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In this paper, we are interested in algorithms that take in input an arbitrary graph G , and that enumerate in output all the (inclusion-wise) maximal "subgraphs" of G which fulfil a given property Π. All over this paper, we study several different properties Π , and the notion of subgraph under consideration (induced or not) will vary from a result to another. More precisely, we present efficient algorithms to list all maximal split subgraphs, maximal induced cographs and maximal threshold graphs of a given input graph. All the algorithms presented here run in polynomial delay, and moreover for split graphs it only requires polynomial space. In order to develop an algorithm for maximal split (edge-)subgraphs, we establish a bijection between the maximal split subgraphs and the maximal stable sets of an auxiliary graph. For cographs and threshold graphs, the algorithms rely on a framework recently introduced by Conte & Uno (2019) called Proximity Search. Finally we consider the extension problem, which consists in deciding if there exists a maximal induced subgraph satisfying a property Π that contains a set of prescribed vertices and that avoids another set of vertices. We show that this problem is NP-complete for every non-trivial hereditary property Π. We extend the hardness result to some specific edge version of the extension problem. [ABSTRACT FROM AUTHOR]

In this paper, we consider how to accurately solve the product eigenvalue problem for the class of sign regular (SR) matrices with signature (1 , ⋯ , 1 , − 1) and the class of totally nonnegative (TN) matrices, which tend to be extremely ill-conditioned. We present algorithms with O (n 3) complexity to accurately compute the parameter matrices of products of TN matrices and SR matrices with signature (1 , ... , 1 , − 1). Based on the accurate parameter matrices, all eigenvalues of the product matrix are computed to high relative accuracy. Numerical experiments are provided to confirm the claimed high relative accuracy. [ABSTRACT FROM AUTHOR]

Interpolation by polynomials on equispaced points is not always convergent due to the Runge phenomenon, and also, the interpolation process is exponentially ill-conditioned. By taking advantage of the optimality of the interpolation processes on the Chebyshev-Lobatto nodes, one of the best strategies to defeat the Runge phenomenon is to use the mock-Chebyshev nodes for polynomial interpolation. Mock-Chebyshev nodes asymptotically follow the Chebyshev distribution, and they are selected from a sufficiently large set of equispaced nodes. However, there are few studies in the literature regarding the computation of these points. In a recent paper [1] , we have introduced a fast algorithm for computing the mock-Chebyshev nodes for a given set of (n + 1) Chebyshev-Lobatto points using the distance between each pair of consecutive points. In this study, we propose a modification of the algorithm by changing the function to compute the quotient of the distance and show that this modified algorithm is also fast and stable; and gives a more accurate grid satisfying the conditions of a mock-Chebyshev grid with the complexity being O (n). Some numerical experiments using the points obtained by this modified algorithm are given to show its effectiveness and numerical results are also provided. A bivariate generalization of the mock-Chebyshev nodes to the Padua interpolation points is discussed. [ABSTRACT FROM AUTHOR]

In this paper, we describe some Krylov subspace methods for computing eigentubes and eigenvectors (eigenslices) for large and sparse third-order tensors. This work provides projection methods for computing some of the largest (or smallest) eigentubes and eigenslices using the t-product. In particular, we use the tensor Arnoldi's approach for the non-hermitian case and the tensor Lanczos's approach for f-hermitian tensors. We also use the tensor block Arnoldi method to approximate the extreme eigentubes of a large tensor. Computed examples are given to illustrate the effectiveness of these methods. [ABSTRACT FROM AUTHOR]

In this paper, we study a posteriori error estimates of the fast L 1 − 2 scheme for time discretization of time fractional parabolic differential equations. To overcome the huge workload caused by the nonlocality of fractional derivative, a fast algorithm is applied to the construction of the L 1 − 2 scheme. Employing the numerical solution obtained by the fast L 1 − 2 scheme, a piecewise continuous function approximating the exact solution is constructed. Then, by exploring the error equations, a posteriori error estimates are obtained in different norms, which depend only on the discretization parameters and the data of the problems. Various numerical experiments for the fractional parabolic equations with smooth or nonsmooth exact solutions on different time meshes, including the frequently-used graded mesh, are carried out to verify and complement our theoretical results. Based on the obtained a posteriori error estimates, a time adaptive algorithm is proposed to reduce the computational cost substantially and provides efficient error control for the solution. • We derive a posteriori error estimates for the fast L 1 − 2 method for solving TFPDEs. • We design an adaptive fast algorithm based on these error estimates. • Theoretical analysis reveals how the error depends on the a posteriori quantities. • The a posteriori error estimators of the fast L 1 − 2 method are convergent of order 2. • The adaptive mesh can recover the convergence order of the a posteriori error estimators. [ABSTRACT FROM AUTHOR]

Let i be a positive integer, an i -star denoted by S i is a complete bipartite graph K 1 , i. An { S 2 , S 3 } -packing of a graph G is a collection of vertex-disjoint subgraphs of G in which each subgraph is a 2-star or a 3-star. The maximum { S 2 , S 3 } -packing problem is to find an { S 2 , S 3 } -packing of a given graph containing the maximum number of vertices. The { S 2 , S 3 } -factor problem is to answer whether there is an { S 2 , S 3 } -packing containing all vertices of the given graph. The { S 2 , S 3 } -factor problem is NP-complete in cubic graphs. In this paper we design a quadratic-time algorithm for finding an { S 2 , S 3 } -packing of G that covers at least thirteen-sixteenths of its vertices with only a few exceptions. We also present some (2 , 3) -regular graphs with their maximum { S 2 , S 3 } -packings covering exactly thirteen-sixteenths of their vertices. [ABSTRACT FROM AUTHOR]

