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Investigating the research trends within a scientific domain by analyzing semantic information extracted from scientific journals has been a topic of interest in the natural language processing (NLP) field. A research trend evaluation is generally based on the time evolution of the term occurrence or the term topic, but it neglects an important aspect—research publication latency. The average time lag between the research and its publication may vary from one month to more than one year, and it is a characteristic that may have significant impact when assessing research trends, mainly for rapidly evolving scientific areas. To cope with this problem, the present paper is the first work that explicitly considers research publication latency as a parameter in the trend evaluation process. Consequently, we provide a new trend detection methodology that mixes auto-ARIMA prediction with Mann–Kendall trend evaluations. The experimental results in an electronic design automation case study prove the viability of our approach.

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 work presents an optimization proposal to better the computational convergence time in convection-diffusion and driven-cavity problems by applying a simulated annealing (SA) metaheuristic, obtaining optimal values in relaxation factors (RF) that optimize the problem convergence during its numerical execution. These relaxation factors are tested in numerical models to accelerate their computational convergence in a shorter time. The experimental results show that the relaxation factors obtained by the SA algorithm improve the computational time of the problem convergence regardless of user experience in the initial low-quality RF proposal.

The rationalization of logistics activities and processes is very important in the business and efficiency of every company. In this respect, transportation as a subsystem of logistics, whether internal or external, is potentially a huge area for achieving significant savings. In this paper, the emphasis is placed upon the internal transport logistics of a paper manufacturing company. It is necessary to rationalize the movement of vehicles in the company’s internal transport, that is, for the majority of the transport to be transferred to rail transport, because the company already has an industrial track installed in its premises. To do this, it is necessary to purchase at least two used wagons. The problem is formulated as a multi-criteria decision model with eight criteria and eight alternatives. The paper presents a new approach based on a combination of the Simple Additive Weighting (SAW) method and rough numbers, which is used for ranking the potential solutions and selecting the most suitable one. The rough Best–Worst Method (BWM) was used to determine the weight values of the criteria. The results obtained using a combination of these two methods in their rough form were verified by means of a sensitivity analysis consisting of a change in the weight criteria and comparison with the following methods in their conventional and rough forms: the Analytic Hierarchy Process (AHP), Technique for Ordering Preference by Similarity to Ideal Solution (TOPSIS) and MultiAttributive Border Approximation area Comparison (MABAC). The results show very high stability of the model and ranks that are the same or similar in different scenarios.

In order to solve the Sylvester equations more efficiently, a new four parameters positive and skew-Hermitian splitting (FPPSS) iterative method is proposed in this paper based on the previous research of the positive and skew-Hermitian splitting (PSS) iterative method. We prove that when coefficient matrix A and B satisfy certain conditions, the FPPSS iterative method is convergent in the parameter&rsquo, s value region. The numerical experiment results show that compared with previous iterative method, the FPPSS iterative method is more effective in terms of iteration number IT and runtime.

Direct current transformer (DCT) is a key piece of equipment in direct current (DC) microgrids, and the mainstream topologies mainly include LLC resonant converter (LLC) and dual active bridge (DAB). In this paper, a novel bi-directional buck/boost + CLLLC cascade topology is proposed for the input-series-output-parallel cascade converter system of a DC microgrid. To solve the problem that frequency variation causes the converter to deviate from the optimal operating point, resulting in low efficiency, and the inability to achieve a soft switching function. The CLLLC converter operates near the resonant frequency point as a DCT, only providing electrical isolation and voltage matching, while the buck/boost converter controls the output voltage and the voltage and current sharing of each module. Compared to other cascaded converter systems, the cascaded converter proposed in this paper has high efficiency, simplifies the parameter design, and is suitable for wide input and wide output operating conditions. The system adopts a three-loop control strategy, establishes the small-signal modeling of the system, and its stability is verified by theoretical analysis and simulation. The simulation and experimental results verify the correctness of the proposed cascaded converter based on buck/boost + CLLLC and the effectiveness of the control strategy.

The state feedback controller design for a class of Generalized Proportional Fractional Order (GPFO) Nonlinear Systems is presented in this paper. The design is based on the combination of the One-Sided Lipschitz (OSL) system class with GPFO modeling. The main contribution of this study is that, to the best of the authors’ knowledge, this work presents the first state feedback control design for GPFO systems. The suggested state feedback controller is intended to ensure the system’s generalized Mittag Leffler (GML) stability and to deliver optimal performance. The findings of this paper show that the proposed strategy is effective in stabilizing Generalized Proportional Fractional Order Nonlinear Systems. A numerical example is presented to demonstrate the usefulness of the stated theoretical conclusions.

In this paper, the impact of one of the challenges of the power transmission system, namely three-phase short-circuits, on the stability of the system is discussed. This fault causes the speed change of the synchronous generators, and the control system needs to quickly zero this speed difference. This paper introduces a completely new and innovative method for power system stabilizer design. In the proposed method, there is a PID controller with a type-2 fuzzy compensator whose optimal parameter values are obtained using an improved virus colony search (VCS) algorithm at any time. In the simulation section, both transient short-circuits (timely operation of breakers and protection relays) and permanent short-circuits (failure of breakers and protection relays) are applied. For transient short-circuits, the three control systems of type-1 fuzzy-PID, type-2 fuzzy-PID, and optimized type-2 fuzzy-PID based on VCS for the nominal load and heavy load modes were compared in the simulations. Apart from the three control systems mentioned earlier, the response of a standalone PID controller was also evaluated in the context of the permanent short-circuit mode. According to the simulation results, the proposed method demonstrates superior performance and high efficiency. In contrast, the standalone PID exhibits divergence.

A positively invariant set is an important concept in dynamical systems. The study of positively invariant set conditions for discrete-time systems is one interesting topic in both theoretical studies and practical applications research. Different methods for characterizing the invariance of different types of sets have been established. For example, the ellipsoidal and the Lorenz cone, which are quadratic convex sets, have different properties from a polyhedral set. This paper presents an optimization method and a dual optimization method to characterize the positive invariance of the ellipsoidal and the Lorenz cone. The proposed methods are applicable to both linear and nonlinear discrete-time systems. Using nonlinear programming and an induced norm, the positive invariance condition problems are transformed into optimization problems, and the dual optimization method is also used to give equivalent dual forms. Fewer results on the positive invariance condition of Lorenz cones can be found than for the other type of set; this paper fulfills the results of this problem. In addition, the proposed methods in this paper provide more options for checking the positive invariance of quadratic convex sets from the perspective of optimization and dual optimization. The effectiveness of this method is demonstrated by numerical examples.

