Degree Of Smoothness Research Articles

A unified geographically weighted regression model

Spatial heterogeneity and spatial dependence are two cornerstones of spatial data research. It becomes more and more important to simultaneously deal with them in analyzing today’s complex spatial datasets. Along this direction, we introduce a new class of geographically weighted regression models, called unified geographically weighted regression (UGWR) models, to generalize existing geographically weighted regression models. In UGWR, the regression coefficients of all covariates can vary over the space. Moreover, the dependent variable and the disturbance are considered to be spatial autoregressive, and their spatial autoregression coefficients can also vary over the space. We propose a reconstruction parameterization approach to estimate these varying coefficients. This approach can flexibly use different bandwidths to fit various smoothness degrees of the coefficients. Based on the estimators, we also provide prediction, hypothesis testing, and model selection methods under UGWR. Simulation results indicate that the UGWR model can better fit complex datasets than existing geographically weighted regression models. An empirical study on a China’s regional GDP dataset also shows the effectiveness of the proposed methods.

Determinantal point processes in the flat limit

Determinantal point processes (DPPs) are repulsive point processes where the interaction between points depends on the determinant of a positive-semi definite matrix. In this paper, we study the limiting process of L-ensembles based on kernel matrices, when the kernel function becomes flat (so that every point interacts with every other point, in a sense). We show that these limiting processes are best described in the formalism of extended L-ensembles and partial projection DPPs, and the exact limit depends mostly on the smoothness of the kernel function. In some cases, the limiting process is even universal, meaning that it does not depend on specifics of the kernel function, but only on its degree of smoothness. Since flat-limit DPPs are still repulsive processes, this implies that practically useful families of DPPs exist that do not require a spatial length-scale parameter.

FT-IR Spectral Model of Polyester-Cotton Fabrics with Corona Plasma Treatment using Artificial Neural Networks (ANNs)

<p class="Abstract">Corona plasma technology has been studied as a surface modification for the adhesive bonding of polymers. Although corona plasma (C.P.) is becoming more popular in nanotechnology, the influence of corona plasma treatment parameters on the FT-IR spectra is a problem that has yet to be addressed. The purpose of this study is to use an artificial neural network to study the influence of corona plasma (C.P.) treatment parameters on textile polymer and evaluate the ability of this model to predict FT-IR spectral information from FT-IR measurements. In this study, polymers were modified under various corona plasma treatment conditions. We investigated FT-IR spectra information of polymers from FT-IR measurements by varying corona plasma treatment variables. We used three input parameters in this study: wavenumber, voltage, and exposure time—two output parameters: fabric roughness with SEM according to the degree of smoothness and percent transmission with FT-IR. The novel aspect of this study is that we used ANN to model the plasma treatment on polyester-cotton fabrics and the FT-IR spectra accurately enough for the first time. According to this study, the model that used four nodes (neurons) in the hidden layer, three input parameters (x<sub>1</sub>,x<sub>2</sub>,x<sub>3</sub>), and 20 iterations is appropriate for determining fabric surface roughness (S.R.) and percent transmission (T%). Based on this research, the values of R<sup>2</sup> for determining fabric surface roughness (S.R.) and percent transmission (T%) were 99.79 percent and 67.18 percent, respectively. The results showed that the developed ANNs could accurately predict the experimental data in detail. This study is significant because it uses artificial intelligence to calculate and simulate the FT-IR spectra and fabric surface roughness of plasma treatment on textile fabrics. This study's scientific application is that it will help experts, researchers, and engineers understand the implications of plasma on the chemical structure of textile materials.</p>

