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This study introduces a novel approach for integrating a compact mechanism into the Marine Predator Algorithm (MPA), subsequently proposing innovative parallel and communication strategies. The synergistic combination of these methodologies substantially augments the global search efficiency and accelerates the convergence rate of the original MPA. The paper culminates in presenting an enhanced version of the Marine Predator Algorithm, termed PCMPA, which leverages compact parallel technology. The performance of PCMPA, alongside a range of comparative algorithms, is rigorously evaluated using the CEC2013 benchmark test functions. These comparative algorithms encompass recent variants of MPA, PSO, DE, and other newly developed algorithms. Evaluation results reveal that PCMPA outperforms its counterparts in a more extensive array of test functions. To corroborate PCMPA's efficacy in real-world scenarios, the algorithm is applied to parameter optimization in Backpropagation neural network (BNN) and targeted engineering optimization challenges. This application demonstrates that PCMPA consistently achieves enhanced performance in practical implementations. • The study presents a novel variant of the Marine Predators Algorithm, dubbed PCMPA. • The paper benchmarks PCMPA against other Marine Predators Algorithm variants and other Algorithms. • The research applies PCMPA to optimize parameters of BNNs and to tackle engineering optimization challenges. [ABSTRACT FROM AUTHOR]

In this paper, a temporal second order two-grid difference scheme is proposed for the two-dimensional nonlinear time-fractional partial integro-differential equations with a weakly singular kernel. The first-order backward difference and L 1 formula are used in the temporal direction to estimate the first level of time, the L 2 − 1 σ formula and L 1 -type formula are used in the temporal direction for later time steps, and the central difference formula is used in the spatial directions. To improve the computational efficiency of nonlinear system, an efficient time two-grid algorithm is proposed. This algorithm firstly solves a nonlinear system on the coarse grid, and then the Lagrangian linear interpolation is applied on the coarse grid to estimate the function values on the fine grid. The stability and convergence of the two-grid difference scheme are analyzed by the energy method. The convergence order of the two-grid difference scheme is O (τ F 2 + τ C 4 + h x 2 + h y 2) , where τ F and τ C are the time step sizes of fine grid and coarse grid respectively, while h x and h y are the space step sizes. Numerical experiments show that the accuracy of the theoretical analysis and the efficiency of the two-grid algorithm. [ABSTRACT FROM AUTHOR]

This paper studies the mirror descent algorithm for distributed optimization, where the underlying digraph is assumed to be weight-unbalanced. Within this framework, a novel distributed mirror descent algorithm based on gradient weighting technique is developed. Theoretically, different from the existing works, which prove that the function value corresponding to the estimates converge to the optimal value of the optimization problem, this paper proves that (1) the proposed algorithm can achieve exact convergence of the estimates to the solution of the optimization problem; and (2) the algorithm has a convergence rate O (1 T) with a given time horizon T. Further, taking into account the fact that the cost functions in many significant optimization problems are dynamic, the distributed online optimization based on the proposed algorithm is studied. Especially, it is shown that the individual regret of the proposed algorithm is bounded by O (T). Finally, the theoretical results are verified through some simulation examples. [ABSTRACT FROM AUTHOR]

Implementations that follow the functional programming paradigm are being used in more and more domains. As functional programming paradigm has mathematical reference transparency, refinement to functional programs contributes to improving the reliability of the transformation process and simplifying the refinement steps. However, it is a challenge to generate functional programs from specifications. Most existing transformation methods refine specifications into abstract algorithm-level programs based on loop invariants rather than functional programs. This paper proposes a novel functional program generation method based on the partition-recursion refinement rule. It establishes a novel program refinement framework based on functional theory for the first time. This is the first study to regard the whole program refinement process as a composition of abstract functions. This paper designs a recurrence-based algorithm design language (Radl+) and implements a software prototype to map Radl+ algorithms into executable Haskell programs. To prove the feasibility and efficiency of this method, this paper transforms the polynomial multiplication problem from a specification into an executable Haskell program. This case shows that compared with existing approaches, the proposed method can simplify the transformation steps and reduce the number of lines of generated code from 38 to 10. • Novel refinement framework provides a new approach to generating a functional program. • The composition of abstract functions explains the program refinement process. • Substitution rule and Recursion rule have none of the side effects. • Software prototype transforms the polynomial multiplication problem into Haskell program. [ABSTRACT FROM AUTHOR]

To investigate accurately unique and advanced wave properties in elastic metamaterials advanced and efficient numerical methods are needed. The paper presents an extended boundary integral equation method for simulating elastic wave scattering by doubly periodic arrays of rectangular crack-like voids. The convergence of the arising double series is proved and the convergence rate is carefully analyzed. Employing the results of the investigation of the convergence rate, an algorithm for fast numerical calculation of double series is proposed to reduce computational costs through preliminary analytical evaluation and the proposed summation strategy. The efficiency of the extended boundary integral equation method is demonstrated and examples of the calculated transmission coefficients exhibiting the influence of the introduction of the doubly periodic array are given. [ABSTRACT FROM AUTHOR]

This paper concerns a new incremental approach to mining data streams. It is known that patterns in a data stream may evolve over time. In many cases, we need to track and analyze the nature of these changes. In the paper, the probabilistic neural networks are considered as basic models for tracking changes in data streams. We present globally convergent stream data mining algorithms applied to problems of regression, classification, and density estimation in a time-varying (drifting) environment. The algorithms are derived from the Parzen kernel-based probabilistic neural networks working in the online mode. For each problem, a theorem is presented ensuring the L 2 convergence of the algorithm designed for tracking drifting regression, density, or discriminant functions. Illustrative examples explain in detail how to choose the bandwidth of the Parzen kernel and the learning rate of the online algorithm. The performance of all algorithms is shown in exemplary simulations. It should be noted that this paper is one of very few, in the existing literature, presenting mathematically justified stream data mining algorithms. • The incremental version of the Generalized Regression Neural Network (IGRNN) able to track drifting regression functions. • The incremental version of the Probabilistic Neural Network (IPNN) working in non-stationary environments. • Application of IPNN for tracking drifting discriminant functions. • Mathematical proofs of the L 2 convergence of all the proposed estimators. [ABSTRACT FROM AUTHOR]