The transmission rate is an important indicator for characterizing a virus and estimating the risk of its outbreak in a certain area, but it is hard to measure. COVID-19, for instance, has greatly affected the world for more than 3 years since early 2020, but scholars have not yet found an effective method to obtain its timely transmission rate due to the fact that the value of COVID-19 transmission rate is not constant but dynamic, always changing over time and places. Therefore, in order to estimate the timely dynamic transmission rate of COVID-19, we performed the following: first, we utilized a rolling time series to construct a time-varying transmission rate model and, based on the model, managed to obtain the dynamic value of COVID-19 transmission rate in mainland China; second, to verify the result, we used the obtained COVID-19 transmission rate as the explanatory variable to conduct empirical research on the impact of the COVID-19 pandemic on China’s stock markets. Eventually, the result revealed that the COVID-19 transmission rate had a significant negative impact on China’s stock markets, which, to some extent, confirms the validity of the used measurement method in this paper. Notably, the model constructed in this paper, combined with local conditions, can not only be used to estimate the COVID-19 transmission rate in mainland China but also in other affected countries or regions and would be applicable to calculate the transmission rate of other pathogens, not limited to COVID-19, which coincidently fills the gaps in the research. Furthermore, the research based on this model might play a part in regulating anti-pandemic governmental policies and could also help investors and stakeholders to make decisions in a pandemic setting.

The modal and vibration-noise response characteristics of plate structures are closely related to their boundary effects, and the analytical modeling and solution of the dynamics of plate structures with complex boundary conditions can reveal mechanisms of the influence of the boundary structure parameters on the modal characteristics. This paper proposes a new method for dynamic modeling of rectangular plates with periodic boundary conditions based on the energy equivalence principle (mixed-variable variational principle) of equating complex boundary “geometric constraints” to “mathematical physical constraints”, taking a rectangular plate structure with periodic boundaries commonly used in engineering as the object. First, the boundary external potential energy of the periodic boundary rectangular plate is obtained by equating the bending moment and deflection to the boundary conditions. Next, we establish the total potential energy model, the amplitude boundary equation, as well as the frequency equation of the periodic boundary rectangular plate in turn. Solving by numerical method, the natural frequency of the theoretical model is obtained. The validity of the theoretical model is then verified by modal test experiments. Finally, the law of the parameters such as the form of boundary constraint, the number of periods, and the clamp support ratio on the natural frequency of the rectangular plate is investigated. The results show that the natural frequency of the rectangular plate is closely related to the boundary form and period distribution of the plate. The modal frequencies of the plate structure can be tuned by the design of the boundary conditions for a certain size of the plate structure. The research in this paper provides a theoretical and technical basis for the vibration noise control of complex boundary plate structures.

The existing estimators for the drift coefficient in the diffusion model with jumps involve jump components and possess larger boundary error. How to effectively estimate the drift function is an important issue that faces challenges and has theoretical significance. In this paper, the gamma asymmetric kernel for boundary correction and threshold function eliminating jump impacts are combined to estimate the unknown drift coefficient in the jump diffusion process of interest rate. The asymptotic large sample property and the better finite sample property through the Monte Carlo numerical simulation experiment and the empirical analysis of SHIBOR and LIBOR for the corresponding estimator are considered in detail. It is found that the estimator proposed in this paper can correct the estimation error near or far away from the origin point, which provides a more asymptotic unbiased estimator for the drift function in diffusion models with jumps.

Flow Direction Algorithm (FDA) has better searching performance than some traditional optimization algorithms. To give the basic Flow Direction Algorithm more effective searching ability and avoid multiple local minima under the searching space, and enable it to obtain better search results, an improved FDA based on the Lévy flight strategy and the self-renewable method (LSRFDA) was proposed in this paper. The Lévy flight strategy and the self-renewable approach were added to the basic Flow Direction Algorithm. Random parameters generated by the Lévy flight strategy can increase the algorithm’s diversity of feasible solutions in a short calculation time and greatly enhance the operational efficiency of the algorithm. The self-renewable method lets the algorithm quickly obtain a better possible solution and jump to the local solution space. Then, this paper tested different mathematical testing functions, including low-dimensional and high-dimensional functions, and the test results were compared with those of different algorithms. This paper includes iterative figures, box plots, and search paths to show the different performances of the LSRFDA. Finally, this paper calculated different engineering optimization problems. The test results show that the proposed algorithm in this paper has better searching ability and quicker searching speed than the basic Flow Direction Algorithm.

To ensure the safety of concrete dams, a large number of monitoring instruments are embedded in the bodies and foundations of the dams. However, monitoring data are often missing due to failure of monitoring equipment, human error and other factors that cause difficulties in diagnosis of dam safety and failure to precisely predict their deformation. In this paper, a new method for imputing missing deformation data is proposed. First, since the traditional deformation increment speed distance index of the deformation similarity index does not take into account the fact that there is little change in deformations occurring in two consecutive days, the denominator of the index tends to be equal to zero. In this paper, an improved index for solving this problem is proposed. A combined weighting method for calculating the deformation similarity comprehensive index and the k-means clustering method is then proposed and used to classify deformation monitoring points. Subsequently, a panel data model that imputes different types of missing data is established. The method proposed in this paper can impute missing concrete dam deformation data more accurately; therefore, it can effectively solve the missing deformation monitoring data problem.

The inverse conductivity problem in electrical impedance tomography involves the solving of a nonlinear and under-determined system of equations. This paper presents a new approach, which leads to a quadratic and overdetermined system of equations. The aim of the paper is to establish new research directions in handling of the inverse conductivity problem. The basis of the proposed method is that the material, which can be considered as an isotropic continuum, is modeled as a linear network with concentrated parameters. The weights of the obtained graph represent the properties of the discretized continuum. Further, the application of the developed procedure allows for the dielectric constant to be used in the multi-frequency approach, as a result of which the optimized system of equations always remains overdetermined. Through case studies, the efficacy of the reconstruction method by changing the mesh resolution applied for discretizing is presented and evaluated. The presented results show, that, due to the application of discrete, symmetric mathematical structures, the new approach even at coarse mesh resolution is capable of localizing the inhomogeneities of the material.

