Symmetry doi: 10.3390/sym16091213

Authors: Weitao Cai Xiaozu Zhang Dongtao Wang Wenping Weng Zibin Wu Hiromi Nagaumi

The process of symmetrical multidirectional pressure was adopted to inhibit the macrosegregation of eutectic Si in squeeze cast A356 alloy. Five pressure modes were applied to study the effects of multidirectional pressure and the timing of pressure application on the macrosegregation of eutectic Si. The results show that the directional movement of the solute-rich liquid phase could be inhibited by symmetrical multidirectional pressure. Therefore, the macrosegregation of eutectic Si in the casting part was inhibited. Moreover, the timing of pressure application should be matched with the local pressure position. After the effective inhibition of the macrosegregation of eutectic Si, the elongation of the alloy was significantly improved, reaching up to 7.12%. In addition, the plastic deformation region was observed at the local pressure position. The grains in the plastic deformation region were refined. The proportion of low-angle grain boundaries in the deformed region was about 30%, which was much higher than that in the other undeformed region. The size of the Fe-containing intermetallics in the deformed region decreased to 5&ndash;10 &mu;m, which is favorable for the mechanical properties of the alloy.

]]>Symmetry doi: 10.3390/sym16091212

Authors: Kazuki Sugiyama Yoshihiro Kubota Osamu Mochizuki

Insect wing vein networks facilitate blood transport with unknown haemodynamic effects on their structures. Fruit flies have the posterior cross vein (PCV) that disrupts the symmetry of the network topology and reduces the total pressure loss during blood transport; however, the impact of its various positions among species has not been examined. This study investigated the haemodynamic effects of this vein with various connecting positions. By analogising venous networks to hydraulic circuits, the flow rates and pressure losses within the veins were derived using Poiseuille&rsquo;s and Kirchhoff&rsquo;s laws. The results showed that the total pressure loss decreased for both PCV connections near the wing&rsquo;s base. In an idealised circuit imitating the network topology, applied high hydraulic resistances as one-sided as those along the edge of the wing, the same pressure loss response as that in the actual network was demonstrated, but not within a symmetric resistance distribution. Therefore, the most proximal PCV minimises the pressure loss within the asymmetric resistance distribution, indicating an evolutionary adaptation to reducing the pressure loss in certain species with this vein near the base. Our findings highlight the possible optimisation of the flies&rsquo; wing morphology to maintain the functions of the liquid transport networks and flight devices simultaneously.

]]>Symmetry doi: 10.3390/sym16091211

Authors: Samer Al-Ghour Dina Abuzaid

The authors of this paper introduce and discuss three weaker forms of soft faint continuity: soft faint semi-continuity, soft faint pre-continuity, and soft faint &beta;-continuity. They characterize each of them in several ways. They also demonstrate how they are preserved under some restrictions. Moreover, they prove that a soft function is also soft faint semi-continuous (resp. soft faint pre-continuous, soft faint &beta;-continuous) if its soft graph function is also soft faint semi-continuous (resp. soft faint pre-continuous, soft faint &beta;-continuous). Moreover, they show that a soft function is soft faint semi-continuous (resp. soft faint pre-continuous, soft faint &beta;-continuous) iff it is soft semi-continuous provided that it has a soft regular codomain. Finally, the symmetry between our new ideas and their analogous topological ones is investigated.

]]>Symmetry doi: 10.3390/sym16091210

Authors: Ximing Fang

A two-step simplified modulus-based matrix splitting iteration method is presented for solving the linear complementarity problem. According to general matrix splitting and special matrix splitting, a general convergence analysis and a specific convergence analysis are described, respectively. Numerical experiments show that the iteration method is effective and that the convergence theories are valid.

]]>Symmetry doi: 10.3390/sym16091209

Authors: Zihan Zhao Tao Yu Shang Wang Huadong Li Zhi Wang

Inertial sensors act as inertial references in space gravitational wave detection missions, necessitating that their internal test mass (TM) maintains minimal residual acceleration noise. High-energy particles and cosmic rays in space, along with ion pumps in ground-based torsion pendulum experiments, can cause charge accumulation on the TM surface, leading to increased residual acceleration noise. Consequently, a charge management system was introduced to control the TM&rsquo;s charge. The complex light path propagation within the electrode housing (EH) makes the TM&rsquo;s charging and discharging process difficult to theoretically calculate and fully simulate. To address this issue, we propose a simulation method for charging and discharging inertial sensors within ultraviolet (UV) charge management systems. This method innovatively considers the impact of photoelectron emission angle and the TM&rsquo;s position offset from symmetry on performance. The method also simulates charging and discharging rates over time under conditions of symmetry and preliminarily examines factors affecting the TM&rsquo;s equilibrium potential. Simulation results indicate that this method effectively models the charge management system&rsquo;s operation, providing a valuable reference for system design.

]]>Symmetry doi: 10.3390/sym16091208

Authors: Shazia Parveen Miin-Shen Yang

Clustering is a technique of grouping data into a homogeneous structure according to the similarity or dissimilarity measures between objects. In clustering, the fuzzy c-means (FCM) algorithm is the best-known and most commonly used method and is a fuzzy extension of k-means in which FCM has been widely used in various fields. Although FCM is a good clustering algorithm, it only treats data points with feature components under equal importance and has drawbacks for handling high-dimensional data. The rapid development of social media and data acquisition techniques has led to advanced methods of collecting and processing larger, complex, and high-dimensional data. However, with high-dimensional data, the number of dimensions is typically immaterial or irrelevant. For features to be sparse, the Lasso penalty is capable of being applied to feature weights. A solution for FCM with sparsity is sparse FCM (S-FCM) clustering. In this paper, we propose a new S-FCM, called S-FCM-Lasso, which is a new type of S-FCM based on the Lasso penalty. The irrelevant features can be diminished towards exactly zero and assigned zero weights for unnecessary characteristics by the proposed S-FCM-Lasso. Based on various clustering performance measures, we compare S-FCM-Lasso with the S-FCM and other existing sparse clustering algorithms on several numerical and real-life datasets. Comparisons and experimental results demonstrate that, in terms of these performance measures, the proposed S-FCM-Lasso performs better than S-FCM and existing sparse clustering algorithms. This validates the efficiency and usefulness of the proposed S-FCM-Lasso algorithm for high-dimensional datasets with sparsity.

]]>Symmetry doi: 10.3390/sym16091207

Authors: Kaihong Zhou Haixu Liu Shu Li

The problem of machining complex surfaces with non-ball-end cutters by strip-width-maximization machining is formulated as a kind of surface fitting problem in which the tool surface envelope feature line approximates the design surface under the movement transform. The theory of surface envelope&minus;approximation is proposed as a general method for optimizing tool movement in single-contact strip-width-maximization machining of sculptured surfaces with non-ball-end cutters. Based on the surface moving frame, the velocity equations and transformation matrices for the tool motion relative to the workpiece, described by the motion-invariant parameters of the tool surface and design surface, are derived. A functional extremum model for optimizing the tool position ensures continuous and symmetrical motion relative to the workpiece to achieve the highest machining efficiency and accuracy. Finally, a Matlab-based simulation example verifies the machining efficiency and accuracy of the envelope approximation theory.

]]>Symmetry doi: 10.3390/sym16091206

Authors: Lorenzo Ledda Annalisa Greco Ilaria Fiore Ivo Caliò

The dynamic stiffness method is developed to analyze the natural vibration characteristics of functionally graded beams, where material properties change continuously across the beam thickness following a symmetric law distribution. The governing equations of motion and associated natural boundary conditions for free vibration analysis are derived using Hamilton&rsquo;s principle and closed-form exact solutions are obtained for both Euler&ndash;Bernoulli and Timoshenko beam models. The dynamic stiffness matrix, which governs the relationship between force and displacements at the beam ends, is determined. Using the Wittrick&ndash;Williams algorithm, the dynamic stiffness matrix is employed to compute natural frequencies and mode shapes. The proposed procedure is validated by comparing the obtained frequencies with those given by approximated well-known formulas. Finally, a parametric investigation is conducted by varying the geometry of the structure and the characteristic mechanical parameters of the functionally graded material.

]]>Symmetry doi: 10.3390/sym16091205

Authors: Xinlin Li Xuzhen Wu Peipei Wang Yalu Xu Yue Gao Yiyang Chen

Circular rail-guided vehicles (RGVs) are widely used in automated warehouses, and their efficiency directly determines the transportation efficiency of the entire system. The congestion frequency of RGVs greatly increases when facing dense multi-type entry and delivery tasks, affecting overall transportation efficiency. This article focuses on the RGV scheduling problem of multi-type parallel transportation tasks in a real-world automated warehouse, considering maximizing efficiency while reducing energy consumption and thus establishing the RGV scheduling optimization model. At the same time, an improved genetic algorithm (GA) based on symmetry selection function and offspring population structure symmetry is proposed to solve the above RGV scheduling problem, achieving the model solution. The case study demonstrates the superiority of the proposed method in breaking local optima and achieving bi-objective optimization in genetic algorithms.

]]>Symmetry doi: 10.3390/sym16091204

Authors: Zahra Abdelmalek Mohammad Yaghoub Abdollahzadeh Jamalabadi

The journal retracts the article titled &ldquo;Numerical Simulation of Micromixing of Particles and Fluids with Galloping Cylinder&rdquo; [...]

]]>Symmetry doi: 10.3390/sym16091203

Authors: Haiyan Zhou Afshin Davarpanah

The journal retracts the article titled &ldquo;Hybrid Chemical Enhanced Oil Recovery Techniques: A Simulation Study&rdquo; [...]

]]>Symmetry doi: 10.3390/sym16091201

Authors: Peng Jiang Xiaodong Cai

In the information age, semantic parsing technology drives efficiency improvement and accelerates the process of intelligence. However, it faces complex understanding, data inflation, inappropriate evaluation, and difficult application of advanced large models. This study analyses the current challenges and looks forward to the development trend of the technology. Specific approaches include: this study adopts a systematic review method and strictly follows the PRISMA framework, deeply analyzes the key ideas, methods, problems, and solutions of traditional and neural network methods, and explores the model performance, API application, dataset, and evaluation mechanism. Through literature analysis, the technology is classified according to its application scenarios. Then, the practical application contributions are summarized, current limitations such as data size, model performance, and resource requirements are analyzed, and future directions such as dataset expansion, real-time performance enhancement, and industrial applications are envisioned. The results of the study show significant advances in semantic parsing technology with far-reaching impacts. Traditional and neural network methods complement each other to promote theoretical and practical innovation. In the future, with the continuous progress and in-depth application of machine learning technology, semantic parsing technology needs to further deepen the research on logical reasoning and evaluation, to better cope with technical challenges and lead the new development of natural language processing and AI.

]]>Symmetry doi: 10.3390/sym16091202

Authors: Ming Li

This paper conducts a tutorial review of the analytic theory of seven classes of fractional vibrations based on elementary functions. We discuss the classification of seven classes of fractional vibrations and introduce the problem statements. Then, the analytic theory of class VI fractional vibrators is given. The analytic theories of fractional vibrators from class I to class V and class VII are, respectively, represented. Furthermore, seven analytic expressions of frequency bandwidth of seven classes of fractional vibrators are newly introduced in this paper. Four analytic expressions of sinusoidal responses to fractional vibrators from class IV to VII by using elementary functions are also newly reported in this paper. The analytical expressions of responses (free, impulse, step, and sinusoidal) are first reported in this research. We dissert three applications of the analytic theory of fractional vibrations: (1) analytical expression of the forced response to a damped multi-fractional Euler&ndash;Bernoulli beam; (2) analytical expressions of power spectrum density (PSD) and cross-PSD responses to seven classes of fractional vibrators under the excitation with the Pierson and Moskowitz spectrum, which are newly introduced in this paper; and (3) a mathematical explanation of the Rayleigh damping assumption.

]]>Symmetry doi: 10.3390/sym16091200

Authors: Victor V. Kuzenov Aleksey Yu. Varaksin Sergei V. Ryzhkov

This paper presents a preliminary analysis of the plasma dynamic modes of operation of end-type magnetoplasma compressor (MPC) discharges. The characteristic methods used to organize the optical pumping of a photodissociation gas laser using an MPC discharge are briefly described. The kinetic and energy characteristics of photodissociation gas optical quantum generators (OQGs) with optical pumping by an MPC discharge were evaluated. Based on the numerical calculations, an analysis of the radiation&ndash;plasma dynamic structures and the spectral brightness characteristics of the MPC discharge in the ohmic mode of plasma heating was carried out.

]]>Symmetry doi: 10.3390/sym16091199

Authors: Najla Altwaijry Silvestru Sever Dragomir Kais Feki

In this paper, we employ a generalization of the Boas&ndash;Bellman inequality for inner products, as developed by Mitrinovi&#263;&ndash;Pe&#269;ari&#263;&ndash;Fink, to derive several upper bounds for the 2p-th power with p&ge;1 of the numerical radius of the off-diagonal operator matrix 0AB*0 for any bounded linear operators A and B on a complex Hilbert space H. While the general matrix is not symmetric, a special case arises when B=A*, where the matrix becomes symmetric. This symmetry plays a crucial role in the derivation of our bounds, illustrating the importance of symmetric structures in operator theory.

