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This paper demonstrates that the space of piecewise-smooth bivariate functions can be well-approximated by the space of the functions defined by a set of simple (non-linear) operations on smooth uniform tensor product splines. The examples include bivariate functions with jump discontinuities or normal discontinuities across curves, and even across more involved geometries such as a three-corner discontinuity. The provided data may be uniform or non-uniform, and noisy, and the approximation procedure involves non-linear least-squares minimization. Also included is a basic approximation theorem for functions with jump discontinuity across a smooth curve. [ABSTRACT FROM AUTHOR]

In atmospheric modeling, sub-grid parameterization is an important method for studying the topographic effects of solar radiation using high-resolution Digital Elevation Model (DEM) data. For reducing the amount of computation, some approximate methods that can lead to errors are used in existing sub-grid parameterization schemes for clear-sky direct solar radiation (SPS-CSDSR). The lack of a high-precision fast terrain occlusion algorithm (HPFTOA) remains one of the biggest constraints in this field. This study proposed an HPFTOA. It mainly uses two kinds of acceleration algorithms. One method is to use a dynamic, lossless, and fast occlusion search radius. Another way is to use the rectangular grid for calculations within the accuracy of DEM data to avoid coordinate projection conversions. The test results indicate that the HPFTOA can carry out large-scale computation based on DEM data with a resolution of 90 m. Because it rarely uses approximation algorithms and considers the curvature of the Earth, SPS-CSDSR can achieve unprecedented precision. The HPFTOA can also be used in the fields of mountain solar energy assessment, remote sensing, and telemetry, including terrain-obscuring the probe. As computer performance improves and algorithms and execution code are optimized, the application prospects will be very broad. [ABSTRACT FROM AUTHOR]

Dimension reduction is a technique used to transform data from a high-dimensional space into a lower-dimensional space, aiming to retain as much of the original information as possible. This approach is crucial in many disciplines like engineering, biology, astronomy, and economics. In this paper, we consider the following dimensionality reduction instance: Given an n-dimensional probability distribution p and an integer m < n , we aim to find the m-dimensional probability distribution q that is the closest to p, using the Kullback–Leibler divergence as the measure of closeness. We prove that the problem is strongly NP-hard, and we present an approximation algorithm for it. [ABSTRACT FROM AUTHOR]

To address the control performance and harmonic suppression issues in maritime vessel rudder permanent magnet servo systems, a fractional-order PID controller was introduced into the existing improved repetitive control strategy. We used the Oustaloup approximation algorithm and particle swarm optimization for tuning the fractional-order PID controller. The optimized parameters substantially improved the control performance. By integrating the fractional-order PID controller with the improved repetitive controller, a composite fractional-order PID repetitive control strategy was formed. Finally, MATLAB/Simulink simulations were conducted to compare and verify the disturbance rejection and harmonic suppression capabilities of the improved control strategy. The results demonstrate its superior control performance, thereby increasing the practicality of the control system in dealing with various situations. [ABSTRACT FROM AUTHOR]

In this paper, the optimal approximation algorithm is proposed to simplify non-linear functions and/or discrete data as piecewise polynomials by using the constrained least squares. In time-sensitive applications or in embedded systems with limited resources, the runtime of the approximate function is as crucial as its accuracy. The proposed algorithm searches for the optimal piecewise polynomial (OPP) with the minimum computational cost while ensuring that the error is below a specified threshold. This was accomplished by using smooth piecewise polynomials with optimal order and numbers of intervals. The computational cost only depended on polynomial complexity, i.e., the order and the number of intervals at runtime function call. In previous studies, the user had to decide one or all of the orders and the number of intervals. In contrast, the OPP approximation algorithm determines both of them. For the optimal approximation, computational costs for all the possible combinations of piecewise polynomials were calculated and tabulated in ascending order for the specific target CPU off-line. Each combination was optimized through constrained least squares and the random selection method for the given sample points. Afterward, whether the approximation error was below the predetermined value was examined. When the error was permissible, the combination was selected as the optimal approximation, or the next combination was examined. To verify the performance, several representative functions were examined and analyzed. [ABSTRACT FROM AUTHOR]

Personalized travel itinerary recommendation algorithms are the focus of research in smart tourism and tourism GIS. Aiming to address issues present in travel itinerary recommendations for the increasingly popular "self-drive tour" mode, this study proposes an algorithm based on comprehensive tourist satisfaction to mitigate problems such as the neglect of important relevant factors and low degree of personalization. First, we construct a model of tourist satisfaction for travel itineraries by comprehensively considering factors including time utilization, the attractiveness of attractions, itinerary feasibility, and the diversity of attraction types. Unlike previous studies, we consider dining and accommodation time during the itinerary, the physical condition of tourists, and the diversity of attraction types, and establish penalty functions to flexibly constrain deviations from the expected conditions in itinerary planning. Then, with the optimization of comprehensive tourist satisfaction as the objective, we design a new algorithm to address the itinerary recommendation problem, supporting tourists in selecting must-visit attractions, restaurants, and hotels, as well as personalized preferences such as the sightseeing sequence. The experimental results demonstrate that our proposed algorithm outperforms two baseline algorithms, providing higher comprehensive tourist satisfaction while also exhibiting greater feasibility in itinerary planning. The proposed algorithm effectively addresses the issue of personalized travel itinerary recommendation, presenting an efficient, feasible, and practical solution. [ABSTRACT FROM AUTHOR]

In this paper, a joint optimization algorithm of offloading decision, energy harvesting time, and unmanned aerial vehicle (UAV) location is proposed for user equipment (UEs)'s task completion latency problem in a communication–sensing–computing integration scenario with wireless energy supply. Under the constraints of causality of energy harvesting consumption by the UEs and conditional mutual information, the total latency minimization problem of the UEs is established. Firstly, the optimization variables of the problem are transformed from three variables of offloading decision, energy harvesting time, and UAV location to two variables of offloading decision and UAV location by means of the derived closed expression, and then the transformed optimization problem is decomposed into the offloading decision optimization sub-problem and the UAV location optimization sub-problem to be solved alternately and iteratively. The genetic algorithm is employed to tackle the optimization sub-problem of offloading decisions, and the successive convex approximation algorithm is applied to the drone positioning optimization sub-problem. Simulation results show that the proposed algorithm in this paper reduces the average task completion latency by 35 percent and 15 percent, respectively, compared to the two baseline algorithms for different numbers of UEs. [ABSTRACT FROM AUTHOR]

