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In this paper, we propose an a posteriori error estimate of the weak Galerkin finite element method (WG‐FEM) solving the Stokes problems with variable coefficients. Its error estimator, based on the property of Stokes' law conservation, Helmholtz decomposition and bubble functions, yields global upper bound and local lower bound for the approximation error of the WG‐FEM. Error analysis is proved to be valid under the mesh assumptions of the WG‐FEM and the way can be extended to other FEMs with the property of Stokes' law conservation, for example, discontinuous Galerkin (DG) FEMs. Finally, we verify the performance of error estimator by performing a few numerical examples. [ABSTRACT FROM AUTHOR]

Detecting the shoreline is an important task for its potential use. The shoreline allows cropping of the image into two separate areas that present the water area and the shore. It is particularly interesting because the images can be used to analyze pollution, land development, or even waterfront erosion. Unfortunately, automatic shoreline detection is a complex problem due to numerous physical and atmospheric issues. In this paper, we present a solution based on a U-net convolutional network, that is trained to shoreline detection on a dedicated database. The database is automatically generated by applying image processing techniques and a heuristic algorithm. Using heuristics, optimal values of mask generation parameters are determined. Consequently, the solution allows for the automation of generating a set of masks by analyzing the boundary line and the efficiency of the segmentation network. The proposed solution allows for the analysis of the coastline, where potential obstacles and even occurring waves can be quickly detected. To evaluate the proposed solution, tests were carried out in real conditions, which showed the effectiveness of the model. In addition, tests were carried out on a publicly available database, which allowed for obtaining higher results than existing methods. [ABSTRACT FROM AUTHOR]

Detecting the shoreline is an important task for its potential use. The shoreline allows cropping of the image into two separate areas that present the water area and the shore. It is particularly interesting because the images can be used to analyze pollution, land development, or even waterfront erosion. Unfortunately, automatic shoreline detection is a complex problem due to numerous physical and atmospheric issues. In this paper, we present a solution based on a U-net convolutional network, that is trained to shoreline detection on a dedicated database. The database is automatically generated by applying image processing techniques and a heuristic algorithm. Using heuristics, optimal values of mask generation parameters are determined. Consequently, the solution allows for the automation of generating a set of masks by analyzing the boundary line and the efficiency of the segmentation network. The proposed solution allows for the analysis of the coastline, where potential obstacles and even occurring waves can be quickly detected. To evaluate the proposed solution, tests were carried out in real conditions, which showed the effectiveness of the model. In addition, tests were carried out on a publicly available database, which allowed for obtaining higher results than existing methods.

The job shop scheduling problem (JSSP) is to find the optimal jobs sequence to optimise one or more performance indicators and makespan is the most common optimisation target. In solving NP-hard problems such as JSSPs by genetic algorithm (GA), trapping in local extremum, low search efficiency and instability are often encountered, especially unable to find the optimisation direction. To restrain this condition, a new neighbourhood structure with adaptive GA was put forward. The crossover probability (Pc) and mutation probability (Pm) can be adjusted in nonlinear and adaptive based on the dispersion of the fitness of population in the evolution. The idle time before critical operations can be made full use of through the multi-operations combination and adjustment. To research the performance of the proposed method in solving JSSPs, a detailed application scheme was given out for the process of it. In the solving scheme, the chromosome active decoding algorithm with the objective function of maximum makespan was proposed. From the results of testing of 28 JSSP benchmark instances in 3 adaptive strategies and 3 neighbourhood strategies, the new neighbourhood structure with adaptive GA has been significant improvement in solution accuracy and convergence efficiency. [ABSTRACT FROM AUTHOR]

