baroque, classical and romantic piano repertoire) on pianists&rsquo; upper limbs represents a research topic for both the musical and medical fields. Twenty piano students were examined using a MicroFet2 dynamometer after playing three sonatas (Scarlatti K. 1 Sonata as a representative of the baroque style, Haydn Sonata no. 60 for the classical style and Chopin second Sonata for the romantic style). The phase sequence was randomised for each subject: firstly, continuous interpretation of 10 bars of a sonata was conducted 10 times, with the metronome tempo set by the investigator; secondly, the subject interpreted 10 bars of a different sonata continuously, standardised by tempo, which was carried out 10 times; finally, the continuous interpretation of 10 bars of the remaining third sonata, standardised by tempo, was carried out 10 times. After each performance of the 10 bars, the elbow extensor&rsquo;s isometric muscle force was measured. Significant differences were found between the elbow extensor&rsquo;s isometric muscle force assessed after playing Scarlatti&rsquo;s sonata and Haydn&rsquo;s sonata (p = 0.005 for left arm, p = 0.03 for right arm), between Scarlatti&rsquo;s sonata and Chopin&rsquo;s sonata (p &lt; 0.0001 for both left and right arms) and between Haydn&rsquo;s sonata and Chopin&rsquo;s sonata (p = 0.01 for left arm, p &lt; 0.0001 for right arm). In healthy piano students, the dynamometric assessment of elbow extensors&rsquo; isometric muscle force after playing three different sonatas (baroque, classical and romantic) showed that the lowest values were recorded after playing the baroque style. Our results showed bilateral symmetry in the elbow extensor&rsquo;s isometric muscle force for all three piano styles. The testing of arm muscles, besides that of the fingers, should be considered as a regular evaluation for future professional pianists with regard to the prevention of musculoskeletal complaints.

]]>Symmetry doi: 10.3390/sym14091926

Authors: Ján Šimon Branislav Ftorek

A knot is the weakest point of every rope, and the knot efficiency measures the portion of original rope strength taken away by the knot. Despite possible safety implications, surprisingly little attention has been paid to this life-critical quantity in research papers. Knot efficiency is directly immeasurable and the only way to obtain it is by calculation from rope breaking strength. However, this complication makes room for a wide spectrum of misleading concepts. The vast majority of authors do not treat knot efficiency as a random variable, and published results mostly suffer from incorrect statistical processing. The main goal of the presented paper is to fix this issue by proposing correct statistical tools needed for knot efficiency assessment. The probability density function of knot efficiency &psi;(&eta;) has been derived in general, as well as for normally distributed breaking strength. Statistical properties of knot efficiency PDF have been discussed, and a less complex approximation of knot efficiency PDF has been proposed and investigated.

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