Truncation Parameter Research Articles

Efficiency high-order discontinuous Galerkin method for low speeds flows with time-derivative preconditioning

A local preconditioning high-order discontinuous Galerkin (DG) method is introduced to enhance the efficiency and accuracy of the density-based approach for low-speed flows. The method is based on the time-derivative preconditioning technique typically employed in finite volume methods. Traditional approximation methods that only precondition low-order derivatives lead to incompatibility of the equations. To extend the preconditioning technique to the DG method, we employ an analytic preconditioning mass matrix derived from the DG formulation of the preconditioned Navier–Stokes equations. Modified numerical flux functions and a self-adaptive local velocity truncation parameter are employed for DG systems with preconditioning. We demonstrate the efficiency and accuracy of the preconditioned DG method using explicit and implicit schemes for steady flows and a dual-time scheme for unsteady flows. The method has been implemented and used to compute a variety of flow problems, including inviscid and laminar flows, utilizing various degrees of polynomial approximations. Computations with and without preconditioning are performed to analyze the influence of spatial discretization on the accuracy and convergence of the DG solutions at low Mach numbers. Numerical results underscore the enhanced accuracy and convergence properties of the proposed method for low-speed flows, indicating significant performance improvements over traditional methods.

De la Vallée Poussin filtered polynomial approximation on the half–line

On the half line, we introduce a new sequence of near-best uniform approximation polynomials, easily computable by the values of the approximated function at a truncated number of Laguerre zeros. Such approximation polynomials come from a discretization of filtered Fourier–Laguerre partial sums, which are filtered using a de la Vallée Poussin (VP) filter. They have the peculiarity of depending on two parameters: a truncation parameter that determines how many of the n Laguerre zeros are considered, and a localization parameter, which determines the range of action of the VP filter we will apply. As n→∞, under simple assumptions on such parameters and the Laguerre exponents of the involved weights, we prove that the new VP filtered approximation polynomials have uniformly bounded Lebesgue constants and uniformly convergence at a near–best approximation rate, for any locally continuous function on the semiaxis.The numerical experiments have validated the theoretical results. In particular, they show a better performance of the proposed VP filtered approximation versus the truncated Lagrange interpolation at the same nodes, especially for functions a.e. very smooth with isolated singularities. In such cases, we see a more localized approximation and a satisfactory reduction of the Gibbs phenomenon.

Basis-Set Limit CCSD(T) Energies for Large Molecules with Local Natural Orbitals and Reduced-Scaling Basis-Set Corrections.

The calculation of density-based basis-set correction (DBBSC), which remedies the basis-set incompleteness (BSI) error of the correlation energy, is combined with local approximations. Aiming at large-scale applications, the procedure is implemented in our efficient local natural orbital-based coupled-cluster singles and doubles with perturbative triples [LNO-CCSD(T)] scheme. To this end, the range-separation function, which characterizes the one-electron BSI in space, is decomposed into the sum of contributions from individual localized molecular orbitals (LMOs). A compact domain is constructed around each LMO, and the corresponding contributions are evaluated only within these restricted domains. Furthermore, for the calculation of the complementary auxiliary basis set (CABS) correction, which significantly improves the Hartree-Fock (HF) energy, the local density fitting approximation is utilized. The errors arising from the local approximations are examined in detail, efficient prescreening techniques are introduced to compress the numerical quadrature used for DBBSC, and conservative default thresholds are selected for the truncation parameters. The efficiency of the DBBSC-LNO-CCSD(T) method is demonstrated through representative examples of up to 1000 atoms. Based on the numerical results, we conclude that the corrections drastically reduce the BSI error using double-ζ basis sets, often to below 1 kcal/mol compared to the reliable LNO-CCSD(T) complete basis set references, while significant improvements are also achieved with triple-ζ basis sets. Considering that the calculation of the DBBSC and CABS corrections only moderately increases the wall-clock time required for the post-HF steps in practical applications, the proposed DBBSC-LNO-CCSD(T) method offers a highly efficient and robust tool for large-scale calculations.

Structure preserving finite element schemes for the Navier-Stokes-Cahn-Hilliard system with degenerate mobility

In this work we present two new numerical schemes to approximate the Navier-Stokes-Cahn-Hilliard system with degenerate mobility using finite differences in time and finite elements in space. The proposed schemes are conservative, energy-stable and preserve the maximum principle approximately (the amount of the phase variable being outside of the interval [0,1] goes to zero in terms of a truncation parameter). Additionally, we present several numerical results to illustrate the accuracy and the well behavior of the proposed schemes, as well as a comparison with the behavior of the Navier-Stokes-Cahn-Hilliard model with constant mobility.

