Symmetry

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

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

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

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

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

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

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

The functions $\sqrt{1+z}$, $e^z$, $1+Az$, $A\in (0,1]$ map the unit disc $\mathbb{D}$ to a domain which is symmetric about the x-axis. The Regular Coulomb wave function (RCWF) ${\mathtt{F}}_{L,\eta }$ is a function involving two parameters L and $\eta$, and ${\mathtt{F}}_{L,\eta }$ is symmetric about these. In this article, we derive conditions on the parameter L and $\eta$ for which the normalized form ${\mathtt{f}}_L$ of ${\mathtt{F}}_{L,\eta }$ are subordinated by $\sqrt{1+z}$. We also consider the subordination by $e^z$ and $1+Az$, $A\in (0,1]$. A few more subordination properties involving RCWF are discussed, which leads to the star-likeness of normalized Regular Coulomb wave functions. Full article

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

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

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

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

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

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

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

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

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

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

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