Related papers: Persistent topology of the reionization bubble net…
We present a new formalism for studying the topology of HII regions during the Epoch of Reionisation, based on persistent homology theory. With persistent homology, it is possible to follow the evolution of topological features over time.…
The distribution of ionised hydrogen during the epoch of reionization (EoR) has a complex morphology. We propose to measure the three-dimensional topology of ionised regions using the Betti numbers. These quantify the topology using the…
Using a set of $\Lambda$CDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We…
Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…
Using the largest cosmological reionization simulation to-date (~24 billion particles), we use the genus curve to quantify the topology of neutral hydrogen distribution on scales > 1 Mpc as it evolves during cosmological reionization. We…
We trace the connectivity of the cosmic web as defined by haloes in the Planck-Millennium simulation using a persistence and Betti curve analysis. We normalise clustering up to the second-order correlation function, and use our systematic…
Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…
Reionization is inhomogeneous for two reasons: the clumpiness of the intergalactic medium (IGM) and clustering of the discrete ionizing sources. While numerical simulations can in principle take both into account, they are at present…
The epoch of reionization is one of the least known chapters in the evolutionary history of the Universe. This thesis investigates two major approaches to unveil the reionization history of the Universe using HI 21-cm maps.The most…
Despite the great advancement of experimental tools and theoretical models, a quantitative characterization of the microscopic structures of ion aggregates and its associated water hydrogen-bonding networks still remains a challenging…
This paper is second in the series, following Pranav et al. (2019), focused on the characterization of geometric and topological properties of 3D Gaussian random fields. We focus on the formalism of persistent homology, the mainstay of…
Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features (2000) as one varies a tuning parameter. Features with short…
Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…
We present general properties of ionized hydrogen (HII) bubbles and their growth based on a state-of-the-art large-scale (100 Mpc/h) cosmological radiative transfer simulation. The simulation resolves all halos with atomic cooling at the…
This study details an approach for the analysis of social media collected political data through the lens of Topological Data Analysis, with a specific focus on Persistent Homology and the political processes they represent by proposing a…
We introduce a versatile and spatially resolved morphological characterisation of binary fields, rooted in the opening transform of mathematical morphology. We subsequently apply it to the thresholded ionization field in simulations of…
We introduce a multiscale topological description of the Megaparsec weblike cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of…
We consider the degree to which "21 cm tomography" of the high-redshift Universe can distinguish different ionization histories. Using a new analytic model for the size distribution of HII regions that associates these ionized bubbles with…
The study of tunnel failure characteristics under the load of external explosion source is an important problem in tunnel design and protection, in particular, it is of great significance to construct an intelligent topological feature…