Related papers: Proxy principles in combinatorial set theory
The article continues the study of the 'regular' arrangement of a collection of sets near a point in their intersection. Such regular intersection or, in other words, transversality properties are crucial for the validity of qualification…
Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…
We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed for…
A Souslin algebra is a complete Boolean algebra whose main features are ruled by a tight combination of an antichain condition with an infinite distributive law. The present article divides into two parts. In the first part a representation…
We give two consistent constructions of trees $T$ whose finite power $T^{n+1}$ is sharply different from $T^n$: 1. An $\aleph_1$-tree $T$ whose interval topology $X_T$ is perfectly normal, but $(X_T)^2$ is not even countably metacompact. 2.…
We analyze an evolving network model of Krapivsky and Redner in which new nodes arrive sequentially, each connecting to a previously existing node b with probability proportional to the p-th power of the in-degree of b. We restrict to the…
In this paper we study predictive pattern mining problems where the goal is to construct a predictive model based on a subset of predictive patterns in the database. Our main contribution is to introduce a novel method called safe pattern…
This study addresses the predictive limitation of probabilistic circuits and introduces transformations as a remedy to overcome it. We demonstrate this limitation in robotic scenarios. We motivate that independent component analysis is a…
Vine copula models have become highly popular and practical tools for modelling multivariate probability distributions due to their flexibility in modelling different kinds of dependences between the random variables involved. However,…
Supertree construction is the process by which a set of phylogenetic trees, each on a subset of the overall set X of species, is combined into a tree on the full set S. The traditional use of supertree methods is the assembly of a large…
Motivated by a question from a recent paper by Gilton, Levine and Stejskalova, we obtain a new characterization of the ideal $J[\kappa]$, from which we confirm that $\kappa$-Souslin trees exist in various models of interest. As a corollary…
We introduce a method of constructing a forcing along a simplified $(\kappa,1)$-morass such that the forcing satisfies the $\kappa$-chain condition. Alternatively, this may be seen as a method to thin out a larger forcing to get a chain…
We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…
For the $q-$state Potts model new order parameters projecting on a group of spins instead of a single spin are introduced. On a Cayley tree this allows the physical interpretation of the Potts model at noninteger values q of the number of…
We generalize the combinatorial principles $C_n(\kappa), C^s_n(\kappa)$ and $Princ(\kappa)$ introduced by various authors, and prove some of their properties and connections between them. We also answer a question asked by Juhasz-Kunen…
In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on…
Parsing spoken dialogue presents challenges that parsing text does not, including a lack of clear sentence boundaries. We know from previous work that prosody helps in parsing single sentences (Tran et al. 2018), but we want to show the…
The tree share structure proposed by Dockins et al. is an elegant model for tracking disjoint ownership in concurrent separation logic, but decision procedures for tree shares are hard to implement due to a lack of a systematic theoretical…
Ramsey theory and forcing have a symbiotic relationship. At the RIMS Symposium on Infinite Combinatorics and Forcing Theory in 2016, the author gave three tutorials on Ramsey theory in forcing. The first two tutorials concentrated on…
Previous work has suggested that the structural restrictions of graphs from classes of bounded expansion--locally dense pockets in a globally sparse graph--naturally coincide with common properties of real-world networks such as clustering…