Related papers: A Microscopic approach to Souslin-tree constructio…
A class of structures is monadically dependent if one cannot interpret all graphs in colored expansions from the class using a fixed first-order formula. A tree-ordered $\sigma$-structure is the expansion of a $\sigma$-structure with a…
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 purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
We construct forests that span $\mathbb{Z}^d$, $d\geq2$, that are stationary and directed, and whose trees are infinite, but for which the subtrees attached to each vertex are as short as possible. For $d\geq3$, two independent copies of…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
This paper proposes a regression tree procedure to estimate conditional copulas. The associated algorithm determines classes of observations based on covariate values and fits a simple parametric copula model on each class. The association…
We initiate the study of the spectrum $Vspec(\kappa)$ of sets that can be realized as the vanishing levels $V(T)$ of a normal $\kappa$-tree $T$. The latter is an invariant in the sense that if $T$ and $T'$ are club-isomorphic, then the…
The ability to adequately model risks is crucial for insurance companies. The method of "Copula-based hierarchical risk aggregation" by Arbenz et al. offers a flexible way in doing so and has attracted much attention recently. We briefly…
Many complex systems have been shown to share universal properties of organization, such as scale independence, modularity and self-similarity. We borrow tools from statistical physics in order to study structural preferential attachment…
Existing techniques to reconstruct tree models of progression for accumulative processes, such as cancer, seek to estimate causation by combining correlation and a frequentist notion of temporal priority. In this paper, we define a novel…
In this paper we will develop an axiomatic foundation for the geometric study of straight edge, protractor, and compass constructions, which while being related to previous foundations, will be the first to have all axioms written and all…
In this paper we investigate the problem of the distributivity of Kurepa trees. We show that it is consistent that there are Kurepa trees and for every Kurepa tree there is a small forcing notion which adds a branch to it without collapsing…
There are several tools available to infer phylogenetic trees, which depict the evolutionary relationships among biological entities such as viral and bacterial strains in infectious outbreaks, or cancerous cells in tumor progression trees.…
We show it is consistent that there is a Souslin tree $S$ such that after forcing with $S$, $S$ is Kurepa and for all clubs $C \subset \omega_1$, $S\upharpoonright C$ is rigid. This answers Fuchs's questions in Club degrees of rigidity and…
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…
Learning discriminative global features plays a vital role in semantic segmentation. And most of the existing methods adopt stacks of local convolutions or non-local blocks to capture long-range context. However, due to the absence of…
Sparse shortcuttings of trees -- equivalently, sparse 1-spanners for tree metrics with bounded hop-diameter -- have been studied extensively (under different names and settings), since the pioneering works of [Yao82, Cha87, AS87, BTS94],…
We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bond-bond…
We assess advantages of expressing tree-structured Ising models via their mean parameterization rather than their commonly chosen canonical parameterization. This includes fixedness of marginal distributions, often convenient for dependence…
Understanding the evolution of a set of genes or species is a fundamental problem in evolutionary biology. The problem we study here takes as input a set of trees describing {possibly discordant} evolutionary scenarios for a given set of…