Many real-life problems can be formulated as numerical optimization problems. Such problems pose a challenge for researchers when designing efficient techniques that are capable of finding the desired solution without suffering from premature convergence. This paper proposes a novel evolutionary algorithm that blends the exploitative and explorative merits of two main evolutionary algorithms, namely the Stochastic Fractal Search (SFS) and a Differential Evolution (DE) variant. This amalgam has an effective interaction and cooperation of an ensemble of diverse strategies to derive a single framework called Iterative Cyclic Tri-strategy with adaptive Differential Stochastic Fractal Evolutionary Algorithm (Ic3-aDSF-EA). The component algorithms cooperate and compete to enhance the quality of the generated solutions and complement each other. The iterative cycles in the proposed algorithm consist of three consecutive phases. The main idea behind the cyclic nature of Ic3-aDSF-EA is to gradually emphasize the work of the best-performing algorithm without ignoring the effects of the other inferior algorithm during the search process. The cooperation of component algorithms takes place at the end of each cycle for information sharing and the quality of solutions for the next cycle. The algorithm's performance is evaluated on 43 problems from three different benchmark suites. The paper also investigates the application to a set of real-life problems. The overall results show that the proposed Ic3-aDSF-EA has a propitious performance and a reliable scalability behavior compared to other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive generalized Nash equilibrium (GNE) seeking algorithm is designed, in order to address the non-cooperative game with private inequality constraints under high-dimensional input dead-zone. That is to say, the dead-zone dynamics may be thought of as a generic high-dimensional convex set, and the introduction of two methods distinguishes our works in seeking the GNE of non-cooperative games. On the one hand, a two-time-scale structure based on singular perturbation method is led into the design of GNE seeking algorithm, where the fast dynamics part rapidly eliminates the influence of input dead-zone, and the slow dynamics part drives the players' action to the GNE. On the other hand, adaptive penalty method is utilized to ensure the player's action enters the inequality constraints set without a prior estimation of centralized information for penalty parameters. The algorithm in this paper realizes complete distribution and parameter independence, making it easy to apply in practical programming. At last, several numerical examples regarding the electricity markets are employed to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper appends three proposed heuristic algorithms, viz. Initialization Algorithm, Fraction Repair Algorithm and Negative Repair Algorithm, to Particle Swarm Optimization (PSO) and extends its application to Pure Integer Linear Solid Transportation Problem (STP). The chief contribution of the paper is that the proposed Hybrid Particle Swarm Optimization (HPSO) algorithm discretizes the continuous search space of PSO so that it can operate in the discrete solution space of STP with any of the valid parameter settings. The Initialization Algorithm is developed to generate the sufficient number of random solutions for initiating HPSO with a diverse population of given size. Whereas Fraction Repair and Negative Repair Algorithms are developed to ensure that each successive population obtained with HPSO remains in the solution space of STP. The validity of HPSO is examined and illustrated by solving a numerical problem with certain parameter settings. Further, the HPSO demonstrates its ability to obtain an optimal or near optimal solution along with the alternate optimal solution, if it exists. It searches for the solutions even without adhering to the rigid conditions of traditional methods that every solution of STP must have a fixed number of non-zero decision variables. Moreover, the performance of HPSO is tested with three different parameter settings and compared amongst each other to analyze their significance in solving the problem. The performance of HPSO and the variants of parameters are statistically validated through an extensive experimental design. [ABSTRACT FROM AUTHOR]

Telemedicine provides remote online services for digital diagnosis and treatment via the Internet. However, there is a risk of data leakage during transmission. Therefore, data protection is an important challenge for telemedicine. Chaos is widely used in image, audio, and EEG encryption because of its unique characteristics of unpredictability, nonlinearity, and sensitivity to an initial state. However, some chaotic maps have various security issues. To solve these problems, this paper proposes a K-sine-transform-based coupled chaotic system (K-STBCCS), combining any two one-dimensional chaotic mappings to generate a new chaos mapping. To demonstrate the reliability of the system, this paper generates three new chaotic mappings using K-STBCCS and analyzes their performance. Using the chaotic mapping generated by K-STBCCS, this paper further proposes an EEG signal encryption scheme based on the confusion-diffusion principle. The purpose of confusion is to separate adjacent EEG signals, while the purpose of diffusion is to change the value of EEG signals. Among them, the diffusion operation uses positive and negative diffusion to reduce the correlation between the ciphertext and the original signals. The experimental results and security analysis show that the proposed EEG signal encryption scheme performs well and passes the rigorous cryptographic security test. [ABSTRACT FROM AUTHOR]

Telemedicine provides remote online services for digital diagnosis and treatment via the Internet. However, there is a risk of data leakage during transmission. Therefore, data protection is an important challenge for telemedicine. Chaos is widely used in image, audio, and EEG encryption because of its unique characteristics of unpredictability, nonlinearity, and sensitivity to an initial state. However, some chaotic maps have various security issues. To solve these problems, this paper proposes a K-sine-transform-based coupled chaotic system (K-STBCCS), combining any two one-dimensional chaotic mappings to generate a new chaos mapping. To demonstrate the reliability of the system, this paper generates three new chaotic mappings using K-STBCCS and analyzes their performance. Using the chaotic mapping generated by K-STBCCS, this paper further proposes an EEG signal encryption scheme based on the confusion-diffusion principle. The purpose of confusion is to separate adjacent EEG signals, while the purpose of diffusion is to change the value of EEG signals. Among them, the diffusion operation uses positive and negative diffusion to reduce the correlation between the ciphertext and the original signals. The experimental results and security analysis show that the proposed EEG signal encryption scheme performs well and passes the rigorous cryptographic security test. [ABSTRACT FROM AUTHOR]

In this paper, an enhanced hybrid chameleon swarm algorithm (CSA) is proposed and applied to the degree reduction problem of disk Wang–Ball (DWB) curve. CSA is a novel population-based algorithm inspired by the hunting behavior of chameleons, its simplicity and easy implementation make it applied to different fields. However, it suffers from premature convergence and easy to fall into local optimum, especially in the face of complex optimization problems. Therefore, this paper proposes an enhanced hybrid CSA (CCECSA, for short). Compared with the classic CSA, the proposed CCECSA mainly introduces three improvements: (1) The crisscross optimization algorithm is mixed to avoid premature convergence, in which the horizontal and vertical crossover can generate moderation solutions to increase the diversity of the population. (2) Elite guidance mechanism is introduced to speed up the convergence. (3) Competitive substitution mechanism is added to replace the worst individual, and an interference strategy is set to prevent the algorithm from falling into a local optimum. The efficiency and robustness of the proposed CCECSA are demonstrated by the comparison results with some advanced meta-heuristic algorithms on CEC2014, CEC2017, and 4 engineering design examples. In addition, for the degree reduction problem of DWB curves, the multi-degree reduction optimization models of its center curve and radius function are established respectively. At the same time, the optimal center curve and radius function of the approximating DWB curves of lower degree are obtained by the proposed CCECSA. The experimental results show that the proposed CCECSA achieves the optimal solution with better convergence and robustness. The source code of CCECSA is publicly available in the supplementary material related to this article. [ABSTRACT FROM AUTHOR]

