Study of large axial space rebinning algorithm in γ-photon industrial tomography image reconstruction

The accuracy of the existing single slice and Fourier rebinning algorithms depends on the projection angle of the line of response. The increase of such projection angle with the detector size, typical in the large axial space of γ-photon industrial detection, and the loss of some projection data after rebinning, result in the degradation of the image quality. In addition, those algorithms consider the probability of positron annihilation equally distributed along the line of response, which prevents to estimate accurately the positions of the annihilation point, and can originate artifacts and noise in the reconstructed image. In this work, we propose an alternative large axial space rebinning algorithm. In that algorithm, initially the line of response is divided into transverse and axial components. Then, each line of response is uniformly rebinned into all the 2D sinogram data intersecting with it. To improve the accuracy of the estimate of the annihilation point location and suppress the noise effectively, we assign a Gaussian weight coefficient to the projection data, and optimise the rebinning algorithm with it. Finally, we reconstruct the image on the basis of the 2D sinograms with the optimised weights. On the computational side, the algorithm is also accelerated by making use of parallel computing. Both simulation and experimental results show that the proposed method improves the contrast and spatial resolution of 2D reconstructed images. Furthermore, the reconstruction time is not affected by the new method, which is therefore expected to meet the demand of γ-photon industrial inspection imaging.

Development and verification of meshless diffuse approximate method for simulation of compressible flow between parallel plates

A meshless numerical model is developed to simulate single-phase, Newtonian, compressible flow in the Cartesian coordinate system. The coupled set of partial differential equations, i.e., mass conservation, momentum conservation, energy conservation, and equation of state is solved by using Diffuse Approximate Method (DAM) and Pressure Implicit with Splitting of Operators (PISO) pressure correction algorithm on an irregular node arrangement. DAM is structured by using the second-order polynomial basis functions and the Gaussian weight function, leading to the weighted least squares approximation on overlapping sub-domains. Implicit time discretization is performed for the predictor step of PISO, while in the corrector steps the equations are discretized explicitly. The numerical model is validated for flow between parallel plates with helium obeying ideal gas law. The solver’s accuracy is assessed by investigating the shape of the Gaussian weight and the number of the nodes in the local subdomains. The calculated velocity, temperature and pressure fields are compared with the Finite Volume Method (FVM) results obtained by OpenFOAM software and show a reasonably good agreement.

UNDERSTANDING AND STUDY OF WEIGHT INITIALIZATION IN ARTIFICAL NEURAL NETWORKS WITH BACK PROPAGATION ALGORITHM

There are various important choices that need to be assumed when building and training a neural network. One has to determine which loss function to be used, how many layers to be include, what stride and kernel size to use for each layer, which optimization algorithm is best suited for the network and so on. Assuming all the above condition, it decided to initialize the neural network training by different weight initialization techniques. This process is carried out in affiliation or with respect to with random learning rate so that we can get better result. We have calculated the mean test error for newly proposed paradigm and traditional approach. The newly proposed paradigm Xavier Weight Initialization less error in comparison to the traditional approach of Uniform and Gaussian Weight initialization (Random Initialization).

A degenerate Gaussian weight connected with Painlevé equations and Heun equations

In this paper, we study the recurrence coefficients of a deformed Hermite polynomials orthogonal with respect to the weight [Formula: see text] where [Formula: see text] and [Formula: see text]. It is an extension of Chen and Feigin [J. Phys. A., Math. Gen. 39 (2006) 12381–12393]. By using the ladder operator technique, we show that the recurrence coefficients satisfy a particular Painlevé IV equation and the logarithmic derivative of the associated Hankel determinant satisfies the Jimbo–Miwa–Okamoto [Formula: see text] form of the Painlevé IV. Furthermore, the asymptotics of the recurrence coefficients and the Hankel determinant are obtained at the hard-edge limit and can be expressed in terms of the solutions to the Painlevé XXXIV and the [Formula: see text]-form of the Painlevé II equation at the soft-edge limit, respectively. In addition, for the special case [Formula: see text], we obtain the asymptotics of the Hankel determinant at the hard-edge limit via semi-classical Laguerre polynomials with respect to the weight [Formula: see text], which reproduced the result in Charlier and Deano, [Integr. Geom. Methods Appl. 14(2018) 018 (p. 43)].

Propagation of the Measurement Error and the Measured Mean of a Physical Quantity for Elementary Functions ax and loga x

Rules have been obtained for the propagation of the error and the mean value for a measured physical quantity onto another one with a functional relation of the type ax or loga x between them. In essence, these rules are inherently based on the Gaussian weight scheme. Therefore, they should be valid in the framework of a real Gaussian weight scheme applied to discrete data of a real physical experiment (a sample). An analytical form that was used to present the rules concerned (“analytical propagation rules”) and their character allow the processing and the analysis of experimental data to be simplified and accelerated.