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Symmetry, Volume 14, Issue 8 (August 2022) – 257 articles

Cover Story (view full-size image): N-heterocyclic carbenes (NHCs) represent an attractive class of ligands for both main-group and transition metals thanks to the easy modulation of their steric and electronic properties. The possibility of introducing chirality into an NHC framework has paved the way to the design of chiral NHC ligands and contributed to enhancing their potential for applications in different chemistry fields. This paper provides an overview on the use of C2-symmetric NHCs as ancillary ligands for transition metal complexes and their most relevant applications in asymmetric catalysis. View this paper
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24 pages, 406 KiB  
Review
Dynamics of Open Quantum Systems—Markovian Semigroups and Beyond
by Artur Czerwinski
Symmetry 2022, 14(8), 1752; https://doi.org/10.3390/sym14081752 - 22 Aug 2022
Cited by 19 | Viewed by 3475
Abstract
The idea of an open quantum system was introduced in the 1950s as a response to the problems encountered in areas such as nuclear magnetic resonance and the decay of unstable atoms. Nowadays, dynamical models of open quantum systems have become essential components [...] Read more.
The idea of an open quantum system was introduced in the 1950s as a response to the problems encountered in areas such as nuclear magnetic resonance and the decay of unstable atoms. Nowadays, dynamical models of open quantum systems have become essential components in many applications of quantum mechanics. This paper provides an overview of the fundamental concepts of open quantum systems. All underlying definitions, algebraic methods and crucial theorems are presented. In particular, dynamical semigroups with corresponding time-independent generators are characterized. Furthermore, evolution models that induce memory effects are discussed. Finally, measures of non-Markovianity are recapped and interpreted from a perspective of physical relevance. Full article
19 pages, 772 KiB  
Article
Quality Evaluation Method of Automatic Software Repair Using Syntax Distance Metrics
by Yukun Dong, Daolong Tang, Xiaotong Cheng and Yufei Yang
Symmetry 2022, 14(8), 1751; https://doi.org/10.3390/sym14081751 - 22 Aug 2022
Viewed by 1517
Abstract
In recent years, test-based automatic program repair has attracted widespread attention. However, the test suites in practice are not perfect ways to guarantee the correctness of patches generated by repair tools, and weak test suites lead to a large number of incorrect patches [...] Read more.
In recent years, test-based automatic program repair has attracted widespread attention. However, the test suites in practice are not perfect ways to guarantee the correctness of patches generated by repair tools, and weak test suites lead to a large number of incorrect patches produced by the existing repair tool. To reduce the number of incorrect patches generated by repair tools, we propose a patch quality evaluation method based on syntax distance metrics, which measures the syntax distance of patches through four evaluation features—variable, expression, structure, and repair location. By fusing the distance values of the four features, the quality of a patch can be evaluated. Our method evaluates 368 patches from multiple famous repair tools, such as jKali, Nopol, SimFix, DynaMoth, and CapGen; 95% of the correct patches were ranked in the top one of the plausible patches for each defect, which indicates our method can find high-quality patches. Full article
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20 pages, 5957 KiB  
Article
An Intelligent Vision-Based Tracking Method for Underground Human Using Infrared Videos
by Xiaoyu Li, Shuai Wang, Wei Chen, Zhi Weng, Weiqiang Fan and Zijian Tian
Symmetry 2022, 14(8), 1750; https://doi.org/10.3390/sym14081750 - 22 Aug 2022
Cited by 1 | Viewed by 1354
Abstract
The underground mine environment is dangerous and harsh, tracking and detecting humans based on computer vision is of great significance for mine safety monitoring, which will also greatly facilitate identification of humans using the symmetrical image features of human organs. However, existing methods [...] Read more.
The underground mine environment is dangerous and harsh, tracking and detecting humans based on computer vision is of great significance for mine safety monitoring, which will also greatly facilitate identification of humans using the symmetrical image features of human organs. However, existing methods have difficulty solving the problems of accurate identification of humans and background, unstable human appearance characteristics, and humans occluded or lost. For these reasons, an improved aberrance repressed correlation filter (IARCF) tracker for human tracking in underground mines based on infrared videos is proposed. Firstly, the preprocess operations of edge sharpening, contrast adjustment, and denoising are used to enhance the image features of original videos. Secondly, the response map characteristics of peak shape and peak to side lobe ratio (PSLR) are analyzed to identify abnormal human locations in each frame, and the method of calculating the image similarity by generating virtual tracking boxes is used to accurately relocate the human. Finally, using the value of PSLR and the highest peak point of the response map, the appearance model is adaptively updated to further improve the robustness of the tracker. Experimental results show that the average precision and success rate of the IARCF tracker in the five underground scenarios reach 0.8985 and 0.7183, respectively, and the improvement of human tracking in difficult scenes is excellent. The IARCF tracker can effectively track underground human targets, especially occluded humans in complex scenes. Full article
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15 pages, 7010 KiB  
Article
First Results on the Revealing of Cognate Ancestors among the Particles of the Primary Cosmic Rays That Gave Rise to Extensive Air Showers Observed by the GELATICA Network
by Yuri Verbetsky, Manana Svanidze, Ophir Ruimi, Tadeusz Wibig, Levan Kakabadze, Piotr Homola, David E. Alvarez-Castillo, Dmitry Beznosko, Edward K. Sarkisyan-Grinbaum, Olaf Bar, Oleksandr Sushchov and Arman Tursunov
Symmetry 2022, 14(8), 1749; https://doi.org/10.3390/sym14081749 - 22 Aug 2022
Cited by 2 | Viewed by 1953
Abstract
For the data on the observation times and directions of the motion of extensive air showers, which are observed at two stations of the GELATICA network, for the first time we apply the method we have developed previously for identifying pairs of mutually [...] Read more.
