Symmetry doi: 10.3390/sym13091718

Authors: Chengzhi Jiang Chuanfeng Huang Qiwei Huang Jian Shi

The multi-source data collected by the power Internet of Things (IoT) provide the data foundation for the power big data analysis. Due to the limited computational capability and large amount of data collection terminals in power IoT, the traditional security mechanism has to be adapted to such an environment. In order to ensure the security of multi-source data in the power monitoring networks, a security system for multi-source big data in power monitoring networks based on the adaptive combined public key algorithm and an identity-based public key authentication protocol is proposed. Based on elliptic curve cryptography and combined public key authentication, the mapping value of user identification information is used to combine the information in a public and private key factor matrix to obtain the corresponding user key pair. The adaptive key fragment and combination method are designed so that the keys are generated while the status of terminals and key generation service is sensed. An identification-based public key authentication protocol is proposed for the power monitoring system where the authentication process is described step by step. Experiments are established to validate the efficiency and effectiveness of the proposed system. The results show that the proposed model demonstrates satisfying performance in key update rate, key generation quantity, data authentication time, and data security. Finally, the proposed model is experimentally implemented in a substation power IoT environment where the application architecture and security mechanism are described. The security evaluation of the experimental implementation shows that the proposed model can resist a series of attacks such as counterfeiting terminal, data eavesdropping, and tampering.

]]>Symmetry doi: 10.3390/sym13091717

Authors: Lei Wu Jiewu Leng Bingfeng Ju

Ultra-Precision Machining (UPM) is a kind of highly accurate processing technology developed to satisfy the manufacturing requirements of high-end cutting-edge products including nuclear energy producers, very large-scale integrated circuits, lasers, and aircraft. The information asymmetry phenomenon widely exists in the design and control of ultra-precision machining. It may lead to inconsistency between the designed performance and operational performance of the UPM equipment on stiffness, thermal stability, and motion accuracy, which result from its design, manufacturing, and control, and determine the form accuracy and surface roughness of machined parts. The performance of the UPM equipment should be improved continuously. It is still challenging to realize the real-time and self-adaptive control, in which building a high-fidelity and computationally efficient digital twin is a valuable solution. Nevertheless, the incorporation of the digital twin technology into the UPM design and control remains vague and sometimes contradictory. Based on a literature search in the Google Scholar database, the critical issues in the UPM design and control, and how to use the digital twin technologies to promote it, are reviewed. Firstly, the digital twins-based UPM design, including bearings module design, spindle-drive module design, stage system module design, servo module design, and clamping module design, are reviewed. Secondly, the digital twins-based UPM control studies, including voxel modeling, process planning, process monitoring, vibration control, and quality prediction, are reviewed. The key enabling technologies and research directions of digital twins-based design and control are discussed to deal with the information asymmetry phenomenon in UPM.

]]>Symmetry doi: 10.3390/sym13091716

Authors: Gang Yao Yujia Sun Mingpu Wong Xiaoning Lv

Many structures in civil engineering are symmetrical. Crack detection is a critical task in the monitoring and inspection of civil engineering structures. This study implements a lightweight neural network based on the YOLOv4 algorithm to detect concrete surface cracks. In the extraction of backbone and the design of neck and head, the symmetry concept is adopted. The model modules are improved to reduce the depth and complexity of the overall network structure. Meanwhile, the separable convolution is used to realize spatial convolution, and the SPP and PANet modules are improved to reduce the model parameters. The convolutional layer and batch normalization layer are merged to improve the model inference speed. In addition, using the focal loss function for reference, the loss function of object detection network is improved to balance the proportion of the cracks and the background samples. To comprehensively evaluate the performance of the improved method, 10,000 images (256 × 256 pixels in size) of cracks on concrete surfaces are collected to build the database. The improved YOLOv4 model achieves an mAP of 94.09% with 8.04 M and 0.64 GMacs. The results show that the improved model is satisfactory in mAP, and the model size and calculation amount are greatly reduced. This performs better in terms of real-time detection on concrete surface cracks.

]]>Symmetry doi: 10.3390/sym13091715

Authors: Chen Zhang Zhang Xiong Fan Ma

For non-linear systems (NLSs), the state estimation problem is an essential and important problem. This paper deals with the nonlinear state estimation problems in nonlinear and non-Gaussian systems. Recently, the Bayesian filter designer based on the Bayesian principle has been widely applied to the state estimation problem in NLSs. However, we assume that the state estimation models are nonlinear and non-Gaussian, applying traditional, typical nonlinear filtering methods, and there is no precise result for the system state estimation problem. Therefore, the larger the estimation error, the lower the estimation accuracy. To perfect the imperfections, a projection filtering method (PFM) based on the Bayesian estimation approach is applied to estimate the state. First, this paper constructs its projection symmetric interval to select the basis function. Second, the prior probability density of NLSs can be projected into the basis function space, and the prior probability density solution can be solved by using the Fokker–Planck Equation (FPE). According to the Bayes formula, the proposed estimator utilizes the basis function in projected space to iteratively calculate the posterior probability density; thus, it avoids calculating the partial differential equation. By taking two illustrative examples, it is also compared with the traditional UKF and PF algorithm, and the numerical experiment results show the feasibility and effectiveness of the novel nonlinear state estimation filter algorithm.

]]>Symmetry doi: 10.3390/sym13091713

Authors: Pijush Kanti Dutta Pramanik Sanjib Biswas Saurabh Pal Dragan Marinković Prasenjit Choudhury

In mobile crowd computing (MCC), smart mobile devices (SMDs) are utilized as computing resources. To achieve satisfactory performance and quality of service, selecting the most suitable resources (SMDs) is crucial. The selection is generally made based on the computing capability of an SMD, which is defined by its various fixed and variable resource parameters. As the selection is made on different criteria of varying significance, the resource selection problem can be duly represented as an MCDM problem. However, for the real-time implementation of MCC and considering its dynamicity, the resource selection algorithm should be time-efficient. In this paper, we aim to find out a suitable MCDM method for resource selection in such a dynamic and time-constraint environment. For this, we present a comparative analysis of various MCDM methods under asymmetric conditions with varying selection criteria and alternative sets. Various datasets of different sizes are used for evaluation. We execute each program on a Windows-based laptop and also on an Android-based smartphone to assess average runtimes. Besides time complexity analysis, we perform sensitivity analysis and ranking order comparison to check the correctness, stability, and reliability of the rankings generated by each method.

]]>Symmetry doi: 10.3390/sym13091714

Authors: Yan Qiu Jing Sun Yunlong Shang Dongchang Wang

The frequent occurrence of electric vehicle fire accidents reveals the safety hazards of batteries. When a battery fails, its symmetry is broken, which results in a rapid degradation of its safety performance and poses a great threat to electric vehicles. Therefore, accurate battery fault diagnoses and prognoses are the key to ensuring the safe and durable operation of electric vehicles. Thus, in this paper, we propose a new fault diagnosis and prognosis method for lithium-ion batteries based on a nonlinear autoregressive exogenous (NARX) neural network and boxplot for the first time. Firstly, experiments are conducted under different temperature conditions to guarantee the diversity of the data of lithium-ion batteries and then to ensure the accuracy of the fault diagnosis and prognosis at different working temperatures. Based on the collected voltage and current data, the NARX neural network is then used to accurately predict the future battery voltage. A boxplot is then used for the battery fault diagnosis and early warning based on the predicted voltage. Finally, the experimental results (in a new dataset) and a comparative study with a back propagation (BP) neural network not only validate the high precision, all-climate applicability, strong robustness and superiority of the proposed NARX model but also verify the fault diagnosis and early warning ability of the boxplot. In summary, the proposed fault diagnosis and prognosis approach is promising in real electric vehicle applications.

]]>Symmetry doi: 10.3390/sym13091712

Authors: Flavio Mercati Paula Reichert

We discuss the total collision singularities of the gravitational N-body problem on shape space. Shape space is the relational configuration space of the system obtained by quotienting ordinary configuration space with respect to the similarity group of total translations, rotations, and scalings. For the zero-energy gravitating N-body system, the dynamics on shape space can be constructed explicitly and the points of total collision, which are the points of central configuration and zero shape momenta, can be analyzed in detail. It turns out that, even on shape space where scale is not part of the description, the equations of motion diverge at (and only at) the points of total collision. We construct and study the stratified total-collision manifold and show that, at the points of total collision on shape space, the singularity is essential. There is, thus, no way to evolve solutions through these points. This mirrors closely the big bang singularity of general relativity, where the homogeneous-but-not-isotropic cosmological model of Bianchi IX shows an essential singularity at the big bang. A simple modification of the general-relativistic model (the addition of a stiff matter field) changes the system into one whose shape-dynamical description allows for a deterministic evolution through the singularity. We suspect that, similarly, some modification of the dynamics would be required in order to regularize the total collision singularity of the N-body model.

]]>Symmetry doi: 10.3390/sym13091711

Authors: Antonio Profico Carlotta Zeppilli Ileana Micarelli Alessandro Mondanaro Pasquale Raia Damiano Marchi Giorgio Manzi Paul O’Higgins

In biological anthropology, parameters relating to cross-sectional geometry are calculated in paired long bones to evaluate the degree of lateralization of anatomy and, by inference, function. Here, we describe a novel approach, newly added to the morphomap R package, to assess the lateralization of the distribution of cortical bone along the entire diaphysis. The sample comprises paired long bones belonging to 51 individuals (10 females and 41 males) from The New Mexico Decedent Image Database with known biological profile, occupational and loading histories. Both males and females show a pattern of right lateralization. In addition, males are more lateralized than females, whereas there is not a significant association between lateralization with occupation and loading history. Body weight, height and long-bone length are the major factors driving the emergence of asymmetry in the humerus, while interestingly, the degree of lateralization decreases in the oldest individuals.

]]>Symmetry doi: 10.3390/sym13091710

Authors: Wen-An Yong Yizhou Zhou

This paper is concerned with modeling nonequilibrium phenomena in spatial domains with boundaries. The resultant models consist of hyperbolic systems of first-order partial differential equations with boundary conditions (BCs). Taking a linearized moment closure system as an example, we show that the structural stability condition and the uniform Kreiss condition do not automatically guarantee the compatibility of the models with the corresponding classical models. This motivated the generalized Kreiss condition (GKC)—a strengthened version of the uniform Kreiss condition. Under the GKC and the structural stability condition, we show how to derive the reduced BCs for the equilibrium systems as the classical models. For linearized problems, the validity of the reduced BCs can be rigorously verified. Furthermore, we use a simple example to show how thus far developed theory can be used to construct proper BCs for equations modeling nonequilibrium phenomena in spatial domains with boundaries.

]]>Symmetry doi: 10.3390/sym13091708

Authors: Robert Reynolds Allan Stauffer

In this manuscript, the authors derive a double integral whose kernel involves the logarithmic function a polynomial raised to a power and a quotient function expressed it in terms of the Lerch function. All the results in this work are new.

]]>Symmetry doi: 10.3390/sym13091709

Authors: Małgorzata Stefańska Katarzyna Bulińska Marek Woźniewski Andrzej Szuba Wioletta Dziubek

The aim of this study was to evaluate the relationship of the ankle-brachial index (ABI) level with kinetic and kinematic parameters of the gait pattern and force-velocity parameters generated by lower limb muscles. Methods: The study group consisted of 65 patients with peripheral arterial disease (PAD). The ABI value, kinetic and kinematic parameters of gait and force-velocity parameters of knee and ankle extensors and flexors were determined in all subjects. The values obtained for right and left limbs as well as the limbs with higher and lower ABI were compared. Results: Regardless of the method of analysis, the values of the gait’s kinematic and kinetic parameters of both lower limbs did not differ significantly. However, significant differences were noted in the values of peak torque, work and power of the extensor muscles of the knee and the flexor muscles of the ankle with the higher and lower ABI. Conclusion: This study demonstrated that a higher degree of ischemia worsened the level of strength, endurance, and performance of ankle flexors and extensors of the knee joint. ABI is not related to the gait pattern. The above-mentioned relationship should be taken into account in the rehabilitation process and methodological assessment.

]]>Symmetry doi: 10.3390/sym13091707

Authors: Bo Li Hongsheng Deng Jue Wang

A microgrid is an efficient method of uniting distributed generations. To ensure the applicability and symmetry of the microgrid, the environmental benefits and economic costs are considered to comprehensively model the optimal operation of the microgrid under the grid-connected operation mode, at the same time, considering the effect of interruptible load on the operating cost of the microgrid, the power shifting for interruptible load is attempted on the basis of battery storage capacity. By adaptively adjusting the migration rate using the habitat suitability index of a normalized individual and adding a certain differential perturbation to the migration operator of the migration mechanism, an improved biogeography-based optimization algorithm is proposed and the microgrid optimization dispatching algorithm based on the improved biogeography-based optimization is applied. The advancement and effectiveness of the proposed algorithm and model is verified by the example, and the simulation results indicate that the implementation of the power dispatching scheme proposed in this paper can effectively reduce the total cost of the system. Moreover, the proper consideration of shifting interruptible load, the effective load management and guiding the electricity consumption behavior of users are of certain significance for optimizing the utilization of renewable energy and improving the system efficiency and economy.

