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  Stochastic models such as mixture models, graphical models, Markov random fields and hidden Markov models have key role in probabilistic data analysis. In this paper, we have learned Gaussian mixture model to the pixels of an image. The parameters of the model have estimated by EM-algorithm.

  In addition pixel labeling corresponded to each pixel of true image is made by Bayes rule. In fact, we introduce a new numerically method of finding maximum a posterior estimation by using EM-algorithm and Gaussians mixture distribution. In this algorithm, we have made a sequence of priors, posteriors and they converge to a posterior probability that is called the reference posterior probability. Maximum a posterior estimated can determine by the reference posterior probability that will make labeled image. This labeled image shows our segmented image with reduced noises. We show this method in several experiments.

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In this paper, a novel data driven approach for improving the performance of wastewater management and pumping system is proposed, which is getting knowledge from data mining methods as the input parameters of optimization problem to be solved in nonlinear programming environment. As the first step, we used CART classifier decision tree to classify the operation mode -number of active pumps- based on the historical data of the Austin-Texas infrastructure. Then SOM is applied for clustering customers and selecting the most important features that might have effect on consumption pattern. Furthermore, the extracted features will be fed to Levenberg-Marquardt (LM) neural network which will predict the required outflow rate of the period for each operation mode, classified by CART. The result show that F-measure of the prediction is 90%, 88%, 84% for each operation mode 1,2,3, respectively. Finally, the nonlinear optimization problem is developed based on the data and features extracted from previous steps, and it is solved by artificial immune algorithm. We have compared the result of the optimization model with observed data, and it shows that our model can save up to 2%-8% of outflow rate and wastewater, which is significant improvement in the performance of pumping system.

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Given the increasing human need for health systems and the costs of using such systems, the problem of optimizing health-related systems has attracted the attention of many researchers. One of the most critical cases in this area is the operating room scheduling. Much of the cost of health systems is related to operating room costs. Therefore, planning and scheduling of operating rooms can play an essential role in increasing the efficiency of health systems as well as reducing costs. Given the uncertain factors involved in such matters, attention to uncertainty in this problem is one of the most critical factors in the results. In this study, the problem of the daily scheduling of the operating room with uncertain surgical time was investigated. For minimizing overhead costs and maximizing the number of surgeries to reduce patients' waiting time, after introducing a mathematical model, a chance-constrained programming approach is used to deal with its uncertainty. In this study, also, a harmony search algorithm is proposed to solve the model because of its NP-Hardness. By performing the numerical analysis and comparing the presented algorithm result with a genetic algorithm, the results show that the proposed algorithm has a better performance.

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