For the data on the observation times and directions of the motion of extensive air showers, which are observed at two stations of the GELATICA network, for the first time we apply the method we have developed previously for identifying pairs of mutually remote extensive air showers, the ancestor particles of which arose, possibly, in a single process. A brief description of the GELATICA network, a review of the properties of used samples of data on shower observations at two stations of the network during the 2019–2021 session, and the result of applying the above method to them are given. Some properties of a single peculiar pair of remote showers are discussed. A side question arose about the cause of the observed temporal asymmetry in the locations of the regions of mutual approach of independent primary cosmic ray particles. Full article
(This article belongs to the Section Physics)
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2 pages, 158 KiB  
Editorial
Graph Algorithms and Graph Theory-Symmetry Special Issue
by Manuel Lafond
Symmetry 2022, 14(8), 1748; https://doi.org/10.3390/sym14081748 - 22 Aug 2022
Viewed by 1023
Abstract
Understanding the structure of graphs and the interplay between their parameters is a fundamental question that has been actively researched over the last century [...] Full article
(This article belongs to the Special Issue Graph Algorithms and Graph Theory)
8 pages, 251 KiB  
Article
New Obstructions to Warped Product Immersions in Complex Space Forms
by Mohd. Aquib, Adela Mihai, Ion Mihai and Siraj Uddin
Symmetry 2022, 14(8), 1747; https://doi.org/10.3390/sym14081747 - 22 Aug 2022
Cited by 1 | Viewed by 1120
Abstract
In this paper, we obtain a geometric inequality for warped product pointwise semi-slant submanifolds of complex space forms endowed with a semi-symmetric metric connection and discuss the equality case of this inequality. We provide some applications concerning the minimality and compactness of such [...] Read more.
In this paper, we obtain a geometric inequality for warped product pointwise semi-slant submanifolds of complex space forms endowed with a semi-symmetric metric connection and discuss the equality case of this inequality. We provide some applications concerning the minimality and compactness of such submanifolds. Full article
(This article belongs to the Special Issue Topological Graph Theory and Discrete Geometry)
30 pages, 5742 KiB  
Article
Fledgling Quantum Spin Hall Effect in Pseudo Gap Phase of Bi2212
by Udai Prakash Tyagi, Kakoli Bera and Partha Goswami
Symmetry 2022, 14(8), 1746; https://doi.org/10.3390/sym14081746 - 22 Aug 2022
Cited by 1 | Viewed by 1591
Abstract
We studied the emergence of the quantum spin Hall (QSH) states for the pseudo-gap (PG) phase of Bi2212 bilayer system, assumed to be D-density wave (DDW) ordered, starting with a strong Rashba spin-orbit coupling (SOC) armed, and the time reversal symmetry (TRS) complaint [...] Read more.
We studied the emergence of the quantum spin Hall (QSH) states for the pseudo-gap (PG) phase of Bi2212 bilayer system, assumed to be D-density wave (DDW) ordered, starting with a strong Rashba spin-orbit coupling (SOC) armed, and the time reversal symmetry (TRS) complaint Bloch Hamiltonian. The presence of strong SOC gives rise to non-trivial, spin-momentum locked spin texture tunable by electric field. The emergence of quantum anomalous Hall effect with TRS broken Chiral DDW Hamiltonian of Das Sarma et al. is found to be possible. Full article
(This article belongs to the Special Issue Magnetism, Skyrmions and Chirality)
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15 pages, 1588 KiB  
Article
Hypernetwork Representation Learning with Common Constraints of the Set and Translation
by Yu Zhu, Haixing Zhao, Jianqiang Huang and Xiaoying Wang
Symmetry 2022, 14(8), 1745; https://doi.org/10.3390/sym14081745 - 22 Aug 2022
Viewed by 1119
Abstract
Different from conventional networks with only pairwise relationships among the nodes, there are also complex tuple relationships, namely the hyperedges among the nodes in the hypernetwork. However, most of the existing network representation learning methods cannot effectively capture the complex tuple relationships. Therefore, [...] Read more.
