Related papers: Persistent Homology and Non-Gaussianity
Persistent homology is a central methodology in topological data analysis that has been successfully implemented in many fields and is becoming increasingly popular and relevant. The output of persistent homology is a persistence diagram --…
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…
We analyze WMAP 3 year data using the one-point distribution functions to probe the non-Gaussianity in the Cosmic Microwave Background (CMB) Anisotropy data. Computer simulations are performed to determine the uncertainties of the results.…
We present an analysis of the Minkowski Functionals (MFs) describing the WMAP three-year temperature maps to place limits on possible levels of primordial non-Gaussianity. In particular, we apply perturbative formulae for the MFs to give…
Persistent homology is an important methodology in topological data analysis which adapts theory from algebraic topology to data settings. Computing persistent homology produces persistence diagrams, which have been successfully used in…
The forthcoming Planck experiment will provide high sensitivity polarization measurements that will allow us to further tighten the f_NL bounds from the temperature data. Monte Carlo simulations of non-Gaussian CMB maps have been used as a…
Across many scientific domains, practitioners rely on coarse, discretized summaries to track the evolving structure of complex systems under noise, measurement error, and changing system size. Understanding when such summaries are reliable…
Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…
The identification of non-Gaussian signatures in cosmic microwave background (CMB) temperature maps is one of the main cosmological challenges today. We propose and investigate altenative methods to analyse CMB maps. Using the technique of…
Computational topologists recently developed a method, called persistent homology to analyze data presented in terms of similarity or dissimilarity. Indeed, persistent homology studies the evolution of topological features in terms of a…
Topological Data Analysis (TDA) has been applied with success to solve problems across many scientific disciplines. However, in the setting of a point cloud $X$ sampled from a shape $\mathcal{S}$ of low intrinsic dimension embedded within…
We introduce a new mathematical tool (a direction-dependent probe) to analyse the randomness of purported isotropic Gaussian random fields on the sphere. We apply the probe to assess the full-sky cosmic microwave background (CMB)…
Recently a symmetry-based method to test for statistical isotropy of the cosmic microwave background was developed. We apply the method to template-cleaned 3-year and 5-year WMAP-$DA$ maps. We examine a wide range of angular multipoles from…
Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such…
We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving…
Persistence diagrams are important tools in the field of topological data analysis that describe the presence and magnitude of features in a filtered topological space. However, current approaches for comparing a persistence diagram to a…
Surface roughness plays an important role in analyzing engineering surfaces. It quantifies the surface topography and can be used to determine whether the resulting surface finish is acceptable or not. Nevertheless, while several existing…
In this work, we introduce persistent homology for the analysis of cryo-electron microscopy (cryo-EM) density maps. We identify the topological fingerprint or topological signature of noise, which is widespread in cryo-EM data. For low…
Visualization in the emerging field of topological data analysis has progressed from persistence barcodes and persistence diagrams to display of two-parameter persistent homology. Although persistence barcodes and diagrams have permitted…
We investigate the non-Gaussian signatures in Cosmic Microwave Background (CMB) maps induced by the intervening large-scale structure through weak lensing. In order to measure the deviation from the Gaussian behavior of the intrinsic…