The uncertainty of intuitionistic fuzzy numbers (IFNs) is further enhanced by the existence of the degree of hesitation (DH). The shortcomings of existing researches are mainly reflected in the following situations: when comparing IFNs, the comparison rules of IFNs are difficult to apply to the comparison of any two IFNs, or the relevant methods do not fully consider the uncertainty expressed by DH. Thus, the rationality of the decision results needs to be improved. On the other hand, multi-attribute decision making (DADM) based on IFNs is often not objective due to the need to determine the attribute weight. Moreover, the strict condition of attribute aggregation of classical dominance relation makes it a method that fails considering the practical application. Aiming at the comparison problem of IFNs, this paper takes probability conversion as the starting point and proposes an IFN comparison method based on the area method, which can better deal with the comparison problem of “either superior or inferior” IFNs. In addition, aiming at the MADM problem of an intuitionistic fuzzy information system, we propose an intuitionistic fuzzy probabilistic dominance relation model and construct the MADM method under the probabilistic dominance relation. The series properties of IFNs and probabilistic dominance relation were summarized and proved, which theoretically ensured the scientificity and rigor of the method. The results show that the comparison and ranking method of IFNs proposed in this paper can be applied to the comparison of any two IFNs, and the dominance degree of IFNs is presented in the form of probability, which is more flexible and practical than the classical method. The probabilistic dominance relation method based on IFNs avoids the problem of determining attribute weights subjectively or objectively, and the decision maker can reflect decision preference by adjusting decision parameters to better match the actual problem. The application of this model to a campus express site evaluation further verifies the feasibility of the proposed method and the rationality of the results. In addition, various extension problems of the model and method proposed in this paper are discussed, which pave the way for future related research. This paper constructs a complete decision-making framework through theoretical analysis and application from practical problems, which provides a reference for enriching and improving uncertain decision-making theory and the MADM method.

In the present energy scenario, wind energy is the fastest-growing renewable energy resource on the globe. However, wind-energy-based generation systems are also associated with increasing demands for power quality and active power control in the power network. With the advancements in power-electronics-based technology and its use in non-conventional energy conversion systems, it has witnessed tremendous growth in wind energy conversion systems (WECSs). At the same time, integrating wind farms into the grid system also results in many power quality issues in the power system that involve these renewable energy sources feeding power networks. This paper reports the effectiveness of grid-connected doubly fed induction generator (DFIG)-based WECS with a battery energy storage system (BESS) under variable wind conditions. In this study, a rotor side converter (RSC) is controlled to achieve the optimal torque for a given maximal wind power. The control scheme is simulated using MATLAB for a 2 MW-rated DFIG used in a WECS. Additionally, in this paper, a new fraction order proportional integral derivative (FOPID) controller is introduced into the system’s RSC, and its performance is also observed. The BESS technique is used with a DC link to improve the overall performance of the DFIG-based WECS under different wind conditions. To control the BESS, a proportional integral (PI) controller is introduced to increase the charging and discharging rates. Two models are developed in MATLAB/Simulink: one model is a basic model, and other model is equipped with a BESS and a PI controller in the BESS. The results validate the effectiveness of the proposed PI-controller-equipped BESS at improving the overall performance of the WECS system under study.

When studying an unfamiliar system, we first look for the symmetry that the system has, so that we can make many predictions about the possible properties of the system. The symmetry in ship network security needs to maintain a stable state and maintain a constant state of ship network security. With the rapid development of network information technology, smart ships have become a new hot spot in the international shipping industry. The smart ships cybersecurity discussion is also at the top of the list in the maritime field. More and more shipping companies feel that their smart ship systems need to be upgraded and the main reason behind this is that the systems are maliciously attacked by cyber hackers. Therefore, it is extremely important to detect and protect the security of intelligent ship network systems in real time. The issue of network security has always accompanied the whole process of the development of the Internet. At the same time, with the development of Internet technology, network hacking attacks against the Internet have never stopped developing, and traditional ship network security risk detection and protection cannot achieve good results. After understanding the operation mode of intelligent ship networks, this paper deeply studied the characteristics of cloud computing technology and proposed a real-time risk detection method and protection strategy for intelligent ship network security based on cloud computing. This paper mainly used multi-sensor nodes to analyze data containing malicious attack information and implemented self-execution protection strategy generation nodes to intercept and protect from the attack, so as to achieve the purpose of maintaining the network security of intelligent ships. Through experiments, the virus intrusion detection and defense rate of the algorithm proposed in this paper was able to reach 85% to 95%, while the virus intrusion detection defense rate of the traditional intelligent ship network security protection algorithm was 55% to 65%. The detection rate of the algorithm proposed in this paper was able to reach 96.95% and the false positive rate was 2.56%. The detection rate of the traditional algorithm was only 70.76%, while the false positive rate reached 4.69%. All of the proposed algorithm’s data were significantly better than that of traditional algorithms, which proved that the performance of cloud computing-based real-time risk detection and protection algorithms for intelligent ship network security was significantly better than that of traditional algorithms.

The methods that use memory using accelerating parameters for computing multiple roots are almost non-existent in the literature. Furthermore, the only paper available in this direction showed an increase in the order of convergence of 0.5 from the without memory to the with memory extension. In this paper, we introduce a new fifth-order without memory method, which we subsequently extend to two higher-order with memory methods using a self-accelerating parameter. The proposed with memory methods extension demonstrate a significant improvement in the order of convergence from 5 to 7, making this the first paper to achieve at least a 2-order improvement. In addition to this improvement, our paper is also the first to use Hermite interpolating polynomials to approximate the accelerating parameter in the proposed with memory methods for multiple roots. We also provide rigorous theoretical proofs of convergence theorems to establish the order of the proposed methods. Finally, we demonstrate the potential impact of the proposed methods through numerical experimentation on a diverse range of problems. Overall, we believe that our proposed methods have significant potential for various applications in science and engineering.

