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In this study, we extended the applicability of a derivative-free algorithm to encompass the solution of operators that may be either differentiable or non-differentiable. Conditions weaker than the ones in earlier studies are employed for the convergence analysis. The earlier results considered assumptions up to the existence of the ninth order derivative of the main operator, even though there are no derivatives in the algorithm, and the Taylor series on the finite Euclidian space restricts the applicability of the algorithm. Moreover, the previous results could not be used for non-differentiable equations, although the algorithm could converge. The new local result used only conditions on the divided difference in the algorithm to show the convergence. Moreover, the more challenging semi-local convergence that had not previously been studied was considered using majorizing sequences. The paper included results on the upper bounds of the error estimates and domains where there was only one solution for the equation. The methodology of this paper is applicable to other algorithms using inverses and in the setting of a Banach space. Numerical examples further validate our approach. [ABSTRACT FROM AUTHOR]

Product disassembly is an effective means of waste recycling and reutilization that has received much attention recently. In terms of disassembly efficiency, the number of disassembly skills possessed by workers plays a crucial role in improving disassembly efficiency. Therefore, in order to effectively and reasonably disassemble discarded products, this paper proposes a partial parallel disassembly line balancing problem (PP-DLBP) that takes into account the number of worker skills. In this paper, the disassembly tasks and the disassembly relationships between components are described using AND–OR graphs. In this paper, a multi-objective optimization model is established aiming to maximize the net profit of disassembly and minimize the number of skills for the workers. Based on the bat algorithm (BA), we propose an improved discrete bat algorithm (IDBA), which involves designing adaptive composite optimization operators to replace the original continuous formula expressions and applying them to solve the PP-DLBP. To demonstrate the advantages of IDBA, we compares it with NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA/D. Experimental results show that IDBA outperforms the other five algorithms in real disassembly cases and exhibits high efficiency. [ABSTRACT FROM AUTHOR]

In this paper, a new full-Newton step feasible interior-point method for convex quadratic programming is presented and analyzed. The idea behind this method is to replace the complementarity condition with a non-negative weight vector and use the algebraic equivalent transformation for the obtained equation. Under the selection of appropriate parameters, the quadratic rate of convergence of the new algorithm is established. In addition, the iteration complexity of the algorithm is obtained. Finally, some numerical results are presented to demonstrate the practical performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Developing efficient path-planning algorithms is an essential topic in modern robotics and control theory. Autonomous rovers and wheeled and tracked robots require path generators that can efficiently cover the explorable space with minimal redundancy. In this paper, we present a new path-planning algorithm based on the chaotic behavior of the Courbage–Nekorkin neuron model with a coverage control parameter. Our study aims to reduce the number of iterations required to cover the chosen investigated area, which is a typical efficiency criterion for this class of algorithms. To achieve this goal, we implemented a pseudorandom bit generator (PRBG) based on a Courbage–Nekorkin chaotic map, which demonstrates chaotic behavior and successfully passes all statistical tests for randomness. The proposed PRBG generates a bit sequence that can be used to move the tracked robot in four or eight directions in an operation area of arbitrary size. Several statistical metrics were applied to evaluate the algorithm's performance, including the percentage of coverage of the study area and the uniformity of coverage. The performance of several competing path-planning algorithms was analyzed using the chosen metrics when exploring two test areas of the sizes 50 × 50 cells and 100 × 100 cells, respectively, in four and eight directions. The experimental results indicate that the proposed algorithm is superior compared to known chaotic path-planning methods, providing more rapid and uniform coverage with the possibility of controlling the covered area using tunable parameters. In addition, this study revealed the high dependence of the coverage rate on the starting point. To investigate how the coverage rate depends on the choice of chaotic map, we implemented six different PRBGs using various chaotic maps. The obtained results can be efficiently used for solving path-planning tasks in both real-life and virtual (e.g., video games) applications. [ABSTRACT FROM AUTHOR]

This paper deals with p-maxian problem on cycles with an upper bound on the distances of all facilities. We consider the case of p = 2 and show that, in the worst case, the optimal solution contains at least one vertex of the underlying cycle, which helps to develop an efficient algorithm to solve the constrained 2-maxian problem. Based on this property, we develop a linear time algorithm for the constrained 2-maxian problem on a cycle. We also discuss the relations between the constrained and unconstrained 2-maxian problems on which the underlying graphs are cycles. [ABSTRACT FROM AUTHOR]

In this paper, we present an effective method for analyzing patterns in the Russia–Ukraine war based on the Lanchester model. Due to the limited availability of information on combat powers of engaging forces, we utilize the loss of armored equipment as the primary data source. To capture the intricate dynamics of modern warfare, we partition the combat loss data into disjoint subsets by examining their geometric properties. Separate systems of ordinary differential equations for these subsets are then identified using the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm under a generalized formulation of the historical Lanchester model. We provide simulations of our method to demonstrate its effectiveness and performance in analyzing contemporary warfare dynamics. [ABSTRACT FROM AUTHOR]

The mathematical side of applied problems in multiple subject areas (biology, pattern recognition, etc.) is reduced to the problem of discrete optimization in the following mathematical method. We were provided a network and graphs in its leaves, for which we needed to find a rearrangement of graphs by non-leaf nodes, in which the given functional reached its minimum. Such a problem, even in the simplest case, is NP-hard, which means unavoidable restrictions on the network, on graphs, or on the functional. In this publication, this problem is addressed in the case of all graphs being so-called "structures", meaning directed-loaded graphs consisting of paths and cycles, and the functional as the sum (over all edges in the network) of distances between structures at the endpoints of every edge. The distance itself is equal to the minimal length of sequence from the fixed list of operations, the composition of which transforms the structure at one endpoint of the edge into the structure at its other endpoint. The list of operations (and their costs) on such a graph is fixed. Under these conditions, the given discrete optimization problem is called the reconstruction problem. This paper presents novel algorithms for solving the reconstruction problem, along with full proofs of their low error and low polynomial complexity. For example, for the network, the problem is solved with a zero error algorithm that has a linear polynomial computational complexity; and for the tree the problem is solved using an algorithm with a multiplicative error of at most two, which has a second order polynomial computational complexity. [ABSTRACT FROM AUTHOR]