Different from conventional networks with only pairwise relationships among the nodes, there are also complex tuple relationships, namely the hyperedges among the nodes in the hypernetwork. However, most of the existing network representation learning methods cannot effectively capture the complex tuple relationships. Therefore, in order to resolve the above challenge, this paper proposes a hypernetwork representation learning method with common constraints of the set and translation, abbreviated as HRST, which incorporates both the hyperedge set associated with the nodes and the hyperedge regarded as the interaction relation among the nodes through the translation mechanism into the process of hypernetwork representation learning to obtain node representation vectors rich in the hypernetwork topology structure and hyperedge information. Experimental results on four hypernetwork datasets demonstrate that, for the node classification task, our method outperforms the other best baseline methods by about 1%. As for the link prediction task, our method is almost entirely superior to other baseline methods. Full article
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9 pages, 260 KiB  
Article
Subordination Results on the q-Analogue of the Sălăgean Differential Operator
by Alina Alb Lupaş
Symmetry 2022, 14(8), 1744; https://doi.org/10.3390/sym14081744 - 22 Aug 2022
Cited by 9 | Viewed by 1218
Abstract
Aspects related to applications in the geometric function theory of q-calculus are presented in this paper. The study concerns the investigation of certain q-analogue differential operators in order to obtain their geometrical properties, which could be further developed in studies. Several [...] Read more.
Aspects related to applications in the geometric function theory of q-calculus are presented in this paper. The study concerns the investigation of certain q-analogue differential operators in order to obtain their geometrical properties, which could be further developed in studies. Several interesting properties of the q-analogue of the Sălăgean differential operator are obtained here by using the differential subordination method. Full article
18 pages, 1519 KiB  
Article
Reduction in Waiting Time in an M/M/1/N Encouraged Arrival Queue with Feedback, Balking and Maintaining of Reneged Customers
by Ismailkhan Enayathulla Khan and Rajendran Paramasivam
Symmetry 2022, 14(8), 1743; https://doi.org/10.3390/sym14081743 - 22 Aug 2022
Cited by 14 | Viewed by 1839
Abstract
In this research, we look at the work associated with the encouraged arrival line with feedback, balking and maintaining reneged clients. We analyse the quality control policy for the Markovian model using an iterative method to the nth customer in the system. [...] Read more.
In this research, we look at the work associated with the encouraged arrival line with feedback, balking and maintaining reneged clients. We analyse the quality control policy for the Markovian model using an iterative method to the nth customer in the system. We derive performance measures for the expected number of units in the system, as well as in the queue and the average number of occupied services and the expected waiting time in the system, as well as in the queue. To show the effectiveness, we provide numerical examples for the average default rate and average retention rate. The developed formula also satisfies Little’s formula. Full article
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20 pages, 583 KiB  
Article
New Iterative Schemes to Solve Nonlinear Systems with Symmetric Basins of Attraction
by Alicia Cordero, Smmayya Iqbal, Juan R. Torregrosa and Fiza Zafar
Symmetry 2022, 14(8), 1742; https://doi.org/10.3390/sym14081742 - 22 Aug 2022
Cited by 1 | Viewed by 1487
Abstract
We present a new Jarratt-type family of optimal fourth- and sixth-order iterative methods for solving nonlinear equations, along with their convergence properties. The schemes are extended to nonlinear systems of equations with equal convergence order. The stability properties of the vectorial schemes are [...] Read more.
We present a new Jarratt-type family of optimal fourth- and sixth-order iterative methods for solving nonlinear equations, along with their convergence properties. The schemes are extended to nonlinear systems of equations with equal convergence order. The stability properties of the vectorial schemes are analyzed, showing their symmetric wide sets of converging initial guesses. To illustrate the applicability of our methods for the multidimensional case, we choose some real world problems such as kinematic syntheses, boundary value problems, Fisher’s and Hammerstein’s integrals, etc. Numerical comparisons are given to show the performance of our schemes, compared with the existing efficient methods. Full article
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17 pages, 347 KiB  
Article
A General Picard-Mann Iterative Method for Approximating Fixed Points of Nonexpansive Mappings with Applications
by Rahul Shukla, Rajendra Pant and Winter Sinkala
Symmetry 2022, 14(8), 1741; https://doi.org/10.3390/sym14081741 - 21 Aug 2022
Cited by 2 | Viewed by 1809
Abstract
Fixed point theory provides an important structure for the study of symmetry in mathematics. In this article, a new iterative method (general Picard–Mann) to approximate fixed points of nonexpansive mappings is introduced and studied. We study the stability of this newly established method [...] Read more.
Fixed point theory provides an important structure for the study of symmetry in mathematics. In this article, a new iterative method (general Picard–Mann) to approximate fixed points of nonexpansive mappings is introduced and studied. We study the stability of this newly established method which we find to be summably almost stable for contractive mappings. A number of weak and strong convergence theorems of such iterative methods are established in the setting of Banach spaces under certain geometrical assumptions. Finally, we present a number of applications to address various important problems (zero of an accretive operator, mixed equilibrium problem, convex optimization problem, split feasibility problem, periodic solution of a nonlinear evolution equation) appearing in the field of nonlinear analysis. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Analysis and Fixed Point Theory)
13 pages, 461 KiB  
Article
Fault Tolerant Addressing Scheme for Oxide Interconnection Networks
by Asim Nadeem, Agha Kashif, Sohail Zafar, Amer Aljaedi and Oluwatobi Akanbi
Symmetry 2022, 14(8), 1740; https://doi.org/10.3390/sym14081740 - 21 Aug 2022
Cited by 2 | Viewed by 1485
Abstract
The symmetry of an interconnection network plays a key role in defining the functioning of a system involving multiprocessors where thousands of processor-memory pairs known as processing nodes are connected. Addressing the processing nodes helps to create efficient routing and broadcasting algorithms for [...] Read more.
