Global Smoothness Research Articles

Adversarial training regularization for negative sampling based network embedding

The aim of network embedding is to learn compact node representations. This has been shown to be effective in various downstream learning tasks, such as link prediction and node classification. Most methods focus on preserving different network structures and properties, ignoring the fact that networks are usually noisy and incomplete, thus such methods potentially lack robustness and suffer from the overfitting issue. Recently, generative adversarial networks based methods have been exploited to impose a prior distribution on node embeddings to encourage a global smoothness, but their model architecture is very complicated and they suffer from the non-convergence problem. Here, we propose adversarial training (AdvT), a more succinct and effective local regularization method, for negative-sampling-based network embedding to improve model robustness and generalization ability. Specifically, we first define the adversarial perturbations in the embedding space instead of in the discrete graph domain to circumvent the challenge of generating discrete adversarial examples. Then, to enable more effective regularization, we design the adaptive l2 norm constraints on adversarial perturbations that depend upon the connectivity pattern of node pairs. We integrate AdvT into several famous models including DeepWalk, LINE and node2vec, and conduct extensive experiments on benchmark datasets to verify its effectiveness.

Two-Step Chemical Mechanical Polishing of 4H-SiC (0001) Wafer

Chemical mechanical polishing (CMP), as a widely used global smoothing technique, requires a high polishing rate and a low surface roughness. However, it is difficult to meet these requirements with single-step polishing. To obtain a perfect 4H-SiC wafer surface, we studied a two-step CMP 4H-SiC wafer using a-Al2O3-based slurry and nano-SiO2-based slurry. Before the two-step process was determined, the effect of concentration of KMnO4 and pH on the polishing rate of 4H-SiC was first studied with Al2O3 as the abrasive, and the maximum polishing rate of 1400 nm h−1 was determined under the condition of pH of 2.00 and KMnO4 concentration of 6.5 wt% in the step. Furthermore, the effect of H2O2 concentration on the polishing rate of 4H-SiC was investigated using SiO2 as the abrasive and V2O5 as the catalyst. It was determined that under the condition of V2O5 concentration of 4 wt% and H2O2 concentration of 10 wt%, the maximum polishing rate of the second step polishing was 150 nm h−1, and a perfect surface was obtained, with a surface roughness of 0.066 nm. In addition, the in situ friction coefficients have used to characterize the two-step process. At the end, the CMP mechanisms of the above two slurry have been deduced and preliminarily demonstrated.

Fog Reduction in an Images using Global Guided Image Filtering

Under poor weather conditions such as fog, haze, rain, and so on, images of outdoor scenes suffer from faint colour, slight contrasts, and changed luminosity. The contrasts of artefacts and the distortion of air light colour are vastly increased as fog is minimized. The same configuration is used in the editing methods, such as the 'Guided Image Filter' and the 'Weighted Guided Image Filter.' In this article, we suggest a novel approach called Global guided image filter from the Global Channel of Structural sharing and the Global Edge Preservative Smoothing to obtain fine structures and to eliminate the fog in the input image. The structure exchange channel contributions exist an image to distinguish, moreover, a vector path field. The structure remains well-defined by vector path field as well as exchanged for a structure exchange channel to isolate the image by analysis of the experimental effects. In comparison with GIF as well as WGIF, it reveals that a fine structure is maintained.

Fifth-Order Hermite Targeted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws

We present a targeted essentially non-oscillatory (TENO) scheme based on Hermite polynomials for solving hyperbolic conservation laws. Hermite polynomials have already been adopted in weighted essentially non-oscillatory (WENO) schemes (Qiu and Shu in J Comput Phys 193:115–135, 2003). The Hermite TENO reconstruction offers major advantages over the earlier reconstruction; namely, it is a compact Hermite-type reconstruction and has low dissipation by virtue of TENO’s stencil voting strategy. Next, we formulate a new high-order global reference smoothness indicator for the proposed scheme. The flux calculations and time-advancing schemes are carried out by the local Lax–Friedrichs flux and third-order strong-stability-preserving Runge–Kutta methods, respectively. The scalar and system of the hyperbolic conservation laws are demonstrated in numerical tests. In these tests, the proposed scheme improves the shock-capturing performance and inherits the good small-scale resolution of the TENO scheme.

Development of a Modified Seventh-Order WENO Scheme with New Nonlinear Weights

The aim of this paper is the presentation of a new modified weighted essentially non-oscillatory scheme with a seventh-order of accuracy, and, a novel nonlinear weighting method. Local smoothness indicators of this scheme constructed using Lagrange’s interpolation polynomial. We developed a new high-order global smoothness indicator, which guarantees the optimal order of accuracy of the scheme at critical points. We used the linear advection equation for verification of the order of accuracy at critical points. Later, we used a series of one- and two-dimensional benchmark problems to verify the shock-capturing capabilities and improved numerical resolution of the new scheme.