The problem of the interferometric phase unwrapping in radar remote sensing of Earth systems is considered. Such interferograms are widely used in the problems of creating and updating maps of the relief of the Earth's surface in geodesy, cartography, environmental monitoring, geological, hydrological and glaciological studies, and for monitoring transport communications. Modern radar systems have ultra-high spatial resolution and a wide band, which leads to the need to unwrap large interferograms from several tens of millions of elements. The implementation of calculations by these methods requires a processing time of several days. In this paper, an effective method for equalizing the inverse vortex field for phase unwrapping is proposed, which allows solving a problem with quasi-linear computational complexity depending on the interferogram size and the number of singular points on it. To implement the method, a parallel algorithm for solving the problem on a multi-core processor using OpenMP technology was developed. Numerical experiments on radar data models were carried out to investigate the effectiveness of the algorithm depending on the size of the source data, the density of singular points and the number of processor cores. [ABSTRACT FROM AUTHOR]

In this paper, we construct a new two-grid algorithm of the finite element method for the Schrödinger equation in backward Euler and Crank–Nicolson fully discrete schemes. On the coarser grid, we solve coupled real and imaginary parts of the Schrödinger equation. On the fine grid, real and imaginary parts of the Schrödinger equation are decoupled, and we solve the elliptic equation about real and imaginary parts, respectively. Then, we obtain error estimates of the exact solution with the two-grid solution in the H 1 -norm and carry out two numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we propose an inertial parametric Douglas–Rachford splitting method for minimizing the sum of two nonconvex functions, which has a wide range of applications. The proposed algorithm combines the inertial technique, the parametric technique, and the Douglas–Rachford method. Subsequently, in theoretical analysis, we construct a new merit function and establish the convergence of the sequence generated by the inertial parametric Douglas–Rachford splitting method. Finally, we present some numerical results on nonconvex feasibility problems to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Fault detection and localization are vital for ensuring the stability of data center networks (DCNs). Specifically, adaptive fault diagnosis is deemed a fundamental technology in achieving the fault tolerance of systems. The highly scalable data center network (HSDC) is a promising structure of server-centric DCNs, as it exhibits the capacity for incremental scalability, coupled with the assurance of low cost and energy consumption, low diameter, and high bisection width. In this paper, we first determine that both the connectivity and diagnosability of the m-dimensional complete HSDC, denoted by H S D C m (m) , are m. Further, we propose an efficient adaptive fault diagnosis algorithm to diagnose an H S D C m (m) within three test rounds, and at most N + 4 m (m − 2) tests with m ≥ 3 (resp. at most nine tests with m = 2 ), where N = m · 2 m is the total number of nodes in H S D C m (m) . Our experimental outcomes demonstrate that this diagnosis scheme of HSDC can achieve complete diagnosis and significantly reduce the number of required tests. [ABSTRACT FROM AUTHOR]

Variable (feature) selection plays an important role in data analysis and mathematical modeling. This paper aims to address the significant lack of formal evaluation benchmarks for feature selection algorithms (FSAs). To evaluate FSAs effectively, controlled environments are required, and the use of synthetic datasets offers significant advantages. We introduce a set of ten synthetically generated datasets with known relevance, redundancy, and irrelevance of features, derived from various mathematical, logical, and geometric sources. Additionally, eight FSAs are evaluated on these datasets based on their relevance and novelty. The paper first introduces the datasets and then provides a comprehensive experimental analysis of the performance of the selected FSAs on these datasets including testing the FSAs' resilience on two types of induced data noise. The analysis has guided the grouping of the generated datasets into four groups of data complexity. Lastly, we provide public access to the generated datasets to facilitate bench-marking of new feature selection algorithms in the field via our Github repository. The contributions of this paper aim to foster the development of novel feature selection algorithms and advance their study. [ABSTRACT FROM AUTHOR]

The problem of information security and copyright protection of video is becoming increasingly prominent. The current video watermarking algorithm does not have strong anti-compression, which has a significant impact on the visual effect of video. To solve this problem, this paper proposes a video watermarking algorithm based on H.264/AVC. The algorithm combines the non-zero quantization coefficient and the energy factor to select the appropriate chroma subblock, and then an optimized modulation is designed to embed the watermark into its DCT quantization coefficients in order to minimize the number of modifications of the subblocks. The invisibility and robustness experiments of the algorithm are conducted in the paper, and the Structural Similarity Indexes are above 0.99, and the False Bit Rates are all below 0.03. The results show that the algorithm has good invisibility, anti-compression performance and obvious advantages compared with other similar methods. [ABSTRACT FROM AUTHOR]

Path-planning research has been the key to mobile-robot-navigation technology. However, traditional path-planning algorithms have some shortcomings. To solve these problems, this paper proposes a fusion algorithm that combines the kinematical constrained A* algorithm with the Dynamic Window Approach (DWA) algorithm. The kinematical constrained A* algorithm can plan the global path, and then the DWA algorithm can plan the local path under the global path's guidance. Firstly, combined with robot kinematics, we improve the node-expansion method and heuristic-function model of the A* algorithm, which improves the search efficiency, reduces the number of path bends and lowers the computational cost so that the path generated by the A* algorithm better meets the needs of robot motion. Secondly, we optimize the trajectory-evaluation function of the DWA algorithm so that the local paths planned by the DWA algorithm are smoother and more coherent, which is easier for robot-motion execution. Finally, we extract the key nodes from the global path planned by the A* algorithm to guide the DWA algorithm for local path planning and dynamic-obstacle avoidance and to make the local path closer to the global path. Through simulation and practical experiments, the effectiveness of the fusion algorithm proposed in this paper is verified. [ABSTRACT FROM AUTHOR]

