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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]

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, based on the Lagrange multiplier method, we construct a maximum principle preserving scheme for the time-fractional Allen-Cahn equation of 2- α (0 < α < 1) order. The correction energy of this scheme is increased by a term compared to the original energy, which is O (τ α). We prove that our scheme is unconditionally stable related to the corrected energy and verify the convergence, maximum principle, and energy conservation properties of the algorithm through numerical examples. We also find that the larger the α , the faster the evolution of the time-fractional Allen-Cahn equation. [ABSTRACT FROM AUTHOR]

Diffeomorphic registration is a widely used technique for finding a smooth and invertible transformation between two coordinate systems, which are measured using template and reference images. The point-wise volume-preserving constraint det ⁡ (∇ φ (x)) = 1 is effective in some cases, but may be too restrictive in others, especially when local deformations are relatively large. This can result in poor matching when enforcing large local deformations. In this paper, we propose a new bi-variant diffeomorphic image registration model that introduces a soft constraint on the Jacobian equation det ⁡ (∇ φ (x)) = f (x) > 0. This allows local deformations to shrink and grow within a flexible range 0 < κ m < det ⁡ (∇ φ (x)) < κ M. The Jacobian determinant of transformation is explicitly controlled by optimizing the relaxation function f (x). To prevent deformation folding and improve the smoothness of the transformation, a positive constraint is imposed on the optimization of the relaxation function f (x) , and a regularizer is used to ensure the smoothness of f (x). Furthermore, the positivity constraint ensures that f (x) is as close to one as possible, which helps to achieve a volume-preserving transformation on average. We also analyze the existence of the minimizer for the variational model and propose a penalty-splitting algorithm with a multilevel strategy to solve this model. Numerical experiments demonstrate the convergence of the proposed algorithm and show that the positivity constraint can effectively control the range of relative volume without compromising the accuracy of the registration. Moreover, the proposed model generates diffeomorphic maps for large local deformations and outperforms several existing registration models in terms of performance. • A novel bi-variant diffeomorphic image registration model with relaxed Jacobian determinant constraints is proposed. • The existence of the minimizer for the variational model is proved. • A penalty splitting algorithm with a multilevel strategy is designed to solve the new model. • Numerical experiments show that the proposed algorithm is convergent and the new model has good performance. [ABSTRACT FROM AUTHOR]

In this paper, we devise a stochastic extragradient-like algorithm incorporated with inertial terms, which requires a single projection onto our feasible set and employs a stochastic approximation version of an Armijo-type line search scheme along a feasible direction, for solving pseudomonotone stochastic variational inequalities. In the algorithm, two different stepsize strategies are employed to update steplength sequences without using the prior knowledge of the Lipschitz constant of involved operators. In the process of the stochastic approximation, we iteratively reduce the variance of stochastic errors. The almost sure convergence, the complexity analysis, and rates are provided in a dimensional space under reasonable conditions. Finally, some numerical experiments with graphical illustrations are reported to demonstrate the applicability and the efficiency of our algorithm in comparison with some projection type methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper we provide a tetrahedra-free algorithm to compute low-cardinality quadrature rules with a given degree of polynomial exactness, positive weights and interior nodes on a polyhedral element with arbitrary shape. The key tools are the notion of Tchakaloff discretization set and the solution of moment-matching equations by Lawson-Hanson iterations for NonNegative Least-Squares. Several numerical tests are presented. The method is implemented in Matlab as open-source software. [ABSTRACT FROM AUTHOR]

A k -class domination coloring (k -cd-coloring) is a partition of the vertex set of a graph G into k independent sets V 1 , ... , V k , where each V i is dominated by some vertex u i of G. The least integer k such that G admits a k -cd-coloring is called the cd-chromatic number, χ c d (G) , of G. A subset S of the vertex set of a graph G is called a subclique in G if d G (x , y) ≠ 2 for every x , y ∈ S. The cardinality of a maximum subclique in G is called the subclique number, ω s (G) , of G. In this paper, we present algorithms to compute an optimal cd-coloring and a maximum subclique of (i) trees with time complexity O (n) and (ii) co-bipartite graphs with time complexity O (n 2. 5). This improves O (n 3) algorithms by Shalu et al. (2017, 2020). In addition, we prove tight upper bounds for the subclique number of the class of (i) P 5 -free graphs and (ii) double-split graphs. [ABSTRACT FROM AUTHOR]

Earth observation satellite (EOS) scheduling is critical for improving the performance of Earth observation system. Most of the existing studies on satellite observation scheduling problems focus on static tasks and real-time dynamic tasks also known as emergency tasks while few attempts have been made for common dynamic tasks yet. The common dynamic tasks are characterized by uncertain arrival times and delayable observations while the emergency tasks require immediate observations. The number of common dynamic tasks is rapidly increasing with the expansion of satellite observation applications, which poses great challenges to EOS observation scheduling. To address this issue, this paper investigates the satellite observation scheduling problem with common dynamic tasks. Firstly, a centralized onboard dynamic scheduling framework based on a periodic-triggered rolling horizontal optimization (RHO) strategy is proposed and a novel two-stage mathematical model is established for the periodic rescheduling problem. Secondly, we propose a low-complexity onboard periodic rescheduling algorithm (OPR), which consists of a greedy-based task allocation algorithm, a pointer network (Ptr-network) based task scheduling algorithm and an iterative local search algorithm. In the greedy-based task allocation algorithm, we define a Task-EOS Fitness Indicator (TEFI) and each task is greedily allocated to the EOS with maximum TEFI. In the Ptr-network based task scheduling algorithm, the allocated task sets of all EOSs are fed into the Ptr-network in parallel to generate the observation scheduling result. Afterward, an iterative local search algorithm is proposed to further improve the quality of the observation scheduling result. Finally, extensive experiments are conducted to demonstrate the superiority of the OPR algorithm for the satellite observation scheduling problem with common dynamic tasks. [ABSTRACT FROM AUTHOR]

