The cosmological principle (CP)—the notion that the Universe is spatially isotropic and
homogeneous on large scales—underlies a century of progress in cosmology. It is …

One of the most elusive challenges within the area of topological data analysis is
understanding the distribution of persistence diagrams arising from data. Despite much effort …

Persistence landscapes map persistence diagrams into a function space, which may often
be taken to be a Banach space or even a Hilbert space. In the latter case, it is a feature map …

This work introduces the Topological CNN (TCNN), which encompasses several
topologically defined convolutional methods. Manifolds with important relationships to the …

This study presents a numerical analysis of the topology of a set of cosmologically
interesting 3D Gaussian random fields in terms of their Betti numbers β0, β1, and β2. We …

In this paper we study the connection between the zeros of the expected Euler characteristic
curve and the phenomenon which we refer to as homological percolation—the formation of …

Using a set of Lambda cold dark matter simulations of cosmic structure formation, we study
the evolving connectivity and changing topological structure of the cosmic web using state-of …

We propose a novel approach for comparing the persistent homology representations of two
spaces (or filtrations). Commonly used methods are based on numerical summaries such as …

We study the topology generated by the temperature fluctuations of the cosmic microwave
background (CMB) radiation, as quantified by the number of components and holes, formally …

This paper proposes a novel topological learning framework that integrates networks of
different sizes and topology through persistent homology. Such challenging task is made …