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)

A long-standing difficulty for connectionist modeling has been how to represent variable-sized recursive data structures, such as trees and lists, in fixed-width patterns. This paper presents a connectionist architecture which automatically develops compact distributed representations for such compositional structures, as well as efficient accessing mechanisms for them. Patterns which stand for...

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...

Bucketization is the splitting of large amount of data into smaller chunks and storing the parts in different sub servers called buckets. This paper deals with ordered bucketization (OB), which makes use of a random key generator algorithm and a deterministic bucketing algorithm, to propose a secure storage and retrieval system for multimedia files. In OB, plaintext-space is split into a number...

The maximum density still life problem (MDSLP) is a hard constraint optimization problem based on Conway’s game of life. It is a prime example of weighted constrained optimization problem that has been recently tackled in the constraint-programming community. Bucket elimination (BE) is a complete technique commonly used to solve this kind of constraint satisfaction problem. When the memory requ...