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We investigated the influence of mental imagery expertise in 15 pen and paper role-players as an expert group compared to the gender-matched control group of computer role-players in the difficult Vandenberg and Kuse mental rotation task. In this task, the participants have to decide which two of four rotated figures match the target figure. The dependent measures were performance speed and accuracy. In our exploratory investigation, we further examined midline frontal theta band activation, parietal alpha band activation, and parietal alpha band asymmetry in EEG as indicator for the chosen rotation strategy. Additionally, we explored the gender influence on performance and EEG activation, although a very small female sample section was given. The expected gender difference concerning performance accuracy was negated by expertise in pen and paper role-playing women, while the gender-specific difference in performance speed was preserved. Moreover, gender differences concerning electro-cortical measures revealed differences in rotation strategy, with women using top-down strategies compared to men, who were using top-down strategies and active inhibition of associative cortical areas. These strategy uses were further moderated by expertise, with higher expertise leading to more pronounced activation patters, especially during successful performance. However, due to the very limited sample size, the findings of this explorative study have to be interpreted cautiously.

This issue of featured papers from 2020 is related to the study of symmetry phenomena in various different fields, but mainly in theoretical physics [...]

This editorial is a short review of papers accepted in the Mathematics and Symmetry/Asymmetry section in 2020–2021 about the symmetry methods [...]

This Special issue contains top-tier physics-related and mathematical research, among other topics, written by scholars who are well-known in their field [...]

The International Institute of Knowledge Innovation and Invention (IIKII) is an institute that promotes the exchange of innovations and inventions, and establishes a communication platform for international innovations and researches. In 2019, IIKII cooperated with the Institute of Electrical and Electronics Engineers (IEEE) Tainan Section Sensors Council to hold IEEE conferences such as IEEE ICIASE 2019, IEEE ECBIOS 2019, IEEE ICKII 2019, ICUSA-GAME 2019, and IEEE ECICE 2019. This Special Issue entitled “Selected Papers from IIKII 2019 conferences” aims to select excellent papers from IIKII 2019 conferences, including symmetry in physics, chemistry, biology, mathematics, and computer science, etc. It selected 21 excellent papers from 750 papers presented in IIKII 2019 conferences on the topic of symmetry. The main goals of this Special Issue are to encourage scientists to publish their experimental and theoretical results in as much detail as possible, and to discover new scientific knowledge relevant to the topic of symmetry.

This comment is devoted to the paper “Lie Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Spatially Two-Dimensional Burgers–Huxley Equation” (Symmery, 2020, vol.12, 170), in which several results are either incorrect, or incomplete, or misleading.

In order to recognize outstanding papers that have been published in Symmetry, the Editorial Board established an annual “Symmetry Best Paper Award”. We are pleased to announce the first “Symmetry Best Paper Award” for 2015. Nominations were selected by the Editorial Board Office, with all research articles published in 2013 and 2014 eligible for consideration. Following review and voting by the Symmetry Best Paper Award Committee, the following three papers have won Symmetry Best Paper Awards for 2015:

Recently, various types of single valued neutrosophic (SVN) rough set models were presented based on the same inclusion relation. However, there is another SVN inclusion relation in SVN sets. In this paper, we propose a new type of SVN covering rough set model based on the new inclusion relation. Furthermore, the graph and matrix representations of the new SVN covering approximation operators are presented. Firstly, the notion of SVN β 2 -covering approximation space is proposed, which is decided by the new inclusion relation. Then, a type of SVN covering rough set model under the SVN β 2 -covering approximation space is presented. Moreover, there is a corresponding SVN relation rough set model based on a SVN relation induced by the SVN β 2 -covering, and two conditions under which the SVN β 2 -covering can induce a symmetric SVN relation are presented. Thirdly, the graph and matrix representations of the new SVN covering rough set model are investigated. Finally, we propose a novel method for decision making (DM) problems in paper defect diagnosis under the new SVN covering rough set model.

