Reconstructed Interpolating Differential Operator Method with Arbitrary Order of Accuracy for the Hyperbolic Equation

We propose a family of multi-moment methods with arbitrary orders of accuracy for the hyperbolic equation via the reconstructed interpolating differential operator (RDO) approach. Reconstruction up to arbitrary order can be achieved on a single cell from properly allocated model variables including spatial derivatives of varying orders. Then we calculate the temporal derivatives of coefficients of the reconstructed polynomial and transform them into the temporal derivatives of the model variables. Unlike the conventional multi-moment methods which evolve different types of moments by deriving different equations, RDO can update all derivatives uniformly via a simple linear transform more efficiently. Based on difference in introducing interaction from adjacent cells, the central RDO and the upwind RDO are proposed. Both schemes enjoy high-order accuracy which is verified by Fourier analysis and numerical experiments.

Comparison among Some Methods for Estimating the Parameters of Truncated Normal Distribution

The aim of this study is to investigate the effect of different truncation combinations on the estimation of the normal distribution parameters. In addition, is to study methods used to estimate these parameters, including MLE, moments, and L-moment methods. On the other hand, the study discusses methods to estimate the mean and variance of the truncated normal distribution, which includes sampling from normal distribution, sampling from truncated normal distribution and censored sampling from normal distribution. We compare these methods based on the mean square errors, and the amount of bias. It turns out that the MLE method is the best method to estimate the mean and variance in most cases and the L-moment method has a performance in some cases.

Reliability Analysis of Circular Footing by Using GP and MPMR

Circular footings are designed to bear a load of super structures. Studies have been done on the influence of soil properties on bearing capacity of shallow foundations. The use of circular foundation is practical in geotechnical engineering. During the design of circular footing, bearing capacity of soil is taken into consideration, and cohesion (c), unit weight (γ), and angle of internal friction (ϕ) are the most variable parameters. Reliability analysis is used frequently for the design of circular footing. Most of the authors have used first order second moment methods (FOSM). However, FOSM is a time-consuming method. Drawbacks of FOSM have been overcome by genetic programming (GP), minimax probability machine regression (MPMR). This article gives a distinct analysis between the developed MPMR based FOSM and GP-based FOSM.

Combining ILC and moment expansion techniques for extracting average-sky signals and CMB anisotropies

The method of weighted addition of multi-frequency maps, more commonly referred to as Internal Linear Combination (ILC), has been extensively employed in the measurement of cosmic microwave background (CMB) anisotropies and its secondaries along with similar application in 21cm data analysis. Here we argue and demonstrate that ILC methods can also be applied to data from absolutely-calibrated CMB experiments to extract average-sky signals in addition to the conventional CMB anisotropies. The performance of the simple ILC method is, however, limited, but can be significantly improved by adding constraints informed by physics and existing empirical information. In recent work, a moment description has been introduced as a technique of carrying out high precision modeling of foregrounds in the presence of inevitable averaging effects. We combine these two approaches to construct a heavily constrained form of the ILC, dubbed MILC, which can be used to recover tiny monopolar spectral distortion signals in the presence of realistic foregrounds and instrumental noise. This is a first demonstration for measurements of the monopolar and anisotropic spectral distortion signals using ILC and extended moment methods. We also show that CMB anisotropy measurements can be improved, reducing foreground biases and signal uncertainties when using the MILC. While here we focus on CMB spectral distortions, the scope extends to the 21cm monopole signal and B-mode analysis. We briefly discuss augmentations that need further study to reach the full potential of the method.