Given a graph G , Min-Max-Acy-Matching is the problem of finding a maximal matching M in G of minimum cardinality such that the set of M -saturated vertices induces an acyclic subgraph in G. The decision version of Min-Max-Acy-Matching is known to be NP -complete. In this paper, we strengthen this result by proving that the decision version of Min-Max-Acy-Matching is NP -complete even for dually chordal graphs. Also, we give the first positive algorithmic result for Min-Max-Acy-Matching by proposing a linear-time algorithm for computing a minimum cardinality maximal acyclic matching in proper interval graphs, a subclass of dually chordal graphs. [ABSTRACT FROM AUTHOR]

We investigate the problem of candidate keys enumeration of a relational schema. The notion of candidate keys is also known as minimal generators in lattice or FCA terminologies or as implicates in logic. Given an implicational base or a set of functional dependencies, Lucchesi and Osborn gave in Lucchesi and Osborn (1978) an incremental polynomial time algorithm to enumerate all candidate keys of a relation schema. Using the state of the art of enumeration techniques (see Elbassioni, 2015), however, it turns out to be a polynomial delay algorithm and exponential space (see Ennaoui, 2018 and Bérczi et al., 2022). In this paper we exploit the presence of unary functional dependencies that define a partial order over the set of attributes. We use a bijection between key-ideal sets (ideal associated to a key) and candidate keys, and we show that the number of key-ideal sets can be exponential in the number of minimal key-ideal sets. Moreover, if there is a polynomial delay and space algorithm to enumerate minimal key-ideal sets then there is one for all candidate keys. We also give a polynomial delay algorithm to enumerate all minimal key-ideal sets. As a consequence, we derive a polynomial delay hybrid 1 1 Hybrid means that two algorithms are combined to enumerate candidate keys. algorithm to enumerate all candidate keys using space bounded by the number of minimal key-ideal sets. [ABSTRACT FROM AUTHOR]

In this paper, we provide an efficient algorithm to construct almost optimal (k , n , d) -superimposed codes with runlength constraints. A (k , n , d) -superimposed code of length t is a t × n binary matrix such that any two 1's in each column are separated by a run of at least d 0's, and such that for any column c and any other k − 1 columns, there exists a row where c has 1 and all the remaining k − 1 columns have 0. These combinatorial structures were introduced by Agarwal et al. (2020), in the context of Non-Adaptive Group Testing algorithms with runlength constraints. By using Moser and Tardos' constructive version of the Lovász Local Lemma, we provide an efficient randomized Las Vegas algorithm of complexity Θ (t n 2) for the construction of (k , n , d) -superimposed codes of length t = O (d k log n + k 2 log n). We also show that the length of our codes is shorter, for n sufficiently large, than that of the codes whose existence was proved in Agarwal et al. (2020). [ABSTRACT FROM AUTHOR]

This paper proposes a numerical method for solving the time-fractional Stokes-Darcy problem using a partitioned time stepping algorithm with the Beavers-Joseph-Saffman condition. The stability of the method is established under a moderate time step restriction, τ ≤ C where C represents physical parameters, by utilizing a discrete fractional Gronwall type inequality. Additionally, error estimates are derived to provide insight into the accuracy of the proposed method. Numerical experiments that support the theoretical results are presented. [ABSTRACT FROM AUTHOR]

The paper addresses the challenges of task migration and resource allocation in heterogeneous cloud–edge environments, where dynamic and stochastic conditions complicate efficient scheduling. To tackle this, the authors propose a novel scheduling algorithm combining soft actor–critic (SAC) agent with masked layer and graph convolutional network (GCN), namely MGSAC algorithm. MGSAC utilizes GCN to extract hidden structural features from the environment, enabling better adaptation to dynamic changes. Additionally, a learnable mask layer filters out ineffective actions, refining the selection of scheduling strategies and improving overall performance. By evaluating MGSAC on the real-world Bit-Brain dataset and simulating it using Cloud-Sim, experimental results demonstrate its superiority over existing algorithms in energy consumption, task response time, task migration time, and task Service-Level-Agreement violations rate, showcasing its effectiveness in real-world scenarios. [ABSTRACT FROM AUTHOR]

The complex continuous-time algebraic Riccati equation (CCARE) is quadratic, which is closely related to the analysis of the optimal control problem. In this paper, we apply Newton method as the outer iteration and an efficient general alternating-direction implicit (GADI) method as the inner iteration to solve CCARE. Meanwhile, we propose the inexact Newton-GADI method to further improve the efficiency of the algorithm. We give the convergence analysis of our proposed method and prove that its convergence rate is faster than the classical Newton-ADI method. Finally, some numerical examples are given to illustrate the effectiveness of our algorithms and the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