Hemodynamic timing in resting-state and breathing-task BOLD fMRI

The blood flow response to a vasoactive stimulus demonstrates regional heterogeneity across both the healthy brain and in cerebrovascular pathology. The timing of a regional hemodynamic response is emerging as an important biomarker of cerebrovascular dysfunction, as well as a confound within fMRI analyses. Previous research demonstrated that hemodynamic timing is more robustly characterized when a larger systemic vascular response is evoked by a breathing challenge, compared to when only spontaneous fluctuations in vascular physiology are present (i.e., in resting-state data). However, it is not clear whether hemodynamic delays in these two conditions are physiologically interchangeable, and how methodological signal-to-noise factors may limit their agreement. To address this, we generated whole-brain maps of hemodynamic delays in nine healthy adults. We assessed the agreement of voxel-wise gray matter (GM) hemodynamic delays between two conditions: resting-state and breath-holding. We found that delay values demonstrated poor agreement when considering all GM voxels, but increasingly greater agreement when limiting analyses to voxels showing strong correlation with the GM mean time-series. Voxels showing the strongest agreement with the GM mean time-series were primarily located near large venous vessels, however these voxels explain some, but not all, of the observed agreement in timing. Increasing the degree of spatial smoothing of the fMRI data enhanced the correlation between individual voxel time-series and the GM mean time-series. These results suggest that signal-to-noise factors may be limiting the accuracy of voxel-wise timing estimates and hence their agreement between the two data segments. In conclusion, caution must be taken when using voxel-wise delay estimates from resting-state and breathing-task data interchangeably, and additional work is needed to evaluate their relative sensitivity and specificity to aspects of vascular physiology and pathology.

Nonlinear disturbance observer based multiple‐model adaptive explicit model predictive control for nonlinear MIMO system

AbstractIn this article, a nonlinear disturbance observer‐based multiple‐model adaptive explicit model predictive control (NDO‐MMAEMPC) scheme is developed for a nonlinear MIMO system with parametric uncertainty as well as an external disturbance. The proposed method manages external disturbances without affecting the degree of smoothness of the control signals. Further, to cope with the unknown system uncertainty, blending‐based adaptive identification schemes are used for the same class of systems. For each identification model, an explicit nonlinear model predictive controller is computed off‐line for the corresponding model in advance, which saves computation power during operation. The generated control inputs from the set of explicit controllers are being blended online using adaptive weight. An extended Kalman filter algorithm is employed for the estimation of the unavailable states of the nonlinear system. Using an aerodynamic laboratory setup, the effectiveness of the proposed control algorithm is verified.

Multifold Cross-Validation Model Averaging for Generalized Additive Partial Linear Models

Generalized Additive Partial Linear Models (GAPLMs) are appealing for model interpretation and prediction. However, for GAPLMs, the covariates and the degree of smoothing in the nonparametric parts are often difficult to determine in practice. To address this model selection uncertainty issue, we develop a computationally feasible Model Averaging (MA) procedure. The model weights are data-driven and selected based on multifold Cross-Validation (CV) (instead of leave-one-out) for computational saving. When all the candidate models are misspecified, we show that the proposed MA estimator for GAPLMs is asymptotically optimal in the sense of achieving the lowest possible Kullback-Leibler loss. In the other scenario where the candidate model set contains at least one quasi-correct model, the weights chosen by the multifold CV are asymptotically concentrated on the quasi-correct models. As a by-product, we propose a variable importance measure to quantify the importances of the predictors in GAPLMs based on the MA weights. It is shown to be able to asymptotically identify the variables in the true model. Moreover, when the number of candidate models is very large, a model screening method is provided. Numerical experiments show the superiority of the proposed MA method over some existing model averaging and selection methods. Supplementary materials for this article are available online.

Оценка геометрических параметров отпечатка и давления в зоне контакта рабочего инструмента с заготовкой при реверсивном поверхностном пластическом деформировании

The article presents the results of modeling and determining the influence of the parameters of reverse surface plastic deformation on the geometric characteristics of the plastic imprint and the pressure in the contact zone of the working tool under static and reverse impact. Using the software for 3D design SOLID WORKS-2019 and computational modeling in ANSYS-19.1, a finite element model of the contact zone was built to determine the geometric characteristics of the plastic indentation and the contact pressure between the working tool and the surface of the workpiece, depending on the geometry of the working tool, reversing frequency its rotation, the initial angle of installation and the amplitude of the angle of reverse rotation of the working tool. Based on the obtained results, to increase the pressure in the contact zone of the working tool with the workpiece, which affects the degree of hardening and smoothing of microroughnesses of the workpiece surface and the formation of compressive residual stresses, it is recommended to use the following parameters and hardening modes: working roller with a diameter of 20–30 mm, with a profile radius of 2 –2.5 mm, distance between tops of working roller profile 1.5–2 mm, initial installation angle of the working roller 90о, amplitude of the reverse rotation angle of the working roller ±6 – ±8о and reverse speed of the working roller 200–240 double strokes/min.

