Related papers: Polystore Mathematics of Relational Algebra
Several constructive homological methods based on noncommutative Gr\"obner bases are known to compute free resolutions of associative algebras. In particular, these methods relate the Koszul property for an associative algebra to the…
The goal of unsupervised representation learning is to extract a new representation of data, such that solving many different tasks becomes easier. Existing methods typically focus on vectorized data and offer little support for relational…
Relational and noSQL storages are developed for the fast processing of the large data sets having a stable structure, while the ontologies are used to rep-resent complex and dynamic sets of information of a limited size. In the in-dustrial…
Some aspects of Computer Algebra (notably Computation Group Theory and Computational Number Theory) have some good databases of examples, typically of the form "all the X up to size n". But most of the others, especially on the polynomial…
Shapley-like values, including the Shapley and Banzhaf values, provide a principled way to quantify how individual tuples contribute to a query result. Their exact computation, however, is intractable because it requires aggregating…
In this project we are presenting a grammar which unify the design and development of spatial databases. In order to make it, we combine nominal and spatial information, the former is represented by the relational model and latter by a…
Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…
Algebraic effects offer a versatile framework that covers a wide variety of effects. However, the family of operations that delimit scopes are not algebraic and are usually modelled as handlers, thus preventing them from being used freely…
With the continuous development of NoSQL databases, more and more developers choose to use semi-structured data for development and data management, which puts forward requirements for schema management of semi-structured data stored in…
With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics…
Schema evolution is a crucial aspect in database management. The proposed taxonomies of schema changes have neglected the set of operations that involves relationships between entity types: aggregation and references, as well as the…
Tables have gained significant attention in large language models (LLMs) and multimodal large language models (MLLMs) due to their complex and flexible structure. Unlike linear text inputs, tables are two-dimensional, encompassing formats…
Query tractability has been traditionally defined as a function of input database and query sizes, or of both input and output sizes, where the query result is represented as a bag of tuples. In this report, we introduce a framework that…
The natural join and the inner union combine in different ways tables of a relational database. Tropashko [18] observed that these two operations are the meet and join in a class of lattices-called the relational lattices- and proposed…
Relational databases play a central role in many information systems. Their schema contains structural (e.g. tables and columns) and behavioral (e.g. stored procedures or views) entity descriptions. Then, just like for ``normal'' software,…
The purpose of data warehouses is to enable business analysts to make better decisions. Over the years the technology has matured and data warehouses have become extremely successful. As a consequence, more and more data has been added to…
Querying tables with unstructured data is challenging due to the presence of text (or image), either embedded in the table or in external paragraphs, which traditional SQL struggles to process, especially for tasks requiring semantic…
A common approach to data analysis involves understanding and manipulating succinct representations of data. In earlier work, we put forward a succinct representation system for relational data called factorised databases and reported on…
Optimization tasks over relational data, such as clustering, often suffer from the prohibitive cost of join operations, which are necessary to access the full dataset. While geometric data structures like BBD trees yield fast approximation…
We explored ways of doing spatial search within a relational database: (1) hierarchical triangular mesh (a tessellation of the sphere), (2) a zoned bucketing system, and (3) representing areas as disjunctive-normal form constraints. Each of…