Related papers: Use of Topology in physical problems
Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…
The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
We extend the notion of the distance to a measure from Euclidean space to probability measures on general metric spaces as a way to do topological data analysis in a way that is robust to noise and outliers. We then give an efficient way to…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
The topology of orientable (2 + 1)d spacetimes can be captured by certain lumps of non-trivial topology called topological geons. They are the topological analogues of conventional solitons. We give a description of topological geons where…
We give an exposition of Natural Topology (NToP), which highlights its advantages for exact computation. The NToP-definition of the real numbers (and continuous real functions) matches recent expert recommendations for exact real…
A datatset $X$ on $R^2$ is a finite topological space. Current research of a dataset focuses on statistical methods and the algebraic topological method \cite{carlsson}. In \cite{hu}, the concept of typed topological space was introduced…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function $ d$, or by the world function $\sigma =d^{2}/2$. One suggests a new general method of the…
We survey a variety of cosmological problems where the issue of generality has arisen. This is aimed at providing a wider context for many claims and deductions made when philosophers of science choose cosmological problems for…
The structure of topological spaces is analysed here through the lenses of fibrous preorders. Each topological space has an associated fibrous preorder and those fibrous preorders which return a topological space are called spacial. A…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…
The phenomenon of quantum number fractionalization is explained. The relevance of non-trivial phonon field topology is emphasized.
Recent observations seem to indicate that we live in a universe whose spatial sections are nearly or exactly flat. Motivated by this we study the problem of observational detection of the topology of universes with flat spatial sections. We…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
A topology on a nonempty set $X$ specifies a natural subset of $\mathcal{P}(X)$. By identifying $\mathcal{P}(\mathcal{P}(X))$ with the totally disconnected compact Hausdorff space $2^{\mathcal{P}(X)}$, the lattice $Top(X)$ of all topologies…
The role of topology in QIS with physical connection to the noncommutativity, discretization,supersymmetry, entanglement, nonseparability and CP violation in physics is discussed.
Given a data set with a notion of distance, such as a point cloud in Euclidean space, topological data analysis (TDA) uses techniques from algebraic topology and metric geometry to infer the topology of a hypothetical manifold from which…