Estimation and bootstrap for stochastically monotone Markov processes

The Markov property is shared by several popular models for time series such as autoregressive or integer-valued autoregressive processes as well as integer-valued ARCH processes. A natural assumption which is fulfilled by corresponding parametric versions of these models is that the random variable at time t gets stochastically greater conditioned on the past, as the value of the random variable at time t-1 increases. Then the associated family of conditional distribution functions has a certain monotonicity property which allows us to employ a nonparametric antitonic estimator. This estimator does not involve any tuning parameter which controls the degree of smoothing and is therefore easy to apply. Nevertheless, it is shown that it attains a rate of convergence which is known to be optimal in similar cases. This estimator forms the basis for a new method of bootstrapping Markov chains which inherits the properties of simplicity and consistency from the underlying estimator of the conditional distribution function.

Efficient estimation in varying coefficient regression models

Varying coefficient models have been studied for many years, and local kernel estimation is an important method to estimate the coefficient functions. Since same bandwidth parameter is used for each coefficient function, local kernel estimation is not effective when the degree of smoothness is different for each coefficient function. In this paper, a new global estimation method based on kernel function and backfitting is proposed. In this method, different bandwidth parameters can be used for each coefficient function to improve the estimation accuracy, and asymptotic properties of the estimators are proved. To reduce the computational complexity, an adaptive global estimation method, which is based on an estimation of the bandwidth ratio and has only one bandwidth parameter to be selected, is proposed. Simulation results show that the proposed methods work well, and two real data examples further demonstrate the potential of the proposed methods.

An Improved Material Point Method with Aggregated and Smoothed Bernstein Functions

Nodal shape functions and their gradients are vital in transferring physical information within the material point method (MPM). Their continuity is related to numerical stability and accuracy, and their support domain size affects computational efficiency. In this paper, a scheme of aggregated and smoothed Bernstein functions is proposed to improve the MPM. In detail, the Bernstein polynomials are smoothed with a convolution reformation to eliminate the cell crossing error, and an aggregation strategy is implemented to cut down the node amount required for field probing. Hierarchical MPM variants are obtained with choices of original Bernstein polynomials and degrees of smoothing. Numerical examples show that mass, momentum, and energy conservations are all well met, and no cell crossing noise exists. In addition, solution accuracy and numerical stability are significantly improved in large deformation problems.

Bi-smooth constraints for accelerated dynamic MRI with low-rank plus sparse tensor decomposition

The long data acquisition required for dynamic magnetic resonance imaging (DMRI) has limited its development. This paper proposes a low-rank plus sparse tensor decomposition model with bi-smooth constraints to reconstruct DMR images from under-sampled k-t space data. The DMR images can be naturally decomposed into a low-rank and sparse tensor to exploit the spatiotemporal correlation to improve the reconstruction quality. Different degrees of smoothness in the foreground and background parts of the DMR images are analyzed and utilized to further exploit the smoothness with a divide-and-conquer strategy. By imposing the bi-smooth constraints on these two parts, more edges and details of DMR images can be preserved. The experimental results show that the proposed method can achieve better reconstruction performance than the existing state-of-the-art methods.

DECOMPOSITION METHODS FOR DETERMINING COMPLEX ONE-PARAMETER GENERALIZED INVERSE MOORE-PENROSE MATRICES (I)

Analytical and numerical-analytical decomposition methods for determining complex one-parameter generalized inverse Moore-Penrose matrices are suggested. Analytical methods are based on the first two Moore-Penrose conditions. It is shown that in both cases the same solution to the problem is obtained, as it should be. Numerical-analytical methods are based on the obtained analytical relations and differential Pukhov transformations. In contrast to the known methods, in which we operate with rectangular generalized inverse matrices, in all the proposed analytical and numerical-analytical methods, we operate with square generalized (ordinary) inverse matrices. In view of this circumstance, an exact but not an approximate solution to the problem is obtained. A model example with a square matrix is considered, for which an analytical solution is obtained using two approaches - the determination of the usual inverse one-parameter matrix and the decomposition method for determining the same matrix. This matrix is defined in exactly the same way as numerical-analytical decomposition methods. In this paper, exact analytical and approximate numerical-analytical computational methods for determining complex one-parameter generalized inverse Moore-Penrose matrices are proposed. Numerical-analytical computational methods are easily implemented using modern information technologies, since they are based on simple recurrent computational procedures. It is assumed that all elements of the corresponding one-parameter matrices have a sufficient degree of smoothness at the center of approximation of solutions.

