Related papers: Quantifying the Topology of Large-Scale Structure
Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from…
Two-phase random textures abound in a host of contexts, porous and composite media, ecological structures, biological media and astrophysical structures. Questions surrounding the spatial structure of such textures continue to pose many…
We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…
In this paper we describe a numerical method designed for modelling different kinds of astrophysical flows in three dimensions. Our method is a standard explicit finite difference method employing the local shearing-box technique. To model…
The global topology of the Universe could, in principle, affect quantum systems through boundary condition constraints. We investigate this connection by analyzing how compact, flat, cosmologically inspired topologies, specifically the…
Observations of microwave background fluctuations can yield information not only about the geometry of the universe, but potentially about the topology of the universe. If the universe is negatively curved, then the characteristic scale for…
We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and…
Tomography is a widely used tool for analyzing microstructures in three dimensions (3D). The analysis, however, faces difficulty because the constituent materials produce similar grey-scale values. Sometimes, this prompts the image…
Methods for the statistical characterization of the large-scale structure in the Universe will be the main topic of the present text. The focus is on geometrical methods, mainly Minkowski functionals and the J-function. Their relations to…
We provide a covariant and gauge-invariant approach to the question of how a first order pressure can be incorporated self-consistently in a cosmological scenario. The approximation is relevant, in the linear regime, to weakly…
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…
In order to investigate whether galaxy structures are compatible with the predictions of the standard LCDM cosmology, we focus here on the analysis of several simple and basic statistical properties of the galaxy density field. Namely, we…
Cosmic structure simulations have improved enormously over the past decade, both in terms of the resolution which can be achieved, and with the addition of hydrodynamic and other techniques to formerly purely gravitational methods. This is…
We use a quantitative topological characterization of complex dynamics to measure geometric structures. This approach is used to analyze the weakly turbulent state of spiral defect chaos in experiments on Rayleigh-Benard convection.…
The cosmic web is a complex spatial pattern of walls, filaments, cluster nodes and underdense void regions. It emerged through gravitational amplification from the Gaussian primordial density field. Here we infer analytical expressions for…
This paper presents the first approach to visualize the importance of topological features that define classes of data. Topological features, with their ability to abstract the fundamental structure of complex data, are an integral…
The topological charge density and topological susceptibility are determined by multi-probing approximation using overlap fermions in quenched SU(3) gauge theory. Then we investigate the topological structure of the quenched QCD vacuum, and…
We study the geometry and topology of the large-scale structure traced by galaxy clusters in numerical simulations of a box of side 320 $h^{-1}$ Mpc, and compare them with available data on real clusters. The simulations we use are…
We address the problem of comparing and aligning spatial point configurations in $\mathbb{R}^3$ arising from structured geometric patterns. Each pattern is decomposed into arms along which we define a normalized finite-difference operator…
The cosmic large scale structure encodes the formation and evolution of a weblike network of dark matter and galaxies within the Universe. The cosmological information is wrapped up in non-Gaussian statistics requiring characterisation…