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.

Aims Karun River, which is the largest river in Iran, represents a unique ecosystem. However, increased anthropogenic activities result in the formation of this river is seriously affected by a large range of pollutants especially the heavy metal pollutants which may be toxic to human and aquatic fauna. Therefore, there is a need for continuous monitoring of pollution levels in the river. Materials & Methods In this study, water, sediment, and algae samples were collected from six different stations along the course of the river in September 2015 to investigate the quality of Karun’ s River in terms of heavy metals (Pb, Zn, Cr, and Cd) at the basin of drinking water treatment in Ahwaz and Mollasani cities. After drying and digestion of samples, heavy metal concentrations were determined using an atomic absorption spectrophotometry (Perkin Elmer-Analyst 300). Findings The highest concentration of trace metals was found in sediment samples with Zn having the highest mean concentration values in all stations. The heavy metal concentrations in the downstream indicated an increase in the pollution load due to the flow of water from upstream to downstream of the river resulted in the movement and accumulation of all contaminants to the river in the downstream; hence, there was the highest concentration of metals in basin of the Kut Abdollah treatment (downstream) and the lowest in Mollasani (upstream). Conclusion Comparison of the concentration of metals in the sediments with some universal standards including EPA3050 and the criterion of sediments quality standard from NOAA and Canadian Environment Agency showed that the concentration of chromium and cadmium in stations was higher than the allowable limit of EPA3050 standards and some environmental standards of Canada among all metals. Since algae samples have been able to accumulate a significant amount of heavy metals, therefore, these are suitable bio-indicators to determine the concentration of heavy metals in this aquatic ecosystems.

The objective of this study was to develop a forecast model to determine the rate of generation of municipal solid waste in the municipalities of the Cuenca del Cañ ó n del Sumidero, Chiapas, Mexico. MULTIPLE LINEAR REGRESSION was used with social and demographic explanatory variables. The compiled database consisted of 9 variables with 118 specific data per variable, which were analyzed using a multicolLINEARity test to select the most important ones. Initially, different REGRESSION models were generated, but only 2 of them were considered useful, because they used few predictors that were statistically significant. The most important variables to predict the rate of waste generation in the study area were the population of each municipality, the migration and the population density. Although other variables, such as daily per capita income and average schooling are very important, they do not seem to have an effect on the response variable in this study. The model with the highest parsimony resulted in an adjusted coefficient of 0. 975, an average absolute percentage error of 7. 70, an average absolute deviation of 0. 16 and an average root square error of 0. 19, showing a high influence on the phenomenon studied and a good predictive capacity.

This study presents some mathematical methods for estimating the critical properties of 40 different types of alkanes and their derivatives including critical temperature, critical pressure and critical volume. This algorithm used QSPR modeling based on graph theory, several structural indices, and geometric descriptors of chemical compounds. MULTIPLE LINEAR REGRESSION was used to estimate the correlation between these critical properties and molecular descriptors using proper coefficients. To achieve this aim, the most appropriate molecular descriptors were chosen from among 11 structural and geometric descriptors in order to determine the critical properties of the intended molecules. The results showed that among all the proposed models to predict critical temperature, pressure and volume, a model including the combination of such descriptors as hyper-Wiener, Platt, MinZL is the most appropriate one.

