Local Smoothing Research Articles

A comparison of three error indicators for adaptive high-order large eddy simulation

We use a discontinuous high-order method to evaluate three error indicators, specifically designed for mesh adaptation in large eddy simulation (LES). The indicators are based on specific physical and numerical arguments. The first indicator is based on the unsteady residual. The second indicator is based on a local smoothness indicator. The third indicator is based on an estimate for small scale turbulent kinetic energy. We test the three error indicators at driving autonomous mesh refinement on implicit LES, evaluating the error indicators on two widely used benchmark simulations of the T106 LP turbine cascade. We compare the adaptively meshed simulations against direct numerical simulation (DNS) results to judge their effectiveness at reducing solution error in LES.

Image inpainting via Smooth Tucker decomposition and Low-rank Hankel constraint

Image inpainting, aiming at exactly recovering missing pixels from partially observed entries, is typically an ill-posed problem. As a powerful constraint, low-rank priors have been widely applied in image inpainting to transform such problems into well-posed ones. However, the low-rank assumption of original visual data is only in an approximate mode, which in turn results in suboptimal recovery of fine-grained details, particularly when the missing rate is extremely high. Moreover, a single prior cannot faithfully capture the complex texture structure of an image. In this paper, we propose a joint usage of Smooth Tucker decomposition and Low-rank Hankel constraint (STLH) for image inpainting, which enables simultaneous capturing of the global low-rankness and local piecewise smoothness. Specifically, based on the Hankelization operation, the original image is mapped to a high-order structure for capturing more spatial and spectral information. By employing Tucker decomposition for optimizing the Hankel tensor and simultaneously applying Discrete Total Variation (DTV) to the Tucker factors, sharper edges are generated and better isotropic properties are enhanced. Moreover, to approximate the essential rank of the Tucker decomposition and avoid facing the uncertainty problem of the upper-rank limit, a reverse strategy is adopted to approximate the true rank of the Tucker decomposition. Finally, the overall image inpainting model is optimized by the well-known alternate least squares (ALS) algorithm. Extensive experiments show that the proposed method achieves state-of-the-art performance both quantitatively and qualitatively. Particularly, in the extreme case with 99% pixels missed, the results from STLH are averagely ahead of others at least 0.9dB in terms of PSNR values.

Right-censored partially linear regression model with error in variables: application with carotid endarterectomy dataset.

This paper considers a partially linear regression model relating a right-censored response variable to predictors and an extra covariate with measured error. The main problem here is that censorship and measurement error problems need to be solved to estimate the model correctly. In this sense, we propose three modified semiparametric estimators obtained from local polynomial regression, kernel smoothing, and B-spline smoothing methods based on kernel deconvolution approach and synthetic data transformation. Here, kernel deconvolution technique is used to solve the measurement error problem in the model and synthetic data transformation is considered to add the effect of censorship to the estimation procedure, which is a very common method in the literature. The performances of the introduced estimators are compared in the detailed Monte-Carlo simulation study. In addition, Carotid endarterectomy data is used as real-world data example and results are presented. According to the results, it is seen that the deconvoluted local polynomial method gives more qualified estimates than other two methods.

Human Behavior Recognition via Hierarchical Patches Descriptor and Approximate Locality-Constrained Linear Coding.

Human behavior recognition technology is widely adopted in intelligent surveillance, human-machine interaction, video retrieval, and ambient intelligence applications. To achieve efficient and accurate human behavior recognition, a unique approach based on the hierarchical patches descriptor (HPD) and approximate locality-constrained linear coding (ALLC) algorithm is proposed. The HPD is a detailed local feature description, and ALLC is a fast coding method, which makes it more computationally efficient than some competitive feature-coding methods. Firstly, energy image species were calculated to describe human behavior in a global manner. Secondly, an HPD was constructed to describe human behaviors in detail through the spatial pyramid matching method. Finally, ALLC was employed to encode the patches of each level, and a feature coding with good structural characteristics and local sparsity smoothness was obtained for recognition. The recognition experimental results on both Weizmann and DHA datasets demonstrated that the accuracy of five energy image species combined with HPD and ALLC was relatively high, scoring 100% in motion history image (MHI), 98.77% in motion energy image (MEI), 93.28% in average motion energy image (AMEI), 94.68% in enhanced motion energy image (EMEI), and 95.62% in motion entropy image (MEnI).

