Related papers: Algebraic Data Integration
During the last two decades, it has been increasingly acknowledged that the engineering of information systems usually requires a huge effort in integrating master data and business processes. This has led to a plethora of proposals, both…
Researchers have derived many theoretical models for specifying users' insights as they interact with a visualization system. These representations are essential for understanding the insight discovery process, such as when inferring user…
Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of…
Category theory is the language of homological algebra, allowing us to state broadly applicable theorems and results without needing to specify the details for every instance of analogous objects. However, authors often stray from the realm…
Enterprise application integration (EAI) solutions are the centrepiece of current enterprise IT architectures (e.g., cloud and mobile computing, business networks), however, require the formalization of their building blocks, represented by…
Searching learning or rules in relational database for data mining purposes with characteristic or classification/discriminant rule in attribute oriented induction technique can be quicker, easy, and simple with simple SQL statement. With…
We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad…
We introduce a framework for automatically choosing data structures to support efficient computation of analytical workloads. Our contributions are twofold. First, we introduce a novel low-level intermediate language that can express the…
We provide a foundation for working with homological and homotopical methods in categorical algebra. This involves two mutually complementary components, namely (a) the strategic selection of suitable axiomatic frameworks, some well known…
We develop the theory of motivic integration for formal schemes
Integrating heterogeneous data sources and expert knowledge is essential for overcoming data scarcity and enhancing estimation accuracy. Two main frameworks naturally arise to perform the integration of these multiple sources: sequential…
Inference algorithms for probabilistic programming are complex imperative programs with many moving parts. Efficient inference often requires customising an algorithm to a particular probabilistic model or problem, sometimes called…
Students in introductory data management courses are often taught how to write queries in SQL. This is a useful and practical skill, but it gives limited insight into how queries are processed by relational database engines. In contrast,…
In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…
The Calculus of Conjunctive Queries (CCQ) has foundational status in database theory. A celebrated theorem of Chandra and Merlin states that CCQ query inclusion is decidable. Its proof transforms logical formulas to graphs: each query has a…
In this paper, we define a category DB, called the category of simplicial databases, whose objects are databases and whose morphisms are data-preserving maps. Along the way we give a precise formulation of the category of relational…
Data clustering is an approach to seek for structure in sets of complex data, i.e., sets of "objects". The main objective is to identify groups of objects which are similar to each other, e.g., for classification. Here, an introduction to…
Datatype-generic programming increases program abstraction and reuse by making functions operate uniformly across different types. Many approaches to generic programming have been proposed over the years, most of them for Haskell, but…
Automata learning is a popular technique used to automatically construct an automaton model from queries. Much research went into devising ad hoc adaptations of algorithms for different types of automata. The CALF project seeks to unify…
The Algebraic lambda-calculus and the Linear-Algebraic lambda-calculus extend the lambda-calculus with the possibility of making arbitrary linear combinations of terms. In this paper we provide a fine-grained, System F-like type system for…