Related papers: Simplicial Databases
We give a new construction of the Joyal model structure on the category of simplicial sets, and we provide a simple characterization of the fibrations in it. We characterize the inner anodyne maps in terms of categorical equivalences and…
We continue the investigation of tabular algebras with trace (a certain class of associative ${\Bbb Z}[v, v^{-1}]$-algebras equipped with distinguished bases) by determining the extent to which the tabular structure may be recovered from a…
In this paper we will present the two basic operations for database schemas used in database mapping systems (separation and Data Federation), and we will explain why the functorial semantics for database mappings needed a new base category…
Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane…
Most NoSQL systems are schema-on-read: data can be stored without first having to declare a Schema that imposes a structure. This schemaless feature offers flexibility to evolve data-intensive applications when data frequently change.…
Text-to-SQL is emerging as a practical interface for real world databases. The dominant paradigm for Text-to-SQL is cross-database or schema-independent, supporting application schemas unseen during training. The schema of a database…
It is increasingly common to find complex data represented through the graph model. Contrary to relational models, graphs offer a high capacity for executing analytical tasks on complex data. Since a huge amount of data is still presented…
A natural language interface (NLI) to databases is an interface that translates a natural language question to a structured query that is executable by database management systems (DBMS). However, an NLI that is trained in the general…
Relational database management systems (RDBMSs) are powerful because they are able to optimize and answer queries against any relational database. A natural language interface (NLI) for a database, on the other hand, is tailored to support…
Simplicial complexes are a versatile and convenient paradigm on which to build all the tools and techniques of the logic of knowledge, on the assumption that initial epistemic models can be described in a distributed fashion. Thus, we can…
There exists a wide set of techniques to perform keyword-based search over relational databases but all of them match the keywords in the users' queries to elements of the databases to be queried as first step. The matching process is a…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
A topology preserving skeleton is a synthetic representation of an object that retains its topology and many of its significant morphological properties. The process of obtaining the skeleton, referred to as skeletonization or thinning, is…
We consider the general model for dynamical systems defined on a simplicial complex. We describe the conjugacy classes of these systems and show how symmetries in a given simplicial complex manifest in the dynamics defined thereon,…
Structured Query Language (SQL) remains the standard language used in Relational Database Management Systems (RDBMSs) and has found applications in healthcare (patient registries), businesses (inventories, trend analysis), military,…
Clustering is one of the major tasks in data mining. In the last few years, Clustering of spatial data has received a lot of research attention. Spatial databases are components of many advanced information systems like geographic…
Collections of measures on compact metric spaces form a model category ("data complexes"), whose morphisms are marginalization integrals. The fibrant objects in this category represent collections of measures in which there is a measure on…
This document is centered around a main idea: simplicial categories, by which we mean simplicial objects in the category of categories, can be treated as a two-fold categorical structure and their double category theory is homotopically…
We consider the problem of privately answering queries defined on databases which are collections of points belonging to some metric space. We give simple, computationally efficient algorithms for answering distance queries defined over an…