This research seeks to answer the question, what are the theoretical and quantitative criticisms of the good governance model? From a methodological point of view, this research is a theoretical effort and a quantitative comparative method based on structural equation modeling using secondary data has also been used. According to the latest data output of the United Nations (2019), 193 countries are members of this organization, and the data required for this research were available for 103 countries and were selected as the research sample. Quantitative findings showed that the good governance model does not have a good fit, but it improves with the inclusion of the social inequality variable in the model. Also, in the theoretical dimension, despite the positive effects that the implementation of the good governance model can have, there are also criticisms that have been suggested to include indicators of corruption control, efficiency and effectiveness of the government, security, political stability and non-violence, rule of law, quality of regulation, accountability, accountability and the right to express opinions, citizen satisfaction, consensus-oriented, reducing social inequality, lack of domination and domination, transparency, adherence to the interests and wishes of citizens, public monitoring, welfare and social empowerment, meritocracy, freedom and enjoyment of rights and noninterference in the public and private domain should be added to the governance model evaluation criteria. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Irrigation & Drainage is the property of Journal of Irrigation & Drainage Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Chemical Engineering (China) / Huaxue Gongcheng is the property of Hualu Engineering Science & Technology Co Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A novel adaptive spectral method has been recently developed to numerically solve partial differential equations (PDEs) in unbounded domains. To achieve accuracy and improve efficiency, the method relies on the dynamic adjustment of three key tunable parameters: the scaling factor, a displacement of the basis functions, and the spectral expansion order. In this paper, we perform the first numerical analysis of the adaptive spectral method using generalized Hermite functions in both one- and multi-dimensional problems. Our analysis reveals why adaptive spectral methods work well when a “frequency indicator” of the numerical solution is controlled. We then investigate how the implementation of the adaptive spectral methods affects numerical results, thereby providing guidelines for the proper tuning of parameters. Finally, we further improve performance by extending the adaptive methods to allow bidirectional basis function translation, and the prospect of carrying out similar numerical analysis to solving PDEs arising from realistic difficult-to-solve unbounded models with adaptive spectral methods is also briefly discussed.

Neural Networks (NNs) can be used for energy management of hybrid vehicles, but they are hard to tune in inference to adapt to different driving conditions. To make the NN-based energy management strategy more flexible, this paper proposes a controllable NN for optimal energy management of fuel cell hybrid electric vehicles. Inspired by the equivalent factor in the Equivalent Consumption Minimization Strategy (ECMS), we introduce an adjustable target variable for the final state as an input to the NN-based strategy. During training, classification and regression networks with single-step and multi-step inputs are considered. An efficient shooting method and an adaptive method are then introduced to realize the precise control of the final state and online parameter adaptation. Simulations of the proposed method and the benchmarking method are carried out in different battery discharge modes. Results demonstrate that the proposed shooting neural classifier can achieve 99.7% fuel optimality of dynamic programming in a similar computational time to the shooting ECMS, and the proposed adaptive neural classifier can adapt to different driving conditions and has better fuel economy than the adaptive ECMS. • A controllable neural model for energy management of fuel cell vehicles is proposed. • Neural regressors and classifiers are trained under single-step and multi-step inputs. • A shooting method and an adaptive method for neural models are proposed. • The proposed method is comprehensively analyzed and compared with benchmarks. [ABSTRACT FROM AUTHOR]

In real-world scenarios, the facial expression recognition task faces several challenges, including lighting variations, image noise, face occlusion, and other factors, which limit the performance of existing models in dealing with complex situations. To cope with these problems, we introduce the CoT module between the CNN and ViT frameworks, which improves the ability to perceive subtle differences by learning the correlations between local area features at a fine-grained level, helping to maintain the consistency between the local area features and the global expression, and making the model more adaptable to complex lighting conditions. Meanwhile, we adopt an adaptive learning method to effectively eliminate the interference of noise and occlusion by dynamically adjusting the parameters of the Transformer Encoder's self-attention weight matrix. Experiments demonstrate the accuracy of our CoT_AdaViT model in the Oulu-CASIA dataset as (NIR: 87.94%, VL: strong: 89.47%, weak: 84.76%, dark: 82.28%). As well as, CK+, RAF-DB, and FERPlus datasets achieved 99.20%, 91.07%, and 90.57% recognition results, which achieved excellent performance and verified that the model has strong recognition accuracy and robustness in complex scenes. [ABSTRACT FROM AUTHOR]

We propose the method for numerical solution of four-wave kinetic equations that arise in the wave turbulence (weak turbulence) theory when describing a homogeneous isotropic interaction of waves. To calculate the collision integral in the right-hand side of equation, the cubature formulas of high rate of convergence are developed, which allow for adaptation of the algorithm to the singularities of the solutions and of the integral kernels. The convergence tests in the problems of integration arising from real applications are done. To take into account the multi-scale nature of turbulence problems in our algorithm, rational approximations of the solutions and a new time marching scheme are implemented and tested. The efficiency of the developed algorithm is demonstrated by modelling the inverse cascade of Bose gas particles during the formation of a Bose–Einstein condensate. [ABSTRACT FROM AUTHOR]

