Related papers: Transforming Geospatial Ontologies by Homomorphism…
Ontology-based approaches for predicting gene-disease associations include the more classical semantic similarity methods and more recently knowledge graph embeddings. While semantic similarity is typically restricted to hierarchical…
Worldwide visual geo-localization aims to determine the geographic location of an image anywhere on Earth using only its visual content. Despite recent progress, learning expressive representations of geographic space remains challenging…
We present a precise definition of extended homotopy quantum field theories and develop an orbifold construction for these theories when the target space is the classifying space of a finite group $G$, i.e. for $G$-equivariant topological…
In this paper, we present that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. Quotient space can be considered as mathematically-defined phenotype space in the evolutionary…
It has recently been recognized by the author that the quantum contextuality paradigm may be formulated in terms of the properties of some subgroups of the two-letter free group $G$ and their corresponding point-line incidence geometry…
A geometrical pattern is a set of points with all pairwise distances (or, more generally, relative distances) specified. Finding matches to such patterns has applications to spatial data in seismic, astronomical, and transportation…
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…
Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in…
In this work, we introduce {\em topological representations of a quiver} as a system consisting of topological spaces and its relationships determined by the quiver. Such a setting gives a natural connection between topological…
We define notions of generically and coarsely computable relations and structures and functions between structures. We investigate the existence and uniqueness of equivalence structures in the context of these definitions
We study the interaction between various analytification functors, and a class of morphisms of rings, called homotopy epimorphisms. An analytification functor assigns to a simplicial commutative algebra over a ring $R$, along with a choice…
A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…
Homomorphic encryption is a sophisticated encryption technique that allows computations on encrypted data to be done without the requirement for decryption. This trait makes homomorphic encryption appropriate for safe computation in…
There are investigated the generalized methods of cognition of the Existing, i.e. everything that is able to influence to the cognizer, and everything differed from the Existing is postulated as indistinguishable from the non-existing and…
This article records basic topological, as well as homological properties of the space of homomorphisms Hom(L,G) where L is a finitely generated discrete group, and G is a Lie group, possibly non-compact. If L is a free abelian group of…
It is a well known result in the covering groups that a subgroup $G$ of the fundamental group at the identity of a semi-locally simply connected topological group determines a covering morphism of topological groups with characteristic…
The fundamental groupoid of a space becomes enriched over the category of topological spaces when the hom-sets are endowed with topologies intimately related to universal constructions of topological groups. This paper is devoted to a…
Homomorphisms are defined between the multiplicative group of an etale algebra of dimension 4 and the multiplicative group of a canonically associated etale algebra of degree 6 over an arbitrary field. These homomorphisms are used to relate…
We study the homotopy theory of locally ordered spaces, that is manifolds with boundary whose charts are partially ordered in a compatible way. Their category is not particularly well-behaved with respect to colimits. However, this category…
The fundamental bigroupoid of a topological space is one way of capturing its homotopy 2-type. When the space is semilocally 2-connected, one can lift the construction to a bigroupoid internal to the category of topological spaces, as Brown…