Related papers: Assigned rational functions of a rooted tree
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.
In this paper, we study functions of the roots of a univariate polynomial in which the roots have a given multiplicity structure $\mu$. Traditionally, root functions are studied via the theory of symmetric polynomials; we extend this theory…
To every automorphism w of an infinite rooted regular binary tree we associate a two variable generating function \Phi_w that encodes information on the orbit structure of w. We prove that this is a rational function if w can be described…
We apply the concept of parking functions to rooted labelled trees and functional digraphs of mappings (i.e., functions $f : [n] \to [n]$) by considering the nodes as parking spaces and the directed edges as one-way streets: Each driver has…
We show that a weighted shift on a directed tree is related to a multiplier algebra of coefficients of analytic functions. We use this relation to study spectral properties of the operators in question.
Representing a signal as a linear combination of a set of basis functions is central in a wide range of applications, such as approximation, de-noising, compression, shape correspondence and comparison. In this context, our paper addresses…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
We tackle the problem of building explainable recommendation systems that are based on a per-user decision tree, with decision rules that are based on single attribute values. We build the trees by applying learned regression functions to…
A landmark result from rational approximation theory states that $x^{1/p}$ on $[0,1]$ can be approximated by a type-$(n,n)$ rational function with root-exponential accuracy. Motivated by the recursive optimality property of Zolotarev…
A grounded M-Lipschitz function on a rooted d-ary tree is an integer-valued map on the vertices that changes by at most along edges and attains the value zero on the leaves. We study the behavior of such functions, specifically, their…
A phylogenetic tree shows the evolutionary relationships among species. Internal nodes of the tree represent speciation events and leaf nodes correspond to species. A goal of phylogenetics is to combine such trees into larger trees, called…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…
Heterogeneous Robot Teams can provide a wide range of capabilities and therefore significant benefits when handling a mission. However, they also require new approaches to capability and mission definition that are not only suitable to…
In this paper, we study merge trees induced by a discrete Morse function on a tree. Given a discrete Morse function, we provide a method to constructing an induced merge tree and define a new notion of equivalence of discrete Morse…
The classical matrix tree theorem relates the number of spanning trees of a connected graph with the product of the nonzero eigenvalues of its Laplacian matrix. The class of regular matroids generalizes that of graphical matroids, and a…
The theme of this article is the algebraic combinatorics of leaf-labeled rooted binary trees and forests of such trees. The structure of a Hopf operad is defined on the vector spaces spanned by forests of leaf-labeled, rooted, binary trees.…
We investigate the randomized decision tree complexity of a specific class of read-once threshold functions. A read-once threshold formula can be defined by a rooted tree, every internal node of which is labeled by a threshold function…
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…
Functions with singularities are notoriously difficult to approximate with conventional approximation schemes. In computational applications, they are often resolved with low-order piecewise polynomials, multilevel schemes, or other types…