Related papers: Tree series and pattern avoidance in syntax trees
We introduce the zip tree, a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank…
The Learnable Tree Filter presents a remarkable approach to model structure-preserving relations for semantic segmentation. Nevertheless, the intrinsic geometric constraint forces it to focus on the regions with close spatial distance,…
The perturbation expansion of the solution of a fixed point equation or of an ordinary differential equation may be expressed as a power series in the perturbation parameter. The terms in this series are indexed by rooted trees and depend…
We construct an operad $\mathrm{Phyl}$ whose operations are the edge-labelled trees used in phylogenetics. This operad is the coproduct of $\mathrm{Com}$, the operad for commutative semigroups, and $[0,\infty)$, the operad with unary…
Information, stored or transmitted in digital form, is often structured. Individual data records are usually represented as hierarchies of their elements. Together, records form larger structures. Information processing applications have to…
The decision tree is one of the most fundamental programming abstractions. A commonly used type of decision tree is the alphabetic binary tree, which uses (without loss of generality) ``less than'' versus ''greater than or equal to'' tests…
We consider questions related to the existence of spanning trees in graphs with the property that after the removal of any path in the tree the graph remains connected. We show that, for planar graphs, the existence of trees with this…
Deciding whether there is a single tree -a supertree- that summarizes the evolutionary information in a collection of unrooted trees is a fundamental problem in phylogenetics. We consider two versions of this question: agreement and…
Tree-structured neural networks encode a particular tree geometry for a sentence in the network design. However, these models have at best only slightly outperformed simpler sequence-based models. We hypothesize that neural sequence models…
Attack Trees (ATs) are a widely used tool for security analysis. ATs can be employed in quantitative security analysis through metrics, which assign a security value to an AT. Many different AT metrics exist, and there exist multiple…
We will define an operad $\mathcal{B}^0$ on planar rooted trees. $\mathcal{B}^0$ is analgous to the $NAP$-operad in the non-planar tree setting. We will define a family of "current-preserving" operads $\mathcal{B}^\lambda$ depending on a…
A zero-one sequence describes a path through a rooted directed binary tree $T$; it also encodes a real number in $[0,1]$. We regard the level of the external node of $T$ along the path as a function on the unit interval, the silhouette of…
The associative operad is a certain algebraic structure on the sequence of group algebras of the symmetric groups. The weak order is a partial order on the symmetric group. There is a natural linear basis of each symmetric group algebra,…
We introduce a framework for constructing fractal trees via analytic generator fields, replacing discrete affine transformations and symbolic rewriting rules by the integration of smooth vector fields in an internal state space. In this…
We define a category $\mathsf{List}$ whose objects are sets and morphisms are mappings which assign to an element in the domain an ordered sequence (list) of elements in the codomain. We introduce and study a category of simplicial objects…
SYNTAGMA is a rule-based parsing system, structured on two levels: a general parsing engine and a language specific grammar. The parsing engine is a language independent program, while grammar and language specific rules and resources are…
We provide the first formal foundation of SAND attack trees which are a popular extension of the well-known attack trees. The SAND attack tree formalism increases the expressivity of attack trees by introducing the sequential conjunctive…
In the last half-decade, the field of natural language processing (NLP) has undergone two major transitions: the switch to neural networks as the primary modeling paradigm and the homogenization of the training regime (pre-train, then…
We introduce a neural network that represents sentences by composing their words according to induced binary parse trees. We use Tree-LSTM as our composition function, applied along a tree structure found by a fully differentiable natural…
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.…