Related papers: Simplicial Databases
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…
The advent of data-driven science in the 21st century brought about the need for well-organized structured data and associated infrastructure able to facilitate the applications of Artificial Intelligence and Machine Learning. We present an…
Probabilistic databases (PDBs) introduce uncertainty into relational databases by specifying probabilities for several possible instances. Traditionally, they are finite probability spaces over database instances. Such finite PDBs…
Much of the homotopical and homological structure of the categories of chain complexes and topological spaces can be deduced from the existence and properties of the 'simple' functors Tot : {double chain complexes} -> {chain complexes} and…
Morphisms, structure preserving maps, are everywhere in Mathematics as useful tools for thinking and problem solving, or as objects to study. Here, we argue that the idea of operations being compatible across two domains goes beyond its…
A traditional database systems is organized around a single data model that determines how data can be organized, stored and manipulated. But the vision of this paper is to develop new principles and techniques to manage multiple data…
A hidden database refers to a dataset that an organization makes accessible on the web by allowing users to issue queries through a search interface. In other words, data acquisition from such a source is not by following static…
Since the early days of relational databases, it was realized that acyclic hypergraphs give rise to database schemas with desirable structural and algorithmic properties. In a by-now classical paper, Beeri, Fagin, Maier, and Yannakakis…
Graph databases have emerged as the fundamental technology underpinning trendy application domains where traditional databases are not well-equipped to handle complex graph data. However, current graph databases support basic graph…
We describe the construction of a database of genus 2 curves of small discriminant that includes geometric and arithmetic invariants of each curve, its Jacobian, and the associated L-function. This data has been incorporated into the…
In this paper we put a cofibrantly generated model category structure on the category of small simplicial categories. The weak equivalences are a simplicial analogue of the notion of equivalence of categories.
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
In this paper, we cast the classic problem of achieving k-anonymity for a given database as a problem in algebraic topology. Using techniques from this field of mathematics, we propose a framework for k-anonymity that brings new insights…
In this article we discuss an approach to database optimisation in which a conceptual schema is optimised by applying a sequence of transformations. By performing these optimisations on the conceptual schema, a large part of the database…
We construct a model structure on the category of ordered simplicial complexes, Quillen equivalent to the standard model structure on simplicial sets. This shows that simplicial complexes, which are fully combinatorial in nature, provide a…
Recursive graph queries are increasingly popular for extracting information from interconnected data found in various domains such as social networks, life sciences, and business analytics. Graph data often come with schema information that…
In this paper we develop an algebraic approach to data integration by combining techniques from functional programming, category theory, and database theory. In our formalism, database schemas and instances are algebraic (multi-sorted…
This paper describes a unique approach to perform application behavioral analysis for identifying how tables might be related to each other. The analysis techniques are based on the properties of primary and foreign keys and also the data…
Graph databases (GDB) have recently been arisen to overcome the limits of traditional databases for storing and managing data with graph-like structure. Today, they represent a requirement for many applications that manage graph-like data,…
Database migration is a key task in software modernization, increasingly involving transformations across heterogeneous data models such as relational and NoSQL systems. Existing approaches are typically designed for specific source-target…