For the design of feeder lines within a region, previous studies assume that the hub port is given in advance. It is necessary to investigate locating hub port together with designing feeder lines for a region. This paper proposes a hub port location and routing problem for a single-hub feeder network, which addresses feeder line design and hub port location. The proposed problem also considers liner shipping network connectivity (the connection between feeder lines and main lines via container transshipment at hub ports). It is described by a mixed integer linear program, which is solved by a genetic algorithm devised. Numerical experiments show that: i) the devised algorithm can efficiently solve our model; ii) due to considering liner shipping network connectivity, the optimal solution of hub port location and feeder line design becomes more rational, as compared with that without considering liner shipping network connectivity. • Investigate hub port location and routing for a single-hub feeder network. • Propose a mixed integer linear program. • Devise a genetic algorithm. [ABSTRACT FROM AUTHOR]

Many applications of multi-agent systems have to execute some tasks in certain formations, while not all nodes have access to localization technologies such as GPS. This paper investigates the problem of formation control for multi-agent systems in three-dimensional space relying on distances between nodes and positions of anchor nodes. The position information of all nodes is represented using generalized spatial barycentric coordinates, and the condition that the formation shape can be uniquely represented by the barycentric coordinates is given. Then, based on this representation method, a distributed spatial formation algorithm is proposed to guide all agents from their initial positions towards the desired ones. Finally, simulation studies have been presented to validate the effectiveness and correctness of the proposed algorithm and design conditions. • A formation shape representation using spatial barycentric coordinates is proposed. • The condition when the formation can be uniquely formed is provided. • A 3D distributed formation algorithm based on barycentric coordinates is proposed. • Simulations are provided to validate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a set of Nash equilibrium tracking control strategies based on mixed zero-sum (MZS) game for the continuous-time nonlinear multi-player systems with deferred asymmetric time-varying (DATV) full-state constraints and unknown initial state. Firstly, an improved shift transformation is used to modify the original constrained system with an unknown initial state into a barrier transformable constrained system. Then, based on the barrier transformable constrained system and predefined reference trajectory, an unconstrained augmented system is formed through the application of the barrier function (BF) transformation. Furthermore, the MZS game Nash equilibrium tracking control strategies are derived by establishing the tracking error related quadratic cost functions and corresponding HJ functions for different players. On this basis, a critic-only structure is established to approximate the control strategy of every player online. By employing Lyapunov theory, it is proven that the neural network weights and tracking error are uniformly ultimately bounded (UUB) within DATV full-state constraints. Simulation experiments of a three-player nonlinear system demonstrate that our algorithm successfully handles deferred state constraints and unknown initial conditions, ensuring that the system states follow the desired reference trajectories. Simulation results further validate the uniform ultimate boundedness of neural network weights and tracking errors. • A set of Nash equilibrium strategies for continuous-time nonlinear multi-player systems with state constraints and unknown initial conditions are introduced. • An improved shift transformation is applied for barrier transformability and control strategy development. • An unconstrained system is constructed using barrier function transformation. [ABSTRACT FROM AUTHOR]

In mathematics, a dissection of a square (or rectangle) into non-congruent rectangles is a Mondrian partition. If all the rectangles have the same area, it is called a perfect Mondrian partition. In this paper, we present a computational result by which we can affirm that there is no perfect Mondrian partition of a length n square for n ≤ 1000. Using the same algorithm we have been able to establish that there is no perfect Mondrian partition of a n × m rectangle for n , m ≤ 400. [ABSTRACT FROM AUTHOR]

Sweep cover is a basic issue in wireless sensor networks, which uses mobile sensors to inspect points of interest (PoIs) periodically. There are many studies on the problem assuming that all mobile sensors have a uniform velocity, while some literature shows that using heterogeneous velocities may greatly increase the difficulty of research. In this paper, we study a minimum energy partial sweep cover (MinEPSC) problem on a line, the goal of which is to minimize energy consumption to sweep-cover at least K PoIs, where the energy consumption of a mobile sensor is related with its velocity in somewhat arbitrary but monotone manner. We design algorithms with theoretically guaranteed approximation ratios under different assumptions on the candidate velocity sets. [ABSTRACT FROM AUTHOR]

For an integer k ≥ 2 , a k - community structure in an undirected graph is a partition of its vertex set into k sets called communities , each of size at least two, such that every vertex of the graph has proportionally at least as many neighbours in its own community as in any other community. In this paper, we give a necessary and sufficient condition for a forest on n vertices to admit a k -community structure. Furthermore, we provide an O (k 2 ⋅ n 2) -time algorithm that computes such a k -community structure in a forest, if it exists. These results extend a result of Bazgan et al., 2018. We also show that if communities are allowed to have size one, then every forest with n ≥ k ≥ 2 vertices admits a k -community structure that can be found in time O (k 2 ⋅ n 2). We then consider threshold graphs and show that every connected threshold graph admits a 2-community structure if and only if it is not isomorphic to a star; also if such a 2-community structure exists, we explain how to obtain it in linear time. We further describe an infinite family of disconnected threshold graphs, containing exactly one isolated vertex, that do not admit any 2-community structure. Finally, we present a new infinite family of connected graphs that may contain an even or an odd number of vertices without 2-community structures, even if communities are allowed to have size one. [ABSTRACT FROM AUTHOR]

In Steinerberger (2021) [23] and Shao (2023) [21] , two new types of Kaczmarz algorithms, which share some similarities, for consistent linear systems were proposed. These two algorithms not only compete with many previous Kaczmarz algorithms but, more importantly, reveal some interesting new geometric properties of solutions to linear systems that are not obvious from the standard viewpoint of the Kaczmarz algorithm. In this paper, we comprehensively study these two algorithms. First, we theoretically analyse the algorithms for solving least squares, which is more common in practice. Second, we extend the two algorithms to block versions and provide their rigorous estimate on the convergence rates. Third, as a theoretical complement, we provide more results on properties of the convergence rate. All these results contribute to a more thorough understanding of these algorithms. [ABSTRACT FROM AUTHOR]

