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With the rapid development of information technology, the transmission of information has become convenient. In order to prevent the leakage of information, information security should be valued. Therefore, the data hiding technique has become a popular solution. The reversible data hiding technique (RDH) in particular uses symmetric encoding and decoding algorithms to embed the data into the cover carrier. Not only can the secret data be transmitted without being detected and retrieved completely, but the cover carrier also can be recovered without distortion. Moreover, the encryption technique can protect the carrier and the hidden data. However, the encrypted carrier is a form of ciphertext, which has a strong probability to attract the attention of potential attackers. Thus, this paper uses the generative adversarial networks (GAN) to generate meaningful encrypted images for RDH. A four-stage network architecture is designed for the experiment, including the hiding network, the encryption/decryption network, the extractor, and the recovery network. In the hiding network, the secret data are embedded into the cover image through residual learning. In the encryption/decryption network, the cover image is encrypted into a meaningful image, called the marked image, through GMEI-GAN, and then the marked image is restored to the decrypted image via the same architecture. In the extractor, 100% of the secret data are extracted through the residual learning framework, same as the hiding network. Lastly, in the recovery network, the cover image is reconstructed with the decrypted image and the retrieved secret data through the convolutional neural network. The experimental results show that using the PSNR/SSIM as the criteria, the stego image reaches 45.09 dB/0.9936 and the marked image achieves 38.57 dB/0.9654. The proposed method not only increases the embedding capacity but also maintains high image quality in the stego images and marked images.

This paper considers the Modified Autonomous Van der Pol–Duffing equation subjected to dynamic state feedback, which can well characterize the dynamic behaviors of the nonlinear dynamical systems. Both the issues of local stability switches and the Hopf bifurcation versus time delay are investigated. Associating with the τ decomposition strategy and the center manifold theory, the delay stable intervals and the direction and stability of the Hopf bifurcation are all determined. Specifically, the computation of purely imaginary roots (symmetry to the real axis), the positive real root formula for cubic equation and the sophisticated bilinear form of adjoint operators are proposed, which make the calculations mentioned in our discussion unified and simple. Finally, the typical numerical examples are shown to illustrate the correctness and effectiveness of the practical technique.

Symmetries play a crucial role in the dynamics of physical systems. As an example, microworld and quantum physics problems are modeled on principles of symmetry. These problems are then formulated as equations defined on suitable abstract spaces. Then, these equations can be solved using iterative methods. In this article, an Ostrowski-type method for solving equations in Banach space is extended. This is achieved by finding a stricter set than before containing the iterates. The convergence analysis becomes finer. Due to the general nature of our technique, it can be utilized to enlarge the utilization of other methods. Examples finish the paper.

Owning to the importance and great interest of differential operators, two generalized differential operators, which may be symmetric or assymetric, are newly introduced in the present paper. Motivated by the familiar Jackson’s second and third Bessel functions, we derive necessary and sufficient conditions for which the new generalized operators belong to the class of q-starlike functions of order alpha. Several corollaries and consequences of the main results are also pointed out.

This paper is interested in establishing some new reverse Hilbert-type inequalities, by using chain rule on time scales, reverse Jensen’s, and reverse Hölder’s with Specht’s ratio and mean inequalities. To get the results, we used the Specht’s ratio function and its applications for reverse inequalities of Hilbert-type. Symmetrical properties play an essential role in determining the correct methods to solve inequalities. The new inequalities in special cases yield some recent relevance, which also provide new estimates on inequalities of these type.

Nowadays, it is common to see large public buildings, e.g., stadiums, with some equipment or substructure suspended from the center of the roof. These substructures will tend to be larger and heavier the more gear is needed, which may have negative impacts on the dynamic performance of the roof structures. In this paper, to explore the dynamic response of a large-span roof structure with a suspended substructure, a real structure model is simplified into a two-degrees-of-freedom system. The essential consideration of nonlinear vibration is elaborated in the equations of motions. Approximate analytical solutions for free and forced vibrations are derived using perturbation methods, while numerical analysis is carried out to validate the solutions. The ratio of linear to nonlinear amplitude is proposed to represent the nonlinear effect of the primary structure, and the nonlinear effect, varying with structural parameters of frequency ratio, mass ratio, excitation ratio, and external force to the primary structure, is investigated. It is shown that internal resonance occurs when the structural frequency ratio is close to 1:2 and that secondary resonance takes place due to certain external excitations; internal resonance and secondary resonance will magnify the amplitude of the primary structure during vibration. Finally, a case of a designed practical dome with a suspended substructure is studied to verify the outcomes from the above research. According to these findings, some design proposals for this type of structure are provided.