Extended AbstractBackground and ObjectivesArtificial intelligence models as powerful methods in modeling nonLINEAR complex problems, have a significant ability and this has been proven in numerous articles. Artificial intelligence has been used in various issues, including engineering, medicine, etc. The success of this method in comparison with analytical and numerical methods, their easiness, speed and accuracy caused to open their place among researchers as much as possible. Today, Considering that one of the challenges of human life is the issues related to water resources management, so in this study, an attempt has been made to investigate the performance of artificial intelligence and REGRESSION models in the cases of water resources. Various researches have been done in the case of modeling and parametric analysis of water resources. However, in this study, artificial intelligence (Learning Machine) models were used to simulate the qualitative and quantitative parameters of water. The models used in this study are: Self-Adapting Extreme Learning Machine (SAELM), Least Square Support Vector Machine (LSSVR), Adaptive Neuro Fuzzy Inference System (ANFIS) and MULTIPLE LINEAR REGRESSION (MLR) model which was used to predict changes in hydrogeological parameters. Today, due to the growing global population, one of the most important challenges is access to safe drinking water. In our country, Iran, due to its location in the semi-arid region and low rainfall, this danger is felt more than ever. One of the serious issues is the salinity leakage into groundwater resources. In this study, an attempt has been made to simulate the leakage of salinity dynamic flow into the freshwater resources of the coastal aquifer, using artificial intelligence and statistical models. At the end, the simulation results and the accuracy of the models are given. The study area in this work, is Mighan Wetland and Mighan aquifer in Markazi province. Annual rainfall occurs in small amounts in this area. According to the statistical results provided by synoptic and rain gauge stations in the region, the maximum and minimum rainfall values range from 461 mm in the northeast to 208 mm in the center of Arak plain. The hydraulic outlet of the aquifer to the Mighan plain is located in the center of the plain. The water entering the Mighan plain and leaves the system due to evaporation from the water table. Observatory wells were used to sampling this lake due to its saline water. The wells were located in an area called Vismeh near the lake.MethodologyIn this study, qualitative and quantitative parameters: water salinity, total dissolved solids (TDS), chlorine ion (cl), sampling time (t), electrical conductivity (EC), Salinity and groundwater level (GWL) were simulated. In this work, Adaptive Neuro Fuzzy Inference System (ANFIS), Least square support vector machine (LSSVM), Self Adaptive Extreme learning machine (SAELM) and MULTIPLE LINEAR REGRESSION (MLR) models were used for simulation. In this study, data from 173 months of sampling were used. 70% of the sample size was used for training and 30% for testing models.FindingsSimulation was performed using artificial intelligence models and REGRESSION model. The simulation results showed higher accuracy of artificial intelligence models. After simulation and obtaining the results, then the uncertainty analysis was performed by Wilson Score method without continuity correction. In this method, the prediction error (ei), the mean prediction error (Mean) and the standard deviation of the error is (Se). If the mean error value of a model in predicting the target variable is positive, it means that the performance of the model is Over Estimated. Also, if the average value of the model error is negative, the performance of the model is Under Estimated. Moreover, the results of Uncertainty Analysis with a significance of 5% were obtained. and finally we briefly write the subsequent performance Over Estimated (OS) and Under Estimated (US).ConclusionsThe results showed that different models were successful in predicting water parameters. In order to comprehensively evaluate the accuracy of the models in the simulation, the performance of the models was measured by five approaches. The proposed approaches were: 1) Evaluation of prediction by accuracy chart, 2) Performance evaluation by mathematical indices, 3) Performance evaluation, by Uncertainty Analysis by Wilson Score method without continuity correction, 4) Accuracy evaluation by error distribution charts and 5) Performance evaluation by discrepancy rate (DR) charts. Finally, all the results are given at the end of each section, respectively.Approach 1- According to the prediction accuracy charts, 16 charts were drawn and the most accurate models of which are depicted in Figures 4 to 7. After modeling, the results showed that the most accurate models in simulating groundwater parameters were SAELM model in GWL simulation. According to the results, SAELM model in GWL and EC simulation, LSSVM in TDS simulation and MLR in Salinity simulation were the superior midel, Respectively.Approach 2- According to the performance measurement indices, finally the results showed that SAELM model was the best model in simulating parameters (EC) and (GWL). The LSSVM model was also the most accurate model in modeling (TDS). MLR model was the best model in (Salinity) parameter simulation.Approach 3- Uncertainty analysis was performed based on Wilson score method. The performance of the models in the simulation showed that the performance of the SAELM model was determined as Under estimated and other superior models in simulation had Over estimated performance.Approach 4- Based on the error distribution diagrams, the best accuracy was assigned to SAELM and MLR models.Approach 5- Based on the discrepancy ratio, SAELM and MLR models were estimated to be the most accurate models in the simulation.

This paper describes 3D-QSAR analysis and biological evaluation of 1, 5- benzodiazepine analogues. Benzodiazepine nucleus with its simple structure gives a good opportunity for further modification regarding an increase of its antimicrobial activity.We synthesized a series of benzodiazepine analogues from condensation of various chalcones and halo substituted o-phenelynene diamines. All compounds were assayed in vitro against, E. coli, P. aeruginosa, S. aureus. The models were generated on the Vlife MDS 3.5; selected models showed a correlation coefficient (r2) above 0.9 with cross-validated correlation coefficient (q2) above 0.8, respectively, for all the selected organisms. The 3D-QSAR models generated were externally validated for all models using a test set of 6 molecules for which the predictive r 2 (r2 -pred) was found to be above 0.45. The results of 3D-QSAR indicate that contours can be used to design some potent antibacterial agents.