We present three types of polyhedral surfaces, which are continuously flexible and have not only an initial pose, where all faces are coplanar, but pass during their self-motion through another pose with coplanar faces (“flat pose”). These surfaces are examples of so-called rigid origami, since we only admit exact flexions, i.e., each face remains rigid during the motion; only the dihedral angles vary. We analyze the geometry behind Miura-ori and address Kokotsakis’ example of a flexible tessellation with the particular case of a cyclic quadrangle. Finally, we recall Bricard’s octahedra of Type 3 and their relation to strophoids.

Over the past four decades, the prophecy from computer pundits and prognosticators pointed to the looming arrival of the paperless office era. However, forty years later, physical paper documents are still playing a significant role due to the ease of use, superior readability, and availability. The drawbacks of paper sheets are that they are hard to modify and retrieve, have limited space, and are environmentally unfriendly. Augmenting paper documents with digital information from mobile devices extends the two-dimensional space of physical paper documents. Various camera-based recognition and detection devices have been proposed to augment paper documents with digital information. However, there are still some limitations that exist in these systems. This paper presents a novel, low cost, spatially aware, mobile system called Ultrasonic PhoneLens. The Ultrasonic PhoneLens adopts two-dimensional dynamic image presentation and ultrasonic sound positioning techniques. It consists of two ultrasonic sound sensors, one Arduino mini-controller board, and one android mobile device. Based on the location of the mobile device over the physical paper, Ultrasonic PhoneLens can retrieve pre-saved digital information from a mobile database for the object (such as a text, a paragraph, or an image) in a paper document. An empirical study was conducted to evaluate the system performance. The results indicate that our system has a better performance in tasks such as browsing multivalent documents and sharing digital information than the Wiimote PhoneLens system.

The circulation of digital assets has become increasingly crucial in today’s digital economy, reflecting both its growing importance and the challenges it faces. Blockchain technology, with its inherent symmetry, has emerged as a transformative force in facilitating digital asset circulation, addressing various issues related to security, efficiency, and transparency. This paper aims to advance the development of digital asset circulation technologies by focusing on four key blockchain-based technologies: smart contracts, consensus algorithms, cross-chain technology, and decentralized exchanges. These technologies embody symmetry in their structure and operation, ensuring balanced and secure asset management across decentralized networks. This paper reviews the evolution of these key technologies, highlighting their contributions to the digital asset ecosystem. It explores effective application cases and analyzes the current challenges each technology faces. Additionally, this paper provides insights into potential future developments and directions to address these challenges and enhance the overall efficiency and reliability of digital asset circulation.

A bicluster consists of a subset of rows and columns of a given matrix, whose intersection defines the region (bicluster) of values of precisely defined condition. Through the decades, a variety of biclustering techniques have been successfully developed. Recently, it was proved that many possible patterns defined in two-dimensional data could be found with the application of Boolean reasoning. The provided theorems showed that any existing pattern in the data could be unequivocally encoded as an implicant of a proper Boolean function. Moreover, a prime implicant of that function encoded the inclusion-maximal (non-extendable) pattern. On the other hand, the definition of some two-dimensional patterns may be easily extended to three-dimensional patterns (triclusters) as well as to any number of dimensions (n-clusters). This paper presents a new approach for searching for three- and higher-dimensional simple patterns in continuous data with Boolean reasoning. Providing the definition of the Boolean function for this tasks, it is shown that the similar correspondence—implicants encode patterns, and prime implicants encode inclusion-maximal patterns—has a strong mathematical background: the proofs of appropriate theorems are also presented in this paper.

In this paper, delayed stochastic integral equations with an initial condition and a drift coefficient given as interval-valued mappings are considered. These equations have a certain symmetric form that distinguishes them from classical single-valued stochastic integral equations and has implications for the properties of the diameter of the values of the solutions of the equations. The main result of the paper is the theorem that there is a unique solution to the equation considered. It was obtained under the assumptions of continuity of the kernels and Lipschitz continuity of the drift and diffusion coefficients. The proof of the existence of the solution is carried out by the method of iterating successive approximations. The paper ends with theorems about the continuous dependence of the solution on the initial function, kernels and nonlinearities.