Whale optimization algorithm (WOA), as an advanced optimization algorithm with simple structure, has been favored by various fields. However, there are some disadvantages of WOA, such as slow convergence speed, low precision and falling into local optimal value easily. In this paper, a novel improved whale optimization algorithm (IWOA) with multi-strategy and hybrid algorithm is proposed to overcome above shortcomings. Firstly, IWOA initializes the population by chaotic mapping to avoid the initial population distribution of WOA deviating from the optimal value. Secondly, IWOA combines the pheromone of the black widow algorithm and the opposition-based learning strategy to modify the population, which improves the convergence speed and the global performance of WOA respectively. Finally, the adaptive coefficients and the new update modes replace the original update modes, which makes the structure of WOA simpler and more accurate. In addition, the convergence of IWOA is also proved in this paper. On the one hand, to demonstrate the effectiveness of IWOA, 23 benchmark functions are used to test various performance of the algorithm. On the other hand, in order to prove the superiority of IWOA, the experimental results are compared and analyzed with other optimization algorithms. Simulation results show that IWOA proposed in this paper owns excellent performance in convergence speed, stability, accuracy and global performance, compared with other algorithms. [ABSTRACT FROM AUTHOR]

Bonobo optimizer (BO) is a recent metaheuristic algorithm inspired by the social behavior of bonobos. BO maintains a robust search strategy based on two distinct phases that involve interesting mechanisms, such as the fission–fusion method for selection and an efficient process for producing new candidate solutions. Despite its remarkable capacity, BO presents a critical flaw that corresponds to an inappropriate balance between exploration and exploitation. Under such conditions, suboptimal or even poor solutions can be obtained. This paper proposes a modified BO algorithm in which the trajectory of each search agent is modified dynamically through the adaptation of the main parameters of the algorithm. With this new mechanism, the algorithm allows for the exploration and exploitation of different regions of the solution space and determines the global optimum in a faster manner. The performance of the proposed algorithm is evaluated by considering two scenarios. One is the optimization of 23 benchmark functions and the second is the problem of power allocation in wireless networks. The results show that the proposed scheme enhances the performance of the basic BO method by increasing the robustness and providing a better solution quality. [ABSTRACT FROM AUTHOR]

The paper deals with the approximation and numerical realization of the Stokes system in 3D with Coulomb's slip boundary conditions. The weak velocity–pressure formulation leads to an implicit inequality type problem which is discretized by the P1+bubble/P1 elements. To regularize the discrete non-smooth slip term and to release the discrete impermeability condition the duality approach is used. For numerical realization of the resulting saddle-point problem two strategies are proposed, namely (i) its fixed-point formulation solved by the method of successive approximations (i i) the direct numerical solution of the saddle-point problem. The semi-smooth Newton method is used to solve non-smooth equations appearing in both these approaches. [ABSTRACT FROM AUTHOR]

This paper proposes a novel importance-based persistent coverage for environments with hotspots. Multiple quadrotors are utilized to maintain coverage while acquiring high-quality information over prioritized regions by lowering the altitude. To achieve this, the approach utilizes distributed communication protocols and cost functions to address the tradeoff between wider coverage and better quality information. The cost functions determine three-dimensional waypoints based on coverage levels, sensor resolution, and Euclidean distance. Voronoi tessellations are used locally for efficient computation and collision avoidance. Trajectories of the quadrotors are generated based on quadrotor dynamics using error functions that take into account state information and desired waypoints. The proposed approach is validated through simulations, comparisons, and experiments for multi-agent systems under quadrotor dynamics. Further, metrics of performance analysis are formulated that show consistent coverage levels and differences to assess the novel importance-based approach. The simulations and experiments demonstrate the feasibility and effectiveness of the approach, with prioritized regions receiving higher sensor resolution while maintaining persistent coverage of the environment. • Novel importance-based persistent coverage for information acquisition over hotspots. • Quadrotor waypoints based on information resolution and decaying environmental costs. • Distributed communication protocols for scalability and low computational complexity. • Real-time importance-based persistent coverage for multi-quadrotor dynamical systems. • Proposed coverage with varying velocities is verified by simulation and experiments. [ABSTRACT FROM AUTHOR]

In this paper, we consider a distributed economic dispatch problem (EDP) in smart grids, where each generator only communicates with its neighbors and minimizes its own cost in the presence of network-wide equality constraints and local capacity limits. Distributed algorithms to solve this problem have become an attractive focus of engineering research due to their multiple advantages. Many existing methods are time-triggered, whereas few works have been dedicated to solving the problem using an event-triggered approach. This problem gets more challenging when further accelerated convergence is desired. To solve such a problem, we carefully design an event-triggered parameter distributed accelerated algorithm, named as ET-PDA. On the one hand, the choice of different parameters in ET-PDA will lead to different momentum (Nesterov or heavy-ball) methods, which facilitates the accelerated convergence of the algorithm. On the other hand, the event-triggered mechanism in ET-PDA makes the time gap between two continuous interaction moments of each generator larger than the iteration interval, contributing to improved communication efficiency. In particular, ET-PDA achieves linear convergence when the local cost function of each generator is smooth and strongly convex, moreover, it precludes Zeno-like behavior. The effectiveness of ET-PDA is also verified through a series of simulation experiments. [ABSTRACT FROM AUTHOR]

The control input derived from model predictive control (MPC) scheme depends on the receding horizon whose length needs to be determined. Design length is also a trade-off between computational complexity and optimization metrics. To this end, a framework for adaptive selection of the horizon length has been developed for discrete systems in previous works. In this paper, this framework is extended to continuous nonlinear systems. A new algorithm is presented to solve the problem of how to adaptively select the horizon length. Then, according to the traditional method and the robust MPC scheme based on tubes, the recursive feasibility and robustness of the algorithm (the adaptive horizon nonlinear model predictive control, called AH-NMPC) for quasi-infinite time domain adaptive horizontal continuous-time nonlinear systems are proved. Finally, the NMPC controller is used to perform path-tracking experiments on an autonomous vehicle to verify the good effects of the algorithm (AH-NMPC). [ABSTRACT FROM AUTHOR]

