Related papers: The tree structure in staircase tableaux
Latent tree analysis seeks to model the correlations among a set of random variables using a tree of latent variables. It was proposed as an improvement to latent class analysis --- a method widely used in social sciences and medicine to…
Physical construction---the ability to compose objects, subject to physical dynamics, to serve some function---is fundamental to human intelligence. We introduce a suite of challenging physical construction tasks inspired by how children…
Several structural learning algorithms for staged tree models, an asymmetric extension of Bayesian networks, have been defined. However, they do not scale efficiently as the number of variables considered increases. Here we introduce the…
We propose to compose dynamic tree structures that place the objects in an image into a visual context, helping visual reasoning tasks such as scene graph generation and visual Q&A. Our visual context tree model, dubbed VCTree, has two key…
This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that…
In this paper, in the context of the ``Dessins d'enfants'' theory, we give a combinatorial criterion for a plane tree to cover a tree from the classes of "chains" or "stars''. Besides, we discuss some applications of this result which are…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
To most mathematicians and computer scientists the word ``tree'' conjures up, in addition to the usual image, the image of a connected graph with no circuits. In the last few years various types of trees have been the subject of much…
Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form…
In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on…
Rooted, weighted continuum random trees are used to describe limits of sequences of random discrete trees. Formally, they are random quadruples $(\mathcal{T},d,r,p)$, where $(\mathcal{T},d)$ is a tree-like metric space, $r\in\mathcal{T}$ is…
Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…
Causal reasoning is a crucial part of science and human intelligence. In order to discover causal relationships from data, we need structure discovery methods. We provide a review of background theory and a survey of methods for structure…
Motivated by a fundamental geometrical object, the cut locus, we introduce and study a new combinatorial structure on graphs.
We explain how the moments of the (weight function of the) Askey Wilson polynomials are related to the enumeration of the staircase tableaux introduced by the first and fourth authors. This gives us a direct combinatorial formula for these…
We revisit the model of the ballistic deposition studied in \cite{bdeposition} and prove several combinatorial properties of the random tree structure formed by the underlying stochastic process. Our results include limit theorems for the…
In the framework of the connection theory, a contravariant analog of the Sternberg coupling procedure is developed for studying a natural class of Poisson structures on fiber bundles, called coupling tensors. We show that every Poisson…
We investigate the structure of trees that have minimal algebraic connectivity among all trees with a given degree sequence. We show that such trees are caterpillars and that the vertex degrees are non-decreasing on every path on…
The purpose of this paper is twofold. First we answer to a question asked by Steingrimsson and Williams about certain permutation tableaux: we construct a bijection between binary trees and the so-called Catalan tableaux. These tableaux are…
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…