Uncertain differential equations, as an alternative to stochastic differential equations, have proved to be extremely powerful across various fields, especially in finance theory. The issue of parameter estimation for uncertain differential equations is the key step in mathematical modeling and simulation, which is very difficult, especially when the corresponding terms are driven by some complicated uncertain processes. In this paper, we propose the uncertainty counterpart of the threshold Ornstein–Uhlenbeck process in probability, named the uncertain threshold Ornstein–Uhlenbeck process, filling the gaps of the corresponding research in uncertainty theory. We then explore the parameter estimation problem under different scenarios, including cases where certain parameters are known in advance while others remain unknown. Numerical examples are provided to illustrate our method proposed. We also apply the method to study the term structure of the U.S. Treasury rates over a specific period, which can be modeled by the uncertain threshold Ornstein–Uhlenbeck process mentioned in this paper. The paper concludes with brief remarks and possible future directions.

In this paper, the final stage of the Petrov classification is carried out. As it is known, the Killing vector fields specify infinitesimal transformations of the group of motions of space V4. In the case where the group of motions G3 acts in a simply transitive way in the homogeneous space V4, the geometry of the non-isotropic hypersurface is determined by the geometry of the transitivity space V3 of the group G3. In this case, the metric tensor of the space V3 can be given by a nonholonomic reper consisting of three independent vectors ℓ(a)α, which define the generators of the group G3 of finite transformations in the space V3. The representation of the metric tensor of V4 spaces by means of vector fields ℓ(a)α has a great physical meaning and makes it possible to substantially simplify the equations of mathematical physics in such spaces. Therefore, the Petrov classification should be complemented by the classification of vector fields ℓ(a)α connected to Killing vector fields. For homogeneous spaces, this problem has been largely solved. A complete solution of this problem is presented in the present paper, where I refine the Petrov classification for homogeneous spaces in which the group G3, which belongs to type VIII according to the Petrov classification, acts simply transitively. In addition, this paper provides the complete classification of vector fields ℓ(a)α for space V4 in which the group G3 acts simply transitivity on isotropic hypersurfaces.

In this paper, we focus on the existence of positive periodic solutions of generalized Leslie–Gower-type population models. Using the topological degree, we provide sufficient conditions to demonstrate the existence of positive periodic solutions to the considered models. It is interesting that the positive periodic solutions in this paper are general positive functions, not e exponential functions, which generalizes and improves the existing results. We note that due to the symmetrical property of periodic solutions, the results of this paper provide a deeper understanding of the periodic behavior of biological populations. Two numerical examples show the effectiveness of our main results.

This paper offers a historical review of the evolution of mathematical methods in economics, tracing their development from the earliest attempts in the 18th century to the sophisticated models of the late 20th century. The study begins by examining the initial integration of mathematical techniques into economic thought, highlighting key milestones that shaped the field. Symmetry concepts are naturally embedded in many of these mathematical frameworks, particularly in the balance and equilibrium found in economic models. Symmetry in economics often reflects proportional relationships and equilibrium conditions that are central to both micro- and macroeconomic analyses. Then, the paper elaborates on the progression of economic growth models, including the foundational Solow–Swan model, which introduced the concept of technological progress (knowledge) as a key factor influencing growth. The review also encompasses the Lucas growth model and the Mankiw–Romer–Weil model, both of which incorporate human capital into the growth equation, highlighting its importance in driving economic development. Finally, the paper addresses the Nonneman–Vanhoudt model, which extends the analysis of growth by integrating multiple types of capital, providing a more comprehensive framework for understanding economic dynamics. By documenting these developments, the paper demonstrates the significant role that mathematical modeling has played in advancing economic theory, providing tools to quantitatively analyze complex economic phenomena and driving the discipline towards greater analytical precision and rigor. This analysis emphasizes how symmetry principles, such as balance between inputs and outputs, equilibrium in supply and demand, and proportionality in growth models, underpin many economic theories.

