Related papers: Kleisli Database Instances
Main contribution of this paper is an investigation of expressive power of the database category DB. An object in this category is a database-instance (set of n-ary relations). Morphisms are not functions but have complex tree structures…
The proliferation of modern data processing tools has given rise to open-source columnar data formats. The advantage of these formats is that they help organizations avoid repeatedly converting data to a new format for each application.…
Over the past two decades the notion of a strong monad has found wide applicability in computing. Arising out of a need to interpret products in computational and semantic settings, different approaches to this concept have arisen. In this…
Redis is an in-memory data structure store, often used as a database, with a Haskell interface Hedis. Redis is dynamically typed --- a key can be discarded and re-associated to a value of a different type, and a command, when fetching a…
The universally applied Codd's relational model has two constructs: a stored relation, with stored attributes only and a view, only with the inherited ones. In 1992, we have proposed third construct, mixing both types of attributes.…
This article summarizes the main ideas behind creating an open database proposed for use in the exploration of generalized parton distributions (GPDs). This lightweight database is well suited for GPD phenomenology and is designed to store…
It is informally understood that the purpose of modal type constructors in programming calculi is to control the flow of information between types. In order to lend rigorous support to this idea, we study the category of classified sets, a…
In a recent paper by Ambr\'osio et al. [arXiv:2405.14799], it was shown that the gravitational force law of the Modified Newtonian Dynamics (MOND) phenomenology can be derived within the framework of entropic gravity and the holographic…
We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal…
Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning…
There are classification tasks that take as inputs groups of images rather than single images. In order to address such situations, we introduce a nested multi-instance deep network. The approach is generic in that it is applicable to…
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…
These notes present an approach to obtaining monoid operations which are compatible with a given family of mappings in the sense that the mappings become left translations in the monoid. This can be applied to various situations such as the…
We present a categorical denotational semantics for a database mapping, based on views, in the most general framework of a database integration/exchange. Developed database category DB, for databases (objects) and view-based mappings…
Decisional systems are based on multidimensional databases improving OLAP analyses. The paper describes a new OLAP operator named "BLEND" to perform multigradual analyses. The operation transforms multidimensional structures during querying…
This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database, can search a database in a single query (a query is defined as any question to the database to which the database…
Category theory provides a compact method of encoding mathematical structures in a uniform way, thereby enabling the use of general theorems on, for example, equivalence and universal constructions. In this article we develop the method of…
Compressed bitmap indexes are used to speed up simple aggregate queries in databases. Indeed, set operations like intersections, unions and complements can be represented as logical operations (AND,OR,NOT) that are ideally suited for…
Efficient processing of aggregated range queries on two-dimensional grids is a common requirement in information retrieval and data mining systems, for example in Geographic Information Systems and OLAP cubes. We introduce a technique to…
This paper presents a study of the characteristics of transactional databases used in frequent itemset mining. Such characterizations have typically been used to benchmark and understand the data mining algorithms working on these…