Global smoothing of short line segment toolpaths by control-point-assigning-based geometric smoothing and FIR filtering-based motion smoothing

The toolpaths for curved surfaces generated by most existing computer-aided-manufacturing applications are always consisted by short line segments. Due to the first-order discontinuity of the short line segment toolpath, the precise following of them must result in frequent acceleration/decelerations, which is easy to excite structural vibration of the machine tools, thus degrading the machining quality. To solve this problem, local corner rounding approaches are widely researched, however, most areas on the toolpath after corner rounding remains linear segments, unlike the global smoothing method who replaces all short line segments to spline curves thus obtaining smoother feed motion. Compared with the local corner rounding method, the global smoothing always requires iterative computes to satisfy the accuracy requirement, which makes it so time consuming that can hardly be utilized in CNC systems. To deal with above problem, this paper proposes a highly stable global smoothing method which does not need iterative computations. This is realized by a control-point-assigning-based global geometric smoothing algorithm and a FIR (Finite Impulse Response) filtering-based global motion smoothing algorithm. During global geometric smoothing, the short line segment toolpath is replaced by piecewise B-spline curve segments whose control points are directly assigned under the error tolerance constraint. During the global motion smoothing, a fast spline interpolation method based on FIR filtering is provided to generate smooth axial position references of the piecewise B-spline curve segments under the axial drive constraint. The whole global smoothing approach does not require pre-processing or iterative computation, which makes it easy to be applied. Extensive illustrations including numerical tests and experimental verification/comparison tests demonstrate the favorable effects of the proposed method in real-time capability and motion smoothing performance. Comparing with typical local corner rounding approach, the proposed global smoothing approach results in shorter motion time and better smoothness. Comparing with typical existing global smoothing method, the proposed method performs better in no required pre-processing and high-order motion smoothness.

Global smoothing for five-axis linear paths based on an adaptive NURBS interpolation algorithm

The five-axis tool path generated by CAM software usually consists of a series of linear paths. The tangent direction at the corner of the adjacent line segment will suddenly change, and the curvature is also discontinuous, which will cause vibration and shock during the machining process. Thus, a global corner smoothing algorithm based on cubic NURBS interpolation is proposed to smooth the linear paths in this paper, so as to achieve G2 continuous for five-axis linear paths. The algorithm proposed does not require matrix operations to solve the control points, and it can also reduce the number of control points while satisfying the interpolation error. The algorithm is then used to generate smooth NURBS path for ceramic core burrs and blockage repair. The simulation and experiment show that the algorithm proposed can satisfy the error constraints, reduce the vibration of the motion axis, and improve the surface quality of laser cutting.

Rates of convergence to equilibrium for potlatch and smoothing processes

We analyze the local and global smoothing rates of the smoothing process and obtain convergence rates to stationarity for the dual process known as the potlatch process. For general finite graphs we connect the smoothing and convergence rates to the spectral gap of the associated Markov chain. We perform a more detailed analysis of these processes on the torus. Polynomial corrections to the smoothing rates are obtained. They show that local smoothing happens faster than global smoothing. These polynomial rates translate to rates of convergence to stationarity in L2-Wasserstein distance for the potlatch process on Zd.

Variational time discretizations of higher order and higher regularity

We consider a family of variational time discretizations that are generalizations of discontinuous Galerkin (dG) and continuous Galerkin–Petrov (cGP) methods. The family is characterized by two parameters. One describes the polynomial ansatz order while the other one is associated with the global smoothness that is ensured by higher order collocation conditions at both ends of the subintervals. Applied to Dahlquist’s stability problem, the presented methods provide the same stability properties as dG or cGP methods. Provided that suitable quadrature rules of Hermite type are used to evaluate the integrals in the variational conditions, the variational time discretization methods are connected to special collocation methods. For this case, we present error estimates, numerical experiments, and a computationally cheap postprocessing that allows to increase both the accuracy and the global smoothness by one order.

Nernst–Planck–Navier–Stokes Systems far from Equilibrium

We consider ionic electrodiffusion in fluids, described by the Nernst-Planck-Navier-Stokes system. We prove that the system has global smooth solutions for arbitrary smooth data: arbitrary positive Dirichlet boundary conditions for the ionic concentrations, arbitrary Dirichlet boundary conditions for the potential, arbitrary positive initial concentrations, and arbitrary regular divergence-free initial velocities. The result holds for any positive diffusivities of ions, in bounded domains with smooth boundary in three space dimensions, in the case of two ionic species, coupled to Stokes equations for the fluid. The result also holds in the case of Navier-Stokes coupling, if the velocity is regular. The global smoothness of solutions is also true for arbitrarily many ionic species, if all their diffusivities are the same.