With the wide application of the artificial ground freezing method in municipal underground engineering, the annular layout of freezing pipes is often adopted to form a frozen soil cylinder. However, there is still no analytical solution that can calculate the temperature distribution of frozen soil formed in this case. In this paper, a mathematical model of a steady-state temperature field of single-circle freezing is established, in which the inside of the freeze ring is completely frozen; that is, the temperature of all excavation sections is below the freezing point. Then, the analytical solution of temperature distribution is deduced through the complex variable method and potential superposition method. Comparison results of the analytical solution with those of the numerical simulation show that the analytical solution is precise enough. The temperature distribution of the main section and the intersection is approximately the same on the inner side, but the freezing effect of the main section is relatively better near the freezing pipes and outside the freeze ring. Besides, according to the derived analytical solution and common freezing parameters, a simplified formula to calculate the temperature field with enough accuracy was proposed, and the error can be controlled below 1‰. Finally, based on the simplified formula, a calculation method for frozen soil thickness and the average temperature is also given in this paper.

Dynamic vibration absorbers (DVAs) are widely used in engineering practice because of their good vibration control performance. Structural design or parameter optimization could improve its control efficiency. In this paper, the viscoelastic Maxwell-type DVA model with an inerter and multiple stiffness springs is investigated with the combination of the traditional theory and an intelligent algorithm. Firstly, the expressions and approximate optimal values of the system parameters are obtained using the fixed-point theory to deal with the H∞ optimization problem, which can provide help with the range of parameters in the algorithm. Secondly, we innovatively introduce the particle swarm optimization (PSO) algorithm to prove that the algorithm could adjust the value of the approximate solution to minimize the maximum amplitude by analyzing and optimizing the single variable and four variables. Furthermore, the validity of the parameters is further verified by simulation between the numerical solution and the analytical solution using the fourth-order Runge–Kutta method. Finally, the DVA demonstrated in this paper is compared with typical DVAs under random excitation. The timing sequence and variances, as well as the decreased ratios of the displacements, show that the presented DVA has a more satisfactory control performance. The inerter and negative stiffness spring can indeed bring beneficial effects to the vibration absorber. Remarkably, the intelligent algorithm can make the resonance peaks equal in the parameter optimization of the vibration absorber, which is quite difficult to achieve with theoretical methods at present. The results may provide a theoretical and computational basis for the optimization design of DVA.

Hermite–Hadamard inequalities and their refinements have been investigated for a long period of time. In this paper, we obtained refinements of the Hermite–Hadamard inequality of tensorial type for the convex functions of self-adjoint operators in Hilbert spaces. The obtained inequalities generalize the previously obtained inequalities by Dragomir. We also provide useful Lemmas which enabled us to obtain the results. The examples of the obtained inequalities for specific convex functions have been given in the example and consequences section. Symmetry in the upper and lower bounds can be seen in the last Theorem of the paper given, as the upper and lower bounds differ by a constant.

At the beginning of the COVID-19 pandemic, the entire world was waiting for a medical solution (for example, vaccines) in order to return to normality. Sanitary restrictions changed our consumption behaviors and feelings. Therefore, this paper analyzes the stochastic properties of consumer sentiment during the COVID-19 episode and the appearance of vaccines against the virus in December 2020 in the United States of America. This study adds a new dimension to the literature because it is the first research paper that uses advanced methodologies based on fractional integration and fractional cointegration analysis to understand the statistical properties of these time series and their behavior in the long term. The results using fractional integration methodologies exhibit a high degree of persistence, finding behavior of mean reversion during the pandemic episode. Therefore, the shock duration in consumer sentiment will be transitory, recovering to its previous trend in the short run. Focusing on the cointegrating part, we arrive at two main conclusions. First, an increase in total vaccination produces a positive reaction or impact on the behavior of consumers. On the other hand, an increase in new COVID-19 cases negatively affects the behavior of the consumer.

The selection of a pharmaceutical e-commerce platform is a typical multi-attribute group decision-making (MAGDM) problem. MAGDM is a common problem in the field of decision-making, which is full of uncertainty and fuzziness. A probabilistic hesitant fuzzy multi-attribute group decision-making method based on generalized TODIM is proposed for the selection of pharmaceutical e-commerce under an uncertain environment. Firstly, the credibility of a probabilistic hesitant fuzzy element is defined, and a credibility-based method for adjusting the weights of decision-makers and determining attribute weights is proposed, which fully considers the reliability of information provided by the decision-makers. Secondly, the power average (PA) operator is extended to the probabilistic hesitant fuzzy environment. The probabilistic hesitant fuzzy power average (PHFPA) operator and the probabilistic hesitant fuzzy power weighted average (PHFPWA) operator are defined, and their properties are discussed. Thirdly, considering the usual information expression of decision-makers in real life and the different risk attitudes towards gain and loss, the generalized TODIM method is extended to the probabilistic hesitant fuzzy environment to construct a prospect theory-based group decision-making method in the probabilistic hesitant fuzzy environment. Finally, the feasibility of the method in this paper is proved through the case of pharmaceutical e-commerce platform selection, and the stability of the method in this paper is verified by sensitivity analysis.

In multiquadratic radial basis function (MQ-RBF) interpolation, shape parameters have a direct effect on the interpolation accuracy. The paper presents an MQ-RBF interpolation technique with optimized shape parameters for estimating the parameters of sine wave signals. At first, we assessed the impact of basic sinusoidal parameters on the MQ-RBF interpolation outcomes through numerical experiments. The results indicated that the angular frequency of a sine wave is a crucial determinant of the corresponding MQ-RBF interpolation shape parameters. A linear regression method was then used to establish the optimal parameter selection formula for a single-frequency sine wave, based on a large volume of experimental data. For multi-frequency sinusoidal signals, appropriate interpolation shape parameters were selected using the random walk algorithm to create datasets. These datasets were subsequently used to train several regression models, which were then evaluated and compared. Based on its operational cost and prediction accuracy, the random forest algorithm was chosen to establish the shape parameter selection model for multi-frequency sinusoidal signals. The inclusion of the Bayesian optimizer resulted in a highly accurate model. The establishment of this model enabled the adaptive selection of the corresponding shape parameters for any sine wave signal, providing a convenient means of selecting MQ-RBF interpolation shape parameters. Furthermore, the paper proposes an MQ-RBF interpolation subdivision least squares method that significantly improves the estimation accuracy of sine wave parameters. The practicality of the method was validated by successfully applying it in the calibration of the clock delay mismatch of a time-interleaved analog-to-digital converter system.