]]>Symmetry doi: 10.3390/sym13091706

Authors: Pu Lan Kewen Xia Yongke Pan Shurui Fan

An improved equilibrium optimizer (EO) algorithm is proposed in this paper to address premature and slow convergence. Firstly, a highly stochastic chaotic mechanism is adopted to initialize the population for range expansion. Secondly, the capability to conduct global search to jump out of local optima is enhanced by assigning adaptive weights and setting adaptive convergence factors. In addition 25 classical benchmark functions are used to validate the algorithm. As revealed by the analysis of the accuracy, speed, and stability of convergence, the IEO algorithm proposed in this paper significantly outperforms other meta-heuristic algorithms. In practice, the distribution is asymmetric because most logging data are unlabeled. Traditional classification models have difficulty in accurately predicting the location of oil layer. In this paper, the oil layers related to oil exploration are predicted using long short-term memory (LSTM) networks. Due to the large amount of data used, however, it is difficult to adjust the parameters. For this reason, an improved equilibrium optimizer algorithm (IEO) is applied to optimize the parameters of LSTM for improved performance, while the effective IEO-LSTM is applied for oil layer prediction. As indicated by the results, the proposed model outperforms the current popular optimization algorithms including particle swarm algorithm PSO and genetic algorithm GA in terms of accuracy, absolute error, root mean square error and mean absolute error.

]]>Symmetry doi: 10.3390/sym13091705

Authors: Lamis Hamrouni Mohammed Lamine Kherfi Oussama Aiadi Abdellah Benbelghit

In this paper, we propose a novel method for plant leaves recognition by incorporating an unsupervised convolutional auto-encoder (CAE) and Siamese neural network in a unified framework by considering Siamese as an alternative to the conventional loss of CAE. Rather than the conventional exploitation of CAE and Siamese, in our case we have proposed to extend CAE for a novel supervised scenario by considering it as one-class learning classifier. For each class, CAE is trained to reconstruct its positive and negative examples and Siamese is trained to distinguish the similarity and the dissimilarity of the obtained examples. On the contrary and asymmetric to the related hierarchical classification schemes which require pre-knowledge on the dataset being recognized, we propose a hierarchical classification scheme that doesn’t require such a pre-knowledge and can be employed by non-experts automatically. We cluster the dataset to assemble similar classes together. A test image is first assigned to the nearest cluster, then matched to one class from the classes that fall under the determined cluster using our novel one-class learning classifier. The proposed method has been evaluated on the ImageCLEF2012 dataset. Experimental results have proved the superiority of our method compared to several state-of-the art methods.

]]>Symmetry doi: 10.3390/sym13091703

Authors: Yunhua Ding Teague D. Olewiler Mohammad Farhan Rawnak

An overview of recent progress on testing Lorentz and CPT symmetry using Penning traps is presented. The theory of quantum electrodynamics with Lorentz-violating operators of mass dimensions up to six is summarized. Dominant shifts in the cyclotron and anomaly frequencies of the confined particles and antiparticles due to Lorentz and CPT violation are derived. Existing results of the comparisons of charge-to-mass ratios and magnetic moments involving protons, antiprotons, electrons, and positrons are used to constrain various coefficients for Lorentz violation.

]]>Symmetry doi: 10.3390/sym13091704

Authors: Savita Rathee Priyanka Gupta Vishnu Narayan Mishra Thabet Abdeljawad Nabil Mlaiki

This paper aims to prove fixed point results for cyclic compatible contraction and Hardy–Rogers cyclic contraction in symmetric spaces. Our results generalize the results of Kumari and Panthi (2016) proved for cyclic compatible contraction and modified Hardy–Rogers cyclic contraction in the generating space of a b-quasi metric family and b-dislocated metric family. After that, as an application, we prove a fixed point result in symmetric pre-probabilistic metric spaces (PPM-spaces).

]]>Symmetry doi: 10.3390/sym13091702

Authors: Ana Carpio María-Luisa Rapún

Detecting objects hidden in a medium is an inverse problem. Given data recorded at detectors when sources emit waves that interact with the medium, we aim to find objects that would generate similar data in the presence of the same waves. In opposition, the associated forward problem describes the evolution of the waves in the presence of known objects. This gives a symmetry relation: if the true objects (the desired solution of the inverse problem) were considered for solving the forward problem, then the recorded data should be returned. In this paper, we develop a topological derivative-based multifrequency iterative algorithm to reconstruct objects buried in attenuating media with limited aperture data. We demonstrate the method on half-space configurations, which can be related to problems set in the whole space by symmetry. One-step implementations of the algorithm provide initial approximations, which are improved in a few iterations. We can locate object components of sizes smaller than the main components, or buried deeper inside. However, attenuation effects hinder object detection depending on the size and depth for fixed ranges of frequencies.

]]>Symmetry doi: 10.3390/sym13091701

Authors: Jean-Louis Sikorav Alan Braslau Arach Goldar

It is often stated that there are no laws in biology, where everything is contingent and could have been otherwise, being solely the result of historical accidents. Furthermore, the customary introduction of fundamental biological entities such as individual organisms, cells, genes, catalysts, and motors remains largely descriptive; constructive approaches involving deductive reasoning appear, in comparison, almost absent. As a consequence, both the logical content and principles of biology need to be reconsidered. The present article describes an inquiry into the foundations of biology. The foundations of biology are built in terms of elements, logic, and principles, using both the language and the general methods employed in other disciplines. This approach assumes the existence of a certain unity of human knowledge that transcends discipline boundaries. Leibniz’s principle of sufficient reason is revised through a study of the complementary concepts of symmetry and asymmetry and of necessity and contingency. This is used to explain how these concepts are involved in the elaboration of theories or laws of nature. Four fundamental theories of biology are then identified: cell theory, Darwin’s theory of natural selection, an informational theory of life (which includes Mendel’s theory of inheritance) and a physico-chemical theory of life. Atomism and deductive reasoning are shown to enter into the elaboration of the concepts of natural selection, individual living organisms, cells, and their reproduction, genes, as well as catalysts and motors. This work contributes to clarify the philosophical and logical structure of biology and its major theories. This should ultimately lead to a better understanding of the origin of life, of system and synthetic biology, and of artificial life.

]]>Symmetry doi: 10.3390/sym13091700

Authors: Fan Xie Shuaijie Cui Dongqi Sun

Three-dimensional laser scanning technology has been more mature, and its application fields are expanding. It is being used in key projects and important work such as ancient building recording, restoration and reconstruction. In this paper, the technology is applied to the 3D scanning, data splicing and model simplification of Heping temple building complex in Beijing. After innovative research on ancient architecture, it is found that the group layout, single form and local components of Heping temple building complex in Beijing show symmetry everywhere, vividly reflecting the extensive and profound ancient architectural culture and order. This points out a new direction for the development and application of 3D laser scanning technology and opens up a new path for the in-depth study of the protection of ancient buildings in China.

]]>Symmetry doi: 10.3390/sym13091699

Authors: Leonid V. Bogdanov

We construct a map from solutions of the dispersionless BKP (dBKP) equation to solutions of the Manakov–Santini (MS) system. This map defines an Einstein–Weyl structure corresponding to the dBKP equation through the general Lorentzian Einstein–Weyl structure corresponding to the MS system. We give a spectral characterisation of reduction in the MS system, which singles out the image of the dBKP equation solution, and also consider more general reductions of this class. We define the BMS system and extend the map defined above to the map (Miura transformation) of solutions of the BMS system to solutions of the MS system, thus obtaining an Einstein–Weyl structure for the BMS system.

]]>Symmetry doi: 10.3390/sym13091698

Authors: Dagmara Iwańska Piotr Tabor Olga Grabowska Andrzej Mastalerz

Background: This study assesses curved track effects on fatigue symmetry and lower limb muscle activity while taking maximum velocity running kinematics into account. Methods: Polish master class athletes were examined (age 24.6 ± 3.67 years, bm 78.9 ± 6.02 kg, and bh 186.1 ± 6.63 cm). The measurements were made on a 400 m synthetic surface athletics track. The DelSys 16 channel system was employed to measure the activity of the right and left leg muscles. The kinematic variables of the run were obtained using a 3-axis accelerometer built into the recorder. Results: The study revealed curved track effects on asymmetric muscle activity and running kinematics in the first two sections of the run. On the first curve, the symmetry index (SI) was 8.1%, while in on straight, it was 11.5%. Moreover, significantly lower values of the fatigue index b were found for the right limb (F(3.36) = 6.504; p = 0.0152). Conclusions: A reduction of asymmetric muscle activity is linked with compensatory muscle stimulation triggered by the nervous system and with adjusting running kinematics to changing external conditions. Therefore, the main focus further research should be on the optimal interaction between stride length and frequency in relation to the muscle activity corresponding to the track geometry.

]]>Symmetry doi: 10.3390/sym13091697

Authors: Leandro Pinto Fava João Carlos Furtado Gilson Augusto Helfer Jorge Luis Victória Barbosa Marko Beko Sérgio Duarte Correia Valderi Reis Quietinho Leithardt

This work presents a multistart algorithm for solving the capacitated vehicle routing problem with 2D loading constraints (2L-CVRP) allowing for the rotation of goods. Research dedicated to graph theory and symmetry considered the vehicle routing problem as a classical application. This problem has complex aspects that stimulate the use of advanced algorithms and symmetry in graphs. The use of graph modeling of the 2L-CVRP problem by undirected graph allowed the high performance of the algorithm. The developed algorithm is based on metaheuristics, such as the Constructive Genetic Algorithm (CGA) to construct promising initial solutions; a Tabu Search (TS) to improve the initial solutions on the routing problem, and a Large Neighborhood Search (LNS) for the loading subproblem. Although each one of these algorithms allowed to solve parts of the 2L-CVRP, the combination of these three algorithms to solve this problem was unprecedented in the scientific literature. In our approach, a parallel mechanism for checking the loading feasibility of routes was implemented using multithreading programming to improve the performance. Additionally, memory structures such as hash-tables were implemented to save time by storing and querying previously evaluated results for the loading feasibility of routes. For benchmarks, tests were done on well-known instances available in the literature. The results proved that the framework matched or outperformed most of the previous approaches. As the main contribution, this work brings higher quality solutions for large-size instances of the pure CVRP. This paper involves themes related to the symmetry journal, mainly complex algorithms, graphs, search strategies, complexity, graph modeling, and genetic algorithms. In addition, the paper especially focuses on topic-related aspects of special interest to the community involved in symmetry studies, such as graph algorithms and graph theory.

]]>Symmetry doi: 10.3390/sym13091696

Authors: Les Coleman

This article is motivated by uncertainty in experimental determinations of the gravitational constant, G, and numerous anomalies of up to 0.5 percent in Newtonian gravitational force on bodies within the solar system. The analysis sheds new light through six natural experiments within the solar system, which draw on published reports and astrophysical databases, and involve laboratory determinations of G, orbital dynamics of the planets and the moons of Earth and Mars, and non-gravitational acceleration (NGA) of ‘Oumuamua and comets. In each case, values are known for all variables in Newton’s Law , except for the gravitational constant, G. Analyses determine the gravitational constant’s observed value, , which—across the six settings—varies with the mass of the smaller, moving body, m, so that . While further work is required, this examination shows a scale-related Newtonian gravity effect at scales from benchtop to Solar System, which contributes to the understanding of symmetry in gravity and has possible implications for Newton’s Laws, dark matter, and formation of structure in the universe.

]]>Symmetry doi: 10.3390/sym13091695

Authors: Jui-Jung Liao Hari Mohan Srivastava Kun-Jen Chung Shih-Fang Lee Kuo-Nan Huang Shy-Der Lin

This article considers an inventory model for non-instantaneous deteriorating items with expiration dates, such as seasonal items, first-hand vegetables, and fruits. Interestingly, an inspection will be performed to manage the quality of the items during the state of no deterioration because it is difficult to purchase items with 100% perfection. Additionally, we assume that the upstream member has the power of controlling or influencing downstream members’ decisions. That is, the supplier asks the retailer for a partial advance payment to avoid cancellation of orders and offers them a credit payment to stimulate sales; in turn, the customer must pay some cash when placing an order and pay the remainder in credit for the retailer. The goal of this article is to determine an optimal replenishment cycle and the total annual cost function, so we explore the functional properties of the total annual cost function and show that the total annual cost function is convex. Theoretical analysis of the optimal properties shows the existence and uniqueness of the optimal solution. Then, we obtain simple and easy solution procedures for the inventory system. Moreover, numerical analysis of the inventory model is conducted, and the corresponding examples are considered with a view to illustrating the application of the supply chain model that we have investigated in this article. Finally, in the concluding section, we have not only provided the motivation and the need for our usages of mathematical analytic solution procedures based upon the convexity, monotonicity (increasing and decreasing) and differentiability properties of the object function (that is, the total annual cost function), which involve some symmetry aspects of the object function, but we have also indicated the limitations and shortcomings in our investigation, which will naturally lead to some potential directions for further research on the supply chain model, which we have considered and mathematically analyzed in this article.

]]>Symmetry doi: 10.3390/sym13091694

Authors: Jianhong Chen Chaoqun Chen Qinghua Song Yifei Zhao Longxin Deng Raoqing Xie Shan Yang

The rumor-free equilibrium state and rumor-endemic equilibrium state are two symmetric descriptions of the status of a system. The constant spreading of rumors would affect the smooth operation of emergency management procedures and cause unnecessary social and economic loss. To reduce the negative effect of rumor propagation, in this paper, we introduce a compartmental model of rumor propagation, which considers the rumor refutation of public and information feedback. By deriving mean-field equations that describe the dynamics of the model, we use analytical and numerical solutions of these equations to investigate the threshold and dynamics of the model in both the closed system and open system. The results imply that the initial equilibrium point is not stable and there exists a rumor-free equilibrium point; in the open system, there exists a threshold beyond which rumors can spread; the stability of the initial equilibrium point is related to the threshold R0 = (φ*α)/μ, and there exists a rumor-endemic equilibrium point. The development process of rumor propagation can be divided into four stages: latent period, progressive period, intense period, and recession period. Under the influence of population, rumor spreading can exceed the threshold readily because the migration rate μ is usually less than the proportion of ignorants without critical ability φ, and the rumor spreading process in an open system presents a fluctuating development, the rumor would not disappear in this autonomous system. Based on the analysis, we propose some measures, such as providing open and efficient information queries and exchange platforms, etc.