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

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

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

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

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

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

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

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

Analysis of non-stationary and nonlinear sound signals obtained from dynamical processes is one of the greatest challenges in signal processing. Turning machine operation is a highly dynamic process influenced by many events, such as dynamical responses, chip formations and the operational conditions of machining. Traditional and widely used fast Fourier transformation and spectrogram are not suitable for processing sound signals acquired from dynamical systems as their results have significant deficiencies because of stationary assumptions and having an a priori basis. A relatively new technique, discrete wavelet transform (DWT), which uses Wavelet decomposition (WD), and the recently developed technique, Hilbert–Huang Transform (HHT), which uses empirical mode decomposition (EMD), have notably better properties in the analysis of nonlinear and non-stationary sound signals. The EMD process helps the HHT to locate the signal’s instantaneous frequencies by forming symmetrical envelopes on the signal. The objective of this paper is to present a comparative study on the decomposition of multi-component sound signals using EMD and WD to highlight the suitability of HHT to analyze tool-emitted sound signals received from turning processes. The methodology used to achieve the objective is recording a tool-emitted sound signal by way of conducting an experiment on a turning machine and comparing the results of decomposing the signal by WD and EMD techniques. Apart from the short mathematical and theoretical foundations of the transformations, this paper demonstrates their decomposition strength using an experimental case study of tool flank wear monitoring in turning. It also concludes HHT is more suitable than DWT to analyze tool-emitted sound signals received from turning processes.

This paper deals with the problem of multi-robot task scheduling in the Antarctic environments with crevasses. Because the crevasses may cause hazardous situations when robots are operated in the Antarctic environments, robot navigation should be planned to safely avoid the positions of crevasses. However, the positions of the crevasses may be inaccurately measured due to the lack of sensor performance, the asymmetry of sensor data, and the possibility of crevasses drifting irregularly as time passes. To overcome these uncertain and asymmetric problems, this paper proposes a probabilistic multi-robot task scheduling method based on the Nearest Neighbors Test (NNT) algorithm and the probabilistic modeling of the positions of crevasses. The proposed method was tested with a Google map of the Antarctic environments and showed a better performance than the Ant Colony Optimization (ACO) algorithm and the Genetic Algorithm (GA) in the context of total cost and computational time.

The popularity of global GPS location services and location-enabled personal terminal applications has contributed to the rapid growth of location-based social networks. Users can access social networks at anytime and anywhere to obtain services in the relevant location. While accessing services is convenient, there is a potential risk of leaking users’ private information. In data processing, the discovery of issues and the generation of optimal solutions constitute a symmetrical process. Therefore, this paper proposes a symmetry–trajectory differential privacy-protection mechanism based on multi-dimensional prediction (TPPM-MP). Firstly, the temporal attention mechanism is designed to extract spatiotemporal features of trajectories from different spatiotemporal dimensions and perform trajectory-sensitive prediction. Secondly, class-prevalence-based weights are assigned to sensitive regions. Finally, the privacy budget is assigned based on the sensitive weights, and noise conforming to localized differential privacy is added. Validated on real datasets, the proposed method in this paper enhanced usability by 22% and 37% on the same dataset compared with other methods mentioned, while providing equivalent privacy protection.

