相关论文: Persistent Homology and Non-Gaussianity
Motivated by the rapidly increasing relevance of virtual material design in the domain of materials science, it has become essential to assess whether topological properties of stochastic models for a spatial tessellation are in accordance…
In this work we investigate the standard deviation of the Cosmic Microwave Background (CMB) temperature gradient field as a signature for a multiply connected nature of the Universe. CMB simulations of a spatially infinite universe model…
Using analytical methods and Monte Carlo simulations, we analyze a new statistic designed to detect isolated step-like discontinuities which are coherent over large areas of Cosmic Microwave Background (CMB) pixel maps. Such coherent…
We present limits to the amplitude of non-Gaussian primordial fluctuations in the WMAP 1-year cosmic microwave background sky maps. A non-linear coupling parameter, f_NL, characterizes the amplitude of a quadratic term in the primordial…
Local-type primordial non-Gaussianity couples statistics of the curvature perturbation \zeta on vastly different physical scales. Because of this coupling, statistics (i.e. the polyspectra) of \zeta in our Hubble volume may not be…
In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…
We study statistical anisotropies generated in the observed two-point function of the cosmic microwave background (CMB) fluctuations if the primordial statistics are non-Gaussian. Focusing on the dipole modulations of the anisotropies, we…
To minimize instrumentally induced systematic errors, cosmic microwave background (CMB) anisotropy experiments measure temperature differences across the sky using paires of horn antennas, temperature map is recovered from temperature…
In the last few decades, advances in observational cosmology have given us a standard model of cosmology. We know the content of the universe to within a few percent. With more ambitious experiments on the way, we hope to move beyond the…
We propose a fast and efficient bispectrum statistic for Cosmic Microwave Background (CMB) temperature anisotropies to constrain the amplitude of the primordial non-Gaussian signal measured in terms of the non-linear coupling parameter…
We test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using observations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature, but also…
By their nature it is difficult to differentiate chaotic dynamical systems through measurement. In recent years, work has begun on using methods of Topological Data Analysis (TDA) to qualitatively type dynamical data by approximating the…
This application paper presents a comprehensive experimental evaluation of the suitability of Topological Data Analysis (TDA) for the quantitative comparison of turbulent flows. Specifically, our study documents the usage of the persistence…
In topological data analysis, we want to discern topological and geometric structure of data, and to understand whether or not certain features of data are significant as opposed to simply random noise. While progress has been made on…
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…
One of the primary areas of interest in applied algebraic topology is persistent homology, and, more specifically, the persistence diagram. Persistence diagrams have also become objects of interest in topological data analysis. However,…
Despite the wealth of $Planck$ results, there are difficulties in disentangling the primordial non-Gaussianity of the Cosmic Microwave Background (CMB) from the secondary and the foreground non-Gaussianity (NG). For each of these forms of…
In a first paper (Forni & Aghanim 1999), we developed several statistical discriminators to test the non-gaussian nature of a signal. These tests are based on the study of the coefficients in a wavelet decomposition basis. In this paper, we…
Based on the relationship between thermodynamics and gravity we propose, with the aid of Verlinde's formalism, an alternative interpretation of the dynamical evolution of the Friedmann-Robertson-Walker Universe. This description takes into…
In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…