Global Smoothness Research Articles

Multivariate Approximation Using Symmetrized and Perturbed Hyperbolic Tangent-Activated Multidimensional Convolution-Type Operators

In this article, we introduce, for the first time, multivariate symmetrized and perturbed hyperbolic tangent-activated convolution-type operators in three forms. We present their approximation properties, that is, their quantitative convergence to the unit operator via the multivariate modulus of continuity. We continue with the multivariate global smoothness preservation of these operators. We present, in detail, the related multivariate iterative approximation, as well as, multivariate simultaneous approximation, and their combinations. Using differentiability in our research, we produce higher rates of approximation, and multivariate simultaneous global smoothness preservation is also achieved.

Nonstationary adaptive S-wave leakage suppression of ocean-bottom node data

Ocean-bottom nodes (OBNs) are widely used because of their wide azimuth, long-offset, and low-frequency advantages. However, in the vertical component of the OBN geophone, a significant amount of S-wave induced noise may be recorded. This significantly impacts the quality of the vertical component data and may affect the follow-up merging of dual-sensor data. Some commercially available methods apply normal-moveout correction, which requires velocity data. We avoid this with an adaptive matching method, which relies solely on seismic data. Therefore, we develop a novel adaptive subtraction method for S-wave leakage suppression using the horizontal component as the noise model. Our method effectively handles the nonstationarity of the input seismic data in all time and space directions, mitigating instability caused by manual selection of the smoothing radius. A method is introduced for estimating a global nonstationary smoothing radius using the noise model. Compared with commercial and stationary smoothing methods, our method can better suppress S-wave noise while balancing residual noise and signal leakage more effectively. Synthetic and field data examples demonstrate significant improvement with our method.

Approximation by Symmetrized and Perturbed Hyperbolic Tangent Activated Convolution-Type Operators

In this article, for the first time, the univariate symmetrized and perturbed hyperbolic tangent activated convolution-type operators of three kinds are introduced. Their approximation properties are presented, i.e., the quantitative convergence to the unit operator via the modulus of continuity. It follows the global smoothness preservation of these operators. The related iterated approximation as well as the simultaneous approximation and their combinations, are also extensively presented. Including differentiability and fractional differentiability into our research produced higher rates of approximation. Simultaneous global smoothness preservation is also examined.

Evolution of pre-damaged ITER grade plasma facing components under WEST plasma exposure: smoothing and tungsten sources

The evaluation of the impact of plasma-facing units (PFUs) damage on subsequent plasma operation is an important issue for ITER. This is one of the topic addressed by the operation of dedicated PFUs in WEST. From the start of WEST in 2017, few ITER grade divertor PFUs were tested in the lower divertor for short plasma exposure (experimental campaigns C1–C5). A PFU is an assembly of tungsten blocks on CuCrZr tube via pure copper interlayer. Since 2022, WEST operates with a lower divertor fully equipped with ITER grade PFUs (experimental campaign C6–C7) with long duration plasma exposure capabilities. To test the ageing of the ITER-grade PFUs on an accelerated basis, well controlled damage was implemented on purpose with electron beam loading on the plasma facing surface of two different PFUs (pre-damage#1 and #2 featuring different level of damage). Damage tackled in this study is induced by the loading with numerous transient heat loading events to mimic the ELM impact on the ITER grade PFU. This paper presents the damage before and after WEST plasma exposure and shows the tungsten sources and temperature of the block measured during the operation. On damaged area, surface roughening is heterogeneous. With WEST campaigns (C3, C4 and C7) respectively ended in (2018, 2019 and 2023) a global smoothing of the pre-damaged surfaces, in particular those located in the high loaded erosion area, is observed. No evolution of the crack is observed in the electron beam loaded area, while new cracking are observed on non pre-damaged area on the tungsten top surfaces in highly loaded areas (outer strike point) after significant plasma duration and cumulated energy (first observation in C4 and tends to be confirmed with preliminary observations after the C7 campaign). Smoothing is less pronounced after the 2018 campaign, which may be due to the related short plasma duration. The surface smoothing of blocks also depends on their poloidal position. For PFU which has no shaping, toroidal positioning within a block has no influence on the surface smoothing. After 2019 and 2023 campaigns, equivalent relative smoothing is obtained (between 19 and 32%). For the explored plasma conditions, damage has no influence on the maximum brightness of W.

