Related papers: Mnesors for databases
``Fusion rules'' are laws of multiplication among eigenspaces of an idempotent. We establish fusion rules for flexible power-associative algebras, following Albert. We define the notion of an axis in the noncommutative setting (compare with…
The annotation of the results of database transformations was shown to be very effective for various applications. Until recently, most works in this context focused on positive query languages. The provenance semirings is a particular…
!-graphs provide a means of reasoning about infinite families of string diagrams and have proven useful in manipulation of (co)algebraic structures like Hopf algebras, Frobenius algebras, and compositions thereof. However, they have…
Additive models can be used for interpretable machine learning for their clarity and simplicity. However, In the classical models for high-order data, the vectorization operation disrupts the data structure, which may lead to degenerated…
We present a new approach to classification that combines data and knowledge. In this approach, data mining is used to derive association rules (possibly with negations) from data. Those rules are leveraged to increase the predictive…
Separate programming models for data transformation (declarative) and computation (procedural) impact programmer ergonomics, code reusability and database efficiency. To eliminate the necessity for two models or paradigms, we propose a…
This paper defines a constraint-based model dedicated to multidimensional databases. The model we define represents data through a constellation of facts (subjects of analyse) associated to dimensions (axis of analyse), which are possibly…
We formulate a general prescription for spurion analysis in particle-physics models whose selection rules are described by commutative non-invertible fusion algebras. The construction applies to fusion algebras containing non-invertible…
Analytical queries often require a mixture of relational and linear algebra operations applied to the same data. This poses a challenge to analytic systems that must bridge the gap between relations and matrices. Previous work has mainly…
In the current paper, we propose to fuse together stored data (tables) and their functional dependencies (FDs) inside a DBMS. We aim to make FDs first-class citizens: objects which can be queried and used to query data. Our idea is to allow…
Let $D$ and $U$ be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomial-type identities for $D$ and $U$ assuming that either their commutator $[D,U]$ or the second…
We contribute to the knowledge of the quantifier completions and their applications by using the language of doctrines. This algebraic presentation allows us to properly analyse the behaviour of the existential and universal quantifiers. We…
Capturing the composition patterns of relations is a vital task in knowledge graph completion. It also serves as a fundamental step towards multi-hop reasoning over learned knowledge. Previously, several rotation-based translational methods…
We define and study multiplicative connections in the tangent bundle of a Lie groupoid. Multiplicative connections are linear connections satisfying an appropriate compatibility with the groupoid structure. Our definition is natural in the…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
We introduce a generalized notion of inference system to support more flexible interpretations of recursive definitions. Besides axioms and inference rules with the usual meaning, we allow also coaxioms, which are, intuitively, axioms which…
We introduce a new OpenMath content dictionary, named tensor1, containing symbols for the expression of tensor formulas. These symbols support the expression of non-Cartesian coordinates and invariant, multilinear expressions in the context…
We present a notion of mutation of hyperbolic polyhedra, analogous to mutation in knot theory, and then present a general question about commensurability of mutant pairs of polyhedra. We motivate that question with several concrete examples…
We present a dataset of word usage graphs (WUGs), where the existing WUGs for multiple languages are enriched with cluster labels functioning as sense definitions. They are generated from scratch by fine-tuned encoder-decoder language…
In this note, we examine the gauging of the $\mathbb{Z}/2\mathbb{Z}$ permutation action on the tensor square of a modular tensor category. When $\mathcal{C}$ has no nontrivial invertible objects, we provide formulas for the fusion rules of…