Network-based modeling of complex systems and data using the language of graphs has
become an essential topic across a range of different disciplines. Arguably, this graph-based …

A great success of solid state physics comes from the characterization of crystal structures in
the reciprocal (wave vector) space. The power of structural characterization in Fourier space …

The continued and dramatic rise in the size of data sets has meant that new methods are
required to model and analyze them. This timely account introduces topological data …

A suitable feature representation that can both preserve the data intrinsic information and
reduce data complexity and dimensionality is key to the performance of machine learning …

Persistent homology (PH) is a method used in topological data analysis (TDA) to study
qualitative features of data that persist across multiple scales. It is robust to perturbations of …

In topological data analysis (TDA), one often studies the shape of data by constructing a
filtered topological space, whose structure is then examined using persistent homology …

This paper introduces persistent homology, which is a powerful tool to characterize the
shape of data using the mathematical concept of topology. We explain the fundamental idea …

In most applications of nanoporous materials the pore structure is as important as the
chemical composition as a determinant of performance. For example, one can alter …

Persistence diagrams (PDs) play a key role in topological data analysis (TDA), in which they
are routinely used to describe succinctly complex topological properties of complicated …

Accelerated materials development with machine learning (ML) assisted screening and high
throughput experimentation for new photovoltaic materials holds the key to addressing our …