A tuple (Z 1 , ... , Z p) of matrices of size r × r is said to be a commuting extension of a tuple (A 1 , ... , A p) of matrices of size n × n if the Z i pairwise commute and each A i sits in the upper left corner of a block decomposition of Z i (here, r and n are two arbitrary integers with n < r). This notion was discovered and rediscovered in several contexts including algebraic complexity theory (in Strassen's work on tensor rank), in numerical analysis for the construction of cubature formulas and in quantum mechanics for the study of computational methods and the study of the so-called "quantum Zeno dynamics." Commuting extensions have also attracted the attention of the linear algebra community. In this paper we present 3 types of results: (i) Theorems on the uniqueness of commuting extensions for three matrices or more. (ii) Algorithms for the computation of commuting extensions of minimal size. These algorithms work under the same assumptions as our uniqueness theorems. They are applicable up to r = 4 n / 3 , and are apparently the first provably efficient algorithms for this problem applicable beyond r = n + 1. (iii) A genericity theorem showing that our algorithms and uniqueness theorems can be applied to a wide range of input matrices. [ABSTRACT FROM AUTHOR]

In the known Interval Scheduling problem with Machine Availabilities (ISMA), each machine has a contiguous availability interval, and each job has a specific time interval which has to be scheduled. The objective is to schedule all jobs such that the machines' availability intervals are respected or to decide that there exists no such schedule. We extend ISMA by introducing machine capacities and flexible machine end times. Using machine capacities we model parallel processing of multiple jobs per machine, which leads to the Multithread Interval Scheduling with Machine Availabilities (MISMA). Limited machine availabilities are usually due to maintenance. Time slots for maintenance at the end of a processing period are often predetermined by staff schedules before the slots are assigned to specific machines. This motivates a variant of MISMA in which the end times of the machines' availability intervals can be permuted, the Flexible Multithread ISMA (FLEXMISMA). In this paper, we determine a tight classification of conditions that are required for obtaining a polynomial-time algorithm for both MISMA and FLEXMISMA. More specifically, we show that FLEXMISMA is at least as hard as MISMA. For FLEXMISMA, we present polynomial-time algorithms for instances (i) with at most two available machines at a time, and (ii) with constantly many parallel jobs at each point in time, which both also solve MISMA; (iii) with arbitrarily many machines of capacity one each, in which case MISMA is known to be NP -hard; and (iv) with jobs having length one or two, for which the complexity of MISMA remains open Furthermore, we complement result (i) by showing that both problems are NP -hard already for instances with three machines as a special case of the Vertex-Disjoint Paths problem. In contrast to (iii), we prove that increasing the capacity of machines from one to two renders FLEXMISMA NP -hard as well for arbitrarily many machines. [ABSTRACT FROM AUTHOR]

The elastic bending energy model is commonly used to describe the shape transformation of biological lipid vesicles, making it a classical phase field model. In this paper, by coupling the elastic bending energy with the total variation (TV) regularization, we develop an elastic bending-TV model for image inpainting. By solving the energy minimization problem of this model, we obtain the results for image processing. We adopt an operator splitting method for the model and the numerical scheme involves the introduction of two vector- and scalar-valued functions to reconstruct this functional. The energy minimization problem is transformed into finding the steady state solution of artificial time-dependent PDE systems. At each fractional step, we can find either a closed-form solution or being solved by an efficient algorithm, which is a very robust and stable algorithm. Experimental results validate the superiority of our model and the effectiveness of the scheme for image inpainting. [ABSTRACT FROM AUTHOR]

Despite the effectiveness of deep neural networks, feed-forward neural networks (FFNNs) continue to play a crucial role in many applications, especially when dealing with limited data availability. The primary challenge in FFNNs is determining the optimal weights during the training process, aiming to minimise the disparity between actual and predicted outputs. Although gradient-based techniques like backpropagation (BP) have traditionally been popular for FFNN training, they come with inherent limitations, such as sensitivity to initial weights and susceptibility to getting trapped in local optima. To overcome these challenges, we introduce a novel approach based on the Gaining-Sharing Knowledge-based(GSK) algorithm. To the best of our knowledge, this paper represents the first exploration of GSK for neural network training. After obtaining the appropriate weights for the FFNN by the GSK, the weights and biases are utilised to initialise a Levenberg–Marquardt backpropagation (LMBP) algorithm, serving as a local search component. In other words, our proposed algorithm, GSK-LocS, leverages the global search capabilities of the GSK algorithm and combines them with the local search capabilities of LMBP for neural network training. This integration mitigates sensitivity to initial values and reduces the risk of being trapped in local optima. Experimental results conducted on classification and approximation problems provide compelling evidence that our proposed algorithm is highly competitive compared to other existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a two-grid algorithm for solving parabolic equation with nonlinear compressibility coefficient, spatially discretized by the weak Galerkin finite element method. The optimal error estimates are established. We further show that both grid solutions can achieve the same accuracy as long as the grid size satisfies H = O (h 1 / 2). Compared with Newton iteration, the two-grid algorithm could greatly reduce the computational cost. We verify the effectiveness of the algorithm by performing numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, a vision-aided inertial navigation method for planetary landing based on the direct method is proposed. This approach requires only a monocular camera and an inertial measurement unit (IMU) to be equipped on the lander. Unlike traditional feature-based visual-aided inertial navigation algorithms, which entail extracting and matching image features and thus incurring high computational costs, the proposed method utilizes the direct method that tracks any pixel with a sufficient intensity gradient. By jointly optimizing photometric and inertial errors, the proposed algorithm estimates the camera motion and sparse map of the scene. Simulation results demonstrate that the proposed method reduces computation by nearly 65 % compared to the feature point method, with a slight decrease in navigation accuracy. • The direct method is applied in the planetary landing mission. • The proposed algorithm reduces the computation cost with slight accuracy loss. • This algorithm can obtain the map of the landing area while navigating. [ABSTRACT FROM AUTHOR]

