Related papers: Transforming Geospatial Ontologies by Homomorphism…
Geological modeling currently uses various computer-based applications. Data harmonization at the semantic level by means of ontologies is essential for making these applications interoperable. Since geo-modeling is currently part of…
Geospatial semantics is a broad field that involves a variety of research areas. The term semantics refers to the meaning of things, and is in contrast with the term syntactics. Accordingly, studies on geospatial semantics usually focus on…
Isomorphism is central to the structure of mathematics and has been formalized in various ways within dependent type theory. All previous treatments have done this by replacing quantification over sets with quantification over groupoids of…
The aim of this article is to describe a new perspective on functoriality of persistent homology and explain its intrinsic symmetry that is often overlooked. A data set for us is a finite collection of functions, called measurements, with a…
Ontology matching is a core task when creating interoperable and linked open datasets. In this paper, we explore a novel structure-based mapping approach which is based on knowledge graph embeddings: The ontologies to be matched are…
One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…
Homology-based invariants can be used to characterize the geometry of datasets and thereby gain some understanding of the processes generating those datasets. In this work we investigate how the geometry of a dataset changes when it is…
Current approaches to semantics in the geospatial domain are mainly based on ontologies, but ontologies, since continue to build entirely on the symbolic methodology, suffers from the classical problems, e.g. the symbol grounding problem,…
A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…
Spatial omics has transformed our understanding of tissue architecture by preserving spatial context of gene expression patterns. Simultaneously, advances in imaging AI have enabled extraction of morphological features describing the…
By Rickard's work, two rings are derived equivalent if there is a tilting complex, constructed from projective modules over the first ring such that the second ring is the endomorphism ring of this tilting complex. In this work I describe,…
Mappings between related ontologies are increasingly used to support data integration and analysis tasks. Changes in the ontologies also require the adaptation of ontology mappings. So far the evolution of ontology mappings has received…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions.…
Ontologies represent the conceptual knowledge of a domain. At the core of an ontology is the taxonomy of concepts and subconcepts that represent specific entities, which can be complex to build. In many cases, information is available in…
When two or more subsystems of a quantum system interact with each other they can become entangled. In this case the individual subsystems can no longer be described as pure quantum states. For systems with only 2 subsystems this…
This Ontologies are widely used as a means for solving the information heterogeneity problems on the web because of their capability to provide explicit meaning to the information. They become an efficient tool for knowledge representation…
In this chapter we propose Generic Ontology Design Patterns, GODPs, as a methodology for representing and instantiating ontology design patterns in a way that is adaptable, and allows domain experts (and other users) to safely use them…
Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…
We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of…