]]>Symmetry doi: 10.3390/sym16091198

Authors: Dongkeun Lee Seowon Han Kang Hoon Lee

Virtual reality offers ordinary users the ability to observe and interact with various abstract or concrete objects visualized in a three-dimensional space from different angles. Users can manipulate, transform, or reconstruct these objects similarly to how they might in a real environment. Manipulating objects in virtual reality is not as effortless as in the real world, due to the lack of sensory feedback and limited input freedom. However, it also offers new advantages that the real world cannot provide, such as the ability to easily select and control remote objects and the support of various auxiliary user interfaces. In particular, when it is necessary to alternately manipulate objects of various sizes, scaling the user&rsquo;s avatar symmetrically allows for more effective manipulation than in the real world. However, manual scaling interfaces can be cumbersome and may induce dizziness. This study proposes an interaction technique that allows users to conveniently manipulate objects of various sizes without manual scale adjustment, by automatically and instantly adjusting the scale factor according to the size of the selected object and its adjacent objects. To compensate for the change in scale, we also implement a position correction mechanism that adjusts the user&rsquo;s position in the virtual environment. Preliminary experiments with a small group of participants confirmed that automatic scale adjustment produces significant effects. Based on the feedback from these experiments, a more refined distance calculation method and the timing for scale adjustment were derived. In the main experiment with 14 participants, it was confirmed that the automatic scale adjustment method proposed in this study led to higher accuracy and lower discomfort in task completion compared to the conventional manual scale adjustment method. We expect that the results of this study will effectively contribute to the creation of virtual reality content that requires interaction with objects of various sizes in the future.

]]>Symmetry doi: 10.3390/sym16091197

Authors: Ming Li

The novelty and main contributions of this paper are reflected in four aspects. First, we introduce multi-fractional phasor in Theorem 1. Second, we propose the motion phasor equations of seven types of multi-fractional vibrators in Theorems 2, 12, 22, 32, 43, 54, and 65, respectively. Third, we present the analytical expressions of response phasors of seven types of multi-fractional vibrators in Theorems 10, 20, 30, 41, 52, 63, and 74, respectively. Fourth, we bring forward the analytical expressions of stationary sinusoidal responses of seven types of multi-fractional vibrators in Theorems 11, 21, 31, 42, 53, 64, and 75, respectively. In addition, by using multi-fractional phasor, we put forward the analytical expressions of vibration parameters (equivalent mass, equivalent damping, equivalent stiffness, equivalent damping ratio, equivalent damping free natural angular frequency, equivalent damped natural angular frequency, equivalent frequency ratio) and frequency transfer functions of seven types of multi-fractional vibrators. Demonstrations exhibit that the effects of multi-fractional orders on stationary sinusoidal responses of those multi-fractional vibrators are considerable.

]]>Symmetry doi: 10.3390/sym16091196

Authors: Jue Wang

Large language models (LLMs) are widely integrated into autonomous driving systems to enhance their operational intelligence and responsiveness and improve self-driving vehicles&rsquo; overall performance. Despite these advances, LLMs still struggle between hallucinations&mdash;when models either misinterpret the environment or generate imaginary parts for downstream use cases&mdash;and taxing computational overhead that relegates their performance to strictly non-real-time operations. These are essential problems to solve to make autonomous driving as safe and efficient as possible. This work is thus focused on symmetrical trade-offs between the reduction of hallucination and optimization, leading to a framework for these two combined and at least specifically motivated by these limitations. This framework intends to generate a symmetry of mapping between real and virtual worlds. It helps in minimizing hallucinations and optimizing computational resource consumption reasonably. In autonomous driving tasks, we use multimodal LLMs that combine an image-encoding Visual Transformer (ViT) and a decoding GPT-2 with responses generated by the powerful new sequence generator from OpenAI known as GPT4. Our hallucination reduction and optimization framework leverages iterative refinement loops, RLHF&mdash;reinforcement learning from human feedback (RLHF)&mdash;along with symmetric performance metrics, e.g., BLEU, ROUGE, and CIDEr similarity scores between machine-generated answers specific to other human reference answers. This ensures that improvements in model accuracy are not overused to the detriment of increased computational overhead. Experimental results show a twofold improvement in decision-maker error rate and processing efficiency, resulting in an overall decrease of 30% for the model and a 25% improvement in processing efficiency across diverse driving scenarios. Not only does this symmetrical approach reduce hallucination, but it also better aligns the virtual and real-world representations.

]]>Symmetry doi: 10.3390/sym16091195

Authors: Ke Xu Baoyi Chen

We studied the photoproduction of dileptons from strong electromagnetic fields generated by the nucleus in relativistic heavy-ion collisions. The production of dileptons is calculated based on the Equivalent Photon Approximation (EPA) method, which depends on the strength of the electromagnetic fields and the density of protons in the nucleus. With the EPA method, we construct the connections between dilepton photoproduction and the electromagnetic form factors in the nucleus. Finally, the nuclear proton densities can be determined with the dilepton photoproduction, which is employed to extract the neutron skin in the nucleus. Our calculations indicate that the dilepton photoproduction varies evidently with different proton densities in the nucleus, suggesting a deeper symmetry underlying the connections between proton density (or the neutron skin) and the dilepton photoproduction. This offers a new way to study the neutron skin in the nucleus.

]]>Symmetry doi: 10.3390/sym16091194

Authors: Aliyu Isa Aliyu Jibrin Sale Yusuf Malik Muhammad Nauman Dilber Uzun Ozsahin Baba Galadima Agaie Juliana Haji Zaini Huzaifa Umar

In this study, we investigate the symmetry analysis and explicit solutions for the Estevez&ndash;Mansfield&ndash;Clarkson (EMC) equation. Our main objectives are to identify the Lie point symmetries of the EMC equation, construct an optimal system of one-dimensional subalgebras, and reduce the EMC equation to a set of ordinary differential equations (ODEs). We employ the Riccati&ndash;Bernoulli sub-ODE method (RBSODE) to solve these reduced ODEs and obtain explicit solutions for the EMC model. The obtained solutions are validated using numerical analyses, and corresponding figures are presented to illustrate the physical implications of the derived solutions.

]]>Symmetry doi: 10.3390/sym16091193

Authors: Cemil Tunç Jen-Chih Yao Mouffak Benchohra Ahmed M. A. El-Sayed

The fractional calculus is a specific case of classical calculus, as is well known [...]

]]>Symmetry doi: 10.3390/sym16091192

Authors: Xiaochun Luo Kai Kang Lin Lu Youan Ke

In the context of supply disruption, having a resilient supply chain is crucial for the survival and growth of enterprises. It is also essential for gaining a competitive advantage in a turbulent environment. Enterprises need to invest in supply chain resilience to better deal with future uncertainties. This paper constructs a Stackelberg game model with the manufacturer as the leader and the retailer as the follower. We explored how supply chain-related factors under supply interruption risk affect supply chain resilience investment, and studied how to choose supply chain coordination strategies to improve the effectiveness of manufacturer capacity recovery and mutual profits in the context of supply interruption. The study also analyzes the asymmetrical impact of changes in product order quantity, supply disruption probability, and the capacity recovery coefficient on retailer decision-making and the profits of supply chain members. The results indicate that manufacturer profits are negatively correlated with supply disruption probability, while retailer profits are positively correlated with supply disruption probability when product order quantities are low and negatively correlated when product order quantities are high. The supply chain resilience investment is positively correlated with the supply disruption probability. Furthermore, the effectiveness of the cost-sharing contract is closely related to product order quantity and supply disruption probability. When the product order quantity d&lt;&alpha;L&minus;c[1&minus;&xi;aL+&xi;aH]+s&alpha;H&xi;+w&alpha;L(1&minus;&xi;)k or &alpha;H&minus;c[1&minus;&xi;aL+&xi;aH]+s&alpha;H&xi;+w&alpha;L(1&minus;&xi;)k&lt;d&lt;&alpha;H[1&minus;&xi;aL+&xi;aH](w&minus;c)k, manufacturers can withstand the risk of supply interruption by investing in supply chain resilience alone. But when the product order quantity is &alpha;L&minus;c[1&minus;&xi;aL+&xi;aH]+s&alpha;H&xi;+w&alpha;L(1&minus;&xi;)k&lt;d&lt;&alpha;H&minus;c[1&minus;&xi;aL+&xi;aH]+s&alpha;H&xi;+w&alpha;L(1&minus;&xi;)k and &alpha;H[1&minus;&xi;aL+&xi;aH](w&minus;c)k&lt;d, the use of cost-sharing contracts is more effective. Additionally, when the sensitivity analysis is conducted, the capacity recovery coefficient positively correlates with supply chain profits in a decentralized mode. However, under the cost-sharing contract mode, it exhibits a U-shaped fluctuation pattern, indicating that the impact of improving capacity recovery efficiency on the profits of both parties is not symmetrical and linear. As &xi; approaches 0.5, the profits of manufacturers and retailers decrease. Instead, it undergoes an initial decline followed by a subsequent increase, highlighting the nonlinear benefits of capacity recovery strategies under the cooperative approach.

]]>Symmetry doi: 10.3390/sym16091186

Authors: Dongwook Kim Abraham Puig Faranak Rabiei Erial J. Hawkins Talia F. Hernandez Chang K. Sung

The Zika virus has been shown to infect glioblastoma stem cells via the membrane receptor &alpha;v&beta;5, which is activated by the stem-specific transcription factor SOX2. Since the expression level of SOX2 is an important predictive marker for successful virotherapy, it is important to understand the fundamental mechanisms of the role of SOX2 in the dynamics of cancer stem cells and Zika viruses. In this paper, we develop a mathematical ODE model to investigate the effects of SOX2 expression levels on Zika virotherapy against glioblastoma stem cells. Our study aimed to identify the conditions under which SOX2 expression level, viral infection, and replication can reduce or eradicate the glioblastoma stem cells. Analytic work on the existence and stability conditions of equilibrium points with respect to the basic reproduction number are provided. Numerical results were in good agreement with analytic solutions. Our results show that critical threshold levels of both SOX2 and viral replication, which change the stability of equilibrium points through population dynamics such as transcritical and Hopf bifurcations, were observed. These critical thresholds provide the optimal conditions for SOX2 expression levels and viral bursting sizes to enhance therapeutic efficacy of Zika virotherapy against glioblastoma stem cells. This study provides critical insights into optimizing Zika virus-based treatment for glioblastoma by highlighting the essential role of SOX2 in viral infection and replication.

]]>Symmetry doi: 10.3390/sym16091191

Authors: Fangfu Lin Wu Song Yan Li Wanni Xu

Background: Symmetry is a special kind of balance. This study aims to systematically explore and apply the role of balanced composition in aesthetic judgments by focusing on balanced composition features and employing research methods from computational aesthetics and neuroaesthetics. Methods: First, experimental materials were classified by quantifying balanced composition using several indices, including symmetry, center of gravity, and negative space. An EEG experiment was conducted with 18 participants, who were asked to respond dichotomously to the same stimuli under different judgment tasks (balance and aesthetics), with both behavioral and EEG data being recorded and analyzed. Subsequently, participants&rsquo; data were combined with balanced composition indices to construct and analyze various SVM classification models. Results: Participants largely used balanced composition as a criterion for aesthetic evaluation. ERP data indicated that from 300&ndash;500 ms post-stimulus, brain activation was more significant in the aesthetic task, with unbeautiful and imbalanced stimuli eliciting larger frontal negative waves and occipital positive waves. From 600&ndash;1000 ms, beautiful stimuli caused smaller negative waves in the PZ channel. The results of the SVM models indicated that the model incorporating aesthetic subject data (ACC = 0.9989) outperforms the model using only balanced composition parameters of the aesthetic object (ACC = 0.7074). Conclusions: Balanced composition is a crucial indicator in aesthetics, with similar early processing stages in both balance and aesthetic judgments. Multi-modal data models validated the advantage of including human factors in aesthetic evaluation systems. This interdisciplinary approach not only enhances our understanding of the cognitive and emotional processes involved in aesthetic judgments but also enables the construction of more reasonable machine learning models to simulate and predict human aesthetic preferences.

]]>Symmetry doi: 10.3390/sym16091190

Authors: Yanling Bao Shumin Cheng

Hesitant fuzzy information systems have been widely applied in decision-making due to their ability to handle uncertain information. In addition, dominance relationships are often taken into account in many practical decision-making problems. Therefore, it is of great significance to conduct research on hesitant fuzzy information systems involved with dominance relations. In this study, we introduce dominance relations in a hesitant fuzzy information system to make it a dominance-based hesitant fuzzy information system, which can provide a solid new idea for comparing hesitant fuzzy elements. Furthermore, a hesitant fuzzy dominance-based rough set model is constructed, and an attribute reduction method is designed to simplify the dominance-based hesitant fuzzy information system. Further, we propose lower and upper approximation discernibility matrices in the dominance-based hesitant fuzzy decision information system to extract decision rules. In addition, two numerical examples are given to demonstrate the effectiveness of the proposed attribute reduction methods.

]]>Symmetry doi: 10.3390/sym16091188

Authors: Leszek Gasiński Gregoris Makrides Nikolaos S. Papageorgiou

We consider a Dirichlet problem driven by the anisotropic (p,q) Laplacian. In the reaction, we have a parametric partially concave term plus a &ldquo;superlinear&rdquo; perturbation (convex term) which need not satisfy the Ambrosetti&ndash;Rabinowitz condition. Using variational tools, we show that for all small values of the parameter &lambda;&gt;0, the problem has at least two nontrivial smooth solutions.

