Related papers: Projective sets, intuitionistically
We investigate the enumerative geometry of point configurations in projective space. We define "projective configuration counts": these enumerate configurations of points in projective space such that certain specified subsets are in fixed…
Probabilistic sentential decision diagrams are a class of structured-decomposable probabilistic circuits especially designed to embed logical constraints. To adapt the classical LearnSPN scheme to learn the structure of these models, we…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We study two form of selective selective separability, $SS$ and $SS^+$, on countable spaces with an analytic topology. We show several Ramsey type properties which imply $SS$. For analytic spaces $X$, $SS^+$ is equivalent to have that the…
Neighborhood regression has been a successful approach in graphical and structural equation modeling, with applications to learning undirected and directed graphical models. We extend these ideas by defining and studying an algebraic…
We further develop a forcing notion known as Coding with Perfect Trees and show that this poset preserves, in a strong sense, definable $P$-points, definable tight MAD families and definable selective independent families. As a result, we…
We study the arithmetic structure of the exceptional set of projections. For any bounded subset $E\subset \mathbb{R}^d$, let $$ \Omega=\{\xi\in \mathbb{R}: \dim_B(E+\xi E)=\dim_B E\}. $$ We prove that either $\Omega=\{0\}$ or $\Omega$ is a…
In the field of mathematics, a purely combinatorial equivalent to a simplicial complex, or more generally, a down-set, is an abstract structure known as a family of sets. This family is closed under the operation of taking subsets, meaning…
We investigate the computational properties of basic mathematical notions pertaining to $\mathbb{R}\rightarrow \mathbb{R}$-functions and subsets of $\mathbb{R}$, like finiteness, countability, (absolute) continuity, bounded variation,…
In the general context of computable metric spaces and computable measures we prove a kind of constructive Borel-Cantelli lemma: given a sequence (constructive in some way) of sets $A_{i}$ with effectively summable measures, there are…
We announce two breakthrough results concerning important questions in the Theory of Computational Complexity. In this expository paper, a systematic and comprehensive geometric characterization of the Subset Sum Problem is presented. We…
We give a framework to produce constructible functions from natural functors between categories, without need of a morphism of moduli spaces to model the functor. We show using the Riemann-Hilbert correspondence that any natural (derived)…
We analyse a class of quantum field theory models illustrating some of the possibilities that have emerged in the general study of the short distance properties of superselection sectors, performed in a previous paper (together with R.…
A subset $\mathcal X$ of a C*-algebra $\mathcal A$ is called irredundant if no $A\in \mathcal X$ belongs to the C*-subalgebra of $\mathcal A$ generated by $\mathcal X\setminus \{A\}$. Separable C*-algebras cannot have uncountable…
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…
A graph $G$ is said to be a `set graph' if it admits an acyclic orientation that is also `extensional', in the sense that the out-neighborhoods of its vertices are pairwise distinct. Equivalently, a set graph is the underlying graph of the…
Graph separation is a central tool in parameterized algorithm design, and important separators are among its most successful ingredients. They yield small, structured families of separators that can be enumerated efficiently, and underlie…
A relatively new topic in computability theory is the study of notions of computation that are robust against mistakes on some kind of small set. However, despite the recent popularity of this topic relatively foundational questions about…
Consider the semialgebraic structure over the real field. More generally, let an ominimal structure be over a real closed field. We show that a definable metric space X with a definable metric d is embedded into a Euclidean space so that…
We prove general results about separation and weak$^\#$-convergence of boundedly finite measures on separable metric spaces and Souslin spaces. More precisely, we consider an algebra of bounded real-valued, or more generally a $*$-algebra…