Related papers: Simplicial Databases
Both simplicial sets and simplicial spaces are used pervasively in homotopy theory as presentations of spaces, where in both cases we extract the "underlying space" by taking geometric realization. We have a good handle on the category of…
Database system architectures are undergoing revolutionary changes. Algorithms and data are being unified by integrating programming languages with the database system. This gives an extensible object-relational system where non-procedural…
A simple sql statement can be used to search learning or rule in relational database for data mining purposes particularly for classification rule. With just only one simple sql statement, characteristic and classification rule can be…
We address a fundamental question concerning spatio-temporal database systems: ``What are exactly spatio-temporal queries?'' We define spatio-temporal queries to be computable mappings that are also generic, meaning that the result of a…
We define a category $\mathsf{List}$ whose objects are sets and morphisms are mappings which assign to an element in the domain an ordered sequence (list) of elements in the codomain. We introduce and study a category of simplicial objects…
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…
Variability inherently exists in databases in various contexts which creates database variants. For example, variants of a database could have different schemas/content (database evolution problem), variants of a database could root from…
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…
Within the big data tsunami, relational databases and SQL are still there and remain mandatory in most of cases for accessing data. On the one hand, SQL is easy-to-use by non specialists and allows to identify pertinent initial data at the…
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…
Collective Adaptive Systems often consist of many heterogeneous components typically organised in groups. These entities interact with each other by adapting their behaviour to pursue individual or collective goals. In these systems, the…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…
We combine two recent ideas: cartesian differential categories, and restriction categories. The result is a new structure which axiomatizes the category of smooth maps defined on open subsets of $\R^n$ in a way that is completely algebraic.…
The logic of Dependence and Independence Bunched Implications (DIBI) is a logic to reason about conditional independence (CI); for instance, DIBI formulas can characterise CI in probability distributions and relational databases, using the…
Graph similarity search algorithms usually leverage the structural properties of a database. Hence, these algorithms are effective only on some structural variations of the data and are ineffective on other forms, which makes them hard to…
We construct a category, $\Omega$, of which the objects are pointed categories and the arrows are pointed correspondences. The notion of a "spec datum" is introduced, as a certain relation between categories, of which one has been given a…
The web, through many search engine sites, has popularized the keyword-based search paradigm, where a user can specify a string of keywords and expect to retrieve relevant documents, possibly ranked by their relevance to the query. Since a…
This is Part II of a three article series on using databases for Finite Element Analysis (FEA). It discusses (1) db design, (2) data loading, (3) typical use cases during grid building, (4) typical use cases during simulation (get and put),…
The variety of data is one of the important issues in the era of Big Data. The data are naturally organized in different formats and models, including structured data, semi-structured data, and unstructured data. Prior research has…
We define a class of probability distributions that we call simplicial mixture models, inspired by simplicial complexes from algebraic topology. The parameters of these distributions represent their topology and we show that it is possible…