Laboratory Abnormal Behavior Detection Based on Multimodal Information Fusion

The traditional laboratory anomaly detection methods mainly focus on the hidden dangers caused by chemical leaks and other items, ignoring the impact of abnormal behaviors such as incorrect operations and improper behavior on safety in the laboratory. This paper proposes a laboratory abnormal behavior detection method based on multimodal information fusion. The method generates a dense optical flow field of RGB image sequences based on optical flow theory and global smoothing constraints, and mines motion mode information. Meanwhile, the contour modal information of behavior is captured through convolution and adjacency matrix operations. Using decision level and proximity functions to integrate student behavior motion mode information and contour mode information, and using the maximum value as the behavior detection result. The experimental results show that the method can effectively detect abnormal behavior in the laboratory environment, with small detection errors and a specificity close to 1.00, effectively ensuring the safety of the laboratory environment.

The second order modulus revisited: remarks, applications, problems

Several questions concerning the second order modulus of smoothness are addressed in this note. The central part is a refined analysis of a construction of certain smooth functions by Zhuk and its application to several problems in approximation theory, such as degree of approximation and the preservation of global smoothness. Lower bounds for some optimal constants introduced by Sendov are given as well. We also investigate an alternative approach using quadratic splines studied by Sendov.

WELL-TO-WELL (W2W) ELECTROMAGNETIC TOMOGRAPHY MODELING ADVANCEMENT: IMPROVING PRECISION AND EFFECTIVENESS WITH REGULARIZATION

This research describes the direct and inverse problems of cross-well electromagnetic tomography. The model geometry has azimuthal symmetry, which simplifies the forward modeling and the inversion procedure. In the direct problem, the finite element method is used in the numerical solution of the Helmholtz equation. In the inverse problem, the study discusses the use of three stabilizer functionals: Global Smoothness (GS), Total Variation (TV), and Absolute Equality (AE). The first uses a smoothing function in the L2 norm, while the latter uses smoothing in the L1 norm, for it accepts abrupt changes between adjacent parameters. The results show that the TV method generated good estimates of both geometry and conductivity of the bodies, both for small and large conductivity contrast between the targets and the surrounding environment. Through the results, one can also observe that the regularization of the Total Variation presented a better estimate of the parameters than the Global Smoothness. In most of the synthetic models used in this work, the best estimates of the proposed model occurred when Absolute Equality constraints were used on the cells at the edges of the inversion grid, in addition to the stabilizer functional.

Monocular Depth and Ego-motion Estimation with Scale Based on Superpixel and Normal Constraints

3D perception in intelligent VR/AR and autonomous vehicles (AV) applications is critical and attracting significant attention. The self-supervised monocular depth and ego-motion estimation serves as a more intelligent learning approach that provides the required scene depth and location for 3D perception. However, the existing self-supervised learning methods suffer from scale ambiguity, boundary blur and imbalanced depth distribution, limiting the practical applications of VR/AR and AV. In this paper, we propose a new self-supervised learning framework based on superpixel and normal constraints to address these problems. Specifically, we formulate a novel 3D edge structure consistency loss to alleviate the boundary blur of depth estimation. To address the scale ambiguity of estimated depth and ego-motion, we propose a novel surface normal network for efficient camera height estimation. The surface normal network is composed of a deep fusion module and a full-scale hierarchical feature aggregation module. Meanwhile, to realize the global smoothing and boundary discriminability of the predicted normal map, we introduce a novel fusion loss which is based on the consistency constraints of the normal in edge domains and superpixel regions. Experiments are conducted on several benchmarks, and the results illustrate that the proposed approach outperforms the state-of-the-art methods in depth, ego-motion and surface normal estimation.

International convergence towards a climate-neutral economy: modeling the agricultural sector