]]>Symmetry doi: 10.3390/sym16091189

Authors: Chunfen Xia Jianqiang Lv

In medical image analysis, precise retinal vessel segmentation is crucial for diagnosing and managing ocular diseases as the retinal vascular network reflects numerous health indicators. Despite decades of development, challenges such as intricate textures, vascular ruptures, and undetected areas persist, particularly in accurately segmenting small vessels and addressing low contrast in imaging. This study introduces a novel segmentation approach called MPCCN that combines position-aware cyclic convolution (PCC) with multi-scale resolution input to tackle these challenges. By integrating standard convolution with PCC, MPCCN effectively captures both global and local features. A multi-scale input module enhances feature extraction, while a weighted-shared residual and guided attention module minimizes background noise and emphasizes vascular structures. Our approach achieves sensitivity values of 98.87%, 99.17%, and 98.88%; specificity values of 98.93%, 97.25%, and 99.20%; accuracy scores of 97.38%, 97.85%, and 97.75%; and AUC values of 98.90%, 99.15%, and 99.05% on the DRIVE, STARE, and CHASE_DB1 datasets, respectively. In addition, it records F1 scores of 90.93%, 91.00%, and 90.55%. Experimental results demonstrate that our method outperforms existing techniques, especially in detecting small vessels.

]]>Symmetry doi: 10.3390/sym16091187

Authors: Mengdi Yin Dimitri D. Vvedensky

Martensitic transformations, viewed as continuous mappings between triply periodic minimal surfaces (TPMSs), as suggested by Hyde and Andersson (Z. Kristallogr. 1986, 174, 225&ndash;236), are extended to include paths between the initial and final phases. Reversible transformations, which correspond to shape-memory materials, occur only if lattice points remain at flat points on a TPMS throughout a continuous transformation. For the shape-memory material NiTi, the density functional calculations by Hatcher et al. [Phys. Rev. B2009, 80, 144203] yield irreversible and reversible paths with and without energy barriers, respectively, in agreement with our theory. Although there are TPMSs for face-centered and body-centered cubic crystals for iron, the deformation between them is not reversible, in agreement with the non-vanishing energy barriers obtained from the density functional calculations of Zhang et al. (RSC Advances2021, 11, 3043&ndash;3048).

]]>Symmetry doi: 10.3390/sym16091185

Authors: Andras Kovacs Giorgio Vassallo

The Fermi&ndash;Dirac and Bose&ndash;Einstein statistics are considered to be key concepts in quantum mechanics, and they are used to explain the occupancy limit of electron orbitals. We investigate the physical origin of these two statistics and uncover that the key determining factor is whether an individual electron spin is measurable or not. Microscopically, a system with individually measurable electron spins corresponds to the presence of Larmor spin precession in electron&ndash;electron interactions, while the non-measurability of individual electron spins corresponds to the absence of Larmor spin precession. Both interaction types are possible, and the favored interaction type is thermodynamically determined. The absence of Larmor spin precession is realized in coherent electron states, and coherent electrons therefore obey Bose&ndash;Einstein statistics.

]]>Symmetry doi: 10.3390/sym16091184

Authors: Kaijian Ou Shilin Gao Yuhong Wang Bingjie Zhai Wei Zhang

The rapid growth of renewable energy presents significant challenges for power grid operation, making the efficient integration of renewable energy crucial. This paper proposes a method to evaluate the power system&rsquo;s capacity to accommodate renewable energy based on the Gaussian mixture model (GMM) from a symmetry perspective, underscoring the symmetrical interplay between load and renewable energy sources and highlighting the balance necessary for enhancing grid stability. First, a 10th-order GMM is identified as the optimal model for analyzing power system load and wind power data, balancing accuracy with computational efficiency. The Metropolis&ndash;Hastings (M-H) algorithm is used to generate sample spaces, which are integrated into power flow calculations to determine the maximum renewable energy integration capacity while ensuring system stability. Short-circuit ratio calculations and N-1 fault simulations validate system robustness under high renewable energy integration. The consistency between the results from the M-H algorithm, Gibbs sampling, and Monte Carlo simulation (MCS) confirms the approach&rsquo;s accuracy.

]]>Symmetry doi: 10.3390/sym16091183

Authors: Weiwei Miao Xinjian Zhao Ce Wang Shi Chen Peng Gao Qianmu Li

The expansion of Internet of Things (IoT) technology and the rapid increase in data in smart grid business scenarios have led to a need for more dynamic and adaptive security strategies. Traditional static security measures struggle to meet the evolving low-voltage security requirements of state grid systems under this new IoT-driven environment. By incorporating symmetry in metaheuristic algorithms, we can further improve performance and robustness. Symmetrical properties have the potential to lead to more efficient and balanced solutions, improving the overall stability of the grid. We propose a gnn-enhanced ant colony optimization method for orchestrating grid security strategies, which trains across combinatorial optimization problems (COPs) that are representative scenarios in the state grid business scenarios, to learn specific mappings from instances to their heuristic measures. The learned heuristic metrics are embedded into the ant colony optimization (ACO) to generate the optimal security policy adapted to the current security situation. Compared to the ACO and adaptive elite ACO, our method reduces the average time consumption of finding a path within a limited time in the capacitated vehicle routing problem by 67.09% and 66.98%, respectively. Additionally, ablation experiments verify the effectiveness and necessity of the individual functional modules.

]]>Symmetry doi: 10.3390/sym16091182

Authors: Han Wang Yang Liu Haiyan Shi

In the field of statistics, uncertain regression analysis occupies an important position. It can thoroughly analyze data sets contained in complex uncertainties, aiming to quantify and reveal the intricate relationships between variables. It is worth noting that the traditional least squares method only takes into account the reduction in the deviations between predictions and observations, and fails to fully consider the inherent characteristics of the correlation uncertainty distributions under the uncertain regression framework. In light of this, this paper constructs a statistical invariant with symmetric uncertainty distribution based on the observations and the disturbance term. It also proposes the least squares estimation of unknown parameters and disturbance term in the uncertain regression model based on the least squares principle and, combined with the mathematical properties of the normal uncertainty distribution, gives a numerical algorithm for solving specific estimates. Finally, in order to verify the effectiveness of the least squares estimation method proposed in this paper, we also design two numerical examples and an empirical study of forecasting of electrical power output.

]]>Symmetry doi: 10.3390/sym16091181

Authors: Pramote Sittijuk Kreangsak Tamee

We introduce the random high-local performance client selection strategy, termed Fed-RHLP. This approach allows opportunities for higher-performance clients to contribute more significantly by updating and sharing their local models for global aggregation. Nevertheless, it also enables lower-performance clients to participate collaboratively based on their proportional representation determined by the probability of their local performance on the roulette wheel (RW). Improving symmetry in federated learning involves IID Data: symmetry is naturally present, making model updates easier to aggregate and Non-IID Data: asymmetries can impact performance and fairness. Solutions include data balancing, adaptive algorithms, and robust aggregation methods. Fed-RHLP enhances federated learning by allowing lower-performance clients to contribute based on their proportional representation, which is determined by their local performance. This fosters inclusivity and collaboration in both IID and Non-IID scenarios. In this work, through experiments, we demonstrate that Fed-RHLP offers accelerated convergence speed and improved accuracy in aggregating the final global model, effectively mitigating challenges posed by both IID and Non-IID Data distribution scenarios.

]]>Symmetry doi: 10.3390/sym16091180

Authors: Ahmet Mehmet Karadeniz Áron Ballagi László T. Kóczy

This research introduces an innovative approach for End-to-End steering angle prediction and its control in electric power steering (EPS) systems. The methodology integrates transfer learning-based computer vision techniques for prediction and control with fuzzy signatures-enhanced fuzzy systems. Fuzzy signatures are unique multidimensional data structures that represent data symbolically. This enhancement enables the fuzzy systems to effectively manage the inherent imprecision and uncertainty in various driving scenarios. The ultimate goal of this work is to assess the efficiency and performance of this combined approach by highlighting the pivotal role of steering angle prediction and control in the field of autonomous driving systems. Specifically, within EPS systems, the control of the motor directly influences the vehicle&rsquo;s path and maneuverability. A significant breakthrough of this study is the successful application of transfer learning-based computer vision techniques to extract respective visual data without the need for large datasets. This represents an advancement in reducing the extensive data collection and computational load typically required. The findings of this research reveal the potential of this approach within EPS systems, with an MSE score of 0.0386 against 0.0476, by outperforming the existing NVIDIA model. This result provides a 22.63% better Mean Squared Error (MSE) score than NVIDIA&rsquo;s model. The proposed model also showed better performance compared with all other three references found in the literature. Furthermore, we identify potential areas for refinement, such as decreasing model loss and simplifying the complex decision model of fuzzy systems, which can represent the symmetry and asymmetry of human decision-making systems. This study, therefore, contributes significantly to the ongoing evolution of autonomous driving systems.

]]>Symmetry doi: 10.3390/sym16091179

Authors: Ramandeep Behl Ioannis K. Argyros

Many problems in scientific research are reduced to a nonlinear equation by mathematical means of modeling. The solutions of such equations are found mostly iteratively. Then, the convergence order is routinely shown using Taylor formulas, which in turn make sufficient assumptions about derivatives which are not present in the iterative method at hand. This technique restricts the usage of the method which may converge even if these assumptions, which are not also necessary, hold. The utilization of these methods can be extended under less restrictive conditions. This new paper contributes in this direction, since the convergence is established by assumptions restricted exclusively on the functions present on the method. Although the technique is demonstrated on a two-step Traub-type method with usually symmetric parameters and weight functions, due to its generality it can be extended to other methods defined on the real line or more abstract spaces. Numerical experimentation complement and further validate the theory.

]]>Symmetry doi: 10.3390/sym16091178

Authors: Peibo Yu Jianjie Zhang Baobao Zhang Jianhui Cao Yihang Peng

The diagnosis of bearing faults is a crucial aspect of ensuring the optimal functioning of mechanical equipment. However, in practice, the use of small samples and variable operating conditions may result in suboptimal generalization performance, reduced accuracy, and overfitting for these methods. To address this challenge, this study proposes a bearing fault diagnosis method based on a symmetric two-stream convolutional neural network (CNN). The method employs hybrid signal processing techniques to address the issue of limited data. The method employs a symmetric parallel convolutional neural network (CNN) for the analysis of bearing data. Initially, the data are transformed into time&ndash;frequency maps through the utilization of the short-time Fourier transform (STFT) and the simultaneous compressed wavelet transform (SCWT). Subsequently, two sets of one-dimensional vectors are generated by reconstructing the high-resolution features of the faulty samples using a symmetric parallel convolutional neural network (CNN). Feature splicing and fusion are then performed to generate bearing fault diagnosis information and assist fault classification. The experimental results demonstrate that the proposed mixed-signal processing method is effective on small-sample datasets, and verify the feasibility and generality of the symmetric parallel CNN-support vector machine (SVM) model for bearing fault diagnosis under small-sample conditions.

]]>Symmetry doi: 10.3390/sym16091177

Authors: Tamrat D. Chala László T. Kóczy

In this study, the concept of symmetry is employed to implement an intelligent fuzzy traffic signal control system for complex intersections. This approach suggests that the implementation of reduced fuzzy rules through the reduction method, without compromising the performance of the original fuzzy rule base, constitutes a symmetrical approach. In recent decades, urban and city traffic congestion has become a significant issue because of the time lost as a result of heavy traffic, which negatively affects economic productivity and efficiency and leads to energy loss, and also because of the heavy environmental pollution effect. In addition, traffic congestion prevents an immediate response by the ambulance, police, and fire brigades to urgent events. To mitigate these problems, a three-stage intelligent and flexible fuzzy traffic control system for complex intersections, using a novel hybrid reduction approach was proposed. The three-stage fuzzy traffic control system performs four primary functions. The first stage prioritizes emergency car(s) and identifies the degree of urgency of the traffic conditions in the red-light phase. The second stage guarantees a fair distribution of green-light durations even for periods of extremely unbalanced traffic with long vehicle queues in certain directions and, especially, when heavy traffic is loaded for an extended period in one direction and the short vehicle queues in the conflicting directions require passing in a reasonable time. The third stage adjusts the green-light time to the traffic conditions, to the appearance of one or more emergency car(s), and to the overall waiting times of the other vehicles by using a fuzzy inference engine. The original complete fuzzy rule base set up by listing all possible input combinations was reduced using a novel hybrid reduction algorithm for fuzzy rule bases, which resulted in a significant reduction of the original base, namely, by 72.1%. The proposed novel approach, including the model and the hybrid reduction algorithm, were implemented and simulated using Python 3.9 and SUMO (version 1.14.1). Subsequently, the obtained fuzzy rule system was compared in terms of running time and efficiency with a traffic control system using the original fuzzy rules. The results showed that the reduced fuzzy rule base had better results in terms of the average waiting time, calculated fuel consumption, and CO2 emission. Furthermore, the fuzzy traffic control system with reduced fuzzy rules performed better as it required less execution time and thus lower computational costs. Summarizing the above results, it may be stated that this new approach to intersection traffic light control is a practical solution for managing complex traffic conditions at lower computational costs.