This paper is devoted to studying approximations of symmetric continuous functions by symmetric analytic functions on a Banach space X with a symmetric basis. We obtain some positive results for the case when X admits a separating polynomial using a symmetrization operator. However, even in this case, there is a counter-example because the symmetrization operator is well defined only on a narrow, proper subspace of the space of analytic functions on X. For X=c0, we introduce ε-slice G-analytic functions that have a behavior similar to G-analytic functions at points x∈c0 such that all coordinates of x are greater than ε, and we prove a theorem on approximations of uniformly continuous functions on c0 by ε-slice G-analytic functions.

Unmanned aerial vehicle (UAV) clusters usually face problems such as complex environments, heterogeneous combat subjects, and realistic interference factors in the course of mission assignment. In order to reduce resource consumption and improve the task execution rate, it is very important to develop a reasonable allocation plan for the tasks. Therefore, this paper constructs a heterogeneous UAV multitask assignment model based on several realistic constraints and proposes an improved half-random Q-learning (HR Q-learning) algorithm. The algorithm is based on the Q-learning algorithm under reinforcement learning, and by changing the way the Q-learning algorithm selects the next action in the process of random exploration, the probability of obtaining an invalid action in the random case is reduced, and the exploration efficiency is improved, thus increasing the possibility of obtaining a better assignment scheme, this also ensures symmetry and synergy in the distribution process of the drones. Simulation experiments show that compared with Q-learning algorithm and other heuristic algorithms, HR Q-learning algorithm can improve the performance of task execution, including the ability to improve the rationality of task assignment, increasing the value of gains by 12.12%, this is equivalent to an average of one drone per mission saved, and higher success rate of task execution. This improvement provides a meaningful attempt for UAV task assignment.

In this paper, we prove an asymptotic formula for the sum of the values of the periodic zeta-function at the nontrivial zeros of the Riemann zeta-function (up to some height) which are symmetrical on the real line and the critical line. This is an extension of the previous results due to Garunkštis, Kalpokas, and, more recently, Sowa. Whereas Sowa’s approach was assuming the yet unproved Riemann hypothesis, our result holds unconditionally.

Over recent years, the incidence of data breaches and cyberattacks has increased significantly. This has highlighted the need for sectoral organizations to share information about such events so that lessons can be learned to mitigate the prevalence and severity of cyber incidents against other organizations. Sectoral organizations embody a governance relationship between cross-sector public and private entities, called public-private partnerships (PPPs). However, organizations are hesitant to share such information due to a lack of trust and business-critical confidentially issues. This problem occurs because of the absence of any protocols that guarantee privacy protection and protect sensitive information. To address this issue, this paper proposes a novel protocol, Putra-Ramli Secure Cyber-incident Information Sharing (PURA-SCIS), to secure cyber incident information sharing. PURA-SCIS has been designed to offer exceptional data and privacy protection and run on the cloud services of sectoral organizations. The relationship between organizations in PURA-SCIS is symmetrical, where the entities must collectively maintain the security of classified cyber incident information. Furthermore, the organizations must be legitimate entities in the PURA-SCIS protocol. The Scyther tool was used for protocol verification in PURA-SCIS. The experimental results showed that the proposed PURA-SCIS protocol provided good security properties, including public verifiability for all entities, blockless verification, data privacy preservation, identity privacy preservation and traceability, and private information sharing. PURA-SCIS also provided a high degree of confidentiality to protect the security and integrity of cyber-incident-related information exchanged among sectoral organizations via cloud services.