In this paper, the vibration control design of the Euler–Bernoulli beam with time-varying constraints is studied when the mass, bending stiffness and tension of the system parameters are known or unknown. For satisfying the time-varying constraints, the controller is designed and the system stability is analysed based on the tangent barrier Lyapunov function (TAN-BLF). Among them, the uncertainty of system parameters is dealt with by the adaptive method. In both cases, the vibration of the Euler–Bernoulli beam can be well restrained without violating the constraint conditions, and all signals in the system are bounded. Finally, the effectiveness of the proposed method is illustrated by a simulation example. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Computer-Aided Design & Computer Graphics / Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

CFRP/Ti stacks composed of carbon fiber-reinforced plastic composites (CFRP) and titanium alloys (Ti) are widely used in aerospace fields. However, in the integrated hole-making process of CFRP/Ti stacks, the machining characteristics of various materials are significantly different, and constant machining parameters cannot simultaneously meet the high-quality machining requirements of two materials. In addition, errors exist between the actual thickness of each material layer and the theoretical value, which causes an impediment to the monitoring of the machining interface and the corresponding adjustment of parameters. An adaptive machining method for the helical milling of CFRP/Ti stacks based on interface identification is proposed in this paper. The machining characteristics of the pneumatic spindle and the interface state in the helical milling of CFRP/Ti stacks are analyzed using self-developed portable helical milling equipment, and a new algorithm for the real-time monitoring of the machining interface position and adaptive adjustment of the machining parameters according to the interface identification result is proposed. Helical milling experiments were carried out, the results show that the proposed method can effectively identify the position of the machining interface with good identification accuracy. Moreover, the proposed parameter-adaptive optimized machining method for CFRP/Ti stacks can significantly improve hole diameter accuracy and machining quality. [ABSTRACT FROM AUTHOR]

Convergence and convergence rate analyses of adaptive methods, such as Adaptive Moment Estimation (Adam) and its variants, have been widely studied for nonconvex optimization. The analyses are based on assumptions that the expected or empirical average loss function is Lipschitz smooth (i.e., its gradient is Lipschitz continuous) and the learning rates depend on the Lipschitz constant of the Lipschitz continuous gradient. Meanwhile, numerical evaluations of Adam and its variants have clarified that using small constant learning rates without depending on the Lipschitz constant and hyperparameters ( β 1 and β 2 ) close to one is advantageous for training deep neural networks. Since computing the Lipschitz constant is NP-hard, the Lipschitz smoothness condition would be unrealistic. This paper provides theoretical analyses of Adam without assuming the Lipschitz smoothness condition in order to bridge the gap between theory and practice. The main contribution is to show theoretical evidence that Adam using small learning rates and hyperparameters close to one performs well, whereas the previous theoretical results were all for hyperparameters close to zero. Our analysis also leads to the finding that Adam performs well with large batch sizes. Moreover, we show that Adam performs well when it uses diminishing learning rates and hyperparameters close to one. [ABSTRACT FROM AUTHOR]

In this paper, we propose a stochastic primal-dual adaptive method based on an inexact augmented Lagrangian function to solve non-convex programs, referred to as the SPDAM. Different from existing methods, SPDAM incorporates adaptive step size and momentum-based search directions, which improve the convergence rate. At each iteration, an inexact augmented Lagrangian subproblem is solved to update the primal variables. A post-processing step is designed to adjust the primal variables to meet the accuracy requirement, and the adjusted primal variable is used to compute the dual variable. Under appropriate assumptions, we prove that the method converges to the ε-KKT point of the primal problem, and a complexity result of SPDAM less than O(ε−112) is established. This is better than the most famous O(ε−6) result. The numerical experimental results validate that this method outperforms several existing methods with fewer iterations and a lower running time.

The paper is devoted to subgradient methods with switching between productive and nonproductive steps for problems of minimization of quasiconvex functions under functional inequality constraints. For the problem of minimizing a convex function with quasiconvex inequality constraints, a result is obtained on the convergence of the subgradient method with an adaptive stopping rule. Further, based on an analog of a sharp minimum for nonlinear problems with inequality constraints, results are obtained on the geometric convergence of restarted versions of subgradient methods. Such results are considered separately in the case of a convex objective function and quasiconvex inequality constraints, as well as in the case of a quasiconvex objective function and convex inequality constraints. The convexity may allow to additionally suggest adaptive stopping rules for auxiliary methods, which guarantee that an acceptable solution quality is achieved. The results of computational experiments are presented, showing the advantages of using such stopping rules. [ABSTRACT FROM AUTHOR]

