Related papers: Persistent Homology and Non-Gaussianity
We derive analytical formulae for the Minkowski Functions of the cosmic microwave background (CMB) and large-scale structure (LSS) from primordial non-Gaussianity. These formulae enable us to estimate a non-linear coupling parameter, f_NL,…
Rapid progress has been made in observations of the temperature anisotropies of the Cosmic Microwave Background (CMB). These observations have enabled cosmologists to characterize the state of the universe at recombination, and…
A time-delay embedding (TDE), grounded in the framework of Takens's Theorem, provides a mechanism to represent and analyze the inherent dynamics of time-series data. Recently, topological data analysis (TDA) methods have been applied to…
Persistent homology is a fundamental tool in Topological Data Analysis. The associated algebraic structure is the persistence module, a sequence of vector spaces connected by linear maps. Persistence modules admit a complete and…
We present cosmological constraints from Dark Energy Survey Year 3 (DES Y3) weak lensing data using persistent homology, a topological data analysis technique that tracks how features like clusters and voids evolve across density…
[Abridged] In recent works we have proposed two new large-angle non-Gaussianity indicators based on skewness and kurtosis of patches of CMB sky-sphere, and used them to find out significant deviation from Gaussianity in frequency bands and…
The Cosmological Principle assumes a statistically isotropic Universe, but the Cosmic Microwave Background (CMB) exhibits some anomalous statistical features, such as the hemispherical power asymmetry, that challenge this core assumption.…
Persistent homology is a branch of computational algebraic topology that studies shapes and extracts features over multiple scales. In this paper, we present an unsupervised approach that uses persistent homology to study divergent behavior…
Persistence diagrams, the most common descriptors of Topological Data Analysis, encode topological properties of data and have already proved pivotal in many different applications of data science. However, since the (metric) space of…
The persistent homology of a stationary point process on ${\bf R}^N$ is studied in this paper. As a generalization of continuum percolation theory, we study higher dimensional topological features of the point process such as loops,…
We use the two-point correlation function of the extrema points (peaks and valleys) in the COBE Differential Microwave Radiometers (DMR) 2-year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background…
The standard cosmological model, which assumes statistical isotropy and parity invariance, predicts the absence of correlations between even-parity and odd-parity observables of the cosmic microwave background (CMB). Contrary to these…
The extraction of cosmological parameters from microwave background observations relies on specific assumptions about the statistical properties of the data, in particular that the p-point distributions of temperature fluctuations are…
We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…
The standard cosmological model predicts statistically isotropic cosmic microwave background (CMB) fluctuations characterized by the CMB temperature coefficients $a_{\ell m}$ being independent Gaussian random variables with zero mean and…
We study the angular distribution of temperature fluctuations in the cosmic microwave background (CMB) to probe the statistical isotropy of the universe by using precise full-sky CMB data with a model-independent approach. We investigated…
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 demonstrate how to use persistent homology for cosmological parameter inference in a tomographic cosmic shear survey. We obtain the first cosmological parameter constraints from persistent homology by applying our method to the…
We present results from a test for the Gaussianity of the whole sky sub-degree scale CMB temperature anisotropy measured by the Wilkinson Microwave Anisotropy Probe (WMAP). We calculate the genus from the foreground-subtracted and…
A detection of the level of non-Gaussianity in the CMB data is essential to discriminate among inflationary models and also to test alternative primordial scenarios. However, the extraction of primordial non-Gaussianity is a difficult…