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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]