This paper is concerned with model predictive control (MPC) for multisensor linear systems. In order to fully utilize information and achieve higher control accuracy, two fusion MPC algorithms are proposed. The first algorithm is named estimation-fusion model predictive controller (E-F MPC), which local estimations are fused and then fusion control input is obtained by the fusion estimation. The second algorithm is named control-fusion model predictive controller (C-F MPC), which fuses the control inputs obtained from local systems. The relationships, differences and complexity of the two algorithms are analyzed. The advantages of E-F MPC are that it is simple and easy to implement with high control accuracy, while the disadvantage is the bad robustness because of the heavy estimation, prediction and control tasks for the fusion node. For C-F MPC, with a small loss of accuracy, network throughput and computational cost of its fusion node will be greatly reduced, which makes it good robustness and flexibility. Simulation analysis verifies the effectiveness and correctness of the conclusion. [ABSTRACT FROM AUTHOR]

This paper studies non-cooperative games, in which each player's local objective function depends on its own decisions as well as those of other players. In these games, each player's local objective function is differentiable, its decision is constrained by a local feasibility constraint, and the decisions of all players are coupled with an equality constraint. By analyzing the variational problem of the games, a distributed generalized Nash equilibrium seeking algorithm with fixed step sizes is developed based on the backward-reflected-forward–backward splitting. Each player performs a backward step followed by a forward–backward step, and the pseudo-gradient is evaluated at a reflection term. Moreover, the convergence of the proposed distributed algorithm is analyzed under standard assumptions using the operator theory and the convex analysis theory. Finally, the simulation results verify the effectiveness of the algorithm and the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper presents a numerical investigation of the spectral conjugate directions formulation for optimizing unconstrained problems. A novel modified algorithm is proposed based on the conjugate gradient coefficient method. The algorithm employs the Wolfe inexact line search conditions to determine the optimum step length at each iteration and selects the appropriate conjugate gradient coefficient accordingly. The algorithm is evaluated through several numerical experiments using various unconstrained functions. The results indicate that the algorithm is highly stable, regardless of the starting point, and has better convergence rates and efficiency compared to classical methods in certain cases. Overall, this research provides a promising approach to solving unconstrained optimization problems. [ABSTRACT FROM AUTHOR]

• A many objective evolutionary algorithm based on decomposition and moth search is proposed. • Random and adaptive weights is used to break the limitation of uniform distribution weights. • Mutual evaluation value is used to evaluate the optimal individual in the neighborhood. • Improving scale factor α in MSA is to improve the performance of the proposed algorithm. Decomposition-based multi-objective evolutionary algorithm (MOEA/D) has good performance in solving multi-objective problems (MOPs) but poor performance in solving many-objective optimization problems (MaOPs). The weight vectors in MOEA/D are relatively fixed, which results in poor performance when dealing with complex MaOPs. In this paper, random and adaptive weights are introduced into MOEA/D to break the limitation of fixed weight vectors. And the moth search algorithm (MSA) is used as an operator to improve global search ability. The updating strategies in MSA are more consistent with the neighborhood learning strategy adopted in MOEA/D. In addition, to enable MSA to find the optimal solution in the neighborhood on the MaOPs to update other individuals. This paper introduces mutual evaluation value for evaluating the optimal individual in the neighborhood, and the proposed algorithm is abbreviated as MOEA/DMS. In comparative experiments on the MaF test suite, hypervolume (HV) and inverted generational distance (IGD) are used to measure MOEA/DMS and other many-objective evolutionary algorithms (MaOEAs). The results show that MOEA/DMS has an excellent performance in dealing with MaOPs. Besides, MOEA/DMS is compared with other state-of-the-art MaOEAs on two combinatorial MaOPs. The results show that MOEA/DMS also has significant advantages in dealing with combinatorial MaOPs. [ABSTRACT FROM AUTHOR]

This paper proposes a fast bit-level chaotic image encryption algorithm. The goal is to make the difference between 0 and 1 in the bit-level ciphertext as small as possible. By introducing the concept of the difference between 0 and 1, constantly adjust the number of binary 0 and 1 in the ciphertext, and the difference is fed back to the encryption system until the difference reaches the preset accuracy, so as to quickly achieve a secure encryption effect. To verify the security of the algorithm, this paper selects multiple chaotic systems for testing and applies different chaotic systems to the encryption algorithm. Moreover, the proposed algorithm is compared with the bit-level and non-bit-level image encryption algorithms proposed by other scholars in recent years, and the results show that the proposed algorithm has higher security than other algorithms. [ABSTRACT FROM AUTHOR]

The boundary element method (BEM) employing the partial pivot adaptive cross approximation (PACA) algorithm has been observed to experience convergence failures and reduced solution accuracy when solving elasticity problems, especially at large scales. To address this issue, this paper proposes an improved algorithm for both 2D and 3D elasticity problems. Our investigations revealed that when the normal of an element is parallel to the coordinate axes and the element is in the same plane as the source point, zero entries with regular distributions will appear in the coefficient matrix. This results in the premature satisfaction of the convergence criterion of the PACA algorithm, leading to the omission of some rows and columns of the coefficient matrix. To address this issue, this paper proposes improvements to the PACA algorithm through the Coordinate Rotation Method (CRM) and the Component Traversal Method (CTM), and validates the effectiveness of these two improved methods. Furthermore, we investigate reasons behind the decrease in accuracy when employing the CTM to solve large-scale problems. We attribute this to the oscillatory nature of the estimated relative error and propose the modified PACA (M-PACA) algorithm. M-PACA not only maintains the advantages of the PACA algorithm in reducing storage space and accelerating coefficient matrix generation but also addresses its limitations, ensuring more accurate and reliable solutions for elasticity problems. [ABSTRACT FROM AUTHOR]

The fast multipole boundary element method (FMBEM) is a powerful technique for solving large-scale problems. Its effectiveness heavily relies on the iterative solver, which in turn depends crucially on the performance of the preconditioner. Although a leaf-based preconditioner has proven effective in the single domain FMBEM (SFB), it encounters challenges in the multi-domain FMBEM (MFB). To overcome this challenge, this paper proposes a cell renumbering algorithm to construct a leaf-based preconditioner for MFB. This algorithm renumbers the cells in the tree structure, taking into account the influence of the tree structure's traversal order on the coefficient matrix distribution. This renumbering enables the generation of a leaf-based preconditioner matrix for MFB, with specialized processing for sub-matrix blocks associated with the interface, accommodating both aligned and misaligned cells on both sides of the interface. In cases where the tree structure is not aligned, each interface-related submatrix may correspond to two or more leaves, resulting in a larger matrix size and increased computational cost for preconditioner calculations. To mitigate this computational burden, this paper proposes an improved cell renumbering scheme, which directly manipulates the index set to align the cell indices within the tree structure, thereby reducing computational costs. The utilization of this renumbered preconditioner in MFB not only achieves fast convergence of iterative solvers but also retains the advantages as in SFB. Through these techniques, this paper proposes a new approach to MFB. Numerical results presented in this paper demonstrate the effectiveness and universality of the proposed cell renumbering algorithm and preconditioner for MFB. [ABSTRACT FROM AUTHOR]