The symmetry of an interconnection network plays a key role in defining the functioning of a system involving multiprocessors where thousands of processor-memory pairs known as processing nodes are connected. Addressing the processing nodes helps to create efficient routing and broadcasting algorithms for the multiprocessor interconnection networks. Oxide interconnection networks are extracted from the silicate networks having applications in multiprocessor systems due to their symmetry, smaller diameter, connectivity and simplicity of structure, and a constant number of links per node with the increasing size of the network can avoid overloading of nodes. The fault tolerant partition basis assigns unique addresses to each processing node in terms of distances (hops) from the other subnets in the network which work in the presence of faults. In this manuscript, the partition and fault tolerant partition resolvability of oxide interconnection networks have been studied which include single oxide chain networks (SOXCN), rhombus oxide networks (RHOXN) and regular triangulene oxide networks (RTOXN). Further, an application of fault tolerant partition basis in case of region-based routing in the networks is included. Full article
(This article belongs to the Special Issue Graph Theory and Its Applications)
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15 pages, 4796 KiB  
Article
Combining Two Exponentiated Families to Generate a New Family of Distributions
by Eatemad Alsolami and Dawlah Alsulami
Symmetry 2022, 14(8), 1739; https://doi.org/10.3390/sym14081739 - 20 Aug 2022
Cited by 2 | Viewed by 1095
Abstract
This article presents a new technique to generate distributions that have the ability to fit any complex data called the exponentiated exponentiated Weibull-X (EEW-X) family, and the exponentiated exponentiated Weibull exponential (EEWE) distribution is presented as a member of this family. The new [...] Read more.
This article presents a new technique to generate distributions that have the ability to fit any complex data called the exponentiated exponentiated Weibull-X (EEW-X) family, and the exponentiated exponentiated Weibull exponential (EEWE) distribution is presented as a member of this family. The new distribution’s unknown parameters were calculated by applying the maximum likelihood method. Some statistical properties, such as quantile, Rényi entropy, order statistics, and median are obtained for the proposed distribution. A simulation study was performed for different cases to investigate the estimation method’s performance. Three real datasets have been applied in which the new distribution has shown more flexibility compared to some other distributions. Full article
(This article belongs to the Section Mathematics)
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12 pages, 363 KiB  
Article
Quantifying Complementarity via Robustness of Asymmetry
by Xin Lü
Symmetry 2022, 14(8), 1738; https://doi.org/10.3390/sym14081738 - 20 Aug 2022
Viewed by 1371
Abstract
Complementarity plays a central role in the conceptual development of quantum mechanics, and also provides practical applications in quantum information technologies. How to properly quantify it is an important problem in quantum foundations, and there exists different types of complementarity relations. In this [...] Read more.
Complementarity plays a central role in the conceptual development of quantum mechanics, and also provides practical applications in quantum information technologies. How to properly quantify it is an important problem in quantum foundations, and there exists different types of complementarity relations. In this paper, a complementarity relation is established with the robustness of asymmetry. Specifically, the two complementary aspects are quantified by applying the robustness of asymmetry corresponding to two cyclic groups whose generators are linked by the Fourier matrix. This complementarity relation is compared with known results and considered in other perspectives, especially its operational meaning regarding quantum state discrimination. We conclude that the internal asymmetry of quantum states is closely related to other fundamental concepts, such as complementarity and coherence, and it is possible to quantitatively investigate complementarity and quantum state discrimination using the robustness of asymmetry. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quantum Mechanics)
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30 pages, 14306 KiB  
Article
A Path-Curvature Measure for Word-Based Strategy Searches in Semantic Networks
by Haim Cohen, Yinon Nachshon, Anat Maril, Paz M. Naim, Jürgen Jost and Emil Saucan
Symmetry 2022, 14(8), 1737; https://doi.org/10.3390/sym14081737 - 19 Aug 2022
Cited by 1 | Viewed by 1556
Abstract
Building on a modified version of the Haantjes path-based curvature, this article offers a novel measure that considers the direction of a stream of associations in a semantic network and estimates the extent to which any single association attracts the upcoming associations to [...] Read more.
Building on a modified version of the Haantjes path-based curvature, this article offers a novel measure that considers the direction of a stream of associations in a semantic network and estimates the extent to which any single association attracts the upcoming associations to its environment—in other words, to what degree one explores that environment. We demonstrate that our measure differs from Haantjes curvature and confirm that it expresses the extent to which a stream of associations remains close to its starting point. Finally, we examine the relationship between our measure and accessibility to knowledge stored in memory. We demonstrate that a high degree of attraction facilitates the retrieval of upcoming words in the stream. By applying methods from differential geometry to semantic networks, this study contributes to our understanding of strategic search in memory. Full article
(This article belongs to the Special Issue Topological Graph Theory and Discrete Geometry)
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11 pages, 1745 KiB  
Article
Effects of the Vertices on the Topological Bound States in a Quasicrystalline Topological Insulator
by Simone Traverso, Niccolò Traverso Ziani and Maura Sassetti
Symmetry 2022, 14(8), 1736; https://doi.org/10.3390/sym14081736 - 19 Aug 2022
Cited by 1 | Viewed by 1533
Abstract
The experimental realization of twisted bilayer graphene strongly pushed the inspection of bilayer systems. In this context, it was recently shown that a two layer Haldane model with a thirty degree rotation angle between the layers represents a higher order topological insulator, with [...] Read more.
