Related papers: Functorial Data Migration
Although most business application data is stored in relational databases, programming languages and wire formats in integration middleware systems are not table-centric. Due to costly format conversions, data-shipments and faster…
This thesis introduces quantum natural language processing (QNLP) models based on a simple yet powerful analogy between computational linguistics and quantum mechanics: grammar as entanglement. The grammatical structure of text and…
Optics, aka functional references, are classes of tools that allow composable access into compound data structures. Usually defined as programming language libraries, they provide combinators to manipulate different shapes of data such as…
We introduce a hierarchical categorical framework for Schema-Based Learning (SBL) structured across four interconnected levels. At the schema level, a free multicategory $Sch_{syn}$ encodes fundamental schemas and transformations. An…
This paper deals with an extended model of computations which uses the parameterized families of entities for data objects and reflects a preliminary outline of this problem. Some topics are selected out, briefly analyzed and arranged to…
Functional dependencies are an integral part of database design. However, they are only defined when we exclude null markers. Yet we commonly use null markers in practice. To bridge this gap between theory and practice, researchers have…
Formal Concept Analysis (FCA) is a mathematical theory based on the formalization of the notions of concept and concept hierarchies. It has been successfully applied to several Computer Science fields such as data mining,software…
Baseline is a platform for richly structured data supporting change in multiple dimensions: mutation over time, collaboration across space, and evolution through design changes. It is built upon Operational Differencing, a new technique for…
The digital transformation of companies has led to the evolution of databases towards Big Data. Our work is part of this context and concerns more particularly the mechanisms to extract datasets stored in a Data Lake and to store the data…
Databases, and datasets more generally, evolve continuously through updates, transformations, versioning, schema changes, streaming operations, and other mechanisms. While prior work has noted connections among some of these areas, they…
Large, data centric applications are characterized by its different attributes. In modern day, a huge majority of the large data centric applications are based on relational model. The databases are collection of tables and every table…
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
Stock and flow diagrams are already an important tool in epidemiology, but category theory lets us go further and treat these diagrams as mathematical entities in their own right. In this chapter we use communicable disease models created…
Functional dependencies -- traditional, approximate and conditional are of critical importance in relational databases, as they inform us about the relationships between attributes. They are useful in schema normalization, data…
This paper develops a methodology for representing machine learning models as models of formal theories, grounded in the perspective that machine learning models are a form of database and that databases are models of theories in coherent…
Any natural language can be considered as a tool for producing large databases (consisting of texts, written, or discursive). This tool for its description in turn requires other large databases (dictionaries, grammars etc.). Nowadays, the…
The paper introduces the principles of object-oriented translation for target machine which provides executing the sequences of elementary operations on persistent data presented as a set of relations (programmable relational system). The…
A notion of a coring extension is defined and it is related to the existence of an additive functor between comodule categories that factorises through forgetful functors. This correspondence between coring extensions and factorisable…
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…
Throughout the history of functional programming, recursion has emerged as a natural method for describing loops in programs. However, there does often exist a substantial cognitive distance between the recursive definition and the simplest…