This paper investigates the analytical fuzzy findings of a two-dimensional fuzzy fractional-ordered heat problem including some source of terms under certain conditions. The Sumudu residual power series scheme (SRPSS) is an innovative novel to deal with the combine form of the Sumudu transform (ST) and the residual power series scheme (RPSS) which efficiently generate analytical results in rapidly converging series forms. The Caputo derivative is applied to model the physical problem. The most notable aspect of this algorithm is its ability to generate results quickly and without difficulty as compared to the conventional RPSS. We present three numerical cases of 2D heat problem with fuzzy fractional order to express the performance and validity of suggested scheme. Graphical analysis from the derived solutions reveals that SRPSS is straightforward, accurate, and suitable to analyze the findings of fuzzy fractional problems. [ABSTRACT FROM AUTHOR]

The performance of kernel adaptive filtering algorithms (KAFs) with nonlinear recurrent structures surpasses traditional KAFs, attributed to the nonlinear contribution of feedback. Nevertheless, the existing nonlinear recurrent KAFs primarily focus on a single feedback output, potentially limiting their latent filtering capabilities. In this paper, we introduce a novel alternative, named nonlinear recurrent kernel normalized least-mean-square with multiple feedbacks (NR-KNLMS-MF), which leverages the information from multiple feedback outputs. Additionally, to tackle the computational complexity challenges associated with KAFs, we integrate random Fourier features (RFF) into NR-KNLMS-MF, resulting in an efficient variant called as RFF-NR-KNLMS-MF. Furthermore, we conduct a theoretical analysis of the mean-square convergence for RFF-NR-KNLMS-MF. Simulation results on time-series predictions demonstrate the superiority of our proposed algorithms over other competing alternatives, validating their effectiveness. • We introduce a novel nonlinear recurrent KLMS with multiple feedbacks. • We integrate the RFF into NR-KNLMS-MF resulting in an efficient variant. • For RFF-NR-KNLMS-MF, we take a theoretical analysis of the mean-square convergence. • Simulation results demonstrate the superiority of the proposed algorithms. [ABSTRACT FROM AUTHOR]

The hypergravity centrifugal shaking table (HCST) is the most effective means for studying the disaster effects of rock and soil earthquakes, and the accurate control of acceleration waveform recurrence is the critical problem. This paper compares the dynamic characteristics of the normal gravity shaking table (NGST) and the HCST, highlighting the latter's particularities, and analyzes the limitations of the existing control strategy. Meanwhile, a hypergravity unidirectional airborne shaking table (HUAST) is designed, and a data-driven iterative learning control and two-degree-of-freedom control-based acceleration waveform reproduction strategy is proposed and experimentally verified. • The research object is based on the hypergravity shaking table. • A 2-DOF servo control structure of shaking table is proposed. • The iterative learning was combined with the data-driven identification algorithm. • The shaking table is used to verify the effectiveness and advancement of the proposed composite control strategy. [ABSTRACT FROM AUTHOR]

The paper discusses the possibility of increasing the effectiveness of strategic management of research and development activities in higher education institutions. To achieve this goal, the authors proposed an algorithm for selecting competencies, which allows for the distribution of university employees and students among research and development teams in accordance with their individual competencies for carrying out research and development work. The paper covers the problem statement of competence selection, an overview of natural language processing methods for algorithm development, problematic areas of the algorithm, and prospects for its implementation in university management. [ABSTRACT FROM AUTHOR]

This paper proposes a novel nature-inspired meta-heuristic algorithm, named Snow Geese Algorithm. It is inspired by the migratory behavior of snow geese and emulates the distinctive "Herringbone" and "Straight Line" shaped flight patterns observed during their migration. The algorithm is structured into three main phases for benchmark testing. In the first phase, the Snow Geese Algorithm's numerical results are compared with those of several classical meta-heuristic algorithms using the same test functions and original data from these algorithms. In the second phase, in order to minimize potential variations during the comparison, all algorithms undergo evaluation on a standardized testing platform. In the third phase, this paper applies the Snow Geese Algorithm to solve four widely recognized engineering optimization problems: the tubular column design, piston lever optimization design, reinforced concrete beam design and car side impact design. These real-world engineering problems serve as test cases to assess Snow Geese Algorithm problem-solving capabilities. The primary objective of the Snow Geese Algorithm is to provide an alternative perspective for tackling complex optimization problems. Please note that the complete source code for the Snow Geese Algorithm is publicly available at https://github.com/stones3421/SGA-project. • Snow Geese Algorithm: A novel meta-heuristic approach inspired by snow geese flight behavior, tackling optimization problems. • Two-stage Strategy: Mimics snow geese exploration and exploitation patterns, setting it apart from traditional methods. • Performance Evaluation: Multiple algorithms are assessed on different problems. • Algorithm Features: Experimental results validate the effectiveness of the Snow Geese Algorithm. • Practical Applications: Snow Geese Algorithm shows potential in engineering optimization, aiding accurate decision-making. [ABSTRACT FROM AUTHOR]