The aims of this article are twofold. One is to prove some results regarding the existence of best proximity points of multivalued non-self quasi-contractions of b−metric spaces (which are symmetric spaces) and the other is to obtain a characterization of completeness of b−metric spaces via the existence of best proximity points of non-self quasi-contractions. Further, we pose some questions related to the findings in the paper. An example is provided to illustrate the main result. The results obtained herein improve some well known results in the literature.

Previous studies on the synchronization behaviors of neuronal networks were constructed by integer-order neuronal models. In contrast, this paper proposes that the above topics of symmetrical neuronal networks are constructed by fractional-order Hindmarsh–Rose (HR) models under electromagnetic radiation. They are then investigated numerically. From the research results, several novel phenomena and conclusions can be drawn. First, for the two symmetrical coupled neuronal models, the synchronization degree is influenced by the fractional-order q and the feedback gain parameter k1. In addition, the fractional-order or the parameter k1 can induce the synchronization transitions of bursting synchronization, perfect synchronization and phase synchronization. For perfect synchronization, the synchronization transitions of chaotic synchronization and periodic synchronization induced by q or parameter k1 are also observed. In particular, when the fractional-order is small, such as 0.6, the synchronization transitions are more complex. Then, for a symmetrical ring neuronal network under electromagnetic radiation, with the change in the memory-conductance parameter β of the electromagnetic radiation, k1 and q, compared with the fractional-order HR model’s ring neuronal network without electromagnetic radiation, the synchronization behaviors are more complex. According to the simulation results, the influence of k1 and q can be summarized into three cases: β&gt, 0.02, −0.06&lt, β&lt, 0.02 and β&lt, −0.06. The influence rules and some interesting phenomena are investigated.

Over the last two decades (2000–2020), the Internet has rapidly evolved, resulting in symmetrical and asymmetrical Internet consumption patterns and billions of users worldwide. With the immense rise of the Internet, attacks and malicious behaviors pose a huge threat to our computing environment. Brute-force attack is among the most prominent and commonly used attacks, achieved out using password-attack tools, a wordlist dictionary, and a usernames list—obtained through a so-called an enumeration attack. In this paper, we investigate username enumeration attack detection on SSH protocol by using machine-learning classifiers. We apply four asymmetrical classifiers on our generated dataset collected from a closed-environment network to build machine-learning-based models for attack detection. The use of several machine-learners offers a wider investigation spectrum of the classifiers’ ability in attack detection. Additionally, we investigate how beneficial it is to include or exclude network ports information as features-set in the process of learning. We evaluated and compared the performances of machine-learning models for both cases. The models used are k-nearest neighbor (K-NN), naïve Bayes (NB), random forest (RF) and decision tree (DT) with and without ports information. Our results show that machine-learning approaches to detect SSH username enumeration attacks were quite successful, with KNN having an accuracy of 99.93%, NB 95.70%, RF 99.92%, and DT 99.88%. Furthermore, the results improve when using ports information.

High computation complexity restricts the application prospects of the interval type-2 fuzzy variable (IT2-FV), despite its high degree of freedom in representing uncertainty. Thus, this paper studies the fuzzy operations for the regular symmetric triangular IT2-FVs (RSTIT2-FVs)—the simplest IT2-FVs having the greatest membership degrees of 1. Firstly, by defining the medium of an RSTIT2-FV, its membership function, credibility distribution, and inverse distribution are analytically and explicitly expressed. Secondly, an operational law for fuzzy arithmetic operations regarding mutually independent RSTIT2-FVs is proposed, which can simplify the calculations and directly output the inverse credibility of the functions. Afterwards, the operational law is applied to define the expected value operator of the IT2-FV and prove the linearity of the operator. Finally, some comparative examples are provided to verify the efficiency of the proposed operational law.

This paper investigates 1-moment exponential stability and exponential mean-square stability (EMS stability) under average dwell time (ADT) and the preset deterministic switching mechanism of dual switching linear continuous-time positive systems when a numerical realization does not exist. The signs of subsystem matrices, but not their structures of magnitude, are key information that causes a qualitative concept of stability called sign stability. Both 1-moment exponential stability and EMS stability, which are the traditional stability concepts, are generalized intrinsically. Hence, both 1-moment exponential sign stability and EMS sign stability are introduced and are proven based on sign equivalency. It is shown that they are symmetrically and qualitatively stable. Notably, the notion of stability can be checked quantitatively using some examples.

