Related papers: Dichotomy for Axiomatising Inclusion Dependencies …

The basic random $k$-SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables, is the conjunction of these clauses satisfiable? Here we…

We establish a dichotomy theorem characterizing the circumstances under which a treeable Borel equivalence relation E is essentially countable. Under additional topological assumptions on the treeing, we in fact show that E is essentially…

We establish conditions under which an inclusion of finitely aligned left-cancellative small categories induces inclusions of twisted C*-algebras. We also present an example of an inclusion of finitely aligned left-cancellative monoids that…

With the increasing popularity of graph-based methods for dimensionality reduction and representation learning, node embedding functions have become important objects of study in the literature. In this paper, we take an axiomatic approach…

We revisit Pollard's classical result on consistency for $k$-means clustering in Euclidean space, with a focus on extensions in two directions: first, to problems where the data may come from interesting geometric settings (e.g., Riemannian…

We propose and axiomatize preferences on a product state space in light of uncertainty regarding the dependency of different payoff-relevant factors. Dependence structures allow to decompose probabilities and allow to pin down behavior…

We study certain triangulated categories of $K$-motives $DK(-)$ over a wide class of base schemes, and define certain "weights" for them. We relate the weights of particular $K$-motives to (negative) homotopy invariant $K$-groups (tensored…

Link prediction is critical for the application of incomplete knowledge graph (KG) in the downstream tasks. As a family of effective approaches for link predictions, embedding methods try to learn low-rank representations for both entities…

Codd's relational model describes just one possible world. To better cope with incomplete information, extended database models allow several possible worlds. Vague tables are one such convenient extended model where attributes accept sets…

The threshold behaviour of the K-Satisfiability problem is studied in the framework of the statistical mechanics of random diluted systems. We find that at the transition the entropy is finite and hence that the transition itself is due to…

The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies…

We propose the \emph{weighted K-harmonic means} (WKHM) clustering algorithm, a regularized variant of K-harmonic means designed to ensure numerical stability while enabling soft assignments through inverse-distance weighting. Unlike…

Entropy is a fundamental concept in quantum information theory that allows to quantify entanglement and investigate its properties, for example its monogamy over multipartite systems. Here, we derive variational formulas for relative…

We show that the classifying category C(T) of a dependent type theory T with axioms for identity types admits a non-trivial weak factorisation system. We provide an explicit characterisation of the elements of both the left class and the…

Different attribution scores have been proposed to quantify the relevance of database tuples for query answering in databases; e.g. Causal Responsibility, the Shapley Value, the Banzhaf Power-Index, and the Causal Effect. They have been…

Codd's rule of entity integrity stipulates that every table has a primary key. Hence, the attributes of the primary key carry unique and complete value combinations. In practice, data cannot always meet such requirements. Previous work…

We study functional dependencies together with two different probabilistic dependency notions: unary marginal identity and unary marginal distribution equivalence. A unary marginal identity states that two variables x and y are identically…

In the kernel density estimation (KDE) problem one is given a kernel $K(x, y)$ and a dataset $P$ of points in a Euclidean space, and must prepare a data structure that can quickly answer density queries: given a point $q$, output a…

The concept of a k-translatable groupoid is explored in depth. Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatable groupoids are proved. Necessary and sufficient…

Multi-column dependencies in relational databases come associated with two different computational tasks. The detection problem is to decide whether a dependency of a certain type and size holds in a given database, the discovery problem…