We consider a stochastic system of N$$ N $$ interacting particles with constant diffusion coefficient and drift linear in space, time‐depending on two unknown deterministic functions. Our concern here is the nonparametric estimation of these functions from a continuous observation of the process on [0,T]$$ \left[0,T\right] $$ for fixed T$$ T $$ and large N$$ N $$. We define two collections of projection estimators belonging to finite‐dimensional subspaces of 핃2([0,T]). We study the 핃2‐risks of these estimators, where the risk is defined either by the expectation of an empirical norm or by the expectation of a deterministic norm. Afterwards, we propose a data‐driven choice of the dimensions and study the risk of the adaptive estimators. The results are illustrated by numerical experiments on simulated data. [ABSTRACT FROM AUTHOR]

Complex industrial scenarios are accompanied by many disturbances, especially when arcs are used as a industrial technique method in the process flow. Arc interference can cause disturbances such as contrast reduction, color deviation, instantaneous overexposure, low illumination, and loss of detail to the captured images, as hinders the development of industry toward the intelligent direction industrial intelligence. Due to the particularity of arc interference, none of the existing studies can be applied to the inpainting of such images. In this study, we constructed the Arc Interference—Distance, Light intensity, and Color (AI-DLC) model by analyzing the characteristics of arc light and its mechanism of interference to the image, which was used to measure the local interference of arc light. Based on this model, we propose the adaptive arc area inpainting and image enhancement method. This method, firstly, splits the original image into several equal-sized patches. Secondly, it classifies them according to the model values. Finally, the patches are processed by each adaptive module. Through experiments in real industrial scenes, compared with commonly used image restoration methods, this method can effectively repair the arc area, enhance image information, and improve image quality. [ABSTRACT FROM AUTHOR]

This work presents an adaptive superfast proximal augmented Lagrangian (AS-PAL) method for solving linearly-constrained smooth nonconvex composite optimization problems. Each iteration of AS-PAL inexactly solves a possibly nonconvex proximal augmented Lagrangian (AL) subproblem obtained by an aggressive/adaptive choice of prox stepsize with the aim of substantially improving its computational performance followed by a full Lagrange multiplier update. A major advantage of AS-PAL compared to other AL methods is that it requires no knowledge of parameters (e.g., size of constraint matrix, objective function curvatures, etc) associated with the optimization problem, due to its adaptive nature not only in choosing the prox stepsize but also in using a crucial adaptive accelerated composite gradient variant to solve the proximal AL subproblems. The speed and efficiency of AS-PAL is demonstrated through extensive computational experiments showing that it can solve many instances more than ten times faster than other state-of-the-art penalty and AL methods, particularly when high accuracy is required. [ABSTRACT FROM AUTHOR]

This paper is a follow-up to a previous work where we defined and generated the set of all possible compromises of multilevel multiobjective linear programming problems (ML-MOLPP). We introduce a new algorithm to solve ML-MOLPP in which the adaptive method of linear programming is nested. First, we start by generating the set of all possible compromises (set of all non-dominated solutions). After that, an algorithm based on the adaptive method of linear programming is developed to select the best compromise among all the possible settlements achieved. This method will allow us to transform the initial multilevel problem into an ML-MOLPP with bonded variables. Then, apply the adaptive method which is the most efficient to solve all the multiobjective linear programming problems involved in the resolution process instead of the simplex method. Finally, all the construction stages are carefully checked and illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

This study was conducted to promote a new adaptive cone algorithm (ACA) algorithm. ACA is a metaheuristic technique based on swarm intelligence. ACA contains three steps. Each agent moves closer to the global reference in the first step. Then, each agent searches for a better solution around the current solution in the second step. The global reference searches for better solutions around it in the third step. This algorithm is named cone because the local space size declines linearly during the iterative process. ACA introduces a new adaptability model to improve the exploration strategy when a better solution cannot be achieved. It is conducted by enlarging the local solution space. ACA is challenged to find the final solution for theoretical and practical problems. The 23 functions are chosen as theoretical optimization problems. The portfolio optimization problem is selected as the practical problem. ACA is compared with five algorithms: particle swarm optimization (PSO), grey wolf optimizer (GWO), marine predator optimization (MPA), average subtraction-based optimizer (ASBO), and pelican optimization algorithm (POA). The result shows that ACA is competitive in finding the optimal solution for 23 functions and outperforms all sparing algorithms in achieving the highest total capital gain in tackling the portfolio optimization problem. ACA is superior to PSO, GWO, MPA, ASBO, and POA in solving 20, 11, 13, 4, and 21 functions, respectively. In the future, ACA can be implemented in solving various practical optimization problems. [ABSTRACT FROM AUTHOR]