The present research paper considers a three-level atom (3LA) that interacts with a field mode primarily in a photon-added coherent state of Morse potential (PACSMP). The dynamics of entanglement, the photon statistics, and the quantum Fisher information are investigated. The statistics of field photons are discussed by evaluating the Mandel parameter. We check the influence of the energy dissipation and intensity-dependent function. Finally, we detect the relationship between the entanglement, the field’s nonclassical characteristics, and atomic quantum Fisher information throughout the evolution of time. The findings illustrate the important role of the number of added photons and CSMP in affecting the entanglement’s time evolution, the quantum Fisher information, and the Mandel parameter. Based on the obtained results, we reached significant physical phenomena, including the sudden birth and death of the nonlocal correlation between atom-Morse potential field structures.

In this paper, we investigate the semi-Hyers–Ulam–Rassias stability of a Volterra integro-differential equation of order I with a convolution type kernel. To this purpose the Laplace transform is used. The results obtained show that the stability holds for problems formulated with various functions: exponential and polynomial functions. An important aspect that appears in the form of the studied equation is the symmetry of the convolution product.

In this paper, a Caputo fractional-order HCV Periodic immune response model with saturation incidence, cell-to-cell and drug control was proposed. We derive two different basic reproductive numbers and their relation with infection-free equilibrium and the immune-exhausted equilibrium. Moreover, there exists some symmetry in the relationship between the two equilibria and the basic reproduction numbers. We obtain the global stability of the infection-free equilibrium by using Lyapunov function and the local stability of the immune-exhausted equilibrium. The optimal control problem is also considered and two control strategies are given, one is for ITX5061 monotherapy, the other is for ITX5061 and DAAs combination therapy. Matlab numerical simulation shows that combination therapy has lower objective function value, therefore, it is worth trying to use combination therapy to treat HCV infection.

In traditional cloud computing research, it is often considered that the network resources between edge devices and cloud platform are sufficient, and the symmetry between the upward link from edge devices to the cloud platform and the downward link from cloud platform to edge devices is definite. However, in many application scenarios, the network resources between edge devices and cloud platform might be limited, and the link symmetry may not be guaranteed. To solve this problem, network relay nodes are introduced to realize the data transmission between edge devices and the cloud platform. The environment in which network relay nodes that can cooperate with the cloud platform is called cloud network collaborative environment (CNCE). In CNCE, how to optimize data transmission from edge devices to cloud platform through relay nodes has become one of the most important research topics. In this paper, we focus on the following two influencing factors that previous studies ignored: (1) the multi-link and multi-constraint transmission process, and (2) the timely resource state of the relay node. Taking these factors into consideration, we design a novel data transmission scheduling algorithm, called ant colony based transmission scheduling approach (ACTS). First, we propose a multi-link optimization mechanism to optimize the constraint limits. This mechanism divides the transmission into two links called the downlink relay link and uplink relay link. For the downlink relay link, we use the store-and-forward method for the optimization. For the uplink relay link, we use the min–min method for the optimization. We use the ant colony algorithm for the overall optimization of the two links. Finally, we improve the pheromone update rule of the ant colony algorithm to avoid the algorithm from falling into a local optimum. Extensive experiments demonstrate that our proposed approach has better results in transmission efficiency than other advanced algorithms.

The symmetry principle of circuit system shows that we can equate a complex structure in the circuit network to a simple circuit. Hence, this paper only considers a simple series RL circuit and first presents an uncertain RL circuit model based on multifactor uncertain differential equation by considering the external noise and internal noise in an actual electrical circuit system. Then, the solution of uncertain RL circuit equation and the inverse uncertainty distribution of solution are derived. Some applications of solution for uncertain RL circuit equation are also investigated. Finally, the method of moments is used to estimate the unknown parameters in uncertain RL circuit equation.