• OCR-detected characters or words in an image require line segmentation to reunite into word or sentence. • Projection based line segmentation cannot be applied to Chinese historical texts. • Columns in Chinese historical texts exhibit a sub-divided column format. • Adjacent character detection (ACD) algorithm can deal with the unique column structure. • Performance of ACD algorithm as a post-processing of OCR is discussed. In recent times, the advent of AI-based optical character recognition (OCR) has garnered significant attention in the realm of digital text conversion. However, it is imperative to note that OCR solely identifies individual characters or words, and lacks the ability to reunite them into cohesive units such as words or sentences. Consequently, the manual sorting of them to establish the appropriate reading order has emerged as a bottleneck. In this paper, we present an algorithm termed adjacent character detection (ACD), designed to serve as a post-processing of OCR, facilitating automatic digital text conversion. The algorithm involves line segmentation through a quad-ACD scan (up-down-down-up), allowing it to consecutively discern characters within a column based on their adjacency relations. Conventional projection profile analyses have struggled to effectively partition the distinct internal structure of Chinese historical text, where two annotation columns often subdivide from a single body column. In contrast, our ACD algorithm employs an approach, reuniting adjacent characters rather than fragmenting the entire text into isolated entities. Additionally, ACD algorithm enabled body/annotation classification for OCR-detected characters based on the pattern analysis of its quad scan. This cumulative information empowers the conversion of digital text in a desired reading order. To assess the efficacy of the proposed algorithm, a set of ground-truth OCR result was subjected to rigorous testing, culminating in a reading order accuracy of 98.6%. Noteworthy robustness was also demonstrated in the face of misaligned columns, experimentally induced by applying tilt, warp, and wavy noises to the original digital images. Lastly, the algorithm was integrated with two pre-developed OCR models, resulting in a reading order accuracy of 97.7%. [Display omitted] [ABSTRACT FROM AUTHOR]

• Dynamics of multi-layer membrane structure with elastic spacers is studied. • An optimization criterion to eliminate the crossing modes is proposed. • The optimal spacer positions are calculated by Particle Swarm Optimizer algorithm. In recent years, there has been a growing interest in the dynamics of space membrane structures. However, existing research primarily focuses on single-layer membrane structures, leaving a significant research gap in the study of multi-layer structures with elastic spacers. To address this gap, this paper studies the dynamics and interlayer spacing accuracy of multi-layer membrane structures with elastic spacers. Specifically, the research focuses on the placement optimization of elastic spacers. A novel optimization criterion for the elastic spacers has been proposed, and the Particle Swarm Optimizer (PSO) algorithm has been utilized to calculate the optimal spacers positions. Results show that optimally placed elastic spacers can eliminate the crossing modes and improve the interlayer spacing accuracy during vibration. [ABSTRACT FROM AUTHOR]

Two key challenges in optimal control include efficiently solving high-dimensional problems and handling optimal control problems with state-dependent running costs. In this paper, we consider a class of optimal control problems whose running costs consist of a quadratic on the control variable and a convex, non-negative, piecewise affine function on the state variable. We provide the analytical solution for this class of optimal control problems as well as a Hopf-type representation formula for the corresponding Hamilton-Jacobi partial differential equations. Finally, we propose efficient numerical algorithms based on our Hopf-type representation formula, convex optimization algorithms, and min-plus techniques. We present several high-dimensional numerical examples, which demonstrate that our algorithms overcome the curse of dimensionality. We also describe a field-programmable gate array (FPGA) implementation of our numerical solver whose latency scales linearly in the spatial dimension and that achieves approximately a 40 times speedup compared to a parallelized central processing unit (CPU) implementation. Thus, our numerical results demonstrate the promising performance boosts that FPGAs are able to achieve over CPUs. As such, our proposed methods have the potential to serve as a building block for solving more complicated high-dimensional optimal control problems in real-time. [ABSTRACT FROM AUTHOR]

