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This paper introduced the use of two new adsorbents, Akrosorb soda-lime and Bentonite clay, for refinery flare flue gas capture and storage. This study also developed a novel pilot plant model with 409.7149 kg/h capacity refinery flare emission capture with a novel adsorption column configuration using Akrosorb soda-lime and Bentonite clay adsorbents. The flare flue gas adsorption unit was designed, fabricated, test run, and commissioned. The adsorption column temperature is 28 ± 10 °C and has a pressure of 131.7 kPa. The novel plant RSM optimization result shows that 93.24% of CO2 and 62.18% of CO were absorbed, while 86.14% of NOx and 55.87% of HC were absorbed. The established optimum conditions of CO2, NOx, HC, and CO removal efficiency are 22 °C, 2 atm, and 60 min. The variation in flare gas emission could impact the removal efficiency of the plant. The results show the maximum adsorption ability or capacity of 314.30 mg/g, and 68.90 mg/g was reached at 60 min for Akrosorb soda-lime and molded Bentonite adsorbents. Therefore, the developed novel technology for CO2 and other GHG capture is technically feasible and friendly. The combined usage of both adsorbents will enhance the capture of GHG at a low cost compared to using Akrosorb alone as an adsorbent.

This paper proposes a modification of the imperialist competitive algorithm to solve multi-objective optimization problems with hybrid methods (MOHMICA) based on a modification of the imperialist competitive algorithm with hybrid methods (HMICA). The rationale for this is that there is an obvious disadvantage of HMICA in that it can only solve single-objective optimization problems but cannot solve multi-objective optimization problems. In order to adapt to the characteristics of multi-objective optimization problems, this paper improves the establishment of the initial empires and colony allocation mechanism and empire competition in HMICA, and introduces an external archiving strategy. A total of 12 benchmark functions are calculated, including 10 bi-objective and 2 tri-objective benchmarks. Four metrics are used to verify the quality of MOHMICA. Then, a new comprehensive evaluation method is proposed, called “radar map method”, which could comprehensively evaluate the convergence and distribution performance of multi-objective optimization algorithm. It can be seen from the four coordinate axes of the radar maps that this is a symmetrical evaluation method. For this evaluation method, the larger the radar map area is, the better the calculation result of the algorithm. Using this new evaluation method, the algorithm proposed in this paper is compared with seven other high-quality algorithms. The radar map area of MOHMICA is at least 14.06% larger than that of other algorithms. Therefore, it is proven that MOHMICA has advantages as a whole.

Botnet is an urgent problem that will reduce the security and availability of the network. When the bot master launches attacks to certain victims, the infected users are awakened, and attacks start according to the commands from the bot master. Via Botnet, DDoS is an attack whose purpose is to paralyze the victim’s service. In all kinds of DDoS, SYN flood is still a problem that reduces security and availability. To enhance the security of the Internet, IDS is proposed to detect attacks and protect the server. In this paper, the concept of centroid-based classification is used to enhance performance of the framework. An anomaly-based IDS framework which combines K-means and KNN is proposed to detect SYN flood. Dimension reduction is designed to achieve visualization, and weights can adjust the occupancy ratio of each sub-feature. Therefore, this framework is also suitable for use on the modern symmetry or asymmetry architecture of information systems. With the detection by the framework proposed in this paper, the detection rate is 96.8 percent, the accuracy rate is 97.3 percent, and the false alarm rate is 1.37 percent.

This paper presents an alternative system called the axial-flux dual-stator toothless permanent magnet machine (AFDSTPMM) system for flywheel energy storage. This system lowers self-dissipation by producing less core loss than existing structures; a permanent magnet (PM) array is put forward to enhance the air–gap flux density of the symmetrical air gap on both sides. Moreover, its vertical stability is strengthened through the adoption of an axial-flux machine, so expensive active magnetic bearings can be replaced. The symmetry configuration of the AFDSTPMM system is shown in this paper. Then, several parts of the AFDSTPMM system are optimized thoroughly, including stator windings, number of pole pairs and the PM parameters. Further, the performance of the proposed PM array, including back-EMFs, air–gap flux density, average torque, torque ripple and over-load capacity, are compared with the Halbach PM array and spoke PM array, showing the superiority of proposed configuration. Finally, 3D simulations were made to testify for the 2D analyses.

The urban public transportation system is an important part of urban transportation, and the rationality of public transportation routes layout plays a vital role in the transportation of the city. Improving the efficiency of public transportation can have a positive impact on the operation of the public transportation system. This paper uses complex network theory and the symmetry of the up and down bus routes and stations to establish an urban public transit network model and calculates the probability of passengers choosing different routes in the public transit network according to passenger travel impedance. Based on passenger travel impedance, travel path probability and passenger travel demand, the links are weighed, and the network efficiency calculation method is improved. Finally, the public transit network optimization model was established with network efficiency as the objective function and solved by the ant colony algorithm. In order to verify the effectiveness of the model and the solution method, this paper selects areas in Nanguan District of Changchun City for example analysis. The result shows that the efficiency of the optimized network is 8.5% higher than that of the original network, which proves the feasibility of the optimized model and solution method.