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

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

Role-based access control (RBAC) is a widely adopted access control model in various domains for defining security management. Role mining is closely related to role-based access control, as the latter employs role assignments to offer a flexible and scalable approach to managing permissions within an organization. The edge role mining problem (Edge RMP), a variant of the role mining problem (RMP), has long been recognized as an effective strategy for role assignment. Role mining, which groups users with similar access permissions into the same role, bears some resemblance to symmetry. Symmetry categorizes objects or graphics with identical characteristics into one group. Both involve a certain form of “classification” or “induction”. Edge-RMP reduces the associations between users and permissions, thereby lowering the security risks faced by the system. While an algorithm based on Boolean matrix factorization exists for this problem, it fails to further refine the resulting user–role assignment (UA) and role–permission assignment (PA) relationships. Additionally, this algorithm does not address constraint-related issues, such as cardinality constraints, user exclusion constraints, and user capabilities. Furthermore, it demonstrates significant redundancy of roles when handling large datasets, leaving room for further optimization of Edge-RMP results. To address these concerns, this paper proposes the MFC-RMA algorithm based on Boolean matrix factorization. The method achieves significant optimization of Edge-RMP results by handling relationships between roles possessing various permissions. Furthermore, this paper clusters, compresses, modifies, and optimizes the original data based on the similarity between users, ensuring its usability for role mining. Both theoretical and practical considerations are taken into account for different types of constraints, and algorithms are devised to reallocate roles incorporating these constraints, thereby generating UA and PA matrices. The proposed approach yields optimal numbers of generated roles and the sum of the minimum number of generated edges to address the aforementioned issues. Experimental results demonstrate that the algorithm reduces management overhead, provides efficient execution results, and ensures the accuracy of generated roles.

Abstract: This paper is concerned with applying the Bayesian and E-Bayesian approaches to estimating the unknown parameters of the modified Topp–Leone–Chen distribution under a progressive Type-II censored sample plan. The paper explores the complexities of different estimating methods and investigates the behavior of the estimates through some computations. The Bayes and E-Bayes estimators are obtained under two distinct loss functions, the balanced squared error loss function, as a symmetric loss function, and the balanced linear exponential loss function, as an asymmetric loss function. The estimators are derived using gamma prior and uniform hyperprior distributions. A numerical illustration is given to examine the theoretical results through using the Metropolis–Hastings algorithm of the Markov chain Monte Carlo method of simulation by the R programming language. Finally, real-life data sets are applied to prove the flexibility and applicability of the model.

In this paper, a stability analysis and the controller improvement of T-S fuzzy Descriptor system are studied. Firstly, by making full use of the related theory of fuzzy affiliation function and combining the design method of fuzzy Lyapunov function with the method of inequality deflation, a stability condition with wider admissibility and less system conservatism is proposed. The advantage of this method is that it is not necessary to ensure that each fuzzy subsystem is progressively stable. We also maximise the boundary of the derivatives of the affiliation function mined. Secondly, a PDC controller and a Non-PDC controller are designed, and the deflation conditions for the linear matrix inequalities of the two controllers are constructed. Finally, some arithmetic simulations and practical examples are given to demonstrate the effectiveness of the method studied in this paper, and the results obtained are less conservative and have larger feasible domains than previous methods.

The effects of the helical trajectories of the perturbing electrons in magnetized plasmas on the dynamical Stark width of hydrogen or deuterium spectral lines have been studied analytically in our previous two papers—specifically in the situation where the magnetic field B is so strong that the dynamical Stark width of these lines reduces to the so-called adiabatic Stark width because the so-called nonadiabatic Stark width is completely suppressed. This situation corresponds, for example, to DA and DBA white dwarfs. We obtained those analytical results by using the formalism of the so-called conventional (or standard) theory of the impact Stark broadening: namely, by performing calculations in the second order of the Dyson perturbation expansion. The primary outcome was that the dynamical Stark broadening was found to not depend on the magnetic field B (for sufficiently strong B). In the present paper, we use the O4 symmetry of hydrogen atoms for performing the corresponding non-perturbative analytical calculations equivalent to accounting for all orders of the Dyson perturbation expansion. The results, obtained by using the O4 symmetry of hydrogen atoms, differ from our previous ones not only quantitatively, but—most importantly—qualitatively. Namely, the dynamical Stark broadening does depend on the magnetic field B, even for strong B. These results should be important for revising the interpretation of the hydrogen Balmer lines observed in DA and DBA white dwarfs. We also address confusion in the literature on this subject.