Privacy-preserving neural networks offer a promising solution to train and predict without user privacy leakage, and fully homomorphic encryption (FHE) stands out as one of the key technologies, as it enables homomorphic operations over encrypted data. However, only addition and multiplication homomorphisms are supported by FHE, and thus, it faces huge challenges when implementing non-linear functions with ciphertext inputs. Among the non-linear functions in neural networks, one may refer to the activation function, the argmax function, and maximum pooling. Inspired by using a composition of low-degree minimax polynomials to approximate sign and argmax functions, this study focused on optimizing the homomorphic argmax approximation, where argmax is a mathematical operation that identifies the index of the maximum value within a given set of values. For the method that uses compositions of low-degree minimax polynomials to approximate argmax, in order to further reduce approximation errors and improve computational efficiency, we propose an improved homomorphic argmax approximation algorithm that includes rotation accumulation, tree-structured comparison, normalization, and finalization phases. And then, the proposed homomorphic argmax algorithm was integrated into a neural network structure. Comparative experiments indicate that the network with our proposed argmax algorithm achieved a slight increase in accuracy while significantly reducing the inference latency by 58 % , as the homomorphic sign and rotation operations were rapidly reduced. [ABSTRACT FROM AUTHOR]

When using traditional Euler deconvolution optimization strategies, it is difficult to distinguish between anomalies and their corresponding Euler tails (those solutions are often distributed outside the anomaly source, forming "tail"-shaped spurious solutions, i.e., misplaced Euler solutions, which must be removed or marked) with only the structural index. The nonparametric estimation method based on the normalized B-spline probability density (BSS) is used to separate the Euler solution clusters and mark different anomaly sources according to the similarity and density characteristics of the Euler solutions. For display purposes, the BSS needs to map the samples onto the estimation grid at the points where density will be estimated in order to obtain the probability density distribution. However, if the size of the samples or the estimation grid is too large, this process can lead to high levels of memory consumption and excessive computation times. To address this issue, a fast linear binning approximation algorithm is introduced in the BSS to speed up the computation process and save time. Subsequently, the sample data are quickly projected onto the estimation grid to facilitate the discrete convolution between the grid and the density function using a fast Fourier transform. A method involving multivariate B-spline probability density estimation based on the FFT (BSSFFT), in conjunction with fast linear binning appropriation, is proposed in this paper. The results of two random normal distributions show the correctness of the BSS and BSSFFT algorithms, which is verified via a comparison with the true probability density function (pdf) and Gaussian kernel smoothing estimation algorithms. Then, the Euler solutions of the two synthetic models are analyzed using the BSS and BSSFFT algorithms. The results are consistent with their theoretical values, which verify their correctness regarding Euler solutions. Finally, the BSSFFT is applied to Bishop 5X data, and the numerical results show that the comprehensive analysis of the 3D probability density distributions using the BSSFFT algorithm, derived from the Euler solution subset of  x 0 , y 0 , z 0 , can effectively separate and locate adjacent anomaly sources, demonstrating strong adaptability. [ABSTRACT FROM AUTHOR]

A dominating set of a graph is a subset of vertices such that every vertex not in the subset has at least one neighbor within the subset. The corresponding optimization problem is known to be NP-hard. It is proved to be beneficial to separate the solution process in two stages. First, one can apply a fast greedy algorithm to obtain an initial dominating set and then use an iterative procedure to purify (reduce) the size of this dominating set. In this work, we develop the purification stage and propose new purification algorithms. The purification procedures that we present here outperform, in practice, the earlier known purification procedure. We have tested our algorithms for over 1300 benchmark problem instances. Compared to the estimations due to known upper bounds, the obtained solutions are about seven times better. Remarkably, for the 500 benchmark instances for which the optimum is known, the optimal solutions are obtained for 46.33% of the tested instances, whereas the average error for the remaining instances is about 1.01. [ABSTRACT FROM AUTHOR]

This paper presents an approach to community detection in complex networks by simultaneously incorporating a connectivity-based metric and Max-Min Modularity. By leveraging the connectivity-based metric and employing a heuristic algorithm, we develop a novel complementary graph for the Max-Min Modularity that enhances its effectiveness. We formulate community detection as an integer programming problem of an equivalent yet more compact counterpart model of the revised Max-Min Modularity maximization problem. Using a row generation technique alongside the heuristic approach, we then provide a hybrid procedure for near-optimally solving the model and discovering high-quality communities. Through a series of experiments, we demonstrate the success of our algorithm, showcasing its efficiency in detecting communities, particularly in extensive networks. [ABSTRACT FROM AUTHOR]

Vegetable oils, which are considered potential lubricants, are composed of different types and proportions of fatty acids. Because of their diverse types and varying compositions, they exhibit different lubrication performances. The genetic function approximation algorithm was used to model the quantitative structure–property relationship between fatty acid structure and the wear scar diameter and friction coefficients measured by four-ball friction and wear tests. Based on the models with adjusted R2 greater than 0.9 and fatty acid compositions of vegetable oils, the wear scar diameter and friction coefficients of Xanthoceras sorbifolia bunge oil and Soybean oil as validation oil samples were predicted. The difference between the predicted and experimental values was small, indicating that the models could accurately predict the lubrication performances of vegetable oils. The lubrication performances of 14 kinds of vegetable oils were predicted by GFA-QSPR models, and the primary factors influencing their lubrication properties were studied by cluster analysis. The results show that the content of C18:1 has a positive effect on the lubrication performances of vegetable oils, while the content of C18:3 has a negative effect, and the length of the carbon chain of fatty acids significantly affects their lubrication properties. [ABSTRACT FROM AUTHOR]

The advancement of autonomous capabilities in maritime navigation has gained significant attention, with a trajectory moving from decision support systems to full autonomy. This push towards autonomy has led to extensive research focusing on collision avoidance, a critical aspect of safe navigation. Among the various possible approaches, dynamic programming is a promising tool for optimizing collision avoidance maneuvers. This paper presents a DP formulation for the collision avoidance of autonomous vessels. We set up the problem framework, formulate it as a multi-stage decision process, define cost functions and constraints focusing on the actual requirements a marine maneuver must comply with, and propose a solution algorithm leveraging parallel computing. Additionally, we present a greedy approximation to reduce algorithm complexity. We put the proposed algorithms to the test in realistic navigation scenarios and also develop an extensive test on a large set of randomly generated scenarios, comparing them with the RRT* algorithm using performance metrics proposed in the literature. The results show the potential benefits of an autonomous navigation or decision support framework. [ABSTRACT FROM AUTHOR]

