Using the formation constants of 74 charge–transfer complexes in which iodine and iodine monochloride act as acceptors, quantitative structure–property relationships models were developed for predicting these constants for the first time. The procedure was based on reducing a large number of the descriptors based on the variable importance in projection and subsequent selection by stepwise regression and genetic algorithm. The most important variables influencing the charge–transfer interactions were identified and interpreted. Models were obtained by linear methods of multiple linear regression and partial LEAST SQUARES regression and the nonlinear method of RADIAL BASIS function–partial LEAST SQUARES. The best predictions were obtained with the Gaussian RADIAL BASIS function with s=0.9 and LV=10. The obtained results confirm the capability of the proposed approach to give predictive models for KCT.

The Mixed LEAST SQUARES Meshfree (MDLSM) method has shown its appropriate efficiency for solving Partial Differential Equations (PDEs) governing the engineering problems. The method is based on the minimizing the residual functional. The residual functional is defined as a summation of the weighted residuals on the governing PDEs and the boundaries. The Moving LEAST SQUARES (MLS) is usually applied in the MDLSM method for constructing the shape functions. Although the required consistency and compatibility for the approximation function is satisfied by the MLS, the method loss its appropriate efficiency when the nodal points cluster too much. In the current study, the mentioned drawback is overcome using the novel approximation function called Mapped Moving LEAST SQUARES (MMLS). In this approach, the cluster of closed nodal points maps to standard nodal distribution. Then the approximation function and its derivatives compute noting the some consideration. The efficiency of suggested MMLS for overcoming the drawback of MLS is evaluated by approximating the mathematical function. The obtained results show the ability of suggested MMLS method to solve the drawback. The suggested approximation function is applied in MDLSM method, and used for solving the Burgers equations. Obtained results approve the efficiency of suggested method.

Management and exploitation in mines require a continuous and relatively smooth surface of the mineral grades. While assessing the various mineral elements, the scattered exploratory cavities are irregularly excavated. Producing a continuous surface from measured data requires interpolation methods. Several factors, including the characteristics of the data, affect the efficiency of the interpolation methods. For this reason, the efficiency of different methods in various cases is inconsistence, and choosing the appropriate interpolation method is also challenging. Interpolation methods can be categorized into two groups of mesh-based and meshless methods. Despite the efficiency and capabilities of meshless methods, they have a fundamental shortcoming due to the fixed size of the support domain. On the one hand, the distribution of exploratory cavities in mines is usually irregular, and in some areas, it is very dense, and in others, it is very sparse. On the other hand, the grade values of minerals at the surface of the region can be very variable with high changes. Conventional interpolation methods do not have sufficient efficiency and flexibility in confronting these two aforementioned issues. In this study, a precise, reliable, and flexible method is developed for interpolation of minerals through integrating the moving LEAST SQUARES and recursive LEAST SQUARES methods. In the proposed method for crack detection, the residuals statistical test of LEAST SQUARES computations is used. In this method, for the central point, a continuity threshold (non-continuity) is determined based on the standard deviation of field values, so that points with crack are revealed and removed from the calculation of the value of the central point. Moreover, the size of the support domain is determined dynamically based on the recursive property of the method. In this method, an individual radius for the support domain is assigned to each central point according to the values and distributions of the surrounding field points. The dynamic size of the support domain allows a precise and reliable estimation of polynomial coefficients and the values of the central points. The efficiency of the proposed method is evaluated by applying it to simulated data as well as comparing it with the results of conventional interpolation methods on real mineral data. The results of the simulation data indicate the ability of the proposed method to reveal the non-continuity and fractures of surfaces with determining the dynamics size of the support domain based on the data structure. To compare the results of the proposed method with conventional interpolation methods including LPI, IDW, Kriging, and RBF, the root mean square error (RMSE), mean and median of errors are used. In this way, in addition to the overall accuracy of each method, the distribution of errors is also determined. The RMSE, mean and median errors of the proposed method, using the 10-fold cross-validation method for chromium (Cr), are 28. 020, 0. 2. 201 and 2. 874, respectively, and for iron (Fe) are 1. 074, 0. 017 and 0. 094, respectively. Comparison of these results with conventional interpolation methods indicates the efficiency of the proposed method for both groups of high concentration and significant changes in the values and low concentration and almost uniform level of values. The results indicate the ability of the proposed method in detecting the jumps and non-continuity in the support domain and removal of some field points within the dynamic process, lead to a significant increase in the efficiency of the method compared to conventional methods.