An analytical local tool path smoothing method with curvature control

In traditional multi-axis machining, the linear tool path generated by computer-aided manufacturing systems is still in a broad tool path format, resulting in discontinuities at the corners, which slow down tool motion, and also trigger tool vibration, reducing machining accuracy and surface quality. In order to ensure the C3 continuity of the tool during the multi-axis machining process, this paper proposes an analytical B-spline local smoothing method with curvature control. The tool position trajectory and tool orientation are both smoothed by a 5th spline curve with 9 control points. Optimal control points are determined for position and orientation splines to achieve C3 continuity at the junctions between the spline and linear segment while preserving the predefined geometric tolerance limits and minimizing the maximum curvature of the inserted B-spline curve. The smoothed tool path is expected to have less curvature fluctuation, which can significantly improve both the kinematic performance of the machine tool and the machining efficiency. Both computer simulations and physical printing experiments are carried out to demonstrate the improvements of our proposed method in motion smoothness and tracking accuracy in multi-axis machining tasks.

Estimation and Inference on Time-Varying FAVAR Models

ABSTRACT We introduce a time-varying (TV) factor-augmented vector autoregressive (FAVAR) model to capture the TV behavior in the factor loadings and the VAR coefficients. To consistently estimate the TV parameters, we first obtain the unobserved common factors via the local principal component analysis (PCA) and then estimate the TV-FAVAR model via a local smoothing approach. The limiting distribution of the proposed estimators is established. To gauge possible sources of TV features in the FAVAR model, we propose three L 2 -distance-based test statistics and study their asymptotic properties under the null and local alternatives. Simulation studies demonstrate the excellent finite sample performance of the proposed estimators and tests. In an empirical application to the U.S. macroeconomic dataset, we document overwhelming evidence of structural changes in the FAVAR model and show that the TV-FAVAR model outperforms the conventional time-invariant FAVAR model in predicting certain key macroeconomic series.

(118) The Atherosclerotic Cardiovascular Disease Risk Score is a Reliable Tool to Identify Patients with Arteriogenic Erectile Dysfunction at Dynamic Penile Color Doppler Duplex Ultrasound – Findings From a Real-life Cross-sectional Study

