We investigate extremal statistical properties such as the maximal and the minimal heights of randomly generated binary trees. By analyzing the master evolution equations we show that the cumulative distribution of extremal heights approaches a traveling wave form. The wave front in the minimal case is governed by the small-extremal-height tail of the distribution, and conversely, the front in ...

It has been shown that height measurements obtained by airborne laser scanning (ALS) with high point density (>7–8 m ́2) can be used to detect small trees in the alpine tree line—an ecotone sensitive to climate change. Because the height measurements do not discriminate between trees and other convex structures with positive height values, this study aimed at assessing the contribution of ALS ba...

Inspired by the results of Baik, Deift and Johansson on the limiting distribution of the lengths of the longest increasing subsequences in random permutations, we find those limiting distributions for pattern-restricted permutations in which the pattern is any one of the six patterns of length 3. We show that the (132)-avoiding case is identical to the distribution of heights of ordered trees, ...

investigation on structure and dynamics of natural forest ecosystems is an important issue for silvicultural decisions. the aim of this study is to analysis dynamics and structure of a beech stand during 5-year period in the shast kalateh forest in the caspian region, north of iran. data were collected from a 16.9ha permanent research plot established in a natural unlogged stand in 2006. all li...

This paper is a rst step towards an understanding of the inherent limitations of distributed data structures. We propose a model of distributed search trees that is based on few natural assumptions. We prove that any class of trees within our model satis es a lower bound of (pm) on the worst case height of distributed search trees for m keys. That is, unlike in the single site case, balance in ...

The purpose of this paper is to compare major models for height estimation of Picea orientalis L trees based on the individual tree diameter and certain other stand variables. The data were collected from 440 trees of pure and even-aged P. orientalis stands that are located near Artvin in the northeastern part of Turkey. The data from 406 trees were used for model development and the remaining ...

Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached parent chosen randomly proportionally its weight. Under some assumptions on the sequence of weights, first order for height such has been recently established one authors. In this paper, we obtain second and third orders in asymptotic expansion weighted trees, und...