In 2008, Hedetniemi et al. introduced (1,k)-domination in graphs. The research on this concept was extended to the problem of existence of independent (1,k)-dominating sets, which is an NP-complete problem. In this paper, we consider independent (1,1)- and (1,2)-dominating sets, which we name as (1,1)-kernels and (1,2)-kernels, respectively. We obtain a complete characterization of generalized corona of graphs and G-join of graphs, which have such kernels. Moreover, we determine some graph parameters related to these sets, such as the number and the cardinality. In general, graph products considered in this paper have an asymmetric structure, contrary to other many well-known graph products (Cartesian, tensor, strong).

The redundancy of functional blocks and critical assemblies in radio-electronic equipment is among the most widely used techniques for increasing reliability. Complex redundant systems raise the problem of electromagnetic compatibility (EMC). Ignoring EMC requirements can lead to partial or complete REE failures. In this paper, the authors analyze a noise-protective electrical circuit with triple modal reservation (a promising type of cold redundancy). A multilayer stripline is investigated, the conductors of which are symmetrically arranged relative to two planes. On account of the strong electromagnetic coupling, this protective circuit can decompose dangerous ultra-wideband (UWB) interference received at the input of the primary or redundant circuits into unipolar pulses of lower amplitude. Using this approach, due to the symmetry of the conductors, equal decomposition efficiency could be achieved. However, the effect of UWB interference at the input of one of the conductors produces bipolar pulses at the output of the other conductors. In this paper, the authors evaluate the dangers of unipolar and bipolar decomposed pulses and use modal analysis to mathematically determine the polarities and amplitudes of the decomposed pulses at all output nodes for a pseudo-matched structure. By using the quasistatic approach with and without losses, the time responses to a trapezoidal pulse with a total duration of 60 ps, which simulates UWB interference, are obtained. To confirm the results of modal analysis and quasistatic simulation, an experimental study is performed. Using a stroboscopic oscilloscope DSA 8300, the authors obtained a transient response to a step excitation. Then, taking the derivative, the response to a trapezoidal pulse with a total duration of 140 ps was obtained. To analyze the criticality of the decomposed pulses, N-norms are used. In the general case, it is shown that the UWB interference is decomposed into four pulses of lower amplitude. At the same time, the value of each N-norm indicates its significant attenuation. For example, the amplitude of the UWB pulse acting on the input of the reserved conductor decreases by 10.31–8.93 times. Such results numerically demonstrate the high efficiency of the suggested approach when it comes to protecting equipment against UWB interference. It is also shown that the probability of dielectric breakdown and damage to electronic components in redundant circuits is lower than in a primary circuit. This is due to the fact that the value of N3 in the redundant circuit is 2.38 times less than in the primary circuit. However, the results demonstrate that arcing is highly probable both in primary and redundant circuits. Finally, aspects of symmetry/asymmetry in the problem under investigation are emphasized.

Multi-Criteria Decision Making (MCDM) methods have rapidly developed and have been applied to many areas for decision making in engineering. Apart from that, the process to select fault-diagnosis sensor for Fuel Cell Stack system in various options is a multi-criteria decision-making (MCDM) issue. However, in light of the choosing of fault diagnosis sensors, there is no MCDM analysis, and Fuel Cell Stack companies also urgently need a solution. Therefore, in this paper, we will use MCDM methods to analysis the fault-diagnosis sensor selection problem for the first time. The main contribution of this paper is to proposed a fault-diagnosis sensor selection methodology, which combines the rank reversal resisted AHP and TOPSIS and supports Fuel Cell Stack companies to select the optimal fault-diagnosis sensors. Apart from that, through the analysis, among all sensor alternatives, the acquisition of the optimal solution can be regarded as solving the symmetric or asymmetric problem of the optimal solution, which just maps to the TOPSIS method. Therefore, after apply the proposed fault-diagnosis sensor selection methodology, the Fuel Cell Stack system fault-diagnosis process will be more efficient, economical, and safe.

This paper proposes a new multi-objective bi-level programming model for the ring road bus lines and fare design problems. The proposed model consists of two layers: the traffic management operator and travelers. In the upper level, we propose a multi-objective bus lines and fares optimization model in which the operator’s profit and travelers’ utility are set as objective functions. In the lower level, evolutionary multi agent model of travelers’ bounded rational reinforcement learning with social interaction is introduced. A solution algorithm for the multi-objective bi-level programming is developed on the basis of the equalization algorithm of OD matrix. A numerical example based on a real case was conducted to verify the proposed models and solution algorithm. The computational results indicated that travel choice models with different degrees of rationality significantly changed the optimization results of bus lines and the differentiated fares; furthermore, the multi-objective bi-level programming in this paper can generate the solution to reduce the maximum section flow, increase the profit, and reduce travelers’ generalized travel cost.

Based on the principle of energy variation, a calculation model for the free vibration characteristics of a cylindrical shell with a finite submerged depth considering the influence of the free liquid surface is established in this paper. First, the Euler beam function is used instead of the shell axial displacement function to obtain the shell kinetic energy and potential energy. Then, by using the mirror image method, the analytical expression of the fluid velocity potential considering the free surface is obtained, and the flow field is added to the system energy functional in the form of fluid work. Then the energy functional is changed to obtain the shell–liquid coupled vibration equation. Solving the equation can obtain the natural frequencies and modes of the structure. The comparison with the finite element calculation results verifies the accuracy of the calculation model in this paper. The research on the influence of the free liquid surface shows that compared to the infinite domain, the free liquid surface destroys the symmetry of the entire system, resulting in a difference in the natural frequency of the positive and negative modes of the shell, and the circumferential mode shapes are no longer mutually uncoupled trigonometric functions. The existence of free liquid surface will also increase the natural frequency of the same order mode, and the closer to the free surface, the natural frequency is greater. As the immersion depth increases, the free vibration characteristics will quickly tend to the result of infinite domain. Additionally, when the immersion depth is equal to or greater than four times the radius of the shell structure, it can be considered that the free liquid surface has no effect. These law and phenomena have also been explained from the mechanism. The method in this paper provides a new analytical solution pattern for solving this type of problem.