]]>Symmetry doi: 10.3390/sym16091176

Authors: Shih Yu Chang Yimin Wei

The original Choi&ndash;Davis&ndash;Jensen&rsquo;s inequality, known for its extensive applications in various scientific and engineering fields, has inspired researchers to pursue its generalizations. In this study, we extend the Choi&ndash;Davis&ndash;Jensen&rsquo;s inequality by introducing a nonlinear map instead of a normalized linear map and generalize the concept of operator convex functions to include any continuous function defined within a compact region. Notably, operators can be matrices with structural symmetry, enhancing the scope and applicability of our results. The Stone&ndash;Weierstrass theorem and the Kantorovich function play crucial roles in the formulation and proof of these generalized Choi&ndash;Davis&ndash;Jensen&rsquo;s inequalities. Furthermore, we demonstrate an application of this generalized inequality in the context of statistical physics.

]]>Symmetry doi: 10.3390/sym16091175

Authors: Sergio Elaskar Pascal Bruel Luis Gutiérrez Marcantoni

Many physical processes feature random telegraph signals, e.g., a time signal c(t) that randomly switches between two values over time. The present study focuses on the class of telegraphic processes for which the transition rates are formulated by using fractal-like expressions. By considering various restrictive hypotheses regarding the statistics of the waiting times, the present analysis provides the corresponding expressions of the unconditional and conditional probabilities, the mean waiting times, the mean phase duration, the autocorrelation function and the associated integral time scale, the spectral density, and the mean switching frequency. To assess the relevance of the various hypotheses, synthetically generated signals were constructed and used as references to evaluate the predictive quality of the theoretically derived expressions. The best predictions were obtained by considering that the waiting times probability density functions were Dirac peaks centered on the corresponding mean values.

]]>Symmetry doi: 10.3390/sym16091174

Authors: Irina Volokitina Andrey Volokitin Evgeniy Panin Bolat Makhmutov

This article presents the results of research on a new combined process involving multi-cycle wire-drawing and subsequent cryogenic cooling after each deformation stage. For theoretical research, modeling in the Deform software was performed. The analysis of temperature fields and the martensitic component in all models showed that for both considered thicknesses, the most effective option is a low deformation velocity and the conduct of a process without heating. The least effective option is to use an increased thickness of the workpiece at an increased deformation velocity and the conduct of a process without of heating to ambient temperature, which acts as a local cooling of the axial zone of the workpiece with an increase in the workpiece thickness. An analysis of laboratory studies on this combined process revealed that in the absence of intermediate heating of a wire between deformation cycles, 100% martensite is formed in the structure. However, if intermediate heating to 20 &deg;C between deformation cycles is carried out, a gradient distribution of martensite can be obtained. And, since the wire has a circular cross-section, in all cases, martensite is distributed symmetrically about the center of the workpiece.

]]>Symmetry doi: 10.3390/sym16091173

Authors: Liping Zhou Xu Liu Ruiqing Tian Wuqi Wang Guowei Jin

The osprey optimization algorithm (OOA) is a metaheuristic algorithm with a simple framework, which is inspired by the hunting process of ospreys. To enhance its searching capabilities and overcome the drawbacks of susceptibility to local optima and slow convergence speed, this paper proposes a modified osprey optimization algorithm (MOOA) by integrating multiple advanced strategies, including a L&eacute;vy flight strategy, a Brownian motion strategy and an RFDB selection method. The L&eacute;vy flight strategy and Brownian motion strategy are used to enhance the algorithm&rsquo;s exploration ability. The RFDB selection method is conducive to search for the global optimal solution, which is a symmetrical strategy. Two sets of benchmark functions from CEC2017 and CEC2022 are employed to evaluate the optimization performance of the proposed method. By comparing with eight other optimization algorithms, the experimental results show that the MOOA has significant improvements in solution accuracy, stability, and convergence speed. Moreover, the efficacy of the MOOA in tackling real-world optimization problems is demonstrated using five engineering optimization design problems. Therefore, the MOOA has the potential to solve real-world complex optimization problems more effectively.

]]>Symmetry doi: 10.3390/sym16091169

Authors: Alhanouf Ali Alhomaidhi Sami Alabiad Nawal A. Alsarori

Let u,v, and w be indeterminates over Fpm and let R=Fpm+uFpm+vFpm+wFpm, where p is a prime. Then, R is a ring of order p4m, and R&cong;Fpm[u,v,w]I with maximal ideal J=uFpm+vFpm+wFpm of order p3m and a residue field Fpm of order pm, where I is an appropriate ideal. In this article, the goal is to improve the understanding of linear codes over local non-chain rings. In particular, we investigate the symmetrized weight enumerators and generator matrices of linear codes of length N over R. In order to accomplish that, we first list all such rings up to the isomorphism for different values of the index of nilpotency l of J, 2&le;l&le;4. Furthermore, we fully describe the lattice of ideals of R and their orders. Next, for linear codes C over R, we compute the generator matrices and symmetrized weight enumerators, as shown by numerical examples.

]]>Symmetry doi: 10.3390/sym16091171

Authors: Mingyao Huang Wenjing Shi Lu Li

Metal carbenes are widely acknowledged as a category of highly effective intermediates that facilitate otherwise inaccessible transformations. In recent decades, carbene chemistry has made considerable advances and has demonstrated remarkable abilities in the formation of diverse chemical bonds and the synthesis of structurally distinctive molecules. Nevertheless, the majority of research within this field has concentrated on &alpha;-carbon-substituted carbenes, with comparatively little investigation of carbenes that have been functionalized with a wider structural variety, particularly those that have been substituted with heteroatoms (e.g., O, N, P, S, Si, Ge, Sn and B). The objective of this review is to elucidate the advancements in enantioselective transfer reactions involving metal carbenes substituted with these elements, thereby highlighting their contribution to the expansion of the structural diversity and synthetic utility of carbenes in contemporary chemistry.

]]>Symmetry doi: 10.3390/sym16091172

Authors: Nasser H. Sweilam Seham M. Al-Mekhlafi Waleed S. Abdel Kareem Ghader Alqurishi

Two novel crossover models for breast cancer that incorporate &Psi;-Caputo fractal variable-order fractional derivatives, fractal fractional-order derivatives, and variable-order fractional stochastic derivatives driven by variable-order fractional Brownian motion and the crossover model for breast cancer that incorporates Atangana&ndash;Baleanu Caputo fractal variable-order fractional derivatives, fractal fractional-order derivatives, and variable-order fractional stochastic derivatives driven by variable-order fractional Brownian motion are presented here, where we used a simple nonstandard kernel function &Psi;(t) in the first model and a non-singular kernel in the second model. Moreover, we evaluated our models using actual statistics from Saudi Arabia. To ensure consistency with the physical model problem, the symmetry parameter &zeta; is introduced. We can obtain the fractal variable-order fractional Caputo and Caputo&ndash;Katugampola derivatives as special cases from the proposed &Psi;-Caputo derivative. The crossover dynamics models define three alternative models: fractal variable-order fractional model, fractal fractional-order model, and variable-order fractional stochastic model over three-time intervals. The stability of the proposed model is analyzed. The &Psi;-nonstandard finite-difference method is designed to solve fractal variable-order fractional and fractal fractional models, and the Toufik&ndash;Atangana method is used to solve the second crossover model with the non-singular kernel. Also, the nonstandard modified Euler&ndash;Maruyama method is used to study the variable-order fractional stochastic model. Numerous numerical tests and comparisons with real data were conducted to validate the methods&rsquo; efficacy and support the theoretical conclusions.

]]>Symmetry doi: 10.3390/sym16091170

Authors: Vasile Dragan Ioan-Lucian Popa

This paper focuses on addressing the linear quadratic (LQ) optimal control problem on an infinite time horizon for stochastic systems controlled by impulses. No constraint regarding the sign of the quadratic functional is applied. That is why our first concern is to find conditions which guarantee that the considered optimal control problem is well posed. Then, when the optimal control problem is well posed, it is natural to look for conditions which guarantee the attainability of the optimal control problem that is being evaluated. The main tool involved in the solution of the problems stated before is a backward jump matrix linear differential equation (BJMLDE) with a Riccati-type jumping operator. This is formulated using the matrix coefficients of the controlled system and the weight matrices of the performance criterion. We show that the well posedness of the optimal control problem under investigation is guaranteed by the existence of the maximal and bounded solution of the associated BJMLDE with a Riccati-type jumping operator. Further, we show that when the associated BJMLDE with a Riccati-type jumping operator has a maximal solution which satisfies a suitable sign condition, then the optimal control problem is attainable if and only if it has an optimal control in a state feedback form, or if and only if the maximal solution of the BJMLDE with a Riccati-type jumping operator is a stabilizing solution. In order to make the paper more self-contained, we present a set of conditions that correspond to the existence of the maximal solution of the BJMLDE satisfying the desired sign condition.

]]>Symmetry doi: 10.3390/sym16091168

Authors: Maria Pia Lucia Claudia Salera Pierpaolo Zivi Marco Iosa Anna Pecchinenda

A visual stimulus that is divided in harmonic proportions is often judged as more pleasant than others. This is well known by artists that often used two main types of geometric harmonic patterns: symmetry and the golden ratio. Symmetry refers to the property of an object to have two similar halves, whereas the golden ratio consists of dividing an object in a major and a minor part so that their proportion is the same as that between the whole object and its major part. Here we investigated looking behaviour and explicit preferences for different regularities including symmetry and golden ratio. We selected four Mark Rothko&rsquo;s paintings, a famous abstract expressionism artist, characterized by two main areas depicted by different colours: one symmetric (ratio between areas: 50&ndash;50%), one in golden ratio (38&ndash;62%), one in an intermediate ratio (46&ndash;54%), and one in a ratio exceeding the golden ratio (32&ndash;68%). Thirty-six healthy participants (24.75 &plusmn; 3.71 years old) completed three tasks: observation task (OT), pleasantness task (PT), and harmony task (HT). Findings for explicit ratings of pleasantness and harmony were very similar and were not significantly correlated with patterns of looking behaviour. Eye Dwell Time mainly depended on stimuli orientation (p &lt; 0.001), but for the harmony task also by ratio and their interaction. Our results showed that the visual scanning behaviour of abstract arts primarily depends on the orientation of internal components, whereas their proportion is more important for the pleasantness and harmony explicit judgments.

]]>Symmetry doi: 10.3390/sym16091167

Authors: Mengyan Xie Qing-Wen Wang Yang Zhang

In this paper, we develop an effective iterative algorithm to solve a generalized Sylvester tensor equation over quaternions which includes several well-studied matrix/tensor equations as special cases. We discuss the convergence of this algorithm within a finite number of iterations, assuming negligible round-off errors for any initial tensor. Moreover, we demonstrate the unique minimal Frobenius norm solution achievable by selecting specific types of initial tensors. Additionally, numerical examples are presented to illustrate the practicality and validity of our proposed algorithm. These examples include demonstrating the algorithm&rsquo;s effectiveness in addressing three-dimensional microscopic heat transport and color video restoration problems.

]]>Symmetry doi: 10.3390/sym16091166

Authors: Fuqiang Yang Yue Zhang Xuechen Zhao Shengnan Pang

In the realm of artificial intelligence, knowledge graphs (KGs) serve as an essential structured framework, capturing intricate relationships between diverse entities and supporting a broad spectrum of AI applications. Despite their utility, the static characteristic of KGs poses challenges in dynamically evolving information landscapes. This has catalyzed the development of temporal knowledge graphs (TKGs), which introduce a temporal layer to KGs, facilitating the representation of knowledge progression through time. This study zeroes in on the critical task of TKG extrapolation, which is vital for forecasting future occurrences and offering foresight into emerging situations across a variety of fields. Most contemporary approaches to TKG extrapolation are predicated on the symmetrical encoder&ndash;decoder paradigm, wherein the processes of representation learning and reasoning are harmoniously intertwined. While the encoder often garners the most attention due to its role in capturing and encoding information, the pivotal role of the decoder, which is often overlooked, is essential for direct inference and the accurate projection of temporal dynamics. To this end, we present the Householder-transformation-based temporal knowledge graph extrapolation (HTKGE) method: a groundbreaking encoder&ndash;decoder framework that reimagines the decoder&rsquo;s contribution to TKG extrapolation. Our approach spotlights an adaptive decoder propelled by Householder transformations, which engage dynamically with the temporal encoding from the encoder. This interaction fosters a nuanced comprehension of the TKG&rsquo;s temporal trajectory. Our empirical evaluations across four benchmark TKG datasets substantiate HTKGE&rsquo;s consistent efficacy in TKG extrapolation tasks.

]]>Symmetry doi: 10.3390/sym16091165

Authors: Gautham Krishnamoorthy Nasim Gholizadeh

There is a prevailing consensus that most Computational Fluid Dynamics (CFD) frameworks can accurately predict global variables under laminar flow conditions within the Food and Drug Administration (FDA) benchmark nozzle geometry. However, variations in derived variables, such as strain rate and vorticity, may arise due to differences in numerical solvers and gradient evaluation methods, which can subsequently impact predictions related to blood damage and non-Newtonian flow behavior. To examine this, flow symmetry indices, vortex characteristics, and blood damage&mdash;were assessed using Newtonian and four non-Newtonian viscosity models with CFD codes Ansys Fluent and OpenFOAM on identical meshes. At Reynolds number (Re) 500, symmetry breakdown and complex vortex shapes were predicted with some non-Newtonian models in both OpenFOAM and Ansys Fluent, whereas these phenomena were not observed with the Newtonian model. This contradicted the expectation that employing a non-Newtonian model would delay the onset of turbulence. Similarly, at Re 2000, symmetry breakdown occurred sooner (following the sudden expansion section) with the non-Newtonian models in both Ansys Fluent and OpenFOAM. Vortex identification based on the Q-criterion resulted in distinctly different vortex shapes in Ansys Fluent and OpenFOAM. Blood damage assessments showed greater prediction variations among the non-Newtonian models at lower Reynolds numbers.