A fully real-time spline interpolation algorithm with axial jerk constraint based on FIR filtering

Interpolators play a core and important role in CNC systems, and the scheduling of feedrate is a main task of CNC interpolators. It is routine to schedule the feedrate of linear/circular toolpaths because of their regular geometry; however, the feedrate scheduling of spline toolpaths remains challenging due to the freely and unpredictable geometric shape. Most of the existing methods require looking ahead or pre-processing to acquire sufficient toolpath information for generating drive-bounded smooth feedrate profile, which limits the integral machining efficiency. This paper presents a FIR (finite impulse response) filtering-based interpolation algorithm for spline toolpath, thus realizing the fully real-time capability without using time-consuming optimization such as looking ahead or pre-processing. The presented method merely utilizes the curvature radius information of the current interpolation point on the spline toolpath, and the scheduled feedrate can be generated within one step. Furthermore, the global tangential smoothness of the feedrate profile is guaranteed by directly applying convolution with a chain of two cascaded FIR filters. However, the FIR filtering induces interpolation error which plays as a negative cost during the one-step feedrate scheduling. To solve this issue, the principle of the filtering induced error is analyzed, so that it is computed by feed parameters and curvature radius, and the maximum error is added as an extra constraint beyond the commonly considered axial kinematic constraints. Effectiveness of the presented approach is demonstrated by both numerical illustration and experimental tests.

Large time existence of Euler–Korteweg equations and two-fluid Euler–Maxwell equations with vorticity

The aim of this paper is to study the influence of the vorticity on the existence time in fluid systems for which global smoothness and decay are known in the case of small irrotational data. We focus on two examples: the Euler–Korteweg system and the two-fluid Euler–Maxwell system. We prove that the lower bound of the lifespan of these systems is no less than the inverse of the Hs(s>5∕2) norm of the rotational part of the initial velocity. Our approach is based on energy estimates and the fast time decay results of global solutions to these systems with irrotational initial data.

Inhomogeneous image segmentation based on local constant and global smoothness priors

In this article, we propose a new variational model for segmenting images with intensity inhomogeneity. The proposed model applies simultaneously the local constant and global smoothness priors to describe the bias part such that our model can obtain more precise segmentation results. This is different from the existing models in which either of such two priors is considered. Also, our method is developed to segment the multiphase inhomogeneous image with noise. Theoretically, we show the existence of minimizers of the proposed variational model. Moreover, by using the alternating minimization method, we design an effective algorithm to numerically solve the solution of the model. Numerical experimental results are provided to verify the better performance of our method than other test methods.

Improved weighted NND scheme for shock-capturing

Aimed at decreasing the numerical dissipation of weighted non-oscillatory and non-free-parameter dissipation (WNND) scheme, we present an improved counterpart for shock-capturing. The new algorithm is based on the framework of Z-type weighting procedure with new local and global smoothness indicators. The performances of the proposed scheme are evaluated on several numerical tests governed by one-dimensional Euler equations. Numerical results indicate that the improved WNND scheme has advantages over the original WNND and third-order WENO-JS and WENO-Z schemes.

Approximation by multivariate generalized Poisson–Cauchy type singular integral operators

This research and survey work deals exclusively with the study of the approximation of generalized multivariate Poisson–Cauchy type singular integrals to the identity-unit operator. Here we study quantitatively most of their approximation properties. These operators are not in general positive linear operators. In particular we study the rate of convergence of these integral operators to the unit operator, as well as the related simultaneous approximation. These are given via Jackson type inequalities and by the use of multivariate high order modulus of smoothness of the high order partial derivatives of the involved function. Also we study the global smoothness preservation properties of these integral operators. These multivariate inequalities are nearly sharp and in one case the inequality is attained, that is sharp. Furthermore we give asymptotic expansions of Voronovskaya type for the error of approximation. The above properties are studied with respect to $$L_{p}$$ norm, $$1\le p\le \infty $$ .

Software Architecture for Autonomous and Coordinated Navigation of UAV Swarms in Forest and Urban Firefighting

Advances in the field of unmanned aerial vehicles (UAVs) have led to an exponential increase in their market, thanks to the development of innovative technological solutions aimed at a wide range of applications and services, such as emergencies and those related to fires. In addition, the expansion of this market has been accompanied by the birth and growth of the so-called UAV swarms. Currently, the expansion of these systems is due to their properties in terms of robustness, versatility, and efficiency. Along with these properties there is an aspect, which is still a field of study, such as autonomous and cooperative navigation of these swarms. In this paper we present an architecture that includes a set of complementary methods that allow the establishment of different control layers to enable the autonomous and cooperative navigation of a swarm of UAVs. Among the different layers, there are a global trajectory planner based on sampling, algorithms for obstacle detection and avoidance, and methods for autonomous decision making based on deep reinforcement learning. The paper shows satisfactory results for a line-of-sight based algorithm for global path planner trajectory smoothing in 2D and 3D. In addition, a novel method for autonomous navigation of UAVs based on deep reinforcement learning is shown, which has been tested in 2 different simulation environments with promising results about the use of these techniques to achieve autonomous navigation of UAVs.