Abnormal passenger behavior in rail transit has become a top priority, as it affects operational safety. Passenger travel time is the main basis for identifying abnormal behavior while considering the flexibility of travel time. Currently, the main method is to use absolute threshold discrimination based on the distribution of travel time. However, there is a problem of missing abnormal passenger behavior due to the large difference in travel time between the Origin-Destinations (ODs). Therefore, this paper proposes a method of setting corresponding thresholds for each OD. By analyzing the percentile curves of the overall and individual OD pairs, it was found that the turning point of the curve had a significant feature, and the difference between the two sides of the curve was obvious. This paper proposes a bilateral fitting method, and the results show that this method can calculate the relative threshold for different OD pairs. The significant advantages of this method are its low cost and wide coverage.

In this paper, we study a new type of distribution that generalizes distributions from the gamma and beta classes that are widely used in applications. The estimators for the parameters of the digamma distribution obtained by the method of logarithmic cumulants are considered. Based on the previously proved asymptotic normality of the estimators for the characteristic index and the shape and scale parameters of the digamma distribution constructed from a fixed-size sample, we obtain a statement about the convergence of these estimators to the scale mixtures of the normal law in the case of a random sample size. Using this result, asymptotic confidence intervals for the estimated parameters are constructed. A number of examples of the limit laws for sample sizes with special forms of negative binomial distributions are given. The results of this paper can be widely used in the study of probabilistic models based on continuous distributions with an unbounded non-negative support.

In this paper, we establish a random epidemic model with double vaccination and spontaneous variation of the virus. Firstly, we prove the global existence and uniqueness of positive solutions for a stochastic epidemic model. Secondly, we prove the threshold R0* can be used to control the stochastic dynamics of the model. If R0*0, the disease can almost certainly continue to exist, and there is a unique stable distribution. Finally, we give some numerical examples to verify our theoretical results. Most of the existing studies prove the stochastic dynamics of the model by constructing Lyapunov functions. However, the construction of a Lyapunov function of higher-order models is extremely complex, so this method is not applicable to all models. In this paper, we use the definition method suitable for more models to prove the stationary distribution. Most of the stochastic infectious disease models studied now are second-order or third-order, and cannot accurately describe infectious diseases. In order to solve this kind of problem, this paper adopts a higher price five-order model.

This paper recovers quiescent optical solitons that are self-sustaining, localized wave packets that maintain their shape and amplitude over long distances due to a balance between nonlinearity and dispersion. When a soliton is in a state of quiescence, it means that it is stationary in both space and time. Quiescent optical solitons are typically observed in optical fibers, where nonlinearity and dispersion can lead to the formation of solitons. The concatenation model is considered to understand the behavior of optical pulses propagating through nonlinear media. Here, we consider the familiar nonlinear Schrödinger equation, the Lakshmanan–Porsezian–Daniel equation, and the Sasa–Satsuma equation. The current paper also addresses the model with nonlinear chromatic dispersion, a phenomenon that occurs in optical fibers and other dispersive media, where the chromatic dispersion of the material is modified by nonlinear effects. In the presence of nonlinearities, such as self-phase modulation and cross-phase modulation, the chromatic dispersion coefficient becomes a function of the optical intensity, resulting in nonlinear chromatic dispersion. A full spectrum of stationary optical solitons, along with straddled stationary solitons, are obtained. There are four integration schemes that made this retrieval possible. The numerical simulations are also included for these solitons. The parameter constraints also indicate the existence criteria for these quiescent solitons.

Neuronal models have remained an important area of research in computer science. The dendritic neuron model (DNM) is a novel neuronal model in recent years. Previous studies have focused on training DNM using more appropriate algorithms. This paper proposes an improvement to DNM based on the activity of excitation and proposes three new models. Each of the three improved models are designed to mimic the excitation and inhibition activity of neurons. The improved model proposed in this paper is shown to be effective in the experimental part. All three models and original DNM have their own strengths, so it can be considered that the new model proposed in this paper well enriches the diversity of neuronal models and contributes to future research on networks models.

The focus of the research presented in this paper is on a new generalized family of degenerate three-variable Hermite–Appell polynomials defined here using a fractional derivative. The research was motivated by the investigations on the degenerate three-variable Hermite-based Appell polynomials introduced by R. Alyosuf. We show in the paper that, for certain values, the well-known degenerate Hermite–Appell polynomials, three-variable Hermite–Appell polynomials and Appell polynomials are seen as particular cases for this new family. As new results of the investigation, the operational rule for this new generalized family is introduced and the explicit summation formula is established. Furthermore, using the determinant formulation of the Appell polynomials, the determinant form for the new generalized family is obtained and the recurrence relations are also determined considering the generating expression of the polynomials contained in the new generalized family. Certain applications of the generalized three-variable Hermite–Appell polynomials are also presented showing the connection with the equivalent results for the degenerate Hermite–Bernoulli and Hermite–Euler polynomials with three variables.

The architecture of cloud–edge collaboration can improve the efficiency of Internet of Things (IoT) systems. Recent studies have pointed out that using IoT terminal devices as destinations for computing offloading can promote further optimized allocation of computational resources. However, in practice, this idea encounters the problem that participants might lack the motivation to take over computational tasks from others. Although the edge and the terminal are provided with symmetrical positions in collaborative offloading, their computational resources and capabilities are asymmetric. To mitigate this issue, this paper designs a distributed strategy for the trading of computational resources. The most prominent feature of our strategy is its multi-preference optimization objective that takes into account the overall satisfaction with task delay, energy cost, trading prices, and user reputation of participants. In addition, this paper proposes a system architecture based on the Blockchain-as-a-Service (BaaS) design to give full play to the good distributed technology features of blockchain, such as decentralization, traceability, immutability, and automation. Meanwhile, BaaS delivers decentralized identifier (DID) based distributed identity infrastructure for the distributed computational resource trading stakeholders as well. In the simulation evaluation, we compare our trading strategy based on a matching mechanism called multi-preference matching (MPM) to trading using the classical double auction (DA) matching mechanism. The results show that our computational resource trading strategy is able to offload and execut more tasks, achieving a better throughput compared to the DA-based strategy.