The experimental realization of twisted bilayer graphene strongly pushed the inspection of bilayer systems. In this context, it was recently shown that a two layer Haldane model with a thirty degree rotation angle between the layers represents a higher order topological insulator, with zero-dimensional states isolated in energy and localized at the physical vertices of the nanostructure. We show, within a numerical tight binding approach, that the energy of the zero dimensional states strongly depends on the geometrical structure of the vertices. In the most extreme cases, once a specific band gap is considered, these bound states can even disappear just by changing the vertex structure. Full article
(This article belongs to the Special Issue Symmetry, Topology and Phases of Condensed Matter)
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22 pages, 912 KiB  
Review
Review of Model Predictive Control of Distributed Energy Resources in Microgrids
by Darioush Razmi, Oluleke Babayomi, Alireza Davari, Tohid Rahimi, Yuntao Miao and Zhenbin Zhang
Symmetry 2022, 14(8), 1735; https://doi.org/10.3390/sym14081735 - 19 Aug 2022
Cited by 10 | Viewed by 2362
Abstract
In recent years, in response to increasing environmental concerns, advances in renewable energy technology and reduced costs have caused a significant increase in the penetration of distributed generation resources in distribution networks. Nonetheless, the connection of distributed generation resources to distribution networks has [...] Read more.
In recent years, in response to increasing environmental concerns, advances in renewable energy technology and reduced costs have caused a significant increase in the penetration of distributed generation resources in distribution networks. Nonetheless, the connection of distributed generation resources to distribution networks has created new challenges in the control, operation, and management of network reliability. This article is a review on the model predictive control (MPC) for distributed energy resources (DER) in microgrids. The solutions of MPC for energy conversion of solar photovoltaic, wind, and energy storage systems are covered in detail. MPC’s applications for increasing reliability of grid-connected converters under (a)symmetrical grid faults are also discussed. The promising potentials of the applications of MPC to the stable multi-variable control performance of DERs are highlighted. This work reflects strong symmetry on MPC control strategies and provides guidance map for readers to facilitate future research works in these exciting fields. Full article
(This article belongs to the Section Engineering and Materials)
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13 pages, 313 KiB  
Article
Some Generalization of the Method of Stability Investigation for Nonlinear Stochastic Delay Differential Equations
by Leonid Shaikhet
Symmetry 2022, 14(8), 1734; https://doi.org/10.3390/sym14081734 - 19 Aug 2022
Cited by 2 | Viewed by 1089
Abstract
It is known that the method of Lyapunov functionals is a powerful method of stability investigation for functional differential equations. Here, it is shown how the previously proposed method of stability investigation for nonlinear stochastic differential equations with delay and a high order [...] Read more.
It is known that the method of Lyapunov functionals is a powerful method of stability investigation for functional differential equations. Here, it is shown how the previously proposed method of stability investigation for nonlinear stochastic differential equations with delay and a high order of nonlinearity can be extended to nonlinear mathematical models of a much more general form. An important feature is the combination of the method of Lyapunov functionals with the method of Linear Matrix Inequalities (LMIs). Some examples of applications of the proposed method of stability research to known mathematical models are given. Full article
(This article belongs to the Section Mathematics)
19 pages, 3693 KiB  
Article
A Metaheuristics-Based Inputs Selection and Training Set Formation Method for Load Forecasting
by Ioannis Panapakidis, Michail Katsivelakis and Dimitrios Bargiotas
Symmetry 2022, 14(8), 1733; https://doi.org/10.3390/sym14081733 - 19 Aug 2022
Cited by 4 | Viewed by 1366
Abstract
Load forecasting is a procedure of fundamental importance in power systems operation and planning. Many entities can benefit from accurate load forecasting such as generation companies, systems operators, retailers, prosumers, and others. A variety of models have been proposed so far in the [...] Read more.