In active noise control (ANC) systems, the traditional filtered-x least mean square (FxLMS) algorithm has poor control effect on impulsive noise. To overcome this drawback, a robust cost function was designed in this paper by embedding the cost function of the FxLMS algorithm into the framework of hyperbolic tangent function; this paper thus proposes a robust filtered-x least hyperbolic tangent (FxLHT) algorithm in ANC systems. Moreover, the value of λ in the FxLHT algorithm greatly affects the robustness and convergence performance of the algorithm. Therefore, a variable λ-parameter was proposed to enhance the performance of the FxLHT algorithm. Simulation results show that in the active control of impulsive noise, compared with the FxLMS algorithm and other robust ANC algorithms, the proposed FxLHT algorithm and variable λ-parameter FxLHT algorithm not only exhibit good robustness and noise reduction performance but also have a better tracking ability.

This paper improves the timeliness of satellite mission planning to cope with the rapid response to changes. In this paper, satellite mission planning is investigated. Firstly, the satellite dynamics model and mission planning model are established, and an improved Monte Carlo tree (Improved-MCTS) algorithm is proposed, which utilizes the Monte Carlo tree search in combination with the state uncertainty network (State-UN) to reduce the time of exploring the nodes (At the MCTS selection stage, the exploration of nodes specifically refers to the algorithm needing to decide whether to choose nodes that have already been visited (exploitation) or nodes that have not been visited yet (exploration)). The results show that this algorithm performs better in terms of profit (in this paper, the observation task is given a weight of 0–1, and each planned task will receive a profit; that is, a profit will be assigned at the initial moment) and convergence speed compared to the ant colony algorithm (ACO) and the asynchronous advantage actor critic (A3C).

This paper presents an innovative mathematical model of solid fuel gasification, which is not described in the available literature. The calculation of the components of the heterogeneous phase (including both solid and gaseous phases) as well as the calculation of the homogeneous phase (only gaseous components) is based on the balance of the total amounts of carbon, oxygen, hydrogen, and nitrogen entering the reactor space. Additionally, this paper introduces a new method for calculating the composition of the gaseous phase, based on reducing the heterogeneous mixture (composed of solid and gaseous phases) to a homogeneous gaseous phase. This approach to calculating the gaseous phase composition in the solid fuel gasification process has not been found by the authors in the cited literature. This paper also presents a model for calculating the heterogeneous and gaseous phases using the number of moles that participate in the assumed chemical reactions of the solid fuel gasification process. This approach to calculating the composition of the heterogeneous and gaseous phases of the solid fuel gasification process is also not represented in the cited literature. For comparison with the literature data, municipal solid waste (MSW) and cashew nut shell (Cashew Shell Char (CNSC)) were used as fuels in the calculation of gasification composition. The results of the calculation of the gaseous phase composition using the model presented in the paper show good agreement with the data from the literature. The calculation of the composition of the heterogeneous mixture during the steam gasification of MSW (α = 0.4) shows the presence of a solid phase (carbon) up to approximately 735 °C. At that temperature, the synthetic gas contains only gaseous components: CO = 33.10%, H2 = 52.70%, CH4 = 2.54%, CO2 = 4.97, H2O = 5.93% and N2 = 0.76%. Increasing the temperature above 735 °C eliminates the solid phase from the equilibrium mixture. The literature data on solid fuel gasification generally do not consider the proportion of the solid phase (carbon) in the equilibrium mixture. To satisfy the material balance at the input and output of the gasification reactor, it is necessary to determine the proportion of the solid phase (carbon) in the equilibrium mixture. Since the proportion of the solid phase (carbon) in the heterogeneous equilibrium mixture can only be determined through measurement, the development and application of a mathematical model in engineering practice is of great importance, so this developed model can be considered a useful tool for simulating the influence of process parameters on gas characteristics.