Introduction: Soil aggregate stability is a key factor in soil resistivity to mechanical stresses, including theimpacts of rainfall and surface runoff, and thus to water erosion (Canasveras et al., 2010). Various indicatorshave been proposed to characterize and quantify soil aggregate stability, for example percentage of water-stableaggregates (WSA), mean weight diameter (MWD), geometric mean diameter (GMD) of aggregates, and waterdispersible clay (WDC) content (Calero et al., 2008). Unfortunately, the experimental methods available todetermine these indicators are laborious, time-consuming and difficult to standardize (Canasveras et al., 2010).Therefore, it would be advantageous if aggregate stability could be predicted indirectly from more easilyavailable data (Besalatpour et al., 2014). The main objective of this study is to investigate the potential use ofsupport vector machines (SVMs) method for estimating soil aggregate stability (as quantified by GMD) ascompared to MULTIPLE LINEAR REGRESSION approach.Materials and Methods: The study area was part of the Bazoft watershed (31o37′ to 32o39′ N and 49o34′to 50o32′ E), which is located in the Northern part of the Karun river basin in central Iran. A total of 160 soilsamples were collected from the top 5 cm of soil surface. Some easily available characteristics includingtopographic, vegetation, and soil properties were used as inputs. Soil organic matter (SOM) content wasdetermined by the Walkley-Black method (Nelson & Sommers, 1986). Particle size distribution in the soilsamples (clay, silt, sand, fine sand, and very fine sand) were measured using the procedure described by Gee & Bauder (1986) and calcium carbonate equivalent (CCE) content was determined by the back-titration method (Nelson, 1982). The modified Kemper & Rosenau (1986) method was used to determine wet-aggregate stability (GMD). The topographic attributes of elevation, slope, and aspect were characterized using a 20-m by 20-mdigital elevation model (DEM). The data set was divided into two subsets of training and testing. The trainingsubset was randomly chosen from 70% of the total set of the data and the remaining samples (30% of the data) were used as the testing set. The correlation coefficient (r), mean square error (MSE), and error percentage (ERROR%) between the measured and the predicted GMD values were used to evaluate the performance of themodels.Results and Discussion: The description statistics showed that there was little variability in the sampledistributions of the variables used in this study to develop the GMD prediction models, indicating that theirvalues were all normally distributed. The constructed SVM model had better performance in predicting GMDcompared to the traditional MULTIPLE LINEAR REGRESSION model. The obtained MSE and r values for the developedSVM model for soil aggregate stability prediction were 0.005 and 0.86, respectively. The obtained ERROR%value for soil aggregate stability prediction using the SVM model was 10.7% while it was 15.7% for theREGRESSION model. The scatter plot figures also showed that the SVM model was more accurate in GMDestimation than the MLR model, since the predicted GMD values were closer in agreement with the measuredvalues for most of the samples. The worse performance of the MLR model might be due to the larger amount ofdata that is required for developing a sustainable REGRESSION model compared to intelligent systems. Furthermore, only the LINEAR effects of the predictors on the dependent variable can be extracted by LINEAR models while inmany cases the effects may not be LINEAR in nature. Meanwhile, the SVM model is suitable for modellingnonLINEAR relationships and its major advantage is that the method can be developed without knowing the exactform of the analytical function on which the model should be built. All these indicate that the SVM approachwould be a better choice for predicting soil aggregate stability.Conclusion: The pixel-scale soil aggregate stability predicted that using the developed SVM and MLRmodels demonstrates the usefulness of incorporating topographic and vegetation information along with the soilproperties as predictors. However, the SVM model achieved more accuracy in predicting soil aggregate stabilitycompared to the MLR model. Therefore, it appears that support vector machines can be used for prediction of some soil physical properties such as geometric mean diameter of soil aggregates in the study area. Furthermore, despite the high predictive accuracy of the SVM method compared to the MLR technique which was confirmedby the obtained results in the current study, the advantages of the SVM method such as its intrinsic effectivenesswith respect to traditional prediction methods, less effort in setting up the control parameters for architecture design, the possibility of solving the learning problem according to constrained quadratic programming methods, etc., should motivate soil scientists to work on it further in the future.

A methodology for characterizing ground water quality of watersheds using hydrochemical data that mingle MULTIPLE LINEAR REGRESSION and structural equation modeling is presented. The aim of this work is to analyze hydrochemical data in order to explore the compositional of phreatic aquifer groundwater samples and the origin of water mineralization, using mathematical method and modeling, in Maknassy Basin, central Tunisia). Principal component analysis is used to determine the sources of variation between parameters. These components show that the variations within the dataset are related to variation in sulfuric acid and bicarbonate, sodium and cloride, calcium and magnesium which are derived from water-rock interaction. Thus, an equation is explored for the sampled ground water. Using Amos software, the structural equation modeling allows, to test in simultaneous analysis the entire system of variables (sodium, magnesium, sulfat, bicarbonate, cloride, calcium), in order to determine the extent to which it is consistent with the data. For this purpose, it should investigate simultaneously the interactions between the different components of ground water and their relationship with total dissolved solids. The integrated result provides a method to characterize ground water quality using statistical analyses and modeling of hydrochemical data in Maknassy basin to explain the ground water chemistry origin.