Related papers: Persistent Homology and Non-Gaussianity
Topological data analysis (TDA) studies the shape patterns of data. Persistent homology is a widely used method in TDA that summarizes homological features of data at multiple scales and stores them in persistence diagrams (PDs). In this…
In the recent years, non-Gaussianity and statistical isotropy of the Cosmic Microwave Background (CMB) was investigated with various statistical measures, first and foremost by means of the measurements of the WMAP satellite. In this…
Persistence diagrams are common objects in the field of Topological Data Analysis. They are topological summaries that capture both topological and geometric structure within data. Recently there has been a surge of interest in developing…
In the context of inflationary scenarios, the observed large angle anisotropy of the Cosmic Microwave Background (CMB) temperature is believed to probe the primordial metric perturbations from inflation. Although the perturbations from…
The concept of topological persistence, introduced recently in computational topology, finds applications in studying a map in relation to the topology of its domain. Since its introduction, it has been extended and generalized in various…
We present an extensive frequentist analysis of the one-point statistics (number, mean, variance, skewness and kurtosis) and two-point correlation functions determined for the local extrema of the cosmic microwave background temperature…
Persistent homology computes topological invariants from point cloud data. Recent work has focused on developing statistical methods for data analysis in this framework. We show that, in certain models, parametric inference can be performed…
The two fundamental assumptions of the standard cosmological model - that the initial fluctuations are statistically isotropic and Gaussian - are rigorously tested using maps of the cosmic microwave background (CMB) anisotropy from the…
Cosmic microwave background (CMB) anisotropy (spatial inhomogeneity) data provide the tightest constraints on the Hubble constant, matter density, spatial curvature, and dark energy dynamics. Other data, sensitive to the evolution of only…
We test the consistency of estimates of the non-linear coupling constant f_{NL} using non-Gaussian CMB maps generated by the method described in (Liguori, Matarrese and Moscardini 2003). This procedure to obtain non-Gaussian maps differs…
Non-linear evolution of cosmological energy density fluctuations triggers deviations from Gaussianity in the temperature distribution of the cosmic microwave background. A method to estimate these deviations is proposed. N-body simulations…
We search the high-latitude portion of the COBE Differential Microwave Radiometers (DMR) 4-year sky maps for evidence of a non-Gaussian temperature distribution in the cosmic microwave background. The genus, 3-point correlation function,…
Geometric characteristics of random fields are exploited to test the consistency of density perturbation model spectra with COBE data. These CMB maps are analyzed using the number of anisotropy hot spots and their boundary curvature. CMB…
Cytometry experiments yield high-dimensional point cloud data that is difficult to interpret manually. Boolean gating techniques coupled with comparisons of relative abundances of cellular subsets is the current standard for cytometry data…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
We consider a universe with a non-classical stringy topology that has fixed points. We concentrate on the simplest example, an orbifold point, and study its observable imprints on the cosmic microwave background (CMB). We show that an…
It is possible to classify pixels of a smoothed cosmic microwave background (CMB) fluctuation map according to their local curvature in ``hill'', ``lake'' and ``saddle'' regions. In the Gaussian case, fractional areas occupied by pixels of…
Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding…
Persistent homology naturally addresses the multi-scale topological characteristics of the large-scale structure as a distribution of clusters, loops, and voids. We apply this tool to the dark matter halo catalogs from the Quijote…
Since cosmic-microwave-background (CMB) and large-scale-structure (LSS) data will shortly improve dramatically with the Microwave Anisotropy Probe (MAP) and Planck Surveyor, and the Anglo-Australian 2-Degree Field (2dF) and Sloan Digital…