Meta-analysis of RNA-seq studies with an adaptive weight and truncation p-value combination test

For RNA-seq studies, an important task is to identify genes that are differentially expressed between groups. Nevertheless, the identification of differentially expressed (DE) genes from a single study can be challenging as the small number of samples and the high sensitivity of data perturbations. Combining p-values from multiple RNA-seq studies can increase the statistical power and the accuracy in detecting DE genes. In this paper, we propose a weight and truncation p-value combination test for meta-analyzing RNA-seq studies. We show that with proper weight and truncation parameters, our new test has a higher statistical power over the existing tests, when the genes are weakly expressed in most studies and the sample size is unbalanced. We then present simulations and apply to two real data analysis. Finally, we provide some practical guidance for our new test and some existing p-value combination tests.

Tight focusing of azimuthally polarized Laguerre–Gaussian vortex beams by diffractive axicons

This study presents a comprehensive theoretical investigation into the focusing properties of azimuthally polarized Laguerre–Gaussian vortex (APLGV) beams when interacting with different optical elements, including a linear axicon, binary axicon, and lens based on the Debye approximation. The research findings highlight the intriguing combination of polarization and vortex singularities within the APLGV beam, which result in distinctive focal shapes when interacting with these optical elements. The focal shapes achieved include multiple tightly focused spots and optical needles, which can be controlled by adjusting optical system parameters and beam characteristics such as the numerical aperture (NA), truncation parameter, beam order, and annular obstruction. These parameters can be carefully selected to achieve specific focal shapes with applications in multi-optical manipulation, particle acceleration, and trapping. By harnessing the unique properties of APLGV beams and optimizing the optical setup, researchers can explore new possibilities for advanced optical manipulation and control.

Exploring the potential of StyleGAN for modeling high-quality and diverse digital wood textures: Towards advancements in the wood industry

Wood texture is pivotal in maximizing the value of trees and timber resources. Consequently, digital modeling and simulation of wood texture have become essential in wood science and industry. Therefore, researching simulation modeling techniques for digital wood texture has significant implications for advancing wood science and industry. This paper introduces a novel approach to modeling and simulating wood texture, focusing on the perspective of deep learning. The proposed method explored the viability of utilizing the StyleGAN model to generate digital wood texture. Fréchet Inception Distance(FID), visual Turing tests, and 1/f fluctuation spectrum analysis were used to evaluate the effectiveness of the digital wood texture models. Additionally, various control techniques were discussed for generating digital wood texture using StyleGAN models. The experimental results strongly indicated that the StyleGAN model exhibits robust capabilities in generating digital wood texture, as evidenced by an FID index of 13. Moreover, the visual Turing tests revealed that professional identification was similar to random guessing, while the fluctuation spectrum analysis demonstrated pixel distribution frequencies similar to those observed in real wood textures. Furthermore, in terms of controlling the simulation of digital wood texture, the StyleGAN model demonstrated remarkable abilities surpassing any previous models based on physical modeling. By fine-tuning truncation parameters and employing network layer mixing techniques, the model could generate the wood texture of various tree species, demonstrating outstanding generalization capabilities.

Parameter estimation of the multivariate unrestricted skew-normal distribution using ECM algorithm

The probability density function of the multivariate unrestricted skew-normal (SUN) distribution, corresponding to a screened normal density, allow to modeling skewness and kurtosis in data in terms of a skewness parameter vector and a truncation parameter matrix. These parameters are related to the shape and heavy-tails of the density. In this article, we present the Expectation/Conditional Maximization (ECM) algorithm for the SUN distribution based on a hierarchical stochastic representation. In addition, behavior of ECM algorithm’s steps is measured using an information theoretic approach based on Jeffrey’s divergence and related homogeneity test. Usefulness of the proposed method is illustrated by an application to Chilean economic perception data.

Energy-stable and boundedness preserving numerical schemes for the Cahn-Hilliard equation with degenerate mobility

Two new numerical schemes to approximate the Cahn-Hilliard equation with degenerate mobility (between stable values 0 and 1) are presented, by using two different non-centered approximation of the mobility. We prove that both schemes are energy stable and preserve the maximum principle approximately, i.e. the amount of the solution being outside of the interval [0,1] goes to zero in terms of a truncation parameter. Additionally, we present several numerical results in order to show the accuracy and the well behavior of the proposed schemes, comparing both schemes and the corresponding centered scheme.

