相关论文: Persistent homology of the cosmic web. I: Hierarch…

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…

In this research, we investigate the structural evolution of the cosmic web, employing advanced methodologies from Topological Data Analysis. Our approach involves leveraging LITE, an innovative method from recent literature that embeds…

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…

We present the second paper in our program characterizing the impact of massive neutrinos on the multiscale cosmic web using global topology and persistent homology. Building on the methodology established in Paper I, based on discrete…

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…

Cosmological constraints on neutrino mass offer a promising avenue for advancing our understanding of both fundamental particle physics and the evolution of cosmic large-scale structure. To overcome challenges associated with traditional…

Topological analysis of galaxy distributions has gathered increasing attention in cosmology, as they are able to capture non-Gaussian features of large-scale structures (LSS) that are overlooked by conventional two-point clustering…

We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology,…

Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…

We study the topology of the network of ionized and neutral regions that characterized the intergalactic medium during the Epoch of Reionization. Our analysis uses the formalism of persistent homology, which offers a highly intuitive and…

In recent years, cosmic shear has emerged as a powerful tool to study the statistical distribution of matter in our Universe. Apart from the standard two-point correlation functions, several alternative methods like peak count statistics…

In this work, we study the evolution of Betti curves obtained by persistent-homological analysis of point clouds formed by halos in different cosmological $N$-body simulations. We show that they can be approximated with a scaled log-normal…

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…

Cosmic connectivity and multiplicity, i.e. the number of filaments globally or locally connected to a given cluster is a natural probe of the growth of structure and in particular of the nature of dark energy. It is also a critical…

We show that persistence-based topology of the 21 cm forest encodes information about Cosmic Dawn that is complementary to traditional amplitude- or correlation-based statistics. Applying topological data analysis to simulated…

In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…

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…

We study how the topology of feature embedding space changes as it passes through the layers of a well-trained deep neural network (DNN) through Betti numbers. Motivated by existing studies using simplicial complexes on shallow fully…

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…