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International Journal of Mathematics and Mathematical Sciences, 2005 The number of local maxima (resp., local minima) in a tree T∈𝒯n rooted at r∈[n] is denoted by Mr(T) (resp., by mr(T)). We find exact formulas as rational functions of n for the expectation and variance of M1(T) and mn(T) when T∈𝒯n is chosen randomly ...
Lane Clark
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Spatial patterns and intra-specific competition of Chestnut-leaved oak (Quercus castaneifolia C. A. Mey.) using O- ring statistic (Case study: Neka Forest, Iran) [PDF]
تحقیقات جنگل و صنوبر ایران, 2015 The spatial patterns of trees in different stages of their life provide important information related to forest regeneration and succession processes.
Farideh Omidvar Hosseini +3 more
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Extremal properties of random trees
, 2001 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
Ben-Naim, E. +2 more
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Rooted trees and moments of large sparse random matrices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2003 In these expository paper we describe the role of the rooted trees as a base for convenient tools in studies ofrandom matrices. Regarding the Wigner ensemble of random matrices, we represent main ingredients ofthis approach.
Oleksiy Khorunzhiy
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Packing and Hausdorff measures of stable trees [PDF]
, 2010 In this paper we discuss Hausdorff and packing measures of random continuous trees called stable trees. Stable trees form a specific class of L\'evy trees (introduced by Le Gall and Le Jan in 1998) that contains Aldous's continuum random tree (1991 ...
A Berlinkov +35 more
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Random environment on coloured trees
, 2007 In this paper, we study a regular rooted coloured tree with random labels assigned to its edges, where the distribution of the label assigned to an edge depends on the colours of its endpoints.
Menshikov, Mikhail +2 more
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Finding Rumor Sources on Random Trees [PDF]
, 2015 We consider the problem of detecting the source of a rumor which has spread in a network using only observations about which set of nodes are infected with the rumor and with no information as to \emph{when} these nodes became infected.
Shah, Devavrat, Zaman, Tauhid
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Random hyperplane search trees in high dimensions
Journal of Computational Geometry, 2015 Given a set S of n ≥ d points in general position in Rd, a random hyperplane split is obtained by sampling d points uniformly at random without replacement from S and splitting based on their affine hull. A random hyperplane search tree is a binary space
Luc Devroye, James King
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Predicting the Pillar Stability of Underground Mines with Random Trees and C4.5 Decision Trees
Applied Sciences, 2020 Predicting pillar stability in underground mines is a critical problem because the instability of the pillar can cause large-scale collapse hazards. To predict the pillar stability for underground coal and stone mines, two new models (random tree and C4 ...
Mahmood Ahmad +5 more
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