The Susceptible–Infected–Susceptible (SIS) model in complex networks is one of the critical models employed in the modeling of virus spread. The study of the heterogeneous SIS model with a non-homogeneous nodal infection rate in finite-size networks has attracted little attention. Investigating the statistical properties of heterogeneous SIS epidemic dynamics in finite networks is thus intriguing. In this paper, we focus on the measure of variability in the number of infected nodes for the heterogeneous SIS epidemic dynamics in finite-size bipartite graphs and star graphs. Specifically, we investigate the metastable-state variance of the number of infected nodes for the SIS epidemic process in finite-size bipartite graphs and star graphs with heterogeneous nodal infection rates. We employ an extended individual-based mean-field approximation to analyze the heterogeneous SIS epidemic process in finite-size bipartite networks and star graphs. We derive the approximation solutions of the variance of the infected number. We verify the proposed theory by simulations. The proposed theory has the potential to help us better understand the fluctuations of SIS models like epidemic dynamics with a non-homogeneous infection rate. [ABSTRACT FROM AUTHOR]

This paper investigates the potential of active reconfigurable intelligent surfaces (RIS) to enhance wireless-powered communication networks (WPCNs), addressing the evolving connectivity needs of the internet of things (IoT). Active RIS, capable of amplifying and reflecting signals, offers a solution to surpass the limitations of passive RIS, such as double-fading attenuation, aiming to significantly improve network throughput and coverage. Our research focuses on exploiting the amplification capabilities of active RIS to boost the overall network sum throughput, engaging in a comprehensive optimization of critical network parameters, including time allocation, reflection coefficients, and phase shift matrices specific to active RIS. The formulated problem is non-convex and highly complex due to the coupling of optimization variables. We employed a successive convex approximation algorithm to solve the throughput maximization problem by converting the non-convex constraints into approximated convex constraints and solving them iteratively. Through extensive simulations, we demonstrate that our active RIS-assisted network substantially outperforms networks facilitated by passive RIS, marking a significant advancement in WPCN performance. These findings underscore the potential of active RIS technology in realizing the full capabilities of IoT connectivity. [ABSTRACT FROM AUTHOR]

In this paper, we study the regular sensory data collection of Points of Interest (PoIs) with multiple Unmanned Aerial Vehicles (UAVs) during an extended monitoring period, where each PoI is visited multiple times before its data update deadline to keep the data fresh. We observe that most existing studies ignored the important differences in the data stored in the PoIs, scheduled a plan that dispatched UAVs to visit all PoIs before the same deadline, and simply repeated the plan during the monitoring period, which undoubtedly increased the service cost of the UAVs. Considering the specific data update deadline of each PoI, we formulate a novel UAV cost minimization problem to collect the data stored in each PoI before its deadline by finding a series of plans for UAVs such that the service cost of the UAVs during the monitoring period is minimized; the service cost of the UAVs is composed of the consumed energy of the UAVs utilized for hovering for data collection and the consumed energy of the UAVs utilized for flying. To deal with the above NP-hard problem, we devise an approximation algorithm by grouping the PoIs and accessing them in batches. Then, we analyze the proposed algorithm and evaluate the performance of the algorithm through experimental simulations. The experimental results show that the proposed algorithm is very promising. [ABSTRACT FROM AUTHOR]

Solving combinatorial problems on complex networks represents a primary issue which, on a large scale, requires the use of heuristics and approximate algorithms. Recently, neural methods have been proposed in this context to find feasible solutions for relevant computational problems over graphs. However, such methods have some drawbacks: (1) they use the same neural architecture for different combinatorial problems without introducing customizations that reflects the specificity of each problem; (2) they only use a nodes local information to compute the solution; (3) they do not take advantage of common heuristics or exact algorithms. Following this interest, in this research we address these three main points by designing a customized attention-based mechanism that uses both local and global information from the adjacency matrix to find approximate solutions for the Minimum Vertex Cover Problem. We evaluate our proposal with respect to a fast two-factor approximation algorithm and a widely adopted state-of-the-art heuristic both on synthetically generated instances and on benchmark graphs with different scales. Experimental results demonstrate that, on the one hand, the proposed methodology is able to outperform both the two-factor approximation algorithm and the heuristic on the test datasets, scaling even better than the heuristic with harder instances and, on the other hand, is able to provide a representation of the nodes which reflects the combinatorial structure of the problem. [ABSTRACT FROM AUTHOR]

Numerical algorithms for calculating the left- and right-sided Riemann–Liouville fractional integrals and the left- and right-sided fractional derivatives in the Caputo sense using spline interpolation techniques are derived. The spline of the fifth degree (the so-called quintic spline) is mainly taken into account, but the linear and cubic splines are also considered to compare the quality of the developed method and numerical calculations. The estimation of errors for the derived approximation algorithms is presented. Examples of the numerical evaluation of the fractional integrals and derivatives are executed using 128-bit floating-point numbers and arithmetic routines. For each derived algorithm, the experimental orders of convergence are calculated. Also, an illustrative computational example showing the action of the considered fractional operators on the symmetric function in the interval is presented. [ABSTRACT FROM AUTHOR]

Bayesian optimization algorithms are widely used for solving problems with a high computational complexity in terms of objective function evaluation. The efficiency of Bayesian optimization is strongly dependent on the quality of the surrogate models of an objective function, which are built and refined at each iteration. The quality of surrogate models, and hence the performance of an optimization algorithm, can be greatly improved by selecting the appropriate hyperparameter values of the approximation algorithm. The common approach to finding good hyperparameter values for each iteration of Bayesian optimization is to build surrogate models with different hyperparameter values and choose the best one based on some estimation of the approximation error, for example, a cross-validation score. Building multiple surrogate models for each iteration of Bayesian optimization is computationally demanding and significantly increases the time required to solve an optimization problem. This paper suggests a new approach, called exploratory landscape validation, to find good hyperparameter values with less computational effort. Exploratory landscape validation metrics can be used to predict the best hyperparameter values, which can improve both the quality of the solutions found by Bayesian optimization and the time needed to solve problems. [ABSTRACT FROM AUTHOR]

Aiming to address problems such as low sampling success rate and long computation time in the motion planning of a dual-arm cooperative system with multiple constraints, this paper proposes an Informed-Bi-Quick RRT* algorithm based on offline sampling. First, in the process of pre-sampling, the new algorithm relaxes the approximation of constrained manifolds by introducing the idea of incremental construction, and it incorporates the stochastic gradient descent method to replace global random sampling with local random sampling, which enriches the data set and shortens the offline sampling time of the data set. Second, the new algorithm improves the original Quick-RRT* algorithm by combining the two-tree idea and the multi-target bias expansion strategy, and it improves the adaptability of the algorithm to different obstacle environments. In addition, the loosely constrained motion and tightly constrained motion in the two-arm cooperative system are analyzed, and the adaptive planning of the two-arm trajectory in different motions is described in detail. In this paper, the two-arm cooperative model constructed with UR5 and UR10 robot arms is studied, and the ability of the proposed algorithm to deal with multiple constraints is verified by simulating assembly and handling tasks. The experimental results show that compared with other methods, the proposed algorithm has obvious advantages in path quality and planning efficiency. [ABSTRACT FROM AUTHOR]