Purpose. This article aims to construct a comprehensive convergent model for assessing the global and EU’s progress, degree of consolidation and symmetry of agricultural economies towards climate neutrality in the context of key international green initiatives. Methodology / approach. This research employs both qualitative and quantitative analyses to assess convergence measures in the agricultural sector’s carbon emissions. The quantitative component relies on the sigma and beta convergence models to evaluate international convergence in carbon emissions CO2 dynamics. The dimensions of modeling are as follows: global sample within 194 countries with reliable emissions data; European Union, focusing on convergence within the EU27 member states, the United Kingdom, and Ukraine. The time period covers open data from 1972–2022. The dynamics of sigma and beta convergence is determined for the points, namely UN Stockholm Conference (1972), UN Rio Conference (1992), Kyoto Protocol (entry into force in 2005), Paris Agreement (2015). Additionally, statistical indicators of variation, skewness, Gini and Theil indices were calculated for delineating global smoothness and the concentration of agricultural emissions. Results. The results of the study reveal an inertial and divergent trend of the agricultural economy towards decarbonisation, which slows down the overall movement towards “net zero” due to the presence of clubs of lagging agricultural countries that increase emissions in violation of international agreements. The reduction in emissions skewness in recent years shows that more countries are “pulling” decarbonisation due to their high capacity to move towards net zero, but this is not enough. The EU is the most prominent example of accelerated climate convergence, but markers of its weakening in recent years are identified due to the inability of economies to maintain the pace of decarbonisation caused by economic constraints, technological barriers, policy and regulatory issues, and misunderstandings of climate neutrality goals. It is shown that the long-term decarbonisation capacity of the agricultural sector is the key trigger for a country to make a positive contribution to the global convergence towards climate neutrality. At the current stage, the pace of decarbonisation plays a much greater role for consolidating efforts in the agricultural economy and achieving climate neutrality than the initial level of emissions in the sector. Factors in this process include proactive compliance with global climate agreements, technology sharing and cooperation, digitalisation and smart agriculture, and green financing and investment. Its implementation requires a three-way integration of stakeholder actions, strategy selection and results evaluation. Originality / scientific novelty. The study’s originality lies in its large-scale analysis of over 50 years of emissions dynamics and the context of five key green agreements that provided support for the green transition. It allows studying international convergence in agricultural sectors globally and within the EU. The novelty implies the integrated use of sigma and beta convergence models that identifies predictors of convergent and divergent processes and separates countries into leaders and laggards of agricultural decarbonisation. This approach provides a comprehensive view of modern climate policy, the impact of international green initiatives, and the position of individual towards climate neutrality in agriculture. Practical value / implications. The practical value lies in the ability to adjust climate policies for the agricultural economy’s decarbonisation, facilitating the determination of prospective outcomes for achieving climate neutrality. The aforementioned factors facilitate the process of governmental decision-making. The assessment of international programmatic agreements' effectiveness is enhanced through these models. The study offers a framework for global convergence towards climate neutrality in agriculture, highlighting the importance of digital technologies and smart agriculture as significant factors in global convergence.

NSVDNet: Normalized Spatial-Variant Diffusion Network for Robust Image-Guided Depth Completion

Depth images captured by low-cost three-dimensional (3D) cameras are subject to low spatial density, requiring depth completion to improve 3D imaging quality. Image-guided depth completion aims at predicting dense depth images from extremely sparse depth measurements captured by depth sensors with the guidance of aligned Red–Green–Blue (RGB) images. Recent approaches have achieved a remarkable improvement, but the performance will degrade severely due to the corruption in input sparse depth. To enhance robustness to input corruption, we propose a novel depth completion scheme based on a normalized spatial-variant diffusion network incorporating measurement uncertainty, which introduces the following contributions. First, we design a normalized spatial-variant diffusion (NSVD) scheme to apply spatially varying filters iteratively on the sparse depth conditioned on its certainty measure for excluding depth corruption in the diffusion. In addition, we integrate the NSVD module into the network design to enable end-to-end training of filter kernels and depth reliability, which further improves the structural detail preservation via the guidance of RGB semantic features. Furthermore, we apply the NSVD module hierarchically at multiple scales, which ensures global smoothness while preserving visually salient details. The experimental results validate the advantages of the proposed network over existing approaches with enhanced performance and noise robustness for depth completion in real-use scenarios.

A global smoothing method with geometric continuity conditions of piecewise curve fitting for toolpath of massive micro-line segments in CNC

A global smoothing method with geometric continuity conditions of piecewise curve fitting for toolpath of massive micro-line segments in CNC

A modified fifth‐order WENO‐Z scheme based on the weights of the reformulated adaptive order WENO scheme

AbstractA modified fifth‐order WENO‐Z scheme is proposed by analogy with the non‐normalized weights of the reformulated fifth‐order adaptive order (AO) WENO scheme. We show that if the original fifth‐order WENO‐AO scheme is rewritten as the form of the conventional WENO combination, the resulting non‐normalized weights can be divided into three parts: a constant one term, a local stencil smoothness measure term and a global stencil smoothness measure term. In order to make use of the latter two terms for constructing a modified WENO‐Z scheme with enhanced performance, we change the form of the third term and introduce an adaptive scaling factor to adjust the contributions from the second and third terms. Numerical examples show that the modified fifth‐order WENO‐Z scheme has the advantage of high resolution in smooth regions and sharp capturing of discontinuities, and it can obtain evidently better results for shocked flows with small‐scale structures compared with the recently developed WENO‐Z+ and WENO‐Z+M schemes.