This paper analyzes a parareal approach based on fractional-step methods for the nonstationary Navier-Stokes equations. As an efficient parallel computing framework, the coarse propagator often determines the performance of the parareal algorithm. We present a parareal algorithm using the fractional-step method, a very efficient time discrete scheme for the Naiver-Stokes equations, as the coarse propagator for the Navier-Stokes equations. Then we give the specific stability and convergence analysis of this specific parareal algorithm. Finally, numerical experiments are done to show efficiency and illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, elliptic control problems with the integral constraint on the gradient of the state and the box constraint on the control are considered. The optimality conditions for the problem are proved. To numerically solve the problem, a finite element duality-based inexact majorized accelerated block coordinate descent (FE-dABCD) algorithm is proposed. Specifically, both the state and the control are discretized by piecewise linear functions. An inexact majorized ABCD algorithm is employed to solve the discretized problem via its dual, which is a multi-block unconstrained convex optimization problem, but the primal variables are also generated in each iteration. Thanks to the inexactness of the FE-dABCD algorithm, the subproblems at each iteration are allowed to be solved inexactly. For the smooth subproblem, we use the preconditioned generalized minimal residual (GMRES) method to solve it. For the two nonsmooth subproblems, one of them has a closed form solution through introducing an appropriate proximal term, and another one is solved by the line search Newton's method. Based on these efficient strategies, we prove that our proposed FE-dABCD algorithm enjoys O (1 k 2 ) iteration complexity. Moreover, to make the algorithm more efficient and further reduce its computation cost, based on the mesh-independence of ABCD method, we propose an FE-dABCD algorithm with a warm-start strategy (wFE-dABCD). Some numerical experiments are done and the numerical results show the efficiency of the FE-dABCD algorithm and wFE-dABCD algorithm. [ABSTRACT FROM AUTHOR]

Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory dynamics, like spiral waves, relaxation oscillations and spatio-temporal Turing instability. Inspired by the classical "divide and conquer" approach, we propose a piecewise version of DMD (pDMD) to overcome this problem. The main idea is to split the original dataset in N submatrices and then apply the exact (randomized) DMD method in each subset of the obtained partition. We describe the pDMD algorithm in detail and we introduce some error indicators to evaluate its performance when N is increased. Numerical experiments show that very accurate reconstructions are obtained by pDMD for datasets arising from time snapshots of certain reaction-diffusion PDE systems, like the FitzHugh-Nagumo model, a λ - ω system and the DIB morpho-chemical system for battery modeling. Finally, a discussion about the overall computational load and the future prediction features of the new algorithm is also provided. [ABSTRACT FROM AUTHOR]

In this paper, the multi-parameter time fractional radially symmetric anomalous diffusion model used in porous media with initial singularity is considered. Both the direct numerical solution problem and the multi-parameter identification inverse problem are studied. Given the singularity in the initial time, a stable numerical scheme on nonuniform grid mesh is derived by using the L 2 − 1 σ method. To conduct the multi-parameter inversion problem, a novel hybrid Black Widow Optimization and Cuckoo Search (BWOCS) algorithm is proposed to combine the advantages of both the BWO algorithm and the CS algorithm, in order to improve the convergence speed and to achieve high-accuracy optimal results. Numerical examples are given to verify the efficiency and accuracy of the proposed numerical scheme and parameter inversion algorithm. Results show that the nonuniform grid L 2 − 1 σ scheme is efficient to deal with the time fractional radially symmetric anomalous diffusion problem with initial singularity, and the hybrid BWOCS algorithm has high precision and well convergence speed, compared with both the BWO and CS algorithms, which can be extended to other fractional inverse problems. [ABSTRACT FROM AUTHOR]

We address the problem of Multi-Source Domain Adaptation (MSDA), which trains a neural network using multiple labeled source datasets and an unlabeled target dataset, and expects the trained network to well classify the unlabeled target data. The main challenge in this problem is that the datasets are generated by relevant but different joint distributions. In this paper, we propose to address this challenge by estimating and minimizing the mutual information in the network latent feature space, which leads to the alignment of the source joint distributions and target joint distribution simultaneously. Here, the estimation of the mutual information is formulated into a convex optimization problem, such that the global optimal solution can be easily found. We conduct experiments on several public datasets, and show that our algorithm statistically outperforms its competitors. Video and code are available at https://github.com/sentaochen/Mutual-Information-Estimation-and-Minimization. [ABSTRACT FROM AUTHOR]

Heat exchanger network (HEN) synthesis is a vibrant research field in process system engineering, with substantial contributions to energy conservation and emissions reduction initiatives. The optimal design of a heat exchanger network is not an easy task due to the abundance of local optima in the solution space caused by the non-linear, non-convex, and discontinuous nature of the problem. Generally, several heuristic algorithms employ a greedy evolutionary mechanism, optimize through greedily accepting the decrease in the objective function, and converge to obtain the optimal solution. The Random Walk algorithm has a simple evolutionary mechanism, is prone to mutation, and exhibits high flexibility. However, the algorithm's inherent persistent greediness in searching restrict the scope of the search. Thus, this paper proposes an anti-greedy concept based on the Random Walk method to serve as the basis of a new synthesis approach called the Anti-greedy Random Walk algorithm. Two strategies are proposed in the algorithm, which broaden the solution domain by slowing down rapid unit reduction and accepting imperfect solutions, respectively. One strategy is to thoroughly search for the integer and continuous variables of the HEN problem by covering a much larger search space. Another is to escape the local extrema and move forward to discover more possibilities. Quantitative data demonstrates the algorithm's ability to avoid the local extrema and enhance the search effectiveness. Three different scales of classical cases are used in this work and the obtained results are superior to the published ones. [Display omitted] • An improved Random Walk algorithm is presented for heat exchanger network synthesis. • Two anti-greedy strategies are proposed from an objective and structural perspective. • Both integer and continuous variables are explored by covering a larger search space. • Three benchmark cases were solved with better results than previously literature. [ABSTRACT FROM AUTHOR]