Over the past few decades, there has been a significant increase in the number of Earth observation satellites, and the area of ground targets requiring observation has also been expanding. To effectively utilize the capabilities of these satellites and capture larger areas of ground targets, it has become essential to plan imaging tasks for large regional coverage using multiple satellites. First, we establish a 0-1 integer programming model to accurately describe the problem and analyze the challenges associated with solving the model. Second, we propose a heuristic algorithm based on the triple grids method. This approach utilizes a generated grid to create fewer candidate strips, a calculation grid to determine the effective coverage area more accurately, and a refined grid to solve the issue of repeated coverage of strips. Furthermore, we employ an approximation algorithm to further improve the solutions obtained from the heuristic algorithm. By comparing the proposed method to the traditional greedy heuristic algorithm and three evolutionary algorithms, the results show that our method has better performance in terms of coverage and efficiency. [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]

Recently, networks have faced a significant challenge in terms of security due to constant unauthorized access by hackers, resulting in the compromise of network user data. To enhance network security, there are various approaches that can be employed, including the utilization of firewalls, encryption, and antivirus software. Among these methods, one type of system that can be implemented is an intrusion detection system (IDS), which actively monitors the network to identify any intrusions. In order to effectively detect any unauthorized or malicious activities, sophisticated techniques such as genetic algorithms, cuckoo searches, and FLAME are employed. This research proposes a novel IDS that aims to improve the detection of intrusions. The proposed IDS initially conducts feature filtration using fuzzy clustering through the local approximation of the membership algorithm (FLAME), which effectively reduces the number of features that need to be analyzed and processed. Subsequently, the system detects attacks by implementing an extended classifier system (XCS) that incorporates a genetic algorithm (GA) to enhance the accuracy of intrusion detection. By incorporating the cuckoo search and selection within GA, while considering different crossover and mutation probabilities, instead of solely relying on traditional GA, it is anticipated that intrusion detection accuracy will be improved. To evaluate the performance of the proposed IDS, it was tested on the KDD99 dataset and compared with several other IDSs that were also tested on the same dataset. The experimental results clearly indicate that the proposed IDS significantly enhances the detection rate (DR) and accuracy while also significantly reducing the false alarm rate (FAR) and these impressive results were 100%, 99.99% and 0.05% respectively. The performance comparisons reveal that, overall, the proposed IDS outperforms several existing IDSs in terms of intrusion detection performance. [ABSTRACT FROM AUTHOR]

Multi-h continuous phase modulation (CPM), with extremely high spectral efficiency, involves the plague of high demodulation complexity with a large number of matched filters and a complex trellis. In this paper, an efficient all-digital demodulator for multi-h continuous phase modulation (CPM) is proposed based on a low-complexity decision-directed synchronization algorithm. Based on the maximum-likelihood estimation of the carrier phase and timing errors, we propose a reduced-complexity timing error detector with linear phase approximation (LPA) to the phase of the multi-h CPM. Compared with the traditional synchronization methods, it avoids derivative matched filtering and reduces about 2/3 of matched filters. The estimated accuracy and bit error rate (BER) performance of the LPA-based synchronization algorithm have no loss, as shown by the numerical simulation. Its stability is verified by the derived S-curve. Then, the receivers with the LPA-based synchronization for the three kinds of promising multi-h CPM are implemented on a Xilinx Kintex-7 FPGA platform. The experimental results show that the onboard tested BER of the proposed design has an ignorable loss in the numerical simulation. The implementation overhead on FPGA is significantly reduced by about 27% slices, 64% DSPs, and 70% block RAMs compared with the conventional method. [ABSTRACT FROM AUTHOR]

The goal of this paper is to find a stabilizing and optimal control policy for a class of systems dictated by Euler–Lagrange dynamics, that also satisfies predetermined response criteria. The proposed methodology builds upon two stages. Initially, a neural network is trained online via an iterative process to capture the system dynamics, which are assumed to be unknown. Subsequently, a successive approximation algorithm is applied, employing the acquired dynamics from the previous step, to find a near-optimal control law that takes into consideration prescribed performance specifications, such as convergence speed and steady-state error. In addition, we concurrently guarantee that the system evolves exclusively within the compact set for which sufficient approximation capabilities have been acquired. Finally, we validate our claims through various simulated studies that confirm the success of both the identification process and the minimization of the cost function. [ABSTRACT FROM AUTHOR]

The identifying code problem for a given graph involves finding a minimum subset of vertices such that each vertex of the graph is uniquely specified by its nonempty neighborhood within the identifying code. The combinatorial optimization problem has a wide variety of applications in location and detection schemes. Finding an identifying code of minimum possible size is a difficult task. In fact, it has been proven to be computationally intractable (NP-complete). Therefore, the use of heuristics to provide good approximations in a reasonable amount of time is justified. In this work, we present a new population-based local search algorithm for finding identifying codes of minimum cost. Computational experiments show that the proposed approach was found to be more effective than other state-of-the-art algorithms at generating high-quality solutions in different types of graphs with varying numbers of vertices. [ABSTRACT FROM AUTHOR]

The minimum vertex cover (MVC) problem is a canonical NP-hard combinatorial optimization problem aiming to find the smallest set of vertices such that every edge has at least one endpoint in the set. This problem has extensive applications in cybersecurity, scheduling, and monitoring link failures in wireless sensor networks (WSNs). Numerous local search algorithms have been proposed to obtain "good" vertex coverage. However, due to the NP-hard nature, it is challenging to efficiently solve the MVC problem, especially on large graphs. In this paper, we propose an efficient local search algorithm for MVC called TIVC, which is based on two main ideas: a 3-improvements (TI) framework with a tiny perturbation and edge selection strategy. We conducted experiments on real-world large instances of a massive graph benchmark. Compared with three state-of-the-art MVC algorithms, TIVC shows superior performance in accuracy and possesses a remarkable ability to identify significantly smaller vertex covers on many graphs. [ABSTRACT FROM AUTHOR]