This paper proposes a road crack detection algorithm based on an improved SparseInst network, called the SparseInst-CDSM algorithm, aimed at solving the problems of low recognition accuracy and poor real-time detection of existing algorithms. The algorithm introduces the CBAM module, DCNv2 convolution, SPM strip pooling module, MPM mixed pooling module, etc., effectively improving the integrity and accuracy of crack recognition. At the same time, the central axis skeleton of the crack is extracted using the central axis method, and the length and maximum width of the crack are calculated. In the experimental comparison under the self-built crack dataset, SparseInst-CDSM has an accuracy of 93.66%, a precision of 67.35%, a recall of 66.72%, and an IoU of 84.74%, all higher than mainstream segmentation models such as Mask-RCNN and SOLO that were compared, reflecting the superiority of the algorithm proposed in this paper. The comparison results of actual measurements show that the algorithm error is within 10%, indicating that it has high effectiveness and practicality. [ABSTRACT FROM AUTHOR]

Community structure is a significant characteristic of complex networks, and community detection has valuable applications in network structure analysis. Non-negative matrix factorization (NMF) is a key set of algorithms used to solve the community detection issue. Nevertheless, the localization of feature vectors in the adjacency matrix, which represents the characteristics of complex network structures, frequently leads to the failure of NMF-based approaches when the data matrix has a low density. This paper presents a novel algorithm for detecting sparse network communities using non-negative matrix factorization (NMF). The algorithm utilizes local feature vectors to represent the original network topological features and learns regularization matrices. The resulting feature matrices effectively reveal the global structure of the data matrix, demonstrating enhanced feature expression capabilities. The regularized data matrix resolves the issue of localized feature vectors caused by sparsity or noise, in contrast to the adjacency matrix. The approach has superior accuracy in detecting community structures compared to standard NMF-based community detection algorithms, as evidenced by experimental findings on both simulated and real-world networks. [ABSTRACT FROM AUTHOR]

To address the drawbacks of the slow convergence speed and lack of individual information exchange in the cuckoo search (CS) algorithm, this study proposes an improved cuckoo search algorithm based on a sharing mechanism (ICSABOSM). The enhanced algorithm reinforces information sharing among individuals through the utilization of a sharing mechanism. Additionally, new search strategies are introduced in both the global and local searches of the CS. The results from numerical experiments on four standard test functions indicate that the improved algorithm outperforms the original CS in terms of search capability and performance. Building upon the improved algorithm, this paper introduces a numerical solution approach for differential equations involving the coupling of function approximation and intelligent algorithms. By constructing an approximate function using Fourier series to satisfy the conditions of the given differential equation and boundary conditions with minimal error, the proposed method minimizes errors while satisfying the differential equation and boundary conditions. The problem of solving the differential equation is then transformed into an optimization problem with the coefficients of the approximate function as variables. Furthermore, the improved cuckoo search algorithm is employed to solve this optimization problem. The specific steps of applying the improved algorithm to solve differential equations are illustrated through examples. The research outcomes broaden the application scope of the cuckoo optimization algorithm and provide a new perspective for solving differential equations. [ABSTRACT FROM AUTHOR]

The phenomenon of missing data can be seen everywhere in reality. Most typical attribute reduction models are only suitable for complete systems. But for incomplete systems, we cannot obtain the effective reduction rules. Even if there are a few reduction approaches, the classification accuracy of their reduction sets still needs to be improved. In order to overcome these shortcomings, this paper first defines the similarities of intra-cluster objects and inter-cluster objects based on the tolerance principle and the mechanism of knowledge granularity. Secondly, attributes are selected on the principle that the similarity of inter-cluster objects is small and the similarity of intra-cluster objects is large, and then the knowledge granularity attribute model is proposed under the background of clustering; then, the IKAR algorithm program is designed. Finally, a series of comparative experiments about reduction size, running time, and classification accuracy are conducted with twelve UCI datasets to evaluate the performance of IKAR algorithms; then, the stability of the Friedman test and Bonferroni–Dunn tests are conducted. The experimental results indicate that the proposed algorithms are efficient and feasible. [ABSTRACT FROM AUTHOR]

This paper introduces novel enhancements to the most recent versions of DIRECT-type algorithms, especially when dealing with solutions located at the hyper-rectangle vertices. The BIRECT algorithm encounters difficulties in efficiently sampling points at the boundaries of the feasible region, leading to potential slowdowns in convergence. This issue is particularly pronounced when the optimal solution resides near the boundary. Our research explores diverse approaches, with a primary focus on incorporating a grouping strategy for hyper-rectangles of similar sizes. This categorization into different classes, constrained by a predefined threshold, aims to enhance computational efficiency, particularly involving a substantial number of hyper-rectangles of varying sizes. To further improve the new algorithm's efficiency, we implemented a mechanism to prevent oversampling and mitigate redundancy in sampling at shared vertices within descendant sub-regions. Comparisons with several DIRECT-type algorithms highlight the promising nature of the proposed algorithms as a global optimization solution. Statistical analyses, including Friedman and Wilcoxon tests, demonstrated the effectiveness of the improvements introduced in this new algorithm. [ABSTRACT FROM AUTHOR]

