The aim of this paper is to describe some geometric examples of non commutative and cyclic phase spaces, filling a gap in the literature and developing the project of geometrization of semantics for linear logics started in [12]. Besides, we present an algebraic semantics for non commutative linear logic with exponentials.

Some models of set theory are given which contain sets that have some of the important characteristics of being geometric, or spatial, yet do not have any points, in various ways. What’s geometrical is that there are functions to these spaces defined on the ambient spaces which act much like distance functions, and they carry normable Riesz spaces which act like the Riesz spaces of real-valued ...

This thesis explores the geometric description of animal colour vision. It examines the relationship of colour spaces to behavior and to physiology. I provide a derivation of, and explore the limits of, geometric spaces derived from the notion of risk and uncertainty aversion as well as the geometric objects that enumerate the variety of achievable colours. Using these principles I go on to exp...

An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is motivated, and the construction of moduli spaces is reviewed. Topological, arithmetic and algebraic methods for the study of moduli spaces are discussed. Mathema...

In this paper we present a generalization of geometric moments in scale-spaces derived from the general heat diffusion equation, with a particular interest for the min/max flow. As an application of those theoretical developments, two multiscale moments are used to enhance the classical Euclidean registration process. They are computed from a multiscale representation which preserves the global...

A theory of tubular neighborhoods for strata in manifold stratified spaces is developed. In these topologically stratified spaces, manifold stratified approximate fibrations and teardrops play the role that fibre bundles and mapping cylinders play in smoothly stratified spaces. Applications include a multiparameter isotopy extension theorem, neighborhood germ classification and a topological ve...

In evolutionary biology, it is common to study how various entities evolve together, for example, how parasites coevolve with their host, or genes with their species. Coevolution is commonly modelled by considering certain maps or reconciliations from one evolutionary tree P to another H, all of which induce the same map φ between the leaf-sets of P and H (corresponding to present-day associati...

Though path-connectedness is a very geometric and visual property, math lets us formalize it and use it to gain geometric insight into spaces that we cannot visualize. In these notes, we will consider spaces of matrices, which (in general) we cannot draw as regions in R or R. To begin studying these spaces, we first explicitly define the concept of a path. Definition 1.1. A path in X is a conti...

Topological spaces such as classifying spaces, configuration spaces and spacetimes often admit extra directionality. Qualitative invariants on such directed spaces often are more informative, yet more difficult, to calculate than classical homotopy invariants because directed spaces rarely decompose as homotopy colimits of simpler directed spaces. Directed spaces often arise as geometric realiz...