In this paper we study maximal independent sets in trees without including any leaves. In particular, we determine some small and the largest number of these sets in trees. Extremal trees achieving these values are determined too. Mathematics Subject Classification: 05C35, 05C69, 68R10

The paper reviews special Aronszajn trees, both at ω1 and κ + for an uncountable regular κ. It provides a comprehensive classification of the trees and discusses the existence of these trees under different set-theoretical assumptions. The paper provides details and proofs for many folklore results which circulate (often without a proper proof) in the literature.

In this paper, we apply various data mining techniques including continuous numeric and discrete classification prediction models of base oils biodegradability, with emphasis on improving prediction accuracy. The results show that highly biodegradable oils can be better predicted through numeric models. In contrast, classification models did not uncover a similar dichotomy. With the exception o...

In this paper, we determine the fourth and fifth largest number of maximal independent sets in trees. Also, the extremal trees achieving these value are determined. Mathematics Subject Classification: 05C35, 05C69, 68R10

We prove that the sum of two random trees possesses with high probability a perfect matching and the sum of five random trees possesses with high probability a Hamilton cycle. AMS Subject Classification.(1991) 05C80

Recursive partitioning is the core of several statistical methods including Classification and Regression Trees, Random Forest, and AdaBoost. Despite the popularity of tree based methods, to date, there did not exist methods for combining multiple trees into a single tree, or methods for systematically quantifying the discrepancy between two trees. Taking advantage of the recursive structure in...

In this paper, we compare five tree-based machine learning methods within our recent generic image-classification framework based on random extraction and classification of subwindows. We evaluate them on three publicly available object-recognition datasets (COIL-100, ETH-80, and ZuBuD). Our comparison shows that this general and conceptually simple framework yields good results when combined w...

We developed a multiscale object-based classification method for detecting diseased trees (Japanese Oak Wilt and Japanese Pine Wilt) in high-resolution multispectral satellite imagery. The proposed method involved (1) a hybrid Intensity-Hue-Saturation (IHS)/Smoothing Filter-based Intensity Modulation (SFIM) pansharpening approach 10 (IHS-SFIM) to obtain more spatially and spectrally accurate im...

Nowadays decision tree learning is one of the most popular classification and regression techniques. Though decision trees are not accurate on their own, they make very good base learners for advanced tree-based methods such as random forests and gradient boosted trees. However, applying ensembles of trees deteriorates interpretability of the final model. Another problem is that decision tree l...

It has been recognized that Classification trees (CART) are unstable; a small perturbation in the input variables or a fresh sample can lead to a very different classification tree. Some approaches exist that try to correct this instability. However, their benefits can, at present, be appreciated only qualitatively. A similarity measure between two classification trees is introduced that can me...