This paper is devoted to further strengthening, in the current asymmetric information environment, the informed level of operators about network performance. Specifically, in view of the burst and perishability of a packet loss event, to better meet the real-time requirements of current high-speed backbone performance monitoring, a model for Packet Loss Measurement at the access network boundary Based on Sampled Flow (PLMBSF) is presented in this paper under the premise of both cost and real-time. The model overcomes problems such as the inability of previous estimation to distinguish between packet losses before and after the monitoring point, deployment difficulties and cooperative operation consistency. Drawing support from the Mathis equation and regression analysis, the measurement for packet losses before and after the monitoring point can be realized when using only the sampled flows generated by the access network boundary equipment. The comparison results with the trace-based passive packet loss measurement show that although the proposed model is easily affected by factors such as flow length, loss rate, sampling rate, the overall accuracy is still within the acceptable range. In addition, the proposed model PLMBSF, compared with the trace-based loss measurement is only different in the input data granularity. Therefore, PLMBSF and its advantages are also applicable to aggregated traffic.

Recently in the paper [Mediterr. J. Math.&nbsp, 2016, 13, 1535–1553], the authors introduced and studied a new operator which was defined as a convolution of the three popular linear operators, namely the Sǎlǎgean operator, the Ruscheweyh operator and a fractional derivative operator. In the present paper, we consider an operator which is a convolution operator of only two linear operators (with lesser restricted parameters) that yield various well-known operators, defined by a symmetric way, including the one studied in the above-mentioned paper. Several results on the subordination of analytic functions to this operator (defined below) are investigated. Some of the results presented are shown to involve the familiar Appell function and Hurwitz–Lerch Zeta function. Special cases and interesting consequences being in symmetry of our main results are also mentioned.

Background: Some medical and technological tasks lead to the geometrical problem of how to cover the unit circle as much as possible by n congruent circles of given radius r, while r varies from the radius in the maximum packing to the radius in the minimum covering. Proven or conjectural solutions to this partial covering problem are known only for n = 2 to 5. In the present paper, numerical solutions are given to this problem for n = 6 and 7. Method: The method used transforms the geometrical problem to a mechanical one, where the solution to the geometrical problem is obtained by finding the self-stress positions of a generalised tensegrity structure. This method was developed by the authors and was published in an earlier publication. Results: The method applied results in locally optimal circle arrangements. The numerical data for the special circle arrangements are presented in a tabular form, and in drawings of the arrangements. Conclusion: It was found that the case of n = 6 is very complicated, whilst the case n = 7 is very simple. It is shown in this paper that locally optimal arrangements may exhibit different types of symmetry, and equilibrium paths may bifurcate.

The sum of Big Data generated from different sources is increasing significantly with each passing day to extent that it is becoming challenging for traditional storage methods to store this massive amount of data. For this reason, most organizations have resolved to use third-party cloud storage to store data. Cloud storage has advanced in recent times, but it still faces numerous challenges with regard to security and privacy. This paper discusses Big Data security and privacy challenges and the minimum requirements that must be provided by future solutions. The main objective of this paper is to propose a new technical framework to control and manage Big Data security and privacy risks. A design science research methodology is used to carry out this project. The proposed framework takes advantage of Blockchain technology to provide secure storage of Big Data by managing its metadata and policies and eliminating external parties to maintain data security and privacy. Additionally, it uses mobile agent technology to take advantage of the benefits related to system performance in general. We present a prototype implementation for our proposed framework using the Ethereum Blockchain in a real data storage scenario. The empirical results and framework evaluation show that our proposed framework provides an effective solution for secure data storage in a Big Data environment.

The paper offers a general symbolic method to study the motion in a non-inertial reference frame. In order to achieve this, we use the algebraic and geometric properties of the Lie group of special orthogonal tensors, SO3, and the Lie group of the rigid body displacements, SE3. We obtain a simplified form of the initial value problem that models the non-inertial motion using a tensor instrument introduced in this paper. Thus, the study of the motion in a non-inertial reference frame is transferred into the study of a classical motion in an inertial reference frame. The applications of this method refer to solving the relative motion problem and deriving the straightforward solution to classical theoretical mechanics problems. The motion in a uniform gravitational force field in a rotating reference frame, the motion of a charged particle in non-stationary electric and magnetic fields, the exact solution of the relative rigid body motion in the non-inertial reference frame are studied. Using this symbolic method in studying the motion in a non-inertial reference frame reduces the number of computations. In addition, it offers, in some essential particular cases, exact closed-form coordinate-free analytical solutions.

The present paper continues the study on the relatively new concept of fuzzy differential subordination conducted in some recently published cited papers. In this article, certain fuzzy subordination results for analytical functions involving the Atangana–Baleanu fractional integral of Bessel functions are presented. Theorems giving the best dominants for some fuzzy differential subordinations are proved, and interesting corollaries are provided with the use of particular functions as fuzzy best dominants.