In this paper, a pipeline leakage detection algorithm based on information fusion of pressure and flow is proposed, and its core work is the construction of BPA based on discount factors. The wavelet packet decomposition is carried out for the original signals, and the processed signals are used to train different SVM classifiers to achieve the first identification results. For the samples whose initial classification results are not completely consistent, BPA is calculated according to the confusion matrixes of the initial SVM classifiers. In this paper, static discount factors and dynamic discount factors are constructed using different methods, and dynamic discount factors are modified when decisions fail. Then comprehensive discount factors are constructed based on the combination of different static discount factors and dynamic discount factors. The Shafer discount rule is used to modify BPA. Finally, D-S evidence theory is used to fuse the BPA results of all classifiers under different discount combinations. Experiments show that this algorithm can effectively use the correlation of evidences to reasonably fuse the decision results of multiple sensors, overcome the problem that the accuracy of a single sensor is not high enough for leakage identification, and improve the identification accuracy of pipeline leakage. [ABSTRACT FROM AUTHOR]

This paper introduces the hybrid high-order (HHO) method for solving the nonlinear strongly damped wave equation. We comprehensively analyze the semi-discrete and fully-discrete implicit schemes, including energy and L 2 norm, with convergence rates of m + 1 and m + 2 in space (m ≥ 0), respectively. In addition, we combine the two-grid algorithm (TGA) with the HHO method (TGA-HHO) to improve computational efficiency and analyze the TGA-HHO method. To improve the computational efficiency further, we combine the proper orthogonal decomposition (POD) technique with the TGA-HHO method (POD-TGA-HHO). Finally, we provide numerical examples to validate the effectiveness of the HHO, TGA-HHO, and POD-TGA-HHO algorithms. [ABSTRACT FROM AUTHOR]

In a seminal paper in 1959, Marcus and Ree proved that every n × n bistochastic matrix A satisfies ‖ A ‖ F 2 ≤ max σ ∈ S n ⁡ A i , σ (i) where S n is the symmetric group on { 1 , ... , n }. Erdős asked to characterize the bistochastic matrices for which the equality holds in the Marcus–Ree inequality. We refer to such matrices as Erdős matrices. While this problem is trivial in dimension n = 2 , the case of dimension n = 3 was only resolved recently in [4] in 2023. We prove that for every n , there are only finitely many n × n Erdős matrices. We also give a complete characterization of Erdős matrices that yields an algorithm to generate all Erdős matrices in any given dimension. We also prove that Erdős matrices can have only rational entries. This answers a question of [4]. [ABSTRACT FROM AUTHOR]

This paper is concerned with scattering of electromagnetic waves by an orthotropic infinite cylinder. Such a scattering problem is modeled by a orthotropic media scattering problem. By constructing the Dirichlet-to-Neumann (DtN) operator and introducing a transparent boundary condition, the orthotropic media problem is reformulated as a bounded boundary value problem. An a posteriori error estimate is derived for the finite element method with the truncated DtN boundary operator. The a posteriori error estimate contains the finite element approximation error and the truncation error of the DtN boundary operator, where the latter decays exponentially with respect to the truncation parameter. Based on the a posteriori error estimate, an adaptive finite element algorithm is proposed for solving the orthotropic media problem. Numerical examples are presented to demonstrate the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Contour parallel toolpaths are the most common machining strategies for 2.5D features. To enhance the machining efficiency, different cutting paths for various tool combinations should be considered. However, existing algorithms have paid limited attention to multi-tool cutting, which is nevertheless an industrial practice in roughening and finishing. This paper proposes a rapid generation method for contour parallel toolpaths based on an accurate two-dimensional discrete medial-axis transform (MAT) for complex closed cavities. The accurate discrete MAT was refined using the Delaunay triangulation (DT) method. According to the definition of MAT, the calculated discrete medial axis (MA) points are adjusted to obtain accurate MA points by iterative method. The accurate discrete MAT obtained served as the basis for the toolpath generation. Contour parallel toolpaths can be rapidly generated by applying the discrete MAT and the proposed toolpath generation method. The resulting toolpaths have been validated to closely match the cutting path obtained through commercial software calculations, which require much higher computational efforts. The proposed method introduces a novel accurate discrete medial axis calculation method and enables the rapid computation of multi-tool combination cutting paths., which is more suitable in toolpath generation, cutting time prediction and toolset optimization in practice. • Effective categorization of Delaunay triangles into 4 cases and 10 sub-cases. • Accurate calculation of discrete medial axis transform based on error analysis. • Rapid generation of contour parallel toolpaths with multiple tool combinations. [ABSTRACT FROM AUTHOR]

