We apply the tree-pattern enumeration formulæ of [7], and a new extension thereof, to some recent enumerations of distributions of leaves in ordered trees [4] and in bicolored ordered trees [5], and of distributions of certain subpaths in Dyck lattice paths [22]. the bridge guard’s bucket upside-down to dry. . . fresh leaves —Issa (1818)

Limit theorems are established for some functionals of the distances between two nodes in weighted random b-ary recursive trees. We consider the depth of the nth node and of a random node, the distance between two random nodes, the internal path length and the Wiener index. As application these limit results imply by an imbedding argument corresponding limit theorems for further classes of rand...

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...

Based on uniform recursive trees, we introduce random trees with the factor of time, which are named Yule recursive trees. The structure and the distance between the vertices in Yule recursive trees are investigated in this paper. For arbitrary time t > 0, we first give the probability that a Yule recursive tree Yt is isomorphic to a given rooted tree γ ; and then prove that the asymptotic dist...

Four sampling methods that included A-Vac, D-Vac, pole-bucket, and beat-net devices were evaluated for estimating relative densities of glassy-winged sharpshooter, Homalodisca vitri-pennis (Germar) (Hemiptera: Cicadellidae) nymphs and adults on citrus (Citrus spp.) trees. All four methods produced similar temporal and spatial distribution profiles, although significant differences in quantities...

We present the results concerning the embedding of trees into recursive circulants. Recursive circulant G(N,:,/) is a circulant graph with N vertices and jumps of powers of d. We present dilation 1 embedding of Fibonacci trees and full quaternaly trees in G(Z”, 2), and full binary trees and hinomial trees in G(2”,4).

3 Querying Encrypted Data 7 3.1 Bucket-Based Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Hash-Based Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 B+ Trees Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.4 Other Approaches . . . . . . . . . . . . ...

We introduce random recursive trees, where deterministically weights are attached to the edges according to the labeling of the trees. We will give a bijection between recursive trees and permutations, which relates the arising edge-weights in recursive trees with inversions of the corresponding permutations. Using this bijection we obtain exact and limiting distribution results for the number ...

We study depth properties of a general class of random recursive trees where each node i attaches to the random node biXic and X0, . . . , Xn is a sequence of i.i.d. random variables taking values in [0, 1). We call such trees scaled attachment random recursive trees (sarrt). We prove that the height Hn of a sarrt is asymptotically given by Hn ∼ αmax logn where αmax is a constant depending only...