This paper explores the conditions for determining fixed nodes in structured networks, specifically focusing on directed acyclic graphs (DAGs). We introduce several necessary and sufficient conditions for determining fixed nodes in p -layered DAGs. This is accomplished by defining the problem of maximum disjoint stems, based on the observation that all DAGs can be represented as hierarchical structures with a unique label for each layer. For structured networks, we discuss the importance of fixed nodes by considering their controllability against the variations of network parameters. Moreover, we present an efficient algorithm that simultaneously performs labeling and fixed node search for p -layered DAGs with an analysis of its time complexity. The results presented in this paper have implications for the analysis of controllability at the individual node level in structured networks. [ABSTRACT FROM AUTHOR]

This paper creatively proposes a type of cubic fractal matrix and a new spatiotemporal chaotic system named logistic-logistic cascade coupled map lattice (L-LCCML). Furthermore, based on cubic fractal matrix and L-LCCML, this paper proposes a novel image encryption algorithm. The proposed cubic fractal matrix is three-dimensional, irregular, and self-similar. In particular, the proposed L-LCCML system adopts cascade coupling parameter to ensure the dynamic effect of coupling. Therefore, L-LCCML has excellent chaos and is suitable for information encryption. To provide a more secure approach, the proposed algorithm contains two diffusion operations, one permutation operation, and does not require multiple rounds of encryption. The diffusion operation is based on the cubic fractal matrix, which has good security and high encryption efficiency. In addition, the algorithm adopts sorting permutation based on L-LCCML, which provides good randomness for encryption. Experimental results show that the proposed algorithm has the characteristics of large key space, high sensitivity, fast encryption speed, good statistical properties of cipherd images, and etc. Therefore, the proposed algorithm is a usable alternative for practical secure communication. [ABSTRACT FROM AUTHOR]

• The initial information contribution of nodes is normalized by utilizing their degree and two network properties, and the size of the initial information contribution of nodes is adjusted with the help of a free parameter. • The average degree of the intermediate nodes between the source node and destination node is considered to achieve the global information transmission between them. • The size of the initial information contribution of nodes and three ways of information transmission are applied to construct the algorithm proposed in the paper. • The proposed algorithm has great advantage in the effectiveness, robustness, and practicability of link prediction compared with most benchmark algorithms. Many link prediction algorithms have originated from the process of information transmission between nodes in recent years. Despite these algorithms can obtain great prediction results, there may be also some limitations. For instance, the size of the initial information amount of nodes is ignored when these kinds of algorithms are constructed. Aiming at this issue, a link prediction algorithm based on the initial information contribution of nodes is proposed in this paper. First of all, the initial information contribution of nodes is quantified by utilizing some topological information around them and an adjustable parameter. In the next, three ways of bidirectional information transmission between nodes are analyzed. After that, the total information amount that received by two nodes through three ways of information transmission is applied to measure the structural similarity between them, to design the link prediction algorithm. At last, the experimental results on sixteen real-world networks demonstrate that the proposed algorithm has great advantages in effectiveness and robustness, compared with ten mainstream benchmark indices. More than that, in order to verify the application performance of the proposed algorithm in the practical scenario, our algorithm is also employed in some social domains, such as the Facebook and crime networks. [ABSTRACT FROM AUTHOR]

• Jointly consider the task dependency and edge cloud environment. • Combine deep reinforcement learning and genetic algorithm. • Generate the initial population of genetic algorithm by DQN. Edge computing can greatly decrease the delay between users and cloud servers, which can significantly improve system service performance. However, it remains challenging for more efficient scheduling and allocation of users' application demands with dependence constraints to edge cloud servers. Due to the randomness of the initial population, traditional intelligent optimization algorithms have poor convergence speed in addressing resource scheduling. Therefore, to minimize the execution time of the application, this paper proposes a hybrid algorithm to solve the resource scheduling problem with parallelism and subtask dependency. To improve the convergence speed of the algorithm, this paper makes full use of the features of deep Q networks (DQN) and genetic algorithms (GA). The initial population of GA is generated using DQN. Finally, to evaluate the effectiveness of our proposed algorithm, this paper selects three real scientific workflows for experiments. The experimental results show that the hybrid algorithm can converge quickly and improve the optimization effect in a short time. [ABSTRACT FROM AUTHOR]

This paper designs continuous-time algorithms with linear convergence for solving distributed convex optimization problems without a strongly convex condition. The proposed primal–dual algorithms operate under weight-balanced digraphs and the dual variables are not exchanged with neighbors, which makes the algorithm more efficient. To save communication resources, we propose a class of event-triggered communication (ETC) schemes, which includes static and dynamic counterparts with the latter being more effective in communication resource saving. Furthermore, using Lyapunov theory, we prove that the distributed event-triggered algorithms converge to the optimum set with exact linear convergence rates. Finally, we present a comparison example that validates the effectiveness of the proposed algorithms in reducing communication burdens. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed-time consensus of second-order multi-agent systems subject to matched and mismatched disturbances. The derivatives of disturbances are assumed to be bounded. A novel integral sliding mode-based observer is presented by utilizing the super-twisting algorithm to estimate the agent states. The estimations can achieve the convergence to the leader in a fixed time. Furthermore, the corresponding fixed-time controller is developed to make the agents converge to the estimated states. As the estimated states converge to the leader, the agents will track the leader states with the help of estimated states. In addition, the overall convergence of multi-agent systems is non-monotonic due to the disturbances. It is theoretically shown that the proposed control approach can maintain a bounded convergence and get the consensus of multi-agent systems in a fixed time. Some simulations are presented to verify the effectiveness of the proposed control protocol. [ABSTRACT FROM AUTHOR]

This paper studies the optimal three-dimensional (3D) formation circumnavigation problem for multiple unmanned aerial vehicles (UAVs) with relative measurement and an unknown moving target. First, the 3D formation circumnavigation errors under the relative measurement and directed topology, that is, the spherical enclosing along the normal direction, the latitude surrounding along the north direction, and the longitude formation along the east direction, are constructed. Then, radial basis function neural networks (RBFNNs) based adaptive estimation is designed for each UAV to approximate the unknown target velocity using relative information. Further, to achieve the optimal energy of 3D formation circumnavigation along the normal, north, and east directions with lowered data transmission cost, an event-triggered actor–critic algorithm is designed under limited neighbor and relative target information. The stability of the whole system is analyzed under continuous sampled and event sampled cases, respectively, and the Zeno phenomenon is excluded. The effectiveness is validated through simulation under cases of with and without random noise. Meanwhile, comparative simulations are performed to validate the system energy and convergence time of the proposed method in contrast with two relevant works. [ABSTRACT FROM AUTHOR]

