Related papers: Algebraic Data Integration
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…
Nowadays data sets are available in very complex and heterogeneous ways. Mining of such data collections is essential to support many real-world applications ranging from healthcare to marketing. In this work, we focus on the analysis of…
Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched…
Buildings generate heterogeneous data across their lifecycle, yet integrating these data remains a critical unsolved challenge. Despite three decades of standardization efforts, over 40 metadata schemas now span the building lifecycle, with…
We propose an extension of the join calculus with pattern matching on algebraic data types. Our initial motivation is twofold: to provide an intuitive semantics of the interaction between concurrency and pattern matching; to define a…
Computer Algebra Systems (e.g. Maple) are used in research, education, and industrial settings. One of their key functionalities is symbolic integration, where there are many sub-algorithms to choose from that can affect the form of the…
We propose a new framework for integrating quantifiers with other logical connectives in a higher-categorical setting. Our method systematically incorporates key coherence conditions-including those akin to the Beck-Chevalley property-and…
Ten years ago, it was shown that nominal techniques can be used to design coalgebraic data types with variable binding, so that alpha-equivalence classes of infinitary terms are directly endowed with a corecursion principle. We introduce…
Using data warehouses to analyse multidimensional data is a significant task in company decision-making.The data warehouse merging process is composed of two steps: matching multidimensional components and then merging them. Current…
A data integration system provides transparent access to different data sources by suitably combining their data, and providing the user with a unified view of them, called global schema. However, source data are generally not under the…
This paper presents a study of the metaphorism pattern of relational specification, showing how it can be refined into recursive programs. Metaphorisms express input-output relationships which preserve relevant information while at the same…
The algebraic approach to quantum mechanics has been vital to the development of quantum theory since its inception, and it has evolved into a mathematically rigorous $C^\ast$-algebraic formulation of the theory's axioms. Conversely, the…
Tabular data is a fundamental form of data structure. The evolution of table analysis tools reflects humanity's continuous progress in data acquisition, management, and processing. The dynamic changes in table columns arise from…
We present a doctrinal approach to category theory, obtained by abstracting from the indexed inclusions (via discrete fibrations and opfibrations) of the left and of the right actions of X in Cat in categories over X. Namely, a "weak…
Large language models (LLMs) such as GPT-4 have emerged as frontrunners, showcasing unparalleled prowess in diverse applications, including answering queries, code generation, and more. Parallelly, graph-structured data, an intrinsic data…
We introduce a mathematical formulation of feature-informed data assimilation (FIDA). In FIDA, the information about feature events, such as shock waves, level curves, wavefronts and peak value, in dynamical systems are used for the…
With today's public data sets containing billions of data items, more and more companies are looking to integrate external data with their traditional enterprise data to improve business intelligence analysis. These distributed data sources…
We complete the foundational architecture of Algebraic Phase Theory by developing a categorical and $2$-categorical framework for algebraic phases. Building on the structural notions introduced in Papers~I-III, we define phase morphisms,…
The article suggests a description of a system of tables with a set of special lists absorbing a semantics of data and reflects a fullness of data. It shows how their parallel processing can be constructed based on the descriptions. The…
As the twin movements of open science and open source bring an ever greater share of the scientific process into the digital realm, new opportunities arise for the meta-scientific study of science itself, including of data science and…