Related papers: Mutation effects in ordered trees
The notion of transducer integer sequences is considered through a series of examples. By definition, transducer integer sequences are integer sequences produced, under a suitable interpretation, by finite automata encoding tree morphisms…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of…
In this manuscript we study how the vertex energy of a tree is affected when joined with a bipartite graph. We find an alternating pattern with respect to the coalescence vertex: the energy decreases for vertices located at odd distances…
Often machine learning methods are applied and results reported in cases where there is little to no information concerning accuracy of the output. Simply because a computer program returns a result does not insure its validity. If…
Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…
Baxter permutations are known to be in bijection with a wide number of combinatorial objects. Previously, it was shown that each of these objects had a natural involution which was carried equivariantly by the known bijections, and the…
Periodic trees are combinatorial structures which are in bijection with cluster tilting objects in cluster categories of affine type $\tilde{A}_{n-1}$. The internal edges of the tree encode the $c$-vectors corresponding to the cluster…
We introduce and study a new notion of patterns in Stirling and $k$-Stirling permutations, which we call block patterns. We prove a general result which allows us to compute generating functions for the occurrences of various block patterns…
The in-order traversal provides a natural correspondence between binary trees with a decreasing vertex labeling and endofunctions on a finite set. By suitably restricting the vertex labeling we arrive at a class of trees that we call…
The way a field transforms under rotations determines its statistics--as is easy to see for scalar, Dirac, and vector fields.
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
A method for creating a forest of model trees to fit samples of a function defined on images is described in several steps: down-sampling the images, determining a tree's hyperplanes, applying convolutions to the hyperplanes to handle small…
The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we…
This paper investigates some properties of the number of subtrees of a tree with given degree sequence. These results are used to characterize trees with the given degree sequence that have the largest number of subtrees, which generalizes…
Existing works have studied the impacts of the order of words within natural text. They usually analyze it by destroying the original order of words to create a scrambled sequence, and then comparing the models' performance between the…
Let $T$ be a tree on $n$ vertices. We can regard the edges of $T$ as transpositions of the vertex set; their product (in any order) is a cyclic permutation. All possible cyclic permutations arise (each exactly once) if and only if the tree…
Given a set $Y$ of decreasing plane trees and a permutation $\pi$, how many trees in $Y$ have $\pi$ as their postorder? Using combinatorial and geometric constructions, we provide a method for answering this question for certain sets $Y$…
In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…
A Multinomial Processing Tree (MPT) is a directed tree with a probability associated with each arc. Here we consider an additional parameter associated with each arc, a measure such as the time required to select the arc. MPTs are often…