]]>Symmetry doi: 10.3390/sym13091693

Authors: Jianmin Wang Yuxi Wang Yujia Liu Tianyang Yue Chengji Wang Weiguang Yang Preben Hansen Fang You

With the continuous development of intelligent product interaction technology, the facial expression design of virtual images on the interactive interface of intelligent products has become an important research topic. Based on the current research on facial expression design of existing intelligent products, we symmetrically mapped the PAD (pleasure–arousal–dominance) emotion value to the image design, explored the characteristics of abstract expressions and the principles of expression design, and evaluated them experimentally. In this study, the experiment of PAD scores was conducted on the emotion expression design of abstract expressions, and the data results were analyzed to iterate the expression design. The experimental results show that PAD values can effectively guide designers in expression design. Meanwhile, the efficiency and recognition accuracy of human communication with abstract expression design can be improved by facial auxiliary elements and eyebrows.

]]>Symmetry doi: 10.3390/sym13091692

Authors: Prakasit Prabpal Yuttana Kongjeen Krischonme Bhumkittipich

We designed a battery energy storage system (BESS) based on the symmetrical concept where the required control is by the symmetrical technique known as volt/var control. The integration of BESS into the conventional distribution has significantly impacted energy consumption over the past year. Load demand probability was used to investigate optimal sizing and location of BESS in an electrical power system. The open electric power distribution system simulator (OpenDSS) was interfaced with MATLAB m-file scripts and presented by using time series analysis with load demand. The optimal BESS solution was adapted by using a genetic algorithm (GA) optimization technique and particle swarm optimization (PSO). The simulation results showed that the BESS was directly connected to the power grid with GA and PSO, and it was observed that BESS sizing also varied for these two values of 1539 kW and 1000 kW, respectively. The merit of those values is the power figure of the system, which is necessary for installation. Therefore, optimal sizing and location of the BESS are helpful to reduce the impact from the load demand to the total system loss and levelling of the energy demand from the power system network. The integration of the BESS can be applied to improve grid stability and store surplus energy very well. The grid increased the stability of the power system and reduced the impact from the large scale of BESS penetration.

]]>Symmetry doi: 10.3390/sym13091691

Authors: Shu-Fei Wu Yu-Cheng Wu Chi-Han Wu Wei-Tsung Chang

In this study, the experimental design is developed based on the testing procedure for the lifetime performance index of products following Weibull lifetime distribution under progressive type I interval censoring. This research topic is related to asymmetrical probability distributions and applications across disciplines. The asymptotic distribution of the maximum likelihood estimator of the lifetime performance index is utilized to develop the testing procedure. In order to reach the given power level, the minimum sample size is determined and tabulated. In order to minimize the total cost that occurred under progressive type I interval censoring, the sampling design is investigated to determine the minimum number of inspection intervals and equal interval lengths when the termination time of experiment is fixed or not fixed. For illustrative aims, one practical example is given for the implementation of our proposed sampling design to collect the progressive type I interval censored sample so that the users can use this sample to test if the lifetime performance index exceeds the desired target level.

]]>Symmetry doi: 10.3390/sym13091690

Authors: Ting Dong Zhenkun Guo Guoqing Jiang

As bistable composite laminated plate and shell structures are often exposed to dynamic environments in practical applications, the global and local dynamics of a bistable asymmetric composite laminated shell subjected to the base excitation is presented in this paper. Temperature difference, base excitation amplitude, and detuning parameters are discussed. With the change of temperature difference, the super-critical pitchfork bifurcation occurs. Three equilibrium solutions corresponding to three equilibrium configurations (two stable configurations and one unstable configuration) can be obtained. With the increase of excitation amplitude, local and global dynamics play a leading role successively. The global dynamics between the two stable configurations behave as the periodic vibration, the quasi-periodic vibration, the chaotic vibration and dynamic snap-through when the excitation amplitude is large enough. The local dynamics that are confined to a single stable configuration behave as 1:2 internal resonance, saturation and permeation when the excitation amplitude is small. Dynamic snap-through and large-amplitude vibrations with two potential wells for the global dynamics will lead to a broad application prospect of the bistable asymmetric composite laminated shell in energy harvesting devices.

]]>Symmetry doi: 10.3390/sym13091689

Authors: Bhimraj Basumatary Nijwm Wary Dimacha Dwibrang Mwchahary Ashoke Kumar Brahma Jwngsar Moshahary Usha Rani Basumatary Jili Basumatary

In this paper, we studied some properties of the neutrosophic multi topological group. For this, we introduced the definition of semi-open neutrosophic multiset, semi-closed neutrosophic multiset, neutrosophic multi regularly open set, neutrosophic multi regularly closed set, neutrosophic multi continuous mapping, and then studied the definition of a neutrosophic multi topological group and some of their properties. Moreover, since the concept of the almost topological group is very new, we introduced the definition of neutrosophic multi almost topological group. Finally, for the purpose of symmetry, we used the definition of neutrosophic multi almost continuous mapping to define neutrosophic multi almost topological group and study some of its properties.

]]>Symmetry doi: 10.3390/sym13091688

Authors: Sohyun Park Anna Hartl Denis Sheptyakov Markus Hoelzel Ana Arauzo

The ferri- and antiferromagnetic structures of a hureaulite-type synthetic compound, Mn2+5(PO4)2(PO3(OH))2(HOH)4, were elucidated by high-resolution neutron powder diffraction in combination with magnetic susceptibility and heat capacity measurements. At 6.17 K, the paramagnetic phase (space group: C2/c) transforms to inherit a ferrimagnetic order (magnetic space group: C2′/c′), followed at 1.86 K by an incommensurately modulated antiferromagnetic order (magnetic superspace group: P21/c.1′(α0γ)00s with the propagation vector k(0.523(2), 0, 0.055(1)). In the ferrimagnetic state, antiferromagnetic interactions are dominant for both intra and inter pentamers of Mn2+(O, HOH)6 octahedra. Differently aligned spin-canting sublattices seen in the ferrimagnetic models at 3.4, 4.5, and 6.1 K explain a weak ferromagnetism in the title compound. The observation of magnetic moments vigorously changing in a small temperature range of 6.1–1.5 K adumbrates a high complexity of interplaying structural and magnetic orders in this manganese phosphatic oxyhydroxide.

]]>Symmetry doi: 10.3390/sym13091686

Authors: Soubhagya Kumar Sahoo Hijaz Ahmad Muhammad Tariq Bibhakar Kodamasingh Hassen Aydi Manuel De la Sen

The principal motivation of this paper is to establish a new integral equality related to k-Riemann Liouville fractional operator. Employing this equality, we present several new inequalities for twice differentiable convex functions that are associated with Hermite–Hadamard integral inequality. Additionally, some novel cases of the established results for different kinds of convex functions are derived. This fractional integral sums up Riemann–Liouville and Hermite–Hadamard’s inequality, which have a symmetric property. Scientific inequalities of this nature and, particularly, the methods included have applications in different fields in which symmetry plays a notable role. Finally, applications of q-digamma and q-polygamma special functions are presented.

]]>Symmetry doi: 10.3390/sym13091687

Authors: Irene Sciriha

A spectral inverse problem concerns the reconstruction of parameters of a parent graph from prescribed spectral data of subgraphs. Also referred to as the P–NP Isomorphism Problem, Reconstruction or Exact Graph Matching, the aim is to seek sets of parameters to determine a graph uniquely. Other related inverse problems, including the Polynomial Reconstruction Problem (PRP), involve the recovery of graph invariants. The PRP seeks to extract the spectrum of a graph from the deck of cards each showing the spectrum of a vertex-deleted subgraph. We show how various algebraic methods join forces to reconstruct a graph or its invariants from a minimal set of restricted eigenvalue-eigenvector information of the parent graph or its subgraphs. We show how functions of the entries of eigenvectors of the adjacency matrix A of a graph can be retrieved from the spectrum of eigenvalues of A. We establish that there are two subclasses of disconnected graphs with each card of the deck showing a common eigenvalue. These could occur as possible counter examples to the positive solution of the PRP.

]]>Symmetry doi: 10.3390/sym13091685

Authors: Florin Teleanu Alexandru Topor Diana Serafin Aude Sadet Paul R. Vasos

Solution-state distance restraints for protein structure determination with Ångström-level resolution rely on through-space transfer of magnetization between nuclear spins. Such magnetization transfers, named Overhauser effects, occur via dipolar magnetic couplings. We demonstrate improvements in magnetization transfer using long-lived coherences (LLCs)—singlet-triplet superpositions that are antisymmetric with respect to spin-permutation within pairs of coupled magnetic nuclei—as the magnetization source. Magnetization transfers in the presence of radio-frequency irradiation, known as ‘rotating-frame’ Overhauser effects (ROEs), are predicted by theory to improve by the use of LLCs; calculations are matched by preliminary experiments herein. The LLC-ROE transfers were compared to the transmission of magnetization via classical transverse routes. Long-lived coherences accumulate magnetization on an external third proton, K, with transfer rates that depended on the tumbling regime. I,S&nbsp;→K transfers in the LLC configuration for (I,S) are anticipated to match, and then overcome, the same transfer rates in the classical configuration as the molecular rotational correlation times increase. Experimentally, we measured the LLC-ROE transfer in dipeptide AlaGly between aliphatic protons in different residues K = Ala − Hα and (I,S) = Gly − Hα1,2 over a distance dK,I,S = 2.3 Å. Based on spin dynamics calculations, we anticipate that, for such distances, a superior transfer of magnetization occurs using LLC-ROE compared to classical ROE at correlation times above τC=10&nbsp;ns. The LLC-ROE effect shows potential for improving structural studies of large proteins and offering constraints of increased precision for high-affinity protein-ligand complexes in slow tumbling in the liquid state.

]]>Symmetry doi: 10.3390/sym13091684

Authors: Alessandro Borri Francesco Carravetta Pasquale Palumbo

The double phosphorylation/dephosphorylation cycle consists of a symmetric network of biochemical reactions of paramount importance in many intracellular mechanisms. From a network perspective, they consist of four enzymatic reactions interconnected in a specular way. The general approach to model enzymatic reactions in a deterministic fashion is by means of stiff Ordinary Differential Equations (ODEs) that are usually hard to integrate according to biologically meaningful parameter settings. Indeed, the quest for model simplification started more than one century ago with the seminal works by Michaelis and Menten, and their Quasi Steady-State Approximation methods are still matter of investigation nowadays. This work proposes an effective algorithm based on Taylor series methods that manages to overcome the problems arising in the integration of stiff ODEs, without settling for model approximations. The double phosphorylation/dephosphorylation cycle is exploited as a benchmark to validate the methodology from a numerical viewpoint.

]]>Symmetry doi: 10.3390/sym13091683

Authors: Eligijus Sakalauskas Inga Timofejeva Ausrys Kilciauskas

A new sigma identification protocol (SIP) based on matrix power function (MPF) defined over the modified medial platform semigroup and power near-semiring is proposed. It is proved that MPF SIP is resistant against direct and eavesdropping attacks. Our security proof relies on the assumption that MPF defined in the paper is a candidate for one-way function (OWF). Therefore, the corresponding MPF problem is reckoned to be a difficult one. This conjecture is based on the results demonstrated in our previous studies, where a certain kind of MPF problem was proven to be NP-complete.

]]>Symmetry doi: 10.3390/sym13091682

Authors: Marcin Janczarek Zhishun Wei Tharishinny R. Mogan Lei Wang Kunlei Wang Akio Nitta Bunsho Ohtani Ewa Kowalska

Decahedral anatase particles (DAPs) have been prepared by the gas-phase method, characterized, and analyzed for property-governed photocatalytic activity. It has been found that depending on the reaction systems, different properties control the photocatalytic activity, that is, the particle aspect ratio, the density of electron traps and the morphology seem to be responsible for the efficiency of water oxidation, methanol dehydrogenation and oxidative decomposition of acetic acid, respectively. For the discussion on the dependence of the photocatalytic activity on the morphology and/or the symmetry other titania-based photocatalysts have also been analyzed, that is, octahedral anatase particles (OAP), commercial titania P25, inverse opal titania with and without incorporated gold NPs in void spaces and plasmonic photocatalysts (titania with deposits of gold). It has been concluded that though the morphology governs photocatalytic activity, the symmetry (despite its importance in many cases) rather does not control the photocatalytic performance.

]]>Symmetry doi: 10.3390/sym13091680

Authors: Tong Li Xudong Liu

Electric vehicle has become the main trend of the development of automobile industry. As a highly symmetrical system, the characteristics of drive motor will have a great impact on the driving comfort. Aiming at the control regulation of permanent magnet synchronous motor (PMSM) drive, a model-free and non-cascade sliding mode control with a fast-reaching law is proposed in this paper. Firstly, the mathematical model of PMSM is constructed as an ultra-local model without considering any motor parameters. Then, to improve the response speed, an integral sliding mode method with a fast reaching law is proposed, and the fast convergence can be realized. The controller system adopts single loop non-cascade control, which greatly simplifies the system structure. In order to further improve the anti-disturbance performance of the system, the dual disturbance observers are used to compensate the disturbance through feed-forward control. The stability of the system is proved by Lyapunov. Finally, the experimental results show that the proposed method has faster convergence speed and stronger anti-disturbance ability.