The main purpose of this paper is threefold. One is to study the existence and convergence problem of solutions for a class of generalized mixed quasi-variational hemivariational inequalities. The second one is to study the existence of optimal control for such kind of generalized mixed quasi-variational hemivariational inequalities under given control u∈U. The third one is to study the relationship between the optimal control and the data for the underlying generalized mixed quasi-variational inequality problems and a class of minimization problem. As an application, we utilize our results to study the elastic frictional problem in a class of Hilbert spaces. The results presented in the paper extend and improve upon some recent results.

In this paper, we establish some new Hermite–Hadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for p,q-differentiable preinvex functions in the context of p,q-calculus. We also show that the results established in this paper are generalizations of comparable results in the literature of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.

The canonical skewness vector is an analytically simple function of the third-order, standardized moments of a random vector. Statistical applications of this skewness measure include semiparametric modeling, independent component analysis, model-based clustering, and multivariate normality testing. This paper investigates some properties of the canonical skewness vector with respect to representations, transformations, and norm. In particular, the paper shows its connections with tensor contraction, scalar measures of multivariate kurtosis and Mardia’s skewness, the best-known scalar measure of multivariate skewness. A simulation study empirically compares the powers of tests for multivariate normality based on the squared norm of the canonical skewness vector and on Mardia’s skewness. An example with financial data illustrates the statistical applications of the canonical skewness vector.

Clustering is a major field in data mining, which is also an important method of data partition or grouping. Clustering has now been applied in various ways to commerce, market analysis, biology, web classification, and so on. Clustering algorithms include the partitioning method, hierarchical clustering as well as density-based, grid-based, model-based, and fuzzy clustering. The K-means algorithm is one of the essential clustering algorithms. It is a kind of clustering algorithm based on the partitioning method. This study’s aim was to improve the algorithm based on research, while with regard to its application, the aim was to use the algorithm for customer segmentation. Customer segmentation is an essential element in the enterprise’s utilization of CRM. The first part of the paper presents an elaboration of the object of study, its background as well as the goal this article would like to achieve; it also discusses the research the mentality and the overall content. The second part mainly introduces the basic knowledge on clustering and methods for clustering analysis based on the assessment of different algorithms, while identifying its advantages and disadvantages through the comparison of those algorithms. The third part introduces the application of the algorithm, as the study applies clustering technology to customer segmentation. First, the customer value system is built through AHP; customer value is then quantified, and customers are divided into different classifications using clustering technology. The efficient CRM can thus be used according to the different customer classifications. Currently, there are some systems used to evaluate customer value, but none of them can be put into practice efficiently. In order to solve this problem, the concept of continuous symmetry is introduced. It is very important to detect the continuous symmetry of a given problem. It allows for the detection of an observable state whose components are nonlinear functions of the original unobservable state. Thus, we built an evaluating system for customer value, which is in line with the development of the enterprise, using the method of data mining, based on the practical situation of the enterprise and through a series of practical evaluating indexes for customer value. The evaluating system can be used to quantify customer value, to segment the customers, and to build a decision-supporting system for customer value management. The fourth part presents the cure, mainly an analysis of the typical k-means algorithm; this paper proposes two algorithms to improve the k-means algorithm. Improved algorithm A can get the K automatically and can ensure the achievement of the global optimum value to some degree. Improved Algorithm B, which combines the sample technology and the arrangement agglomeration algorithm, is much more efficient than the k-means algorithm. In conclusion, the main findings of the study and further research directions are presented.

This article belongs to the Section Computer and Engineering Science and Symmetry/Asymmetry. Speech intelligibility is a crucial element in oral communication that can be influenced by multiple elements, such as noise, channel characteristics, or speech disorders. In this paper, we address the task of speech intelligibility classification (SIC) in this last circumstance. Taking our previous works, a SIC system based on an attentional long short-term memory (LSTM) network, as a starting point, we deal with the problem of the inadequate learning of the attention weights due to training data scarcity. For overcoming this issue, the main contribution of this paper is a novel type of weighted pooling (WP) mechanism, called saliency pooling where the WP weights are not automatically learned during the training process of the network, but are obtained from an external source of information, the Kalinli’s auditory saliency model. In this way, it is intended to take advantage of the apparent symmetry between the human auditory attention mechanism and the attentional models integrated into deep learning networks. The developed systems are assessed on the UA-speech dataset that comprises speech uttered by subjects with several dysarthria levels. Results show that all the systems with saliency pooling significantly outperform a reference support vector machine (SVM)-based system and LSTM-based systems with mean pooling and attention pooling, suggesting that Kalinli’s saliency can be successfully incorporated into the LSTM architecture as an external cue for the estimation of the speech intelligibility level. The work leading to these results has been supported by the Spanish Ministry of Economy, Industry and Competitiveness through TEC2017-84395-P (MINECO) and TEC2017-84593-C2-1-R (MINECO) projects (AEI/FEDER, UE), and the Universidad Carlos III de Madrid under Strategic Action 2018/00071/001.

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.

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.

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.

For time-invariant Metzler linear MIMO systems, this paper proposes an original approach reflecting necessary matching conditions, specifically structural system constraints and necessary positiveness in solving the problem of MIMO PID control. Covering the matching conditions by the supporting structure of measurement, refining the controller and system parameter constraints and introducing enhanced equivalent system descriptions, the reformulated design task is consistent with PID control law parameter representation and is formulated as a linear matrix inequality feasibility problem. Characterization of the PID control law parameters is permitted to highlight dynamical properties of the closed-loop system and the structural influence of the control derivative gain value in the design step. For the first time, the paper comprehensively sets the synthesis standard for PID control of MIMO Metzler systems because others for the given task have not been created at present.