The concept of jump system, introduced by Bouchet and Cunningham (1995), is a set of integer points satisfying a certain exchange property. We consider the minimization of a separable convex function on a jump system. It is known that the problem can be solved by a greedy algorithm. In this paper, we are interested in whether the greedy algorithm has the geodesic property, which means that the trajectory of the solutions generated by the algorithm is a geodesic from the initial solution to a nearest optimal solution. We show that a special implementation of the greedy algorithm enjoys the geodesic property, while the original algorithm does not. As a corollary to this, we present a new greedy algorithm for linear optimization on a delta-matroid and show that the algorithm has the geodesic property. [ABSTRACT FROM AUTHOR]

Neural network ensembling is a common and robust way to increase model efficiency. In this paper, we propose a new neural network ensemble algorithm based on Audibert's empirical star algorithm. We provide optimal theoretical minimax bound on the excess squared risk. Additionally, we empirically study this algorithm on regression and classification tasks and compare it to most popular ensembling methods. [ABSTRACT FROM AUTHOR]

In this paper, we present a variable sample-size operator extrapolation algorithm for solving a class of stochastic mixed variational inequalities. One distinctive feature of our algorithm is that it updates a single search sequence by solving a prox-mapping subproblem and computing an evaluation of the expected mapping at each iteration and hence it may significantly reduce computation load. In particular, the iteration sequence generated by our algorithm always belongs to the feasible region. We show that, under some moderate conditions, the proposed algorithm can achieve O (1 / T) ergodic convergence rate in terms of the expected restricted gap function, where T denotes the number of iterations. We derive some results related to the convergence rate of the Bregman distance between iterates and solutions, the iteration complexity, and the oracle complexity for the proposed algorithm when the sample size increases at a geometric rate. We also investigate the sublinear convergence rate in terms of the residual function under the generalized monotonicity condition. Numerical experiments on stochastic network game, stochastic sparse traffic assignment problems and sparse classification problem indicate that the proposed algorithm is promising compared with some existing algorithms. [ABSTRACT FROM AUTHOR]

In this paper, several local and parallel finite element algorithms are proposed and analyzed for the 2D/3D stationary inductionless incompressible magnetohydrodynamic (MHD) equations. The core concept is to guarantee the charge-conservation property by choosing mixed finite element spaces in H 0 (div , Ω) × L 0 2 (Ω) to approximate (J , ϕ) , meantime combining the idea of domain decomposition method to realize parallel operation. The characteristic of the proposed algorithms is that the computational complexity is greatly reduced while ensuring the accuracy of the numerical simulation. With the local a prior estimate as the technical means of theoretical analysis, we give the error estimates of the algorithms. Finally, several numerical experiments are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Actor–critic methods are leading in many challenging continuous control tasks. Advantage estimators, the most common critics in the actor–critic framework, combine state values from bootstrapping value functions and sample returns. Different combinations balance the bias introduced by state values and the variance returned by samples to reduce estimation errors. The bias and variance constantly fluctuate throughout training, leading to different optimal combinations. However, existing advantage estimators usually use fixed combinations that fail to account for the trade-off between minimizing bias and variance to find the optimal estimate. Our previous work on adaptive advantage estimation (AAE) analyzed the sources of bias and variance and offered two indicators. This paper further explores the relationship between the indicators and their optimal combination through typical numerical experiments. These analyses develop a general form of adaptive combinations of state values and sample returns to achieve low estimation errors. Empirical results on simulated robotic locomotion tasks show that our proposed estimators achieve similar or superior performance compared to previous generalized advantage estimators (GAE). [ABSTRACT FROM AUTHOR]

• Bi-level hierarchical distribution of resources is reformulated. • Hooke-Jeeves and Scatter Search algorithms are implemented. • A multi-objective perspective is introduced to tackle the problem. • A multi-objective scatter search algorithm delivers best results for both objectives. • Tailored-made instances were crafted for the problem. The decision regarding the hierarchical distribution of resources is crucial for many organizations that want to allocate such resources efficiently. At the upper level of the hierarchy, a decision-maker may have an objective and a set of feasible solutions partially determined by the lower level. Nevertheless, the upper level can influence but not control the decision-maker at the lower level. Moreover, the objectives of the upper and lower levels are conflicting. Hence, the hierarchical distribution of resources can be formulated as a bi-level programming model. This paper reformulates the hierarchical allocation of resources. The Hooke-Jeeves (HJ) algorithm and the hybrid scatter search–Nelder-Mead (SSNM) method are proposed to solve the newly formulated problem. The problem is also analyzed from a multi-objective perspective to equally prioritize the upper and lower levels while subjecting each to an interdependent set of constraints; a multi-objective scatter search algorithm (MSSA) was developed for that purpose. Tailor-made instances were also designed for the implementation of the developed algorithms. The findings demonstrated that the HJ algorithm provides the best solution according to the upper-level objective function. However, it does not guarantee the best result for the lower level. In comparison, MSSA has a set of best possible solutions for both objectives. The hybrid SSNM method could not match the results provided by the former methods. [ABSTRACT FROM AUTHOR]