This paper proposes an approximation algorithm based on the Legendre and Chebyshev artificial neural network to explore the approximate solution of fractional Lienard and Duffing equations with a Caputo fractional derivative. These equations show the oscillating circuit and generalize the spring–mass device equation. The proposed approach transforms the given nonlinear fractional differential equation (FDE) into an unconstrained minimization problem. The simulated annealing (SA) algorithm minimizes the mean square error. The proposed techniques examine various non-integer order problems to verify the theoretical results. The numerical results show that the proposed approach yields better results than existing methods. [ABSTRACT FROM AUTHOR]

Abnormal electromagnetic radiation associated with seismic activity has been reported across a wide range of frequencies, but its primary energy is concentrated in the super-low-frequency (SLF) and extremely low-frequency (ELF) bands. To estimate the effect of the seismic radiation source, a radiator in a soil foundation was modeled as a horizontal electric dipole (HED), and the propagation characteristics of the electromagnetic fields were studied in the Earth–ionosphere cavity. The expressions of the electromagnetic fields could be obtained according to the reciprocity theorem. Therefore, a new algorithm named the numerical integral algorithm was proposed, which is suitable for both the SLF and ELF bands. The new algorithm was compared with the asymptotic approximation algorithm when the receiving point was not close to the field source and the antipode. The two algorithms were found to be in excellent agreement, confirming the validity of the new algorithm for SLF and ELF bands. [ABSTRACT FROM AUTHOR]

The paper presents two effective methods for discovering process models in the form of partial differential equations based on an evolutionary algorithm and an algorithm for the best subset selection. The methods are designed to work with sparse and noisy data and implement various numerical differentiation techniques, including piecewise local approximation using multidimensional polynomial functions, neural network approximation, and an additional algorithm for selecting differentiation steps. To verify the algorithms, the experiment is carried out on pulsed heating of a viscous liquid (glycerol) by a submerged horizontal cylindrical heat source. Temperature measurements are taken only at six points, which makes the data very sparse. The noise level ranges from 0.2 to 1% of the observed maximum temperature. The algorithms can successfully restore the structure of the heat transfer equation in cylindrical coordinates and determine the thermal diffusivity coefficient with an error of 2.5–20%, depending on the algorithm type and heating mode. Additional synthetic setups are employed to analyze the dependence of accuracy on the noise level. Results also demonstrate the algorithms' ability to identify underlying processes such as convective motion. [ABSTRACT FROM AUTHOR]

Recently, complicated spatial search algorithms have emerged as spatial-information-based applications, such as location-based services (LBS), and have become very diverse and frequent. The aggregate nearest neighbor (ANN) search is an extension of the existing nearest neighbor (NN) search; it finds the object p * that minimizes G { d (p * , q i) , q i ∈ Q } from a set Q of M (≥1) query objects, where G is an aggregate function and d () is the distance between two objects. The flexible aggregate nearest neighbor (FANN) search is an extension of the ANN search by introducing flexibility factor  ϕ (0 < ϕ ≤ 1) ; it finds the object p * that minimizes G { d (p * , q i) , q i ∈ Q ϕ } from Q ϕ , a subset of Q with | Q ϕ | = ϕ | Q | . This paper proposes an efficient ϵ -approximate k-FANN (k ≥ 1) search algorithm for an arbitrary approximation ratio ϵ (≥1) in road networks. In general, ϵ -approximate algorithms are expected to give an improved search performance at the cost of allowing an error ratio of up to the given ϵ. Since the optimal value of ϵ varies greatly depending on applications and cases, the approximate algorithm for an arbitrary ϵ is essential. We prove that the error ratios of the approximate FANN objects returned by our algorithm do not exceed the given ϵ. To the best of our knowledge, our algorithm is the first ϵ -approximate k-FANN search algorithm in road networks for an arbitrary ϵ. Through a series of experiments using various real-world road network datasets, we demonstrated that our approximate algorithm always outperformed the previous state-of-the-art exact algorithm and that the error ratios of the approximate FANN objects were significantly lower than the given ϵ value. [ABSTRACT FROM AUTHOR]

Fuzzy rough set theory has been successfully applied to many attribute reduction methods, in which the lower approximation set plays a pivotal role. However, the definition of lower approximation used has ignored the information conveyed by the upper approximation and the boundary region. This oversight has resulted in an unreasonable relation representation of the target set. Despite the fact that scholars have proposed numerous enhancements to rough set models, such as the variable precision model, none have successfully resolved the issues inherent in the classical models. To address this limitation, this paper proposes an unsupervised attribute reduction algorithm for mixed data based on an improved optimal approximation set. Firstly, the theory of an improved optimal approximation set and its associated algorithm are proposed. Subsequently, we extend the classical theory of optimal approximation sets to fuzzy rough set theory, leading to the development of a fuzzy improved approximation set method. Finally, building on the proposed theory, we introduce a novel, fuzzy optimal approximation-set-based unsupervised attribute reduction algorithm (FOUAR). Comparative experiments conducted with all the proposed algorithms indicate the efficacy of FOUAR in selecting fewer attributes while maintaining and improving the performance of the machine learning algorithm. Furthermore, they highlight the advantage of the improved optimal approximation set algorithm, which offers higher similarity to the target set and provides a more concise expression. [ABSTRACT FROM AUTHOR]

With the advancement of space technology and satellite communications, low-Earth-orbit (LEO) satellite networks have experienced rapid development in the past decade. In the vision of 6G, LEO satellite networks play an important role in future 6G networks. On the other hand, a variety of applications, including many delay-sensitive applications, are continuously emerging. Due to the highly dynamic nature of LEO satellite networks, supporting time-deterministic services in such networks is challenging. However, we can provide latency guarantees for most delay-sensitive applications through data plane traffic shaping and control plane routing optimization. This paper addresses the routing optimization problem for time-sensitive (TS) flows in software-defined low-Earth-orbit (LEO) satellite networks. We model the problem as an integer linear programming (ILP) model aiming to minimize path handovers and maximum link utilization while meeting TS flow latency constraints. Since this problem is NP-hard, we design an efficient longest continuous path (LCP) approximation algorithm. LCP selects the longest valid path in each topology snapshot that satisfies delay constraints. An auxiliary graph then determines the routing sequence with minimized handovers. We implement an LEO satellite network testbed with Open vSwitch (OVS) and an open-network operating system (ONOS) controller to evaluate LCP. The results show that LCP reduces the number of path handovers by up to 31.7% and keeps the maximum link utilization lowest for more than 75% of the time compared to benchmark algorithms. In summary, LCP achieves excellent path handover optimization and load balancing performance under TS flow latency constraints. [ABSTRACT FROM AUTHOR]

