This research used modern machine learning ways to predict the stages of primary biliary cholangitis using data from the Mayo Clinic trial. The research aims to obtain high prediction accuracy while representing balanced evaluation metrics. Important techniques include automated hyperparameters optimization with Optuna and Recursive Feature Elimination to improve model performance. Pre-processing included handling missing values, encoding of categorical features, and addressing class imbalances using SMOTE. A total of twelve machine learning algorithms are evaluated with ensemble-based models such as CatBoost and Extra Trees producing much better results. Evaluation metrics take into account all model predictions, including accuracy, precision, recall, F1 score, and ROC-AUC for performing balanced and interpretative evaluations of performances critical for imbalanced datasets. This endeavor includes clinical and laboratory information illustrating the prospect of machine learning in advancing therapeutic diagnosis, emphasizing the rigor and robustness in evaluation laid groundwork for future research to encompass even more generalizable and robust diagnostic tools.

Our main objective is to study some qualitative behavior of the solutions of the difference equation xn+1 = gxn−k + (axn + bxn−k) / (cxn − dxn−k), n = 0, 1, 2, ..., where the initial conditions x−k,..., x−1, x0 are arbitrary positive real numbers and the coefficients, a, b, c and d are positive constants, while k is a positive integer number.

Introduction: P300 speller is a kind of Brain-Computer Interface (BCI) system in which the user may type words by using the responses obtained from human focus on different characters. The high sensitivity of brain signals against noise in parallel with the similarity of responses obtained from the user focus on different characters makes it difficult to classify the characters based on their respective P300 wave. On the other hand, all areas of the brain does not carry useful P300 information. Methods: In this study, a new method is proposed to improve the performance of speller system which is based on selecting optimal P300 channels. In the proposed method, recursive elimination algorithm is presented for channel optimization, which utilizes deep learning concept (e. g. Convolutional Neural Network) as its cost function. The proposed method is examined on a data set from EEG signals recorded in a P300 speller system, including 64 different channels of responses to 29 characters. Then, its performance is compared with some existing methods. Results: The obtained results showed the ability of the proposed method in recognizing the characters in such way that it could accurately (i. e. 97. 34%) detect 29 characters by using only 24 out of all 64 electrodes. Conclusion: Applying the proposed method in speller systems led to considerable improvement in classification of characters compared to its alternatives. Several experiments proved that utilizing the proposed scheme may increases the accuracy almost 12. 9 percent compared to non-optimized case in parallel with reduction of the number of involved channels by approximately 1/3. Based on these results, the proposed method may be considered as an effective choice for application in P300 speller systems, thanks to reduction of the complexity of the system which is caused by the reduced number of channels and, on the other hand, due to its potential in increasing the accuracy of character recognition.

In this paper it has been attempted to investigate the capability of the consumption-based capital asset pricing model (CCAPM), using the general method of moment (GMM), with regard to the Epstien-zin recursive preferences model for Iran's capital market. Generally speaking, recursive utility permits disentangling of the two psychologically separate concepts of risk aversion and elasticity of intertemporal substitution which are constrained to be equal to the inverse of each other for the traditional time-additive utility functions. Rather than using the stock market as a proxy for wealth, we constructed a more comprehensive return which is the weighted average of stock index return, labor wage growth (as a proxy for human capital return), housing return and deposit return. The empirical results demonstrate that the signs of the coefficient of the relative risk aversion and the intertemporal elasticity of substitution are the same, which means that investors have homogeneous attitudes toward the risk across the states of nature and the risk over time in Iran but different ones in their values. Therefore, the assumption that the relative risk aversion is equal to the reciprocal of the elasticity of substitution is not valid in Iran's stock market.

‎Bucket recursive trees are an interesting and natural generalization of recursive trees‎. ‎In this model the nodes are buckets that can hold up to b≥ 1 labels‎. ‎The (modified) Zagreb index of a graph is defined as the sum of‎ ‎the squares of the outdegrees of all vertices in the graph‎. ‎We give the mean and variance of this index in random bucket recursive trees‎. ‎Also‎, ‎two limiting results on this index are given‎.