Load forecasting is a procedure of fundamental importance in power systems operation and planning. Many entities can benefit from accurate load forecasting such as generation companies, systems operators, retailers, prosumers, and others. A variety of models have been proposed so far in the literature. Among them, artificial neural networks are a favorable approach mainly due to their potential for capturing the relationship between load and other parameters. The forecasting performance highly depends on the number and types of inputs. The present paper presents a particle swarm optimization (PSO) two-step method for increasing the performance of short-term load forecasting (STLF). During the first step, PSO is applied to derive the optimal types of inputs for a neural network. Next, PSO is applied again so that the available training data is split into homogeneous clusters. For each cluster, a different neural network is utilized. Experimental results verify the robustness of the proposed approach in a bus load forecasting problem. Also, the proposed algorithm is checked on a load profiling problem where it outperforms the most common algorithms of the load profiling-related literature. During input selection, the weights update is held in asymmetrical duration. The weights of the training phase require more time compared with the test phase. Full article
(This article belongs to the Special Issue Symmetry in Power and Electronic Engineering)
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21 pages, 1807 KiB  
Article
Computational Study of Methods for Determining the Elasticity of Red Blood Cells Using Machine Learning
by Samuel Molčan, Monika Smiešková, Hynek Bachratý and Katarína Bachratá
Symmetry 2022, 14(8), 1732; https://doi.org/10.3390/sym14081732 - 19 Aug 2022
Cited by 3 | Viewed by 1624
Abstract
RBC (Red Blood Cell) membrane is a highly elastic structure, and proper modelling of this elasticity is essential for biomedical applications that involve computational experiments with blood flow. In this work, we present a new method for estimating one of the key parameters [...] Read more.
RBC (Red Blood Cell) membrane is a highly elastic structure, and proper modelling of this elasticity is essential for biomedical applications that involve computational experiments with blood flow. In this work, we present a new method for estimating one of the key parameters of red blood cell elasticity, which uses a neural network trained on the simulation outputs. We test classic LSTM (Long-Short Term Memory) architecture for the time series regression task, and we also experiment with novel CNN-LSTM (Convolutional Neural Network) architecture. We paid special attention to investigating the impact of the way the three-dimensional training data are reduced to their two-dimensional projections. Such a comparison is possible thanks to working with simulation outputs that are equivalently defined for all dimensions and their combinations. The obtained results can be used as recommendations for an appropriate way to record real experiments for which the reduced dimension of the acquired data is essential. Full article
(This article belongs to the Special Issue Machine Learning and Data Analysis)
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19 pages, 4122 KiB  
Article
Soliton Solutions and Sensitive Analysis of Modified Equal-Width Equation Using Fractional Operators
by Muhammad Bilal Riaz, Adam Wojciechowski, Georgia Irina Oros and Riaz Ur Rahman
Symmetry 2022, 14(8), 1731; https://doi.org/10.3390/sym14081731 - 19 Aug 2022
Cited by 12 | Viewed by 1610
Abstract
In this manuscript, the novel auxiliary equation methodology (NAEM) is employed to scrutinize various forms of solitary wave solutions for the modified equal-width wave (MEW) equation. M-truncated along with Atangana–Baleanu (AB)-fractional derivatives are employed to study the soliton [...] Read more.
In this manuscript, the novel auxiliary equation methodology (NAEM) is employed to scrutinize various forms of solitary wave solutions for the modified equal-width wave (MEW) equation. M-truncated along with Atangana–Baleanu (AB)-fractional derivatives are employed to study the soliton solutions of the problem. The fractional MEW equations are important for describing hydro-magnetic waves in cold plasma. A comparative analysis is utilized to study the influence of the fractional parameter on the generated solutions. Secured solutions include bright, dark, singular, periodic and many other types of soliton solutions. In compared to other methods, the solutions demonstrate that the proposed technique is particularly effective, straightforward, and trustworthy that contains families of solutions. In addition, the symbolic soft computation is used to verify the obtained solutions. Finally, the system is subjected to a sensitive analysis. Integer-order results calculated by the symmetry method present in the literature can be addressed as limiting cases of the present study. Full article
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13 pages, 259 KiB  
Article
Classification of Lorentzian Lie Groups Based on Codazzi Tensors Associated with Yano Connections
by Jiajing Miao, Jinli Yang and Jianyun Guan
Symmetry 2022, 14(8), 1730; https://doi.org/10.3390/sym14081730 - 18 Aug 2022
Viewed by 1326
Abstract
In this paper, we derive the expressions of Codazzi tensors associated with Yano connections in seven Lorentzian Lie groups. Furthermore, we complete the classification of three-dimensional Lorentzian Lie groups in which Ricci tensors associated with Yano connections are Codazzi tensors. The main results [...] Read more.
In this paper, we derive the expressions of Codazzi tensors associated with Yano connections in seven Lorentzian Lie groups. Furthermore, we complete the classification of three-dimensional Lorentzian Lie groups in which Ricci tensors associated with Yano connections are Codazzi tensors. The main results are listed in a table, and indicate that G1 and G7 do not have Codazzi tensors associated with Yano connections, G2, G3, G4, G5 and G6 have Codazzi tensors associated with Yano connections. Full article
(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology)
23 pages, 1837 KiB  
Article
Distributed Optimal Placement Generators in a Medium Voltage Redial Feeder
by Teddy Lekhuleni and Bhekisipho Twala
Symmetry 2022, 14(8), 1729; https://doi.org/10.3390/sym14081729 - 18 Aug 2022
Cited by 3 | Viewed by 1384
Abstract
Distributed generation (DG) is an important issue for distribution networks for power loss improvement. However, the location and size of generators remain a challenge for existing techniques. This work investigates the optimal placement of a distributed generator on a medium voltage radial feeder. [...] Read more.