The mutual confrontation between image steganography and steganalysis causes both to iterate continuously, and as a result, the dimensionality of the steganalytic features continues to increase, leading to an increasing spatio-temporal overhead. To this end, this paper proposes a fast steganalytic feature selection method based on a similar cross-entropy. Firstly, the properties of cross-entropy are investigated, through the discussion of different models, and the intra-class similarity criterion and inter-class similarity criterion based on cross-entropy are presented for the first time. Then, referring to the design principles of Fisher’s criterion, the criterion of feature contribution degree is further proposed. Secondly, the variation of the cross-entropy function of a univariate variable is analyzed in principle, thus determining the normalized range and simplifying the subsequent analysis. Then, within the normalized range, the variation of the cross-entropy function of a binary variable is investigated and the setting of important parameters is determined. Thirdly, the concept of similar cross-entropy is further presented by analyzing the changes in the value of the feature contribution measure under different circumstances, and based on this, the criterion for the feature contribution measure is updated to decrease the complexity of the calculation. Remarkably, the contribution measure criterion devised in this paper is a symmetrical structure, which equitably measures the contribution of features in different situations. Fourth, the feature component with the highest contribution is selected as the final selected feature based on the result of the feature metric. Finally, based on the Bossbase 1.01 image base that is a unique standard and recognized base in steganalysis, the feature selection on 8 kinds of low and high-dimensional steganalytic features is carried out. Through extensive experiments, comparison with several classic and state-of-the-art methods, the method designed in this paper attains competitive or even better performance in detection accuracy, calculation cost, storage cost and versatility.

Wireless sensor networks (WSNs) have good performance for data transmission, and the data transmission of sensor nodes has the function of symmetry. However, the wireless sensor nodes are facing great pressure in data transmission due to the increasing amount and types of data that easily cause premature energy consumption of some nodes and, thus, affects data transmission. Clustering algorithm is a common method to balance energy consumption, but the existing algorithms fail to balance the network oad effectively for big data transmission. Therefore, an optimal data transmission with data-location integration (ODTD-LI) is proposed for WSNs in this paper. For optimal data transmission, we update the network topology once for one round. In the proposed algorithm, we perform calculations of the optimal cluster heads, clustering and data transmission routing through three steps. We first deploy N homogeneous and symmetry nodes in a square area randomly and calculate the optimal number of cluster heads according to the node ocations. then, the optimal number of cluster heads, energy consumption, the distances and degrees of the nodes are taken into consideration during the clustering phase. Direct communication is carried out within a cluster, and the member nodes of the cluster pass the information directly to the cluster head. Lastly, an optimal hybrid routing from each cluster node to Sink is constructed for data transmission after clustering. The simulations verify the good performance of the proposed algorithm in view of the ifetime, average delay, coverage rate (CR) and oad balance of the network compared with the existing algorithms. Through the research conducted in this paper, we find that our work has good performance for selecting the hybrid routing in the network with the nodes randomly arranged.

This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

The purpose of image registration is to find the symmetry between the reference image and the image to be registered. In order to improve the registration effect of unmanned aerial vehicle (UAV) remote sensing imagery with a special texture background, this paper proposes an improved scale-invariant feature transform (SIFT) algorithm by combining image color and exposure information based on adaptive quantization strategy (AQCE-SIFT). By using the color and exposure information of the image, this method can enhance the contrast between the textures of the image with a special texture background, which allows easier feature extraction. The algorithm descriptor was constructed through an adaptive quantization strategy, so that remote sensing images with large geometric distortion or affine changes have a higher correct matching rate during registration. The experimental results showed that the AQCE-SIFT algorithm proposed in this paper was more reasonable in the distribution of the extracted feature points compared with the traditional SIFT algorithm. In the case of 0 degree, 30 degree, and 60 degree image geometric distortion, when the remote sensing image had a texture scarcity region, the number of matching points increased by 21.3%, 45.5%, and 28.6%, respectively and the correct matching rate increased by 0%, 6.0%, and 52.4%, respectively. When the remote sensing image had a large number of similar repetitive regions of texture, the number of matching points increased by 30.4%, 30.9%, and −11.1%, respectively and the correct matching rate increased by 1.2%, 0.8%, and 20.8% respectively. When processing remote sensing images with special texture backgrounds, the AQCE-SIFT algorithm also has more advantages than the existing common algorithms such as color SIFT (CSIFT), gradient location and orientation histogram (GLOH), and speeded-up robust features (SURF) in searching for the symmetry of features between images.

This paper explains a method of constructing algebras, starting with the properties of discrimination in elementary discrete systems. We show how to use points of view about these systems to construct what we call iterant algebras and how these algebras naturally give rise to the complex numbers, Clifford algebras and matrix algebras. The paper discusses the structure of the Schrödinger equation, the Dirac equation and the Majorana Dirac equations, finding solutions via the nilpotent method initiated by Peter Rowlands.

