Related papers: Simplicial Databases
This paper provides a self-contained exploration of subdivisions of simplicial complexes, with emphasis on barycentric subdivision. We present formal definitions of subdivisions, show how the realization of a complex is preserved under…
Structured recursion schemes have been widely used in constructing, optimising, and reasoning about programs over inductive and coinductive datatypes. Their plain forms, catamorphisms and anamorphisms, are restricted in expressiveness. Thus…
Data mining is the task of discovering interesting patterns from large amounts of data. There are many data mining tasks, such as classification, clustering, association rule mining, and sequential pattern mining. Sequential pattern mining…
Reynolds' theory of relational parametricity formalizes parametric polymorphism for System F, thus capturing the idea that polymorphically typed System F programs always map related inputs to related results. This paper shows that Reynolds'…
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…
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…
The monoids of simplicial endomorphisms, i.e. the monoids of endomorphisms in the simplicial category, are submonoids of monoids one finds in Temperley-Lieb algebras, and as the monoids of Temperley-Lieb algebras are linked to situations…
Object-oriented database systems proved very valuable at handling and administrating complex objects. In the following guidelines for embedding neural networks into such systems are presented. It is our goal to treat networks as normal data…
In this paper, we consider a tree-structured data model used in many commercial databases like Dremel, F1, JSON stores. We define identity and referential constraints within each tree-structured record. The query language is a variant of…
Category Theory provides us with a clear notion of what is an internal structure. This will allow us to focus our attention on a certain type of relationship between context and structure.
We study verification of systems whose transitions consist of accesses to a Web-based data-source. An access is a lookup on a relation within a relational database, fixing values for a set of positions in the relation. For example, a…
Data tables in the form of spreadsheets or delimited text files are the most utilised data format in Systems Biology. However, they are often not sufficiently structured and lack clear naming conventions that would be required for…
Comparing relational languages by their logical expressiveness is well understood. Less well understood is how to compare relational languages by their ability to represent relational query patterns. Indeed, what are query patterns other…
The relational data model offers unrivaled rigor and precision in defining data structure and querying complex data. Yet the use of relational databases in scientific data pipelines is limited due to their perceived unwieldiness. We propose…
Database systems have to cater to the growing demands of the information age. The growth of the new age information retrieval powerhouses like search engines has thrown a challenge to the data management community to come up with novel…
The goal of data-driven learning of dynamical systems is to interpret time series as a continuous observation of an underlying dynamical system. This task is not well-posed for a variety of reasons - such as multiple co-existing…
Nowadays, scientific databases have become the bread-and-butter of particle physicists. These databases must be maintained and checked repeatedly to insure the accuracy of their content. The COMPETE collaboration aims at motivating data…
Spurred by a number of recent trends, we make the case that the relational database systems should urgently move beyond supporting the basic object-relational model and instead embrace a more abstract data model, specifically, the…
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…
Defining cellular sheaves beyond graph structures, such as on simplicial complexes containing higher-dimensional simplices, is an essential and intriguing topic in topological data analysis (TDA) and the development of sheaf neural…