Exploring special multi-scroll chaotic systems is meaningful work. This paper studies an expanded multi-scroll chaotic system consisting of eight terms with one nonlinearity. It is generated by modifying the nonlinear term of the newly constructed chaotic system by a polynomial function. The unique mathematical model makes the unstable index-2 equilibria increase in four dimensions, which contributes to the number of scrolls expanding in each phase plane unidirectionally. Dynamic analysis finds that the system can yield complex nested multi-scroll attractors and has single-parameter-based synchronization control of amplitude and offset boosting behavior. Moreover, circuit implementation verifies the physical existence of the proposed system. Also, an image encryption algorithm for remote sensing images is established. Permutation and diffusion operations are performed using new pixel coordinates derived from the data of the chaotic matrix, which comes from the same position as the pixel matrix. Relevant tests suggest that the algorithm is secure and able to resist undesirable interference. • Simple multiscroll chaotic system with various signal control features is proposed. • Complex dynamics, circuit implementation of the proposed system is studied. • New chaos-based image encryption algorithm with high security is designed. [ABSTRACT FROM AUTHOR]

This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method and post-processing technique. The most valuable highlights of the present algorithm are that (1) a global continuous approximate solution is generated via the partition of unity method; (2) by adding an extra coarse grid correction step, the smoothness of the approximate solution is improved; (3) it has a good parallel performance since there requires little communication in solving a series of residual problems in the subdomain of interest. We theoretically derive the L 2 -error estimates both for the approximate velocity and pressure and H 1 -error estimate for the velocity under some necessary conditions. Meanwhile, we numerically perform various test examples to validate the theoretically predicted convergence rate and illustrate the high efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Based on the convex combination technique, we propose a projection-based hybrid conjugate gradient algorithm for solving nonlinear equations with convex constraints in this paper. The conjugate parameter of the proposed algorithm is a convex combination of the modified Polak-Ribière-Polyak and Dai-Yuan type conjugate parameters, and the search direction has the sufficient descent property without the use of a line search strategy. The proposed hybrid algorithm's global convergence is established under appropriate assumptions. The numerical experiments demonstrate that the proposed algorithm is more efficient and competitive than existing methods under some benchmark test problems. Furthermore, it is also extended to solve the sparse signal and impulse noise image restoration problem that arises in compressive sensing. [ABSTRACT FROM AUTHOR]

In this paper, we propose a proximal fully parallel splitting method with a relaxation factor for solving separable convex minimization model with linear constraints, where the objective function is the sum of m individual functions without coupled variables. With a full Jacobian decomposition, we decompose the subproblem associated with the augmented Lagrangian method into m smaller subproblems and then add a quadratic proximal term to each decomposed subproblem, which makes the resulting ones easier to solve for many applications. In order to accelerate the numerical performance, we attach a positive relaxation factor to update the Lagrange multiplier, which also allows more flexibility in the design of algorithms. Moreover, we refine the step size of the underrelaxation step, which enlarges several existing ones in the literature. We prove that the proposed method is globally convergent, and show the worst-case O (1 / k) convergence rate in a nonergodic sense. Finally, the efficiency and robustness of the proposed method are also demonstrated by solving the ℓ 1 norm problem, the ℓ 1 -regularized least squares problem, the exchange problem and the total variation image restoration problem. [ABSTRACT FROM AUTHOR]

Achieving precision in the prediction of buildings' dynamic heat load is crucial for the advancement of smart heating systems. This research highlights the urgent need to enhance the accuracy of models predicting dynamic heat load. Through literature review, distinguished machine learning and regression algorithms were chosen to formulate prediction models. These models employ a data time-step adaptive strategy, a physics-guided loss function, and fundamental principles of heat transfer. Optimization algorithms of a mathematical nature were utilized to fine-tune the parameters and the framework of long short-term memory (LSTM) and multi-layer perceptron (MLP) models. An analytical comparison was undertaken between physics-guided models and those not guided by physics. Principal conclusions are: 1) Pelican optimization algorithm (POA)-LSTM model emerges as superior in heat load prediction accuracy of an office building, with percentage errors for actual and simulated datasets ranging from −6.7 % to 5.8 % and −5.2 %–4.5 %, respectively, and the mean absolute percentage error (MAPE) standing at 2.3 % and 1.3 %. 2) The linear regression model exhibits the lowest precision, with a MAPE of 17.5 % and 4.0 % for the 7-day prediction results in the actual and simulated datasets, respectively. These findings provide support for improving heat load prediction in heating systems. • The authors have implemented a total of 20 physically-guided models for predicting building thermal load, among which the POA-LSTM model demonstrates the highest accuracy. • The disparities in thermal load prediction accuracy between the physically-guided machine learning models and the physically-guided mathematical regression models have been identified. • The accuracy of thermal load prediction was compared between the five physical guidance models proposed in this paper and the five non-physical guidance models mentioned in other papers. [ABSTRACT FROM AUTHOR]