In recent years, crowded stampede incidents have occurred frequently, resulting in more and more serious losses. The common cause of such incidents is that when large-scale populations gather in a limited area, the population is highly unstable. In emergency situations, only when the crowd reaches the safe exit as soon as possible within a limited evacuation time to complete evacuation can the loss and casualties be effectively reduced. Therefore, the safety evacuation management of people in public places in emergencies has become a hot topic in the field of public security. Based on the analysis of the factors affecting the crowd path selection, this paper proposes an improved path-planning algorithm based on BEME (Balanced Evacuation for Multiple Exits). And pedestrian evacuation simulation is carried out in multi-exit symmetrical facilities. First, this paper optimizes the update method of the GSDL list in the BEME algorithm as the basis for evacuating pedestrians to choose an exit. Second, the collision between pedestrians is solved by defining the movement rule and collision avoidance strategy. Finally, the algorithm is compared with BEME and traditional path-planning algorithms. The results show that the algorithm can further shorten the global evacuation distance of the symmetrical evacuation scene, effectively balance the number of pedestrians at each exit and reduce the evacuation time. In addition, this improved algorithm uses a collision avoidance strategy to solve the collision and congestion problems in path planning, which helps to maximize evacuation efficiency. Whether the setting of the scene or the setting of the exit, all studies are based on symmetric implementation. This is more in line with the crowd evacuation in the real scene, making the experimental results more meaningful.

This paper is devoted to the study of the quadruple Roman domination in trees, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. For any positive integer k, a [k]-Roman dominating function ([k]-RDF) of a simple graph G is a function from the vertex set V of G to the set {0,1,2,…,k+1} if for any vertex u∈V with f(u)&lt, k, ∑x∈N(u)∪{u}f(x)≥|{x∈N(u):f(x)≥1}|+k, where N(u) is the open neighborhood of u. The weight of a [k]-RDF is the value Σv∈Vf(v). The minimum weight of a [k]-RDF is called the [k]-Roman domination number γ[kR](G) of G. In this paper, we establish sharp upper and lower bounds on γ[4R](T) for nontrivial trees T and characterize extremal trees.

This paper deals with symmetrical data that can be modelled based on Gaussian distribution, such as linear mixed models for longitudinal data. The latent factor linear mixed model (LFLMM) is a method generally used for analysing changes in high-dimensional longitudinal data. It is usual that the model estimates are based on the expectation-maximization (EM) algorithm, but unfortunately, the algorithm does not produce the standard errors of the regression coefficients, which then hampers testing procedures. To fill in the gap, the Supplemented EM (SEM) algorithm for the case of fixed variables is proposed in this paper. The computational aspects of the SEM algorithm have been investigated by means of simulation. We also calculate the variance matrix of beta using the second moment as a benchmark to compare with the asymptotic variance matrix of beta of SEM. Both the second moment and SEM produce symmetrical results, the variance estimates of beta are getting smaller when number of subjects in the simulation increases. In addition, the practical usefulness of this work was illustrated using real data on political attitudes and behaviour in Flanders-Belgium.

This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In arXiv:2103.05303, we have proposed the notion of $\mathbb{Z}_M$ gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. As shown in the next paper arXiv:2105.02598, the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action., Comment: 29 pages, 10 figures; typos corrected, published version in Symmetry (v2)

The variant, encryption, and confusion of WebShell results in problems in the detection method based on feature selection, such as poor detection effect and weak generalization ability. In order to solve this problem, a method of WebShell detection based on regularized neighborhood component analysis (RNCA) is proposed. The RNCA algorithm can effectively reduce the dimension of data while ensuring the accuracy of classification. In this paper, it is innovatively applied to a WebShell detection neighborhood, taking opcode behavior sequence features as the main research object, constructing vocabulary by using opcode sequence features with variable length, and effectively reducing the dimension of WebShell features from the perspective of feature selection. The opcode sequence selected by the algorithm is symmetrical with the source code file, which has great reference value for WebShell classification. On the issue of the single feature, this paper uses the fusion of behavior sequence features and text static features to construct a feature combination with stronger representation ability, which effectively improves the recognition rate of WebShell to a certain extent.

In this paper, some coefficient problems for starlike analytic functions with respect to symmetric points are considered. Bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates for the following: coefficients, logarithmic coefficients, some cases of the generalized Zalcman coefficient functional, and some cases of the Hankel determinant.

This paper provides three classes of q-summation formulas in the form of general contiguous extensions of the first q-Kummer summation theorem. Their derivations are presented by using three methods, which are along the lines of the three types of well-known proofs of the q-Kummer summation theorem with a key role of the q-binomial theorem. In addition to the q-binomial theorem, the first proof makes use of Thomae’s q-integral representation and the second proof needs Heine’s transformation. Whereas the third proof utilizes only the q-binomial theorem. Subsequently, the applications of these summation formulas in obtaining the general contiguous extensions of the second and the third q-Kummer summation theorems are also presented. Furthermore, the investigated results are specialized to give many of the known as well as presumably new q-summation theorems, which are contiguous to the three q-Kummer summation theorems. This work is motivated by the observation that the basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) gamma and q-hypergeometric functions and basic (or q-) hypergeometric polynomials, are applicable particularly in several diverse areas including Number Theory, Theory of Partitions and Combinatorial Analysis as well as in the study of Combinatorial Generating Functions. Just as it is known in the theory of the Gauss, Kummer (or confluent), Clausen and the generalized hypergeometric functions, the parameters in the corresponding basic or quantum (or q-) hypergeometric functions are symmetric in the sense that they remain invariant when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. A case has therefore been made for the symmetry possessed not only by hypergeometric functions and basic or quantum (or q-) hypergeometric functions, which are studied in this paper, but also by the symmetric quantum calculus itself.