Process parameters and TiAlN coating impact on microwire-EDM of Ti6Al4V using PVD technique in biomedical application

The growing demand for products made of cutting-edge materials with increased attributes motivates material scientists to investigate prospective variants of such materials. Among the various categories of life-saving advanced materials are biomaterials, although shaping most of them according to the needs encounter manufacturing constraints due to their specific mechanical properties. For example, the extremely tough alloy Ti6Al4V, is renowned for its outstanding mechanical compatibility with the human body. Nonconventional means of machining have gained popularity keeping focus on the challenging machining circumstances that are well-known for their very precision and machining accuracy, no matter what type, shape, or hardness is being machined. Electrical discharge machining (EDM), for example, is the most prevalent efficient means of material removal, along with wire EDM (WEDM), [Formula: see text]-WEDM, and so on. Excess material should be removed for more particular applications of complex and baroque shapes, with a high degree of smoothing and finish, is one of the most advantageous characteristics of wedding metal dielectric material ([Formula: see text]-WEDM). In this study, we examined the effect of variable pulse-on (Ton), pulse (Toff), time (to), flushing pressure (FP), wire feed rate (WFR), wire tension (WT), voltage (SV), and peak current (PC) on [Formula: see text]-WEDM’s reliability of the machined section (SR) using physical vapor deposition (PVD) technique to deposit aluminium nitride (TiAlN) coating on the surface of the metal. The results demonstrate a substantial reduction in roughness in the mechanically produced surfaces, further demonstrating, and confirming the biocompatibility of metals dielectric materials ([Formula: see text]-WEDM) with tissues within the human body.

On the problem of smooth approximations in [formula omitted] and connections to subnormal operators

For the class of de Branges-Rovnyak spaces H(b) of the unit disk D defined by extreme points b of the unit ball of H∞, we study the problem of approximation of a general function in H(b) by a function with an extension to the unit circle T of some degree of smoothness, for instance satisfying Hölder estimates or being differentiable. We will exhibit connections between this question and the theory of subnormal operators and, in particular, we will tie the possibility of smooth approximations to properties of invariant subspaces of a certain subnormal operator. This leads us to several computable conditions on b which are necessary for such approximations to be possible. For a large class of extreme points b we use our result to obtain explicit necessary and sufficient conditions on the symbol b which guarantee the density of functions with differentiable boundary values in the space H(b). These conditions include an interplay between the modulus of b on T and the spectrum of its inner factor.

Сравнение способов аппроксимации функции множителей Лагранжа при решении контактных задач методом с независимой границей контакта

The paper considers the contact problem of the elasticity theory in a static spatial two-dimensional formulation without considering friction. For discretization of the elasticity theory equations, the finite element method was introduced using a triangular unstructured grid and linear and quadratic basis functions. To account for the contact boundary conditions, a modified method of Lagrange multipliers with independent contact boundary is proposed. This method implies the ability to construct a contact boundary with the smoothness degree required for the solution precision and to execute approximation of the Lagrange multiplier function independent of the grids inside the contacting bodies. Various types of the Lagrange multiplier function approximations were studied, including piecewise constant, continuous piecewise linear functions and piecewise linear functions with discontinuities at the difference cells boundaries. Examples of test calculations are provided both for problems with rectilinear and curvilinear contact boundaries. In both cases, the use of discontinuous approximations of the Lagrange multiplier function makes it possible to obtain a numerical solution with fewer artificial oscillations and higher rate of convergence at the grid refinement. It is shown that the numerical solution precision could be improved by more detailed discretization of the contact boundary without changing the grids inside the contacting bodies

VOLDIS: A Direct Search for the Size Distribution of Nanoparticles from Small-Angle Scattering Data and Stability of the Solution

The paper considers an algorithm for the direct search for a nonparametric smooth histogram of the particle size distribution from small-angle X-ray and neutron scattering data. The features and details of the implementation of the method, which consists in the sequential search for several solutions with different degrees of smoothness of the distribution contour, are considered. Methods for evaluating the stability of both the whole distribution contour and its individual parts are discussed. The work of the program is illustrated by examples of the analysis of polydisperse spherical particles in silicasol solutions.

