相关论文: Embeddings of Iteration Trees

Recently, deep neural networks have expanded the state-of-art in various scientific fields and provided solutions to long standing problems across multiple application domains. Nevertheless, they also suffer from weaknesses since their…

We consider linear preferential attachment trees, and show that they can be regarded as random split trees in the sense of Devroye (1999), although with infinite potential branching. In particular, this applies to the random recursive tree…

We look for partition theorems for large subtrees for suitable uncountable trees and colourings. We concentrate on sub-trees of $^{\kappa \ge} 2$ expanded by a well ordering of each level. Unlike earlier works, we do not ask the embedding…

We continue the development of the infinitesimal deformation theory of pasting diagrams of k-linear categories begun in Yetter, D.N. "On Deformations of Pasting Diagrams", Theory and Applications of Categories 22 (2009) 24-53. In that…

Numerous computer systems use dynamic control and data structures of unbounded size. These data structures have often the character of trees or they can be encoded as trees with some additional pointers. This is exploited by some currently…

A subset of leaves of a rooted tree induces a new tree in a natural way. The density of a tree $D$ inside a larger tree $T$ is the proportion of such leaf-induced subtrees in $T$ that are isomorphic to $D$ among all those with the same…

We answer three questions posed by Bubeck and Linial on the limit densities of subtrees in trees. We prove there exist positive $\varepsilon_1$ and $\varepsilon_2$ such that every tree that is neither a path nor a star has inducibility at…

This paper addresses the basic question of how well can a tree approximate distances of a metric space or a graph. Given a graph, the problem of constructing a spanning tree in a graph which strongly preserves distances in the graph is a…

Lower bounds are given for the depths of R/I^t for t at least one when I is the edge ideal of a tree or forest. The bounds are given in terms of the diameter of the tree, or in case of a forest, the largest diameter of a connected component…

Frequent tree mining asks us to enumerate tree patterns that occur frequently in a database of rooted trees. This problem is motivated by tree-structured data in bioinformatics, such as glycans and pseudoknot-free RNA secondary structures.…

Text embeddings are a fundamental component in many NLP tasks, including classification, regression, clustering, and semantic search. However, despite their ubiquitous application, challenges persist in interpreting embeddings and…

A grammar-compressed ranked tree is represented with a linear space overhead so that a single traversal step, i.e., the move to the parent or the i-th child, can be carried out in constant time. Moreover, we extend our data structure such…

Deep learning models develop successive representations of their input in sequential layers, the last of which maps the final representation to the output. Here we investigate the informational content of these representations by observing…

This paper explores unsupervised learning of parsing models along two directions. First, which models are identifiable from infinite data? We use a general technique for numerically checking identifiability based on the rank of a Jacobian…

Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of…

Given an edge-weighted tree $T$ with $n$ leaves, sample the leaves uniformly at random without replacement and let $W_k$, $2 \le k \le n$, be the length of the subtree spanned by the first $k$ leaves. We consider the question, "Can $T$ be…

In the context of reconstructing phylogenetic networks from a collection of phylogenetic trees, several characterisations and subsequently algorithms have been established to reconstruct a phylogenetic network that collectively embeds all…

We study whether a Large Language Model can learn the deterministic sequence of trees generated by the iterated prime factorization of the natural numbers. Each integer is mapped into a rooted planar tree and the resulting sequence $…

Phylogenetic (evolutionary) trees and networks are leaf-labeled graphs that are widely used to represent the evolutionary relationships between entities such as species, languages, cancer cells, and viruses. To reconstruct and analyze…

In 1998, B\"{o}cker and Dress gave a 1-to-1 correspondence between symbolically dated rooted trees and symbolic ultrametrics. We consider the corresponding problem for unrooted trees. More precisely, given a tree $T$ with leaf set $X$ and a…