This paper is concerned with the distributed online convex optimization problems with multiple coupled constraints over unbalanced digraphs, which are widely applied in diverse fields such as machine learning, smart grids, and resource allocation problems, etc. In such practical scenarios, multiple coupled constraints, where each coupled constraint might only contain a portion of all nodes, are more general and complex than global coupled constraints. Additionally, due to certain constraint conditions such as energy and communication limitations, each node can only exchange information with other nodes in an identical constraint. Besides, the network connectivity of practical constrained problems might not be only confined to one type of weight matrices. By adopting an augmented Lagrangian method, the multiple coupled constrained optimization problem is converted into a saddle-point problem. To tackle this problem, a novel double accelerated push–pull (DAPP) algorithm is proposed which concurrently employs row-stochastic (RS) and column-stochastic (CS) weight matrices. Specifically, each node pushes gradient information weighted by CS matrices to out-neighbors, while pulls dual variables fused by RS matrices from in-neighbors. Combined with CS matrices, the gradient tracking scheme is employed to promote the efficiency of tracking the averaged gradients. Furthermore, aiming at improving the convergence rate, the heavy-ball method is used to update both primal and dual variables. Then, rigorous theoretical results indicate that DAPP obtains the sublinear bounds of regret and constraint violation. Finally, the plug-in electric vehicles (PEVs) charging problem is utilized to demonstrate the validity of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes an improved iterative algorithm based on a Newton iterative algorithm, which is used to research the stochastic linear quadratic optimal tracking (SLQT) control for stochastic continuous-time systems. Firstly, a Newton iterative algorithm for solving stochastic algebraic Riccati equations (SAREs) is derived based on the Frechet derivative. Secondly, an improved iterative algorithm in an incremental form for indirectly solving SAREs is presented by combining the numerical iterative method with the incremental Newton iterative (INI) algorithm and introducing a tuning parameter. Under a suitable initial condition, the convergence of the improved iterative algorithm is talked over. Finally, numerical simulation experiments are carried out to compare our proposed improved iterative algorithm with some known works. The results show that the improved iterative algorithm has a faster convergence rate. [ABSTRACT FROM AUTHOR]

In this paper, the multi-physical field-circuit co-simulation method coupling the Maxwell's and drift diffusion equations is proposed for the analysis of electromagnetic energy selective surface (ESS). To alleviate the universal feature that multi-physics simulation is extremely time-consuming, the space mapping algorithm is consulted and introduced into the transient calculation process. Thus, the searches for a convergent solution in nonlinear equations are regarded as an optimization procedure, which employs the mapped equivalent model to replace the high-cost multi-physics equations calculation. This operation can considerably minimize the number of multi-physics equations that must be computed, improving analysis efficiency. The great accuracy and efficiency of the proposed method are demonstrated by numerical results. As a result, this approach is an alternative tool to examine electromagnetic-circuit systems, particularly in high-power microwave scenarios. [ABSTRACT FROM AUTHOR]

In recent years, the multitask diffusion least mean square (MD-LMS) algorithm has been extensively applied in distributed parameter estimation and target tracking of multitask network. However, its performance degrades under colored input signals or impulsive noises. To overcome these two drawbacks, this paper introduces the subband adaptive filter (SAF) into a multitask network for the first time, and a robust multitask diffusion normalized M-estimate subband adaptive filtering (MD-NMSAF) algorithm is proposed, which solves the global network optimization problem based on the modified Huber (MH) function in a distributed manner, achieves robustness to impulsive noise, and significantly improves the convergence performance of the MD-LMS algorithm. Compared with existing robust multitask diffusion affine projection algorithms (MD-APAs), the computational complexity of the proposed MD-NMSAF algorithm is greatly reduced. In addition, we analyze the mean and mean-square stability conditions of MD-NMSAF, provide theoretical models characterizing the network mean square deviation (MSD) behaviors of transient and steady-state, and further verify their correctness by computer simulations. Simulation results under different network topologies, input signals, filter lengths and impulsive noise types fully demonstrate the performance advantages of the proposed MD-NMSAF algorithm over its competitors in terms of steady-state estimation accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

Multidimensional fuzzy sets (MFS) is a new extension of fuzzy sets on which the membership values of an element in the universe of discourse are increasingly ordered vectors on the set of real numbers in the interval [ 0 , 1 ]. This paper aims to investigate fuzzy negations on the set of increasingly ordered vectors on [ 0 , 1 ] , i.e. on L ∞ ([ 0 , 1 ]) , MFN in short, with respect to some partial order. In this paper we study partial orders, giving special attention to admissible orders on L n ([ 0 , 1 ]) and L ∞ ([ 0 , 1 ]). In addition, we study the possibility of existence of strong multidimensional fuzzy negations and some properties and methods to construct such operators. In particular, we define the ordinal sums of n-dimensional negations and ordinal sums of multidimensional fuzzy negations on a multidimensional product order. A multi-attribute group decision making algorithm is presented. [ABSTRACT FROM AUTHOR]

A new fractional-order 5D hyperchaotic system based on memristor is constructed in this paper, with the speciality that the system exists chaotic and hyperchaotic states in the fractional-order case, while in periodic state in the integer-order. In addition, it has a variety of special phenomena at fractional-order such as infinite initial value range, parameter-dependent offset-boosting and amplitude control, attractor coexistence, and fractional order complexity greater than integer order. The correctness and feasibility of the system is verified by analog circuit simulation and hardware circuit implementation. Combining this system with image encryption algorithms, two new scrambling algorithms and a diffusion algorithm are proposed. And a high-quality encryption scheme that can be applied to a wide range of color images is proposed. The scheme is found to have excellent security after verification by various security analyses and comparison with other literatures. This paper provides a basis for the superiority of fractional-order chaotic systems and provides new methods in the field of image encryption. • We construct a fractional-order 5D hyperchaotic system based on memristor. • The system is chaotic only to fractional-order and has a rich and complex dynamical behavior. • We propose a possible mechanism for the generation of attractor coexistence. • Designed new encryption algorithms and proposed a new color image encryption scheme [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive security analysis on an improved chaos-based image encryption algorithm. The initial algorithm, proposed by Li et al., involves permutation related to the sum of plaintext pixel values and diffusion associated with 9 specific pixel values in the permuted image. However, a thorough analysis conducted by Liu et al. reveals two major flaws in it: firstly, the 9 specific pixel values are not involved in the diffusion process; secondly, the permutation method exhibits significant vulnerabilities. In response to these shortcomings, Liu et al. proposed targeted improvements on it, which include incorporating a permutation step for the 9 specific pixels and enhancing the original permutation method. In this study, we analyze the improved algorithm and discover that it still possesses security vulnerabilities, rendering it susceptible to chosen-plaintext attack. By constructing three categories of special plaintexts, one can decipher the equivalent permutation and diffusion. Theoretical analysis and experimental results provide strong evidence for the effectiveness of our analysis in this paper. [ABSTRACT FROM AUTHOR]