In daily life, mixed data patterns are often found, namely, those that change at a certain sub-interval or that follow a repeating pattern in a certain trend. To handle this kind of data, a mixed estimator of a Smoothing Spline and a Fourier Series has been developed. This paper describes a simulation study of the estimator in nonparametric regression and its implementation in the case of poor households. The minimum Generalized Cross Validation (GCV) was used in order to select the best model. The simulation study used generation data with a Uniform distribution and a random error with a symmetrical Normal distribution. The result of the simulation study shows that the larger the sample size n, the better the mixed estimator as a model of nonparametric regression for all variances. The smaller the variance, the better the model for all combinations of samples n. Very poor households are characterized predominantly in their consumption of carbohydrates compared to that of fat and protein. The results of this study suggest that the distribution of assistance to poor households is not the same, because in certain groups there are poor households that consume higher carbohydrates, and some households may consume higher fats.

In this paper we introduce and study a new generalization of Fibonacci polynomials which generalize Fibonacci, Jacobsthal and Narayana numbers, simultaneously. We give a graph interpretation of these polynomials and we obtain a binomial formula for them. Moreover by modification of Pascal’s triangle, which has a symmetric structure, we obtain matrices generated by coefficients of generalized Fibonacci polynomials. As a consequence, the direct formula for generalized Fibonacci polynomials was given. In addition, we determine matrix generators for generalized Fibonacci polynomials, using the symmetric matrix of initial conditions.

This paper presents several types of Johnson–Tzitzeica theorems. Graph diagrams are used in this analysis. A symmetric scheme is derived, and new results are obtained and open problems stated. We also present results relating the graphs and the Yang–Baxter equation. This equation has certain symmetries, which are used in finding solutions for it. All these constructions are related to integrable systems.

This paper presents a robust nonlinear control scheme with time-varying output constraint for the electro-hydraulic force control system (EHFCS). Two typical double-rod symmetrical hydraulic cylinders are employed to simulate force environments in the EHFCS. Therefore, in order to improve the performance of the EHFCS, firstly, the model of the EHFCS is established with taking external disturbances, parameter uncertainties as well as structural vibrations into consideration. Secondly, in order to estimate external disturbances, parameter uncertainties and structural vibrations in the EHFCS and compensate them in the following robust controller design, two disturbance observers (DOs) are designed according to the nonlinear system model. Thirdly, with two estimation values from two DOs, a time-varying constraint-based robust controller (TVCRC) is presented in detail. Moreover, the stability of the proposed controller is analyzed by defining a proper Lyapunov functions. Finally, in order to validate the performance of the proposed controller, a series of simulation studies are conducted using the MATLAB/Simulink software. These simulation results give a fine proof of the efficiency of the proposed controller. What’s more, an experimental setup of the EHFCS is established to further validate the performance. Comparative experimental results show that the proposed controller exhibits better performance than the TVCRC without two DOs and a conventional proportional integral (PI) controller.

The electricity distribution system is the coupling point between the utility and the end-user. Typically, these systems have unbalanced feeders due to the variety of customers’ behaviors. Some significant problems occur, the unbalanced loads increase the operational cost and system investment. In radial distribution systems, swapping loads between the three phases is the most effective method for phase balancing. It is performed manually and subjected to load flow equations, capacity, and voltage constraints. Recently, due to smart grids and automated networks, dynamic phase balancing received more attention, thus swapping the loads between the three phases automatically when unbalance exceeds permissible limits by using a remote-controlled phase switch selector/controller. Automatic feeder reconfiguration and phase balancing eliminates the service interruption, enhances energy restoration, and minimize losses. In this paper, a case study from the Irbid district electricity company (IDECO) is presented. Optimal reconfiguration of phase balancing using three techniques: feed-forward back-propagation neural network (FFBPNN), radial basis function neural network (RBFNN), and a hybrid are proposed to control the switching sequence for each connected load. The comparison shows that the hybrid technique yields the best performance. This work is simulated using MATLAB and C programming language.