Abstract Introduction The ASCVD (Atherosclerotic Cardiovascular Disease) risk score is a validated and standardised algorithm predicting the individual 10-year risk of developing acute cardiovascular events (CVs). Patients with erectile dysfunction (ED) are at greater risk of CVs; Objective we aimed to i) apply the ASCVD score at a homogenous cohort of men undergoing dynamic penile color doppler duplex ultrasound (CDDU) for ED, and ii) explore its predictive ability to identify patients with arteriogenic and venogenic ED at CDDU. Methods Complete data of 188 consecutive patients undergoing CDDU for ED were analysed. Health-significant comorbidities were scored using the Charlson comorbidity index. All patients completed the International Index of Erectile Function (IIEF) at baseline. Serum hormones (total testosterone (tT) and luteinising hormone (LH)) were dosed for every patient. The ASCVD score was applied to the entire cohort. According to the ASCVD, patients were segregated into low (≤7.5%) vs. intermediate/high risk (> 7.5%). Descriptive statistics was used to explore differences between the two groups. Logistic regression models tested the potential predictive role of ASCVD scores to predict pathological CDDU parameters (peak systolic velocity (PSV) < 35 cm/s and/or resistance index (RI) ≤ 0.70). Local polynomial smoothing models graphically displayed the probability of pathological CDDU parameters at different ASCVD scores. Results Overall, median (IQR) age was 54 (43-60) yr. Of all, 52 (27.7%) patients reported severe ED, as for IIEF-EF ≤ 11. Overall, 80 (42.6%) showed a pure arteriogenic ED and 15 (8%) pure venogenic ED at CDDU. Intermediate/high-risk patients (52.7%) were found to have lower IIEF-EF scores, higher BMI, higher CCI and presented with a greater rate of PDE5i non-responders compared to those with low-risk (47.3%) according to ASCVD (all p<0.005). Conversely, the two groups did not significantly differ in terms of CDDU parameters. At logistic regression analysis, the ASCVD risk score was identified as a strong predictor for arteriogenic ED at CDDU (OR: 1.07, 95% CI: 1.03-1.13, p = 0.007) after adjusting for BMI. Conversely, the ASCVD score was not identified as a predictor of pure venogenic ED (OR: 1.04, 95% CI: 0.98-1.1, p = 0.22). Figure 1 displays the probability of pathological findings at CDDU (PSV < 35 cm/sec vs. RI < 0.7) at different ASCVD scores. Conclusions The ASCVD risk score can be used as a valuable tool to identify patients with arteriogenic ED at CDDU in real-life settings. Since vasculogenic ED may anticipate CVs even by some years, the accurate identification of patients with deficient cavernosal arterial flow would certainly allow earlier and more effective cardiovascular prevention in this subset of patients. Disclosure No

Graph Convolution Point Cloud Super-Resolution Network Based on Mixed Attention Mechanism

In recent years, point cloud super-resolution technology has emerged as a solution to generate a denser set of points from sparse and low-quality point clouds. Traditional point cloud super-resolution methods are often optimized based on constraints such as local surface smoothing; thus, these methods are difficult to be used for complex structures. To address this problem, we proposed a novel graph convolutional point cloud super-resolution network based on a mixed attention mechanism (GCN-MA). This network consisted of two main parts, i.e., feature extraction and point upsampling. For feature extraction, we designed an improved dense connection module that integrated an attention mechanism and graph convolution, enabling the network to make good use of both global and local features of the point cloud for the super-resolution task. For point upsampling, we adopted channel attention to suppress low-frequency information that had little impact on the up-sampling results. The experimental results demonstrated that the proposed method significantly improved the point cloud super-resolution performance of the network compared to other corresponding methods.

Local smoothing estimates of fractional Schrödinger equations in $$\alpha $$-modulation spaces with some applications

We show some new local smoothing estimates of the fractional Schrödinger equations with initial data in $$\alpha $$ -modulation spaces via decoupling inequalities. Furthermore, our necessary conditions show that the local smoothing estimates are sharp in some cases. As applications, the local smoothing estimates could show some new local well-posedness on modulation spaces of the fourth-order nonlinear Schrödinger equations on the line.

A smoothness indicators free third-order weighted ENO scheme for gas-dynamic Euler equations

To improve the shock-capturing capability of the third-order WENO scheme and enhance its computational efficiency, in this paper, we design a new WENO scheme independent of the local smoothing factor, WENO-SIF. The weight function of the WENO-SIF scheme is the segmentation function of the sub-stencil, which is guaranteed to achieve the desired accuracy at higher order critical points. WENO-SIF does not need to compute the smoothing factor during the computation, which effectively reduces the computational consumption. The present WENO-SIF is compared with WENO-JS and other WENO schemes for numerical experiments at one- and two-dimensional benchmark problems with a suitable choice of $$\lambda =0.13$$ . The results demonstrate that the WENO scheme can further improve the resolution of WENO-JS, achieve optimal accuracy at high-order critical points, and significantly reduce the computational consumption.

The atherosclerotic cardiovascular disease risk score is a reliable tool to identify patients with arteriogenic erectile dysfunction.

