Related papers: Self-embeddings of computable trees

Extreme classification problems are multiclass and multilabel classification problems where the number of outputs is so large that straightforward strategies are neither statistically nor computationally viable. One strategy for dealing…

We study the computational content of various theorems with reverse mathematical strength around Arithmetical Transfinite Recursion ($\mathsf{ATR}_0$) from the point of view of computability-theoretic reducibilities, in particular Weihrauch…

We consider the task of learning Ising models when the signs of different random variables are flipped independently with possibly unequal, unknown probabilities. In this paper, we focus on the problem of robust estimation of…

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…

In this paper, we address computational questions surrounding the enumeration of non-isomorphic Andr\'e planes for any prime power order. We are particularly focused on providing a complete enumeration of all such planes for relatively…

Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…

After stating several tools which can be used to construct indecomposable tree modules for quivers without oriented cycles, we use these methods to construct indecomposable tree modules for every imaginary Schur root. These methods also…

We show that every n-point tree metric admits a (1+eps)-embedding into a C(eps) log n-dimensional L_1 space, for every eps > 0, where C(eps) = O((1/eps)^4 log(1/eps)). This matches the natural volume lower bound up to a factor depending…

CAC for trees is the statement asserting that any infinite subtree of $\mathbb{N}^{<\mathbb{N}}$ has an infinite path or an infinite antichain. In this paper, we study the computational strength of this theorem from a reverse mathematical…

We herein introduce a new method of interpretable clustering that uses unsupervised binary trees. It is a three-stage procedure, the first stage of which entails a series of recursive binary splits to reduce the heterogeneity of the data…

We prove that each finite chain in the two-branching countable ultrahomogeneous pseudotree has finite big Ramsey degrees. This is in contrast to the recent result of Chodounsk\'{y}, Eskew, and Weinert that antichains of size two have…

We show that if $X$ is an indecomposable $PD_3$-complex and $\pi_1(X) is the fundamental group of a reduced finite graph of finite groups but is not virtually cyclic then $X$ is orientable, the underlying graph is a tree, all the edge…

A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary…

This paper considers the enumeration of ternary trees (i.e. rooted ordered trees in which each vertex has 0 or 3 children) avoiding a contiguous ternary tree pattern. We begin by finding recurrence relations for several simple tree…

We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting…

There are several common ways to encode a tree as a matrix, such as the adjacency matrix, the Laplacian matrix (that is, the infinitesimal generator of the natural random walk), and the matrix of pairwise distances between leaves. Such…

Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees,…

Generating trees are a useful technique in the enumeration of various combinatorial objects, particularly restricted permutations. Quite often the generating tree for the set of permutations avoiding a set of patterns requires infinitely…

Given a countable structure $\mathcal{A}$, the degree spectrum of $\mathcal{A}$ is the set of all Turing degrees which can compute an isomorphic copy of $\mathcal{A}$. One of the major programs in computable structure theory is to determine…

In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a…