In this paper, we propose the fractal (2 + 1)-dimensional Zakharov–Kuznetsov equation based on He’s fractal derivative for the first time. The fractal generalized variational formulation is established by using the semi-inverse method and two-scale fractal theory. The obtained fractal variational principle is important since it not only reveals the structure of the traveling wave solutions but also helps us study the symmetric theory. The finding of this paper will contribute to the study of symmetry in the fractal space.

The object of investigation in this paper is a scalar linear fractional differential equation with generalized proportional derivative of Riemann–Liouville type (LFDEGD). The main goal is the obtaining an explicit solution of the initial value problem of the studied equation. Note that the locally solvability, being the same as the existence of solutions to the initial value problem, is connected with the symmetry of a transformation of a system of differential equations. At the same time, several criteria for existence of the initial value problem for nonlinear fractional differential equations with generalized proportional derivative are connected with the linear ones. It leads to the necessity of obtaining an explicit solution of LFDEGD. In this paper two cases are studied: the case of no impulses in the differential equation are presented and the case when instantaneous impulses at initially given points are involved. All obtained formulas are based on the application of Mittag–Leffler function with two parameters. In the case of impulses, initially the appropriate impulsive conditions are set up and later the explicit solutions are obtained.

In this paper, the time-varying formation tracking problem of the general linear multi-agent system is discussed. A distributed formation tracking protocol based on Riccati inequalities with adaptive coupling weights among the follower agents and the leader agent is designed for a leader-following multi-agent system under fixed and switching topologies. The formation configuration involved in this paper is expressed as a bounded piecewise continuously differentiable vector function. The follower agents will achieve the desired formation tracking trajectory of the leader. In traditional static protocols, the coupling weights depend on the communication topology and is a constant. However, in this paper, the coupling weights are updated by the state errors among the neighboring agents. Moreover, the stability analysis of the MAS under switching topology is presented, and proves that the followers also could achieve pre-specified time-varying formation, if the communication graph is jointly connected. Two numerical simulations indicate the capabilities of the algorithms.

The aim of this paper is to show analytically and empirically how ant-based algorithms for medical image edge detection can be enhanced by using an admissible perturbation of demicontractive operators. We thus complement the results reported in a recent paper by the second author and her collaborators, where they used admissible perturbations of demicontractive mappings as test functions. To illustrate this fact, we first consider some typical properties of demicontractive mappings and of their admissible perturbations and then present some appropriate numerical tests to illustrate the improvement brought by the admissible perturbations of demicontractive mappings when they are taken as test functions in ant-based algorithms for medical image edge detection. The edge detection process reported in our study considers both symmetric (Head CT and Brain CT) and asymmetric (Hand X-ray) medical images. The performance of the algorithm was tested visually with various images and empirically with evaluation of parameters.

In the multicast network, network coding has proven to be an effective technique to approach maximum flow capacity. Although network coding has the advantage of improving performance, encoding nodes increases the cost and delay in wireless networks. Therefore, minimizing encoding nodes is of great significance to improve the actual network’s performance under a maximum multicast flow. This paper seeks to achieve partial improvements in the existing selection algorithm of encoding nodes in wireless networks. Firstly, the article gives the condition for an intermediate node to be an encoding node. Secondly, a maximum flow algorithm, which depends on the depth-first search method, is proposed to optimize the search time by selecting the larger augmentation flow in each step. Finally, we construct a random graph model to simulate the wireless network and the maximum multicast flow algorithm to analyze the statistical characteristics of encoding nodes. This paper aims at the optimization to find the minimal number of required coding nodes which means the minimum energy consumption. Meanwhile, the simulations indicate that the curve of coding nodes tends to be a geometric distribution, and that the curve of the maximum flow tends to be symmetric as the network scale and the node covering radius increase.

In decision-making process, decision-makers may make different decisions because of their different experiences and knowledge. The abnormal preference value given by the biased decision-maker (the value that is too large or too small in the original data) may affect the decision result. To make the decision fair and objective, this paper combines the advantages of the power average (PA) operator and the Bonferroni mean (BM) operator to define the generalized fuzzy soft power Bonferroni mean (GFSPBM) operator and the generalized fuzzy soft weighted power Bonferroni mean (GFSWPBM) operator. The new operator not only considers the overall balance between data and information but also considers the possible interrelationships between attributes. The excellent properties and special cases of these ensemble operators are studied. On this basis, the idea of the bidirectional projection method based on the GFSWPBM operator is introduced, and a multi-attribute decision-making method, with a correlation between attributes, is proposed. The decision method proposed in this paper is applied to a software selection problem and compared to the existing methods to verify the effectiveness and feasibility of the proposed method.

This paper deals with uncertainty, asymmetric information, and risk modelling in a complex power system. The uncertainty is managed by using probability and decision theory methods. More specifically, influence diagrams—as extended Bayesian network functions with interval probabilities represented through credal sets—were chosen for the predictive modelling scenario of replacing the most critical circuit breakers in optimal time. Namely, based on the available data on circuit breakers and other variables that affect the considered model of a complex power system, a group of experts was able to assess the situation using interval probabilities instead of crisp probabilities. Furthermore, the paper examines how the confidence interval width affects decision-making in this context and eliminates the information asymmetry of different experts. Based on the obtained results for each considered interval width separately on the action to be taken over the considered model in order to minimize the risk of the power system failure, it can be concluded that the proposed approach clearly indicates the advantages of using interval probability when making decisions in systems such as the one considered in this paper.

