Related papers: Unicoherence in Locales
Coherence is a fundamental notion in quantum mechanics, defined relative to a reference basis. As such, it does not necessarily reveal the locality of interactions nor takes into account the accessible operations in a composite quantum…
Many classically used function space structures (including the topology of pointwise convergence, the compact-open topology, the Isbell topology and the continuous convergence) are induced by a hyperspace structure counterpart. This scheme…
In aperiodic order, non-periodic but "ordered" objects such as tilings, Delone sets, functions and measures are investigated. In this article we depict the common structure of these objects by using the general framework of abstract pattern…
Topology of the spatial coherence function is considered in details. The phase singularity (coherence vortices) structures of coherence function are classified by Hopf index and Brouwer degree in topology. The coherence flux quantization…
Persistent homology is a popular tool in Topological Data Analysis. It provides numerical characteristics of data sets which reflect global geometric properties. In order to be useful in practice, for example for feature generation in…
We characterize the Hurewicz cofibrations between finite topological spaces, that is, the continuous functions between finite topological spaces that have the homotopy extension property with respect to all topological spaces. In…
Connectedness, path connectedness, and uniform connectedness are well-known concepts. In the traditional presentation of these concepts there is a substantial difference between connectedness and the other two notions, namely connectedness…
Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology, singularity theory, and higher algebra. The theory synthesizes elements of classical combinatorial…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to…
A topological space has the fixed point property if every continuous self-map of that space has at least one fixed point. We demonstrate that there are serious restraints imposed by the requirement that there be a choice of fixed points…
Algebraic operations are understood as topologiztion of algebra. They become an example of simplest convergence space. In our article the convergence is a arbitrary multivalued appointment. The continuity of some mapping between two…
In this paper, a geometric resolution of singularities algorithm is developed. This method is elementary in its statement and proof, using explicit coordinate systems as much as possible. Each coordinate change used in the resolution…
The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…
The definition of accessible coherence is proposed. Through local measurement on the other subsystem and one way classical communication, a subsystem can access more coherence than the coherence of its density matrix. Based on the local…
The concept of unified local field theory is considered. According to this concept the quantum description and the classical one must be the levels for investigation of some world solution of the unified field model. It is shown that in the…
We introduce properties of metric spaces and, specifically, finitely generated groups with word metrics which we call coarse coherence and coarse regular coherence. They are geometric counterparts of the classical algebraic notion of…
The main aim of this paper is to provide a description of neighbourhood operators in finitely complete categories with finite coproducts and a proper factorisation system such that the semilattice of admissible subobjects make a…