Convolutional neural networks (CNNs) have achieved remarkable success in fully supervised medical image segmentation tasks. However, the acquisition of large quantities of homogeneous labeled data is challenging, making semi-supervised training methods that rely on a small amount of labeled data and pseudo-labels increasingly popular in recent years. Most existing semi-supervised learning methods, however, underestimate the importance of the unlabeled regions during training. This paper posits that these regions may contain crucial information for minimizing the model’s uncertainty prediction. To enhance the segmentation performance of the left-atrium database, this paper proposes a triple consistency segmentation network based on the squeeze-and-excitation mechanism (SETC-Net). Specifically, the paper constructs a symmetric architectural unit called SEConv, which adaptively recalibrates the feature responses in the channel direction by modeling the inter-channel correlations. This allows the network to adaptively weigh each channel according to the task’s needs, thereby emphasizing or suppressing different feature channels. Moreover, SETC-Net is composed of an encoder and three slightly different decoders, which convert the prediction discrepancies among the three decoders into unsupervised loss through a constructed iterative pseudo-labeling scheme, thus encouraging consistent and low-entropy predictions. This allows the model to gradually capture generalized features from these challenging unmarked regions. We evaluated the proposed SETC-Net on the public left-atrium (LA) database. The proposed method achieved an excellent Dice score of 91.14% using only 20% of the labeled data. The experiments demonstrate that the proposed SETC-Net outperforms seven current semi-supervised methods in left-atrium segmentation and is one of the best semi-supervised segmentation methods on the LA database.

In this paper, we propose a precise Wigner–Weyl calculus for the models defined on the honeycomb lattice. We construct two symbols of operators: the B symbol, which is similar to the one introduced by F. Buot, and the W (or, Weyl) symbol. The latter possesses the set of useful properties. These identities allow us to use it in physical applications. In particular, we derive topological expression for the Hall conductivity through the Wigner-transformed Green function. This expression may be used for the description of the systems with artificial honeycomb lattice, when magnetic flux through the lattice cell is of the order of elementary quantum of magnetic flux. It is worth mentioning that, in the present paper, we do not consider the effect of interactions.

In this paper, we focus on a fractional differential equation 0CDαu(t)+q(t)u(t)=0 with boundary value conditions u(0)=δu(1),u′(0)=γu′(1). The paper begins by pointing out the inadequacies of the study conducted by Ma and Yangin establishing Lyapunov-type inequalities. It then discusses the properties of its Green’s function and investigates extremum problems related to several linear functions. Finally, thorough classification and analysis of various cases for parameters δ and γ are conducted. As a result, a comprehensive solution corresponding to the Lyapunov-type inequality is obtained.

The accurate evaluation of green innovation efficiency is a critical prerequisite for enterprises to achieve sustainable development goals and improve environmental performance and economic efficiency. This paper evaluates the green innovation efficiency of 72 new-energy enterprises by using a hybrid method of Data Envelopment Analysis (DEA) and a random forest model. The non-parametric DEA model is combined with the parametric SFA model to analyze the real green innovation efficiency on the basis of removing environmental factors and random factors. Then, the random forest model based on a nonlinear relationship is used to evaluate factors impacting green innovation efficiency. This paper proposes a comprehensive evaluation method designed to assess the green innovation efficiency of new-energy enterprises. By applying this method, companies can gain a comprehensive understanding of the current performance in green innovation, facilitating informed decision-making and accelerating sustainable development.

In this paper, several classes of rough Marcinkiewicz integral operators along surfaces of revolution on product spaces are investigated. We prove the Lp boundedness of these operators when their kernels functions belong to a class of functions related to a class of functions introduced by Grafakos-Stefanov. The results in this paper extend and improve several known results on Marcinkiewicz integrals over a symmetric space.

