The purpose of this article is to survey recent results on distributional properties of RANDOM binary search TREES. In particular we consider the profile and the height.

In this work, we calculate the limit distribution of the total cost incurred by splitting a tree selected at RANDOM from the set of all finite free TREES. This total cost is considered to be an additive functional induced by a toll equal to the square of the size of tree. The main tools used are the recent results connecting the asymptotics of generating functions with the asymptotics of their Hadamard product, and the method of moments.

We study the limiting distribution of the degree of a given node in a scaled attachment RANDOM recursive tree, a generalized RANDOM recursive tree, which is introduced by Devroye et. al (2011). In a scaled attachment RANDOM recursive tree, every node i is attached to the node labeled [iXi] where X0,…, Xn is a sequence of i.i.d. RANDOM variables, with support in [0, 1) and distribution function F. By imposing a condition on F, we show that the degree of a given node is asymptotically normal.

The main goal of this paper is to study the modified $F$-indices (modified first Zagreb index and modified forgotten topological index) of RANDOM $m$-oriented recursive TREES (RMORTs). First, through two recurrence equations, we compute the mean and the variance of these indices in our RANDOM tree model. Second, we show four convergence in probability based on these indices. Third, the asymptotic normalities, through the martingale central limit theorem, are given.

This paper reviews Polya urn models and their connection to RANDOM TREES. Basic results are presented, together with proofs that underly the historical evolution of the accompanying thought process. Extensions and generalizations are given according to chronology: • Polya-Eggenberger’s urn• Bernard Friedman’s urn• Generalized Polya urns• Extended urn schemes• Invertible urn schemesConnections to RANDOM TREES are surveyed. Numerous applications to TREES common in computer science are discussed, including:• Binary search TREES• Fringe-balanced TREES• m-ary search TREES• 2–3 TREES• Paged binary TREES• Bucket quad TREES• Bucket k–d TREESThe applications also include various types of recursive TREES:• Standard recursive TREES• Pyramids• Plane-oriented recursive TREES• Phylogenetic TREES• Bucket recursive TREES• SproutsLimit distributions, and phase changes therein are presented within the unifying theme of Polya urn models.

‎For a simple graph G‎, ‎the Gordon-Scantlebury index of G is equal to the number of paths of length two in G‎, ‎and the Platt index is equal to the total sum of the degrees of all edges in G‎. ‎In this paper‎, ‎we study these indices in RANDOM plane-oriented recursive TREES through a recurrence equation for the first Zagreb index‎. ‎As n ∊ ∞, ‎the asymptotic normality of these indices are given‎.

Statistical arbitrage is a common investing strategy in inefficient markets which is market neutral and profits from both sides of the market without the need for initial capital. This research aims at designing suitable models for stock statistical arbitrage using deep neural network, RANDOM forest, gradient-boosted TREES and equal-weighted ensemble of these methods whilst analyzes the returns and risks of the designed models. For this purpose, the information of all listed companies in Tehran Stock Exchange from 1385 until 1396 has been used to generate trading signals. The design of the research models and required coding also the testing of the research hypotheses which is analyzed by t-test were performed in R software. The research findings show that the highest daily return is 4. 24% for k = 5 (prior transaction costs) which is for the simple equal-weighted ensemble (ENS). Also deep neural network (DNN) has the lowest value at risk (-4. 45%) and the lowest expected shortfall (-5. 57%) for k = 20. The highest value of the return to standard deviation ratio is 1. 072 which belongs to the RAF model for k = 20. Moreover, research results show that recent returns have higher predictive power than previous returns.

This study aims to employ supervised Advanced machine learning for the classification of lithological facies from geophysical log data in wells without drilling core samples. For this purpose, a dataset from seven wells in a training set from one of the oil fields in southern Iran has been utilized. This dataset includes natural gamma ray (SGR), corrected gamma ray (CGR), bulk density (RHOB), neutron porosity (NPHI), compressional wave slowness (DTSM), and shear wave slowness (DTCO), which directly influence the classification of geomechanical facies. These parameters are employed as independent variables, while lithological facies serve as the dependent variable for classification. This dataset pertains to depths ranging from 3000 to 4000 meters in the Ilam and Sarvak fractured limestone formations (Bangestan Limestone) of the subsurface. As the title suggests in this article, Initially, through artificial intelligence clustering methods and laboratory studies, these formations were categorized into five distinct lithological facies After this stage, eight supervised machine learning methods were employed, including Regression Logistic, K Neighbors Classifier, Decision Tree Classifier, RANDOM Forest Classifier, Gaussian NB, Gradient Boosting Classifier, Extra TREES Classifier, and Support Vector Machine (SVM), to predict lithological facies in wells without existing classifications. The dataset of these wells underwent training and testing stages with each of these algorithms to construct an appropriate model. As a result, facies labels were predicted. The performance of the models was evaluated using multiple metrics including Accuracy, Precision, F1-Score, and Recall through confusion matrices and ROC curves. The Extra TREES Classifier, Gradient Boosting Classifier, and K Neighbors Classifier showed superior results among these methods. Finally, the model's performance in predicting lithological facies of unseen or out-of-sample wells was presented.