相关论文: A New Decidable Class of Tuple Generating Dependen…

The Guarded Fragment (GF) is a well-established decidable fragment of first-order logic. We study an extension of GF with nested equivalence relations, namely a family of distinguished binary predicates $E_1, E_2, \dots$ interpreted as…

We investigate a new notion of regularity for tensor triangulated categories, called residual regularity. We show that residual regularity descends and ascends via finite separable extensions and we classify all finite groups whose derived…

Let $A$ be a graded algebra. It is shown that the derived category of dg modules over $A$ (viewed as a dg algebra with trivial differential) is a triangulated hull of a certain orbit category of the derived category of graded $A$-modules.…

Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned…

We show that the category of projective modules over a graded commutative ring admits a triangulation with respect to module suspension if and only if the ring is a finite product of graded fields and exterior algebras on one generator over…

We study the problem of fitting ontologies and constraints to positive and negative examples that take the form of a finite relational structure. As ontology and constraint languages, we consider the description logics $\mathcal{E\mkern-2mu…

We show that there exists a canonical functor from the category of strict \infty-groupoids to the category of Grothendieck \infty-groupoids and that this functor is fully faithful. As a main ingredient, we prove that free strict…

We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation…

Topological effects continue to fascinate physicists since more than three decades. One of their main applications are high-precision measurements of the resistivity. We propose to make also use of the spatially separated edge states. It is…

In the projective space $\mathrm{PG}(3,q)$, we consider the orbits of lines under the stabilizer group of the twisted cubic. In the literature, lines of $\mathrm{PG}(3,q)$ are partitioned into classes, each of which is a union of line…

Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose…

The genetic product of the groupoids, originating in the theory of DNA recombination, is introduced. It permits a natural generalization of the classical genetic algorithm. The full characterization of all three-element genetic groupoids…

We present a comprehensive survey of the advancements and techniques in the field of tractable probabilistic generative modeling, primarily focusing on Probabilistic Circuits (PCs). We provide a unified perspective on the inherent…

Under a mild condition, the perfect derived category and the finite-dimensional derived category of a graded gentle one-cycle algebra are described as twisted root categories of certain infinite quivers of type $\mathbb{A}_\infty^\infty$.…

Matching Dependencies (MDs) are a relatively recent proposal for declarative entity resolution. They are rules that specify, on the basis of similarities satisfied by values in a database, what values should be considered duplicates, and…

We define a notion of categorical first order deformations for (enhanced) triangulated categories. For a category $\mathcal{T}$, we show that there is a bijection between $\operatorname{HH}^2(\mathcal{T})$ and the set of categorical…

The chase procedure, originally introduced for checking implication of database constraints, and later on used for computing data exchange solutions, has recently become a central algorithmic tool in rule-based ontological reasoning. In…

This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways…

On objects of a triangulated category with a stability condition, we construct a topology.

We unify and generalize several approaches to constructing braid group representations from finite groups, using iterated twisted tensor products. Our results hint at a relationship between the braidings on the $G$-gaugings of a pointed…