We study the gradient method under the assumption that an additively inexact gradient is available for, generally speaking, non-convex problems. The non-convexity of the objective function, as well as the use of an inexactness specified gradient at iterations, can lead to various problems. For example, the trajectory of the gradient method may be far enough away from the starting point. On the other hand, the unbounded removal of the trajectory of the gradient method in the presence of noise can lead to the removal of the trajectory of the method from the desired global solution. The results of investigating the behavior of the trajectory of the gradient method are obtained under the assumption of the inexactness of the gradient and the condition of gradient dominance. It is well known that such a condition is valid for many important non-convex problems. Moreover, it leads to good complexity guarantees for the gradient method. A rule of early stopping of the gradient method is proposed. Firstly, it guarantees achieving an acceptable quality of the exit point of the method in terms of the function. Secondly, the stopping rule ensures a fairly moderate distance of this point from the chosen initial position. In addition to the gradient method with a constant step, its variant with adaptive step size is also investigated in detail, which makes it possible to apply the developed technique in the case of an unknown Lipschitz constant for the gradient. Some computational experiments have been carried out which demonstrate effectiveness of the proposed stopping rule for the investigated gradient methods. [ABSTRACT FROM AUTHOR]

Reconstructing a triangular mesh from images by a differentiable rendering framework often exploits discrete Laplacians on the mesh, e.g., the cotangent Laplacian, so that a stochastic gradient descent-based optimization in the framework can become stable by a regularization term formed with the Laplacians. However, the stability stemming from using such a regularizer often comes at the cost of over-smoothing a resulting mesh, especially when the Laplacian of the mesh is not properly approximated, e.g., too-noisy or overly-smoothed Laplacian of the mesh. This paper presents a new discrete Laplacian built upon a kernel-weighted Laplacian. We control the kernel weights using a local bandwidth parameter so that the geometry optimization in a differentiable rendering framework can be improved by avoiding blurring high-frequency details of a surface. We demonstrate that our discrete Laplacian with a local adaptivity can improve the quality of reconstructed meshes and convergence speed of the geometry optimization by plugging our discrete Laplacian into recent differentiable rendering frameworks. [ABSTRACT FROM AUTHOR]

In real-world scenarios, the facial expression recognition task faces several challenges, including lighting variations, image noise, face occlusion, and other factors, which limit the performance of existing models in dealing with complex situations. To cope with these problems, we introduce the CoT module between the CNN and ViT frameworks, which improves the ability to perceive subtle differences by learning the correlations between local area features at a fine-grained level, helping to maintain the consistency between the local area features and the global expression, and making the model more adaptable to complex lighting conditions. Meanwhile, we adopt an adaptive learning method to effectively eliminate the interference of noise and occlusion by dynamically adjusting the parameters of the Transformer Encoder’s self-attention weight matrix. Experiments demonstrate the accuracy of our CoT_AdaViT model in the Oulu-CASIA dataset as (NIR: 87.94%, VL: strong: 89.47%, weak: 84.76%, dark: 82.28%). As well as, CK+, RAF-DB, and FERPlus datasets achieved 99.20%, 91.07%, and 90.57% recognition results, which achieved excellent performance and verified that the model has strong recognition accuracy and robustness in complex scenes.

CFRP/Ti stacks composed of carbon fiber-reinforced plastic composites (CFRP) and titanium alloys (Ti) are widely used in aerospace fields. However, in the integrated hole-making process of CFRP/Ti stacks, the machining characteristics of various materials are significantly different, and constant machining parameters cannot simultaneously meet the high-quality machining requirements of two materials. In addition, errors exist between the actual thickness of each material layer and the theoretical value, which causes an impediment to the monitoring of the machining interface and the corresponding adjustment of parameters. An adaptive machining method for the helical milling of CFRP/Ti stacks based on interface identification is proposed in this paper. The machining characteristics of the pneumatic spindle and the interface state in the helical milling of CFRP/Ti stacks are analyzed using self-developed portable helical milling equipment, and a new algorithm for the real-time monitoring of the machining interface position and adaptive adjustment of the machining parameters according to the interface identification result is proposed. Helical milling experiments were carried out, the results show that the proposed method can effectively identify the position of the machining interface with good identification accuracy. Moreover, the proposed parameter-adaptive optimized machining method for CFRP/Ti stacks can significantly improve hole diameter accuracy and machining quality.