]]>Symmetry doi: 10.3390/sym16091164

Authors: Eunghyun Lee

Let us consider a two-sided multi-species stochastic particle model with finitely many particles on Z, defined as follows. Suppose that each particle is labelled by a positive integer l, and waits a random time exponentially distributed with rate 1. It then chooses the right direction to jump with probability p, or the left direction with probability q=1&minus;p. If the particle chooses the right direction, it jumps to the nearest site occupied by a particle l&prime;&lt;l (with the convention that an empty site is considered as a particle with labelled 0). If the particle chooses the left direction, it jumps to the next site on the left only if that site is either empty or occupied by a particle l&prime;&lt;l, and in the latter case, particles l and l&prime; swap their positions. We show that this model is integrable, and provide the exact formula of the transition probability using the Bethe ansatz.

]]>Symmetry doi: 10.3390/sym16091163

Authors: Phatlada Sathongpaen Suphawich Jindanate Attapon Amthong

The two-dimensional (2D) hydrogen atom is a fundamental atomic model that is important for various technologies based on 2D materials. Here, the atomic model is revisited to enhance understanding of the hydrogen wavefunctions. Unlike in previous studies, we propose an alternative expression of azimuthal wavefunctions, which are the eigenstates of the square of angular momentum and exhibit rotational symmetry. Remarkably, our expression leads to the rotation and oscillation along the azimuthal direction of the probability densities, which do not appear in the conventional wavefunctions. These behaviors are validated by the numerical results obtained through the 2D finite difference approach. Variation in oscillator strengths due to the rotation of wavefunctions is observed in our proposed 2D hydrogen wavefunctions, whereas those due to the conventional wavefunctions remain constant. More importantly, the proposed wavefunctions&rsquo; advantage is illustrating the orbital shapes of the planar hydrogen states, whose orientation is labeled here using Cartesian representation for the first time. This study can be applied to visualize the orbital characteristics of the states in quantum confinement with a radial potential.

]]>Symmetry doi: 10.3390/sym16091162

Authors: Peter Senger

The investigation of the nuclear matter equation of state (EOS) beyond saturation density has been a fundamental goal of heavy ion collision experiments for more than 40 years. First constraints on the EOS of symmetric nuclear matter at high densities were extracted from heavy ion data measured at AGS and GSI. At GSI, symmetry energy has also been investigated in nuclear collisions. These results of laboratory measurements are complemented by the analysis of recent astrophysical observations regarding the mass and radius of neutron stars and gravitational waves from neutron star merger events. The research programs of upcoming laboratory experiments include the study of the EOS at neutron star core densities and will also shed light on the elementary degrees of freedom of dense QCD matter. The status of the CBM experiment at FAIR and the perspective regarding the studies of the EOS of symmetric and asymmetric dense nuclear matter will be presented.

]]>Symmetry doi: 10.3390/sym16091161

Authors: Yushu Zhang Fangcheng Tang Zeyuan Song Jun Wang

It is widely known that symmetry does exist in management systems, such as economics, management, and even daily life. In addition, effective and qualified decision-making methods can enhance the performance and symmetry of management systems. Hence, this paper focuses on a decision-making method. Linguistic interval-valued q-rung orthopair fuzzy sets (LIVq-ROFSs) have recently been proposed as being effective in describing decision-makers&rsquo; evaluation values in complex situations. This paper proposes a novel multi-attribute group decision-making (MAGDM) method with LIVq-ROFSs to handle realistic decision-making problems. The main contributions of this study are three-fold. First, a new method for determining the weight information of attributes based on decision makers&rsquo; evaluation values is proposed. Second, the classical TODIM is extended into LIVq-ROFSs and a new decision-making method is proposed. Third, our proposed MAGDM method is applied to a real decision-making problem to reveal its effectiveness.

]]>Symmetry doi: 10.3390/sym16091160

Authors: Shanshan Zhang Yaxuan Zhang Waichon Lio Rui Kang

Brucellosis, as an infectious disease that affects both humans and livestock, poses a serious threat to human health and has a severe impact on economic development. Essentially, brucellosis transmission is a kind of study in biological systems, and the epistemic uncertainty existing in the data of confirmed brucellosis cases in China is realized as significant uncertainty that needs to be addressed. Therefore, this paper proposes an uncertain time series model to explore the confirmed brucellosis cases in China. Then, some methods based on uncertain statistics and symmetry of the biological system are applied, including order estimation, parameter estimation, residual analysis, uncertain hypothesis test, and forecast. The proposed model is practically applied to the data of confirmed brucellosis cases in China from January 2017 to December 2020, and the results show that the uncertain model fits the observed data better than the probabilistic model due to the frequency instability inherent in the data of confirmed brucellosis cases. Based on the proposed model and statistical method, this paper develops an approach to rapidly forecast the number of confirmed brucellosis cases in small sample scenarios, which can contribute to epidemic control in real application.

]]>Symmetry doi: 10.3390/sym16091159

Authors: Ayse Yilmaz Ceylan Buket Simsek

The aim of this paper is to derive formulae for the generating functions of the Bernstein type polynomials. We give a PDE equation for this generating function. By using this equation, we give recurrence relations for the Bernstein polynomials. Using generating functions, we also derive some identities including a symmetry property for the Bernstein type polynomials. We give some relations among the Bernstein type polynomials, Bernoulli numbers, Stirling numbers, Dahee numbers, the Legendre polynomials, and the coefficients of the classical superoscillatory function associated with the weak measurements. We introduce some integral formulae for these polynomials. By using these integral formulae, we derive some new combinatorial sums involving the Bernoulli numbers and the combinatorial numbers. Moreover, we define Bezier type curves in terms of these polynomials.

]]>Symmetry doi: 10.3390/sym16091158

Authors: Przemysław Snopiński Marek Barlak Katarzyna Nowakowska-Langier

In recent years, revolutionary improvements in the properties of certain FCC metals have been achieved by increasing the proportion of twin-related, highly symmetric grain boundaries. Various thermomechanical routes of grain boundary engineering (GBE) processing have been employed to enhance the fraction of low &Sigma;CSL grain boundaries, thereby improving the radiation tolerance of many polycrystalline materials. This improvement is due to symmetric twin boundaries acting as effective sinks for defects caused by radiation, thus enhancing the material&rsquo;s performance. In this study, the LPBF AlSi10Mg alloy was post-processed via the KOBO extrusion method. Subsequently, the samples were subjected to irradiation with Ar+ ions at an ion fluence of 5 &times; 1017 cm&minus;2. The microstructures of the samples were thoroughly investigated using electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), and high-resolution TEM (HRTEM). The results showed that KOBO processing led to the formation of an ultrafine-grained microstructure with a mean grain size of 0.8 &micro;m. Moreover, it was revealed that the microstructure of the KOBO-processed sample exhibited an increased fraction of low-&Sigma;CSL boundaries. Specifically, the fraction of &Sigma;11 boundaries increased from approximately 2% to 8%. Post-irradiation microstructural analysis revealed improved radiation tolerance in the KOBO-processed sample, indicating a beneficial influence of the increased grain boundary fraction and low-&Sigma;CSL boundary fraction on the irradiation resistance of the AlSi10Mg alloy. This research provides valuable insights for the development of customized microstructures with enhanced radiation tolerance, which has significant implications for the advancement of materials in nuclear and aerospace applications.

]]>Symmetry doi: 10.3390/sym16091157

Authors: Modjtaba Ghorbani Razie Alidehi-Ravandi Matthias Dehmer

The study delves into the relationship between symmetry groups and automorphism groups in polyhedral graphs, emphasizing their interconnected nature and their significance in understanding the symmetries and structural properties of fullerenes. It highlights the visual importance of symmetry and its applications in architecture, as well as the mathematical structure of the automorphism group, which captures all of the symmetries of a graph. The paper also discusses the significance of groups in Abstract Algebra and their relevance to understanding the behavior of mathematical systems. Overall, the findings offer an inclusive understanding of the relationship between symmetry groups and automorphism groups, paving the way for further research in this area.

]]>Symmetry doi: 10.3390/sym16091156

Authors: Taher S. Hassan Loredana Florentina Iambor Sorin Mureşan Khalid Alenzi Ismoil Odinaev Khudhayr A. Rashedi

This paper investigates second-order functional dynamic equations with mixed nonlinearities on an arbitrary unbounded above-time scale, T. We will use a unified time scale approach and the well-known Riccati technique to derive oscillation criteria of the Nehari-type for second-order dynamic equations. The findings demonstrate a significant improvement in the literature on dynamic equations. The symmetry is beneficial and influential in defining the right style of study for the qualitative behavior of solutions to dynamic equations. We include an example to demonstrate the significance of our results.

]]>Symmetry doi: 10.3390/sym16091155

Authors: Howard E. Haber

Explicit formulae for the 4&times;4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4&times;4 real matrix A, where A is a product of the diagonal matrix diag(+1,&minus;1,&minus;1,&minus;1) and an arbitrary 4&times;4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product &eta;&dagger;&sigma;&macr;&mu;&chi; transforms as a Lorentz four-vector, where &chi; and &eta; are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation &Lambda; reduces to the computation of the trace of a product of 2&times;2 matrices. Both computations are shown to yield equivalent expressions for &Lambda;.

]]>Symmetry doi: 10.3390/sym16091154

Authors: Noor Alam Shahid Ahmad Wani Waseem Ahmad Khan Fakhredine Gassem Anas Altaleb

The primary objective of this research is to introduce and investigate novel polynomial variants termed &Delta;h Laguerre polynomials. This unique polynomial type integrates the monomiality principle alongside operational rules. Through this innovative approach, the study delves into uncharted territory, unveiling fresh insights that build upon prior research endeavours. Notably, the &Delta;h Laguerre polynomials exhibit significant utility in the realm of quantum mechanics, particularly in the modelling of entropy within quantum systems. The research meticulously unveils explicit formulas and elucidates the fundamental properties of these polynomials, thereby forging connections with established polynomial categories. By shedding light on the distinct characteristics and functionalities of the &Delta;h Laguerre polynomials, this study contributes significantly to their comprehension and application across diverse mathematical and scientific domains.

]]>Symmetry doi: 10.3390/sym16091153

Authors: Yue Xiang Jingjing Guo Zhengyan Mao Chao Jiang Mandan Liu

This paper presents a novel algorithm named Five-element Cycle Integrated Mutation Optimization (FECOIMO) for solving the Traveling Thief Problem (TTP). The algorithm introduces a five-element cycle structure that integrates various mutation operations to enhance both global exploration and local exploitation capabilities. In experiments, FECOIMO was extensively tested on 39 TTP instances of varying scales and compared with five common metaheuristic algorithms: Enhanced Simulated Annealing (ESA), Improved Grey Wolf Optimization Algorithm (IGWO), Improved Whale Optimization Algorithm (IWOA), Genetic Algorithm (GA), and Profit-Guided Coordination Heuristic (PGCH). The experimental results demonstrate that FECOIMO outperforms the other algorithms across all instances, particularly excelling in large-scale instances. The results of the Friedman test show that FECOIMO significantly outperforms other algorithms in terms of average solution, maximum solution, and solution standard deviation. Additionally, although FECOIMO has a longer execution time, its complexity is comparable to that of other algorithms, and the additional computational overhead in solving complex optimization problems translates into better solutions. Therefore, FECOIMO has proven its effectiveness and robustness in handling complex combinatorial optimization problems.

]]>Symmetry doi: 10.3390/sym16091152

Authors: Abedel-Karrem Alomari Wael Mahmoud Mohammad Salameh Mohammad Alaroud Nedal Tahat

This research focuses on finding multiple solutions (MSs) to nonlinear fractional boundary value problems (BVPs) through a new development, namely the predictor Laplace fractional power series method. This method predicts the missing initial values by applying boundary or force conditions. This research provides a set of theorems necessary for deriving the recurrence relations to find the series terms. Several examples demonstrate the efficacy, convergence, and accuracy of the algorithm. Under Caputo&rsquo;s definition of the fractional derivative with symmetric order, the obtained results are visualized numerically and graphically. The behavior of the generated solutions indicates that altering the fractional derivative parameters within their domain symmetrically changes these solutions, ultimately aligning them with the standard derivative. The results are compared with the homotopy analysis method and are presented in various figures and tables.