Distributed generation (DG) is an important issue for distribution networks for power loss improvement. However, the location and size of generators remain a challenge for existing techniques. This work investigates the optimal placement of a distributed generator on a medium voltage radial feeder. Simulated annealing optimisation is used to find an optimal bus of connecting a distributed generator variable-spider. The optimisation technique is then applied to a power flow Matlab program that incorporates the Newton–Raphson method. DigSilent PowerFactory simulations software is used to validate the results that are obtained from the Matlab program. The results indicate that the optimal bus for a 14-bus radial feeder loaded at 5 MVA while using a 1.5 MW DG is bus 11. This is because connecting the distributed generator at bus 11 resulted in maximum loss reduction on the feeder. The Matlab tool proposed in this study can be used to find the optimal bus where a distributed generator can be connected to a medium voltage radial feeder, thereby improving power quality and fulfilling load demand with minimal size to make the system economical. Full article
(This article belongs to the Section Engineering and Materials)
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17 pages, 2770 KiB  
Article
A Model of Water Treatment by Nanoparticles in a Channel with Adjustable Width under a Magnetic Field
by Sergei Zuev, Petr Kabalyants and Zakir Hussain
Symmetry 2022, 14(8), 1728; https://doi.org/10.3390/sym14081728 - 18 Aug 2022
Viewed by 1218
Abstract
The process of water treatment by nanoparticles is one of the most considerable subjects in the cross-field of hydrodynamics, chemistry, and mathematics. This paper is dedicated to the case of the flows that appear when squeezing and stretching a channel with mixing of [...] Read more.
The process of water treatment by nanoparticles is one of the most considerable subjects in the cross-field of hydrodynamics, chemistry, and mathematics. This paper is dedicated to the case of the flows that appear when squeezing and stretching a channel with mixing of water, nanoparticles, and contaminants. It is assumed that fluid is homogeneous at the starting moment, the parameters of the nanoparticles and contaminants are known, and there is a constant non-homogeneous magnetic field applied to the system. The flow starts moving when the walls of the channel shift to each other. Exact and numerical solutions of the system of ordinary differential equations are used to obtain the results. The article gives an answer to the question about stability of the flow and proposes the technique to evaluate the essential characteristics of the system to achieve the treatment process efficiency. The main result is that the considered system shows excellent properties concerning purification of water on the selected part of the squeezing stage. This effect does not appear without a magnetic field. The mentioned properties are: decreasing of nanoparticle concentration to zero inside of the unsteady layer under magnetic field close to 1 T and this effect stays until the channel become about 10% of initial width as a result of the squeezing. Full article
(This article belongs to the Special Issue Symmetrical Mathematical Computation in Fluid Dynamics)
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42 pages, 898 KiB  
Article
Two-Dimensional Turbulent Thermal Free Jet: Conservation Laws, Associated Lie Symmetry and Invariant Solutions
by Erick Mubai and David Paul Mason
Symmetry 2022, 14(8), 1727; https://doi.org/10.3390/sym14081727 - 18 Aug 2022
Cited by 3 | Viewed by 1507
Abstract
The two-dimensional turbulent thermal free jet is formulated in the boundary layer approximation using the Reynolds averaged momentum balance equation and the averaged energy balance equation. The turbulence is described by Prandtl’s mixing length model for the eddy viscosity νT with mixing [...] Read more.
The two-dimensional turbulent thermal free jet is formulated in the boundary layer approximation using the Reynolds averaged momentum balance equation and the averaged energy balance equation. The turbulence is described by Prandtl’s mixing length model for the eddy viscosity νT with mixing length l and eddy thermal conductivity κT with mixing length lθ. Since νT and κT are proportional to the mean velocity gradient the momentum and thermal boundaries of the flow coincide. The conservation laws for the system of two partial differential equations for the stream function of the mean flow and the mean temperature difference are derived using the multiplier method. Two conserved vectors are obtained. The conserved quantities for the mean momentum and mean heat fluxes are derived. The Lie point symmetry associated with the two conserved vectors is derived and used to perform the reduction of the partial differential equations to a system of ordinary differential equations. It is found that the mixing lengths l and lθ are proportional. A turbulent thermal jet with νT0 and κT0 but vanishing kinematic viscosity ν and thermal conductivity κ is studied. Prandtl’s hypothesis that the mixing length is proportional to the width of the jet is made to complete the system of equations. An analytical solution is derived. The boundary of the jet is determined with the aid of a conserved quantity and found to be finite. Analytical solutions are derived and plotted for the streamlines of the mean flow and the lines of constant mean thermal difference. The solution differs from the analytical solution obtained in the limit ν0 and κ0 without making the Prandtl’s hypothesis. For ν0 and κ0 a numerical solution is derived using a shooting method with the two conserved quantities as targets instead of boundary conditions. The numerical solution is verified by comparing it to the analytical solution when ν0 and κ0. Because of the limitations imposed by the accuracy of any numerical method the numerical solution could not reliably determine if the jet is unbounded when ν0 and κ0 but for large distance from the centre line, ν>νT and κ>κT and the jet behaves increasingly like a laminar jet which is unbounded. The streamlines of the mean flow and the lines of constant mean temperature difference are plotted for ν=0 and κ=0. Full article
(This article belongs to the Special Issue Recent Advances in the Application of Symmetry Group)
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15 pages, 3189 KiB  
Article
A Novel Reversible Data Hiding Algorithm Based on Enhanced Reduced Difference Expansion
by Thai-Son Nguyen, Van-Thanh Huynh and Phuoc-Hung Vo
Symmetry 2022, 14(8), 1726; https://doi.org/10.3390/sym14081726 - 18 Aug 2022
Cited by 7 | Viewed by 1660
Abstract
Reversible data hiding is a data-hiding technique which has the ability to recover the original version from stego-images after the secret information is extracted. In this paper, we propose a novel reversible data-hiding scheme based on an enhanced reduced difference-expansion technique. In the [...] Read more.