Hyperspectral Image Superresolution Using Global Gradient Sparse and Nonlocal Low-Rank Tensor Decomposition With Hyper-Laplacian Prior

This article presents a novel global gradient sparse and nonlocal low-rank tensor decomposition model with a hyper-Laplacian prior for hyperspectral image (HSI) superresolution to produce a high-resolution HSI (HR-HSI) by fusing a low-resolution HSI (LR-HSI) with an HR multispectral image (HR-MSI). Inspired by the investigated hyper-Laplacian distribution of the gradients of the difference images between the upsampled LR-HSI and latent HR-HSI, we formulate the relationship between these two datasets as a $\ell _{p}$ $(0 -norm term to enforce spectral preservation. Then, the relationship between the HR-MSI and latent HR-HSI is built using a tensor-based fidelity term to recover the spatial details. To effectively capture the high spatio-spectral-nonlocal similarities of the latent HR-HSI, we design a novel nonlocal low-rank Tucker decomposition to model the 3-D regular tensors constructed from the grouped nonlocal similar HR-HSI cubes. The global spatial-spectral total variation regularization is then adopted to ensure the global spatial piecewise smoothness and spectral consistency of the reconstructed HR-HSI from nonlocal low-rank cubes. Finally, an alternating direction method of multipliers-based algorithm is designed to efficiently solve the optimization problem. Experiments on both the synthetic and real datasets collected by different sensors show the effectiveness of the proposed method, from visual and quantitative assessments.

Global Consistent Graph Convolutional Network for Hyperspectral Image Classification

While semisupervised methods based on graph convolutional networks (GCNs) can achieve good results in hyperspectral image (HSI) classification, their performance is limited as they rely only on spatial-spectral similarity when constructing local adjacency graphs. Moreover, relying on local adjacency graphs can limit the ability of the methods to ensure the consistency of global feature in complex hyperspectral remote sensing environments. Using the spatial-spectral information is typically not sufficient for providing a reliable similarity measurement to construct a global graph when the spectral variability is large and the spatial distance is long in intraclass pixels. To address this issue, this article presents a novel globally consistent GCN (GCGCN) for HSI classification. According to the proposed method, a local reliable initial graph is first built from inherent spatial-spectral information by considering this graph as a variable to optimize. Then, adaptive global high-order neighbors are explored to capture the underlying rich spatial contextual information by utilizing the graph topological consistent connectivity instead of the common strategy of using only the spatial-spectral similarity measurement. Finally, the adaptive global high-order graph structure and two-layer networks are combined to achieve the global feature smoothing of the same class samples and maintain high global feature consistency. The proposed GCGCN method is evaluated on three real HSI data sets to demonstrate its superiority compared to ten different classification methods. Moreover, the proposed GCGCN method achieves state-of-the-art classification results on three data sets in terms of four classification evaluation metrics, including overall accuracy (OA), kappa coefficient (KC), average accuracy (AA), and class accuracy (CA).

Global Dynamic Path Planning Fusion Algorithm Combining Jump-A* Algorithm and Dynamic Window Approach

In order to meet the performance requirements of global optimality and path smoothness in robot path planning, a new fusion algorithm of jump-A^* algorithm and dynamic window approach is proposed. First, A^* algorithm is optimized by using the jump point search method and a new distance evaluation function defined by Manhattan and Euclidean distance to obtain global path information. Then take the dynamic window approach as the core by integrating the global path information to safely plan a global optimal path with high smoothness. The experimental results show that the new fusion algorithm proposed in this paper can not only effectively solve the problem of non-continuous curvature and excessive turning angle at the turning points of the path planned by jump-A^* algorithm, but also improve the smoothness of the path and the global optimality. This research is beneficial to the motion control of robots and has certain reference for robot navigation.

一个改进的三阶WENO-Z型格式

Based on the high-order global smoothness factor, a low-dissipation and high-resolution 3rd-order WENO difference scheme was obtained under the WENO-Z scheme framework. A parameter was introduced in the nonlinear weight, the parameter range was determined by convergence analysis, and the optimal parameter value was obtained with combined accuracy and non-oscillation. The scheme can maintain expected 3rd-order accuracy at the 1st-order extremum of the function. Finally, the accuracy recovery of the scheme at various extremum points was verified with exact solution examples, and the low-dissipation and high-resolution characteristics of the scheme were tested with the 1D and 2D Euler equations. The results show that, the proposed scheme is a good shock-capturing method.