Related papers: A microscopic approach to Souslin-tree constructio…
We introduce a new problem, CSPLib problem number 50, to generate all degree sequences that have a corresponding diamond-free graph with secondary properties. This problem arises naturally from a problem in mathematics to do with balanced…
Without access to large compute clusters, building random forests on large datasets is still a challenging problem. This is, in particular, the case if fully-grown trees are desired. We propose a simple yet effective framework that allows…
We present natural constructions of trees and gaps using a quite general construction scheme. In particular, we solve a natural problem about $(\omega_1, \omega_1)$-gaps. As it is well known $(\omega_1, \omega_1)$-gaps can sometimes be…
We provide a complete description of possible covariance matrices consistent with a Gaussian latent tree model for any tree. We then present techniques for utilising these constraints to assess whether observed data is compatible with that…
We present a method to iterate finitely splitting lim-sup tree forcings along non-wellfounded linear orders. We apply this method to construct a forcing (without using an inaccessible or amalgamation) that makes all definable sets of reals…
We prove the consistency of the failure of the weak diamond $\Phi_\lambda$ at strongly inaccessible cardinals. On the other hand, we show that the very weak diamond $\Psi_\lambda$ is equivalent to the statement $2^{<\lambda}<2^\lambda$ and…
We prove that $\mu=\mu^{<\mu}$, $2^\mu=\mu^+$ and ``there is a non reflecting stationary subset of $\mu^+$ composed of ordinals of cofinality $<\mu$'' imply that there is a $\mu$-complete Souslin tree on $\mu^+$.
We present a characterization of Valdivia compact spaces of small weight in terms of path spaces of trees and we use it to obtain (under $\diamondsuit$) a counterexample to a conjecture related to an open problem concerning twisted sums of…
Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of…
Construction of phylogenetic trees has traditionally focused on binary trees where all species appear on leaves, a problem for which numerous efficient solutions have been developed. Certain application domains though, such as viral…
We show that splitting forcing does not have the weak Sacks property below any condition, answering a question of Laguzzi, Mildenberger and Stuber-Rousselle. We also show how some partition results for splitting trees hold or fail and we…
We survey the current state of progress on the Graceful Tree Conjecture, and then we present several new results toward the conjecture, driven by three new ideas: (1) It has been proven that generalized banana trees are graceful by…
For an inaccessible cardinal $\kappa$, the super tree property (ITP) at $\kappa$ holds if and only if $\kappa$ is supercomact. However, just like the tree property, it can hold at successor cardinals. We show that ITP holds at the successor…
We give an explicit construction of the scaling limit of the minimum spanning tree of the complete graph. The limit object is described using a recursive construction involving the convex minorants of a Brownian motion with parabolic drift…
Because of the existence of cubic scalar couplings, there are in general nondecoupling effects at tree level in the scalar sector of any theory with two or more very different mass scales. We show this explicitly in the minimal…
We study the equivalence of Poisson structures around a given symplectic leaf of nonzero dimension. Some criteria of Poisson equivalence are derived from a homotopy argument for coupling Poisson structures. In the case when the transverse…
Entailment trees have been proposed to simulate the human reasoning process of explanation generation in the context of open--domain textual question answering. However, in practice, manually constructing these explanation trees proves a…
In this work, we present a method to extract the skeleton of a self-occluded tree canopy by estimating the unobserved structures of the tree. A tree skeleton compactly describes the topological structure and contains useful information such…
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 introduce a new parametrized diamond principle denoted $\diamondsuit(\mathsf{LP})$. This principle is akin to the parametrized diamonds of Moore, Hru\v{s}\'ak, and D\v{z}amonja, each of which corresponds to some cardinal invariant of the…