Intrusion Detection System (IDS) can ensure the network security by identifying network intrusions according to the abnormal traffic data. However, the intrusion detection data has the problem of high dimensionality and changes with network and attack environments, which leads to the poor performance and poor portability of intrusion detection algorithms. Therefore, this paper proposes an intrusion detection algorithm based on joint symmetric uncertainty and hyperparameter optimized fusion neural network. Firstly, a feature selection method based on symmetric uncertainty and approximate Markov blanket is proposed, which fully considers the correlation and redundancy of features, and also the correlation between combined features and the class label, so as to reduce the data dimensionality. Secondly, the CNN-LSTM classifier fused with Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM) is used to extract the spatial features and temporal features to improve the classification performance. Finally, the Particle Swarm Optimization (PSO) algorithm is improved and used to automatically optimize the hyperparameters of the classifier, so that the classifier can be applied to different intrusion detection datasets with better generalization ability and portability. Experiments have verified the effectiveness and superiority of the proposed algorithm on multiple evaluation indicators. • An effective algorithm for intrusion detection is proposed in this paper. • Feature selection is based on symmetric uncertainty and approximate Markov blanket. • A fusion neural network is constructed to extract the spatial and temporal features. • The PSO algorithm is improved to automatically optimize the hyperparameters. [ABSTRACT FROM AUTHOR]

In the contemporary world, data pervades every facet of human life, and the information contained in this data plays a pivotal role in shaping decision-making and advancing technology. Among the plethora of techniques available, classification methods are highly effective tools for extracting valuable insights from vast volumes of data. The R ule A ggregation C lassifi ER (RACER) is a novel rule-based classification algorithm known for its exceptional performance. A notable limitation of RACER lies in its inability to handle continuous features. In this paper, we address the aforementioned limitation by employing various supervised discretization methods, including CAIM, MDLP, Decision Tree (CART), and ChiMerge. The impact of these methods on RACER's accuracy and understandability is evaluated across nine datasets from the UCI repository. Additionally, the paper conducts a comparative analysis of RACER's accuracy against well-known classifiers such as Naive Bayes, Logistic Regression, SVM, LightGBM, and Decision Tree. The findings indicate that RACER achieves the highest average accuracy when we utilize MDLP as the discretization method, surpassing its initial average accuracy. Moreover, RACER demonstrates superior understandability by generating the lowest number of rules when employing ChiMerge and Decision Tree for discretizing numerical features. Furthermore, RACER outperforms the other five classifiers when employing MDLP. • The discretization unit enables the RACER algorithm to handle continuous data. • The discretization unit improves the classification accuracy of the RACER. • The discretization unit increases the understandability of the RACER rules. [ABSTRACT FROM AUTHOR]

This paper investigates fully distributed scaled non-negative edge-consensus problems of networked systems with actuator saturation and unmeasurable internal states. By using the adaptive control method, output-feedback-based low-gain technique, and graph theory, a new adaptive algorithm is designed to obtain scaled edge-consensus conditions, under which the difficulties caused by the constraints on edge states and controllers are overcome. There are three interesting characteristics that any global information of networks is not used in this paper's algorithm and result, including the number of vertexes and edges; the feasible solutions of the scaled edge-consensus conditions exist and can be easily obtained; the convergence rate of the controller is adjustable. Furthermore, the designed algorithm is expanded in the cases without actuator saturation. Finally, three examples are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper introduces a family of subdivision schemes that generate curves over manifolds from manifold-Hermite data. This data consists of points and tangent directions sampled from a curve over a manifold. Using a manifold-Hermite average based on the De Casteljau algorithm as our main building block, we show how to adapt a geometric approach for curve approximation over manifold-Hermite data. The paper presents the various definitions and provides several analysis methods for characterizing properties of both the average and the resulting subdivision schemes based on it. Demonstrative figures accompany the paper's presentation and analysis. [ABSTRACT FROM AUTHOR]

The enclosed multistory poultry housing is a type of poultry enclosure widely used in industrial caged chicken breeding. Accurate identification and detection of the comb and eyes of caged chickens in poultry farms using this type of enclosure can enhance managers' understanding of the health of caged chickens. However, the accuracy of image detection of caged chickens will be affected by the enclosure's entrance, which will reduce the precision. Therefore, this paper proposes a cage-gate removal algorithm based on big data and deep learning Cyclic Consistent Migration Neural Network (CCMNN). The method achieves automatic elimination and restoration of some key information in the image through the CCMNN network. The Structural Similarity Index Measure (SSIM) between the recovered and original images on the test set is 91.14%. Peak signal-to-noise ratio (PSNR) is 25.34dB. To verify the practicability of the proposed method, the performance of the target detection algorithm is analyzed both before and after applying the CCMNN network in detecting the combs and eyes of caged chickens. Different YOLOv8 detection algorithms, including YOLOv8s, YOLOv8n, YOLOv8m, and YOLOv8x, were used to verify the algorithm proposed in this paper. The experimental results demonstrate that compared to images without CCMNN processing, the precision of comb detection of caged chickens is improved by 11, 11.3, 12.8, and 10.2%. Similarly, the precision of eye detection for caged chickens is improved by 2.4, 10.2, 6.8, and 9%. Therefore, more complete outline images of caged chickens can be obtained using this algorithm and the precision in detecting the comb and eyes of caged chickens can be enhanced. These advancements in the algorithm offer valuable insights for future poultry researchers aiming to deploy enhanced detection equipment, thereby contributing to the accurate assessment of poultry production and farm conditions. [ABSTRACT FROM AUTHOR]