The multi-objective evolutionary algorithm optimization (MOEA) is a challenging but critical approach for tackling complex data analysis problems. However, prevailing MOEAs often rely on single strategies to obtain optimal solutions, leading to concerns such as premature convergence and insufficient population diversity, particularly in high-dimensional data scenarios. In this paper, we propose a novel adversarial population generation algorithm, APG-SMOEA, which synergistically combines the benefits of MOEAs and Generative Adversarial Networks (GANs) to address these limitations. In order to balance the efficiency and quality of offspring selection, we introduce an adaptive population entropy strategy, which includes control parameters based on population entropy and a learning pool for storing and retrieving optimal solutions. Additionally, we attempt to alleviate the training complexity and model collapse problems common in GANs with APG-SMOEA. Experimental results on benchmarks demonstrate that the proposed algorithm is superior to the existing algorithms in terms of solution quality and diversity of low-dimensional or high-dimensional complex data. [ABSTRACT FROM AUTHOR]

Nonstationary fuzzy inference systems (NFIS) are able to tackle uncertainties and avoid the difficulty of type-reduction operation. Combining NFIS and neural network, a first-order sparse TSK nonstationary fuzzy neural network (SNFNN-1) is proposed in this paper to improve the interpretability/translatability of neural networks and the self-learning ability of fuzzy rules/sets. The whole architecture of SNFNN-1 can be considered as an integrated model of multiple sub-networks with a variation in center, variation in width or variation in noise. Thus, it is able to model both "intraexpert" and "interexpert" variability. There are two techniques adopted in this network: the Mean Shift-based fuzzy partition and the Group Lasso-based rule selection, which can adaptively generate a suitable number of clusters and select important fuzzy rules, respectively. Quantitative experiments on six UCI datasets demonstrate the effectiveness and robustness of the proposed model. [ABSTRACT FROM AUTHOR]

For nonlinear discrete systems with dual unknown inputs, there are many limitations regarding previous nonlinear filters. This paper proposes two new, improved square-root cubature Kalman filtering (ISRCKF) algorithms to estimate system states and dual unknown inputs. Improved square-root cubature Kalman filtering 1 (ISRCKF1) introduces an innovation that first obtains the unknown input estimates from the measurement equation, then updates the innovation to derive the unknown input estimates from the state equation, then uses the already obtained estimates of the dual unknown inputs to correct the one-step estimate of the state, and finally the minimum variance unbiased estimate of the state is obtained. Improved square-root cubature Kalman filtering 2 (ISRCKF2) builds a unified innovation feedback model, then applies the minimum variance unbiased estimation (MVUE) criterion to obtain the estimates of system states and dual unknown inputs, refining a more concise recursive filter but requiring stronger assumptions. Finally, simulation results demonstrate that the above two algorithms can achieve the optimal estimates of system states and dual unknown inputs simultaneously, and ISRCKF2 further enhances the accuracy of both state and dual unknown inputs estimation, which verifies the validity of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In rough set theory, a construct is an attribute subset with the same ability to discern objects belonging to different classes as the whole set of attributes, while maintaining the similarity between objects belonging to the same class. Although algorithms for reducts computation can be adapted to compute constructs, practical problems exist where these algorithms cannot compute all constructs within a reasonable time frame. Therefore, this paper introduces an algorithm for computing all constructs of a decision system. The results of experiments with various decision systems (both artificial and real-world) suggest that our algorithm is, in most cases, faster than the state-of-the-art algorithms when the simplified binary discernibility–similarity matrix has a density of less than 0.29. [ABSTRACT FROM AUTHOR]

Hybrid approaches combining machine learning with traditional inverse problem solution methods represent a promising direction for the further development of inverse modeling algorithms. The paper proposes an approach to emission source identification from measurement data for advection–diffusion–reaction models. The approach combines general-type source identification and post-processing refinement: first, emission source identification by measurement data is carried out by a sensitivity operator-based algorithm, and then refinement is done by incorporating a priori information about unknown sources. A general-type distributed emission source identified at the first stage is transformed into a localized source consisting of multiple point-wise sources. The second, refinement stage consists of two steps: point-wise source localization and emission rate estimation. Emission source localization is carried out using deep learning with convolutional neural networks. Training samples are generated using a sensitivity operator obtained at the source identification stage. The algorithm was tested in regional remote sensing emission source identification scenarios for the Lake Baikal region and was able to refine the emission source reconstruction results. Hence, the aggregates used in traditional inverse problem solution algorithms can be successfully applied within machine learning frameworks to produce hybrid algorithms. [ABSTRACT FROM AUTHOR]

To achieve a fundamental reduction in the carbon emissions associated with grinding machines, it is imperative to systematically explore low-carbon considerations in the design phase. The spindle is a significant contributor to carbon emissions in grinding machines, and an effective approach for reducing carbon emissions is the structural optimization of the spindle. Most of the current optimization methods aim at improving processability without considering the reduction of carbon emissions. In this context, the present study addresses the issue of carbon emissions within the spindle design phase. Initially, the determination of the spindle's carbon emissions function and the selection of the optimization objective were undertaken. The structural factors that have a significant influence on the optimization objective were identified as optimization variables. Subsequently, the optimization objective function was established through the application of the fitting method. Finally, the proposed model was refined through the utilization of an enhanced whale algorithm. The findings indicate an 8.22% reduction in carbon emissions associated with the spindle, accompanied by marginal enhancements in both static and dynamic spindle performance. The concluding section of this paper deliberates on the impact of structural parameters on the specified objectives, thereby providing insights for the optimal design of the spindle. [ABSTRACT FROM AUTHOR]

In recent years, a pronounced transition to the exploitation of renewable energy sources has be observed worldwide, driven by current climate concerns and the scarcity of conventional fuels. However, this paradigm shift is accompanied by new challenges for existing power systems. Therefore, the hosting capacity must be exhaustively assessed in order to maximize the penetration of distributed generation while mitigating any adverse impact on the electrical grid in terms of voltage and the operational boundaries of the equipment. In this regard, multiple aspects must be addressed in order to maintain the proper functioning of the system following the new installations' capacities. This paper introduces a sequential methodology designed to determine the maximum hosting capacity of a power system through the optimal allocation of both active and reactive power. To achieve this goal, an Improved Salp Swarm Algorithm is proposed, aiming to establish the appropriate operational planning of the power grid considering extensive distributed generation integration, while still ensuring a safe operation. The case study validates the relevance of the proposed model, demonstrating a successful enhancement of hosting capacity by 14.5% relative to standard models. [ABSTRACT FROM AUTHOR]