This paper presents an uncertain logistic growth model to analyse and predict the evolution of the cumulative number of COVID-19 infection in Czech Republic. Some fundamental knowledge about the uncertain regression analysis are reviewed firstly. Stochastic regression analysis is invalid to model cumulative number of confirmed COVID-19 cases in Czech Republic, by considering the disturbance term as random variables, because that the normality test and the identical distribution test of residuals are not passed, and the residual plot does not look like a null plot in the sense of probability theory. In this case, the uncertain logistic growth model is applied by characterizing the disturbance term as uncertain variables. Then parameter estimation, residual analysis, the forecast value and confidence interval are studied. Additionally, the uncertain hypothesis test is proposed to evaluate the appropriateness of the fitted logistic growth model and estimated disturbance term. The analysis and prediction for the cumulative number of COVID-19 infection in Czech Republic can propose theoretical support for the disease control and prevention. Due to the symmetry and similarity of epidemic transmission, other regions of COVID-19 infections, or other diseases can be disposed in a similar theory and method.

The existence of solutions of nonlocal fractional symmetric Hahn integrodifference boundary value problem is studied. We propose a problem of five fractional symmetric Hahn difference operators and three fractional symmetric Hahn integrals of different orders. We first convert our nonlinear problem into a fixed point problem by considering a linear variant of the problem. When the fixed point operator is available, Banach and Schauder’s fixed point theorems are used to prove the existence results of our problem. Some properties of (q,ω)-integral are also presented in this paper as a tool for our calculations. Finally, an example is also constructed to illustrate the main results.

Symmetry (and group theory) is a fundamental principle of theoretical physics. Finite symmetries, continuous symmetries of compact groups, and infinite-dimensional representations of noncompact Lie groups are at the core of solid physics, particle physics, and quantum physics, respectively. The latter groups now play an important role in many branches of mathematics. In more recent years, we have been faced with the impact of topological quantum field theory (TQFT). Topology and symmetry have deep connections, but topology is inherently broader and more complex. While the presence of symmetry in physical phenomena imposes strong constraints, topology seems to be related to low-energy states and is very likely to provide information about the different dynamical trajectories and patterns that particles can follow. For example, regarding the relationship of topology to low-energy states, Hodge’s theory of harmonic forms shows that the zero-energy states (for differential forms) correspond to the cohomology. Regarding the relationship of topology to particle trajectories, a topological knot can be seen as an orbit with complex properties in spacetime. The various deformations or embeddings of the knot, performed in low or high dimensions, allow defining different equivalence classes or topological types, and interestingly, it is possible from these types to study the symmetries associated with the deformations and their changes. More specifically, in the present work, we address two issues: first, that quantum geometry deforms classical geometry, and that this topological deformation may produce physical effects that are specific to the quantum physics scale, and second, that mirror symmetry and the phenomenon of topological change are closely related. This paper was aimed at understanding the conceptual and physical significance of this connection.

In engineering application, the hot press assembly technology is often used to improve the stability of the rotor structure, but the conventional design methods cannot effectively evaluate the influence of this process on the rotor strength, which easily causes the rotor strength to exceed its safety margin range, and seriously it will lead to the failure of the rotor structure. This paper takes the cylindrical magnet surface-mounted high-speed permanent magnet synchronous motor rotor as the research object. Firstly, the influence of the assembly pressing force on the rotor stresses and interference is analyzed; then, comprehensively considering the assembly pressing force, speed and temperature, the rotor strength’s design method with high structural stability is proposed. Finally, based on the proposed method, the rotor strength of a 100 kW/30,000 rpm high-speed motor is designed, and the feasibility of the design is verified by over-speed experiment.

Cerebrospinal fluid (CSF) is a symmetric flow transport that surrounds brain and central nervous system (CNS). Congenital hydrocephalusis is an asymmetric and unusual cerebrospinal fluid flow during fetal development. This dumping impact enhances the elasticity over the ventricle wall. Henceforth, compression change influences the force of brain tissues. This paper presents a mathematical model to establish the effects of ventricular elasticity through a porous channel. The current model is good enough for immediate use by a neurosurgeon. The mathematical model is likely to be a powerful tool for the better treatment of hydrocephalus and other brain biomechanics. The non-linear dimensionless governing equations are solved using a perturbation technique, and the outcome is portrayed graphically with the aid of MATLAB.