This paper questions the evaluation of innovation systems and innovation measurements and the effectiveness of innovation policies applied at the territorial level by assessing whether the existing European regional scoreboard is effective in providing accurate inputs for decision-makers in mountainous regions. The aim of the research is to provide, through comparative analysis by using statistical multi-methods of two mountainous macro-regions (the Alps and the Carpathians), a possible and available path to develop novel perspectives and alternative views on innovation systems’ performance for informed and territorial-based policy making by using the indicators of the Regional Innovation Scoreboard. The methodology used includes descriptive statistics, chi-square bivariate test, Student’s t test, one-way ANOVA with Bonferroni post hoc multiple comparisons, multilinear regression analysis, and decision tree with CRT (classification and regression trees) algorithm. Our results emphasize the similarities and differences between the Alpine and Carpathian mountain regions, find the best predictors for each mountain region, and provide a scientific basis for the development of a holistic approach linking measurement theory, innovation systems, innovation policies, and their territorial approach toward sustainable development of mountain areas. The paper’s contribution is relevant in the context of remote, rural, and mountain areas, which are usually left behind in terms of innovation chances and in the context of the COVID-19 aftermath with budget constraints. The present results are pertinent for designing effective smart specialization strategies in these regions due to the difficulties that most remote areas and less developed regions are facing in developing innovation policies.

In this paper, a cost-oriented optimization model of station spacing is presented to analyze the influencing factors of station spacing and layout near Shanghai Pudong International Airport. The Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) algorithm is used to cluster and analyze the high population density, and optimize the station layout in the southwest of Pudong International Airport. A spatial analysis of the land use and geological conditions in Pudong New Area is given. Combining the optimal station spacing, ideal location and spatial analysis, five routing schemes to Pudong International Airport are proposed. The DBSCAN and K-means algorithms are used to analyze the “PDIA-SL” dataset. The results show that the space complexity of the HDBSCAN is O(825), and the silhouette coefficient is 0.6043, which has obvious advantages over the results of DBSCAN and K-means. This paper combines urban rail transit planning with the HDBSCAN algorithm to present some suggestions and specific route plans for local governments to scientifically plan rail transit lines. Meanwhile, the research method of station layout, which integrates station spacing, ideal location and spatial analysis optimization, is pioneering and can provide a reference for developing rail transit in metropolises.

In the prediction of a nonlinear time series based on a leaky integrator echo state network (leaky-ESN), building a reservoir related to the specific problem is a key step. For problems such as poor performance of randomly generated reservoirs, it is tough to determine the parameter values of the reservoirs. The work in this paper uses the gravitational search algorithm (GSA) to optimize the global parameters of a leaky-ESN, such as the leaking rate, the spectral radius, and the input scaling factor. The basic GSA has some problems, such as slow convergence and poor balance between exploration and exploitation, and it cannot solve some complex optimization problems well. To solve these problems, an improved gravitational search algorithm (IGSA) is proposed in this paper. First, the best agent and elite agents were archived and utilized to accelerate the exploration phase and improve the convergence rate in the exploitation phase. Second, to improve the effect of the poor fitness agents on the optimization result, a differential mutation strategy was proposed, which generated new individuals to replace original agents with worse fitness, increasing the diversity of the population and improving the global optimization ability of the algorithm. Finally, two simulation experiments showed that the leaky-ESN optimized by the IGSA had better prediction accuracy.

Transcription factors (TFs) and microRNAs (miRNAs) are co-actors in genome-scale decoding and regulatory networks, often targeting common genes. To discover the symmetries and invariants of the transcription and regulation at the scale of the genome, in this paper, we introduce tools of infinite group theory and of algebraic geometry to describe both TFs and miRNAs. In TFs, the generator of the group is a DNA-binding domain while, in miRNAs, the generator is the seed of the sequence. For such a generated (infinite) group π, we compute the SL(2,C) character variety, where SL(2,C) is simultaneously a ‘space-time’ (a Lorentz group) and a ‘quantum’ (a spin) group. A noteworthy result of our approach is to recognize that optimal regulation occurs when π looks similar to a free group Fr (r=1 to 3) in the cardinality sequence of its subgroups, a result obtained in our previous papers. A non-free group structure features a potential disease. A second noteworthy result is about the structure of the Groebner basis G of the variety. A surface with simple singularities (such as the well known Cayley cubic) within G is a signature of a potential disease even when π looks similar to a free group Fr in its structure of subgroups. Our methods apply to groups with a generating sequence made of two to four distinct DNA/RNA bases in {A,T/U,G,C}. We produce a few tables of human TFs and miRNAs showing that a disease may occur when either π is away from a free group or G contains surfaces with isolated singularities.

As cyber attacks grow more complex and sophisticated, new types of malware become more dangerous and challenging to detect. In particular, fileless malware injects malicious code into the physical memory directly without leaving attack traces on disk files. This type of attack is well concealed, and it is difficult to find the malicious code in the static files. For malicious processes in memory, signature-based detection methods are becoming increasingly ineffective. Facing these challenges, this paper proposes a malware detection approach based on convolutional neural network and memory forensics. As the malware has many symmetric features, the saved training model can detect malicious code with symmetric features. The method includes collecting executable static malicious and benign samples, running the collected samples in a sandbox, and building a dataset of portable executables in memory through memory forensics. When a process is running, not all the program content is loaded into memory, so binary fragments are utilized for malware analysis instead of the entire portable executable (PE) files. PE file fragments are selected with different lengths and locations. We conducted several experiments on the produced dataset to test our model. The PE file with 4096 bytes of header fragment has the highest accuracy. We achieved a prediction accuracy of up to 97.48%. Moreover, an example of fileless attack is illustrated at the end of the paper. The results show that the proposed method can detect malicious codes effectively, especially the fileless attack. Its accuracy is better than that of common machine learning methods.

