Background and Objectives: One of the essential factors in the programming and management of water resources is predicting the amount of runoff. Increasing the accuracy in predicting runoff will increase the efficiency of programming and management,therefore, improving the modeling of discharge prediction is a requisite issue. The first aim of this study is to evaluate the efficiency of the multivariable linear regression, M5 decision tree, and time series in predicting the river runoff. The second aim is to analyze the modeling time step (monthly or seasonal) and the effects of model inputs (one delay steps variable against several delay steps variable) on the accuracy of the studied models. Material and Methods: Navrood watershed located in the west part of Guilan province is chosen for the study area in this research. Required data is collected from Kharjgil (1368-1398) and Kholian (1375-1397), including monthly river flow, rainfall, and temperature from Guilan regional water company. The amount of runoff is predicted in two approaches by the received data in monthly and seasonal time steps sing three models of multivariable linear regression, time series, and M5 decision tree. In the first approach, input variables to the model were river flow, rainfall, and temperature with three steps delay. In the second approach, the only variable was river flow with three steps delay. The model evaluation criteria in this research are the mean bias error (MBE), Nash-Sutcliffe efficiency (NSE), and coefficient of determination (𝑅, 2). Results: In the first approach and in monthly timestep, M5 decision tree is selected model with MBE-NSE equal to-0. 04, 0. 80 (train) and 0. 01, 0. 72 (test) in Kharjgil station, and-0. 01, 0. 79 (train) and 0. 00, 0. 86 (test) in Kholian station. In the seasonal time step, the criteria for the M5 decision tree in Kholian station are equal to 0. 02, 0. 78 (train),-0. 02, 0. 86 (test), and in Kholian station are-0. 01, 0. 79 (train), 0. 00, 0. 86 (test). This model was the best in this study for the first approach in the seasonal time step. The second approach has led to different findings considering both monthly and seasonal time steps. In the second approach, the criteria in monthly time step for time series model during train and test in Kharjgil station are respectively-0. 05, 0. 47 and 0. 10, 0. 52 and in Kholian are-0. 02, 0. 63 and 0. 2, 0. 49. The selected model criteria for seasonal time step considering train and test are-0. 42, 0. 58 and 0. 06, 0. 83 in Kharjgil station, and 0. 09, 0. 40 and-0. 10, 0. 62 in Kholian station. The time series model is selected in the second approach in the seasonal time step. Conclusion: The findings of this research have shown that in both stations and time steps, the M5 decision tree model has shown a higher accuracy in prediction than the two other models in the first approach. Meanwhile, the decision tree model does not show accurate results in the second approach. Alternatively, compared to two other models in both stations and both time steps, the time series model had a higher accuracy. Findings of this research have emphatically shown that specific approaches in choosing the model's inputs can effectively influence the selected model and the accuracy of modeling.

1. Introduction: From 1960s several attempts have been made to measuring the rock brittleness index BI. Schwartz (1964) using results of a series of triaxial tests on rock samples, stated that the rock’ s behavior from frangibility to ductility happens in 4. 3 ratios of principal stresses. Altindag (2002; 2003) introduced a new method for prediction of the BI by the division of the uniaxial compressive strength (UCS) of the rock to Brazilian tensile strength (BTS). In the late 1960s punch penetration test (PPT) introduced by Handewith (1971) to measure some physical properties of rock sample related to hardness and toughness of rock. Yagiz (2006) stated that the PPT’ s results for measuring the BI have a very high correlation with TBM penetration rate. Although the PPT has very delightful results, application of this test is very expensive and needs much time as well...

An attempt has been made in this paper to investigate the effect of particle size distribution on coal flotation kinetics. The effect of particle size (Ps) on kinetics constant (k) and maximum theoretical flotation recovery (RI) was investigated while other operational parameters were kept constant. The relationship between flotation kinetics constant and theoretical flotation recovery with particle size was estimated with nonlinear equations. Analysis of variance showed that the effect of particle size on the kinetics constant was statistically significant at 95% confidence level. However, it was not significant on maximum theoretical flotation recovery (RI). Different regression methods were conducted in order to model the effect of coal particle size on flotation kinetics. Results indicated that the quadric regression method gave better prediction of the cumulative recovery for different particle size fractions. The correlation coefficient (R2) values of this model were 0.99, 0.996, 0.98, 0.98 and 0.97 for average of particle sizes of 37.5 mm, 112.5 mm, 225 mm, 400 mm and 625 mm respectively.

In a multiple linear regression model, there are instances where one has to update the regression parameters. In such models as new data become available, by adding one row to the design matrix, the least-squares estimates for the parameters must be updated to reflect the impact of the new data. We will modify two existing methods of calculating regression coefficients in multiple linear regression to make the computations more efficient. By resorting to an initial solution, we first employ the Sherman-Morrison formula to update the inverse of the transpose of the design matrix multiplied by the design matrix. We then modify the calculation of the product of the transpose of design matrix and the design matrix by the Cholesky decomposition method to solve the system. Finally, we compare these two modifications by several appropriate examples.

To evaluate the sedimentation ratio of the proposed area of study area to be studied, i.e. the basin of the Jajrud River at the upper level of the Latian dam, the present study has prefered multivariable regerssion regression method has been preferred. Therefore, by this reason, in order to identify the most important physiographic agent which is effective in flooding, flood-debi equation and then debi-sediment for each sub-basin were obtained by applying these factors to the regression model. Reveiwing Reviewing the equations and putting them with the proposed parameters, the maximum flood-debi were was calculated for sub-basins. Consequenlty Consequently, these equations also helped in presenting a suitable way for anticipated flood-debi or the transported sediment loads. Likewise, for sub-basins (Amameh, Kund and Afjeh) whose data were accessible simultaneously with debi-sediment equations for a longer period of time, the transoported transported sediment loads are acquired only when the rive-debi reaches to its peak. The acquired results indicate that that the Ahar sub-basin has the lowest strength of sedimentation and the best option for water closet because of its lengthiest concentration time, high elongation, mild steep steepness and the lowest condensation level.Similarly, the highest strength of sedimentation is related to the Amameh sub-basin, where the sediment production is about 7853.3 tones tons every day. Wider steep of the Steeper and lengthier basins, bigger length, the lowest shorter concentration time and higher condensation could be presented as the other effective factors in this process.

regression is a statistical technique used in finance, investment, and several other domains to assess the magnitude and precision of the association between a dependent variable (often represented as Y) and a set of other factors (referred to as independent variables). This work introduces a linear programming approach for constructing regression models for Neutrosophic data. To achieve this objective, we use the least absolute deviation approach to transform the regression issue into a linear programming problem. Ultimately, the efficacy of the suggested approach in resolving such problems has been shown via the presentation of a concrete illustration.

In the simulated binary crossover, offspring are generated from parents with a coefficient of variation and uses a probability distribution function for the coefficient and there is a linear relationship between parents and offspring. Most existing methods of crossover operators generate offspring on the solution on the decision space during the search and so far, no suggestion has been proposed on making a regression model for generating the offspring on the objective space. In this paper, a Gaussian linear regression crossover has been proposed. The idea is to apply linear regression to model a relationship between parents and offspring in crossover operations through the Gaussian process. The reason for using this process is that the probability distribution of the simulated binary operator is based on the parent in the mating pool on decision space, while the probability distribution of the proposed method is on objective space in the mating pool. To optimize problems on the combinatorial sets, the proposed method is applied. The performance of the proposed algorithm was tested on Computational Expensive Optimization benchmark tests and indicates that the proposed operator is a competitive and promising approach.