Related papers: Quantifying the Topology of Large-Scale Structure
Spatial organisation of physical form of an urban system, or city, both manifests and influences the way its social form functions. Mathematical quantification of the spatial pattern of a city is, therefore, important for understanding…
Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…
In this study, we improve the topological complexity computations on digital images with introducing the digital topological complexity computations of a surjective and digitally continuous map between digital images. We also reveal…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
We discuss various analytical approximation methods for the evolution of the density fluctuation in the Universe. From primordial density fluctuation, the large-scale structure is formed via its own self-gravitational instability. For this…
The interaction between a turbulent convective boundary layer (CBL) and the underlying land surface is an important research problem in the geosciences. In order to model this interaction adequately, it is necessary to develop tools which…
The purpose of this work is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. This paper concentrates on general…
3+1 dimensional Causal Dynamical Triangulations (CDT) describe a quantum theory of fluctuating geometries without the introduction of a background geometry. If the topology of space is constrained to be that of a three-dimensional torus we…
Spectral measurements of boundary localized in-gap modes are commonly used to identify topological insulators via the bulk-boundary correspondence. This can be extended to high-order topological insulators for which the most striking…
We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding…
Structural disorder can improve the optical properties of metasurfaces, whether it is emerging from some large-scale fabrication methods, or explicitly designed and built lithographically. Correlated disorder, induced by a minimum…
The large-scale structure is a major source of cosmological information. However, next-generation photometric galaxy surveys will only provide a distorted view of cosmic structures due to large redshift uncertainties. To address the need…
Community structure is of paramount importance for the understanding of complex networks. Consequently, there is a tremendous effort in order to develop efficient community detection algorithms. Unfortunately, the issue of a fair assessment…
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
Topological data analysis (TDA) has become an attractive area for the application of quantum computing. Recent advances have uncovered many interesting connections between the two fields. On one hand, complexity theoretic results show that…
We present a two-dimensional (2-D) fitting algorithm (GALFIT, Version 3) with new capabilities to study the structural components of galaxies and other astronomical objects in digital images. Our technique improves on previous 2-D fitting…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
An approach to cosmological modelling is presented that incorporates the inhomogeneous structure of the Cosmic Web, specifically focusing on the interplay between cosmic voids and density walls. We extend the standard homogeneous and…