Railway infrastructures have played a critical role to ensure the continuity of goods and passenger transportation in China. Under extreme loading and environmental conditions, railway structures are vulnerable to deterioration and failure, leading to the interruption of the whole transportation system. Several techniques have been used for the health monitoring of railway structures. Optical fiber sensors are the widely recognized technique due to their inherent advantages such as high sensitivity, anti-electromagnetic interference, light weight, tiny size, corrosion resistance, and easy integration and network configuration. This paper provides a state-of-the-art of optical fiber sensing technologies and their practical application in railway infrastructures. In addition, the strain transfer analysis of optical fiber sensors is described for parameter reflection. A smart concept for artificial intelligence contribution is also declared. Finally, existing and future prospects on smart concept-based optical fiber sensors for railway infrastructure are discussed. The study can provide useful guidance to understand the problems in artificial intelligence which contributed to the Structural Health Monitoring system of railway structures.

In 2002, Agrawal and Kiernan defined six basic requirements, including preventing illegal watermark embedding and authentication, reversibility, robustness, and others, which must be satisfied when a reversible watermark is designed for relational databases. To meet these requirements, in this paper, a lossless watermarking scheme for a categorical relational database called LRW-CRDB (lossless robust watermarking for categorical relational databases) is proposed. In our LRW-CRDB scheme, the database owner needs to generate two secret embedding keys, K1 and K2, in advance. Then, two reference sets are generated based on two different secret embedding keys and a symmetry-based data hiding strategy, and then these are used for the watermark embedding phases. Experimental results confirmed that our LRW-CRDB scheme successfully detects 100% of hidden watermarks, even when more than 95% of the watermarked relational database has been deleted. In other words, the robustness of our proposed LRW-CRDB scheme outperforms other existing schemes under a variety of possible attacks, such as alteration, sorting, deletion, and mix-match attacks.

In this paper, we present an extension of the truncated positive normal (TPN) distribution to model positive data with a high kurtosis. The new model is defined as the quotient between two random variables: the TPN distribution (numerator) and the power of a standard uniform distribution (denominator). The resulting model has greater kurtosis than the TPN distribution. We studied some properties of the distribution, such as moments, asymmetry, and kurtosis. Parameter estimation is based on the moments method, and maximum likelihood estimation uses the expectation-maximization algorithm. We performed some simulation studies to assess the recovery parameters and illustrate the model with a real data application related to body weight. The computational implementation of this work was included in the tpn package of the R software.

The paper analyzes a two-stage oligopoly game of semi-collusion in production described by a system with a symmetric structure. We examine the local stability of a Nash equilibrium and the presence of bifurcations. We discover that the model is capable of exhibiting extremely complicated dynamic behaviors.

This paper highlights algebraic and mathematical properties in symmetry with Petri nets in order to control automated systems such as flexible workshops, which represent one of the most important examples in industry and for discrete event systems in general. This project deals with the problem of forbidden state transition by using a new application of the theory of regions for supervisory control. In the literature, most control synthesis methods suffer greatly from a cumbersome calculation burden of the Petri net supervisor given the complex exploration of the state graph. Our new methodology lightens the computational load of the Petri net supervisor by choosing specific regions on the reachability graph, on which the control is calculated offline using CPLEX. The determined controller is activated online if the process enters the chosen region, and deactivated otherwise. All our experiments were applied in a flexible workshop implemented in our research laboratory, which was used to engrave selected models on glass blocks of different colors.

Path planning plays an essential role in mobile robot navigation, and the A* algorithm is one of the best-known path planning algorithms. However, the conventional A* algorithm and the subsequent improved algorithms still have some limitations in terms of robustness and efficiency. These limitations include slow algorithm efficiency, weak robustness, and collisions when robots are traversing. In this paper, we propose an improved A*-based algorithm called EBHSA* algorithm. The EBHSA* algorithm introduces the expansion distance, bidirectional search, heuristic function optimization and smoothing into path planning. The expansion distance extends a certain distance from obstacles to improve path robustness by avoiding collisions. Bidirectional search is a strategy that searches for a path from the start node and from the goal node at the same time. Heuristic function optimization designs a new heuristic function to replace the traditional heuristic function. Smoothing improves path robustness by reducing the number of right-angle turns. Moreover, we carry out simulation tests with the EBHSA* algorithm, and the test results show that the EBHSA* algorithm has excellent performance in terms of robustness and efficiency. In addition, we transplant the EBHSA* algorithm to a robot to verify its effectiveness in the real world.