Robust function-on-function interaction regression

A function-on-function regression model with quadratic and interaction effects of the covariates provides a more flexible model. Despite several attempts to estimate the model’s parameters, almost all existing estimation strategies are non-robust against outliers. Outliers in the quadratic and interaction effects may deteriorate the model structure more severely than their effects in the main effect. We propose a robust estimation strategy based on the robust functional principal component decomposition of the function-valued variables and [Formula: see text]-estimator. The performance of the proposed method relies on the truncation parameters in the robust functional principal component decomposition of the function-valued variables. A robust Bayesian information criterion is used to determine the optimum truncation constants. A forward stepwise variable selection procedure is employed to determine relevant main, quadratic, and interaction effects to address a possible model misspecification. The finite-sample performance of the proposed method is investigated via a series of Monte-Carlo experiments. The proposed method’s asymptotic consistency and influence function are also studied in the supplement, and its empirical performance is further investigated using a U.S. COVID-19 dataset.

Asymptotic loss of the MLE of a truncation parameter in the presence of a nuisance parameter for a one-sided truncated family of distributions

For a truncated family of distributions with a truncation parameter γ and a parameter θ as a nuisance parameter, we derive the stochastic expansions of bias-adjusted maximum likelihood estimators γ ̂ M L ∗ θ and γ ̂ M L ∗ of γ based on a sample of size n when θ is known and when θ is unknown, respectively. The asymptotic loss of γ ̂ M L ∗ relative to γ ̂ M L ∗ θ is obtained up to the second order, that is the order n −1. The results are a generalization of those for a one-sided truncated exponential family of distributions. Its application to truncated t-distributions is also given.

Magnetization properties of radially polarized Bessel-Gaussian vortex beams with radial phase modulation in a 4π focusing system.

This paper explored the optically induced magnetization properties of radially polarized Bessel-Gaussian vortex beams with radial phase modulation in a 4π high numerical aperture (NA) focusing system, which is based on the vector diffraction theory and the inverse Faraday effect. The results show that in the case of radial modulation parameter L=0, one longitudinal magnetization chain with adjustable length can be obtained by modulating the truncation parameter β. When the radial modulation parameter L=1.3, two magnetization chains can be obtained by modulating the truncation parameter β. By modulating the radial modulation parameter L, two magnetization chains along the optical axis can be generated, each with four dark magnetic traps; meanwhile, the spacing between two magnetization chains can be adjusted. These results may be helpful in high-density all-optical magnetic recording, atom capture, and magnetic resonance microscopy.

A radiation and propagation problem for a Helmholtz equation with a compactly supported nonlinearity

The present paper is devoted to the study of a class of nonlinear Helmholtz equations that is essentially used in mathematical models for the theoretical and numerical analysis of scattering and radiation effects. While well-known works relate to geometrically simple domains (supporting the nonlinearity) and selected nonlinearities, the new aspects lie in the transition to more generally shaped, two- or three-dimensional objects, to more general nonlinearities (including saturation), and in the possibility of an efficient numerical approximation of the electromagnetic fields and derived quantities (such as energy, transmission coefficient, etc.).The paper describes and investigates an approach that consists in transforming the original full-space transmission problem for a nonlinear Helmholtz equation into an equivalent boundary-value problem on a bounded domain by means of a nonlocal Dirichlet-to-Neumann (DtN) operator. It is shown that the transformed nonlinear problem is equivalent to the original one and is uniquely solvable under appropriate conditions. In addition, the effect of truncation of the DtN operator on the resulting solution is investigated. It is shown that the corresponding sesquilinear form satisfies a parameter-uniform inf–sup condition, that the modified nonlinear problem has a unique solution, and that the solution error caused by the truncated DtN operator can be estimated in dependence on the truncation parameter.

Focusing pattern of the Laguerre-Gaussian beam with polarization mixing helical-conical phase modulation.

This paper focuses on the focusing pattern of the Laguerre-Gaussian (LG) beam with polarization mixing helical-conical phase modulation, which is based on the vector diffraction theory. The results show that the topological charge number l can sensitively control the intensity of the intensity peaks. The focal spot will split along the optical axis under different polarization parameters P. When l=1, the spot position and the peak intensity can be modulated by changing the polarization parameter P. The truncation parameter β makes the focusing spot form an optical trap. By adjusting the eccentricity parameter K, the opening direction of the optical trap can be well controlled. These results may be helpful in optical applications such as optical manipulation, optical focusing, and optical information transmission.