Given the challenges associated with accurately modeling complex nonlinear systems with time delays in industrial processes, this paper introduces an advanced model-free control algorithm that combines data-driven and model-driven approaches. Initially, an enhanced algorithm for multi-innovation model-free control, incorporating error feedback, is presented based on the error feedback principle. Subsequently, a novel control strategy is introduced by delving into PID neural network (NN) recognition and control theory, merging PID NN control with multi-innovation feedback control. Through meticulous mathematical derivation, the proposed strategy is proven to ensure system stability. Compared with traditional NN PID controllers, the convergence rate of the proposed scheme is 50 s faster and the steady-state errors are limited to ±1. [ABSTRACT FROM AUTHOR]

In this paper, based on the mixed Gibbs sampling algorithm, a Bayesian estimation procedure is proposed for a new Pareto-type distribution in the case of complete and type II censored samples. Simulation studies show that the proposed method is consistently superior to the maximize likelihood estimation in the context of small samples. Also, an analysis of some real data is provided to test the Bayesian estimation. [ABSTRACT FROM AUTHOR]

Binary codes have a special place in coding theory since they are one of the most commonly used in practice. There are classes of codes specific only to the binary case. One such class is self-complementary codes. Self-complementary linear codes are binary codes that, together with any vector, contain its complement as well. This paper is about binary linear self-complementary codes. A natural goal in coding theory is to find a linear code with a given length n and dimension k such that the minimum distance d is maximal. Codes with these properties are called optimal. Another important issue is classifying the optimal codes, i.e., finding exactly one representative of each equivalence class. In some sense, the classification problem is more general than the minimum distance bounds problem. In this work, we summarize the classification results for self-complementary codes with the maximum possible minimum distance and a length of up to 20. For the classification, we developed a new algorithm that is much more efficient compared to existing ones in some cases. [ABSTRACT FROM AUTHOR]

The presence of nonignorable missing response variables often leads to complex conditional distribution patterns that cannot be effectively captured through mean regression. In contrast, quantile regression offers valuable insights into the conditional distribution. Consequently, this article places emphasis on the quantile regression approach to address nonrandom missing data. Taking inspiration from fractional imputation, this paper proposes a novel smoothed quantile regression estimation equation based on a sampling importance resampling (SIR) algorithm instead of nonparametric kernel regression methods. Additionally, we present an augmented inverse probability weighting (AIPW) smoothed quantile regression estimation equation to reduce the influence of potential misspecification in a working model. The consistency and asymptotic normality of the empirical likelihood estimators corresponding to the above estimating equations are proven under the assumption of a correctly specified parameter working model. Furthermore, we demonstrate that the AIPW estimation equation converges to an IPW estimation equation when a parameter working model is misspecified, thus illustrating the robustness of the AIPW estimation approach. Through numerical simulations, we examine the finite sample properties of the proposed method when the working models are both correctly specified and misspecified. Furthermore, we apply the proposed method to analyze HIV—CD4 data, thereby exploring variations in treatment effects and the influence of other covariates across different quantiles. [ABSTRACT FROM AUTHOR]

In the paper, we consider a generalization of the classical assignment problem, which is called the constrained assignment problem with bounds and penalties (CA-BP). Specifically, given a set of machines and a set of independent jobs, each machine has a lower and upper bound on the number of jobs that can be executed, and each job must be either executed on some machine with a given processing time or rejected with a penalty that we must pay for. No job can be executed on more than one machine. We aim to find an assignment scheme for these jobs that satisfies the constraints mentioned above. The objective is to minimize the total processing time of executed jobs as well as the penalties from rejected jobs. The CA-BP is related to some practical applications such as edge computing, which involves selecting tasks and processing them on the edge servers of an internet network. As a result, a motivation of this study is to improve the efficiency of internet networks by limiting the lower bound of the number of objects processed by each edge server. Our main contribution is modifying the previous network flow algorithms to satisfy the lower capacity constraints, for which we design two exact combinatorial algorithms to solve the CA-BP. Our methodologies and results bring novel perspectives into other research areas related to the assignment problem. [ABSTRACT FROM AUTHOR]

Conceptual distance refers to the degree of proximity between two concepts within a conceptualization. It is closely related to semantic similarity and relationships, but its measurement strongly depends on the context of the given concepts. DIS-C represents an advancement in the computation of semantic similarity/relationships that is independent of the type of knowledge structure and semantic relations when generating a graph from a knowledge base (ontologies, semantic networks, and hierarchies, among others). This approach determines the semantic similarity between two indirectly connected concepts in an ontology by propagating local distances by applying an algorithm based on the All Pairs Shortest Path (APSP) problem. This process is implemented for each pair of concepts to establish the most effective and efficient paths to connect these concepts. The algorithm identifies the shortest path between concepts, which allows for an inference of the most relevant relationships between them. However, one of the critical issues with this process is computational complexity, combined with the design of APSP algorithms, such as Dijkstra, which is n 3 . This paper studies different alternatives to improve the DIS-C approach by adapting approximation algorithms, focusing on Dijkstra, pruned Dijkstra, and sketch-based methods, to compute the conceptual distance according to the need to scale DIS-C to analyze very large graphs; therefore, reducing the related computational complexity is critical. Tests were performed using different datasets to calculate the conceptual distance when using the original version of DIS-C and when using the influence area of nodes. In situations where time optimization is necessary for generating results, using the original DIS-C model is not the optimal method. Therefore, we propose a simplified version of DIS-C to calculate conceptual distances based on centrality estimation. The obtained results for the simple version of DIS-C indicated that the processing time decreased 2.381 times when compared to the original DIS-C version. Additionally, for both versions of DIS-C (normal and simple), the APSP algorithm decreased the computational cost when using a two-hop coverage-based approach. [ABSTRACT FROM AUTHOR]