Locally Self-Adjustive Smoothing for Measurement Noise Reduction with Application to Automated Peak Detection.

Smoothing is a widely used approach for measurement noise reduction in spectral analysis. However, it suffers from signal distortion caused by peak suppression. A locally self-adjustive smoothing method is developed that retains sharp peaks and less distorted signals. The proposed method uses only one parameter that determines the global smoothness of data, while balancing the local smoothness using the data itself. Simulation and real experiments in comparison with existing convolution-based smoothing methods indicate both qualitatively and quantitatively improved noise reduction performance in practical scenarios. We also discuss parameter selection and demonstrate an application for the automated smoothing and detection of a given number of peaks from noisy measurement data.

Terrain point cloud inpainting via signal decomposition

The rapid development of 3D acquisition technology has made it possible to obtain point clouds of real-world terrains. However, due to limitations in sensor acquisition technology or specific requirements, point clouds often contain defects such as holes with missing data. Inpainting algorithms are widely used to patch these holes. However, existing traditional inpainting algorithms rely on precise hole boundaries, which limits their ability to handle cases where the boundaries are not well-defined. On the other hand, learning-based completion methods often prioritize reconstructing the entire point cloud instead of solely focusing on hole filling. Based on the fact that real-world terrain exhibits both global smoothness and rich local detail, we propose a novel representation for terrain point clouds. This representation can help to repair the holes without clear boundaries. Specifically, it decomposes terrains into low-frequency and high-frequency components, which are represented by B-spline surfaces and relative height maps respectively. In this way, the terrain point cloud inpainting problem is transformed into a B-spline surface fitting and 2D image inpainting problem. By solving the two problems, the highly complex and irregular holes on the terrain point clouds can be well-filled, which not only satisfies the global terrain undulation but also exhibits rich geometric details. The experimental results also demonstrate the effectiveness of our method.

Local and global trend Bayesian exponential smoothing models

This paper describes a family of seasonal and non-seasonal time series models that can be viewed as generalisations of additive and multiplicative exponential smoothing models to model series that grow faster than linear but slower than exponential. Their development is motivated by fast-growing, volatile time series. In particular, our models have a global trend that can smoothly change from additive to multiplicative and is combined with a linear local trend. Seasonality, when used, is multiplicative in our models, and the error is always additive but heteroscedastic and can grow through a parameter sigma. We leverage state-of-the-art Bayesian fitting techniques to fit these models accurately, which are more complex and flexible than standard exponential smoothing models. When applied to the M3 competition data set, our models outperform the best algorithms in the competition and other benchmarks, thus achieving, to the best of our knowledge, the best results of per-series univariate methods on this dataset in the literature. An open-source software package of our method is available.

A new global smoothness indicator of fifth order weighted non-oscillatory scheme for hyperbolic conservation laws

A new global smoothness indicator of fifth order weighted non-oscillatory scheme for hyperbolic conservation laws

An Adapted NURBS Interpolator with a Switched Optimized Method of Feed-Rate Scheduling

With the increasing demand for processing precision in the manufacturing industry, feed-rate scheduling is a crucial component in achieving the processing quality of complex surfaces. A smooth feed-rate profile not only guarantees machining quality but also improves machining efficiency. Although the typical offline feed-rate scheduling method possesses good processing efficiency, it may not provide an optimal solution due to the NP-hard problem caused by the feed-rate scheduling of continuous curve segments, which easily results in excess kinetic limitations and feed-rate fluctuations in a real-time interpolation. Instead, the FIR (Finite Impulse Response) method is widely used to realize interpolation in real-time processing. However, the FIR method will filter out a large number of high-frequency signals, leading to a low-processing efficiency. Further, greater acceleration or deceleration is required to ensure the interpolation passes through the segment end at a predefined feed rate and the deceleration in the feed rate profile appears earlier, which allows the interpolation to easily exceed the kinetic limitation. At present, a simple offline or online method cannot realize the global optimization of the feed-rate profile and guarantee the machining efficiency. Moreover, the current feed-rate scheduling that considers both offline and online methods does not consider the situation that the call of offline data and online prediction data will lead to a decrease in the real-time performance of the CNC system. Further, real-time feed-rate scheduling data tend to dominate the whole interpolation process, thus reducing the effect of the offline feed-rate scheduling data. Hence, based on the tool path with C3 continuity (Cubic Continuously Differentiable), this paper first presents a basic interpolation unit relevant to the S-type interpolation feed-rate profile. Then, an offline local smooth strategy is proposed to smooth the feed-rate profile and reduce the exceeding of kinetic limitations and feed-rate fluctuations caused by frequent acceleration and deceleration. Further, a global online smoothing strategy based on the data generated by offline pre-interpolation is presented. What is more, FIR login and logout conditions are proposed to further smooth the feed-rate profile and improve the real-time performance and machining efficiency. The case study validates that the proposed method performs better in kinetic results compared with the typical offline and FIR methods in both the simulation experiment and actual machining experiments. Especially, in actual processing experiments, the proposed method obtains a 28% reduction in contour errors. Further, the proposed method compared with the FIR method obtains a 15% increase in machining efficiency but only a 4% decrease compared with the typical offline method.

