Related papers: A Rigid Kurepa Tree From a Free Suslin Tree
We introduce regenerative tree growth processes as consistent families of random trees with n labelled leaves, n>=1, with a regenerative property at branch points. This framework includes growth processes for exchangeably labelled Markov…
A gluing of two rooted trees is an identification of their leaves and un-subdivision of the resulting 2-valent vertices. A gluing of two rooted trees is subdivergence free if it has no 2-edge cuts with both roots on the same side of the…
A variant of Turing machines is introduced where the tape is replaced by a single tree which can be manipulated in a style akin to purely functional programming. This yields two benefits: first, the extra structure on the tape can be…
This paper proposes FREEtree, a tree-based method for high dimensional longitudinal data with correlated features. Popular machine learning approaches, like Random Forests, commonly used for variable selection do not perform well when there…
From many supercompact cardinals, we show that it is consistent for the tree property to hold at many small successors of singular cardinals, each with a different cofinality. In particular, we construct a model in which the tree property…
The following is consistent: There is a stationary set S such that every Aronszajn tree is S-*-special and there is an Aronszajn tree T such that for every unbounded E we have T is not E-special. This answers a question of Shelah (Proper…
We investigate the structure of crossed product von Neumann algebras arising from Bogoljubov actions of countable groups on Shlyakhtenko's free Araki-Woods factors. Among other results, we settle the questions of factoriality and Connes'…
With the help of various square principles, we obtain results concerning the consistency strength of several statements about trees containing ascent paths, special trees, and strong chain conditions. Building on a result that shows that…
The aim of the present paper is on the one hand to produce examples supporting the conclusion of Y. Namikawa in Remark 2.8 of \cite{N} and improving considerations of Example 1.11 of the same paper. On the other hand, it is intended to give…
A linear order $L$ is strongly surjective if $L$ can be mapped onto any of its suborders in an order preserving way. We prove various results on the existence and non-existence of uncountable strongly surjective linear orders answering…
A relaxed $k$-ary tree is an ordered directed acyclic graph with a unique source and sink in which every node has out-degree $k$. These objects arise in the compression of trees in which some repeated subtrees are factored and repeated…
A theorem of Frieze from 1985 asserts that the total weight of the minimum spanning tree of the complete graph $K_n$ whose edges get independent weights from the distribution $UNIFORM[0,1]$ converges to Ap\'ery's constant in probability, as…
We extend Forester's rigidity theorem so as to give a complete characterization of rigid group actions on trees (an action is rigid if it is the only reduced action in its deformation space, in particular it is invariant under automorphisms…
A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees…
We give a short and elementary proof of the fact that every metric space of finite asymptotic dimension can be embedded into a finite product of trees.
We define and study a new compactification, called the height compactification of the horospheric product of two infinite trees. We will provide a complete description of this compactification. In particular, we show that this…
We present an approach to Morse theory on symmetric products of surfaces using the notion of folded ribbon trees. We introduce an $A_\infty$-category with objects defined as $\kappa$-tuples of Morse functions, where the differential of the…
We define \emph{piecewise rank 1} manifolds, which are aspherical manifolds that generally do not admit a nonpositively curved metric but can be decomposed into pieces that are diffeomorphic to finite volume, irreducible, locally symmetric,…
We introduce a new class of tree-based models, P-Trees, for analyzing (unbalanced) panel of individual asset returns, generalizing high-dimensional sorting with economic guidance and interpretability. Under the mean-variance efficient…
Let $T$ be a tree, a vertex of degree one is a leaf of $T$ and a vertex of degree at least three is a branch vertex of $T$. For two distinct vertices $u,v$ of $T$, let $P_T[u,v]$ denote the unique path in $T$ connecting $u$ and $v.$ For a…