In this paper, we introduce a new representation of semiopenness of L-fuzzy sets in RL-fuzzy bitopological spaces based on the concept of pseudo-complement. The concepts of pairwise RL-fuzzy semicontinuous and pairwise RL-fuzzy irresolute functions are extended and discussed based on the (i,j)-RL-semiopen gradation. Further, pairwise RL-fuzzy semi-compactness of an L-fuzzy set in RL-fuzzy bitopological spaces are given and characterized. As RL-fuzzy bitopology is a generalization of L-bitopology, RL-bitopology, L-fuzzy bitopology, and RL-fuzzy topology, the results of our paper are more general.

The fractional integral is a function known for the elegant results obtained when introducing new operators, it has proved to have interesting applications. In the present paper, differential subordinations and superodinations for the fractional integral of the confluent hypergeometric function introduced in a previously published paper are presented. A sandwich-type theorem at the end of the original part of the paper connects the outcomes of the studies done using the dual theories.

Inventory-pooling (IP) is an effective tool to mitigate demand uncertainty and variability, to reduce operational costs, and consequently to increase the profit. The major assumptions of the previous works in literature on IP include the following: (1) Independents demand, which satisfy the typical normal independent and identically distributed (iid) random variables, (2) dependents (correlated) symmetric demands, which follows to a multivariate normal distribution. The effect of the dependent asymmetric demand is not yet studied. The aim of this paper is to consider this more realistic case. Indeed, the contribution of this paper is twofold. Firstly, it analyzes both the sensitivity of dependence structure and the levels of skewness of distributions on IP policies in terms of optimal total cost and demand satisfaction constraint. Secondly, both symmetric and asymmetric demand distributions are modeled using various beta distribution and the dependance between demands are modeled using various copulas. A newsvendor problem inspired by the literature, with two decentralized locations and two centralized locations, is considered the empirical study. For each dependance situation, three IP models are considered: inventory centralization, regular transshipments, and independent systems. The results suggest divergences in the decisions in about 9% of cases. Bad choice of marginal distributions given that the copula is appropriate can lead to divergences that vary between 2.2% and 4%, depending on whether the demand distributions are symmetric or asymmetric.

Some generalizations of the Gronwall&ndash, Bellman (G&ndash, B) inequality are presented in this paper in continuous form and on time scales. After S. Hilger introduced the time scales theory in 1988, over the years many mathematicians have studied new versions of this inequality according to new results, the purpose of this paper is to present some of them. Therefore, in the Introduction, some generalizations of G&ndash, B inequality in continuous forms, linear and nonlinear are presented. In the second section, some important and interesting results on time scales theory are given. In the third and main part of our paper, G&ndash, B inequalities on time scales and their possible connection with G&ndash, B inequalities presented in the introduction are investigated. In particular, in the third section of this work, more attention is given to G&ndash, B type inequalities on time scales discussed in the last four years.

This paper is concerned with a type of time-symmetric stochastic system, namely the so-called forward&ndash, backward doubly stochastic differential equations (FBDSDEs), in which the forward equations are delayed doubly stochastic differential equations (SDEs) and the backward equations are anticipated backward doubly SDEs. Under some monotonicity assumptions, the existence and uniqueness of measurable solutions to FBDSDEs are obtained. The future development of many processes depends on both their current state and historical state, and these processes can usually be represented by stochastic differential systems with time delay. Therefore, a class of nonzero sum differential game for doubly stochastic systems with time delay is studied in this paper. A necessary condition for the open-loop Nash equilibrium point of the Pontriagin-type maximum principle are established, and a sufficient condition for the Nash equilibrium point is obtained. Furthermore, the above results are applied to the study of nonzero sum differential games for linear quadratic backward doubly stochastic systems with delay. Based on the solution of FBDSDEs, an explicit expression of Nash equilibrium points for such game problems is established.

This paper introduces a general approach to the idea of protection of graphs, which encompasses the known variants of secure domination and introduces new ones. Specifically, we introduce the study of secure w-domination in graphs, where w=(w0,w1,⋯,wl) is a vector of nonnegative integers such that w0&ge, 1. The secure w-domination number is defined as follows. Let G be a graph and N(v) the open neighborhood of v&isin, V(G). We say that a function f:V(G)⟶{0,1,⋯,l} is a w-dominating function if f(N(v))=&sum, u&isin, N(v)f(u)&ge, wi for every vertex v with f(v)=i. The weight of f is defined to be &omega, (f)=&sum, v&isin, V(G)f(v). Given a w-dominating function f and any pair of adjacent vertices v,u&isin, V(G) with f(v)=0 and f(u)&gt, 0, the function fu&rarr, v is defined by fu&rarr, v(v)=1, fu&rarr, v(u)=f(u)&minus, 1 and fu&rarr, v(x)=f(x) for every x&isin, V(G)∖{u,v}. We say that a w-dominating function f is a secure w-dominating function if for every v with f(v)=0, there exists u&isin, N(v) such that f(u)&gt, 0 and fu&rarr, v is a w-dominating function as well. The secure w-domination number of G, denoted by &gamma, ws(G), is the minimum weight among all secure w-dominating functions. This paper provides fundamental results on &gamma, ws(G) and raises the challenge of conducting a detailed study of the topic.