相关论文: Persistent Homology and Non-Gaussianity

Topological Data Analysis (TDA) can be used to detect and characterize holes in an image, such as zero-dimensional holes (connected components) or one-dimensional holes (loops). However, there is currently no widely accepted statistical…

Based on recent observations of the cosmic microwave background (CMB), claims of statistical anomalies in the properties of the CMB fluctuations have been made. Although the statistical significance of the anomalies remains only at the…

Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…

Topological Data Analysis (TDA) is a field that leverages tools and ideas from algebraic topology to provide robust methods for analysing geometric and topological aspects of data. One of the principal tools of TDA, persistent homology,…

We outline the expected constraints on non-Gaussianity from the cosmic microwave background (CMB) with current and future experiments, focusing on both the third (f_{NL}) and fourth-order (g_{NL} and \tau_{NL}) amplitudes of the local…

We address the problem of estimating topological features from data in high dimensional Euclidean spaces under the manifold assumption. Our approach is based on the computation of persistent homology of the space of data points endowed with…

This work is dedicated to the topological analysis of complex transitional networks for dynamic state detection. Transitional networks are formed from time series data and they leverage graph theory tools to reveal information about the…

Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…

We describe and discuss the application of Gumbel statistics, which model extreme events, to WMAP 5-year measurements of the cosmic microwave background. We find that temperature extrema of the CMB are well modelled by the Gumbel formalism…

We assess dataset agreement and late-time predictive adequacy in $\Lambda$CDM and its sign-switching extension, $\Lambda_{\rm s}$CDM, using a suite of Gaussian and exact non-Gaussian consistency diagnostics. Both models are constrained with…

Understanding the structure of high-dimensional data is fundamental to neuroscience and other data-intensive scientific fields. While persistent homology effectively identifies basic topological features such as "holes," it lacks the…

We propose a new method for extracting the non-Gaussian signatures on the isotemperature statistics in the cosmic microwave background (CMB) sky, which is induced by the gravitational lensing due to the intervening large-scale structure of…

Local scaling properties of the co-added foreground-cleaned three-year Wilkinson Microwave Anisotropy Probe (WMAP) data are estimated using weighted scaling indices. The scaling index method (SIM) is - for the first time - adapted and…

Accurate component separation of full-sky maps in the radio and microwave frequencies, such as the cosmic microwave background (CMB), relies on a thorough understanding of the statistical properties of the Galactic foreground emissions.…

Analyses of recent cosmic microwave background (CMB) observations have provided increasing indications for the existence of large scale anisotropy in the universe. Given the far reaching consequences of such an anisotropy for our…

We have independently measured the genus topology of the temperature fluctuations in the cosmic microwave background seen in the Wilkinson Microwave Anisotropy Probe (WMAP) 3-year data. A genus analysis of the WMAP data indicates…

We propose an alternative formalism to simulate CMB temperature maps in $\Lambda$CDM universes with nontrivial spatial topologies. This formalism avoids the need to explicitly compute the eigenmodes of the Laplacian operator in the spatial…

Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…

Characterizing the dynamics of time-evolving data within the framework of topological data analysis (TDA) has been attracting increasingly more attention. Popular instances of time-evolving data include flocking/swarming behaviors in…

Persistence diagrams (PDs), often characterized as sets of death and birth of homology class, have been known for providing a topological representation of a graph structure, which is often useful in machine learning tasks. Prior works rely…