Image inpainting is the process of filling in damaged or missing regions in an image by using information from known regions or known pixels of the image. One of the most important techniques for inpainting is convolution-based methods, in which a Kernel is convolved with the damaged image iteratively. Convolution based algorithms are very quick, but they don’t have good results in structures and textural regions and result in blurring. The Kernel size in the convolution-based algorithm is a critical parameter. The large size results in edge blurring, and if the Kernel size is small, the information may not be sufficient for reconstruction. In this paper, a novel convolution-based algorithm is proposed that uses known gradient of the pixels to construct a convolution mask. In this algorithm, the Kernel size is controlled by the gradient of the image in the known regions. The algorithm computes the weighted sum of the known pixels in a neighborhood around a damaged pixel and replaces the value in the place of that damaged pixel. The proposed algorithm is fast and results in good edges and smooth regions reconstruction. It is an iterative algorithm and its implementation is very simple. Experimental results show the effectiveness of our algorithm.

Introduction: The emergence of single-cell RNA-sequencing (scRNA-seq) technology has provided new information about the structure of cells, and provided data with very high resolution of the expression of different genes for each cell at a single time. One of the main uses of scRNAseq is data clustering based on expressed genes, which sometimes leads to the detection of rare cell populations. However, the results of the proposed methods mainly depend on the shape of the cell populations and the dimensions of the data. Therefore, it is very important to develop a method that can identify cell populations regardless of these obstacles. Method: In the proposed method, which was a library method, at first, the number of clusters (cell populations) was estimated. Estimating the number of clusters is important because in the real world, basic information such as the number and type of cell populations is not available. Thereafter, using a graph-based Gaussian Kernel, while reducing the dimensions of the problem, the cell populations were identified by means of the kmeans++ clustering. Results: The results of the implementation showed that the proposed method can achieve an acceptable improvement compared to other machine learning methods presented in this regard. For example, for the ARI criterion, values of 100, 93. 47 and 84. 69 were obtained for Kolod, Buettner, and Usoskin single-cell data sets, respectively. Conclusion: The proposed method can cluster and thus identify cell populations with high accuracy and quality without having any basic information about the number and type of cell populations, regardless of the high dimensions of the problem.

Distance-based clustering methods categorize samples by optimizing a global criterion, finding ellipsoid clusters with roughly equal sizes. In contrast, density-based clustering techniques form clusters with arbitrary shapes and sizes by optimizing a local criterion. Most of these methods have several hyper-parameters, and their performance is highly dependent on the hyper-parameter setup. Recently, a Gaussian Density Distance (GDD) approach was proposed to optimize local criteria in terms of distance and density properties of samples. GDD can find clusters with different shapes and sizes without any free parameters. However, it may fail to discover the appropriate clusters due to the interfering of clustered samples in estimating the density and distance properties of remaining unclustered samples. Here, we introduce Adaptive GDD (AGDD), which eliminates the inappropriate effect of clustered samples by adaptively updating the parameters during clustering. It is stable and can identify clusters with various shapes, sizes, and densities without adding extra parameters. The distance metrics calculating the dissimilarity between samples can affect the clustering performance. The effect of different distance measurements is also analyzed on the method. The experimental results conducted on several well-known datasets show the effectiveness of the proposed AGDD method compared to the other well-known clustering methods.