This paper introduces a novel application of subloading surface concept to effectively model the elastoplastic behavior of materials in the finite strain regime. The subloading surface approach allows for a smoother and more seamless transition from the elastic to the plastic region. Two time integration schemes are presented in this study, one in the intermediate configuration and the other in the current configuration. In the first time integration scheme, co-rotational objective time rates are not required, and the formulation utilizes the Mandel stress. In the second time integration scheme, implemented in Eulerian description, the Kirchhoff stress defined in the current configuration is utilized. The results obtained for the simple shear deformation case demonstrate the absence of oscillations. Additionally, these results show excellent agreement with experimental data and existing findings from the literature. Furthermore, a computational comparison between the time integration schemes using the subloading surface model and a model discussed in the literature reveals that the proposed algorithms in this paper require significantly fewer increments in the given time integrations. This indicates a higher computational efficiency and reduced computational time for the proposed methods. Overall, the predicted responses of all the analyzed cases from the provided time integrations exhibit excellent agreement with each other, confirming the accuracy and effectiveness of the presented model. • Novel use of subloading surface in finite strain elastoplasticity was introduced. • Proposed algorithms were reduced the increments and computational cost remarkably. • Smoother and more realistic transition from elastic to plastic region was captured. • Proposed time integrations effectively simulated saturation and softening behavior. • No oscillations were seen in simple shear elastoplastic deformation. [ABSTRACT FROM AUTHOR]

High-quality underwater optical images are essential for various applications of underwater vision. However, these images often suffer from severe degradation, complex noise, low contrast, and color cast, leading to poor image quality. To address these issues and accomplish related underwater vision tasks more smoothly, researchers have made many efforts to improve the quality of underwater optical images. This paper presents a comprehensive review of recent research, focusing on specific algorithms published between 2013 and 2023, while also predicting future research trends in this field. In light of the observed ambiguities and inconsistencies in previous review studies' classification frameworks, this paper introduces a novel classification framework, grounded in the specific challenges in this domain, including issues unique to the imaging medium and imaging environment. Additionally, the proposed framework offers a more detailed categorization based on the algorithmic ideology of the authors. Furthermore, this paper addresses a significant gap in the literature by providing an in-depth assessment of the methods for removing marine snow noise from underwater optical images. By complementing existing research, this paper aims to enhance understanding of this subject and provide a clearer, more comprehensive, and in-depth exploration of underwater image quality improvement. [ABSTRACT FROM AUTHOR]

Weighted model counting (WMC) is the task of computing the weighted sum of all satisfying assignments (i.e., models) of a propositional formula. Similarly, weighted model sampling (WMS) aims to randomly generate models with probability proportional to their respective weights. Both WMC and WMS are hard to solve exactly, falling under the # P -hard complexity class. However, it is known that the counting problem may sometimes be tractable, if the propositional formula can be compactly represented and expressed in first-order logic. In such cases, model counting problems can be solved in time polynomial in the domain size, and are known as domain-liftable. The following question then arises: Is it also the case for WMS? This paper addresses this question and answers it affirmatively. Specifically, we prove the domain-liftability under sampling for the two-variables fragment of first-order logic with counting quantifiers in this paper, by devising an efficient sampling algorithm for this fragment that runs in time polynomial in the domain size. We then further show that this result continues to hold even in the presence of cardinality constraints. To empirically validate our approach, we conduct experiments over various first-order formulas designed for the uniform generation of combinatorial structures and sampling in statistical-relational models. The results demonstrate that our algorithm outperforms a state-of-the-art WMS sampler by a substantial margin, confirming the theoretical results. • Model sampling in first-order logic can be liftable, without the need of grounding. • Sampling from two-variable logic with counting is tractable. • Domain recursion is crucial for designing first-order model sampling algorithms. [ABSTRACT FROM AUTHOR]

• Distinct DG Output Modes Validation: The simulation validates distinct DG output modes, impacting prediction. • Mode-Based State Estimation: The paper proposes an innovative mode-based state estimation using IPSO-DBSCAN clustering, overcoming k-means limitations. • Enhanced Data Recovery using DBSCAN: Enhanced data recovery employs DBSCAN with improved secondary clustering, guided by similarity and homogeneity, outperforming traditional methods. • BiGRU-PF State Estimation: BiGRU-PF enhances state estimation accuracy and robustness in distribution networks by detecting DG output modes, addressing k-means limitations, and improving data recovery. This paper proposes a new forecasting-aided state estimation (FASE) method for distribution systems that mitigates issues with uncertain distributed generation (DG) and lost measurements. We utilize an Improved Particle Swarm Optimization (IPSO)-optimized Density-Based Spatial Clustering of Applications with Noise (DBSCAN) for examination of historical DG output data. Based on identified DG output modes, it facilitates precise state prediction and data reconstruction,. The proposed method employs a Bidirectional Gated Recurrent Unit (BiGRU) neural network for state prediction and a particle filter (PF) for final state filtering. The method verification is provided through Python simulations of the Distribution Transformer Unit (DTU)7k distribution network system, demonstrating improved accuracy and robustness against sudden load change and bad data in measurements. [ABSTRACT FROM AUTHOR]