Study of radiation power spectra in the 1-D photonic periodic dielectric structure

We explored the thermal power radiation spectrum ρ (ω, T) of electromagnetic radiation in a 1D photonic periodic structure combining Si and Sio2 with truncated Sio2 media and an absorbing substrate. A theoretical model based on a transfer matrix for both normal and oblique incidence angles together with Kirchhoff’s second rule is used to predict the thermal radiation power spectrum. In order to study the radiation spectra, we used the TE and TM modes with truncation parameters and incidence angles in the mid, left, and right gap frequencies, which correspond to the mid, left, and right mid-gap temperatures. Layers nA&nB are A and B’s indices are considered to be constant and controlled in these modes.

The $ l_\infty $-induced norm of multivariable discrete-time linear systems: Upper and lower bounds with convergence rate analysis

<abstract><p>This paper develops a method for computing the $ l_{\infty} $-induced norm of a multivariable discrete-time linear system, for which an infinite-dimensional matrix should be intrinsically concerned with. To make such a computation feasible, we treat the infinite-dimensional matrix in a truncated fashion, and an upper bound and a lower bound on the $ l_\infty $-induced norm of the original multivariable discrete-time linear system are derived. More precisely, the matrix $ \infty $-norm of the (infinite-dimensional) tail part can be approximately computed by deriving its upper and lower bounds, while that of the (finite-dimensional) truncated part can be exactly obtained. With these values, an upper bound and a lower bound on the original $ l_\infty $-induced norm can be computed. Furthermore, these bounds are shown to converge to each other within an exponential order of $ N $, where $ N $ is the corresponding truncation parameter. Finally, some numerical examples are provided to demonstrate the theoretical validity and practical effectiveness of the developed computation method.</p></abstract>

Energy-Based CNN Pruning for Remote Sensing Scene Classification

Convolutional neural networks (CNNs) have been adopted to classify the remote sensing scene image. However, the application of these complicated networks on the satellite platform is difficult because of the limited computation resources. Therefore, we propose an energy-based filter pruning framework (EFPF) to reduce the size of the original model. The energy can be obtained through the eigenvalues of each weight tensor by singular value decomposition (SVD). Specifically, we calculate the energy of each layer by the ratio of eigenvalues that are lower than a specified truncation parameter and then remove filters from the original layer in light of the degree of energy. The EFPF is reliable because SVD techniques can capture the covariance among all filters from the original weight tensor, and therefore, the energy from the eigenvalues can reflect the redundancy of the filters. (i.e., if the distribution of eigenvalues is sharp, then the energy among filters will be lower, and the redundancy will be higher.) Surprisingly, the EFPF can reduce the FLOPs and parameters, as well as improve the top1 accuracy obviously when the VGG-16 and ResNet-50 are adopted to classify the AID, NWPU45, PatternNet, and WHU19 datasets. Additionally, the EFPF can achieve similar pruning results when the original model is fully-trained (converge) and under-trained (In-converge), which means we can save the training computation resources for the original model.

Comparison of Some Entropy Measures for Non-Central Fisher Probability Distribution

In this paper, many entropy measures of noncentral Fisher distribution were driven including Shannon, Renyi, Sharma, Havrda, Arimoto and Tsallis. A comparison between these entropies was made according to distribution’s shift parameter, distribution’s degrees of freedom, shape parameter and truncation parameter. The entropy that had less relative loss was said to be better than the other. There were significant differences according to all studied parameters except the shift parameter and we found that the best entropy of the mentioned entropies for noncentral Fisher distribution was Renyi entropy.

Separating and transporting of particles using tightly focused radially polarized Bessel–Gaussian beam with conical phase

The intensity distributions near the focus for radially polarized Bessel–Gaussian beam with conical phase by a high numerical aperture objective are computed based on the vector diffraction theory. Results show that the circular focal spot can be changed from one to two on the focal plane by adjusting the truncation parameter β. By increasing the phase modulation parameter L, the focal pattern appeared focal shift. According to the intensity distribution, the forces acting on a particle are calculated. The stability of particle trapping is analyzed. It is shown that a tightly focused radially polarized Bessel–Gaussian beam with conical phase is applicable to trapping, separating and transporting of particles.

Far and near fields of Hermite–Gaussian beams passing through an annular aperture and its numerical simulation by the angular spectrum method

This research focuses on the analysis of the free propagation of Hermite–Gaussian beams diffracted by a symmetrical annular aperture placed at the beam waist plane. The propagation is studied analytically and numerically using the angular spectrum method and the 2D fast Fourier transformation. Numerical simulation examples illustrate the propagation characteristics of the Hermite–Gaussian beams diffracted by an annular aperture. The beam truncation parameters and obscuration ratio influence Hermite–Gaussian beam diffraction properties.