Comparative view of the cost function when using the GWO, GD, and PSO algorithms. [Display omitted] • A Policy Iteration Reinforcement Learning-based control approach is proposed. • A Grey Wolf Optimizer algorithm trains the policy neural network. • A comparison with classical Gradient Descent and metaheuristic PSO is offered. • The validation is done on real-time nonlinear servo system position control. • The fast convergence of the suggested approach is proved. This paper presents a new Reinforcement Learning (RL)-based control approach that uses the Policy Iteration (PI) and a metaheuristic Grey Wolf Optimizer (GWO) algorithm to train the Neural Networks (NNs). Due to an efficient tradeoff to exploration and exploitation, the GWO algorithm shows good results in NN training and solving complex optimization problems. The proposed approach is compared to the classical PI RL-based control approach using the Gradient Descent (GD) algorithm, and with the RL-based control approach which uses the metaheuristic Particle Swarm Optimization (PSO) algorithm. The experiments are conducted using a nonlinear servo system laboratory equipment. Each approach evaluated on how well it solves the optimal reference tracking control for an experimental servo system position control system. The policy NNs specific to all three approaches are implemented as state feedback with integrator controllers to remove the steady-state control errors and thus ensure the convergence of the objective function. Because of the random nature of metaheuristic algorithms, the experiments for GWO and PSO algorithms are run multiple times and the results are averaged before the conclusions are presented. The experimental results shows that for the control objective considered in this paper, the GWO algorithm represents a better solution compared to GD and PSO algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a chaotic strategy-based quadratic opposition-based learning adaptive variable-speed whale optimization algorithm is proposed. The improved algorithm is used to solve the problems that the whale optimization algorithm's convergence accuracy and convergence speed are insufficient. Firstly, the proposed algorithm is initialized by a method based on chaotic maps and quadratic opposition-based learning strategy to obtain a population with better ergodicity. Secondly, by introducing an adaptive variable speed adjustment factor, each search link unites to form a negative feedback regulation network, thereby effectively balancing the algorithm's exploration ability and exploitation ability. Finally, 20 benchmark test functions and 3 complex constrained engineering optimization problems were used to conduct extensive tests on the improved algorithm. The results show that the improved algorithm has better performance than others in terms of convergence speed and convergence accuracy in a majority of cases, and can effectively jump out of the local optimum. [Display omitted] • Firstly, this paper proposed a quadratic Opposition-Base Learning strategy based on Bernoulli map, and successfully obtained a higher quality initial whale population. • Secondly, this paper proposed a new variable speed adjustment factor and a cooperative convergence factor, and combine them with individual fitness to form a negative feedback adjustment network. Experiments show that the algorithm has good self-adjusting ability. • Finally, the range of some of the original random numbers in whale optimization algorithm has been changed. This adjustment allows the algorithm to have a more variable search range. [ABSTRACT FROM AUTHOR]

In this paper, we study structures such as distributive lattices, distributive semilattices, and median graphs from an algorithmic point of view. Such structures are very useful in classification and phylogeny for representing lineage relationships for example. A distributive lattice can be considered as a median graph while a distributive ∨-semilattice can be considered as a median graph provided that some conditions holding on triple of elements are satisfied. Starting from a lattice structure with different representations, we study the problem of building a median graph from such structures. We make precise and propose algorithms for checking how a lattice can be distributive and can be a median graph. Then, we adapt the problem to semilattices as a lattice where the bottom element is removed is a ∨-semilattice. We also state the problem in terms of Formal Concept Analysis and the representation of a lattice as a formal context, i.e., a binary table. Moreover, we also propose as input a system of implications such as the Duquenne-Guigues basis of a lattice, and we study how to compute such a basis for a distributive semilattice. In the paper, we provide algorithms and examples which illustrate the difficulties related to these different classification tasks. In particular, the minimality of the output lattices is a condition which is hard to ensure and which cannot be always achieved. [ABSTRACT FROM AUTHOR]

Distributed coordination of multi-agent systems (MASs) has been investigated for many years, and fractional-order calculus has been proved that it can model the dynamics more accurately in certain circumstances. Hence, in this paper, combining the above two aspects, the distributed coordination of fractional-order MASs (FOMASs) is researched, which is a promising topic. Besides, in this paper, the uncertainty, inherent nonlinearity and external disturbances are taken into consideration, aiming at achieving the robust consensus tracking. In particular, the uncertain parameters will be identified from an optimization perspective using artificial bee colony algorithm (ABC). Firstly, to ameliorate the performance of the standard ABC, a hybrid ABC (hABC) incorporating two groups of searching mechanisms is designed, it facilitates the identification of unknown parameters. After obtaining the identified parameters, an efficient distributed nonlinear controller is raised to fulfill the robust consensus tracking. Finally, experiments prove that the designed parameters identification approach can successfully estimate the uncertain parameters with high accuracy, besides the designed control algorithm can robustly control the FOMASs. [ABSTRACT FROM AUTHOR]

This paper suggests a new hybrid algorithm by integrating two population-based algorithms: Whale Optimization Algorithm (WOA) and Flower Pollination Algorithm (FPA), to solve complex nonlinear systems and unconstrained optimization problems. WOFPA denotes the suggested algorithm, a hybrid Whale Optimization Algorithm and Flower Pollination Algorithm. Nonlinear systems can be cast into unconstrained optimization problems, called merit functions, where the optimal solutions for the merit functions are equivalent to the solutions of nonlinear systems. WOFPA aims to decrease the execution time and the complexity of WOA and FPA. WOFPA has the advantages of WOA and FPA; WOFPA is a high-quality algorithm to solve both problems, nonlinear systems and unconstrained optimization problems. For example, FPA may have a premature convergence in the local optima, and WOFPA subdues the disadvantage of FPA. Numerical experiments of 14 benchmarks nonlinear systems and 30 CEC 2014 benchmarks unconstrained optimization functions with various dimensions are employed to test the performance of WOFPA. To have a further investigation for the performance of WOFPA, WOFPA is compared with WOA, FPA, and other existing algorithms from the literature. Two non-parametric statistical tests, Wilcoxon statistical test and the Friedman test, are conducted for this study to check the performance of the proposed algorithms and other compared algorithms and the significance of our results. The experiment results demonstrate that WOFPA performs better than other algorithms in the literature by getting the optimum solutions for most nonlinear systems and optimization problems and proves its efficiency compared with other existing algorithms. • This paper proposes a new hybridization Whale Optimization Algorithm and Flower Pollination Algorithm. • We solve system of nonlinear equations and unconstrained optimization problem. • The efficiency and effectiveness of our algorithm are provided. • Experimental results prove the superiority of our algorithm over the state-of-the-arts. [ABSTRACT FROM AUTHOR]