Measurement of shock roughness due to phase plate speckle imprinting relevant for x-ray diffraction experiments on 3rd and 4th generation light sources

Laser-shock compression experiments at 3rd and 4th generation light sources generally employ phase plates, which are inserted into the beamline to achieve a repeatable intensity distribution at the focal plane. Here, the laser intensity profile is characterized by a high-contrast, high-frequency laser speckle. Without sufficient smoothing, these laser non-uniformities can translate to a significant pressure distribution within the sample layer and can affect data interpretation in x-ray diffraction experiments. Here, we use a combination of one- and two-dimensional velocity interferometry to directly measure the extent to which spatial frequencies within the laser focal spot intensity pattern are smoothed out during propagation within the laser plasma and a polyimide ablator. We find that the use of thicker polyimide layers results in spatially smoother shock fronts, with the greatest degree of smoothing associated with the highest spatial frequencies. Focal spots with the smallest initial speckle separation produce the most rapid smoothing. Laser systems that employ smoothing by spectral dispersion techniques to rapidly modulate the focal plane intensity distribution are shown to be the most effective ones in producing a spatially smooth shock front. We show that a simple transport model combined with the known polyimide Hugoniot adequately describes the extent of shock smoothness as a function of polyimide thickness. Our results provide a description of spatial structure smoothing across a shock front, which can be used to design targets on x-ray free electron laser facilities.

Effect of material combinations on mechanical properties of flat bottom riveted joint

Flat bottom riveting is a newly developed joining technique. Since the bottom surface of joint is flat, the joint can be applied in areas that need a high degree of smoothness. This article investigated the effect of material combinations on mechanical properties of joints. Four material combinations which involved two kinds of aluminum alloy were produced. Cross sections of joints were observed by metallographic microscope and geometrical parameters of joints were measured. It was found that material combinations exerted significant influence on the geometrical parameters of joints. When the bottom sheet remained the same, with the increase of top sheet hardness, the interlock thickness of joint decreased, while the neck thickness of joint increased. Tensile and shearing tests were conducted on joint to obtain the tensile load and the shearing load of joint. The absorbed energy of joint in shearing test was calculated. Results showed that when joining materials with different hardness values, the joint with high hardness sheet on the top exhibited higher static load than the joint with high hardness sheet on the bottom. In tensile tests, 1060–5052 joint failed in the manner of neck fracture, while other joints failed in the manner of button separation. In shearing tests, 5052–1060 joint failed in the manner of button separation, while other joints failed in the manner of neck fracture.

Broadband low-frequency sound absorbing metastructures composed of impedance matching coiled-up cavity and porous materials

In this work, we propose a sound absorbing metastructure based on impedance matching coiled-up cavity embedded with porous materials (IMCCP), which demonstrates tremendous broadband (e.g., 4.55 times compared to conventional designs) low-frequency absorption capability with deep subwavelength thickness (e.g., ∼λ/10.96 at 602 Hz), without considering multiple units coupling. By tuning the geometric parameters of the non-coupled unit, relative bandwidths ranging from 111.07 % to 142.55 % are achieved. In particular, two notable perfect absorption peaks are obtained in the low- to mid-frequency range by changing the number of coiled-up channels. Theoretical predictions, numerical simulations and experimental measurements are conducted to investigate the acoustic characteristics of IMCCPs, and the results agree well with each other. Physically, the bandwidth broadening stems from the impedance matching effect which increases the degree of smoothness of sound wave propagation inside coiled-up space with strong inherent dissipation. The bandwidth broadening effect is generally confirmed for diverse geometrical and transport parameters of IMCCPs. This work contributes to understanding the sound wave propagation inside porous coiled-up space and designing broadband porous metastructures.

The middle income trap: look closer and you’ll find it, but maybe not where you expected

ABSTRACT The phenomenon of the middle-income trap or growth slowdowns at any range is analysed using non-parametric local regression with the relative change in per capita GNI as a function of per capita GNI relative to the high-income country average. The existence of a middle-income trap or range of relative GNI at which convergence halts is found to be determined by the degree of smoothing in the model. Support is found for the existence of ‘traps’ for lower-(middle)-income countries up to 10–13% of the high-income country average per capita GNI as well as for countries above 54%.