]]>Symmetry doi: 10.3390/sym13091681

Authors: Elizaveta Fedorova Andrey Stavrianidi Irina Minenkova Aleksey Buryak

A combination of theoretical and experimental approaches was applied to determine the chromatographic rules of isomeric compounds’ behavior for preliminary identification. In gas chromatography-mass spectrometry (GC-MS), identification is performed by spectra matching, however, difficulties arise with isomeric compounds, which cannot be distinguished from each other without additional information. The thermodynamic characteristics of the adsorption of symmetric and asymmetric isomers of chlorophenylphenols, dimethoxybiphenyls, tri- and tetrachlorobiphenyls were determined using molecular statistical calculations. By-products in the chlorination of 4-hydroxybiphenyl were identified: 4-hydroxy-2,3′- and 3,2′-dichlorobiphenyls, 4-hydroxy-3,5,2′- and 2,3,6-trichlorobiphenyls. A developed theoretical approach was applied to predict the retention order of tri- and tetra-chlorobiphenyls. The GC-MS data and molecular statistical calculations made it possible to determine the main products of methoxybenzene dimerization as well as identify impurities. Thermodynamic parameters were received to describe the unusual retention behavior of epimers in reversed-phase high-performance liquid chromatography. Molecular descriptors were calculated to determine correlation with retention of both structural isomers and epimers. Descriptor combining surface area and partial charge information turned out to be useful in evaluating retention order for isomers.

]]>Symmetry doi: 10.3390/sym13091679

Authors: Guosheng Su Yuhao Wang Zhitao Han Peirong Zhang Hongxia Zhang Baolin Wang Zhanqiang Liu

The contact stress and heating effect between the cutting tool and workpiece in metal machining is symmetrical. However, the symmetry may be destroyed by changes in the workpiece material mechanical properties, such as ductility. The goal of this study is to reveal the wear characteristics of the cutting tool in machining a ductile metal with the cutting speed at which the metal is embrittled by the high-strain-rate-embrittle effect (HSREE). Orthogonal high-speed turning experiments were carried out. Pure iron type DT8 was cut at different cutting speeds, ranging from 1000 m/min to 9000 m/min. The shape and morphology of the chips obtained in the experiment were observed and analyzed by optical microscope and scanning electron microscope (SEM). Tool wear characteristics at different cutting speeds were observed. It shows that the pure iron becomes completely brittle when the cutting speed is higher than 8000 m/min. On the rake face, the coating of the cutting tool bursts apart and peels off. A matrix crack originates in the cutting edge or rake face and extends to the flank face of the cutting tool. The effects of HSREE on the tool wear is discussed. The findings of this study are helpful for choosing a suitable tool for brittle cutting of the ductile metal pure iron with very high cutting speed and solving the problems in machining due to its high ductility and high stickiness.

]]>Symmetry doi: 10.3390/sym13091678

Authors: Michela Mapelli Filippo Santoliquido Yann Bouffanais Manuel Arca Sedda Maria Celeste Artale Alessandro Ballone

Hierarchical mergers are one of the distinctive signatures of binary black hole (BBH) formation through dynamical evolution. Here, we present a fast semi-analytic approach to simulate hierarchical mergers in nuclear star clusters (NSCs), globular clusters (GCs) and young star clusters (YSCs). Hierarchical mergers are more common in NSCs than they are in both GCs and YSCs because of the different escape velocity. The mass distribution of hierarchical BBHs strongly depends on the properties of first-generation BBHs, such as their progenitor’s metallicity. In our fiducial model, we form black holes (BHs) with masses up to ∼103 M⊙ in NSCs and up to ∼102 M⊙ in both GCs and YSCs. When escape velocities in excess of 100 km s−1 are considered, BHs with mass &gt;103 M⊙ are allowed to form in NSCs. Hierarchical mergers lead to the formation of BHs in the pair instability mass gap and intermediate-mass BHs, but only in metal-poor environments. The local BBH merger rate in our models ranges from ∼10 to ∼60 Gpc−3 yr−1; hierarchical BBHs in NSCs account for ∼10−2–0.2 Gpc−3 yr−1, with a strong upper limit of ∼10 Gpc−3 yr−1. When comparing our models with the second gravitational-wave transient catalog, we find that multiple formation channels are favored to reproduce the observed BBH population.

]]>Symmetry doi: 10.3390/sym13091677

Authors: Qingyi Wang Yiqiong Zhang Shuai Yin Yuduo Wang Genping Wu

In recent years, the problem of underdetermined blind source separation (UBSS) has become a research hotspot due to its practical potential. This paper presents a novel method to solve the problem of UBSS, which mainly includes the following three steps: Single source points (SSPs) are first screened out using the principal component analysis (PCA) approach, which is based on the statistical features of signal time-frequency (TF) points. Second, a mixing matrix estimation method is proposed that combines Ordering Points To Identify the Clustering Structure (OPTICS) with an improved potential function to directly detect the number of source signals, remove noise points, and accurately calculate the mixing matrix vector; it is independent of the input parameters and offers great accuracy and robustness. Finally, an improved subspace projection method is used for source signal recovery, and the upper limit for the number of active sources at each mixed signal is increased from m−1 to m. The unmixing process of the proposed algorithm is symmetrical to the actual signal mixing process, allowing it to accurately estimate the mixing matrix and perform well in noisy environments. When compared to previous methods, the source signal recovery accuracy is improved. The method’s effectiveness is demonstrated by both theoretical and experimental results.

]]>Symmetry doi: 10.3390/sym13091676

Authors: Maria Paola Tramonti Fantozzi Ottavia Marconi Federica Simoni Vincenzo De Cicco Davide De Cicco Enrico Cataldo Massimo Barresi Luca Bruschini Paola d’Ascanio Ugo Faraguna Diego Manzoni

In humans, the asymmetry in the masseter electromyographic (EMG) activity during clenching is positively correlated with the degree of pupil size asymmetry (anisocoria) at rest. Anisocoria reveals an asymmetry in LC activity, which may lead to an imbalance in cortical excitability, detrimental to performance. Hereby, we investigated, in individual subjects, the possibility that occlusal correction, which decreases EMG asymmetry, improves performance by balancing LC activity. Cognitive performance, task-related mydriasis, and pupil size at rest were modified by changing the occlusal condition. Occlusal-related changes in performance and mydriasis were negatively correlated with anisocoria changes in only 12/20 subjects. Within this population, spontaneous fluctuations in mydriasis and anisocoria also appeared negatively coupled. Occlusal-related changes in performance and mydriasis were negatively correlated with those in average pupil size (a proxy of average LC activity) in 19/20 subjects. The strongest association was observed for the pupil changes occurring on the side with higher EMG activity during clenching. These findings indicate that the effects of occlusal conditions on cognitive performance were coupled to changes in the asymmetry of LC activity in about half of the subjects, while they were related to changes in the average tonic LC activity in virtually all of them.

]]>Symmetry doi: 10.3390/sym13091675

Authors: Edgar F. Rauch Patrick Harrison Muriel Véron

ACOM/TEM is an automated electron diffraction pattern indexing tool that enables the structure, phase and crystallographic orientation of materials to be routinely determined. The software package, which is part of ACOM/TEM, has substantially evolved over the last fifteen years and has pioneered numerous additional functions with the constant objective of improving its capabilities to make the tremendous amount of information contained in the diffraction patterns easily available to the user. Initially devoted to the analysis of local crystallographic texture, and as an alternative to both X-ray pole figure measurement and EBSD accessories for scanning electron microscopes, it has rapidly proven itself effective to distinguish multiple different phases contained within a given sample, including amorphous phases. Different strategies were developed to bypass the inherent limitations of transmission electron diffraction patterns, such as 180° ambiguities or the complexity of patterns produced from overlapping grains. Post processing algorithms have also been developed to improve the angular resolution and to increase the computing rate. The present paper aims to review some of these facilities. On-going works on 3D reconstruction are also introduced.

]]>Symmetry doi: 10.3390/sym13091674

Authors: Chao Tang Rong Hou

As we know, the periodic functions are symmetric within a cycle time, and it is meaningful to generalize the periodicity into more general cases, such as almost periodicity or almost automorphy. In this work, we introduce the concept of Poisson Sγ2-pseudo almost automorphy (or Poisson generalized Stepanov-like pseudo almost automorphy) for stochastic processes, which are almost-symmetric within a suitable period, and establish some useful properties of such stochastic processes, including the composition theorems. In addition, we apply a Krasnoselskii–Schaefer type fixed point theorem to obtain the existence of pseudo almost automorphic solutions in distribution for some semilinear stochastic differential equations driven by Lévy noise under Sγ2-pseudo almost automorphic coefficients. In addition, then we establish optimal control results on the bounded interval. Finally, an example is provided to illustrate the theoretical results obtained in this paper.

]]>Symmetry doi: 10.3390/sym13091673

Authors: Aili Wang Chengyang Liu Dong Xue Haibin Wu Yuxiao Zhang Meihong Liu

Although hyperspectral data provide rich feature information and are widely used in other fields, the data are still scarce. Training small sample data classification is still a major challenge for HSI classification based on deep learning. Recently, the method of mining sample relationships has been proved to be an effective method for training small samples. However, this strategy requires high computational power, which will increase the difficulty of network model training. This paper proposes a modified depthwise separable relational network to deeply capture the similarity between samples. In addition, in order to effectively mine the similarity between samples, the feature vectors of support samples and query samples are symmetrically spliced. According to the metric distance between symmetrical structures, the dependence of the model on samples can be effectively reduced. Firstly, in order to improve the training efficiency of the model, depthwise separable convolution is introduced to reduce the computational cost of the model. Secondly, the Leaky-ReLU function effectively activates all neurons in each layer of neural network to improve the training efficiency of the model. Finally, the cosine annealing learning rate adjustment strategy is introduced to avoid the model falling into the local optimal solution and enhance the robustness of the model. The experimental results on two widely used hyperspectral remote sensing image data sets (Pavia University and Kennedy Space Center) show that compared with seven other advanced classification methods, the proposed method achieves better classification accuracy under the condition of limited training samples.

]]>Symmetry doi: 10.3390/sym13091672

Authors: Luis Adrián Lizama-Pérez José Mauricio López-Romero

We present an error reconciliation method for Quantum Key Distribution (QKD) that corrects 100% of errors generated in regular binary frames transmitted over a noisy quantum channel regardless of the quantum channel error rate. In a previous investigation, we introduced a novel distillation QKD algorithm whose secret key rate descends linearly with respect to the channel error rate. Now, as the main achievement of this work, we demonstrate an improved algorithm capable of retaining almost all the secret information enclosed in the regular binary frames. Remarkably, this technique increases quadratically the secret key rate as a function of the double matching detection events and doubly quadratically in the number of the quantum pulses. Furthermore, this reconciliation method opens up the opportunity to use less attenuated quantum pulses, would allow greater QKD distances at drastically increased secret key rate. Since our method can be implemented as a software update, we hope that quantum key distribution technology would be fast deployed over global data networks in the quantum era.

]]>Symmetry doi: 10.3390/sym13091671

Authors: Fanpyn Liu

Wireless sensor networks (WSNs) are the cornerstone of the current Internet of Things era. They have limited resources and features, a smaller packet size than other types of networks, and dynamic multi-hop transmission. WSNs can monitor a particular area of interest and are used in many different applications. For example, during the COVID-19 pandemic, WSNs have been used to measure social distancing/contact tracing among people. However, the major challenge faced by WSN protocols is limited battery energy. Therefore, the whole WSN area is divided into odd clusters using k-means++ clustering to make a majority rule decision to reduce the amount of additional data sent to the base station (or sink) and achieve node energy-saving efficiency. This study proposes an energy-efficient binarized data aggregation (EEBDA) scheme, by which, through a threshold value, the collected sensing data are asserted with binary values. Subsequently, the corresponding cluster head (CH), according to the Hamming weight and the final majority decision, is calculated and sent to the base station (BS). The EEBDA is based on each cluster and divides the entire WSN area into four quadrants. All CHs construct a data-relay transmission link in the same quadrant; the binary value is transferred from the CHs to the sink. The EEBDA adopts a CH rotation scheme to aggregate the data based on the majority results in the cluster. The simulation results demonstrate that the EEBDA can reduce redundant data transmissions, average the energy consumption of nodes in the cluster, and obtain a better network lifetime when compared to the LEACH, LEACH-C, and DEEC algorithms.

]]>Symmetry doi: 10.3390/sym13091670

Authors: Agnese Barbensi Naya Yerolemou Oliver Vipond Barbara I. Mahler Pawel Dabrowski-Tumanski Dimos Goundaroulis

Understanding how knotted proteins fold is a challenging problem in biology. Researchers have proposed several models for their folding pathways, based on theory, simulations and experiments. The geometry of proteins with the same knot type can vary substantially and recent simulations reveal different folding behaviour for deeply and shallow knotted proteins. We analyse proteins forming open-ended trefoil knots by introducing a topologically inspired statistical metric that measures their entanglement. By looking directly at the geometry and topology of their native states, we are able to probe different folding pathways for such proteins. In particular, the folding pathway of shallow knotted carbonic anhydrases involves the creation of a double-looped structure, contrary to what has been observed for other knotted trefoil proteins. We validate this with Molecular Dynamics simulations. By leveraging the geometry and local symmetries of knotted proteins’ native states, we provide the first numerical evidence of a double-loop folding mechanism in trefoil proteins.