In this paper, a new form of critic-only Reinforcement Learning algorithm for continuous state spaces control problems is proposed. Our approach, called Fuzzy-RBF LEAST Square Policy Iteration (FRLSPI), tunes the weight parameters of the fuzzy-RBF network (a hybrid model constituted by combining Takagi-Sugeno fuzzy rule inference system with RBF network) online and is acquired through combining LEAST SQUARES Policy Iteration (LSPI) with fuzzy-RBF network as a function approximator. In FRLSPI, based on the BASIS functions defined in the fuzzy-RBF network, a solution has been provided for the challenge of determining the state-action BASIS functions in LSPI. We also provide positive theoretical results concerning an error bound between the optimal and the approximated Action Value Function (AVF) for FRLSPI. Our proposed method has suitable features such as positive mathematical analysis, learning rate independency and, comparatively good convergence properties. Simulation studies regarding the mountain-car control task and acrobat problem demonstrate the applicability and performance of our learning framework. The overall results indicate that the proposed idea can outperform previously known reinforcement learning algorithms.

In this paper, we propose a nonparametric rank-based alternative to the LEAST-SQUARES independent component analysis algorithm developed. The basic idea is to estimate the squared-loss mutual information, which used as the objective function of the algorithm, based on its copula density version. Therefore, no marginal densities have to be estimated. We provide empirical evaluation of the proposed algorithm through simulation and real data analysis. Since the proposed algorithm uses rank values rather than the actual values of the observations, it is extremely robust to the outliers and suffers less from the presence of noise than the other algorithms.

Image magnification is one of the current issues of image processing in which keeping the quality and structure of images is the main concern. In image magnification, it is necessary to insert information in extra pixels. Adding information to an image should be compatible with the image structure with- out making artificial blocks. In this research, extra pixels are estimated using the surface of LEAST SQUARES, and all the pixels are reviewed according to the suggested edge-improving algorithm. The suggested ethod keeps the edges and minimizes the magnified image opacity and the artificial blocks. Numerical results are presented by using PSNR and SSIM fidelity measures and compared to some other methods. The average PSNR of the original image and image zooming is 32.79 which it shows that image zooming is very similar to the original image. Experimental results show that the proposed method has a better performance than others and provides good image quality.

Determination of the diffusion coefficient on the base of solution of a linear inverse problem of the parameter estimation using the LEAST-square method is presented in this research. For this propose a set of temperature measurements at a single sensor location inside the heat conducting body was considered. The corresponding direct problem was then solved by the application of the heat fundamental solution.

Pedomodels have become a popular topic in soil science and environmental research. They are predictive functions of certain soil properties based on other easily or cheaply measured properties. The common method for fitting pedomodels is to use classical regression analysis, based on the assumptions of data crispness and deterministic relations among variables. In modeling natural systems such as soil system, in which the above assumptions are not held true, prediction is influential and we must therefore attempt to analyze the behavior and structure of such systems more realistically. In this paper we consider fuzzy LEAST SQUARES regression as a means of fitting pedomodels. The theoretical and practical considerations are illustrated by developing some examples of real pedomodels.

This study compared the performance of the partial LEAST SQUARES-structural equation modelling (PLS-SEM) and the robust partial LEAST SQUARES-structural equation modelling (RPLS-SEM) methods through Winsorisation approach The inputs and the outputs used in this model were based on the electricity generation data, derived from the Al-Zawiya Steam Power Plant, Libya. Furthermore, the researchers compared the novel RPLS-SEM approach with the traditional PLS-SEM approach and noted that the novel RPLS-SEM method was more efficient compared to PLS-SEM.