This paper presents a method for unsupervised classification of entities by a group of agents with unknown domains and levels of expertise. In contrast to the existing methods based on majority voting ("wisdom of the crowd") and their extensions by expectation-maximization procedures, the suggested method first determines the levels of the agents' expertise and then weights their opinions by their expertise level. In particular, we assume that agents will have relatively closer classifications in their field of expertise. Therefore, the expert agents are recognized by using a weighted Hamming distance between their classifications, and then the final classification of the group is determined from the agents' classifications by expectation-maximization techniques, with preference to the recognized experts. The algorithm was verified and tested on simulated and real-world datasets and benchmarked against known existing algorithms. We show that such a method reduces incorrect classifications and effectively solves the problem of unsupervised collaborative classification under uncertainty, while outperforming other known methods. [ABSTRACT FROM AUTHOR]

Addressing contemporary challenges in computed tomography (CT) demands precise and efficient reconstruction. This necessitates the optimization of CT methods, particularly by improving the algorithmic efficiency of the most computationally demanding operators—forward projection and backprojection. Every measurement setup requires a unique pair of these operators. While fast algorithms for calculating forward projection operators are adaptable across various setups, they fall short in three-dimensional scanning scenarios. Hence, fast algorithms are imperative for backprojection, an integral aspect of all established reconstruction methods. This paper introduces a general method for the calculation of backprojection operators in any measurement setup. It introduces a versatile method for transposing summation-based algorithms, which rely exclusively on addition operations. The proposed approach allows for the transformation of algorithms designed for forward projection calculation into those suitable for backprojection, with the latter maintaining asymptotic algorithmic complexity. Employing this method, fast algorithms for both forward projection and backprojection have been developed for the 2D few-view parallel-beam CT as well as for the 3D cone-beam CT. The theoretically substantiated complexity values for the proposed algorithms align with their experimentally derived estimates. [ABSTRACT FROM AUTHOR]

This paper provides a real application of a popular swarm-intelligence optimisation method. The aim is to analyse the efficiency of various settings of the marine predator algorithm (MPA). Four crucial numerical parameters of the MPA are statistically analysed to propose the most efficient setting for solving engineering problems. Besides population size, particle velocity parameter P, Lévy flight parameter β , and fish aggregating device (FAD) probabilities are studied. Finally, 193 various settings, including fixed values and dynamic changes of the MPA parameters, are experimentally compared when solving 13 engineering problems. Standard statistical approaches are employed to highlight significant differences in various MPA settings. The setting of two MPA parameters (P, FADs) significantly influences MPA performance. Three newly proposed MPA settings outperform the original variant significantly. The best results provide the MPA variant with the dynamic linear change of P from 0.5 to 0. These parameters influence the velocity of prey and predator individuals in all three stages of the MPA search process. Decreasing the value of P showed that decreasing the velocity of individuals during the search provides good performance. Further, lower efficiency of the MPA with higher FAD values was detected. It means that more occasional use of fish aggregating devices (FADs) can increase the solvability of engineering problems. Regarding population size, lower values ( N = 10 ) provided significantly better results compared with the higher values ( N = 500 ). [ABSTRACT FROM AUTHOR]

In this paper, we study the solution of a singularly perturbed inhomogeneous mixed problem on the half-axis for the Schrödinger equation in the presence of a "strong" turning point for the limit operator on time interval that do not contain focal points. Based on the ideas of the regularization method for asymptotic integration of problems with an unstable spectrum, it is shown how regularizing functions should be constructed for this type of singularity. The paper describes in detail the formalism of the regularization method, justifies the algorithm, constructs an asymptotic solution of any order in a small parameter, and proves a theorem on the asymptotic convergence of the resulting series. [ABSTRACT FROM AUTHOR]

In the face of problems such as information overload and the information cocoon resulting from big data, it is a key point of current research to solve the problem of semantic fuzziness of online reviews and improve the accuracy of personalized recommendation algorithms by using online reviews. Based on the advantage of the probabilistic language term set to deal with fuzzy information and the historical data of online hotel reviews, this paper proposes a collaborative filtering recommendation algorithm for hotels. Firstly, the text data of hotel online reviews are crawled by a crawler and processed by jieba and TF-IDF tools. Secondly, the hotel evaluation attribute set is constructed, and the sentiment analysis of the review statements is carried out with the help of the HowNet sentiment dictionary and manual annotation method. The probabilistic language term set is used to classify the data and derive statistics, and the maximum deviation method is used to determine the weight of each attribute. Then, the cosine similarity formula is fused with the modified cosine similarity formula to calculate the similarity and construct the decision matrix. Finally, combined with the historical data of the user's hotel selection, the hotel recommendation results are generated. This paper collected review data from 10 hotels in Macau from the official "Ctrip" website. The proposed recommendation algorithm model was then applied to process and analyze the data, resulting in the generation of a ranked list of hotel recommendations. To validate the accuracy and effectiveness of this research, the recommendation results were compared with those produced by other algorithms. [ABSTRACT FROM AUTHOR]