]]>Symmetry doi: 10.3390/sym16091151

Authors: Ammar Boulaiche Sofiane Haddad Ali Lemouari

In the last few years, the use of convolutional neural networks (CNNs) in intrusion detection domains has attracted more and more attention. However, their results in this domain have not lived up to expectations compared to the results obtained in other domains, such as image classification and video analysis. This is mainly due to the datasets used, which contain preprocessed features that are not compatible with convolutional neural networks, as they do not allow a full exploit of all the information embedded in the original network traffic. With the aim of overcoming these issues, we propose in this paper a new efficient convolutional neural network model for network intrusion detection based on raw traffic data (pcap files) rather than preprocessed data stored in CSV files. The novelty of this paper lies in the proposal of a new method for adapting the raw network traffic data to the most suitable format for CNN models, which allows us to fully exploit the strengths of CNNs in terms of pattern recognition and spatial analysis, leading to more accurate and effective results. Additionally, to further improve its detection performance, the structure and hyperparameters of our proposed CNN-based model are automatically adjusted using the self-adaptive differential evolution (SADE) metaheuristic, in which symmetry plays an essential role in balancing the different phases of the algorithm, so that each phase can contribute in an equal and efficient way to finding optimal solutions. This helps to make the overall performance more robust and efficient when solving optimization problems. The experimental results on three datasets, KDD-99, UNSW-NB15, and CIC-IDS2017, show a strong symmetry between the frequency values implemented in the images built for each network traffic and the different attack classes. This was confirmed by a good predictive accuracy that goes well beyond similar competing models in the literature.

]]>Symmetry doi: 10.3390/sym16091150

Authors: Oleg I. Kolodiazhnyi Anastasiia O. Kolodiazhna Oleh Faiziiev Yuliia Gurova

The hydrolase-catalyzed kinetic resolution of fluorinated racemates of 3-arylcarboxylic acids is described. Hydrolysis of ethyl esters of fluorinated acids by esterases and hydrolases in all cases resulted in the formation of hydrolyzed (S)-carboxylic acids and unreacted (R)-esters in high yields and high enantiomeric purity. The influence of separation conditions on the efficiency and enantioselectivity of biocatalytic conversion was also studied. The reactions were carried out under normal conditions (stirring with a magnetic stirrer at room temperature) and microwave irradiation in the presence of hydrolases. Amano PS showed excellent selectivity and good yields in the hydrolysis of fluorinated aromatic compounds. The absolute configuration of the resulting compounds was based on biokinetic studies and the use of chiral HPLC. A molecular modeling of the kinetic resolution of carboxylic acid esters was carried out.

]]>Symmetry doi: 10.3390/sym16091149

Authors: Zhaoguo Huang Changxi Ma

To address the symmetry-related resilience issues of stations and lines in urban rail transit networks, we propose a two-stage robust optimization-based approach for urban rail transit network planning. In this context, resilience is conceptualized as the ability of the network to maintain its operational symmetry under normal and disruptive conditions. Firstly, we used passenger flow distributions as decision variables to construct a two-stage symmetry-based urban rail transit network planning model, aiming to simultaneously minimize the total cost and total operating time of the network while preserving its functional symmetry. Secondly, we designed a hybrid evolutionary algorithm with chromosomes having a two-layer encoding structure, where the Niched Pareto Genetic Algorithm served as the main algorithmic framework, and a Large Neighborhood Search mechanism was designed to optimize the connectivity gene layer of individuals, ensuring the symmetry of network connectivity. Finally, we conducted computational verification on randomly generated instances to confirm the effectiveness of the model and algorithm. The experimental results demonstrated that our method could find two sets of Pareto optimal solutions for cost preference and time preference, thereby preserving the operational symmetry of the network under normal and damaged conditions, as well as reducing the total operating time. This effectively improved the overall efficiency and resilience of the network. Our designed hybrid evolutionary algorithm converged to satisfactory objective values in the early iterations, exhibiting strong search and optimization performance and effectively solving the two-stage symmetry-based urban rail transit network planning model.

]]>Symmetry doi: 10.3390/sym16091148

Authors: Emily C. Marcinowski George F. Michel Eliza L. Nelson

How infants engage with objects changes dramatically over the first year of life. While some infants exhibit a consistent hand preference for acquiring objects during this period, others have no identifiable preference. The goal of this study was to test whether lateralization confers an advantage in the development of early object management skills. We examined whether lateralized infants show different rates of growth in how they interact with multiple objects as compared to infants without a hand preference. In a longitudinal study consisting of seven monthly visits from 6 to 12 months, 303 infants were assessed for their hand preference and object management skill (i.e., holding up to three objects). Group-Based Trajectory Modeling (GBTM) identified the following three hand preference trajectory groups: Left, Right, and No Preference (NP). A Hierarchical Generalized Linear Model (HGLM) with the NP infants as the reference group for statistical comparisons revealed that while all the infants showed similar trends in their object management skills over time, the lateralized infants had an advantage over the non-lateralized infants. The infants in the Right and Left groups transitioned from holding one to two objects more quickly relative to the NP infants. Further research is needed to determine if this early object skill advantage cascades to a more complex handling of multiple objects.

]]>Symmetry doi: 10.3390/sym16091147

Authors: Mingzhi Tang Wenfeng Zhou Yanchao Hu Gang Wang Yanguang Yang

A novel decomposition method that adheres to both local time translation symmetry and spatial rotational symmetry is proposed in this study, thereby extending the limitations of existing methods, which are typically restricted to quasi-two-dimensional configurations. Grounded in the FIK and RD identities, this method provides a clear physical and reliable interpretation suitable for arbitrary-curvature profiles. Utilizing this method, an analysis of the aerothermodynamic characteristics of the bistable states of curved compression ramp flows was conducted. The results reveal that the generation of undisturbed and peak Cf is dominated by viscous dissipation. Specifically, flow separation happens when all of the energy input from the work exerted by the adverse pressure gradient (APG) is insufficient to be entirely converted into local viscous dissipation and kinetic energy. Furthermore, the propensity for flow separation at higher wall temperatures is firstly elucidated quantitatively from the perspective of the work by the APG. The peak heat flux is predominantly triggered by the work of viscous stress, with the secondary contribution from energy transport playing a more significant role in the generation of the peak heat flux of the separation state than that of the attachment state.

]]>Symmetry doi: 10.3390/sym16091146

Authors: Iztok Fajfar Žiga Rojec Árpád Bűrmen Matevž Kunaver Tadej Tuma Sašo Tomažič Janez Puhan

Genetic programming (GP) has a long-standing tradition in the evolution of computer programs, predominantly utilizing tree and linear paradigms, each with distinct advantages and limitations. Despite the rapid growth of the GP field, there have been disproportionately few attempts to evolve &rsquo;real&rsquo; Turing-like imperative programs (as contrasted with functional programming) from the ground up. Existing research focuses mainly on specific special cases where the structure of the solution is partly known. This paper explores the potential of integrating tree and linear GP paradigms to develop an encoding scheme that universally supports genetic operators without constraints and consistently generates syntactically correct Python programs from scratch. By blending the symmetrical structure of tree-based representations with the inherent asymmetry of linear sequences, we created a versatile environment for program evolution. Our approach was rigorously tested on 35 problems characterized by varying Halstead complexity metrics, to delineate the approach&rsquo;s boundaries. While expected brute-force program solutions were observed, our method yielded more sophisticated strategies, such as optimizing a program by restricting the division trials to the values up to the square root of the number when counting its proper divisors. Despite the recent groundbreaking advancements in large language models, we assert that the GP field warrants continued research. GP embodies a fundamentally different computational paradigm, crucial for advancing our understanding of natural evolutionary processes.

]]>Symmetry doi: 10.3390/sym16091145

Authors: Feng Qi

In this paper, by means of the Fa&agrave; di Bruno formula, with the help of explicit formulas for partial Bell polynomials at specific arguments of two specific sequences generated by derivatives at the origin of the inverse sine and inverse cosine functions, and by virtue of two combinatorial identities containing the Stirling numbers of the first kind, the author establishes power series expansions for real powers of the inverse cosine (sine) functions and the inverse hyperbolic cosine (sine) functions. By comparing different series expansions for the square of the inverse cosine function and for the positive integer power of the inverse sine function, the author not only finds infinite series representations of the circular constant &pi; and its real powers, but also derives several combinatorial identities involving central binomial coefficients and the Stirling numbers of the first kind.

]]>Symmetry doi: 10.3390/sym16091144

Authors: Mary G. Thoubaan Dheia G. Salih Al-Khafajy Abbas Kareem Wanas Daniel Breaz Luminiţa-Ioana Cotîrlă

This study aims to analyze how the parameter flow rate and amplitude of walling waves affect the peristaltic flow of Jeffrey&rsquo;s fluid through an irregular channel. The movement of the fluid is described by a set of non-linear partial differential equations that consider the influential parameters. These equations are transformed into non-dimensional forms with appropriate boundary conditions. The study also utilizes dynamic systems theory to analyze the effects of the parameters on the streamline and to investigate the position of critical points and their local and global bifurcation of flow. The research presents numerical and analytical methods to illustrate the impact of flow rate and amplitude changes on fluid transport. It identifies three types of streamline patterns that occur: backwards, trapping, and augmented flow resulting from changes in the value of flow rate parameters.

]]>Symmetry doi: 10.3390/sym16091143

Authors: Khalid Alluhydan Yasser A. Amer Ashraf Taha EL-Sayed Marwa Abdelaziz EL-Sayed

This article presents a novel approach to impact regulation of nonlinear vibrational responses in a beam flutter system subjected to harmonic excitation. This study introduces the use of a Nonlinear Integral Positive Position Feedback (NIPPF) controller for this purpose. This technique models the system as a three-degree-of-freedom nonlinear system representing the beam flutter, coupled with a first-order and a second-order filter representing the NIPPF controller. By applying perturbation analysis to the linearized system model, the authors obtain analytical solutions for the autonomous system with the controller. This study aims to reduce vibration amplitudes in a nonlinear dynamic system, specifically when 1:1 internal resonance occurs. The Routh&ndash;Hurwitz criterion is utilized to evaluate the system&rsquo;s stability. Furthermore, the frequency&ndash;response curves (FRCs) exhibit symmetry across a range of parameter values. The findings highlight that the effectiveness of vibration suppression is directly related to the product of the NIPPF control signal after comparing with different controllers. Numerical simulations, conducted using the fourth-order Runge&ndash;Kutta method, validate the analytical solutions and demonstrate the system&rsquo;s amplitude response. The strong correlation between the analytical and numerical results highlights the accuracy and dependability of the proposed method.

]]>Symmetry doi: 10.3390/sym16091142

Authors: Chunfeng Cui Yong Lu Liqun Qi Ligong Wang

In this paper, we study dual quaternion, dual complex unit gain graphs, and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent rigid movements in the 3D space, and have wide applications in robotics and computer graphics. Dual complex numbers have found application in brain science recently. We establish the interlacing theorem for dual unit gain graphs, and show that the spectral radius of a dual unit gain graph is always not greater than the spectral radius of the underlying graph, and these two radii are equal if, and only if, the dual gain graph is balanced. By using dual cosine functions, we establish the closed form of the eigenvalues of adjacency and Laplacian matrices of dual complex and quaternion unit gain cycles. We then show the coefficient theorem holds for dual unit gain graphs. Similar results hold for the spectral radius of the Laplacian matrix of the dual unit gain graph too.

]]>Symmetry doi: 10.3390/sym16091140

Authors: Zefang Fan Yu Wang Xianggao Wang

We herein study the circular orbit stability of a static black hole system composed of multiple Reissner&ndash;Nordstrom (RN) black holes. By comparing the circular orbits of two static black holes, three static black holes (TBHs), four static black holes and five static black holes at different spacetime, we find that the continuity of their stable circular orbits changes, i.e., the peaks of the effective potentials are transformed from single-peaked to bi-peaked, and that the distance a between the black holes is the main reason for this change. This characteristic is completely different from the continuity of the stable circular orbit interval of any kind of single black hole in the past. After calculation, we obtain several critical values that lead to the change in circular orbit stability. The three fundamental frequencies (orbital frequency, radial local frequency, and vertical local frequency) are derived and compared for two different spacetimes of double and three black holes. We also analyse the effect of the black hole distance a on the three fundamental frequencies of circular orbits.

]]>Symmetry doi: 10.3390/sym16091141

Authors: Enrique Gaztanaga

In relativity, the Newtonian concepts of velocity and acceleration are observer-dependent quantities that vary with the chosen frame of reference. It is well established that in the comoving frame, cosmic expansion is currently accelerating; however, in the rest frame, this expansion is actually decelerating. In this paper, we explore the implications of this distinction. The traditional measure of cosmic acceleration, denoted by q, is derived from the comoving frame and describes the acceleration of the scale factor a for a 3D space-like homogeneous sphere. We introduce a new parameter qE representing the acceleration experienced between observers within the light cone. By comparing qE to the traditional q using observational data from Type Ia supernovae (SN) and the radial clustering of galaxies and quasars (BAO)&mdash;including the latest results from DESI2024&mdash;our analysis demonstrates that qE aligns more closely with these data. The core argument of the paper is that &Lambda;&mdash;regardless of its origin&mdash;creates an event horizon that divides the manifold into two causally disconnected regions analogous to conditions inside a black hole&rsquo;s interior, thereby allowing for a rest-frame perspective qE in which cosmic expansion appears to be decelerating and the horizon acts like a friction term. Such a horizon suggests that the universe cannot maintain homogeneity outside. The observed cosmological constant &Lambda; can then be interpreted not as a driver of new dark energy or a modification of gravity but as a boundary term exerting an attractive force, akin to a rubber band, resisting further expansion and preventing event horizon crossings. This interpretation calls for a reconsideration of current cosmological models and the assumptions underlying them.