]]>Symmetry doi: 10.3390/sym13091669

Authors: Ber-Lin Yu Zhongshan Li Sanzhang Xu

An n×n matrix A is called eventually exponentially positive (EEP) if etA=∑k=0∞tkAkk!&gt;0 for all t≥t0, where t0≥0. A matrix whose entries belong to the set {+,−,0} is called a sign pattern. An n×n sign pattern A is called potentially eventually exponentially positive (PEEP) if there exists some real matrix realization A of A that is EEP. Characterizing the PEEP sign patterns is a longstanding open problem. In this article, A is called minimally potentially eventually exponentially positive (MPEEP), if A is PEEP and no proper subpattern of A is PEEP. Some preliminary results about MPEEP sign patterns and PEEP sign patterns are established. All MPEEP sign patterns of orders n≤3 are identified. For the n×n tridiagonal sign patterns Tn, we show that there exists exactly one MPEEP tridiagonal sign pattern Tno. Consequently, we classify all PEEP tridiagonal sign patterns as the superpatterns of Tno. We also classify all PEEP star sign patterns Sn and double star sign patterns DS(n,m) by identifying all the MPEEP star sign patterns and the MPEEP double star sign patterns, respectively.

]]>Symmetry doi: 10.3390/sym13091668

Authors: Abel Cabrera Martínez Luis P. Montejano Juan A. Rodríguez-Velázquez

The authors wish to make the following corrections on paper [...]

]]>Symmetry doi: 10.3390/sym13091665

Authors: Fei Chen Xiaodong Wang

Recently, Discriminative Correlation Filters (DCF) have shown excellent performance in visual object tracking. The correlation for a computing response map can be conducted efficiently in Fourier domain by Discrete Fourier Transform (DFT) of inputs, where the DFT of an image has symmetry on the Fourier domain. To enhance the robustness and discriminative ability of the filters, many efforts have been devoted to optimizing the learning process. Regularization methods, such as spatial regularization or temporal regularization, used in existing DCF trackers aim to enhance the capacity of the filters. Most existing methods still fail to deal with severe appearance variations—in particular, the large scale and aspect ratio changes. In this paper, we propose a novel framework that employs adaptive spatial regularization and temporal regularization to learn reliable filters in both spatial and temporal domains for tracking. To alleviate the influence of the background and distractors to the non-rigid target objects, two sub-models are combined, and multiple features are utilized for learning of robust correlation filters. In addition, most DCF trackers that applied 1-dimensional scale space search method suffered from appearance changes, such as non-rigid deformation. We proposed a 2-dimensional scale space search method to find appropriate scales to adapt to large scale and aspect ratio changes. We perform comprehensive experiments on four benchmarks: OTB-100, VOT-2016, VOT-2018, and LaSOT. The experimental results illustrate the effectiveness of our tracker, which achieved a competitive tracking performance. On OTB-100, our tracker achieved a gain of 0.8% in success, compared to the best existing DCF trackers. On VOT2018, our tracker outperformed the top DCF trackers with a gain of 1.1% in Expected Average Overlap (EAO). On LaSOT, we obtained a gain of 5.2% in success, compared to the best DCF trackers.

]]>Symmetry doi: 10.3390/sym13091667

Authors: Siyuan Sun Nicolas A. Diaz Pavel Nagorny

This communication describes the synthesis of new bis-oxazoline chiral ligands (SPIROX) derived from the C2-symmetric spirocyclic scaffold (SPIROL). The readily available (R,R,R)-SPIROL (2) previously developed by our group was subjected to a three-step sequence that provided key diacid intermediate (R,R,R)-7 in 75% yield. This intermediate was subsequently coupled with (R)- and (S)-phenylglycinols to provide diastereomeric products, the cyclization of which led to two diastereomeric SPIROX ligands (R,R,R,R,R)-3a and (R,R,R,S,S)-3b in 85% and 79% yield, respectively. The complexation of (R,R,R,R,R)-3a and (R,R,R,S,S)-3b with CuCl and Cu(OTf)2 resulted in active catalysts that promoted the asymmetric reaction of α-diazopropionate and phenol. The resultant O–H insertion product was formed in 88% yield, and with excellent selectivity (97% ee) when ligand (R,R,R,R,R)-3a was used.

]]>Symmetry doi: 10.3390/sym13091666

Authors: Tao Yu Quansheng Sun Chunwei Li Yancheng Liu

Carbon fiber-reinforced polymer (CFRP) reinforcement technology has been widely used in the reinforcement of reinforced concrete (RC) beams. At this stage, high prestressed CFRP board reinforcement is often used in actual reinforcement. However, most reinforced bridges are designed for a long time, and the design value of the protective layer is low, and it is impossible to achieve a large prestressed tension. Therefore, this paper proposes the reverse-arch method to paste the CFRP board and apply low prestress to strengthen the symmetrical RC beam. Through the three-point forward loading test, the cracking load, ultimate load, crack width, mid-span deflection, strain and failure mode of a reverse-arch method-pasted CFRP board-reinforced beam, a directly pasted CFRP board-reinforced beam and an unreinforced beam are compared. The results show that the load-bearing capacity and stiffness of the test beam can be improved by pasting CFRP plates with anti-arch method, but the ductility of the test beam is reduced. Compared with the unreinforced beam, the maximum cracking load and ultimate load are increased by 56% and 63% respectively. The reverse-arch method can produce low prestress, improve the stiffness and bearing capacity of members, and has a good prospect of engineering application.

]]>Symmetry doi: 10.3390/sym13091664

Authors: An-Hsu Chen Chih-Hui Chiu Chin-Hsien Hsu I-Lin Wang Kuei-Ming Chou Yung-Shen Tsai Yu-Fang Lin Che-Hsiu Chen

The effect of asymmetry on flexibility and jump in taekwondo athletes and the influence of vibration foam rolling on asymmetry and frequency speed of kick test has not been examined. This study examined the effects of three warm-up protocols on subsequent sports performance in elite male taekwondo athletes. Fifteen elite male taekwondo athletes (20.63 ± 1.18 years) completed three warm-up protocols in a randomized order: general warm-up [GW], GW with vibration foam rolling [GW + VR], and GW with double VR for the weaker leg [GW + double VR]), was delivered before the subsequent tests: flexibility, single-leg countermovement jump (CMJ), 505 agility, hexagon test, and multiple frequency speed of kick tests (FSKTs). Relative to GW, the GW + VR significantly improved the hexagon test (GW + VR = 11.60 ± 1.01 s; GW = 12.80 ± 1.58 s). In addition, the GW + VR and GW + double VR yielded greater kick numbers in FSKT 5 (GW + VR = 21.13 ± 1.96 reps; GW + double VR = 20.93 ± 1.67 reps; GW = 19.27 ± 1.62 reps) and a higher kick decrement index (GW + VR = 5.45 ± 2.57%; GW + double VR = 5.88 ± 3.22%; GW = 9.54 ± 5.00%). However, the GW + VR and GW + double VR did not significantly improve the flexibility and CMJ asymmetry performance. The GW + VR is more beneficial for warming up than the GW is among male collegiate taekwondo athletes.

]]>Symmetry doi: 10.3390/sym13091663

Authors: Alexander Farrugia

Let G be a simple graph and {1,2,…,n} be its vertex set. The polynomial reconstruction problem asks the question: given a deck P(G) containing the n characteristic polynomials of the vertex deleted subgraphs G−1, G−2, …, G−n of G, can ϕ(G,x), the characteristic polynomial of G, be reconstructed uniquely? To date, this long-standing problem has only been solved in the affirmative for some specific classes of graphs. We prove that if there exists a vertex v such that more than half of the eigenvalues of G are shared with those of G−v, then this fact is recognizable from P(G), which allows the reconstruction of ϕ(G,x). To accomplish this, we make use of determinants of certain walk matrices of G. Our main result is used, in particular, to prove that the reconstruction of the characteristic polynomial from P(G) is possible for a large subclass of disconnected graphs, strengthening a result by Sciriha and Formosa.

]]>Symmetry doi: 10.3390/sym13091662

Authors: Marcel Mellmann Markus Scholle

By rigorous analysis, it is proven that from discontinuous Lagrangians, which are invariant with respect to the Galilean group, Rankine–Hugoniot conditions for propagating discontinuities can be derived via a straight forward procedure that can be considered an extension of Noether’s theorem. The use of this general procedure is demonstrated in particular for a Lagrangian for viscous flow, reproducing the well known Rankine–Hugoniot conditions for shock waves.

]]>Symmetry doi: 10.3390/sym13091661

Authors: Janaki Iyer Arvind Hariharan Uyen Minh Nha Cao Simon D. Tran

Facial asymmetry refers to the absence of, or the deviation from the regular mirror image of facial structures, relative to a referenced midline axis. It can be attributed to a wide spectrum of deformities, including congenital, developmental, or acquired conditions, which can originate either prenatally or postnatally. Though highly prevalent, asymmetry commonly goes undiagnosed due to its subtle or relative nature. Among the spectrum of conditions, acquired cases are triggered postnatally, in previously normal individuals, thus subjecting them to sudden, eventful psychological and psychosocial disharmony. When detected early, timely management may help intervene progressive growth of these conditions. This, therefore, emphasizes the need for a thorough diagnostic workup including medical/dental history, clinical examinations, study models, photographic and radiographic records for a case-by-case basis to prevent severe functional and aesthetic complications. Recently, advanced diagnostic procedures, such as stereophotogrammetry, 3D stereolithographic models, skeletal scintigraphy (radionucleotide scans), 3D computed tomographic scans, cone-beam computed tomography, and magnetic resonance imaging, have provided innovative diagnostic instruments for numerous craniofacial defects. This descriptive review aims at focusing on the factors leading to frequently encountered conditions of acquired facial asymmetry and highlights their clinical evaluation, conservative and surgical interventions by a multi-disciplinary team of clinicians.

]]>Symmetry doi: 10.3390/sym13091660

Authors: Mikołaj M. Paraniak Berthold-Georg Englert

Originally conceived as a thought experiment, an apparatus consisting of two Stern–Gerlach apparatuses joined in an inverted manner touched on the fundamental question of the reversibility of evolution in quantum mechanics. Theoretical analysis showed that uniting the two partial beams requires an extreme level of experimental control, making the proposal in its original form unrealizable in practice. In this work, we revisit the above question in a numerical study concerning the possibility of partial-beam recombination in a spin-coherent manner. Using the Suzuki–Trotter numerical method of wave propagation and a configurable, approximation-free magnetic field, a simulation of a transversal Stern–Gerlach interferometer under ideal conditions is performed. The result confirms what has long been hinted at by theoretical analyses: the transversal Stern–Gerlach interferometer quantum dynamics is fundamentally irreversible even when perfect control of the associated magnetic fields and beams is assumed.

]]>Symmetry doi: 10.3390/sym13091659

Authors: Edward Bormashenko Irina Legchenkova Mark Frenkel Nir Shvalb Shraga Shoval

A continuous measure of symmetry and the Voronoi entropy of 2D patterns representing Voronoi diagrams emerging from the Penrose tiling were calculated. A given Penrose tiling gives rise to a diversity of the Voronoi diagrams when the centers, vertices, and the centers of the edges of the Penrose rhombs are taken as the seed points (or nuclei). Voronoi diagrams keep the initial symmetry group of the Penrose tiling. We demonstrate that the continuous symmetry measure and the Voronoi entropy of the studied sets of points, generated by the Penrose tiling, do not necessarily correlate. Voronoi diagrams emerging from the centers of the edges of the Penrose rhombs, considered nuclei, deny the hypothesis that the continuous measure of symmetry and the Voronoi entropy are always correlated. The Voronoi entropy of this kind of tiling built of asymmetric convex quadrangles equals zero, whereas the continuous measure of symmetry of this pattern is high. Voronoi diagrams generate new types of Penrose tiling, which are different from the classical Penrose tessellation.

]]>Symmetry doi: 10.3390/sym13091658

Authors: Javier Murillo Pilar García-Navarro

The numerical modeling of one-dimensional (1D) domains joined by symmetric or asymmetric bifurcations or arbitrary junctions is still a challenge in the context of hyperbolic balance laws with application to flow in pipes, open channels or blood vessels, among others. The formulation of the Junction Riemann Problem (JRP) under subsonic conditions in 1D flow is clearly defined and solved by current methods, but they fail when sonic or supersonic conditions appear. Formulations coupling the 1D model for the vessels or pipes with other container-like formulations for junctions have been presented, requiring extra information such as assumed bulk mechanical properties and geometrical properties or the extension to more dimensions. To the best of our knowledge, in this work, the JRP is solved for the first time allowing solutions for all types of transitions and for any number of vessels, without requiring the definition of any extra information. The resulting JRP solver is theoretically well-founded, robust and simple, and returns the evolving state for the conserved variables in all vessels, allowing the use of any numerical method in the resolution of the inner cells used for the space-discretization of the vessels. The methodology of the proposed solver is presented in detail. The JRP solver is directly applicable if energy losses at the junctions are defined. Straightforward extension to other 1D hyperbolic flows can be performed.