This paper proposes and develops a novel method, namely the Partially Iterative Algorithm (PIA), for high-speed assessment of flatness deviation for point cloud data, which is typically measured data obtained by advanced instruments for precision manufacturing, such as optical scanners and industrial computed tomography. Firstly, an enhanced flatness deviation model is established based on the minimum zone principle, which is strictly adhered to the latest ISO definition. Secondly, the proposed method is detailed, including the Dynamic Point Set (DPS), the update scheme, and the terminal condition. Thirdly, comparisons are conducted with typical methods for flatness deviation assessment, along with a practicability test via the simulated dataset and measuring dataset. The results show that the proposed method can accurately and rapidly assess flatness deviation on point cloud data with massive measuring points. • Quickly evaluating flatness deviation for point cloud with a massive number of points. • The algorithm strictly adheres to ISO standards. • Outperformance other algorithms in calculation time. • Comparison shows its high level of accuracy. [ABSTRACT FROM AUTHOR]

The increase in the number of vehicles on roads has compounded the difficulty in parking them when people go out for movies, shopping, theatre, etc. Thus, this paper proposes smart parking system. The reservation of the parking slots can be made using this proposed smart parking system. Unlike the methods proposed in the existing research, the system proposed in this paper divides the parking area into 3 parts. One for conventional parking, one for vehicles with reservation and the other for the vehicles with and without reservation. Learning automata is used in the proposed system to determine the percentage of the parking area for conventional parking. In general, the proportionate of the slots for reserved parking, conventional parking and common slots need to be assumed. Learning Automata helps in determining this proportionate optimally. The AES-256 encryption algorithm is used to provide security for the details provided by the user during reservation process. Goodput value is maintained for each vehicle which increases or decreases the chances of getting a reservation. The time limit for the reservation of the parking slot is also maintained after which the reservation gets cancelled automatically. Markov Model is used to represent the system. The performance of the proposed algorithm, Learning Automata and Reservation based Secure Smart Parking System (LA-RSSPS) is simulated and evaluated in terms of average waiting time, search time, the probability with which the vehicles do not get parking slot when they do not have reservation and the probability with which the vehicles do not get reservation and is compared with ProNet and iERS. Results have shown that our scheme preforms better than the ProNet and iERS competing schemes. The comparison of analytical and simulations results are also presented. [ABSTRACT FROM AUTHOR]

Let G = (V , E) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex is adjacent to a vertex in S , and every vertex in V − S is adjacent to a vertex in V − S. The total restrained domination number of G , denoted γ t r (G) , is the smallest cardinality of a total restrained dominating set of G. In this paper we show that if G is a K 1 , ℓ -free graph with δ ≥ ℓ ≥ 3 and δ ≥ 5 , then γ t r (G) ≤ n 1 − (2 δ − 3) (2 δ) δ δ − 1 + o δ (1) . [ABSTRACT FROM AUTHOR]

This paper introduces a distributed control approach for optimizing the operation of islanded DC microgrids (µGs), accounting for cyber delays and network failures. Initially, an integrated network emulation platform is utilized to calculate realistic cyber delays for islanded DC µGs employing IEC 61850 communication standard. To address the instability issues arising from cyber delays, the Artstein-Kwon-Pearson reduction technique is employed to convert the system with cyber delays into one without delays. The Subsequently, a consensus-based generation-cost optimization algorithm is designed for maintaining the economic operation of the µG. This algorithm efficiently equalizes the incremental costs (ICs) of all distributed generators (DGs) in a fully distributed manner, while adhering to the DGs capacity limits. Additionally, a fully distributed voltage regulation control is developed to stabilize µG average voltage, ensuring the balance between generation and demand. The efficacy of the formulated control technique is substantiated through diverse case studies, thereby underscoring its superior operational performance. [ABSTRACT FROM AUTHOR]

Efficient real-time power optimization of direct methanol fuel cell (DMFC) system is crucial for enhancing its performance and reliability. The power of DMFC system is mainly affected by stack temperature and circulating methanol concentration. However, the methanol concentration cannot be directly measured using reliable sensors, which poses a challenge for the real-time power optimization. To address this issue, this paper investigates the operating mechanism of DMFC system and establishes a system power model. Based on the established model, reinforcement learning using Q-learning algorithm is proposed to control methanol supply to optimize DMFC system power under varying operating conditions. This algorithm is simple, easy to implement, and does not rely on methanol concentration measurements. To validate the effectiveness of the proposed algorithm, simulation comparisons between the proposed method and the traditional perturbation and observation (P&O) algorithm are implemented under different operating conditions. The results show that proposed power optimization based on Q-learning algorithm improves net power by 1% and eliminates the fluctuation of methanol supply caused by P&O. For practical implementation considerations and real-time requirements of the algorithm, hardware-in-the-loop (HIL) experiments are conducted. The experiment results demonstrate that the proposed methods optimize net power under different operating conditions. Additionally, in terms of model accuracy, the experimental results are well matched with the simulation. Moreover, under varying load condition, compared with P&O, proposed power optimization based on Q-learning algorithm reduces root mean square error (RMSE) from 7.271% to 2.996% and mean absolute error (MAE) from 5.036% to 0.331%. • Proposed power optimization method considers the overall power of the DMFC system. • Methanol supply control can be achieved without requiring concentration information. • Application of Q-learning algorithm is simple, real-time, and greatly reduce the complexity. [ABSTRACT FROM AUTHOR]