The atherosclerotic cardiovascular disease risk score is a validated algorithm predicting an individual's 10-year risk of developing acute cardiovascular events (cardiovascular disease). Patients who suffer from arteriogenic erectile dysfunction are susceptible to developing cardiovascular disease in the future. To apply the atherosclerotic cardiovascular disease score at a homogenous cohort of men with erectile dysfunction undergoing a dynamic penile colour Doppler duplex ultrasound and explore its predictive ability to identify patients with vasculogenic erectile dysfunction at colour Doppler duplex ultrasound. Complete data of 219 patients undergoing colour Doppler duplex ultrasound were analysed. All patients completed the International Index of Erectile Function. The atherosclerotic cardiovascular disease score and Charlson comorbidity index were applied to the entire cohort. Patients were divided into those with normal vs. pathological parameters at colour Doppler duplex ultrasound. Descriptive statistics were used to explore differences between the two groups. Logistic regression models tested the potential role of atherosclerotic cardiovascular disease to predict arteriogenic and/or venogenic erectile dysfunction. Local polynomial smoothing models graphically displayed the probability of pathological colour Doppler duplex ultrasound parameters at different atherosclerotic cardiovascular disease scores. Overall, arteriogenic erectile dysfunction and venous leakage were diagnosed in 88 (40.2%) and 28 (12.8%) patients respectively. The median (interquartile range) atherosclerotic cardiovascular disease score was 7.7 (3.9-14). Patients with pathologic colour Doppler duplex ultrasound were older (59vs. 54 years, p<0.001), had higher Body Mass Index (26.5vs. 25.6kg/m2 , p=0.04), more comorbidities (Charlson comorbidity index ≥ 1) (76.5%vs. 54.4%, p=0.002) and higher median atherosclerotic cardiovascular disease scores (9.95vs. 7, p=0.005), respectively. At logistic regression analysis, a higher atherosclerotic cardiovascular disease risk score was independently associated with arteriogenic erectile dysfunction at colour Doppler duplex ultrasound (odds ratio: 1.03, 95% confidence interval: 1.01-1.08, p=0.02) after adjusting for Body Mass Index, physical activity, alcohol consumption and severe erectile dysfunction. As vasculogenic erectile dysfunction may precede bysome years the onset of acute cardiovascular diseases, the rigorous identification of patients with deficient cavernosal arterial blood flow, would definitely allow the implementation ofearlier and more effective cardiovascular prevention strategies in men with erectile dysfunction. The atherosclerotic cardiovascular disease risk score represents a reliable tool to identify patients with arteriogenic erectile dysfunction in everyday clinical practice.

Square function estimates and local smoothing for Fourier integral operators

AbstractWe prove a variable coefficient version of the square function estimate of Guth–Wang–Zhang. By a classical argument of Mockenhaupt–Seeger–Sogge, it implies the full range of sharp local smoothing estimates for ‐dimensional Fourier integral operators satisfying the cinematic curvature condition. In particular, the local smoothing conjecture for wave equations on compact Riemannian surfaces is settled.

A novel tool path planning and feedrate scheduling algorithm for point to point linear and circular motions of CNC-milling machines

The manufacturing process on CNC machines is directed by the Numerical Control (NC) files which include the main tool paths as a combination of numerous instructions such as lines and arcs specified by the G01 and G02/G03 commands. In the literature, the lines and arcs generally are converted to a parametric curve based on the global tool path smoothing or local corner smoothing algorithms. However, the smoothing methods cause the deflection from the tool path in NC-File. In cases where the deflection from the main tool path is not acceptable, point-to-point motion is necessary instead of the smooth trajectory. This study presents a novel trajectory planning and feedrate scheduling algorithm for point-to-point control of linear and circular paths in the NC-File. The proposed method prevents the feedrate fluctuations at the junction points and generates the tool path without deflection from the NC-File. Also, the feedrate scheduling algorithm decrease the operating time of the machine significantly compared to traditional method of point-to-point motion. This study is verified on an industrial 3-Axis CNC-Milling machine by the operating of the roughing milling, drilling, slotting, and face milling process. The measurements of final product and real-time trajectory tracking results show that the proposed method is effective in industrial applications of CNC-Milling machines in which point-to-point motion is necessary.