]]>Symmetry doi: 10.3390/sym13091657

Authors: Claudia Dolci Fadil Elamin Annalisa Cappella Luisa Barni Daniele M. Gibelli Chiarella Sforza

The evaluation of the symmetry of orbital and ear soft tissues is important for aesthetic and reconstructive surgery. However, little information is available for these facial regions, especially in children. We analyzed the orbital and auricular symmetry in 418 Italian and 206 Sudanese subadult males divided into three age groups (8–11, 12–15, and 16–19 years old). Orbital and auricular height and width were measured for calculating fluctuating and directional asymmetry indices. Differences in asymmetry indices according to ethnicity and age group were assessed through the two-way ANOVA test (p &lt; 0.01), while differences in the prevalence of right or left asymmetry according to ethnicity were assessed through the chi-square test. On average, directional asymmetry indices ranged from −2.1% to 1.1%, while fluctuating asymmetry indices ranged between 2.9% and 5.4%, corresponding to a small effect size and to 1.06–2.34 mm actual dimensions. Sudanese subjects showed a greater asymmetry for all the indices except for the fluctuating asymmetry of orbital height (p &lt; 0.01). The directional asymmetry of auricular width increased with age. A prevalent right-side asymmetry was found for all the orbital indices (p &lt; 0.001) in both populations, although significantly more prevalent in Sudanese individuals (over 83% for both measures), while auricular measures showed a prevalent left asymmetry exclusively in the Sudanese but with lower percentages. Aside from the limited effect size, the results proved the ethnic variability of asymmetry of orbital and auricle regions in children and suggest the need to collect more population data.

]]>Symmetry doi: 10.3390/sym13091656

Authors: Dana Ortansa Dorohoi Dan Gheorghe Dimitriu Ana Cezarina Morosanu Nicoleta Puica Melniciuc Ion Hurjui Mihaela Miron Gabriel Grigore Mariciuc Valentina Closca Corina Cheptea

Four carbanion monosubstituted p-aryl-1,2,4-triazol-1-ium methylids are subjected to a comparative study between their spectral and quantum-mechanical parameters in order to obtain more information about their structural features in hydroxyl solvents as water and ethanol and also on the nature of electronic absorption transitions from the visible range. The quantum mechanical analysis, made by the Spartan’14 program, established a series of molecular parameters of the studied ylids important for their reactivity and for intermolecular interactions with hydroxyl liquids. An extensive solvatochromic study of 1,2,4-triazol-1-ium ylids is impossible due to their limited solubility in liquids. Binary solvent mixtures of water and ethanol with known solvent parameters from the literature were used for this study. The electronic absorption spectra in binary solvents water and ethanol were used to establish the influence of intermolecular interactions on the spectral characteristics of the studied methylids and also on the composition of their first solvation shell in ternary solutions. The difference between the interaction energies in molecular pairs ylid–water and ylid–ethanol was determined based on the statistical cell model applied to the ternary solutions of the type of ylid + water + ethanol. The obtained values are very small due to the hydroxylic nature of the two solvents.

]]>Symmetry doi: 10.3390/sym13091655

Authors: Miguel Ángel Rivas-Fernández Benxamín Varela-López Susana Cid-Fernández Santiago Galdo-Álvarez

Being language a paradigm of structural and functional asymmetry in cognitive processing, the left Inferior Frontal Gyrus has been consistently related to speech production. In fact, it has been considered a key node in cortical networks responsible for different components of naming. However, isolating these components (e.g., lexical, syntactic, and phonological retrieval) in neuroimaging studies is difficult due to the use of different baselines and tasks. In the present study, functional activation and connectivity of the left inferior frontal gyrus was explored using functional magnetic resonance imaging. Participants performed a covert naming task (pressing a button based on a phonological characteristic). Two conditions were compared: drawings of objects and single letters (baseline condition). Differences in activation and functional connectivity were obtained for objects and letters in different areas of the left Inferior Frontal Gyrus. The pars triangularis was involved in the retrieval of lexical-phonological information, showing a pattern of connectivity with temporal areas in the search for the name of objects and with perisylvanian areas for letters. Selection of phonological information seems to involve the pars opercularis both to letters and objects but recruiting supramarginal and superior temporal areas to letters, probably related to orthographic-phonological conversion. The results support the notion of the left Inferior Frontal Gyrus as a buffer forwarding neural information across cortical networks responsible for different components of speech production.

]]>Symmetry doi: 10.3390/sym13091654

Authors: Nicklas Anttu

When modelling the absorption in semiconductor nanowire (NW) arrays for solar cell and photodetector applications, the array is typically assumed to be infinitely periodic such that a single unit cell suffices for the simulations. However, any actual array is of a finite extent and might also show varying types of localized defects such as missing or electrically non-contacted individual NWs. Here, we study InP NWs of 2000 nm in length and 180 nm in diameter, placed in a square array of 400 nm in period, giving a rather optimized absorption of sunlight. We show that the absorption in the center NW of a finite N × N array converges already at N = 5 close to the value found for the corresponding infinite array. Furthermore, we show that a missing NW causes an enhanced absorption in neighboring nanowires, which compensates for 77% of the absorption loss due to the missing NW. In other words, an electrically non-contacted NW, which absorbs light but cannot contribute to the external short-circuit current, is a four times worse defect than a missing NW.

]]>Symmetry doi: 10.3390/sym13091653

Authors: Waggas Galib Atshan Ibtihal Abdul Ridha Rahman Alina Alb Lupaş

In this paper, we introduce new subclasses RΣ,b,cμ,αλ,δ,τ,Φ and KΣ,b,cμ,αλ,δ,η,Φ of bi-univalent functions in the open unit disk U by using quasi-subordination conditions and determine estimates of the coefficients a2 and a3 for functions of these subclasses. We discuss the improved results for the associated classes involving many of the new and well-known consequences. We notice that there is symmetry in the results obtained for the new subclasses RΣ,b,cμ,αλ,δ,τ,Φ and KΣ,b,cμ,αλ,δ,η,Φ, as there is a symmetry for the estimations of the coefficients a2 and a3 for all the subclasses defind in our this paper.

]]>Symmetry doi: 10.3390/sym13091652

Authors: Wanida Panup Rabian Wangkeeree

In this paper, we propose a stochastic gradient descent algorithm, called stochastic gradient descent method-based generalized pinball support vector machine (SG-GPSVM), to solve data classification problems. This approach was developed by replacing the hinge loss function in the conventional support vector machine (SVM) with a generalized pinball loss function. We show that SG-GPSVM is convergent and that it approximates the conventional generalized pinball support vector machine (GPSVM). Further, the symmetric kernel method was adopted to evaluate the performance of SG-GPSVM as a nonlinear classifier. Our suggested algorithm surpasses existing methods in terms of noise insensitivity, resampling stability, and accuracy for large-scale data scenarios, according to the experimental results.

]]>Symmetry doi: 10.3390/sym13091651

Authors: Rajat Kanti Nath Walaa Nabil Taha Fasfous Kinkar Chandra Das Yilun Shang

The commuting graph of a finite non-abelian group G with center Z(G), denoted by Γc(G), is a simple undirected graph whose vertex set is G∖Z(G), and two distinct vertices x and y are adjacent if and only if xy=yx. Alwardi et al. (Bulletin, 2011, 36, 49-59) defined the common neighborhood matrix CN(G) and the common neighborhood energy Ecn(G) of a simple graph G. A graph G is called CN-hyperenergetic if Ecn(G)&gt;Ecn(Kn), where n=|V(G)| and Kn denotes the complete graph on n vertices. Two graphs G and H with equal number of vertices are called CN-equienergetic if Ecn(G)=Ecn(H). In this paper we compute the common neighborhood energy of Γc(G) for several classes of finite non-abelian groups, including the class of groups such that the central quotient is isomorphic to group of symmetries of a regular polygon, and conclude that these graphs are not CN-hyperenergetic. We shall also obtain some pairs of finite non-abelian groups such that their commuting graphs are CN-equienergetic.

]]>Symmetry doi: 10.3390/sym13091649

Authors: Zhuang Li Jingyan Qin Xiaotong Zhang Yadong Wan

Class imbalance, as a phenomenon of asymmetry, has an adverse effect on the performance of most machine learning and overlap is another important factor that affects the classification performance of machine learning algorithms. This paper deals with the two factors simultaneously, addressing the class overlap under imbalanced distribution. In this paper, a theoretical analysis is firstly conducted on the existing class overlap metrics. Then, an improved method and the corresponding metrics to evaluate the class overlap under imbalance distributions are proposed based on the theoretical analysis. A well-known collection of the imbalanced datasets is used to compare the performance of different metrics and the performance is evaluated based on the Pearson correlation coefficient and the ξ correlation coefficient. The experimental results demonstrate that the proposed class overlap metrics outperform other compared metrics for the imbalanced datasets and the Pearson correlation coefficient with the AUC metric of eight algorithms can be improved by 34.7488% in average.

]]>Symmetry doi: 10.3390/sym13091650

Authors: Francesco Silvio Gentile Rosita Diana Barbara Panunzi Ugo Caruso Alexander Platonenko Fabien Pascale Roberto Dovesi

The phase transitions between paraelectric (PE) and ferroelectric (FE) isomorph phases of LiNbO3 have been investigated quantum mechanically by using a Gaussian-type basis set, the B3LYP hybrid functional and the CRYSTAL17 code. The structural, electronic and vibrational properties of the two phases are analyzed. The vibrational frequencies evaluated at the Γ point indicate that the paraelectric phase is unstable, with a complex saddle point with four negative eigenvalues. The energy scan of the A2u mode at −215 cm−1 (i215) shows a dumbbell potential with two symmetric minima. The isotopic substitution, performed on the Li and Nb atoms, allows interpretation of the nontrivial mechanism of the phase transition. The ferroelectric phase is more stable than the paraelectric one by 0.32 eV.

]]>Symmetry doi: 10.3390/sym13091646

Authors: Ahmed T. A. Boraei Matti Haukka Ahmed A. M. Sarhan Saied M. Soliman Abdullah Mohammed Al-Majid Assem Barakat

The synthesis of C2-symmetrical bis(β-enamino-pyran-2,4-dione) derivative 3 connected via 1,6-hexylene linker was reported for the first time. X-ray structures and Hirshfeld studies of the new bis- β-enamino-pyran-2,4-dione derivative 3 along with two structurally related pyran-2,4-dione derivatives 2a,b were discussed. A comparative analysis of the different intermolecular contacts affecting the crystal stability was presented. Generally, the H…H, O…H, and H…C interactions are common in all compounds and are considered the most abundant contacts. In addition, DFT calculations were used to compute the electronic properties as well as the 1H and 13C NMR spectra of the studied systems. All compounds (except 3) are polar where 2a (3.540 Debye) has a higher dipole moment than 2b (2.110 Debye). The NMR chemical shifts were calculated and excellent correlations between the calculated and experimental data were obtained (R2 = 0.93–0.94).

]]>Symmetry doi: 10.3390/sym13091648

Authors: Yingying Fu Jing Li Shuiyan Wu Xiaobo Li

In this paper, the dynamic event-triggered tracking control issue is studied for a class of unknown stochastic nonlinear systems with strict-feedback form. At first, neural networks (NNs) are used to approximate the unknown nonlinear functions. Then, a dynamic event-triggered controller (DETC) is designed through the adaptive backstepping method. Especially, the triggered threshold is dynamically adjusted. Compared with its corresponding static event-triggered mechanism (SETM), the dynamic event-triggered mechanism (DETM) can generate a larger execution interval and further save resources. Moreover, it is verified by two simulation examples that show that the closed-loop stochastic system signals are ultimately fourth moment semi-globally uniformly bounded (SGUUB).

]]>Symmetry doi: 10.3390/sym13091647

Authors: Zunan Fu Guoshuai Wang Yanming Yu Li Shi

The pile–bucket foundation that features a bucket slipped onto a monopile is a new type of symmetric offshore foundation supporting the wind turbine. Its load bearing and deformation resistance capacity are unclear, especially when subjected to cyclic horizontal loadings. In this paper, a model test has been designed and carried out for investigating the cyclic behavior of the pile–bucket foundation embedded in soft marine clay. Cyclic horizontal loads are applied in a displacement-controlled manner with different amplitudes and frequencies. The influences of cyclic loading parameters, including the amplitude, the frequency and the cycle number, have been studied from the perspectives of stiffness-degradation and damping effect that are evaluated from the recorded horizontal force–displacement relationships at the loading point. In addition, the influences of cyclic horizontal loading on the bending moment distribution and on the p–y curve have been presented and discussed. The results show that significant reductions in the foundation stiffness and in the soil resistance may be observed during the first few cycles when the loading displacement is relatively high.

]]>Symmetry doi: 10.3390/sym13091645

Authors: Christian Gaß José M. Gracia-Bondía Jens Mund

Modular localization and the theory of string-localized fields have revolutionized several key aspects of quantum field theory. They reinforce the contention that local symmetry emerges directly from quantum theory, but global gauge invariance remains in general an unwarranted assumption to be examined case by case. Armed with those modern tools, we reconsider here the classical Okubo–Marshak argument on the non-existence of a “strong CP problem” in quantum chromodynamics.

]]>Symmetry doi: 10.3390/sym13091644

Authors: Marina Melchionna Antonio Profico Costantino Buzi Silvia Castiglione Alessandro Mondanaro Antonietta Del Bove Gabriele Sansalone Paolo Piras Pasquale Raia

The observation and the quantification of asymmetry in biological structures are deeply investigated in geometric morphometrics. Patterns of asymmetry were explored in both living and fossil species. In living organisms, levels of directional and fluctuating asymmetry are informative about developmental processes and health status of the individuals. Paleontologists are primarily interested in asymmetric features introduced by the taphonomic process, as they may significantly alter the original shape of the biological remains, hampering the interpretation of morphological features which may have profound evolutionary significance. Here, we provide a new R tool that produces the numerical quantification of fluctuating and directional asymmetry and charts asymmetry directly on the specimens under study, allowing the visual inspection of the asymmetry pattern. We tested this show.asymmetry algorithm, written in the R language, on fossil and living cranial remains of the genus Homo. show.asymmetry proved successful in discriminating levels of asymmetry among sexes in Homo sapiens, to tell apart fossil from living Homo skulls, to map effectively taphonomic distortion directly on the fossil skulls, and to provide evidence that digital restoration obliterates natural asymmetry to unnaturally low levels.