]]>Symmetry doi: 10.3390/sym16091133

Authors: James M. Hill

Lorentz invariance underlies special relativity, and the energy formula and relative velocity formula are well known to be invariant under a Lorentz transformation. Here, we determine the functional forms in terms of four arbitrary functions for those three dimensional velocity fields that are automatically invariant under the most general fully three-dimensional Lorentz transformation. For general three-dimensional motion, using rectangular Cartesian coordinates (x,y,z), we determine the first-order partial differential equations for the three velocity components u(x,y,z,t), v(x,y,z,t) and w(x,y,z,t) in the x&minus;, y&minus; and z&minus;directions respectively. These partial differential equations and the associated partial differential relations connecting energy and momentum are fully compatible with the Lorentz-invariant energy&ndash;momentum relations and appear not to have been given previously in the literature. We determine the spatial and temporal dependence of the functional forms for those three-dimensional velocity fields that are automatically invariant under three-dimensional Lorentz transformations. An interesting special case gives rise to families of particle paths for which the magnitude of the velocity is the speed of light. This is indicative of the abundant possibilities existing in the &ldquo;fast lane&rdquo;.

]]>Symmetry doi: 10.3390/sym16091139

Authors: Rafael Luís Brian Ryals

In this paper, we study the local, global, and bifurcation properties of a planar nonlinear asymmetric discrete model of Ricker type that is derived from a Darwinian evolution strategy based on evolutionary game theory. We make a change of variables to both reduce the number of parameters as well as bring symmetry to the isoclines of the mapping. With this new model, we demonstrate the existence of a forward invariant and globally attracting set where all the dynamics occur. In this set, the model possesses two symmetric fixed points: the origin, which is always a saddle fixed point, and an interior fixed point that may be globally asymptotically stable. Moreover, we observe the presence of a supercritical Neimark&ndash;Sacker bifurcation, a phenomenon that is not present in the original non-evolutionary model.

]]>Symmetry doi: 10.3390/sym16091138

Authors: Dat Ngo Siyeon Han Bongsoon Kang

Multiplication, division, and square root operations introduce significant challenges in digital signal processing (DSP) systems, traditionally requiring multiple operations that increase execution time and hardware complexity. This study presents a novel approach that leverages binary logarithms to perform these operations using only addition, subtraction, and shifts, enabling a unified hardware implementation&mdash;a marked departure from conventional methods that handle these operations separately. The proposed design, involving logarithm and antilogarithm calculations, exhibits an algebraically symmetrical pattern that further optimizes the processing flow. Additionally, this study introduces innovative log-domain correction terms specifically designed to minimize computation errors&mdash;a critical improvement over existing methods that often struggle with precision. Compared to standard hardware implementations, the proposed design significantly reduces hardware resource utilization and power consumption while maintaining high operational frequency.

]]>Symmetry doi: 10.3390/sym16091137

Authors: Alexandru-Nicolae Dimache Ghiocel Groza Marilena Jianu Iulian Iancu

The fractional advection&ndash;dispersion equation is used in groundwater hydrology for modeling the movements of contaminants/solute particles along with flowing groundwater at the seepage velocity in porous media. This model is used for the prediction of the transport of nonreactive dissolved contaminants in groundwater. This paper establishes the existence and the uniqueness of solutions represented as fractional bi-variate power series of some initial-value problems and boundary-value problems for the fractional advection&ndash;dispersion equation. Moreover, a method to approximate the solutions using fractional polynomials in two variables and to evaluate the errors in a suitable rectangle is designed. Illustrative examples showing the applicability of the theoretical results are presented.

]]>Symmetry doi: 10.3390/sym16091135

Authors: M. A. Reyes C. Dalfó M. A. Fiol

The chordal ring (CR) graphs are a well-known family of graphs used to model some interconnection networks for computer systems in which all nodes are in a cycle. Generalizing the CR graphs, in this paper, we introduce the families of chordal multi-ring (CMR), chordal ring mixed (CRM), and chordal multi-ring mixed (CMRM) graphs. In the case of mixed graphs, we can have edges (without direction) and arcs (with direction). The chordal ring and chordal ring mixed graphs are bipartite and 3-regular. They consist of a number r (for r&ge;1) of (undirected or directed) cycles with some edges (the chords) joining them. In particular, for CMR, when r=1, that is, with only one undirected cycle, we obtain the known families of chordal ring graphs. Here, we used plane tessellations to represent our chordal multi-ring graphs. This allowed us to obtain their maximum number of vertices for every given diameter. Additionally, we computationally obtained their minimum diameter for any value of the number of vertices. Moreover, when seen as a lift graph (also called voltage graph) of a base graph on Abelian groups, we obtained closed formulas for the spectrum, that is, the eigenvalue multi-set of its adjacency matrix.

]]>Symmetry doi: 10.3390/sym16091136

Authors: Jing Bai Chunfu Zhang Yanchun Liang Adriano Tavares Lidong Wang Xue Gu Ziyao Meng

The changes in cardiomyocyte action potentials are related to variations in intra- and extracellular ion concentrations. Abnormal ion concentrations can lead to irregular action potentials, subsequently affecting wave propagation in myocardial tissue and potentially resulting in the formation of spiral waves. Therefore, timely monitoring of ion concentration changes is essential. This study presents a novel machine learning classification model that predicts ion concentration changes based on action potential variation data. We conducted simulations using a single-cell model, generating a dataset of 850 action potential variations corresponding to different ion concentration changes. The model demonstrated excellent predictive performance, achieving an accuracy of 0.988 on the test set. Additionally, the causes of spontaneous spiral wave generation in the heart are insufficiently studied. This study presents a new mechanism whereby changes in extracellular potassium ion concentration leads to the spontaneous generation of spiral waves. By constructing composite myocardial tissue containing both myocardial and fibroblast cells, we observed that variations in extracellular potassium ion concentration can either trigger or inhibit cardiomyocyte excitation. We developed three tissue structures, and by appropriately adjusting the extracellular potassium ion concentration, we observed the spontaneous generation of single spiral waves, symmetrical spiral wave pairs, and asymmetrical double spiral waves.

]]>Symmetry doi: 10.3390/sym16091134

Authors: Adeel Ahmad Jianhua Gong Akhter Rasheed Saqib Hussain Asad Ali Zeinebou Cheikh

In our current study, we apply differential subordination and quantum calculus to introduce and investigate a new class of analytic functions associated with the q-differential operator and the symmetric balloon-shaped domain. We obtain sharp results concerning the Maclaurin coefficients the second and third-order Hankel determinants, the Zalcman conjecture, and its generalized conjecture for this newly defined class of q-starlike functions with respect to symmetric points.

]]>Symmetry doi: 10.3390/sym16091132

Authors: Shu-Fei Wu

In many manufacturing industries, the lifetime performance index CL is utilized to assess the manufacturing process performance for products following some lifetime distributions and subjecting them to progressive type I interval censoring. This paper aims to explore the sampling design required to achieve a specified level of significance and test power for products with lifetimes following the Exponentiated Frech&rsquo;et distribution. Since lifetime distribution is an asymmetrical probability distribution, this investigation is related to the topic of asymmetrical probability distributions and applications in various fields. When the termination time is fixed but the number of intervals is variable, the optimal number of inspection intervals and sample sizes yielding the minimized total experimental costs are determined and tabulated. When the termination time is varying, the optimal number of inspection intervals, sample sizes, and equal interval lengths achieving the minimum total experimental costs are determined and tabulated. Optimal parameter values are displayed in tabular form for feasible applications for users. Additionally, a practical example is provided to illustrate how this sampling design can be used to collect data by using the optimal setup of parameters, followed by a testing procedure to assess the capability of the production process.

]]>Symmetry doi: 10.3390/sym16091131

Authors: Grigory E. Volovik

We consider the discrete Z4 symmetry i^, which takes place in the scenario of quantum gravity where the gravitational tetrads emerge as the order parameter&mdash;the vacuum expectation value of the bilinear combination of fermionic operators. Under this symmetry operation, i^, the emerging tetrads are multiplied by the imaginary unit, i^e&mu;a=&minus;ie&mu;a. The existence of such symmetry and the spontaneous breaking of this symmetry are also supported by the consideration of the symmetry breaking scheme in the topological superfluid 3He-B. The order parameter in 3He-B is also the bilinear combination of the fermionic operators. This order parameter is the analog of the tetrad field, but it has complex values. The i^-symmetry operation changes the phase of the complex order parameter by &pi;/2, which corresponds to the Z4 discrete symmetry in quantum gravity. We also considered the alternative scenario of the breaking of this Z4 symmetry, in which the i^-operation changes sign of the scalar curvature, i^R=&minus;R, and thus the Einstein&ndash;Hilbert action violates the i^-symmetry. In the alternative scenario of symmetry breaking, the gravitational coupling K=1/16&pi;G plays the role of the order parameter, which changes sign under i^-transformation.

]]>Symmetry doi: 10.3390/sym16091129

Authors: Xianjian Jin Yinchen Tao Nonsly Valerienne Opinat Ikiela

In this paper, the concept of symmetry is utilized to design the trajectory planning for parallel parking of autonomous ground vehicles&mdash;that is, the construction and the solution of the optimization-based trajectory planning approach are symmetrical. Parking is the main factor that troubles most drivers for their daily driving travel, and it can even lead to traffic congestion in severe cases. With the rise of new intelligent and autonomous vehicles, automatic parking seems to have become a trend. Traditional geometric planning methods are less adaptable to parking scenarios, while the parking paths planned by graph search methods may only achieve local optimality. Additionally, significant computational time is often required by numerical optimization methods to find a parking path when a good initial solution is not available. This paper presents a hierarchical trajectory planning approach for high-quality parallel parking of autonomous ground vehicles. The approach begins with a graph search layer to roughly generate an initial solution, which is refined by a numerical optimization layer to produce a high-quality parallel parking trajectory. Considering the high dimensionality and difficulty of finding an optimal solution for the path planning optimization problem, this paper proposes an improved safe travel corridor (I-STC) with the construction of collision constraints isolated from surrounding environmental obstacles. By constructing collision constraints of the I-STC based on the initial solution, the proposed method avoids the complexities and non-differentiability of traditional obstacle avoidance constraints, and simplifies the problem modeling the subsequent numerical optimization process. The simulation results demonstrate that the I-STC is capable of generating parallel parking trajectories with both comfort and safety.

]]>Symmetry doi: 10.3390/sym16091130

Authors: Jinglei Liu Xiuxin Li Jinyuan Cao Zhengchun Duan Qingzhi Ye Guishuai Feng

To investigate the impact of the geometric parameters of periodic pile barriers on bandgap characteristics in passive vibration isolation, a two-dimensional, three-component unit cell was developed using the finite element method (FEM). This study analyzed the bandgap properties of periodic pile barriers and validated the effectiveness of the FEM through model testing. The FEM was then methodically applied to evaluate the effects of pipe pile thickness, periodic constant, arrangement pattern, and cross-sectional shape on the bandgap characteristics, culminating in the proposition of a novel H-shaped cross-section for the piles. The results demonstrated that the FEM-calculated bandgap frequency range, featuring steel piles arranged in a square pattern, closely aligned with the attenuation zone in the model tests. The lower band frequency (LBF) was primarily influenced by the pipe pile&rsquo;s inner radius, while the upper band frequency (UBF) was predominantly affected by its outer radius. As the periodic constant increased, the LBF, UBF, and the width of band gap (WBG) all decreased. Conversely, changing the arrangement pattern from square to hexagonal led to increases in UBF and WBG, while the LBF diminished. Notably, the WBG of the H-section steel piles, possessing the same cross-sectional area, was 1.31 times greater than that of the steel pipe piles, indicating an enhanced vibration isolation performance. Additionally, the impact of transverse and vertical characteristic dimensions of the H-shaped pile on the band gap distribution was assessed, revealing that the transverse characteristic dimensions exerted a more significant influence than the vertical dimensions.

]]>Symmetry doi: 10.3390/sym16091128

Authors: Adrian Kampa Iwona Paprocka

In the context of the demand for mass customization of products, a trade-off between highly efficient automated systems and flexible manual operators is sought. The linear arrangement of workstations made it possible to divide the process into many simple operations, which increases production efficiency, but also results in an increase in the number of workstations and a significant extension of the line. A human operator is usually treated as a quasi-mechanical object, and a human error is considered, similarly, as a failure of a technical component. However, human behavior is more complex and difficult to predict. A mathematical model of a new production organization is presented, including dividing the traditional production line into shorter sections or replacing the serial assembly line with a U-line with cells. Moreover, the reliability of operator and technical means are distinguished. Work-in-progress inventories are located between line sections to improve system stability. The stability of the assembly line is examined based on the system configuration and probabilistic estimates of human failure. The influence of the symmetry of reliability parameters of people on key performance indicators (KPI (headcount), KPI (surface) and KPI (Overall Equipment Effectiveness) is examined. KPI (solution robustness) and KPI (quality robustness) are also presented in order to evaluate the impact of a disruption on the assembly line performance. New rules for assigning tasks to stations are proposed, taking into account the risk of disruptions in the execution of tasks. For comparison of assembly problems, heuristic methods with newly developed criteria are used. The results show the impact of symmetry/asymmetry on assembly line performance and an asymmetric distribution of manual assembly times that is significantly skewed to the right due to human errors. On the assembly line, the effects of these errors are cumulative and lead to longer assembly times and lower KPIs.