Reversible data hiding is a data-hiding technique which has the ability to recover the original version from stego-images after the secret information is extracted. In this paper, we propose a novel reversible data-hiding scheme based on an enhanced reduced difference-expansion technique. In the proposed scheme, the original image is divided into non-overlapping quad-blocks for embedding data. Then, to enhance the security, the secret bits are encrypted based on the encryption key and a symmetry-based strategy. To improve embedding capacity further, two adjacent encrypted bits are converted into a corresponding decimal digit. Difference expansion (DE) technique is applied to embed a decimal form instead of a binary version. Moreover, to maintain the good image quality, the enhanced reduced difference-expansion technique is used to reduce the original difference values so that it is suitable for decimal embedding. The experimental results demonstrated that the proposed scheme has achieved better performance in comparison with previous solutions. Full article
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14 pages, 305 KiB  
Article
Results on Univalent Functions Defined by q-Analogues of Salagean and Ruscheweh Operators
by Ebrahim Amini, Mojtaba Fardi, Shrideh Al-Omari and Kamsing Nonlaopon
Symmetry 2022, 14(8), 1725; https://doi.org/10.3390/sym14081725 - 18 Aug 2022
Cited by 9 | Viewed by 1273
Abstract
In this paper, we define and discuss properties of various classes of analytic univalent functions by using modified q-Sigmoid functions. We make use of an idea of Salagean to introduce the q-analogue of the Salagean differential operator. In addition, we derive [...] Read more.
In this paper, we define and discuss properties of various classes of analytic univalent functions by using modified q-Sigmoid functions. We make use of an idea of Salagean to introduce the q-analogue of the Salagean differential operator. In addition, we derive families of analytic univalent functions associated with new q-Salagean and q-Ruscheweh differential operators. In addition, we obtain coefficient bounds for the functions in such new subclasses of analytic functions and establish certain growth and distortion theorems. By using the concept of the (q, δ)-neighbourhood, we provide several inclusion symmetric relations for certain (q, δ)-neighbourhoods of analytic univalent functions of negative coefficients. Various q-inequalities are also discussed in more details. Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions)
13 pages, 918 KiB  
Article
Invariants of Bonded Knotoids and Applications to Protein Folding
by Neslihan Gügümcü, Bostjan Gabrovsek and Louis H. Kauffman
Symmetry 2022, 14(8), 1724; https://doi.org/10.3390/sym14081724 - 18 Aug 2022
Cited by 5 | Viewed by 1638
Abstract
In this paper, we study knotoids with extra graphical structure (bonded knotoids) in the settings of rigid vertex and topological vertex graphs. We construct bonded knotoid invariants by applying tangle insertion and unplugging at bonding sites of a bonded knotoid. We demonstrate that [...] Read more.
In this paper, we study knotoids with extra graphical structure (bonded knotoids) in the settings of rigid vertex and topological vertex graphs. We construct bonded knotoid invariants by applying tangle insertion and unplugging at bonding sites of a bonded knotoid. We demonstrate that our invariants can be used for the analysis of the topological structure of proteins. Full article
(This article belongs to the Special Issue Topological Methods in Chemistry and Molecular Biology)
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16 pages, 336 KiB  
Article
Self-Weighted Quasi-Maximum Likelihood Estimators for a Class of MA-GARCH Model
by Danni Xie, Xin Liang and Ruilin Liang
Symmetry 2022, 14(8), 1723; https://doi.org/10.3390/sym14081723 - 18 Aug 2022
Viewed by 1288
Abstract
In financial time series analysis, symmetric and asymmetric GARCH models have become essential models for measuring the characteristics of economic volatility. In this article, we propose the consistency and asymptotic normality properties of the self-weighted quasi-maximum likelihood estimation without assuming the existence of [...] Read more.
In financial time series analysis, symmetric and asymmetric GARCH models have become essential models for measuring the characteristics of economic volatility. In this article, we propose the consistency and asymptotic normality properties of the self-weighted quasi-maximum likelihood estimation without assuming the existence of the second moment for the moving average model with a class of GARCH error. Numerical simulation shows that the parameter estimation performs well; empirical analysis shows that the self-weighted quasi-maximum likelihood estimation of the moving average model with a class of GARCH error can improve the data fitting effect and prediction ability. Full article
(This article belongs to the Section Mathematics)
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