In a previous paper based on the interpolation finite difference method, a calculation system was shown for calculating 1D (one-dimensional) Laplace's equation and Poisson's equation using high-order difference schemes. Finite difference schemes, from the usual second-order to tenth-order differences, including odd number order differences, were systematically and instantaneously derived over equally/unequally spaced grid points based on the Lagrange interpolation function. Using the direct method with the band diagonal matrix algorithm, 1D Poisson equations were numerically calculated under double precision floating arithmetic, but it became clear that high accurate calculations could not be secured in high-order differences because "digit-loss errors" caused by the finite precision of computations occurred in the calculations when using the high-order differences. The double precision calculation corresponds to 15 (significant) digit calculation. In this paper, we systematically investigate how the calculation accuracy changes by high precision calculations (30-digit, and 45-digit calculations). Under 45-digit calculation, where the digit-loss error can be almost ignored, the high-order differences enable extremely high-accurate calculations. [ABSTRACT FROM AUTHOR]

The paper deals with online distributed convex optimization over a multi-agent network, where a swarm of agents attempts to minimize coordinately a sequence of time-changing global loss functions. At per time slot, the global loss function is decomposed into a sum of several local loss functions, each of which is available sequentially and held privately by one agent over the network, and individual agent does not possess prior knowledge of the future global loss function. We are interested in a bandit setting, where only the values of local loss functions at queried points are disclosed to individual agent. Meanwhile, we consider a general multi-agent network where the agents' communication is represented as a sequence of time-changing unbalanced digraphs and the corresponding weight matrices are only row stochastic. We investigate two bandit scenarios including one- and two-point bandit feedback, and then design two corresponding online distributed bandit algorithms for such a class of problems by exploiting the classical dual averaging method. We show that both algorithms can achieve the sub-linear expected dynamic regret provided that the accumulative variation of the benchmark sequence grows sub-linearly with time. In particular, the bounds of the expected static regret obtained in this paper can reduce the relevant results when restricted to the centralized bandit online convex optimization. In contrast to existing algorithms with gradient feedback, numerical tests verify the competitive performances of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper develops a novel insight and procedure that includes a variety of algorithms for finding the best solution in a structured multi-agent system with internal communications and a global purpose. In other words, it finds the optimal communication structure among agents and the optimal policy in this structure. First, a unique reinforcement learning algorithm is proposed to find the optimal policy of each agent in a fixed structure with non-linear function approximators like artificial neural networks (ANN) and with eligibility traces. Secondly, a mechanism is presented to perform self-organization based on the information of the learned policy. Finally, an algorithm that can discover an appropriate inter-structure mapping and then can transfer the previous knowledge to the new structure is developed, which increases the speed of the learning in this new environment after self-organization. This paper is one of the first works that analyzes the problem fully theoretically and devises some algorithms to find the best solution. We use a simplified version of the distributed task allocation problem (DTAP) as our case study. The experimental results verify the stability of our approach and show the high speed of finding the optimal solution as a result of using transfer learning. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a specific type of quasilinear boundary value problem with Dirichlet boundary conditions and with p -Laplacian. We show two ways of proving the existence of nontrivial weak solutions. The first one uses the mountain pass theorem, the other one is based on our new minimax theorem. This method is novel even for p = 2. In the paper, we also present a numerical algorithm based on the introduced approach. The suggested algorithm is illustrated on numerical examples and compared with a current approach to demonstrate its efficiency. [ABSTRACT FROM AUTHOR]

Temporal graphs are graphs whose edges are associated with timestamps. Subgraph matching on temporal graphs retrieves temporal subgraphs whose edge timestamps satisfy user-specified temporal orders. In this paper, a temporal query pattern is composed of a query graph with an arbitrary structure and a partial order on the edge set of the query graph. Moreover, the time span between the minimum and the maximum edge timestamps in a matching is required to be less than or equal to a specified threshold. This paper proposes a temporal subgraph matching algorithm based on two key techniques. First, a memory-efficient index structure called TO-tree is designed to compactly store all necessary information required for finding all temporal subgraph matchings. The TO-tree constructed for a temporal query pattern is much smaller than the temporal graph because unnecessary information is mostly excluded from the TO-tree by three powerful filters. The second technique is a temporal subgraph matching enumeration method that runs on the TO-tree instead of on the temporal graph. This enumeration method expands temporal subgraph matchings in an edge-by-edge manner. Since the TO-tree can fit into the main memory, the enumeration method runs very fast on the TO-tree. An extensive experimental evaluation has been carried out. The experimental results show that the TO-tree index structure is memory-efficient, which in turn enables a fast temporal subgraph matching enumeration. Overall, our algorithm is at least 3X faster than the baseline algorithm adapted from the state-of-the-art non-temporal subgraph matching algorithm CECI and is at least 4X faster than the temporal subgraph matching algorithm HASSE. [ABSTRACT FROM AUTHOR]

• Formulate a problem on three-way concept lattice incremental construction. • Develop AE/OE concept lattices incremental construction algorithms. • Use 3WCA to explore the knowledge discovery of social networks. Three-way concept analysis (3WCA), a combination of three-way decision and formal concept analysis, is widely used in the field of knowledge discovery. Generally, constructing three-way concept lattices requires the original formal context and its complement context simultaneously. Additionally, the existing three-way concept lattice construction algorithms focus on the static formal context, and cannot cope with the dynamic formal context that is an essential representation in social networks. Toward this end, this paper pioneers a novel problem and method for the incremental construction of three-way concept lattice for knowledge discovery in social networks. Aiming to facilitate the construction efficiency, this paper firstly investigates the three-way concept lattice construction for attribute-incremental/object-incremental formal contexts, respectively. Then, the dynamic formal context of a social network can be viewed as a special formal context with both attribute-increment and object-increment. Further, we develop the AE/OE concept lattice incremental construction algorithms, called SNS-AE and SNS-OE. Extensive experiments are conducted on various formal contexts to evaluate the effectiveness of our incremental algorithms. The experimental results demonstrate that our proposed incremental algorithms can significantly decrease the construction time of three-way concept lattice compared to the non-incremental algorithm. [ABSTRACT FROM AUTHOR]