Related papers: Proxy principles in combinatorial set theory
We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal $\lambda$, if $\lambda^{++}$…
In the context of dependent type theory, we show that coinductive predicates have an equivalent topological counterpart in terms of coinductively generated positivity relations, introduced by G. Sambin to represent closed subsets in…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
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…
Variance parameters in additive models are typically assigned independent priors that do not account for model structure. We present a new framework for prior selection based on a hierarchical decomposition of the total variance along a…
A forest is a generalization of a tree, and here we consider the Aronszajn and Suslin properties for forests. We focus on those forests satisfying coherence, a local smallness property. We show that coherent Aronszajn forests can be…
We investigate forcing properties of perfect tree forcings defined by Prikry to answer a question of Solovay in the late 1960's regarding first failures of distributivity. Given a strictly increasing sequence of regular cardinals $\langle…
Bayesian modeling provides a principled approach to quantifying uncertainty in model parameters and model structure and has seen a surge of applications in recent years. Within the context of a Bayesian workflow, we are concerned with model…
Probabilistic transition system specifications (PTSSs) in the ntmufnu/ntmuxnu format provide structural operational semantics for Segala-type systems that exhibit both probabilistic and nondeterministic behavior and guarantee that…
Multinomial processing tree (MPT) models are tools for disentangling the contributions of latent cognitive processes in a given experimental paradigm. The present note analyzes MPT models subject to order constraints on subsets of its…
The compound Poisson process and the Dirichlet process are the pillar structures of Renewal theory and Bayesian nonparametric theory, respectively. Both processes have many useful extensions to fulfill the practitioners needs to model the…
As data sets grow in size, the ability of learning methods to find structure in them is increasingly hampered by the time needed to search the large spaces of possibilities and generate a score for each that takes all of the observed data…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
Neural Networks and Decision Trees: two popular techniques for supervised learning that are seemingly disconnected in their formulation and optimization method, have recently been combined in a single construct. The connection pivots on…
Since being isolated by Viale and Weiss in 2009, the Guessing Model Property has emerged as a particularly prominent and powerful consequence of the Proper Forcing Axiom. In this paper, we investigate connections between variations of the…
Decision trees are important both as interpretable models amenable to high-stakes decision-making, and as building blocks of ensemble methods such as random forests and gradient boosting. Their statistical properties, however, are not well…
Prime path coverage is a powerful structural testing criterion, but generating all prime paths in a directed graph remains computationally challenging due to the potentially exponential number of them. Existing approaches typically rely on…
We present a systematic study of the method of "norms on possibilities" of building forcing notions with keeping their properties under full control. This technique allows us to answer several open problems, but on our way to get the…
We consider strong combinatorial principles for sigma-directed families of countable sets in the ordering by inclusion modulo finite, e.g. P-ideals of countable sets. We try for principles as strong as possible while remaining compatible…
This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…