Based on the traditional control approach, the position-tracking performance of the teleoperation system with communication delay is generally asymptotically stable. In practical applications, the closed-loop system is expected to achieve stable and finite-time convergence performance. A novel finite-time bilateral control scheme for a telerobotics system with communication delay is presented in this paper. On the basis of the traditional proportional damping injection control, this paper proposes and designs a new finite-time control method by introducing the non-integer power to the position error, velocity, and the combined error with position error and velocity. In comparison to existing proportional damping injection and finite-time control structures, the proposed method not only achieves the finite-time convergence performance of position tracking, but it also has the advantages of a simple structure and fewer gain coefficients. The controller also incorporates the radial basis function (RBF) neural network and adaptive approach to compensate unknown dynamics and external forces, thus also avoiding the measurement of force signals. The Lyapunov–Krasovskii function is then defined, and it is demonstrated that the position tracking of closed-loop teleoperation system has bounded stability and finite-time control performance. The simulation experiment is also performed, and the results further illustrated the bounded stability of the system. Moreover, compared to the position tracking errors of other non-finite-time control methods, it is demonstrated that the proposed finite-time control scheme has a faster convergence rate and higher convergence precision.

This paper studies the intra/inter-layer synchronization and quasi-synchronization in two-layer coupled networks via event-triggered control, in which different layers have mutually independent topologies. First, based on Lyapunov stability theory and event-triggered thoughts, hybrid controllers are designed, respectively, for intra-layer synchronization (ALS) and inter-layer synchronization (RLS). Second, a novel event-triggered rule is proposed, under which intra-layer quasi-synchronization (ALQS) and inter-layer quasi-synchronization (RLQS) can be respectively realized, and the event-triggered frequency can be greatly reduced. Moreover, the upper bound of the synchronization error can be flexibly adjusted by changing the parameters in event-triggered conditions, and the Zeno phenomenon about event-triggered control is also discussed in this paper. Finally, numerical examples are provided to confirm the correctness and validity of the proposed scheme.

Recently, in their paper, the authors generalized the notion of differentiability by defining it for all points of the functional domain (not only interior points) in which the notion of differentiability can be considered meaningful. In this paper, the notion of continuous differentiability is introduced for the differentiable function f:X→Rm with a not necessarily open domain X⊆Rn; i.e., the continuity of the mapping df:X→HomRn,Rm is considered. In addition to introducing continuous differentiability in the context of this generalized approach to differentiability, its characterization is also given. It is proved that the continuity of derivatives at some not necessarily interior points of the functional domain in the direction of n linearly independent vectors implies (continuous) differentiability.

Long short-term memory neural networks have been proposed as a means of creating accurate models from large time series data originating from various fields. These models can further be utilized for prediction, control, or anomaly-detection algorithms. However, finding the optimal hyperparameters to maximize different performance criteria remains a challenge for both novice and experienced users. Hyperparameter optimization algorithms can often be a resource-intensive and time-consuming task, particularly when the impact of the hyperparameters on the performance of the neural network is not comprehended or known. Teacher forcing denotes a procedure that involves feeding the ground truth output from the previous time-step as input to the current time-step during training, while during testing feeding back the predicted values. This paper presents a comprehensive examination of the impact of hyperparameters on long short-term neural networks, with and without teacher forcing, on prediction performance. The study includes testing long short-term memory neural networks, with two variations of teacher forcing, in two prediction modes, using two configurations (i.e., multi-input single-output and multi-input multi-output) on a well-known chemical process simulation dataset. Furthermore, this paper demonstrates the applicability of a long short-term memory neural network with a modified teacher forcing approach in a process state monitoring system. Over 100,000 experiments were conducted with varying hyperparameters and in multiple neural network operation modes, revealing the direct impact of each tested hyperparameter on the training and testing procedures.

Let (E,h1,∞) be a nonautonomous discrete dynamical system (briefly, N.D.D.S.) that is defined by a sequence (hj)j=1∞ of continuous maps hj:E→E over a nontrivial metric space (E,d). This paper defines and discusses some forms of ergodicity and sensitivity for the system (E,h1,∞) by upper density, lower density, density, and a sequence of positive integers. Under some conditions, if the rate of convergence at which (hj)j=1∞ converges to the limit map h is “fast enough” with respect to a sequence of positive integers with a density of one, it is shown that several sensitivity properties for the N.D.D.S. (E,h1,∞) are the same as those properties of the system (E,h). Some sufficient conditions for the N.D.D.S. (E,h1,∞) to have stronger sensitivity properties are also presented. The conditions in our results are less restrictive than those in some existing works, and the conclusions of all the theorems in this paper improve upon those of previous studies. Thus, these results are extensions of the existing ones.

In this paper, a singular non-Newton polytropic filtration equation under the initial-boundary value condition is revisited. The finite time blow-up results were discussed when the initial energy E(u0) was subcritical (E(u0)d), with d being the potential depth by using the potential well method and some differential inequalities. The goal of this paper is to give a finite time blow-up result if E(u0) is independent of d. Moreover, the explicit upper bound of the blow-up time is obtained by the classical Levine’s concavity method, and the precise lower bound of the blow-up time is derived by applying an interpolation inequality.

Multicriteria decision making (MCDM) is a field that helps decision makers evaluate alternatives based on multiple criteria and encompasses scoring, distance-based, pairwise comparison, and outranking methods. Recent developments have aimed to solve specific problems and overcoming the limitations of previous methods. This paper proposes a new axial-distance-based aggregated measurement (ADAM) method, which is used in combination with the best-worst method (BWM) to evaluate agri-food circular economy (CE)-based business models (BMs) to create a more sustainable and efficient system for producing and consuming food. This paper proposes nine BMs, which were evaluated against eight criteria. The BWM method was used to obtain the criteria weights, while the ADAM method was used to obtain a final ranking of the BMs. The results indicate that a sustainable circular agri-food supply chain is a BM that can bring companies the most significant progress in business and strengthen their position in the market. We concluded that the ADAM method is effective for solving MCDM problems and that, overall, the model is an effective tool for solving the problem defined in this study. The main contributions are the development of a new MCDM method and a hybrid model, the establishment of the framework for evaluation and selection of CE-based BMs, and the identification of the most important ones.

Noise in an image can affect one’s extraction of image information, therefore, image denoising is an important image pre-processing process. Many of the existing models have a large number of estimated parameters, which increases the time complexity of the model solution and the achieved denoising effect is less than ideal. As a result, in this paper, an improved image-denoising algorithm is proposed based on the TV model, which effectively solves the above problems. The L1 regularization term can make the solution generated by the model sparser, thus facilitating the recovery of high-quality images. Reducing the number of estimated parameters, while using the inverse gradient to estimate the regularization parameters, enables the parameters to achieve global adaption and improves the denoising effect of the model in combination with the TV regularization term. The split Bregman iteration method is used to decouple the model into several related subproblems, and the solutions of the coordinated subproblems are derived as optimal solutions. It is also shown that the solution of the model converges to a Karush–Kuhn–Tucker point. Experimental results show that the algorithm in this paper is more effective in both preserving image texture structure and suppressing image noise.

