相关论文: Generating functions for generating trees

We consider stochastic processes indexed by the vertices of an infinite binary tree having a simple recursive structure. The value at any vertex is some fixed function of the values at the two daughter vertices together with some…

Existing ordinal trees and random forests typically use scores that are assigned to the ordered categories, which implies that a higher scale level is used. Versions of ordinal trees are proposed that take the scale level seriously and…

Motivated by the question of how macromolecules assemble, the notion of an {\it assembly tree} of a graph is introduced. Given a graph $G$, the paper is concerned with enumerating the number of assembly trees of $G$, a problem that applies…

We consider simply generated trees and study multiplicative functions on rooted plane trees. We show that the associated generating functions satisfy differential equations or difference equations. Our approach considers B-series from…

We propose a method for generating explainable rule sets from tree-ensemble learners using Answer Set Programming (ASP). To this end, we adopt a decompositional approach where the split structures of the base decision trees are exploited in…

Deep generative models are able to suggest new organic molecules by generating strings, trees, and graphs representing their structure. While such models allow one to generate molecules with desirable properties, they give no guarantees…

We develop a nonstandard approach to exploring polynomials associated with peaks and runs of permutations. With the aid of a context-free grammar, or a set of substitution rules, one can perform a symbolic calculus, and the computation…

Multiple (simple) context-free tree grammars are investigated, where "simple" means "linear and nondeleting". Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an…

We provide a fundamental result for bucket increasing trees, which gives a complete characterization of all families of bucket increasing trees that can be generated by a tree evolution process. We also provide several equivalent…

We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…

We explore a physical model of ordered sums of integers as trains of rods. The trains for a fixed, possibly infinite, set of rod lengths naturally correspond to nodes in a tree; relations among finite linear recursions encoded in the…

Neural networks with tree-based sentence encoders have shown better results on many downstream tasks. Most of existing tree-based encoders adopt syntactic parsing trees as the explicit structure prior. To study the effectiveness of…

Tree-ensemble algorithms, such as random forest, are effective machine learning methods popular for their flexibility, high performance, and robustness to overfitting. However, since multiple learners are combined, they are not as…

The reconstruction of a central tendency `species tree' from a large number of conflicting gene trees is a central problem in systematic biology. Moreover, it becomes particularly problematic when taxon coverage is patchy, so that not all…

We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…

Industrial robots can solve very complex tasks in controlled environments, but modern applications require robots able to operate in unpredictable surroundings as well. An increasingly popular reactive policy architecture in robotics is…

This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…

A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…

Topologically constrained genome-like polymers often double-fold into tree-like configurations, which can be modelled on the level of folded (ring) polymers or on the level of the underlying random trees. For both descriptions, we have…

The article describes the structural and algorithmic relations between Cartesian trees and Lyndon Trees. This leads to a uniform presentation of the Lyndon table of a word corresponding to the Next Nearest Smaller table of a sequence of…