Multi-patch isogeometric topology optimization for cellular structures with flexible designs using Nitsche’s method

Cellular structures have recently been received a tremendous growth in discussions and applications in the engineering due to their several fascinating structural properties, such as the ultra-lightweight, high stiffness and crashworthiness. However, the discussions on the design of cellular structures in the complex structural domain with the non-conforming mesh are still unavailable, resulting from the fact that the non-conforming mesh causes several difficulties in numerical analysis and design optimization. Hence, the main purpose of the work is to propose a Multi-Patch Isogeometric Topology Optimization (MP-ITO) method with powerful capabilities for periodic or graded cellular structures. Firstly, the Nitsche’s method is applied to couple non-conforming meshes in multiple NURBS patches and conduct multi-patch isogeometric analysis. Secondly, a multi-patch topology description model is developed, in which a local smoothing mechanism and the two-resolution scheme of discretization meshes are constructed to avoid terrible structural features and improve smoothness and continuity of boundaries at the interfaces within adjacent subdomains. The separation and independency of the Density Distribution Function (DDF) at each subdomain can offer high flexibility for cellular designs with the imposing of several kinds of periodic constraints. Thirdly, the MP-ITO method is proposed for complex structures and the mathematical formulation for cellular designs considering periodic constraints is developed. Finally, the effectiveness and indispensability of the local smoothing mechanism and the two-resolution scheme in the MP-ITO are discussed, and several numerical examples are addressed to present the compelling effectiveness and capabilities of the MP-ITO method with the high flexibility on the designs of periodic and graded cellular structures.

On the effectiveness of the Moulinec–Suquet discretization for composite materials

AbstractMoulinec and Suquet introduced a method for computational homogenization based on the fast Fourier transform which turned out to be rather computationally efficient. The underlying discretization scheme was subsequently identified as an approach based on trigonometric polynomials, coupled to the trapezoidal rule to substitute full integration. For problems with smooth solutions, the power of spectral methods is well‐known. However, for heterogeneous microstructures, there are jumps in the coefficients, and the solution fields are not smooth enough due to discontinuities across material interfaces. Previous convergence results only provided convergence of the discretization per se, that is, without explicit rates, and could not explain the effectiveness of the discretization observed in practice. In this work, we provide such explicit convergence rates for the local strain as well as the stress field and the effective stresses based on more refined techniques. More precisely, we consider a class of industrially relevant, discontinuous elastic moduli separated by sufficiently smooth interfaces and show rates which are known to be sharp from numerical experiments. The applied techniques are of independent interest, that is, we employ a local smoothing strategy, utilize Féjer means as well as Bernstein estimates and rely upon recently established superconvergence results for the effective elastic energy in the Galerkin setting. The presented results shed theoretical light on the effectiveness of the Moulinec–Suquet discretization in practice. Indeed, the obtained convergence rates coincide with those obtained for voxel finite element methods, which typically require higher computational effort.

Efficient Distributed Matrix-free Multigrid Methods on Locally Refined Meshes for FEM Computations

This work studies three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening (both h -multigrid), and polynomial global coarsening (a variant of p -multigrid). We have integrated the algorithms into the same framework—the open source finite-element library deal.II —, which allows us to make fair comparisons regarding their implementation complexity, computational efficiency, and parallel scalability as well as to compare the measurements with theoretically derived performance metrics. Serial simulations and parallel weak and strong scaling on up to 147,456 CPU cores on 3,072 compute nodes are presented. The results obtained indicate that global-coarsening algorithms show a better parallel behavior for comparable smoothers due to the better load balance, particularly on the expensive fine levels. In the serial case, the costs of applying hanging-node constraints might be significant, leading to advantages of local smoothing, even though the number of solver iterations needed is slightly higher. When using p - and h -multigrid in sequence ( hp -multigrid), the results indicate that it makes sense to decrease the degree of the elements first from a performance point of view due to the cheaper transfer.