As we all know, YOLOv4 can achieve excellent detection performance in object detection and has been effectively applied in many fields. However, the inconsistency of scale features affects the prediction accuracy of the path aggregation network (PANet) in YOLOv4 for small objects, resulting in low detection accuracy. This paper presents YOLOv4, which uses an adaptive recursive path aggregation network (AR-PANet) to improve the detection accuracy of small objects. First, the output characteristics of the PANet are fed back into the backbone network by using a recursive structure to enrich the characteristic information of the object. Second, an adaptive approach is developed to eliminate conflicting information in multi-scale feature space, thereby enhancing scale invariance and promoting feature extraction accuracy for small objects. Finally, the CBAM is used to map the multi-scale features obtained from the AR-PANet to independent channels and spatial dimensions to achieve feature refinement, thus improving the detection accuracy of small objects. Experimental results show that our proposed method can effectively improve the accuracy of small object detection in multiple datasets, addressing this challenging problem with impressive results. Thus, our proposed approach has great potential and valuable applications in the fields of remote sensing and intelligent transportation.

The paper proposes an adaptive selection method for the shape parameter in the multi-quadratic radial basis function (MQ-RBF) interpolation of two-dimensional (2D) scattered data and achieves good performance in solving integral equations (O-MQRBF). The effectiveness of MQ-RBF interpolation for 2D scattered data largely depends on the choice of the shape parameter. However, currently, the most appropriate parameter is chosen by empirical techniques or trial and error, and there is no widely accepted method. Fourier transform can linearly represent 2D scattering data as a combination of sine and cosine functions. Therefore, the paper employs an improved stochastic walk optimization algorithm to determine the optimal shape parameters for sine functions and their linear combinations, generating a dataset. Based on this dataset, the paper trains a particle swarm optimization backpropagation neural network (PSO-BP) to construct an optimal shape parameter selection model. The adaptive model accurately predicts the ideal shape parameters of the Fourier expansion of 2D scattering data, significantly reducing computational cost and improving interpolation accuracy. The adaptive method forms the basis of the O-MQRBF algorithm for solving one-dimensional integral equations. Compared with traditional methods, this algorithm significantly improves the precision of the solution. Overall, this study greatly facilitates the development of MQ-RBF interpolation technology and its widespread use in solving integral equations. [ABSTRACT FROM AUTHOR]

Three-dimensional deformation is an important input to explore seismic mechanisms and geodynamics. The GNSS and InSAR technologies are commonly used to obtain the co-seismic three-dimensional deformation field. This paper focused on the effect of calculation accuracy caused by the deformation correlation between the reference point and the points involved in the solution, to build a high-accuracy three-dimensional deformation field for a detailed geological explanation. Based on the variance component estimation (VCE) method, the InSAR LOS, azimuthal deformation, and the GNSS horizontal and vertical deformation were integrated to solve the three-dimensional displacement of the study area in combination with the elasticity theory. The accuracy of the three-dimensional co-seismic deformation field of the 2021 Maduo MS7.4 earthquake obtained by the method proposed in this paper, was compared with that obtained from the only InSAR measurements obtained using a multi-satellite and multi-technology approach. The results showed the difference in root-mean-square errors (RMSE) of the integration and GNSS displacement was 0.98 cm, 5.64 cm, and 1.37 cm in the east–west, north–south and vertical direction respectively, which was better than the RMSE of the method using only InSAR and GNSS displacement, which was 5.2 cm and 12.2 cm in the east–west, north–south, and no vertical direction. With the geological field survey and aftershocks relocation, the results showed good agreement with the strike and the position of the surface rupture. The maximum slip displacement was about 4 m, which was consistent with the result of the empirical statistical formula. It was firstly found that the pre-existing fault controlled the vertical deformation on the south side of the west end of the main surface rupture caused by the Maduo MS7.4 earthquake, which provided the direct evidence for the theoretical hypothesis that large earthquakes could not only produce surface rupture on seismogenic faults, but also trigger pre-existing faults or new faults to produce surface rupture or weak deformation in areas far from seismogenic faults. An adaptive method was proposed in GNSS and InSAR integration, which could take into account the correlation distance and the efficiency of homogeneous point selection. Meanwhile, deformation information of the decoherent region could be recovered without interpolation of the GNSS displacement. This series of findings formed an essential supplement to the field surface rupture survey and provided a novel idea for the combination of the various spatial measurement technologies to improve the seismic deformation monitoring. [ABSTRACT FROM AUTHOR]