The early diagnosis of retinopathy is crucial to the prevention and treatment of diabetic retinopathy. The low proportion of positive cases in the asymmetric microaneurysm detection problem causes preprocessing to treat microaneurysms as noise to be eliminated. To obtain a binary image containing microaneurysms, the object was segmented by a symmetry algorithm, which is a combination of the connected components and SSA methods. Next, a candidate microaneurysm set was extracted by multifeature clustering of binary images. Finally, the candidate microaneurysms were mapped to the Radon frequency domain to achieve microaneurysm detection. In order to verify the feasibility of the algorithm, a comparative experiment was conducted on the combination of the connected components and SSA methods. In addition, PSNR, FSIM, SSIM, fitness value, average CPU time and other indicators were used as evaluation standards. The results showed that the overall performance of the binary image obtained by the algorithm was the best. Last but not least, the accuracy of the detection method for microaneurysms in this paper reached up to 93.24%, which was better than that of several classic microaneurysm detection methods in the same period.

Making use of a post-quantum derivative operator, we define two classes of meromorphic analytic functions. For the considered family of functions, we aim to investigate the sharp bounds’ values in the case of the Fekete–Szegö problem. The study of the well-known Fekete–Szegö functional in the post-quantum calculus case for meromorphic functions provides new outcomes for research in the field. With the extended p,q-operator, we establish certain inequalities’ relations concerning meromorphic functions. In the final part of the paper, a new p,q-analogue of the q-Wright type hypergeometric function is introduced. This function generalizes the classical and symmetrical Gauss hypergeometric function. All the obtained results are sharp.

In this paper, we study a boundary value problem involving (p,q)-integrodifference equations, supplemented with nonlocal fractional (p,q)-integral boundary conditions with respect to asymmetric operators. First, we convert the given nonlinear problem into a fixed-point problem, by considering a linear variant of the problem at hand. Once the fixed-point operator is available, existence and uniqueness results are established using the classical Banach’s and Schaefer’s fixed-point theorems. The application of the main results is demonstrated by presenting numerical examples. Moreover, we study some properties of (p,q)-integral that are used in our study.

When working with Markov chains, especially if they are of order greater than one, it is often necessary to evaluate the respective contribution of each lag of the variable under study on the present. This is particularly true when using the Mixture Transition Distribution model to approximate the true fully parameterized Markov chain. Even if it is possible to evaluate each transition matrix using a standard association measure, these measures do not allow taking into account all the available information. Therefore, in this paper, we introduce a new class of so-called "predictive power" measures for transition matrices. These measures address the shortcomings of traditional association measures, so as to allow better estimation of high-order models.

To measure the magnitude among random variables, we can apply a partial order connection defined on a distribution class, which contains the symmetry. In this paper, based on majorization order and symmetry or asymmetry functions, we carry out stochastic comparisons of lifetimes of two series (parallel) systems with dependent or independent heterogeneous Marshall–Olkin Topp Leone G (MOTL-G) components under random shocks. Further, the effect of heterogeneity of the shape parameters of MOTL-G components and surviving probabilities from random shocks on the reliability of series and parallel systems in the sense of the usual stochastic and hazard rate orderings is investigated. First, we establish the usual stochastic and hazard rate orderings for the lifetimes of series and parallel systems when components are statistically dependent. Second, we also adopt the usual stochastic ordering to compare the lifetimes of the parallel systems under the assumption that components are statistically independent. The theoretical findings show that the weaker heterogeneity of shape parameters in terms of the weak majorization order results in the larger reliability of series and parallel systems and indicate that the more heterogeneity among the transformations of surviving probabilities from random shocks according to the weak majorization order leads to larger lifetimes of the parallel system. Finally, several numerical examples are provided to illustrate the main results, and the reliability of series system is analyzed by the real-data and proposed methods.