Related papers: Mutation effects in ordered trees
An evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species. Evolutionary trees are useful for modeling the evolutionary history of…
We model evolution of plants in a world, made up of different locations, with multiple environments (mutually exclusive and collectively exhaustive subsets of locations). Each environment (landmass) has temperature, rainfall, and other…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
We begin a systematic study of the enumerative combinatorics of mixed succession rules, which are succession rules such that, in the associated generating tree, the nodes are allowed to produce their sons at several different levels…
We consider a multitype Galton-Watson process that allows for the mutation and reversion of individual types in discrete and continuous time. In this setting, we explicitly compute the time evolution of quantities such as the mean and…
The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have a definable choice function (by a monadic formula with…
In binary and ordinal regression one can distinguish between a location component and a scaling component. While the former determines the location within the range of the response categories, the scaling indicates variance heterogeneity.…
We study tree-to-tree transformations that can be defined in first-order logic or monadic second-order logic. We prove a decomposition theorem, which shows that every transformation can be obtained from prime transformations, such as…
The Transformed-Transformer family of distributions are the resulting family of distributions as transformed from a random variable $T$ through another transformer random variable $X$ using a weight function $\omega$ of the cumulative…
Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…
The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…
We study the dynamical behaviour of weighted shifts defined on sequence spaces of a directed tree. In particular, we characterize their boundedness as well as when they are hypercyclic, weakly mixing and mixing.
One of the first beings affected by changes in the climate are trees, one of our most vital resources. In this study tree species interaction and the response to climate in different ecological environments is observed by applying a joint…
A new family of tree models is proposed, which we call "differential trees." A differential tree model is constructed from multiple data sets and aims to detect distributional differences between them. The new methodology differs from the…
We consider so-called simple families of labelled trees, which contain, e.g., ordered, unordered, binary and cyclic labelled trees as special instances, and study the global and local behaviour of the number of inversions. In particular we…
In a rooted tree, we call a vertex {\em balanced} if it is at equal distance from all its descendant leaves. We count balanced vertices in three different tree varieties. For decreasing binary trees, we can prove that the probability that a…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
We discuss a notion of shuffle for trees which extends the usual notion of a shuffle for two natural numbers. We give several equivalent descriptions, and prove some algebraic and combinatorial properties. In addition, we characterize…
In this paper we give an ordinal analysis of the theory of second order arithmetic. We do this by working with proof trees -- that is, "deductions" which may not be well-founded. Working in a suitable theory, we are able to represent…
We introduce mutations in replication systems in which the intact copying mechanism is performed by discrete iterations of a complex quadratic map in the family $f_c(z) = z^2+c$. More specifically, we consider a "correct" function $f_{c_1}$…