Control charts play a beneficial role in the manufacturing process by reduction of non-compatible products and improving the final quality. In line with these aims, several adaptive methods in which samples can be taken with variable sampling rates and intervals have been proposed in the area of statistical process control (SPC). In some SPC applications, it is important to monitor a relationship between the response and independent variables—this is called profile monitoring. This article proposes adaptive generalized likelihood ratio (GLR) control charts based on variable sampling interval (VSI) and sequential sampling (SS) techniques for monitoring simple linear profiles. Because in some real-life problems, it may be possible that the user cannot control the values of explanatory variables; thus, in this paper, we focus on such a scenario. The performance of the proposed method is compared under three different situations, i.e., the fixed sampling rate (FSR), VSI, and SS, based on average time to signal (ATS) criteria for phase II analysis. Since the SS approach uses a novel sampling procedure based on the statistic magnitude, it has a superior performance over other competing charts. Several simulation studies indicate the superiority as the SS approach yields lower ATS values when there are single-step changes in the intercept, slope, standard deviation of the error term, and explanatory variables. In addition, some other related sensitivity analysis indicates that other aspects of the proposed methods, such as computational time, comparison with other control charts, and consideration of fixed explanatory variables. Furthermore, the results are supported by a real-life illustrative example from the adhesive manufacturing industry. [ABSTRACT FROM AUTHOR]

In this paper, a highly accurate and efficient Adaptive Local Variational Iteration Method (ALVIM) is presented to fulfil the need of the astrodynamics society for fast and accurate computational methods for guidance and control. The analytical iteration formula of this method is derived by using a general form of the first order nonlinear differential equations, followed by straightforward discretization using Chebyshev polynomials and collocation. The resulting numerical algorithm is very concise and easy to use, only involving highly sparse matrix operations of addition and multiplication, and no inversion of the Jacobian is required. Apart from the simple yet efficient iteration formula, a straightforward adaptive scheme is introduced to refine the step size and the collocation nodes at each time segment. The presented adaptive method guarantees prescribed accuracy without manual tuning of the algorithm. The computational cost of ALVIM, in terms of functional evaluations, is 1–2 orders of magnitude lower than adaptive finite difference methods. Numerical results of a large amplitude pendulum, perturbed two-body problem, and three-body problem validate the high accuracy and efficiency of this easy-to-use adaptive method. [ABSTRACT FROM AUTHOR]

Points of Subjective Equality (PSE) are commonly measured using staircase or constant stimuli methods. However, the staircase method is highly dependent on the step size, and the constant stimuli method is time-consuming. Thus, we wanted to develop an efficient and quick method to estimate both the PSE and the slope of the psychometric function. We developed a random-step algorithm in which a one-up-one-down rule is followed but with a random step size in a pre-defined range of test levels. Each stimulus would be chosen depending on the previous response of the subject. If the subject responded “up”, any random level in the lower range would be picked for the next trial. And if the subject responded “down”, any random level in the upper range would be picked for the next trial. This procedure would result in a bell-shaped distribution of the test levels around the estimated PSE, while a substantial amount of trials would still be dispersed at both bounds of the range. We then compared this method with traditional constant stimuli procedure on a task based on the Pulfrich phenomenon while the PSEs of participants could be varied using different neutral density filters. Our random-step method provided robust estimates of both the PSE and the slope under various noise levels with small trial counts, and we observed a significant correlation between the PSEs obtained with the two methods. The random-step method is an efficient way to measure the full psychometric function when testing time is critical, such as in clinical settings.

The paper deals with a significant extension of the recently proposed class of relatively strongly convex optimization problems in spaces of large dimension. In the present paper, we introduce an analog of the concept of relative strong convexity for variational inequalities (relative strong monotonicity) and study estimates for the rate of convergence of some numerical first-order methods for problems of this type. The paper discusses two classes of variational inequalities depending on the conditions related to the smoothness of the operator. The first of these classes of problems contains relatively bounded operators, and the second, operators with an analog of the Lipschitz condition (known as relative smoothness). For variational inequalities with relatively bounded and relatively strongly monotone operators, a version of the subgradient method is studied and an optimal estimate for the rate of convergence is justified. For problems with relatively smooth and relatively strongly monotone operators, we prove the linear rate of convergence of an algorithm with a special organization of the restart procedure of a mirror prox method for variational inequalities with monotone operators. [ABSTRACT FROM AUTHOR]

Based on the auxiliary subspace techniques, a hierarchical basis a posteriori error estimator is proposed for the Stokes problem in two and three dimensions. For the error estimator, we need to solve only two global diagonal linear systems corresponding to the degree of freedom of velocity and pressure respectively, which reduces the computational cost sharply. The upper and lower bounds up to an oscillation term are shown without saturation assumption. Numerical simulations are performed to demonstrate the reliability of the a posteriori error estimator. [ABSTRACT FROM AUTHOR]