Due to the advantages such as high flexibility, low cost and easy implementation offered by unmanned aerial vehicles (UAVs), a UAV-assisted network is regard as an appealing solution to a seamless coverage, high disaster-tolerant and on-demand wireless system. In this paper, we focus on the downlink transmission in a cache-enabled UAV-assisted wireless communication network, where UAVs cache popular content from a macro base station in advance and cooperatively transfer the content to users. We aim to minimize the average transmission latency of the system and to formulate an optimization problem that jointly optimizes the UAV location, beamforming and caching strategy. However, the formulated problem is very challenging because of its non-convexity and the highly coupled optimization variables. To solve this resulting problem efficiently, we decompose it into two subproblems, namely UAV location and beamforming optimization, and UAV caching strategy optimization. The first subproblem is an NP-hard joint optimization problem, while the second one is a linear programing problem. By adopting the first-order Taylor expansion, we propose a convex optimization algorithm based on the difference-of-convex (DC) method. Specifically, we bring out a method to apply linear approximation in the DC-based algorithm, which is particularly suitable to the problems involving complicated summations. The numerical results demonstrate that the proposed DC-based iterative optimization algorithm can efficiently reduce the average transmission latency of the system. [ABSTRACT FROM AUTHOR]

The article presents the development of new physics-informed evolutionary neural network learning algorithms. These algorithms aim to address the challenges of ill-posed problems by constructing a population close to the Pareto front. The study focuses on comparing the algorithm's capabilities based on three quality criteria of solutions. To evaluate the algorithms' performance, two benchmark problems have been used. The first involved solving the Laplace equation in square regions with discontinuous boundary conditions. The second problem considered the absence of boundary conditions but with the presence of measurements. Additionally, the study investigates the influence of hyperparameters on the final results. Comparisons have been made between the proposed algorithms and standard algorithms for constructing neural networks based on physics (commonly referred to as vanilla's algorithms). The results demonstrate the advantage of the proposed algorithms in achieving better performance when solving incorrectly posed problems. Furthermore, the proposed algorithms have the ability to identify specific solutions with the desired smoothness. [ABSTRACT FROM AUTHOR]

Diversity maximization is a fundamental problem with broad applications in data summarization, web search, and recommender systems. Given a set X of n elements, the problem asks for a subset S of k ≪ n elements with maximum diversity, as quantified by the dissimilarities among the elements in S. In this paper, we study diversity maximization with fairness constraints in streaming and sliding-window models. Specifically, we focus on the max–min diversity maximization problem, which selects a subset S that maximizes the minimum distance (dissimilarity) between any pair of distinct elements within it. Assuming that the set X is partitioned into m disjoint groups by a specific sensitive attribute, e.g., sex or race, ensuring fairness requires that the selected subset S contains k i elements from each group i ∈ [ m ] . Although diversity maximization has been extensively studied, existing algorithms for fair max–min diversity maximization are inefficient for data streams. To address the problem, we first design efficient approximation algorithms for this problem in the (insert-only) streaming model, where data arrive one element at a time, and a solution should be computed based on the elements observed in one pass. Furthermore, we propose approximation algorithms for this problem in the sliding-window model, where only the latest w elements in the stream are considered for computation to capture the recency of the data. Experimental results on real-world and synthetic datasets show that our algorithms provide solutions of comparable quality to the state-of-the-art offline algorithms while running several orders of magnitude faster in the streaming and sliding-window settings. [ABSTRACT FROM AUTHOR]

In this article, we give the sharp bounds of probabilistic Kolmogorov N , δ -widths and probabilistic linear N , δ -widths of the multivariate Sobolev space W 2 A with common smoothness on a S q norm equipped with the Gaussian measure μ , where A ⊂ R d is a finite set. And we obtain the sharp bounds of average width from the results of the probabilistic widths. These results develop the theory of approximation of functions and play important roles in the research of related approximation algorithms for Sobolev spaces. [ABSTRACT FROM AUTHOR]

It is well known that ω -circulant matrices with ω ≠ 0 can be simultaneously diagonalized by a transform matrix, which can be factored as the product of a diagonal matrix, depending on ω , and of the unitary matrix F n associated to the Fast Fourier Transform. Hence, all the sets of ω -circulants form algebras whose computational power, in terms of complexity, is the same as the classical circulants with ω = 1 . However, stability is a delicate issue, since the condition number of the transform is equal to that of the diagonal part, tending to max { | ω | , | ω | − 1 } . For ω = 0 , the set of related matrices is still an algebra, which is the algebra of lower triangular matrices, but they do not admit a common transform since most of them (all except the multiples of the identity) are non-diagonalizable. In the present work, we review two modern applications, ranging from parallel computing in preconditioning of PDE approximations to algorithms for subdivision schemes, and we emphasize the role of such algebra. For the two problems, few numerical tests are conducted and critically discussed and the related conclusions are drawn. [ABSTRACT FROM AUTHOR]

The presented research addresses the problem of dependency analysis of the ultrasonic signal measured by a sensor in an engine oil bath. The dependency analysis is performed on a selected ultrasonic signal sensor solution containing its own generator and an ultrasonic signal receiver detecting the level of the oil in which it is immersed. The influence of the resulting amplitude of the received ultrasonic signal is mainly due to the level of the measured oil level and the oil temperature, as shown by the regression analysis and ANOVA (Analysis of Variance) testing performed. The analyzed dependence of the time determination of the length of the generated ultrasonic signal envelope is given by a set threshold value, which can be dynamically adjusted based on the backtracking evaluation. The analysis results in the form of approximation by the dependency algorithm confirm the assumption of possible standardization of the envelope parameters with the achievement of accuracy up to 99.02%. The analyzed parameters approximated by the temperature and oil level dependence algorithms include the amplitude of the measured signal, steepness of the rising edge, duration of the envelope, and the digitally processed amplitude value. [ABSTRACT FROM AUTHOR]

The travelling salesman problem (TSP) is perhaps the most researched problem in the field of Computer Science and Operations. It is a known NP-hard problem and has significant practical applications in a variety of areas, such as logistics, planning, and scheduling. Route optimisation not only improves the overall profitability of a logistic centre but also reduces greenhouse gas emissions by minimising the distance travelled. In this article, we propose a simple and improved heuristic algorithm named 2-Opt++, which solves symmetric TSP problems using an enhanced 2-Opt local search technique, to generate better results. As with 2-Opt, our proposed method can also be applied to the Vehicle Routing Problem (VRP), with minor modifications. We have compared our technique with six existing algorithms, namely ruin and recreate, nearest neighbour, genetic algorithm, simulated annealing, Tabu search, and ant colony optimisation. Furthermore, to allow for the complexity of larger TSP instances, we have used a graph compression/candidate list technique that helps in reducing the computational complexity and time. The comprehensive empirical evaluation carried out for this research work shows the efficacy of the 2-Opt++ algorithm as it outperforms the other well-known algorithms in terms of the error margin, execution time, and time of convergence. [ABSTRACT FROM AUTHOR]