In modern converter-dominated power systems, total inertia is very variable and depends on the share of power generated by renewable-based converter-interfaced generation (CIG) at each specific moment. As a result, the limits required by the grid codes on the rate of change of frequency and its nadir or zenith during disturbances become challenging to achieve with conventional control approaches. Therefore, the transition to a novel control strategy of CIG with a grid-forming power converter is relevant. For this purpose, a control algorithm based on a virtual synchronous generator (VSG) is used, which simulates the properties and capabilities of a conventional synchronous generation. However, due to continuously changing operating conditions in converter-dominated power systems, the virtual inertia formed by VSG must be adaptive. At the same time, the efficiency of adaptive algorithms strongly depends on the used VSG structure. In this connection, this paper proposes an enhanced VSG structure for which the transfer function of the active power control loop was formed. With the help of it, the advantages over the conventional VSG structure were proven, which are necessary for the effective adaptive control of the VSG parameters. Then, the analysis of the impact of the VSG parameters on the dynamic response using the transient characteristics in the time domain was performed. Based on the results obtained, adaptive algorithms for independent control of the virtual inertia and the parameters of the VSG damper winding were developed. The performed mathematical modeling confirmed the reliable and effective operation of the developed adaptive control algorithms and the enhanced VSG structure. The theoretical and experimental results obtained in this paper indicate the need for simultaneous development and improvement of both adaptive control algorithms and VSG structures used for this purpose. [ABSTRACT FROM AUTHOR]

This study designs a two-stage algorithm to address the bid generation problem of carriers when adding new vehicle routes in the presence of the existing vehicle routes to provide transportation service. To obtain the best auction combination and bid price of the carrier, a hybrid integer nonlinear programming model is introduced. According to the characteristics of the problem, a set of two-stage hybrid algorithms is proposed, innovatively integrating block coding within a genetic algorithm framework with a depth-first search approach. This integration effectively manages routing constraints, enhancing the algorithm's efficiency. The block coding and each route serve as decision variables in the set partition formula, enabling a comprehensive exploration of potential solutions. After a simulation-based analysis, the algorithm has been comprehensively validated analytically and empirically. The improvement of this research lies in the effectiveness of the proposed algorithm, i.e., the ability to handle a broader range of problem scales with less time in addressing complex operator bid generation in combinatorial auctions. [ABSTRACT FROM AUTHOR]

In this paper, we propose an outlier-detection algorithm for detecting network traffic anomalies based on a clustering algorithm and an autoencoder model. The BIRCH clustering algorithm is employed as the pre-algorithm of the autoencoder to pre-classify datasets with complex data distribution characteristics, while the autoencoder model is used to detect outliers based on a threshold. The proposed BIRCH-Autoencoder (BAE) algorithm has been tested on four network security datasets, KDDCUP99, UNSW-NB15, CICIDS2017, and NSL-KDD, and compared with representative algorithms. The BAE algorithm achieved average F-scores of 96.160, 81.132, and 91.424 on the KDDCUP99, UNSW-NB15, and CICIDS2017 datasets, respectively. These experimental results demonstrate that the proposed approach can effectively and accurately detect anomalous data. [ABSTRACT FROM AUTHOR]

The cryptographic system is the foundation of blockchain security mechanisms. This paper constructs a blockchain security mechanism based on the Chinese national cryptographic SM2 algorithm, involving the generation of public–private key pairs and the signing of block information using key pairs. However, the original SM2 algorithm has a high computational complexity, which cannot meet the requirements of low on-chain delay in blockchain applications. To solve this problem, this paper optimizes the SM2 digital signature algorithm. The scalar multiplication operation in the digital signature algorithm has a large computational complexity, which affects the efficiency of a digital signature. To reduce its computational complexity, this paper improves the traditional window non-adjacent form (w-NAF) algorithm for the scalar multiplication operation and proposes a low computational complexity Fw-NAF algorithm based on the prime number precomputation window, which greatly reduces its computational complexity. [ABSTRACT FROM AUTHOR]

Chaos has been one of the most effective cryptographic sources since it was first used in image-encryption algorithms. This paper closely examines the development process of chaos-based image-encryption algorithms from various angles, including symmetric and asymmetric algorithms, block ciphers and stream ciphers, and integration with other technologies. The unique attributes of chaos, such as sensitivity to initial conditions, topological transitivity, and pseudo-randomness, are conducive to cross-referencing with other disciplines and improving image-encryption methods. Additionally, this paper covers practical application scenarios and current challenges of chaotic image encryption, thereby encouraging researchers to continue developing and complementing existing situations, and may also serve as a basis of future development prospects for chaos-based image encryption. [ABSTRACT FROM AUTHOR]

The chi-squared automatic interaction detector (CHAID) algorithm is considered to be one of the most used supervised learning methods as it is adaptable to solving any kind of problem at hand. We are keenly aware of the non-linear relationships among CHAID maps, and they can empower predictive models with stability. However, we do not precisely know how high its accuracy. To determine the perfect scope the CHAID algorithm fits into, this paper presented an analysis of the accuracy of the CHAID algorithm. We introduced the causes, applicable conditions, and application scope of the CHAID algorithm, and then highlight the differences in the branching principles between the CHAID algorithm and several other common decision tree algorithms, which is the first step towards performing a basic analysis of CHAID algorithm. We next employed an actual branching case to help us better understand the CHAID algorithm. Specifically, we used vehicle customer satisfaction data to compare multiple decision tree algorithms and cited some factors that affect the accuracy and some corresponding countermeasures that are more conducive to obtaining accurate results. The results showed that CHAID can analyze the data very well and reliably detect significantly correlated factors. This paper presents the information required to understand the CHAID algorithm, thereby enabling better choices when the use of decision tree algorithms is warranted. [ABSTRACT FROM AUTHOR]

In this research paper, we present a new inertial method with a self-adaptive technique for solving the split variational inclusion and fixed point problems in real Hilbert spaces. The algorithm is designed to choose the optimal choice of the inertial term at every iteration, and the stepsize is defined self-adaptively without a prior estimate of the Lipschitz constant. A convergence theorem is demonstrated to be strong even under lenient conditions and to showcase the suggested method's efficiency and precision. Some numerical tests are given. Moreover, the significance of the proposed method is demonstrated through its application to an image reconstruction issue. [ABSTRACT FROM AUTHOR]