Permeability, porosity and sedimentary facies are the main factors of reservoir characteristics. Porosity indicates the ability of a rock to store fluids. So far, many approaches including linear / nonlinear regressions have been developed to predict porosity. Neural networks have received a lot of attention in recent years, and various types of learning machines based on neural networks have been introduced. Multilayer perceptron neural network (MLP) is one of these networks that proven its ability, but each of these methods has disadvantages. In this research, the support vector machine (SVM) method has been used as the main method for regression and estimation of the reservoir porosity in one of the hydrocarbon reservoirs. This method has been compared with the multilayer perceptron method and the results of each have been investigated. The best way to get accurate values of physical properties of reservoir is to measure them directly in the laboratory. However, this method has disadvantages: high cost, time consuming, lack of access to the entire depth of the well. For these reasons, geologists extract core from a number of wells and from a specific range. Geologists generally use a statistical approach involving multiple linear or nonlinear regressions to relate reservoir characteristics to each other (eg, porosity and permeability). In these contexts, a linear or non-linear relationship is assumed between porosity and other reservoir characteristics. However, these techniques are insufficient for certain issues, such as heterogeneous reservoirs. Recently, geoscientists have used artificial intelligence (AI) methods, especially neural networks (NNs), to predict reservoir parameters. Neural networks have been widely used in various fields of science and engineering. To build a three-dimensional model of a reservoir, a thorough knowledge of permeability, porosity and sedimentary facies is required. Well logs and core information are local measurements that do not reflect the behavior of the reservoir as a whole. In addition, well information does not cover the entire field area, while 3D seismic information covers a larger area. Changes in lithology and fluids cause changes in amplitude, wavelet shape, coherence coefficient, and other seismic attributes. These attributes can provide information for building a repository model. The main purpose of this research is to analyze training machines developed by computer scientists to predict reservoir characteristics such as porosity in vertical and lateral directions with the help of well logs and seismic attributes. The aim is to achieve the following steps to estimate a reliable porosity model of the reservoir: Development of a multilayer perceptron (MLP) to estimate the porosity using well logs. Development of a support vector machine (SVM) to estimate the porosity using well logs. Comparing the proposed methods and choosing the best. Estimation of porosity based on seismic attributes using the selected algorithm. Making a three-dimensional model of the reservoir porosity based on the training machine. As it was expected, these computational intelligence approaches overcome the weakness of the standard regression techniques. Generally, the results show that the performances of Support Vector Machine outperform that Multilayer Perceptron neural networks. In addition, Support Vector Regression (SVR) is more robust, easier and quicker to train. Therefore, it could be concluded that the use of SVM technique will be valuable and powerful for geoscientists to model the reservoir properties.

In the present study, the computer simulation has been used to generate the (1+1) and (2+1) surfaces with two types of correlation function Gaussian and correlation function Exponential forms. For this aim, a random number generator is used to generate the surfaces with Gaussian height distribution with zero mean, and their correlation functions were assumed to have Gaussian and exponential formulas. The calculations have been done for isotropic and anisotropic surfaces.  For monofractal evaluation of rough surfaces, skewness and kurtosis values have been calculated for these (1+1) and (2+1) dimensional surfaces. Moreover, these values have been analyzed by the behavior of probability distribution of height. Also, the Hurst exponents of surfaces have been evaluated to study the irregularity and jaggedness of produced surfaces. Furthermore, the fractal dimension of these rough surfaces has been obtained to describe the complexity of the irregular fractal surfaces.

In this paper, thermal effects of Gaussian and super Gaussian pumping on the rod laser are analytically investigated. The crystal is considered as a rod, with isotropic thermomechanical characterizations, which is end-pumped. The intensity distribution of pumping spot is considered in three-types including Gaussian, second order and third order of super-Gaussian, and effects of any type on the thermal distribution and thermal lensing are compared with each other. First, the heat generations due to emission in the crystal are calculated for Gaussian and super Gaussian pumping and then the equation of temperature distribution is analytically solved and a closed form solution for temperature distribution of the rod laser is obtained. The analytical results are compared with the results of finite element method. Thereupon, the temperature distributions and the values of thermal lens for various pumping powers are calculated. The results show that calculated maximum temperature for Gaussian case is lower than for supper-Gaussian cases. In addition, the distances between focal point and the input pumping plane obtained for super-Gaussian pumping are larger than those calculated for Gaussian pumping.

For transformation optics, comprising two or three cylindrical lenses, incoming standard Hermite Gaussian (SHG) modes are converted to twisted Hermite-Gaussian beams with complex argument if the rotational angle differs fromp/4.We show that these twisted modes can be expressed as a superposition of a set of elegant Hermite-Gaussian (EHG) modes with complex arguments multiplied by a Gaussian function. Expressions for the free propagation of these modes, is then derived for the first time. Examples are given for the far-field distributions of converted modes (using new expression for twisted Hermite-Gaussian with complex arguments).