]]>Symmetry doi: 10.3390/sym16091127

Authors: Xiaoyu Cui Xuanhao Li Zhiyao Zhao Jiabin Yu Di Liu

In this paper, a practical maintenance algorithm is proposed to improve the reliability of actuation systems and their components, specifically addressing the consistency degradation caused by faults in the symmetric actuation system components of more electric aircraft (MEA). By integrating important measures with traditional genetic algorithms, the accuracy of the algorithm is improved. Prior to maintenance, a reasonable classification of components is built to mitigate the adverse effects of extreme fault conditions on the algorithm. This approach improves both the effectiveness and efficiency of the algorithm, rendering the overall maintenance strategy better suited for real-world needs. Finally, comparative simulations confirm the algorithm&rsquo;s superior performance in reliability improvement, demonstrating its substantial contribution to the field of MEA maintenance and reliability.

]]>Symmetry doi: 10.3390/sym16091126

Authors: Mohamed A. Abdoon Abdulrahman B. M. Alzahrani

In this work, the efficacy of fractional models under Atangana&ndash;Baleanu&ndash;Caputo, Caputo&ndash;Fabrizio, and Caputo is compared to the performance of integer-order models in the forecasting of weekly influenza cases using data from the Kingdom of Saudi Arabia. The suggested fractional influenza model was effectively verified using fractional calculus. Our investigation uncovered the topic&rsquo;s essential properties and deepened our understanding of disease progression. Furthermore, we analyzed the numerical scheme&rsquo;s positivity, limitations, and symmetry. The fractional-order models demonstrated superior accuracy, producing smaller root mean square error (RMSE) and mean absolute error (MAE) than the classical model. The novelty of this work lies in introducing the Atangana&ndash;Baleanu&ndash;Caputo fractional model to influenza forecasting to incorporate memory of an epidemic, which leads to higher accuracy than traditional models. These models effectively captured the peak and drop of influenza cases. Based on these findings, it can be concluded that fractional-order models perform better than typical integer-order models when predicting influenza dynamics. These insights should illuminate the importance of fractional calculus in addressing epidemic threats.

]]>Symmetry doi: 10.3390/sym16091125

Authors: Faizan Ahmad Khan Kholood Alnefaie Nidal H. E. Eljaneid Esmail Alshaban Adel Alatawi Mohammed Zayed Alruwaytie

This article aims to adopt some notions for mapping f:Xk&rarr;X, (where integer k is positive) and to prove the nonlinear-Pre&scaron;i&#263;-type results on metric spaces employing a f-reflexive and locally finitely f-transitive binary relation (not necessarily partial order). The outcomes proven herewith are extended and generalized to several fixed point findings of literature. Lastly, examples are provided to support the applicability of these outcomes.

]]>Symmetry doi: 10.3390/sym16091124

Authors: Huiqin Xie Li Yang

In order to design quantum-safe block ciphers, it is crucial to investigate the application of quantum algorithms to cryptographic analysis tools. In this study, we use the Bernstein&ndash;Vazirani algorithm to enhance truncated differential cryptanalysis and boomerang cryptanalysis. We first propose a quantum algorithm for finding truncated differentials, then rigorously prove that the output truncated differentials must have high differential probability for the vast majority of keys in the key space. Subsequently, based on this algorithm, we design a quantum algorithm for finding boomerang distinguishers. The quantum circuits of the two proposed quantum algorithms contain only polynomial quantum gates and qubits. Compared with classical tools for searching truncated differentials or boomerang distinguishers, the proposed algorithms can maintain the polynomial complexity while fully considering the impact of S-boxes and key scheduling.

]]>Symmetry doi: 10.3390/sym16091123

Authors: Khlood Al-Harbi Aisha Fayomi Hanan Baaqeel Amany Alsuraihi

In real-life data, count data are considered more significant in different fields. In this article, a new form of the one-parameter discrete linear-exponential distribution is derived based on the survival function as a discretization technique. An extensive study of this distribution is conducted under its new form, including characteristic functions and statistical properties. It is shown that this distribution is appropriate for modeling over-dispersed count data. Moreover, its probability mass function is right-skewed with different shapes. The unknown model parameter is estimated using the maximum likelihood method, with more attention given to Bayesian estimation methods. The Bayesian estimator is computed based on three different loss functions: a square error loss function, a linear exponential loss function, and a generalized entropy loss function. The simulation study is implemented to examine the distribution&rsquo;s behavior and compare the classical and Bayesian estimation methods, which indicated that the Bayesian method under the generalized entropy loss function with positive weight is the best for all sample sizes with the minimum mean squared errors. Finally, the discrete linear-exponential distribution proves its efficiency in fitting discrete physical and medical lifetime count data in real-life against other related distributions.

]]>Symmetry doi: 10.3390/sym16091122

Authors: Liang Zhang Xinghao Wang Xiaobing Zhang

Symmetry in mathematical models often refers to invariance under certain transformations. In stochastic models, symmetry considerations must also account for the probabilistic nature of inter- actions and events. In this paper, a stochastic vector-borne model with plant virus disease resistance and nonlinear incidence is investigated. By constructing suitable stochastic Lyapunov functions, we show that if the related threshold R0s&lt;1, then the disease will be extinct. By using the reproduction number R0, we establish sufficient conditions for the existence of ergodic stationary distribution to the stochastic model. Furthermore, we explore the results graphically in numerical section and find that random fluctuations introduced in the stochastic model can suppress the spread of the disease, except for increasing plant virus disease resistance and decreasing the contact rate between infected plants and susceptible vectors. The results reveal the correlation between symmetry and stochastic vector-borne models and can provide deeper insights into the dynamics of disease spread and control, potentially leading to more effective and efficient management strategies.

]]>Symmetry doi: 10.3390/sym16091121

Authors: Ali Alqahtani Abdulaziz A. Alsulami Nayef Alqahtani Badraddin Alturki Bandar M. Alghamdi

The Internet of Things (IoT) is an important component of the smart environment, which produces a large volume of data that is considered challenging to handle. In addition, the IoT architecture is vulnerable to many cyberattacks that can target operational devices. Therefore, there is a need for monitoring IoT traffic to analyze, detect malicious activity, and classify cyberattack types. This research proposes a security framework to monitor asymmetrical network traffic in an IoT environment. The framework offers a network intrusion detection system (NIDS) to detect and classify cyberattacks, implemented using a machine learning (ML) model residing in the middleware layer of the IoT architecture. A dimensionality reduction technique known as principal component analysis (PCA) is utilized to facilitate data transmission, which is intended to be sent from the middleware layer to the cloud layer with reduced complexity and fewer unnecessary inputs without compromising the information content. Therefore, the reduced IoT traffic data are sent to the cloud and the PCA data are retransformed to approximate the original data for visualizing the IoT traffic. The NIDS is responsible for reporting the attack type to the cloud in the event of an attack. Our findings indicate that the proposed framework has promising results in classifying the attack type, which achieved a classification accuracy of 98%. In addition, the dimension of the IoT traffic data is reduced by around 50% and it has a similarity of around 90% compared to the original data.

]]>Symmetry doi: 10.3390/sym16091120

Authors: Hsien-Chung Wu

The new solution concepts of interval-valued multiobjective optimization problems using ordering cone are proposed in this paper. An equivalence relation is introduced to divide the collection of all bounded closed intervals into the equivalence classes. The family of all equivalence classes is also called a quotient set. In this case, this quotient set can turn into a vector space under some suitable settings for vector addition and scalar multiplication. The notions of ordering cone and partial ordering on a vector space are essentially equivalent. It means that an ordering in the quotient set can be defined to study the Pareto optimal solution in multiobjective optimization problems. In this paper, we consider the multiobjective optimization problem such that its coefficients are taken to be the bounded closed intervals. With the help of the convex cone, we can study the Pareto optimal solutions of the multiobjective optimization problem with interval-valued coefficients.

]]>Symmetry doi: 10.3390/sym16091119

Authors: Jin Yang Wenke Gao

This paper studies the sampled-data control problem for Takagi-Sugeno (T-S) fuzzy systems with variable sampling. To lessen the conservatism of stability criteria, we introduce a refined looped Lyapunov functional (LLF). These functionals incorporate additional information on split sampling intervals and delayed states. Moreover, sampling-dependent matrix functions are presented to relax the conservativeness of the developed LLFs. By resorting to the refined LLFs, new stability and stabilization criteria for T-S fuzzy systems incorporating an H&infin; performance are established. To validate the established conditions, a nonlinear permanent magnet synchronous motor and the Lorenz system are used to demonstrate the reduced conservatism and the merits of the presented methods.

]]>Symmetry doi: 10.3390/sym16091118

Authors: Xing Fang Chengxu Zhang Chengxi Zhang Yu Lu Gaofei Xu Yujia Shang

To achieve precise control of the symmetrical unmanned surface vehicle (USV) under strong external disturbances, we propose a disturbance estimation and conditional disturbance compensation control (CDCC) scheme. First, the differential flatness method is applied to convert the underactuated model into a fully actuated one, simplifying the controller design. Then, a nonlinear disturbance observer (NDOB) is designed to estimate the lumped disturbance. Subsequently, a continuous disturbance characterization index (CDCI) is proposed, which not only indicates whether the disturbance is beneficial to the system stability but also makes the controller switch smoothly and suppresses the chattering phenomenon greatly. Indicated by the CDCI, the proposed CDCC method can not only utilize the beneficial disturbance but also compensate for the detrimental disturbance, which improves the USV&rsquo;s control performance under strong external disturbances. Moreover, a trajectory-planning method is designed to generate an obstacle avoidance reference trajectory for the controller. Finally, simulations verify the feasibility of applying the proposed control method to USV.

]]>Symmetry doi: 10.3390/sym16091117

Authors: Ruyu Tao Ying Li Mingcui Zhang Xiaochen Liu Musheng Wei

Dual algebra plays an important role in kinematic synthesis and dynamic analysis, but there are still few studies on dual quaternion matrix theory. This paper provides an efficient method for solving the QLY least squares problem of the dual quaternion matrix equation AXB+CYD&asymp;E, where X, Y are unknown dual quaternion matrices with special structures. First, we define a semi-tensor product of dual quaternion matrices and study its properties, which can be used to achieve the equivalent form of the dual quaternion matrix equation. Then, by using the dual representation of dual quaternion and the GH-representation of special dual quaternion matrices, we study the expression of QLY least squares Hermitian solution of the dual quaternion matrix equation AXB+CYD&asymp;E. The algorithm is given and the numerical examples are provided to illustrate the efficiency of the method.

]]>Symmetry doi: 10.3390/sym16091116

Authors: Zhenshan Huang Zhijie Liu Gang Shen Kejun Li Yuanzong Song Baihe Su

Virtual synchronous generator (VSG) control has positive effects on the stability of microgrids. In practical power systems, both single-phase loads and three-phase unbalanced loads are present. The four-leg inverter is an alternative solution for the power supply of unbalanced loads and grid connections. The traditional VSG control strategy still faces challenges when using a four-leg inverter to provide a symmetrical voltage and stable frequency in the load power supply and pre-synchronization. This paper proposes a VSG-based control strategy along with a pre-synchronization method for four-leg inverters. An improved VSG control strategy is put forward for four-leg inverters. The improved virtual impedance control and power calculation methods are integrated into the control loop to suppress the voltage asymmetry and frequency ripples. Building on the improved VSG control strategy, a pre-synchronization control approach is proposed to minimize the amplitude and phase angle discrepancies between the inverter output voltage and the power grid voltage. In addition, an optimized design method for control parameters is presented to improve VSG dynamic performance. A hardware prototype of the four-leg inverter is built; the results show that the voltage unbalance ratio can be reduced by 89%, and the response time can be shortened by 50%.

]]>Symmetry doi: 10.3390/sym16091115

Authors: Alexey S. Bychkov Kirill A. Ushakov Mikhail A. Vasiliev

There was an error in the original publication [...]

]]>Symmetry doi: 10.3390/sym16091114

Authors: Pablo Adasme Andrés Viveros Ali Dehghan Firoozabadi

In this paper, the quadratic p-median optimization problem is discussed, where the goal is to connect users to a selected group of facilities (emergency services, telecommunications servers, healthcare facilities) at the lowest possible cost. The problem is aimed at minimizing the cost of connecting these selected facilities. The costs are symmetric, meaning connecting two different points is the same in both directions. This problem extends the traditional p-median problem, a combinatorial problem used in various fields like facility location, network design, transportation, supply chain networks, emergency services, healthcare, and education planning. Surprisingly, the quadratic version has not been thoroughly considered in the literature. The paper highlights the formulation of two mixed-integer quadratic programming models to find optimal solutions to this problem. One model is a classic formulation, and the other is based on set cover theory. Linear versions and Bender&rsquo;s decomposition formulations for each model are also derived. A Bender&rsquo;s decomposition is solved using an algorithm that adds constraints during each iteration to improve the solution. Lazy constraints in the Gurobi solver&rsquo;s branch and cut algorithm are dynamically added whenever a mixed-integer programming solution is found. Additionally, an efficient local search meta-heuristic is proposed that usually finds optimal solutions for tested instances. Challenging instances with up to 60 facilities and 2000 users are successfully solved. Our results show that Bender&rsquo;s models with lazy constraints are the most effective for Euclidean and random test cases, achieving optimal solutions in less CPU time. The meta-heuristic also finds near-optimal solutions rapidly for these cases.

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