The primary objective of this paper is to address the challenge of designing finite-time fault-tolerant control mechanisms for nonlinear flexible spacecraft systems, which are particularly vulnerable to randomized actuator faults. Diverging from traditional methodologies, our research harnesses the capabilities of the Takagi–Sugeno (T–S) fuzzy framework. A unique feature of our model is the representation of actuator failures as stochastic signals following a Markov process, thereby offering a robust solution for addressing timeliness concerns. In this paper, we introduce a generalized reciprocally convex inequality that includes adjustable parameters, broadening the scope of previous results by accommodating them as special cases. Through the amalgamation of this enhanced inequality and flexible independent parameters, we propose an innovative controller design strategy. This approach establishes a stability standard that guarantees mean-square H∞ performance. In order to validate the efficacy of the suggested strategy, we present a numerical illustration involving a nonlinear spacecraft system, showcasing the practical advantages and feasibility of our proposed technique.

In this paper, we prove the existence and uniqueness of common fixed point of tower type contractive mappings in complete metric (pseudo)modular spaces involving the theoretic relation. However, the newly introduced contraction in this paper further characterize and includes in their full strength several existing results in metrical fixed point theory. Some nontrivial supportive examples were given to justify our result. Our results generalize, improve, and unify some existing results.

Multifactor uncertain differential equations are powerful tools for studying dynamic systems under multi-source noise. A key challenge in this study is how to accurately estimate unknown parameters based on the framework of uncertainty theory in multi-source noise environments. To address this core problem, this paper innovatively proposes a least-squares estimation method. The essence of this method lies in constructing statistical invariants with a symmetric uncertainty distribution based on observational data and determining specific parameters by minimizing the distance between the population distribution and the empirical distribution of the statistical invariant. Additionally, two numerical examples are provided to help readers better understand the practical operation and effectiveness of this method. In addition, we also provide a case study of JD.com’s stock prices to illustrate the advantages of the method proposed in this paper, which not only provides a new idea and method for addressing the problem of dynamic system parameter estimation but also provides a new perspective and tool for research and application in related fields.

The frequency support capacity of power loads is essential for maintaining active power symmetry and balance between the generation and demand sides of power systems. As the proportion of renewable energy sources and power electronic equipment increases, the inertia on the power generation side decreases, highlighting the growing importance of frequency support on the load side. As it is generally believed that the active power balance of power systems determines the frequency stability, few studies have considered the effect of voltage variation on the frequency response dynamics. It is important to note that the node voltage keeps fluctuating throughout the frequency dynamic process, which affects the active power of loads and should not be neglected. Based on the aforementioned rationales, this paper endeavors to investigate the modeling of power load frequency response and analyze its support capability considering the voltage variation effect. This paper initially establishes the small-signal model of dynamic load under frequency dynamics, derives the transfer function relating active power to system frequency deviation, and subsequently develops its frequency response model. Subsequently, commencing with the ZIP model of static load, the power fluctuation of load nodes is derived from the influence of preceding nodes, and the frequency response model of the static load is formulated and its frequency support capacity is scrutinized. Based on this foundation, a comprehensive aggregation model of the complex load is constructed, and its frequency support capability is assessed using actual data. Finally, the proposed model and analysis results are validated through simulation, confirming their correctness and effectiveness.

The fractional reduced differential transform method is a finite iterative method based on infinite fractional expansions. The obtained result is the approximation of the real value. Currently, there are few reports on the approximate error and applicable condition. In this paper, we study the factors related to the approximate errors according to the fractional expansions. Our research shows that the approximate errors relate not only to fractional order but also to time t, and that they increase rapidly with time t. This method can only be applied within a certain time range, and the time range is relevant to fractional order and fractional expansions. We can ascertain this time range according to the absolute error and the relative error. Many obtained achievements may be incorrect if the applicable conditions are not satisfied. Some examples presented in this paper verify our analysis.