Vertices Of Tree Research Articles

On the number of terminal vertices in certain random trees with an application to stemma construction in philology

A fundamental task of philologists is to construct the family tree (stemma) of preserved copies of ancient manuscripts. A simple probabilistic model based on random rooted trees is proposed to assist in the identification of the number of terminal copies. The model provides the distribution of the number of terminal vertices in a random tree. An application to stemma construction is given.

On the number of terminal vertices in certain random trees with an application to stemma construction in philology

A fundamental task of philologists is to construct the family tree (stemma) of preserved copies of ancient manuscripts. A simple probabilistic model based on random rooted trees is proposed to assist in the identification of the number of terminal copies. The model provides the distribution of the number of terminal vertices in a random tree. An application to stemma construction is given.

Locating the vertices of a steiner tree in an arbitrary metric space

Given a tree each of whose terminal vertices is associated with a given point in a compact metric space, the problem is to optimally associate a point in this space to each nonterminal vertex of the tree. The optimality criterion is the minimization of the sum of the lengths, in the metric space, over all edges of the tree. This note shows how a dynamic programming solution to this problem generalizes a number of previously published algorithms in diverse metric spaces, each of which has direct and significant applications to biological systematics or evolutionary theory.

A syntax directed macro processor

A syntax directed translator, developed by extending Strachey's GPM, is described. The semantic input to the translator consists of strings which are attached to vertices of derivation trees of sentences of context-free languages. These strings may contain macro calls which control the translator and its output. The translator may be used for compilation and for some symbol manipulation problems. Some practical as well as theoretical possibilities of this approach are discussed.

Noise in two-way cable-communications systems

Equations for determining the reverse direction noise are provided. This noise results in a reduction of the system signal-to-noise ratio in the forward direction. The resulting correction term describes the reduction and is a function of the type and number of vertices in the system tree.

Locating vertices of trees.

Locating vertices of trees.

On ordering vertices of infinite trees

On ordering vertices of infinite trees

On a certain ordering of the vertices of a tree

On a certain ordering of the vertices of a tree