Finite speed axially symmetric Navier-Stokes flows passing a cone

Let D be the exterior of a cone inside a ball, with its altitude angle at most π/6 in R3, which touches the x3 axis at the origin. For any initial value v0=v0,rer+v0,θeθ+v0,3e3 in a C2(D‾) class, which has the usual even-odd-odd symmetry in the x3 variable and has the partial smallness only in the swirl direction: |rv0,θ|≤1100, the axially symmetric Navier-Stokes equations (ASNS) with Navier-Hodge-Lions slip boundary condition have a finite-energy solution that stays bounded for all time. In particular, no finite-time blowup of the fluid velocity occurs. Compared with standard smallness assumptions on the initial velocity, no size restriction is made on the components v0,r and v0,3. In a broad sense, this result appears to solve 2/3 of the regularity problem of ASNS in such domains in the class of solutions with the above symmetry. Equivalently, this result is connected to the general open question which asks that if an absolute smallness of one component of the initial velocity implies the global smoothness, see e.g. page 873 in Chemin et al. (2017) [6]. Our result seems to give a positive answer in a special setting.As a byproduct, we also construct an unbounded solution of the forced Navier Stokes equation in a special cusp domain that has finite energy. The forcing term, with the scaling factor of −1, is in the standard regularity class, and it can be generated by an electric current in a long and straight wire (i.e. Ampère force). This result confirms the intuition that if the channel of a fluid is very thin, arbitrarily high speed in the classical sense can be attained under a mildly singular, physically reasonable force.

A high-efficiency adaptive TENO scheme with optimal accuracy order for compressible flow simulation

In this paper, we propose a new adaptive cut-off function and develop a fifth-order targeted ENO scheme that achieves optimal accuracy at any order of critical points, which performs excellently in conventional compressible gas dynamics. The cut-off value CT is crucial for controlling the dissipation in TENO schemes. Adjusting CT can improve shock capture and increase dissipation for small-scale features. To address this issue, Fu et al. [27] and Peng et al. [28] developed the TENO-A and TENO-LAD schemes, respectively, with adaptive cut-off values CT. However, these adaptive cutoffs CT are computationally expensive due to additional free parameters and complexity. Furthermore, all TENO schemes, including the adaptive versions, can suffer from loss of accuracy at higher-order critical points. In this paper, a new adaptive cut-off function is proposed that uses a global smoothness indicator correction so that it can be automatically tuned between 0 and a given positive constant λd, ensuring that the new TENO scheme achieves optimal accuracy in smooth regions and good shock-capturing in the less smooth parts. A series of benchmark simulations demonstrate that the presented scheme provides optimal accuracy, better robustness, resolution, and numerical stability, and higher resolution than existing TENO schemes while improving computational efficiency. Due to the simplicity of the new cut-off structure, it can be easily extended to improve other TENO schemes.Program files associated to this article may be found at https://github.com/fourhairs/cfd.

A New Fifth-Order Weighted Compact Nonlinear Scheme with Multi-Order Candidates Weighting for Hyperbolic Conservation Laws

ABSTRACT Based on one 5-point and two 2-point stencils, a nonlinear weighted scheme adaptive to the weighting of multi-order interpolation candidates for shock capturing is proposed. The JS weight function is adopted. The smoothness indicator of the 5-point stencil is specially designed with a higher-order leading term similar to the reference global smoothness indicator τ in the Z weighting. The design maintains that the nonlinear weights satisfy the sufficient condition for the scheme to avoid degradation at extreme points. The form of the weighting is also simplified, obviously reducing the weighting procedure's computational costs. Inviscid and viscous compressible flow problems are simulated to test the performance of the newly designed nonlinear weights based on the weighted compact nonlinear scheme. The numerical results show no obvious oscillations near the discontinuity, and the resolution of both discontinuities and smooth regions is better than JS, Z, and ZQ weighting.