In this paper, by using the invexity (or pseudoinvexity) and Fréchet differentiability of some integral functionals of curvilinear type, we state some relations between the solutions of a new non-linear optimization problem and the associated variational inequality. In order to prove the results derived in this paper, we use the new notion of invex set by considering some given functions. To justify the effectiveness and outstanding applicability of this work, some illustrative examples are provided.

In computer programming languages, partial additive semantics are used. Since partial functions under disjoint-domain sums and functional composition do not constitute a field, linear algebra cannot be applied. A partial ring can be viewed as an algebraic structure that can process natural partial orderings, infinite partial additions, and binary multiplications. In this paper, we introduce the notions of a one-prime partial bi-ideal, a two-prime partial bi-ideal, and a three-prime partial bi-ideal, as well as their extensions to partial rings, in addition to some characteristics of various prime partial bi-ideals. In this paper, we demonstrate that two-prime partial bi-ideal is a generalization of a one-prime partial bi-ideal, and three-prime partial bi-ideal is a generalization of a two-prime partial bi-ideal and a one-prime partial bi-ideal. A discussion of the mpb1,(mpb2,mpb3) systems is presented. In general, the mpb2 system is a generalization of the mpb1 system, while the mpb3 system is a generalization of both mpb2 and mpb1 systems. If Φ is a prime bi-ideal of ℧, then Φ is a one-prime partial bi-ideal (two-prime partial bi-ideal, three-prime partial bi-ideal) if and only if ℧Φ is a mpb1 system (mpb2 system, mpb3 system) of ℧. If Θ is a prime bi-ideal in the complete partial ring ℧ and Δ is an mpb3 system of ℧ with Θ∩Δ=ϕ, then there exists a three-prime partial bi-ideal Φ of ℧, such that Θ⊆Φ with Φ∩Δ=ϕ. These are necessary and sufficient conditions for partial bi-ideal Θ to be a three-prime partial bi-ideal of ℧. It is shown that partial bi-ideal Θ is a three-prime partial bi-ideal of ℧ if and only if HΘ is a prime partial ideal of ℧. If Θ is a one-prime partial bi-ideal (two-prime partial bi-ideal) in ℧, then HΘ is a prime partial ideal of ℧. It is guaranteed that a three-prime partial bi-ideal Φ with a prime bi-ideal Θ does not meet the mpb3 system. In order to strengthen our results, examples are provided.

The current media digitization and artistic strength are more powerful than the previous application. Using its advanced information display methods and technologies, this paper proposed a digital museum built by integrating digital media art with AR technology, which was helpful to analyze and solve the objective problems of current museums’ ecological imbalance and single-system function. Based on the principles and laws of augmented reality technology, the museum guide system is optimized. In the system evaluation experiment, firstly, the cultural relics of six kinds of materials are used as the target image to extract and identify the features of the image. In experiments, the recognition performance of three feature algorithms, Binary Robust Invariant Scalable Keypoints (BRISK), organizational retaliatory behavior (ORB), and Accelerated-KAZE (AKAZE), is compared. Among them, the ORB algorithm is superior to other algorithms in feature richness and recognition speed but is inferior to the other two algorithms in recognition accuracy. Therefore, this paper optimized the ORB algorithm based on the characteristics of the ORB algorithm. The ORB algorithm must calculate the orientation of the feature points before constructing the feature descriptor. After optimizing the parameters, the improved ORB algorithm not only has advantages in feature richness and recognition time but also improves the recognition accuracy up to 98.3%, which is 16% higher than the traditional ORB algorithm. Therefore, the application prospects of AR technology in digital media design are very important.

The study of the flows of curves is one of the most fascinating research areas in differential geometry. In this paper, we investigate the geometry of the flows of timelike curves according to the quasi-frame in Minkowski space R2,1 (In this paper, we refer to these curves as “quasi-timelike curves”). We investigate the evolution of quasi-timelike curves using the velocity functions and obtain the necessary and sufficient conditions for inextensibility. Additionally, we obtain the explicit forms of the time evolution equations for the quasi-orthonormal frames (tangent, quasi-normal, and quasi-binormal vectors) of the quasi-timelike curve as well as the time evolution equations of their quasi-curvatures. We present a new application for motion with velocities equal to the quasi-curvatures of the quasi-timelike curve. In this application, the time evolution equations of the quasi-curvatures arise as a system of partial differential equations with the form of the heat equation, and by solving this system, we visualize the evolution of quasi-curvatures and the evolution of the quasi-timelike curve. In addition, the acceleration functions are used to investigate the flows of inextensible quasi-timelike curves, and an application for accelerations equal to the quasi-curvatures is given. Through this application, the position vector of the quasi-timelike curve satisfies the one-dimensional wave equation, and the time evolution equations of the quasi-curvatures arise as a system of transport equations. We obtain the solutions and graph them using Wolfram Mathematica 12.

Software-defined networks (SDN) can use the control plane to manage heterogeneous devices efficiently, improve network resource utilization, and optimize Mobile Edge-Cloud Computing Networks (MECCN) network performance through decisions based on global information. However, network traffic in MECCNs can change over time and affect the performance of the SDN control plane. Moreover, the MECCN network may need to temporarily add network access points when the network load is excessive, and it is difficult for the control plane to form effective management of temporary nodes. This paper investigates the dynamic controller placement problem (CPP) in SDN-enabled Mobile Edge-Cloud Computing Networks (SD-MECCN) to enable the control plane to continuously and efficiently serve the network under changing network load and network access points. We consider the deployment of a two-layer structure with a control plane and construct the CPP based on this control plane. Subsequently, we solve this problem based on multi-agent DQN (MADQN), in which multiple agents cooperate to solve CPP and adjust the number of controllers according to the network load. The experimental results show that the proposed dynamic controller deployment algorithm based on MADQN for node-variable networks in this paper can achieve better performance in terms of delay, load difference, and control reliability than the Louvain-based algorithm, single-agent DQN-based algorithm, and MADQN- (without node-variable networks consideration) based algorithm.