• A novel water transparency calculation algorithm is introduced, employing deep neural network and image processing technology. This algorithm obviates the need for a water gauge, allowing the calculation of water transparency solely through the analysisof Secchi disk videos. Notably, it demonstrates heightened detection efficiency and success rates. • An enhanced Siamese tracker, termed SiamDCFF (Siamese tracker based on dual correlation feature fusion), is proposed for Secchi disk recognition. Distinguishing features of SiamDCFF include a dual correlation module and a feature fusion module. On the Secchi disk dataset, SiamDCFF achieves the highest success rate, outperforming other methods detailed in this paper. • The simplified 3D-ResNet [41] is leveraged to assess the state of the Secchi disk, transforming the critical position determination problem into an optimization challenge. The objective function involves maximizing the number of visible and invisible Secchi disk images on both sides of the critical position. This method facilitates adaptive critical position determination. • A novel Gated Recurrent Unit based on auto-regression (ARGRU) is proposed, taking into account the motion characteristics of the Secchi disk. ARGRU achieves a higher success detection rate for water transparency compared to the water gauge recognition method. Notably, ARGRU outperforms RNN [42], GRU, and LSTM [43] on the dataset presented in this paper. Water transparency is traditionally assessed through visual inspection using a lowered Secchi disk (SD) into the water, with the disappearance depth of the SD recorded as the measure of transparency. However, manual and visually-dependent frequency measurements of the SD render this process labor-intensive and time-consuming. This paper presents a comprehensive machine-vision-based algorithm designed for the automatic computation of water transparency using Secchi disk videos. The algorithm leverages multiple deep neural networks, including an enhanced Siamese tracking model, a 3D-ResNet, and an improved GRU network. Trained models directly identify the SD in the video, calculating water transparency by processing pixel information. Experimental results demonstrate the algorithm's efficacy in estimating water transparency across diverse natural environments, achieving commendable accuracy (MAE = 3.6 cm MSE = 21.5 cm RMSE = 4.6 cm), rapid processing speed (average 6.87 s), and robust stability. In comparison with the former water-gauge-based algorithm, our proposed algorithm exhibits heightened efficiency and a superior detection success rate. [ABSTRACT FROM AUTHOR]

The fair k -center problem has been paid lots of attention recently. In the fair k -center problem, we are given a set X of points in a metric space and a parameter k ∈ Z + , where the points in X are divided into several groups, and each point is assigned a color to denote which group it is in. The goal is to partition X into k clusters such that the number of cluster centers with each color is equal to a given value, and the k -center problem objective is minimized. In this paper, we consider the fair k -center problem with outliers and capacity constraints, denoted as the fair k -center with outliers (F k CO) problem and the capacitated fair k -center (CF k C) problem, respectively. The outliers constraints allow up to z outliers to be discarded when computing the objective function, while the capacity constraints require that each cluster has size no more than L. In this paper, we design an Fixed-Parameter Tractability (FPT) approximation algorithm and a polynomial approximation algorithm for the above two problems. In particular, our algorithms give (1 + ϵ) -approximations with FPT time for the F k CO and CF k C problems in doubling metric space. Moreover, we also propose a 3-approximation algorithm in polynomial time for the F k CO problem with some reasonable assumptions. [ABSTRACT FROM AUTHOR]

Robust classification algorithms for high-dimensional, small-sample datasets are valuable in practical applications. Faced with the infrared spectroscopic dataset with 568 samples and 3448 wavelengths (features) to identify the origins of Chinese medicinal materials, this paper proposed a novel embedded multiclassification algorithm, ITabNet, derived from the framework of TabNet. Firstly, a refined data pre-processing (DP) mechanism was designed to efficiently find the best adaptive one among 50 DP methods with the help of Support Vector Machine (SVM). Following this, an innovative focal loss function was designed and joined with a cross-validation experiment strategy to mitigate the impact of sample imbalance on algorithm. Detailed investigations on ITabNet were conducted, including comparisons of ITabNet with SVM for the conditions of DP and Non-DP, GPU and CPU computer settings, as well as ITabNet against XGBT (Extreme Gradient Boosting). The numerical results demonstrate that ITabNet can significantly improve the effectiveness of prediction. The best accuracy score is 1.0000, and the best Area Under the Curve (AUC) score is 1.0000. Suggestions on how to use models effectively were given. Furthermore, ITabNet shows the potential to apply the analysis of medicinal efficacy and chemical composition of medicinal materials. The paper also provides ideas for multi-classification modeling data with small sample size and high-dimensional feature. • A TabNet-based deep learning method for high-dimensional small-sample datasets. • A rapid data preprocessing search strategy using Support Vector Machine is established. • An adaptive Focal loss function with adjusting parameters counters sample imbalance. • Chinese herb origin identification via infrared spectroscopy shows impressive results. • Suggestions for Chinese herb further research and method generalization are offered. [ABSTRACT FROM AUTHOR]