In multi-access edge computing (MEC) networks, parallelized service function chains (P-SFCs) can provide low-delay network services for mobile users by deploying virtualized network functions (VNFs) to process user requests in parallel. These VNFs are unreliable due to software faults and server failures. A practical way to address this is to deploy idle backup VNFs (BVNFs) near these active VNFs and activate them when active VNFs fail. However, deploying BVNFs preempts server resources and decreases the number of accepted user requests. Thus, this paper proposes a reliability enhancement approach that uses BVNFs satisfying the delay requirement as active VNFs to form P-SFCs, which contributes to the delay reduction and reliability enhancement. Since the resource capacities of edge servers can only deploy a certain number of P-SFCs and BVNFs, establishing how to deploy the minimum number of P-SFCs and BVNFs to satisfy the delay and reliability requirements of mobile users and maximize the number of accepted user requests is a challenging problem. In this paper, we first model the dynamics of delay and reliability caused by VNF parallelization and BVNFs deployment, then formulate the joint deployment problem of P-SFCs and BVNFs. Next, we design an approximation algorithm to deploy critical VNFs and BVNFs on a target edge server and schedule the data traffic of user requests processed by P-SFCs. Experimental results based on real-world datasets show that our proposed algorithm outperforms two benchmark algorithms in terms of throughput, delay, reliability, and resource utilization. [ABSTRACT FROM AUTHOR]

The Internet of Things (IoT) has become increasingly popular, and its communication requirements have grown beyond what traditional ground networks can handle. The space–air–ground (SAG) integrated network has been proposed as a potential solution, where unmanned aerial vehicles (UAVs) collect data from IoT devices and transmit them to satellites. However, the limited energy of UAVs is one of the key factors restricting communication performance, so it is necessary to consider communication energy efficiency (EE). In addition, the improvement of EE will bring about the decline of spectral efficiency (SE). Therefore we consider the tradeoff between EE and SE. Considering a SAG-IoT network, the focus of the paper is to optimize sub-channel selection, power control, and UAV position deployment to maximize EE and SE of the network, which is a multi-objective optimization (MOO) problem. On this premise, we try to improve the data throughput between IoT devices and UAVs. To solve this MOO problem, we use the ϵ -constraint to convert it into a single-objective optimization problem. We then employ various optimization algorithms such as the Dinkelbach algorithm, successive convex approximation algorithm, Lagrange dual algorithm, and block coordinate descent algorithm to solve the mixed integer non-convex problem. Simulation results show that the proposed algorithm converges to at least one sub-optimal solution. [ABSTRACT FROM AUTHOR]

In this paper, we consider a variant of dominating set problem, i.e., the total dominating set problem. Given an undirected graph G = (V , E) , a subset of vertices T ⊆ V is called a total dominating set if every vertex in V is adjacent to at least one vertex in T. Based on LP relaxation techniques, this paper gives a distributed approximation algorithm for the total dominating set problem in general graphs. The presented algorithm obtains a fractional total dominating set that is, at most, k (1 + Δ 1 k) Δ 1 k times the size of the optimal solution to this problem, where k is a positive integer and Δ is the maximum degree of G. The running time of this algorithm is constant communication rounds under the assumption of a synchronous communication model. [ABSTRACT FROM AUTHOR]

Different types of buildings in different climate zones have their own design specifications and specific user populations. Generally speaking, these populations have similar sensory feedbacks in their perception of environmental thermal comfort. Existing thermal comfort models do not incorporate personal thermal comfort models for specific populations. In terms of an algorithm, the existing work constructs machine learning models based on an established human thermal comfort database with variables such as indoor temperature, clothing insulation, et al., and has achieved satisfactory classification results. More importantly, such thermal comfort models often lack scientific interpretability. Therefore, this study selected a specific population as the research object, adopted the 0-order Takagi–Sugeno–Kang (TSK) fuzzy classifier as the base training unit, and constructed a shared feature-guided new TSK fuzzy classification algorithm with extra feature compensation (SFG-TFC) to explore the perception features of the population in the thermal environment of buildings and to improve the classification performance and interpretability of the model. First, the shared features of subdatasets collected in different time periods were extracted. Second, the extra features of each subdataset were independently trained, and the rule outputs corresponding to the key shared features were reprojected into the corresponding fuzzy classifiers. This strategy not only highlights the guiding role of shared features but also considers the important compensation effect of extra features; thereby, improving the classification performance of the entire classification model. Finally, the least learning machine (LLM) was used to solve the parameters of the "then" part of each basic training unit, and these output weights were integrated to enhance the generalization performance of the model. The experimental results demonstrate that SFG-TFC has better classification performance and interpretability than the classic nonfuzzy algorithms support vector machine (SVM) and deep belief network (DBN), the 0-order TSK, and the multilevel optimization and fuzzy approximation algorithm QI-TSK. [ABSTRACT FROM AUTHOR]

The solution of the multiobjective optimization problem was performed with the help of the Pareto approximation algorithm. The problem of multiobjective optimization of the reaction process conditions for the olefin hydroalumination catalytic reaction, with the presence of organoaluminum compounds diisobutylaluminiumchloride, diisobutylaluminiumhydrate, and triisobutylaluminum, was solved. The optimality criteria are the yield of the reaction resultants. The largest yield of the high-order organoaluminum compound Bu2AlR was observed for the reactions with diisobutylaluminiumhydrate and triisobutylaluminum. Such results were obtained due to the fact that in the case of diisobutylaluminiumchloride, Bu2AlR was used for the formation of ClBuAlR. The yield of the Schwartz reagent Cp2ZrHCl was higher by a third in the reaction in the presence of diisobutylaluminiumchloride. Unlike the experimental isothermal conditions, the temperature optimal control showed the sufficiency of the gradual growth temperature for achieving the same or higher values of optimality criteria. For computational experiments, the algorithm for solving the multi-criteria optimization problem was parallelized using an island model. [ABSTRACT FROM AUTHOR]