In this paper, by applying the supplementary variable method (SVM), some high-order, conformal structure-preserving, linearized algorithms are developed for the damped nonlinear Schrödinger equation. We derive the well-determined SVM systems with the conformal properties and they are then equivalent to nonlinear equality constrained optimization problems for computation. The deduced optimization models are discretized by using the Gauss type Runge-Kutta method and the prediction-correction technique in time as well as the Fourier pseudo-spectral method in space. Numerical results and some comparisons between this method and other reported methods are given to favor the suggested method in the overall performance. It is worthwhile to emphasize that the numerical strategy in this work could be extended to other conservative or dissipative system for designing high-order structure-preserving algorithms. [ABSTRACT FROM AUTHOR]

This study introduces a non-convex fractional-order hyper-Laplacian variational model for Gaussian noise removal. It employs first the primal-dual hybrid gradient algorithm to solve problems involving overlapping group sparse structures. Additionally, this paper designs a new algorithm leveraging the framework of the Chambolle-Pock algorithm with convergence and aims to recover high-quality images. The model, integrating the overlapping group sparse structure of the hyper-Laplacian prior with the non-convex fractional-order total variation, exhibits superior performance in reducing the staircase effect and maintaining sharp edge contours. To further improve the performance of the algorithm, a semi-adaptive p (x) non-convex penalty weight assignment mechanism is designed by introducing the structure tensor, which according to the characteristics of each region of the image and the noise level. The effectiveness and superiority of the proposed algorithm in image denoising with simulation experiments and comparative analyses are fully verified. • A new non-convex fractional-order hyper-Laplace variation model is proposed. • The PDHG algorithm is introduced to solve optimization problems involving OGS-HL for the first time. • The convergence and complexity of the new design algorithm are analyzed. • A semi-adaptive p (x) determined by the structure of the image and the noise level is designed. [ABSTRACT FROM AUTHOR]

The paper proposes algorithm for angular motion control of a dynamically elongated spacecraft. The algorithm is based on the direct Lyapunov method using matrix control coefficients. The calculated mechanical torque is implemented using magnetorquers. Control parameters are selected using Floquet theory to ensure convergence to the required motion. • An algorithm for attitude control of a dynamically elongated spacecraft is proposed. • The algorithm is based on the direct Lyapunov method using matrix control gains. • A methodology for matrix gain selection is based on Floquet theory. • The algorithm performance for 3U CubeSat three-axis stabilization is demonstrated. [ABSTRACT FROM AUTHOR]

Global Nash equilibrium is an optimal solution for each player in a graphical game. This paper proposes an iterative adaptive dynamic programming-based algorithm to solve the global Nash equilibrium solution for optimal containment control problem with robustness analysis to the iterative error. The containment control problem is transferred into the graphical game formulation. Sufficient conditions are given to decouple the Hamilton–Jacobi equations, which guarantee the solvability of the global Nash equilibrium solution. The iterative algorithm is designed to obtain the solution without any knowledge of system dynamics. Conditions of iterative error for global stability are given with rigorous proof. Compared with existing works, the design procedures of control gain and coupling strength are separated, which avoids trivial cases in the design procedure. The robustness analysis exactly quantifies the effect of the iterative error caused by various sources in engineering practice. The theoretical results are validated by two numerical examples with marginally stable and unstable dynamics of the leader. [ABSTRACT FROM AUTHOR]

This paper presents a novel hierarchical control scheme for solving the data-driven optimal cooperative tracking control problem of heterogeneous multi-agent systems. Considering that followers cannot communicate with the leader, a prescribed-time fully distributed observer is devised to estimate the leader's state for each follower. Then, the data-driven decentralized controller is designed to ensure that the follower's output can track the leader's one. Compared with the existing results, the advantages of the designed distributed observer are that the prescribed convergence time is completely predetermined by the designer, and the design of the observer gain is independent of the global topology information. Besides, the advantages of the designed decentralized controller are that neither the follower's system model nor a known initial stabilizing control policy is required. Finally, simulation results exemplify the advantage of the proposed method. • Compared with the existing methods, the advantage of our proposed prescribed-time fully distributed observer is that the leader's state can be accurately estimated within the designer's predetermined time; • Unlike the existing RL-based algorithms that rely on the initial stabilizing control policy associated with the accurate system matrices, the proposed new RL-based algorithm not only does not require a known initial stabilizing control policy, but also ensures the optimal tracking control in a data-driven manner. • Different from the homotopy-based policy iteration algorithm, an improved counterpart is presented, where the design parameter can be directly designed in the data-driven manner. [ABSTRACT FROM AUTHOR]

The predicted Bridge Condition Index (BCI) is a guiding indicator for formulating preventive maintenance strategies for bridges and is hardly available even if using the most advanced neural network prediction model, owing to the few measured BCIs and neural network model defects. In this paper, an improved Back-Propagation Neural Network (BPNN) model named CPSO-BP-MC is proposed to predict BCI, which has a BPNN as its core, combined with the Coordinated Particle Swarm Optimization (CPSO) algorithm aims to faster convergence and avoid local optimal solution even with less training sample, and the Markov Chain (MC) algorithm aims to further revise the fluctuation of CPSO-BP prediction output due to maintenance and reinforcement. A case study is presented to demonstrate the efficiency of CPSO-BP-MC predicting BCI with fewer training samples. Comparing the predicted BCI of CPSO-BP-MC with the measured BCI and other models, the results show that CPSO-BP-MC converges faster than other models, and can predict the BCI more stably and accurately, and the error between prediction and measured BCI is less than 3 %. [ABSTRACT FROM AUTHOR]