Abstract Objective The aim of this study is to demonstrate an adaptive method that is robust toward environmental fluctuations and provides a real-time measure of plant growth by measuring CO2 consumption. To verify the validity of the proposed method, the relation between the plant growth and variation in light conditions with a closed experimental system was investigated. Results The proposed method was used to measure the photosynthetic rate induced by photosynthetic photon flux density (PPFD) and to evaluate plant growth under continuous and pulsed light in arugula plants. The PPFD-dependent change in photosynthetic rate was measured. And in the condition range of 200–10,000 μs pulse period and 50% duty ratio of pulsed light, there was no change in the growth rate of plants assuming the same PPFD as continuous light. These experiments showed the validity of the adaptive method in removing environmental fluctuations without precise control of temperature and humidity.

In this paper, we propose a stochastic primal-dual adaptive method based on an inexact augmented Lagrangian function to solve non-convex programs, referred to as the SPDAM. Different from existing methods, SPDAM incorporates adaptive step size and momentum-based search directions, which improve the convergence rate. At each iteration, an inexact augmented Lagrangian subproblem is solved to update the primal variables. A post-processing step is designed to adjust the primal variables to meet the accuracy requirement, and the adjusted primal variable is used to compute the dual variable. Under appropriate assumptions, we prove that the method converges to the ε -KKT point of the primal problem, and a complexity result of SPDAM less than O (ε − 11 2 ) is established. This is better than the most famous O (ε − 6) result. The numerical experimental results validate that this method outperforms several existing methods with fewer iterations and a lower running time. [ABSTRACT FROM AUTHOR]

A posteriori error estimators for the symmetric mixed finite element methods for linear elasticity problems with Dirichlet and mixed boundary conditions are proposed. Reliability and efficiency of the estimators are proved. Finally, numerical examples are presented to verify the theoretical results.

Efficient and accurate numerical approximation of the full Boltzmann equation has been a longstanding challenging problem in kinetic theory. This is mainly due to the high dimensionality of the problem and the complicated collision operator. In this work, we propose a highly efficient adaptive low rank method for the Boltzmann equation, concerning in particular the steady state computation. This method employs the fast Fourier spectral method (for the collision operator) and the dynamical low rank method to obtain computational efficiency. An adaptive strategy is introduced to incorporate the boundary information and control the computational rank in an appropriate way. Using a series of benchmark tests in 1D and 2D, we demonstrate the efficiency and accuracy of the proposed method in comparison to the full tensor grid approach. [ABSTRACT FROM AUTHOR]

In the presented study, the hyperbolic telegraph equation is taken as the focus point. To solve such an equation, an accurate, reliable, and efficient method has been proposed. The developed method is mainly based on the combination of a kind of mesh-free method and an adaptive method. Multiquadric radial basis function mesh-free method is considered on spatial domain and the adaptive fifth-order Runge–Kutta method is used on time domain. The validity and the performance of the proposed method have been checked on several test problems. The approximate solutions are compared with the exact solution, it is shown that the proposed method has more preferable to the other methods in the literature. [ABSTRACT FROM AUTHOR]

The paper proposes an adaptive selection method for the shape parameter in the multi-quadratic radial basis function (MQ-RBF) interpolation of two-dimensional (2D) scattered data and achieves good performance in solving integral equations (O-MQRBF). The effectiveness of MQ-RBF interpolation for 2D scattered data largely depends on the choice of the shape parameter. However, currently, the most appropriate parameter is chosen by empirical techniques or trial and error, and there is no widely accepted method. Fourier transform can linearly represent 2D scattering data as a combination of sine and cosine functions. Therefore, the paper employs an improved stochastic walk optimization algorithm to determine the optimal shape parameters for sine functions and their linear combinations, generating a dataset. Based on this dataset, the paper trains a particle swarm optimization backpropagation neural network (PSO-BP) to construct an optimal shape parameter selection model. The adaptive model accurately predicts the ideal shape parameters of the Fourier expansion of 2D scattering data, significantly reducing computational cost and improving interpolation accuracy. The adaptive method forms the basis of the O-MQRBF algorithm for solving one-dimensional integral equations. Compared with traditional methods, this algorithm significantly improves the precision of the solution. Overall, this study greatly facilitates the development of MQ-RBF interpolation technology and its widespread use in solving integral equations.