]]>Symmetry doi: 10.3390/sym13091643

Authors: Rasoul Daneshfaraz Ehsan Aminvash Mohammad Bagherzadeh Amir Ghaderi Alban Kuriqi Amir Najibi Ana M. Ricardo

This study aims to provide a way to increase the energy dissipation of flow in the inclined drop with environmental and economic considerations. Eighty-one experiments were performed on three types of simple inclined drop and inclined drop equipped with hole and without hole fishway elements with a 200~600 L/min flow rate. In this study, the effect of using fishway elements on hydraulic parameters regarding flow pattern, energy dissipation, relative downstream depth, relative aeration length, relative length of the hydraulic jump, and downstream Froude number of an inclined drop was investigated through physical modeling following the symmetry law. The results showed that in all experimental models, with increasing the relative critical depth parameter, the energy dissipation values increase, and the downstream Froude number decreases. The parameters of relative downstream depth, relative length of a hydraulic jump, and relative aeration length also increase with increasing relative critical depth. On average, 88% of the flow energy dissipation increases with the design of the fishway elements on the structure compared to the simple drop. Model M7 (with holes fish elements) shows the highest energy dissipation, and Model M2 (without holes fish elements) has the highest flow aeration length and relative downstream water depth.

]]>Symmetry doi: 10.3390/sym13091642

Authors: Laura-Bianca Enache Veronica Anăstăsoaie Cecilia Lete Alina Giorgiana Brotea Ovidiu-Teodor Matica Cristina-Andreea Amarandei Jérémy Brandel Eleonora-Mihaela Ungureanu Marius Enăchescu

A recently synthesized azulene-tetrazole molecular receptor is proposed in this paper to continue the series of azulene substituted compounds that have been developed to build polyazulene-based materials for heavy metal (HM) ion detection. This study focuses on characterization of (E)-5-((6-t-butyl-4,8-dimethylazulen-1-yl) diazenyl)-1H-tetrazole (L) by electrochemical techniques in view of its use for designing electrochemical sensors for HM ion complexation. The character of redox processes was proved by cyclic, differential pulse, and rotating disk electrode voltammetry. An in-depth thermodynamic study of the complexation properties of the free ligand with Pb(II) and Cd(II) from aqueous solutions was performed, and the stoichiometry and stability constant values were determined. Chemically modified electrodes (CMEs) based on L (L-CMEs) prepared by controlled potential electrolysis (CPE) at different applied potentials and charges were characterized by cyclic voltammetry and electrochemical impedance spectroscopy (EIS). Their surface morphology was examined by scanning electron microscopy (SEM). The complexing properties of L-CMEs were investigated towards the detection of HM ions by anodic stripping and compared to the stability constants of the complexes in solution. Voltametric curves showed well-defined peaks for Pb (II), Cd (II), Cu (II) and Hg (II), but the responses differ from each other and vary depending on the ion concentrations in the accumulation solutions. The best results were obtained for Pb(II) and Cd(II) ions. The results obtained for Pb(II) are promising and can be used for its analysis in water solutions (detection limit of about 10−9 M).

]]>Symmetry doi: 10.3390/sym13091641

Authors: Zsolt Benedek Peter Girnt Julianna Olah

Conjugated estrogen medicines, which are produced from the urine of pregnant mares for the purpose of menopausal hormone replacement therapy (HRT), contain the sulfate conjugates of estrone, equilin, and equilenin in varying proportions. The latter three steroid sex hormones are highly similar in molecular structure as they only differ in the degree of unsaturation of the sterane ring “B”: the cyclohexene ring in estrone (which is naturally present in both humans and horses) is replaced by more symmetrical cyclohexadiene and benzene rings in the horse-specific (“equine”) hormones equilin and equilenin, respectively. Though the structure of ring “B” has only moderate influence on the estrogenic activity desired in HRT, it might still significantly affect the reactivity in potential carcinogenic pathways. In the present theoretical study, we focus on the interaction of estrogen orthoquinones, formed upon metabolic oxidation of estrogens in breast cells with purine nucleosides. This multistep process results in a purine base loss in the DNA chain (depurination) and the formation of a “depurinating adduct” from the quinone and the base. The point mutations induced in this manner are suggested to manifest in breast cancer development in the long run. We examine six reactions between deoxyadenosine and deoxyguanosine as nucleosides and estrone-3,4-quinone, equilin-3,4-quinone, and equilenin-3,4-quinone as mutagens. We performed DFT calculations to determine the reaction mechanisms and establish a structure–reactivity relationship between the degree of unsaturation of ring “B” and the expected rate of DNA depurination. As quinones might be present in the cytosol in various protonated forms, we introduce the concept of “effective barriers” to account for the different reactivity and different concentrations of quinone derivatives. According to our results, both equine estrogens have the potential to facilitate depurination as the activation barrier of one of the elementary steps (the initial Michael addition in the case of equilenin and the rearomatization step in the case of equilin) significantly decreases compared to that of estrone. We conclude that the appearance of exogenous equine estrogen quinones due to HRT might increase the risk of depurination-induced breast cancer development compared to the exposure to endogenous estrone metabolites. Still, further studies are required to identify the rate-limiting step of depurination under intracellular conditions to reveal whether the decrease in the barriers affects the overall rate of carcinogenesis.

]]>Symmetry doi: 10.3390/sym13091640

Authors: Chong-Gee Koa Swee-Huay Heng Ji-Jian Chin

Public Key Infrastructure (PKI) is the fundamental of secure digital communications. It provides a secure means to authenticate identities over the Internet. Symmetric or asymmetric encryption schemes are widely used in identity authentication in any kind of PKI. The conventional PKI has several drawbacks due to the centralized and non-transparent design. Several recent research works utilize blockchain technology to overcome the limitations of conventional implementations of PKI. Blockchain-based PKI integrates blockchain technology with PKI to form a new type of decentralized PKI (DPKI). Several works utilize the currency property in blockchains to implement the reward-and-punishment mechanism. In this paper, we propose a smart contract-based PKI which utilizes the Ethereum smart contract to build a new type of blockchain-based PKI with the reward-and-punishment mechanism using ERC-20 tokens. It has several advantages over previous implementations of similar research that use Ethereum’s main currency—Ether.

]]>Symmetry doi: 10.3390/sym13091639

Authors: David Sloan

Dynamical similarities are non-standard symmetries found in a wide range of physical systems that identify solutions related by a change of scale. In this paper, we will show through a series of examples how this symmetry extends to the space of couplings, as measured through observations of a system. This can be exploited to focus on observations that can be used to distinguish between different theories and identify those which give rise to identical physical evolutions. These can be reduced into a description that makes no reference to scale. The resultant systems can be derived from Herglotz’s principle and generally exhibit friction. Here, we will demonstrate this through three example systems: the Kepler problem, the N-body system and Friedmann–Lemaître–Robertson–Walker cosmology.

]]>Symmetry doi: 10.3390/sym13091638

Authors: Robert Reynolds Allan Stauffer

A quadruple integral involving the logarithmic, exponential and polynomial functions is derived in terms of the Lerch function. Special cases of this integral are evaluated in terms of special functions and fundamental constants. Almost all Lerch functions have an asymmetrical zero-distribution. The majority of the results in this work are new.

]]>Symmetry doi: 10.3390/sym13091637

Authors: Anthony J. Lee Jessica K. De La Mare Hannah R. Moore Pamela C. Umeh

Facial symmetry is purportedly attractive, though methods for measuring preference for facial symmetry vary between studies. Some studies have used a two-alternative forced choice (2AFC) task, while others have used a ratings task. How researchers manipulate facial symmetry also varies; some studies have used faces manipulated to be more (or perfectly) symmetrical, while others have used faces manipulated to be more asymmetrical. Here, across three studies, we evaluate and compare these different methods. In Studies 1 and 2 (N = 340 and 256, respectively), we compare facial symmetry preferences as measured by the 2AFC and ratings tasks. Across both studies, we consistently found a significant preference for facial symmetry when using the 2AFC task, but not with the ratings task. Additionally, correlations between facial symmetry preferences as measured by the two tasks were weak or showed no association. In Study 3, 159 participants rated the attractiveness of faces manipulated to be either symmetrical or more asymmetrical. The asymmetrical faces were rated as significantly less attractive compared to the original faces, while the difference in attractiveness ratings between the original and symmetrical versions was comparatively much smaller. These studies suggest that preference for facial symmetry depends greatly on the study design.

]]>Symmetry doi: 10.3390/sym13091636

Authors: Emna Rtibi Benoit Champagne

Density functional theory and time-dependent density functional theory have been enacted to investigate the effects of donor and acceptor on the first hyperpolarizability of Lindquist-type organo-imido polyoxometalates (POMs). These calculations employ a range-separated hybrid exchange-correlation functional (ωB97X-D), account for solvent effects using the implicit polarizable continuum model, and analyze the first hyperpolarizabilities by using the two-state approximation. They highlight the beneficial role of strong donors as well as of π-conjugated spacers (CH=CH rather than C≡C) on the first hyperpolarizabilities. Analysis based on the unit sphere representation confirms the one-dimensional push-pull π-conjugated character of the POMs substituted by donor groups and the corresponding value of the depolarization ratios close to 5. Furthermore, the use of the two-state approximation is demonstrated to be suitable for explaining the origin of the variations of the first hyperpolarizabilities as a function of the characteristics of a unique low-energy charge-transfer excited state and to attribute most of the first hyperpolarizability changes to the difference of dipole moment between the ground and that charge-transfer excited state.

]]>Symmetry doi: 10.3390/sym13091635

Authors: Zhiyong Chen Jianbao Chen

This article deals with symmetrical data that can be modelled based on Gaussian distribution. We consider a class of partially linear additive spatial autoregressive (PLASAR) models for spatial data. We develop a Bayesian free-knot splines approach to approximate the nonparametric functions. It can be performed to facilitate efficient Markov chain Monte Carlo (MCMC) tools to design a Gibbs sampler to explore the full conditional posterior distributions and analyze the PLASAR models. In order to acquire a rapidly-convergent algorithm, a modified Bayesian free-knot splines approach incorporated with powerful MCMC techniques is employed. The Bayesian estimator (BE) method is more computationally efficient than the generalized method of moments estimator (GMME) and thus capable of handling large scales of spatial data. The performance of the PLASAR model and methodology is illustrated by a simulation, and the model is used to analyze a Sydney real estate dataset.

]]>Symmetry doi: 10.3390/sym13091634

Authors: Anna Lipowicz Wojciech Wolański Edyta Kawlewska Patrycja Zwolska Małgorzata Kulesa-Mrowiecka Krzysztof Dowgierd Paweł Linek Andrzej Myśliwiec

Ankyloses in the area of the temporomandibular joint (TMJ) are mentioned as a potential etiological factor of mandibular growth disorders and facial asymmetry. The aim of this case study was to evaluate the changes in the mandible of a child with zygomatic-coronoid ankylosis during the first five years of life, in which two adhesion release procedures were performed. The adopted symmetrical approach is based on the assumption of symmetry of the structure of the stomatognathic system in relation to the sagittal median plane. However, the assessment of pathological changes in the structure of the skeletal system was performed using an asymmetrical approach. Computed tomography techniques and a system of computer-aided diagnosis (CAD) were used in the case study. During the child’s growth, linear and angular measurements were made thrice (at the age of 16, 25 and 54 months). The degree of asymmetry was estimated in the measurements made on the right and left sides of the three-dimensional mandible. Unilateral congenital hypoplasia of the articular process and zygomatic-coronoid adhesion caused asymmetrical growth of the mandible in the child along with shortening of the mandibular branch and body on the damaged side and a visible difference in the size of the mandibular angles. Removal of the adhesions during surgical procedures made it possible to reduce the asymmetry of the mandible and catch-up growth, although at the age of five, the mandible was still smaller than the mandible in healthy peers. It was shown that the early adhesion release procedures supported by the CAD analysis enabled the restoration of mandibular symmetry.

]]>Symmetry doi: 10.3390/sym13091633

Authors: Yang Ding Shuang-Xi Zhou Yong-Qi Wei Tong-Lin Yang Jing-Liang Dong

Wind field (e.g., wind speed and wind direction) has the characteristics of randomness, nonlinearity, and uncertainty, which can be critical and even destructive on a long-span bridge’s hangers, such as vortex shedding, galloping, and flutter. Nowadays, the finite element method is widely used for model calculation, such as in long-span bridges and high-rise buildings. In this study, the investigated bridge hanger model was established by COMSOL Multiphysics software, which can calculate fluid dynamics (CFD), solid mechanics, and fluid–solid coupling. Regarding the wind field of bridge hangers, the influence of CFD models, wind speed, and wind direction are investigated. Specifically, the bridge hanger structure has symmetrical characteristics, which can greatly reduce the calculation efficiency. Furthermore, the von Mises stress of bridge hangers is calculated based on fluid–solid coupling.