We first study the error performances of the Vector Weak Rescaled Pure Greedy Algorithm for simultaneous approximation with respect to a dictionary D in a Hilbert space. We show that the convergence rate of the Vector Weak Rescaled Pure Greedy Algorithm on A 1 (D) and the closure of the convex hull of the dictionary D is optimal. The Vector Weak Rescaled Pure Greedy Algorithm has some advantages. It has a weaker convergence condition and a better convergence rate than the Vector Weak Pure Greedy Algorithm and is simpler than the Vector Weak Orthogonal Greedy Algorithm. Then, we design a Vector Weak Rescaled Pure Greedy Algorithm in a uniformly smooth Banach space setting. We obtain the convergence properties and error bound of the Vector Weak Rescaled Pure Greedy Algorithm in this case. The results show that the convergence rate of the VWRPGA on A 1 (D) is sharp. Similarly, the Vector Weak Rescaled Pure Greedy Algorithm is simpler than the Vector Weak Chebyshev Greedy Algorithm and the Vector Weak Relaxed Greedy Algorithm. [ABSTRACT FROM AUTHOR]

A limited feasible region restricts individuals from evolving optionally and makes it more difficult to solve constrained optimization problems. In order to overcome difficulties such as introducing initial feasible solutions, a novel algorithm called the successive approximation genetic algorithm (SAGA) is proposed; (a) the simple genetic algorithm (SGA) is the main frame; (b) a self-adaptive penalty function is considered and the penalty factor is adjusted automatically by the proportion of feasible and infeasible solutions; (c) a generation-by-generation approach and a three-stages evolution are introduced; and (d) dynamically enlarging and reducing the tolerance error of the constraint violation makes it much easier to generate initial feasible solutions. Then, ten benchmarks and an engineering problem were adopted to evaluate the SAGA in detail. It was compared with the improved dual-population genetic algorithm (IDPGA) and eight other algorithms, and the results show that SAGA finds the optimum in 5 s for an equality constraint and 1 s for an inequality constraint. The largest constraint violation can be accurate to at least three decimal fractions for most problems. SAGA obtains a better value, of 1.3398, than the eight other algorithms for the engineering problem. In conclusion, SAGA is very suitable for solving nonlinear optimization problems with a single constraint, accompanied by more accurate solutions, but it takes a longer time. In reality, SAGA searched for a better solution along the bound after several iterations and converged to an acceptable solution in early evolution. It is critical to improve the running speed of SAGA in the future. [ABSTRACT FROM AUTHOR]

Featured Application: This article assesses different text representations for labeling unmarked dialog data, which can be applied to identify user intents directly relevant to dialog systems. Chatbots are becoming increasingly popular and require the ability to interpret natural language to provide clear communication with humans. To achieve this, intent detection is crucial. However, current applications typically need a significant amount of annotated data, which is time-consuming and expensive to acquire. This article assesses the effectiveness of different text representations for annotating unlabeled dialog data through a pipeline that examines both classical approaches and pre-trained transformer models for word embedding. The resulting embeddings were then used to create sentence embeddings through pooling, followed by dimensionality reduction, before being fed into a clustering algorithm to determine the user's intents. Therefore, various pooling, dimension reduction, and clustering algorithms were evaluated to determine the most appropriate approach. The evaluation dataset contains a variety of user intents across different domains, with varying intent taxonomies within the same domain. Results demonstrate that transformer-based models perform better text representation than classical approaches. However, combining several clustering algorithms and embeddings from dissimilar origins through ensemble clustering considerably improves the final clustering solution. Additionally, applying the uniform manifold approximation and projection algorithm for dimension reduction can substantially improve performance (up to 20%) while using a much smaller representation. [ABSTRACT FROM AUTHOR]

This paper aims to obtain the best shape accuracy evaluation algorithm for silicon nitride ceramic balls after lapping, and to extract the initial signal of the ball surface to improve the accuracy and reliability of the algorithm. The research methods of this paper are as follows: Firstly, an analysis of the uniform envelope of the lapping trajectory of ceramic balls is carried out to verify whether the lapping trajectory after processing can achieve a consistent envelope on the balls' surface. On this basis, it is found through experiments that the standard deviation SD between the roundness deviations of different contour sections is small. The value is maintained at approximately 0.03 μm, and the roundness deviation can approximately replace the spherical deviation. Then the different contour sections of the sphere are sampled by the Taylor roundness instrument. Considering the uncertainty, the sampling points of different contour sections are averaged and used as the original signal of the sphere surface. Then the EMD method is used to process the signal to be detected on the sphere surface. The initial signal of the sphere surface is extracted by judging whether the number of ripples Kc obtained by decomposition is greater than the critical value. Then the initial signal is used as the input value of the approximation algorithm. Through the roundness deviation approximation algorithm based on the least square method, the given minimum approximation domain range is finely processed. The divided fine points are used as the center of the circle to intersect with the initial signal. The maximum, minimum, and range of each circle are calculated to obtain the roundness error based on the minimum circumscribed circle, the maximum inscribed circle, and the minimum region method. Finally, the calculated values are compared with those obtained by the traditional algorithm. The experimental results of this paper show that the algorithm is consistent with the roundness error measured by the instrument, compared with the mainstream evaluation criteria. In summary, the conclusions can be drawn as follows: Through a large number of experimental cases and comparative experiments, the algorithm has high accuracy and reliability. The research results of this paper have essential reference significance for accurately evaluating the shape accuracy of ceramic balls in actual production. [ABSTRACT FROM AUTHOR]

In graph theory, a "dominating vertex set" is a subset of vertices in a graph such that every vertex in the graph is either a member of the subset or adjacent to a member of the subset. In other words, the vertices in the dominating set "dominate" the remaining vertices in the graph. Dominating vertex sets are important in graph theory because they can help us understand and analyze the behavior of a graph. For example, in network analysis, a set of dominant vertices may represent key nodes in a network that can influence the behavior of other nodes. Identifying dominant sets in a graph can also help in optimization problems, as it can help us find the minimum set of vertices that can control the entire graph. Now that there are theories about vagueness, it is important to define parallel ideas in vague structures, such as intuitionistic fuzzy graphs. This paper describes a better way to find dominating vertex sets (DVSs) in intuitive fuzzy graphs (IFGs). Even though there is already an algorithm for finding DVSs in IFGs, it has some problems. For example, it does not take into account the vertex volume, which has a direct effect on how DVSs are calculated. To address these limitations, we propose a new algorithm that can handle large-scale IFGs more efficiently. We show how effective and scalable the method is by comparing it to other methods and applying it to water flow. This work's contributions can be used in many areas, such as social network analysis, transportation planning, and telecommunications. [ABSTRACT FROM AUTHOR]