Optimization algorithms have now played an important role in many fields, and the issue of how to design high-efficiency algorithms has gained increasing attention, for which it has been shown that advanced control theories could be helpful. In this paper, the fixed-time scheme and reset scheme are introduced to design high-efficiency gradient descent methods for unconstrained convex optimization problems. At first, a general reset framework for existing accelerated gradient descent methods is given based on the systematic representation, with which both convergence speed and stability are significantly improved. Then, the design of a novel adaptive fixed-time gradient descent, which has fewer tuning parameters and maintains better robustness to initial conditions, is presented. However, its discrete form introduces undesirable overshoot and easily leads to instability, and the reset scheme is then applied to overcome the drawbacks. The linear convergence and better stability of the proposed algorithms are theoretically proven, and several dedicated simulation examples are finally given to validate the effectiveness. [ABSTRACT FROM AUTHOR]

Polar codes, as the coding scheme for the control channel in fifth-generation mobile communication technology (5G), have attracted widespread attention since their proposal. As a mainstream decoding algorithm for polar codes, the successive cancellation list (SCL) decoder usually improves the error correction performance by increasing the list size, but this method suffers from the problems of high decoding complexity. To address this problem, this paper proposes a layered-search bit-flipping (LS-SCLF) decoding algorithm based on SCL decoding. Firstly, a new flip-bit metric is proposed, which derives a formula to approximate the probability of an error occurring in an information bit. This formula introduces a perturbation parameter to improve the calculation accuracy. Secondly, a compromise scheme for determining the perturbation parameter is proposed. The scheme uses Monte Carlo simulation to determine an optimized parameter for the precise positioning of the first erroneous decoded bit under different decoding conditions. Finally, a layered search strategy is adopted to sequentially search the erroneous decoded bits from the low order to high order, which can correct up to multiple bits at the same time. Simulation results show that the proposed algorithm achieves improved error correction performance with a slight increase in decoding complexity compared to the generalized SCL-Flip (GSCLF) decoding algorithm. This algorithm also achieves a good balance between the error correction performance and decoding complexity. [ABSTRACT FROM AUTHOR]

In recent years, the utilization of dual-arm robots has gained substantial prominence across various industries owing to their collaborative operational capabilities. In order to achieve collision avoidance and facilitate cooperative task completion, efficient path planning plays a pivotal role. The high dimensionality associated with collaborative task execution in dual-arm robots renders existing path planning methods ineffective for conducting efficient exploration. This paper introduces a multi-agent path planning reinforcement learning algorithm that integrates an experience replay strategy, a shortest-path constraint, and the policy gradient method. To foster collaboration and avoid competition between the robot arms, the proposed approach incorporates a mechanism known as "reward cooperation, punishment competition" during the training process. Our algorithm demonstrates strong performance in the control of dual-arm robots and exhibits the potential to mitigate the challenge of reward sparsity encountered during the training process. The effectiveness of the proposed algorithm is validated through simulations and experiments, comparing the results with existing methods and showcasing its superiority in dual-arm robot path planning. [ABSTRACT FROM AUTHOR]

The resolution of small near-wall eddies encountered in high-Reynolds number flows using large eddy simulation (LES) requires very fine meshes that may be computationally prohibitive. As a result, the use of wall-modeled LES as an alternative is becoming more popular. In this paper, the near-wall domain decomposition (NDD) approach that was originally developed for Reynolds-averaged Navier–Stokes simulations (RANSs) is extended to the hybrid RANS/LES zonal decomposition. The algorithm is implemented in two stages. First, the solution is computed everywhere with LES on a coarse grid using a new non-local slip boundary condition for the instantaneous velocity at the wall. The solution is then recomputed in the near-wall region with RANS. The slip boundary conditions used in the first stage guarantee that the composite solution is smooth at the inner/outer region interface. Another advantage of the model is that the turbulent viscosity in the inner region is computed based on the corresponding RANS velocity. This shows improvement over those hybrid models that have only one velocity field in the whole domain obtained from LES. The model is realized in the open source code OpenFOAM with different approximations of turbulent viscosity and is applied to the planar channel flow at frictional Reynolds numbers of Re τ = 950 , 2000, and 4200. Mean streamwise velocity and Reynolds stress intensities are predicted reasonably well in comparison to the solutions obtained with unresolved LES and available DNS benchmarks. No additional forcing at the interface is required, while the log–layer mismatch is essentially reduced in all cases. [ABSTRACT FROM AUTHOR]

This paper is concerned with developing an efficient numerical algorithm for the fast implementation of the sparse grid method for computing the d-dimensional integral of a given function. The new algorithm, called the MDI-SG (multilevel dimension iteration sparse grid) method, implements the sparse grid method based on a dimension iteration/reduction procedure. It does not need to store the integration points, nor does it compute the function values independently at each integration point; instead, it reuses the computation for function evaluations as much as possible by performing the function evaluations at all integration points in a cluster and iteratively along coordinate directions. It is shown numerically that the computational complexity (in terms of CPU time) of the proposed MDI-SG method is of polynomial order O (d 3 N b) (b ≤ 2) or better, compared to the exponential order O (N (log N) d − 1) for the standard sparse grid method, where N denotes the maximum number of integration points in each coordinate direction. As a result, the proposed MDI-SG method effectively circumvents the curse of dimensionality suffered by the standard sparse grid method for high-dimensional numerical integration. [ABSTRACT FROM AUTHOR]

A modified viscosity-type self-adaptive iterative algorithm is presented in this study, having a strong convergence theorem for estimating the common solution to the split generalized equilibrium problem along with the split common null point problem with multiple output sets, subject to some reasonable control sequence restrictions. The suggested algorithm and its immediate consequences are also discussed. The effectiveness of the proposed algorithm is finally demonstrated through analytical examples. The findings presented in this paper will help to consolidate, extend, and improve upon a number of recent findings in the literature. [ABSTRACT FROM AUTHOR]