]]>Symmetry doi: 10.3390/sym13091631

Authors: Hua-Ping Wang Hao Chen Cong Chen Hu-Yuan Zhang Hao Jiang Tao Song Si-Yuan Feng

Carbon fiber reinforced polymer (CFRP) composites have been extensively used in airframes, train bodies, and engine blades for their properties of high strength, low weight, and good stability. The in-service structural performance of CFRP composites is always an important point to be investigated for its influence on structural safety. For this reason, CFRP composite plates assembled with fiber Bragg grating (FBG) sensors were developed, and the in-service structural characteristics of the CFRP plates were interpreted by FBG signals measured through time. A theoretical analysis supported by a numerical method has been provided. Experimental testing was conducted to check the proposed sensing technique for the dynamic response identification of the CFRP plate. The curing process of the bilayer CFRP plated inserted with FBGs in series was also explored. The results showed that the surface-attached FBGs in series could accurately characterize the dynamic response of the CFRP plate, and a good agreement between the numerical and testing results was observed. The strain and temperature distributions during the curing process of the bilayer plate indicated that the in-service structural performance of bilayer CFRP plates can be configured by the assembled FBG sensors. This study can support the structural health monitoring of projects by using CFRP composites.

]]>Symmetry doi: 10.3390/sym13091632

Authors: Asher Yahalom

The current paper is devoted to the introduction of simpler Eulerian variational principles from which all the relevant equations of nonbarotropic stationary magnetohydrodynamics can be derived for magnetic fields that lie on surfaces. A variational principle is given in terms of three independent variables for stationary nonbarotropic magnetohydrodynamic flows. This is a smaller number of variables than the eight variables that appear in the standard equations of nonbarotropic magnetohydrodynamics, which are the magnetic field, the velocity field, the specific entropy, and the density. We further investigate the case in which the flow along magnetic lines is not ideal.

]]>Symmetry doi: 10.3390/sym13091630

Authors: Hang Lin Lixin Liu Zhengjun Zhang

Tail risk is an important financial issue today, but directly hedging tail risks with an ad hoc option is still an unresolved problem since it is not easy to specify a suitable and asymmetric pricing kernel. By defining two ad hoc underlying “assets”, this paper designs two novel tail risk options (TROs) for hedging and evaluating short-term tail risks. Under the Fréchet distribution assumption for maximum losses, the closed-form TRO pricing formulas are obtained. Simulation examples demonstrate the accuracy of the pricing formulas. Furthermore, they show that, no matter whether at scale level (symmetric “normal” risk, with greater volatility) or shape level (asymmetric tail risk, with a smaller value in tail index), the greater the risk, the more expensive the TRO calls, and the cheaper the TRO puts. Using calibration, one can obtain the TRO-implied volatility and the TRO-implied tail index. The former is analogous to the Black-Scholes implied volatility, which can measure the overall symmetric market volatility. The latter measures the asymmetry in underlying losses, mirrors market sentiment, and provides financial crisis warnings. Regarding the newly proposed TRO and its implied tail index, economic implications can be offered to investors, portfolio managers, and policy-makers.

]]>Symmetry doi: 10.3390/sym13091629

Authors: Yun-Hsin Chuang Chin-Laung Lei Hung-Jr Shiu

An anonymous authentication and key agreement (AAKA) protocol provides anonymous members symmetric authentication and establishes a symmetric session key for secure communication in public networks. Today, numerous popular remote services are based on multi-server architecture, such as the internet of things (IoT), smart cities, cloud services, vehicular ad hoc networks (VANET), and telecare medicine information systems (TMIS). Many researchers have attempted to design AAKA protocols in multi-server environments for various applications. However, many of these have security defects, even if they have so-called “formal” security proofs. In this paper, we analyze related AAKA protocols to identify the common design defects, expound the process of designing secure AAKA protocols, and explain why the present AAKA protocols still suffer attacks, despite having security proofs. We instruct readers on how to design a secure AAKA protocol and how to prove the security. This paper will therefore be helpful for the design of new AAKA protocols, and for ensuring their security.

]]>Symmetry doi: 10.3390/sym13091628

Authors: Elena D. Orlova Aleksandra A. Savina Sergey A. Abakumov Anatolii V. Morozov Artem M. Abakumov

The layered oxides LiNixMnyCozO2 (NMCs, x + y + z = 1) with high nickel content (x ≥ 0.6, Ni-rich NMCs) are promising high-energy density-positive electrode materials for Li-ion batteries. Their electrochemical properties depend on Li+/Ni2+ cation disordering originating from the proximity of the Li+ and Ni2+ ionic radii. We synthesized a series of the LiNi0.8Mn0.1Co0.1O2 NMC811 adopting two different disordering schemes: Ni for Li substitution at the Li site in the samples finally annealed in air, and close to Ni↔Li antisite disorder in the oxygen-annealed samples. The defect formation scenario was revealed with Rietveld refinement from powder X-ray diffraction data, and then the reliability of semi-quantitative parameters, such as I003/I104 integral intensity ratio and c/(2√6a) ratio of pseudocubic subcell parameters, was verified against the refined defect concentrations. The I003/I104 ratio can serve as a quantitative measure of g(NiLi) only after explicit correction of intensities for preferred orientation. Being normalized by the total scattering power of the unit cell, the I003/I104 ratio depends linearly on g(NiLi) for each disordering scheme. The c/(2√6a) ratio appears to be not reliable and cannot be used for a quantitative estimate of g(NiLi). In turn, the volume of the R3¯m unit cell correlates linearly with g(NiLi), at least for defect concentrations not exceeding 5%. The microscopy techniques such as high-resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) and electron diffraction tomography (EDT) allow us to study the materials locally, still, there is no proper quantitative approach for comprehensive analysis of defects. In the present work, the TEM-assisted quantitative Li+/Ni2+ disordering analysis with EDT and HAADF-STEM in six Ni-rich NMC samples with various defects content is demonstrated. Noteworthy, while PXRD and EDT methods demonstrate overall defect amounts, HAADF-STEM allows us to quantitatively distinguish regions with various disordering extents. Therefore, the combination of mentioned PXRD and TEM methods gives the full picture of Li+/Ni2+ mixing defects in Ni-rich NMCs.

]]>Symmetry doi: 10.3390/sym13091626

Authors: Renxuan Tang Dongfang Li

In this paper, we use the scalar auxiliary variable (SAV) approach to rewrite the charged particle dynamics as a new family of ODE systems. The systems own a conserved energy. It is shown that a family of symmetrical methods is energy-conserving for a new ODE system but may not be for the original systems. Moreover, the methods have high-order accuracy. Numerical results are given to confirm the theoretical findings.

]]>Symmetry doi: 10.3390/sym13091627

Authors: Kangyu Wang Jun Cao Xinquan Wang Yingjie Ning

Soil arching, which occurs in the piled embankments, plays an important role in stress redistribution between the relatively soft subsoil and the stiffer piles. The formation of the soil arching depends on the differential settlement of the embankment fill above the pile and the subsoil. The soil arching effect is barely investigated in the literature from the perspective of differential settlement of piles and soils. Based on the discrete element method (DEM), this paper develops a classic trapdoor test model to investigate the differential settlement in piled embankment during the downward movement of the trapdoor, and to explore the formation mechanism of soil arching in equal settlement pattern by changing the width of the pile cap and the height of the embankment. Due to symmetry, only one section of the laboratory test model is simulated herein. It was found that the soil arching formed under the equal settlement pattern remained unchanged after a certain degree of development, and the height of the equal settlement did not change at 0.7(s-a), where s is the pile spacing, and a is the width of the pile cap. The height of the embankment (H) and the width of the pile cap (a) have a significant influence on the formation of the equal settlement pattern when the width of the trapdoor is kept constant. Both the decrease in “H” and the increase in “a” facilitate the differential settlement of the soil between the piles and the pile-soil, enabling the slip surface to develop upward gradually, thereby hindering the formation of the equal settlement pattern.

]]>Symmetry doi: 10.3390/sym13091624

Authors: Janos Polonyi Ines Rachid

It is shown that the mixed states of a closed dynamics supports a reduplicated symmetry, which is reduced back to the subgroup of the original symmetry group when the dynamics is open. The elementary components of the open dynamics are defined as operators of the Liouville space in the irreducible representations of the symmetry of the open system. These are tensor operators in the case of rotational symmetry. The case of translation symmetry is discussed in more detail for harmonic systems.

]]>Symmetry doi: 10.3390/sym13091625

Authors: Antonio Branca Giulia Brunetti Andrea Longhin Marco Martini Fabio Pupilli Francesco Terranova

Our knowledge of neutrino cross sections at the GeV scale, instrumental to test CP symmetry violation in the leptonic sector, has grown substantially in the last two decades. Still, their precision and understanding are far from the standard needed in contemporary neutrino physics. Nowadays, the knowledge of the neutrino cross section at O(10%) causes the main systematic uncertainty in oscillation experiments and jeopardizes their physics reach. In this paper, we envision the opportunities for a new generation of cross section experiments to be run in parallel with DUNE and HyperKamiokande. We identify the most prominent physics goals by looking at the theory and experimental limitations of the previous generation of experiments. We highlight the priorities in the theoretical understanding of GeV cross sections and the experimental challenges of this new generation of facilities.

]]>Symmetry doi: 10.3390/sym13091623

Authors: Ningwei Wang Yaze Li Hongzhe Liu

Neural networks have enabled state-of-the-art approaches to achieve incredible results on computer vision tasks such as object detection. However, previous works have tried to improve the performance in various object detection necks but have failed to extract features efficiently. To solve the insufficient features of objects, this work introduces some of the most advanced and representative network models based on the Faster R-CNN architecture, such as Libra R-CNN, Grid R-CNN, guided anchoring, and GRoIE. We observed the performance of Neighbour Feature Pyramid Network (NFPN) fusion, ResNet Region of Interest Feature Extraction (ResRoIE) and the Recursive Feature Pyramid (RFP) architecture at different scales of precision when these components were used in place of the corresponding original members in various networks obtained on the MS COCO dataset. Compared to the experimental results after replacing the neck and RoIE parts of these models with our Reinforced Neighbour Feature Fusion (RNFF) model, the average precision (AP) is increased by 3.2 percentage points concerning the performance of the baseline network.

]]>Symmetry doi: 10.3390/sym13091622

Authors: Irina Radinschi Theophanes Grammenos Gargee Chakraborty Surajit Chattopadhyay Marius Mihai Cazacu

Energy-momentum localization for the four-dimensional static and spherically symmetric, regular Simpson–Visser black hole solution is studied by use of the Einstein and Møller energy-momentum complexes. According to the particular values of the parameter of the metric, the static Simpson–Visser solution can possibly describe the Schwarzschild black hole solution, a regular black hole solution with a one-way spacelike throat, a one-way wormhole solution with an extremal null throat, or a traversable wormhole solution of the Morris–Thorne type. In both prescriptions it is found that all the momenta vanish, and the energy distribution depends on the mass m, the radial coordinate r, and the parameter a of the Simpson–Visser metric. Several limiting cases of the results obtained are discussed, while the possibility of astrophysically relevant applications to gravitational lensing issues is pointed out.

]]>Symmetry doi: 10.3390/sym13091621

Authors: Angel Ricardo Plastino Roseli S. Wedemann Constantino Tsallis

We investigate a one-dimensional, many-body system consisting of particles interacting via repulsive, short-range forces, and moving in an overdamped regime under the effect of a drag force that depends on direction. That is, particles moving to the right do not experience the same drag as those moving to the left. The dynamics of the system, effectively described by a non-linear, Fokker–Planck equation, exhibits peculiar features related to the way in which the drag force depends on velocity. The evolution equation satisfies an H-theorem involving the Sq nonadditive entropy, and admits particular, exact, time-dependent solutions closely related, but not identical, to the q-Gaussian densities. The departure from the canonical, q-Gaussian shape is related to the fact that in one spatial dimension, in contrast to what occurs in two or more spatial dimensions, the drag’s dependence on direction entails that its dependence on velocity is necessarily (and severely) non-linear. The results reported here provide further evidence of the deep connections between overdamped, many-body systems, non-linear Fokker–Planck equations, and the Sq-thermostatistics.

]]>Symmetry doi: 10.3390/sym13091620

Authors: G. Jordan Maclay

This Special Issue “Symmetries in Quantum Mechanics” describes research using two of the most fundamental probes we have in nature [...]

]]>Symmetry doi: 10.3390/sym13091619

Authors: Samata E. Shetgaonkar Shiva Prasad Kollur Renjith Raveendran Pillai Karthick Thangavel Sanja J. Armaković Stevan Armaković Chandan Shivamallu Raghavendra G. Amachawadi Asad Syed Abdallah M. Elgorban Ali H. Bahkali Fateh V Singh

Highly functionalized spirocyclic ketals were synthesized through asymmetric oxidative spirocyclization via carbanion-induced ring transformation of 2H-pyran-2-ones with 1,4-cyclohexandione monoethyleneketal under alkaline conditions. Further acidic-hydrolysis of obtained spirocyclic ketals yields highly substituted 2-tetralone in good yield. Computational analysis based on the DFT calculations and MD simulations has been performed in order to predict and understand global and local reactivity properties of newly synthesized derivatives. DFT calculations covered fundamental reactivity descriptors such as molecular electrostatic potential and average local ionization energies. Nitrogen atom and benzene rings have been recognized as the most important molecular sites from these aspects. Additionally, to predict whether studied compounds are stable towards the autoxidation mechanism, we have also studied the bond dissociation energies for hydrogen abstraction and identified the derivative which might form potentially genotoxic impurities. Interactions with water, including both global and local aspects, have been covered thanks to the MD simulations and calculations of interaction energies with water, counting of formed hydrogen interactions, and radial distribution functions. MD simulations were also used to identify which excipient could be used together with these compounds, and it has been established that the polyvinylpyrrolidone polymer could be highly compatible with these compounds, from the aspect of calculated solubility parameters.

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