The categorical theory of relations and quantizations

In this paper we develope a categorical theory of relations and use this formulation to define the notion of quantization for relations. Categories of relations are defined in the context of symmetric monoidal categories. They are shown to be symmetric monoidal categories in their own right and are found to be isomorphic to certain categories of $A-A$ bicomodules. Properties of relations are defined in terms of the symmetric monoidal structure. Equivalence relations are shown to be commutative monoids in the category of relations. Quantization in our view is a property of functors between monoidal categories. This notion of quantization induce a deformation of all algebraic structures in the category, in particular the ones defining properties of relations like transitivity and symmetry.Comment: corrected typo

Theory of linear G-difference equations

We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants of the symmetry group. Linear equations are modules over the skew group algebra, solutions are morphisms relating a given equation to other equations,symmetries of an equation are module endomorphisms and conserved structures are invariants in the tensor algebra of the given equation. We show that the equations and their solutions can be described through representations of the isotropy group of the symmetry group of the underluing set. We relate our notion of difference equations and solutions to systems of classical difference equations and their solutions and show that our notions include these as a special case.Comment: 34 page

Corroborating indicates nurses’ ethical values in a geriatric ward

The aim of the study was to identify nurses’ ethical values, which become apparent through their behaviour in the interactions with older patients in caring encounters at a geriatric clinic

The era of reference genomes in conservation genomics

Progress in genome sequencing now enables the large-scale generation of reference genomes. Various international initiatives aim to generate reference genomes representing global biodiversity. These genomes provide unique insights into genomic diversity and architecture, thereby enabling comprehensive analyses of population and functional genomics, and are expected to revolutionize conservation genomics