Related papers: Algebraic operators for querying pattern bases
Our aim is to build a set of rules, such that reasoning over temporal dependencies within gene regulatory networks is possible. The underlying transitions may be obtained by discretizing observed time series, or they are generated based on…
In various subjects including mathematics, one can hope to use mathematical thinking well when the right kinds of algebraic structure to consider can be discovered or spotted. Therefore, it would help to understand kinds of algebraic…
This paper argues that certain ontology design problems are profitably addressed by treating ontologies as theories and by defining a set of operations that create new ontologies, including their constraints, out of other ontologies. The…
We apply foundation models to data discovery and exploration tasks. Foundation models include large language models (LLMs) that show promising performance on a range of diverse tasks unrelated to their training. We show that these models…
Knowledge computation tasks are often infeasible for large data sets. This is in particular true when deriving knowledge bases in formal concept analysis (FCA). Hence, it is essential to come up with techniques to cope with this problem.…
A periodic linear graph operator acts on states (functions) defined on the vertices of a graph equipped with a free translation action. Fourier transform with respect to the translation group reveals the central spectral objects, Bloch and…
The use of patterns in predictive models is a topic that has received a lot of attention in recent years. Pattern mining can help to obtain models for structured domains, such as graphs and sequences, and has been proposed as a means to…
Topological data analysis (TDA) is a versatile tool that can be used to extract scientific knowledge from complex pattern formation processes. However, the physics correspondence between the features obtained from TDA and pattern dynamics…
Integrating machine learning into the internals of database management systems requires significant feature engineering, a human effort-intensive process to determine the best way to represent the pieces of information that are relevant to…
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…
In this paper, we motivated the need for relational database systems to support subset query processing. We defined new operators in relational algebra, and new constructs in SQL for expressing subset queries. We also illustrated the…
We develop formal foundations for notions and mechanisms needed to support service-oriented computing. Our work builds on recent theoretical advancements in the algebraic structures that capture the way services are orchestrated and in the…
Goal Recognition is the task by which an observer aims to discern the goals that correspond to plans that comply with the perceived behavior of subject agents given as a sequence of observations. Research on Goal Recognition as Planning…
This text, based on the author's Bachelor's thesis, introduces the theory of Algebraic Operads, a mathematical formalism that provides a unifying framework for modern algebra. We demonstrate how the fundamental theories of associative,…
Patterns are fundamental to human cognition, enabling the recognition of structure and regularity across diverse domains. In this work, we focus on structural repeats, patterns that arise from the repetition of hierarchical relations within…
Graph mining applications analyze the structural properties of large graphs, and they do so by finding subgraph isomorphisms, which makes them computationally intensive. Existing graph mining techniques including both custom graph mining…
Relational concept analysis (RCA) is an extension of formal concept analysis allowing to deal with several related contexts simultaneously. It has been designed for learning description logic theories from data and used within various…
We continue our study of operator algebras with contractive approximate identities (cais). In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain $C^*$-algebraic…
The difficulties of automatic extraction of definitions and methods from scientific documents lie in two aspects: (1) the complexity and diversity of natural language texts, which requests an analysis method to support the discovery of…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…