A modified dual time integration technique for aerodynamic quasi-static and dynamic stall hysteresis

Simulation of the aerodynamic stall phenomenon in both quasi-static and dynamic conditions requires expensive computational resources. The computations become even more costly for static stall hysteresis using an unsteady solver with very slow variation of angle of attack at low reduced frequencies. In an explicit time-marching solver that satisfies the low Courant number condition, that is, [Formula: see text], the computational cost for such simulations becomes prohibitive, especially at higher Reynolds numbers due to the presence of thin-stretched cells with large aspect ratio in the boundary layer. In this paper, a segregated solver method such as the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) is modified as a dual pseudo-time marching method so that the unsteady problem at each time step is reformulated as a steady state problem. The resulting system of equations in the discretized finite volume formulation is then reduced to zero or near-zero residuals using available convergence acceleration methods such as local time stepping, multi-grid acceleration and residual smoothing. The performance and accuracy of the implemented algorithm was tested for three different airfoils at low to moderate Reynolds numbers in both incompressible and compressible flow conditions covering both attached and separated flow regimes. The results obtained are in close agreement with the published experimental and computational results for both quasi-static and dynamic stall and have demonstrated significant savings in computational time.

Local tool path smoothing based on symmetrical NURBS transition curve with look ahead optimal method: experimental and analytical study

Local tool path smoothing based on symmetrical NURBS transition curve with look ahead optimal method: experimental and analytical study

Noise-tolerant clustering via joint doubly stochastic matrix regularization and dual sparse coding

Clustering has received a lot of attention and research in many important fields, such as machine learning and data mining. Especially, the clustering method based on non-negative matrix factorization (NMF) has been widely used. However, the following problems still exist. First, the clustering method based on the traditional NMF cannot handle noise and outliers well, although the reconstruction error can be measured by the l2,1-norm instead Frobenius norm to improve the robustness, the effect is not obvious. Second, NMF based on graph regularization mostly relies on initial similarity graph, the method of constructing the graph is fixed and cannot update the graph adaptively. Third, there is no sparse constraints both on the basis matrix and the coefficient matrix, which may cause important information to be ignored during clustering. Therefore, in order to solve the above problems, we propose a joint doubly stochastic matrix regularization and dual sparse coding framework (DSNMF). Specifically, we use correntropy instead of the Euclidean distance to overcome the influence of non-Gaussian noise and outliers, making NMF more robust. In addition, the adaptive graph learning can learn a high-quality graph through doubly stochastic matrix to fully maintain local smoothness. Furthermore, we perform sparse coding both on the basis matrix and the coefficient matrix to make full use of the sparsity of the matrix. Finally, the experimental results on eleven datasets show that our method is better than other methods in most cases, and our DSNMF is robust to noise and outliers.

NLS: An accurate and yet easy-to-interpret prediction method

Over the last years, the predictive power of supervised machine learning (ML) has undergone impressive advances, achieving the status of state of the art and super-human level in some applications. However, the employment rate of ML models in real-life applications is much slower than one would expect. One of the downsides of using ML solution-based technologies is the lack of user trust in the produced model, which is related to the black-box nature of these models. To leverage the application of ML models, the generated predictions should be easy to interpret while maintaining a high accuracy. In this context, we develop the Neural Local Smoother (NLS), a neural network architecture that yields accurate predictions with easy-to-obtain explanations. The key idea of NLS is to add a smooth local linear layer to a standard network. We show experiments that indicate that NLS leads to a predictive power that is comparable to state-of-the-art machine learning models, but that at the same time is easier to interpret.