Related papers: A binary tree representation for the 2-adic valuat…
We give closed form expressions for the numbers of multi-rooted plane trees with specified degrees of root vertices. This results in an infinite number of integer sequences some of which are known to have an alternative interpretation. We…
We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following…
The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…
We propose a binary representation of categorical values using a linear map. This linear representation preserves the neighborhood structure of categorical values. In the context of evolutionary algorithms, it means that every categorical…
We show that a rational normal scroll can in general be set-theoretically defined by a proper subset of the 2-minors of the associated two-row matrix. This allows us to find a class of rational normal scrolls that are almost set-theoretic…
Random forests are decision tree ensembles that can be used to solve a variety of machine learning problems. However, as the number of trees and their individual size can be large, their decision making process is often incomprehensible. In…
In this paper, we give a simple combinatorial explanation of a formula of A. Postnikov relating bicolored rooted trees to bicolored binary trees. We also present generalized formulas for the number of labeled k-ary trees, rooted labeled…
Arden's Lemma is a classical result in language theory allowing the computation of a rational expression denoting the language recognized by a finite string automaton. In this paper we generalize this important lemma to the rational tree…
Binary phylogenetic trees inferred from biological data are central to understanding the shared history among evolutionary units. However, inferring the placement of latent nodes in a tree is computationally expensive. State-of-the-art…
The aim of this paper is to prove that every non-empty set of valuations centered at a two-dimensional regular domain has an infimum. We also generalize some results related to a non-metric tree.
The Calkin-Wilf tree is an infinite binary tree whose vertices are the positive rational numbers. Each number occurs in the tree exactly once and in the form $a/b$, where are $a$ and $b$ are relatively prime positive integers. For every…
We use the grid consisting of bits of 3^n to motivate the definition of 2-adic numbers. Specifically, we exhibit diagonal stripes in the bits of 3^(2^n), which turn out to be the first in an infinite sequence of such structures. Our…
By weighted tree we understand such connected tree,that: a) each its vertex and each edge have a positive integer weight; b) the weight of each vertex is equal to the sum of weights of outgoing edges. Each tree has a binary structure --- we…
We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…
In this note a simple extension of the complex algebra to higher dimension is proposed. Using the postulated algebra a two dimensional Dirac equation is formulated and its solution is calculated. It is found that there is a sub-algebra…
An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
New invariants for 2-dimensional cell complexes are defined, which can be interpreted as curvature bounds. These invariants are proved to be rational and computable in a companion article. This document is a survey that collects theorems…
Bayesian networks can be used to extract explanations about the observed state of a subset of variables. In this paper, we explicate the desiderata of an explanation and confront them with the concept of explanation proposed by existing…
We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing…